Microsoft® Excel 2010 Data Analysis and Business Modeling

Table of Contents
Introduction
1. What You Should Know Before Reading This Book

Microsoft

Excel

2010:

Data Analysis a

Business Modeli

Wayne L. Wi

PUBLISHED BY

Microsoft Press

A Division of Microsoft Corporation

One Microsoft Way

Redmond, Washington 98052-6399

means without the written permission of the publisher.

Library of Congress Control Number: 2010934987

ISBN: 978-0-7356-4336-9

4 5 6 7 8 9 10 11 12 M 7 6 5 4 3 2

Printed and bound in the United States of America.

Microsoft Press books are available through bookseller

mation

about international editions, contact your local Micr

International directly at fax (425) 936-7329. Visit our c

mspinput@microsoft.com.

Microsoft and the trademarks listed at http://www.micr

Trademarks/EN-US.aspx are trademarks of the Microsoft g

their respective owners.

The example companies, organizations, products, domain

events depicted herein are fctitious. No association wit

e-mail address, logo, person, place, or event is intend

This book expresses the author’s views and opinions. The

any express, statutory, or implied warranties. Neither

distributors will be held liable for any damages caused

this book.

Acquisitions

Rosemary

Editor:

Caperton

Developmental

Devon

Editor:

Musgrave

Project

Rosemary

Editor:

Caperton

Editorial and

John

Production:

Pierce and Waypoint Press

Technical

Mitch

Reviewer:

Tulloch; Technical Review services provi

a member of CM Group, Ltd.

Cover:

Twist

Body Part No. X17-37446

[2012-01-20]

iii

Table of Contents

Introduction

..............................

1 What’s New in....................

Excel 2010

2 Range Names

........................

3 Lookup Functions

......................

4 The INDEX Function

......................

5 The MATCH Function

.....................

6 Text Functions

........................

7 Dates and Date

....................

Functions

8 Evaluating Investments by Using Net P

Criteria

..........................

9 Internal Rate

.....................

of Return

10More Excel Financial

..................

Functions

11Circular References

......................

12IF Statements

........................

13Time and Time....................

Functions

105

14The Paste Special

...................

Command

111

Microsoft is interested in hearing your feedback so we can continually improve our books and learning

resources for you. To participate in a brief online survey, please visit:

www.microsoft.com/learning/booksurvey/

What do you think of this book? We want to hear from you!

Table of Contents

15Three-Dimensional

.................

Formulas

117

16The Auditing

.....................

Tool

121

17Sensitivity Analysis

...............

with Data

127 Tabl

18The Goal Seek..................

Command

137

19Using the Scenario Manager

... for

. 4. 3....

Sens

20The COUNTIF, COUNTIFS, COUNT, COUNT

COUNTBLANK Functions

...................

149

21The SUMIF, AVERAGEIF, SUMIFS, and A

Functions

........................

157

22The OFFSET ....................

Function

163

23The INDIRECT...................

Function

177

24Conditional ...................

Formatting

185

25Sorting in

......................

Excel

209

26Tables

.........................

217

27Spin Buttons, Scroll Bars, Option B

Combo Boxes, and Group

...............

List 229

Boxes

28An Introduction to Optimization

.... 2.41.....

wit

29Using Solver to Determine...

the

2. 45

....

Optim

30Using Solver to Schedule

.......25

Your. 5Workf

.....

31Using Solver to Solve Transportatio

Problems

........................

261

32Using Solver for ...............

Capital Budgeting

267

33Using Solver for ...............

Financial Planning

275

34Using Solver to Rate

...............

Sports 281

Teams

Table of Contents

35Warehouse Location and the GRG Multis

Evolutionary Solver

...................

Engines 287

36Penalties and the ........

Evolutionary

2. 9.7......

Solver

37The Traveling Salesperson

................

Problem

303

38Importing Data from a .....

Text File

3. 0. 7......

or Docu

39Importing Data from

.................

the Internet

313

40Validating

.......................

Data

319

41Summarizing Data by.......

Using Histograms

. 2. 7......

42Summarizing Data by Using

....

Descriptive

3. 3.5..... S

43Using PivotTables and Slicers

..... 3. 49

......

to Descr

44Sparklines

.........................

381

45Summarizing Data with Database

.. 3. 8.7..

Statis

46Filtering Data and .......

Removing 3

.Duplicate

9. 5......

47Consolidating

......................

Data

411

48Creating Subtotals

......................

417

49Estimating Straight

........

Line Relationships

4. 2.3......

50Modeling Exponential

..................

Growth 431

51The Power.......................

Curve

435

52Using Correlations to Summarize

..... 4. 41

......

Relat

53Introduction to Multiple

................

Regression

447

54Incorporating Qualitative Factors int

Regression

.........................

453

55Modeling Nonlinearities

.......

and 46

Interacti

. 3

......

Table of Contents

56Analysis of Variance:

..............

One-Way

471ANOVA

57Randomized Blocks and

.......47

Two-Way. 7ANOVA

.....

58Using Moving Averages to...

Understand

4. 8. 7.... Ti

59Winters’s .....................

Method

491

60Ratio-to-Moving-Average

......

Forecast

4.97.....

61Forecasting in the Presence

..... 5

. of

0. 1....

Spec

62An Introduction to..............

Random Variables

509

63The Binomial, Hypergeometric, and N

Random Variables

.....................

515

64The Poisson and Exponential

..... 5Random

. 23

..... V

65The Normal Random

.................

Variable

527

66Weibull and Beta Distributions: Mod

and Duration ..................

of a Project

535

67Making Probability Statements

..... 5. 41

.....

from F

68Using the Lognormal Random Variable t

Stock Prices

.......................

545

69Introduction to Monte

.............

Carlo 549

Simulat

70Calculating an..................

Optimal Bid

559

71Simulating Stock Prices and

.. 5Asset

. 6.5.. Al

72Fun and Games: Simulating Gambling a

Event Probabilities

.....................

575

73Using Resampling ...............

to Analyze 583

Data

74Pricing Stock

....................

Options

587

75Determining Customer

.................

Value

601

Table of Contents

vii

76The Economic Order Quantity

.....60

Inventory

. 7...... M

77Inventory Modeling with

......

Uncertain

6.13......

Dem

78Queuing Theory: The Mathematics

...619...of Wa

79Estimating a Demand

...................

Curve

625

80Pricing Products.................

by Using Tie-Ins

631

81Pricing Products by Using Subjectively D

Demand

..........................

635

82Nonlinear ......................

Pricing

639

83Array Formulas ..................

and Functions647

84PowerPivot

.........................

665

Index

...........................

675

Microsoft is interested in hearing your feedback so we can continually improve our books and learning

resources for you. To participate in a brief online survey, please visit:

www.microsoft.com/learning/booksurvey/

What do you think of this book? We want to hear from you!

Introduction

Whether you work for a Fortune 500 corporation

or a not-for-proft organization, if you’re rea

Microsoft Excel in your daily work. Your job p

analyzing data. It might also involve building a

profts, reduce costs, or manage operations mor

Since 1999, I’ve taught thousands of analysts a

Squibb, Cisco Systems, Drugstore.com, eBay, El

Intel, Microsoft, NCR, Owens Corning, Pfzer, P

U.S. Department of Defense, and Verizon how to u

in their jobs. Students have often told me tha

have saved them hours of time each week -and pr

proaches for analyzing important business prob

or Excel 2007. With the added power of Excel 2

ever dreamed! To paraphrase Alicia

, Excel

Silverstone

2007 is si

years ago.

I’ve used the techniques described in this boo

business problems. For example, I use Excel to h

evaluate referees, players, and lineups.-Durin

ness modeling and data analysis classes to MBA s

of Business. (As proof of my teaching excellen

consecutive years, and have won the school’s o

like to also note that 95 percent of MBA stude

modeling class even though it is an elective.

The book you have in your hands is an attempt t

everyone. Here is why I think the book will he

■

The materials have been tested while teachi

Fortune 500 corporations and government age

■

I’ve written the book as though I am talkin

transfers the spirit of a successful classr

■

I teach by example, which makes concepts ea

constructed to have a real-world feel. Many o

sent to me by employees of Fortune 500 corp

■

For the most part, I lead you through the a

answer a wide range of data analysis and bu

my explanations by referring to the sample w

Introduction

However, I have also included template fles f

website. If you want to, you can use these te

complete each example on your own.

■

For the most part, the chapters are short and o

should be able to master the content of most c

By looking at the questions that begin each c

of problems you’ll be able to solve after mas

■

In addition to learning about Excel formulas, y

a fairly painless fashion. For example,

you’l

mization models, Monte Carlo simulation,

inve

ics of waiting in line. You will also learn a

thinking, such as real options, customer valu

■

At the end of each chapter, I’ve provided a g

total) that you can work through on your own. T

information in each chapter. Answers to all p

companion website. Many of these problems are b

business analysts at Fortune 500 companies.

■

Most of all, learning should be fun. If you r

U.S. presidential elections, how to set footb

probability of winning at craps, and how to d

winning an NCAA tournament. These examples ar

teach you a lot about solving business proble

■

To follow along with this book, you must have E

book can be used with Excel 2003 or Excel 200

What You Should Know Before Rea

To follow the examples in this book you do not n

key actions you should know how to do are the fo

■

Enter a formula

You should know that formulas must be

You should also know the basic mathematical o

that an asterisk (*) is used for multiplicati

the caret key (^) is used to raise a quantity t

■

Work with cell

You

references

should know that when you copy a f

contains a cell reference such as $A$4 (an ab

by including the dollar signs), the formula s

to. When you copy a formula that contains a c

address), the column remains fxed, but the row c

formula that contains a cell reference such a

and the column of the cells referenced in the f

Introduction

How to Use This Book

As you read along with the examples in this bo

■

You can open the template fle that correspo

and complete each step of the example as yo

how easy this process is and amazed with how m

approach I use in my corporate classes.

■

Instead of working in the template, you can f

fnal version of each sample fle.

Using the Companion Content

This book features a companion website that ma

use in the book’s examples (both the fnal Exce

work with on your own). The workbooks and temp

each chapter. The answers to all chapter-endin

the sample fles. Each answer fle is named so th

fle containing the answer to Problem 2 in Chap

To work through the examples in this book, you n

computer. These practice fles, and other infor

detail page, located at:

http://go.microsoft.com/fwlink/?Linkid=207235

Display the detail page in your Web browser, a

the fles.

Your Companion eBook

The eBook edition of this book allows you to:

■

Search the full text

■

Copy and paste

To download your eBook, please see the instruc

xii

Introduction

Errata and Book Support

We’ve made every effort to ensure the accuracy o

you do fnd an error, please report it on our Mic

Go to

http://microsoftpress.oreilly.com.

In the

Search

box, enter the book’s ISBN or ti

Select your book from the search results.

On your book’s catalog page, under the cover i

Click

View/Submit Errata.

You’ll fnd additional information and services f

additional support, please e-mail Microsoft

Pres

Please note that product support for Microsoft s

addresses above.

We Want to Hear from You

At Microsoft Press, your satisfaction is our top p

valuable asset. Please tell us what you think of thi

http://www.microsoft.com/learning/booksurvey.

The survey is short, and we read

every one

of yo

for your input!

Stay in Touch

Let’s keep the conversation going! We’re on Twit

Introduction

xiii

Acknowledgments

I am eternally grateful to Jennifer Skoog and N

hired me to teach Excel classes for Microsoft

tal in helping design the content and style of th

Lange of Eli Lilly, Pat Keating and Doug Hoppe o

Army also helped me refne my thoughts on teachi

I was blessed to work with John Pierce again, w

Mitch Tulloch did a great job with the technic

managing the book’s production and to proofrea

Rosemary Caperton and Devon Musgrave helped sh

I am grateful to my many students at the organi

School of Business. Many of them have taught m

Alex Blanton, formerly of Microsoft Press, cha

vision of developing a user-friendly text desi

Finally, my lovely and talented wife, Vivian, a

put up with my long weekend hours at the keybo

Chapter 1

What’s New in Excel 2

Microsoft Excel 2010 contains many new feature

including these:

■

Customizable

Now

ribbon

you can completely customize th

ribbon.

■

Sparklines

Cool graphs that summarize lots of dat

■

Slicers

Dashboard controls that make “slicing aa

much easier.

■

PowerPivot

A free add-in that enables you to qui

100 million rows of data based on data from m

and websites).

■

Solver

An improved Solver allows you to fnd the “

problems for which previous versions of the S

■

File

The

tab

new File tab on the ribbon replaces th

access to the File and Print menus.

■

Updated statistical

The accuracy

functions

of Excel statisti

been improved, and several new functions (i

WORKDAY.INTL, and NETWORKDAYS.INTL) have bee

■

Equations

You can now edit equations in Excel by u

similar to the Microsoft Word equation edit

■

Data bars

Data bars have been improved.

■

Paste Special

Paste Special options now include a l

Let’s now examine each of these exciting new f

Customizable Ribbon

In Excel 2007, users were not able to customiz

ribbon. In Excel 2010, it is easy to customize th

selecting File in the upper-left portion of th

Customize Ribbon page shown in Figure 1-1.

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 1-1

How to customize the ribbon.

As an example, suppose you want to show the Deve

the list at the right, and click OK. You can cha

selecting a tab, and then using the Move Up and M

click the drop-down arrow by Main Tabs, you can d

the tabs that appear when a given object is sele

Chart Tools, when you select a Chart object, the D

New Tab button allows you to create a new tab, a

a group within a tab. Of course, you can use the

group or tab.

Don’t Forget About the Quick Acce

The Quick Access Toolbar is an old friend from E

You probably use some Excel commands much more o

between tabs to fnd the command you need might s

Toolbar (see Figure 1-2) allows you to collect y

default location of the Quick Access Toolbar is a

the Excel window.

Fig

URE 1-2

Quick Access Toolbar.

Chapter

What’s

New in Excel

2010

You can add a command to the Quick Access Tool

and choosing Add To Quick Access Toolbar. You c

the upper-left portion of the ribbon. Next cli

the Quick Access Toolbar page (shown in Figure 1

to add, select Add, and click OK. Of course, t

customize the order in which icons appear. You c

Access Toolbar by right-clicking the command, a

Toolbar. You can move the Quick Access Toolbar b

toolbar, and selecting Show Below The Ribbon.

Fig

URE 1-3

You can add, remove, and arrange commands on the Q

People sometimes have trouble fnding commands th

but seem to have disappeared from Excel 2010. F

method used to create PivotTables: the layout m

method, you can fnd it by clicking the drop-dow

and choosing Commands Not In The Ribbon. After s

times is probably quicker!), you will fnd the P

which you can then add to your Quick Access To

Microsoft Excel 2010: Data Analysis and Business Modeling

Sparklines

Sparklines are small charts or graphs that ft in a s

graphical summary of data next to the data. Figu

daily customer counts at bank branches.

Fig

URE 1-4

Example of sparklines.

The sparklines make it clear that each branch is b

discussed in Chapter 44, “Sparklines.”

Slicers

PivotTables are probably the single most used to

“slice and dice your data” and are discussed in C

Summarize Data.” Excel 2010 allows you to use sl

data. The Name and Product slicers in Figure 1-5 e

computed for only the rows of data in which Eric a

investment accounts. Slicers are also discussed i

Fig

URE 1-5

Example of slicers.

Chapter

What’s

New in Excel

2010

PowerPivot

Organizations often have to create reports bas

For example, a bank might have customer data f

database. The bank might then want to create a c

the data from the individual branches. In the p

from different data sources. PowerPivot is a f

easily create PivotTables based on data from d

Using PowerPivot, you can quickly create Pivot

of data! PowerPivot is discussed in Chapter 84

New Excel Solver

The Excel Solver is used to fnd the best way t

cheapest way to meet customer demand by shippi

Excel 2010 contains a much improved version

of th

portant functions (such as IF, MAX, MIN, and A

versions of Excel, use of these functions in a S

an incorrect solution. I discuss the Excel Sol

File Tab

Excel 2007 introduced the Offce button. In Exc

by the File tab. The File tab is located at th

are presented with the choices shown in Figure 1

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 1-6

File tab options.

You can see that the File tab combines the Print a

Excel. Also, selecting Options lets you perform a v

ribbon or the Quick Access Toolbar, or installin

customizing the ribbon) were performed after cli

New Excel Functions

Many new functions (mostly statistical functions th

functions in previous versions)

PERCENTILE.EXC

have been added.

impr

accuracy of the RANK function. Statistical functi

Data by Using Descriptive Statistics,” and Chapt

(see Chapter 12, “IF Statements”) enables calcul

contain errors! The new WORKDAY.INTL

(see

and

Chapter

NETWORK

“Dates and Date Functions”) recognize the fact t

than Saturday and Sunday off from work. The accu

Chapter 10, “More Excel Financial Functions”) ha

Chapter

What’s

New in Excel

2010

New Equation Editor

Many readers of this book are probably long-ti

editor. In Excel 2010 you can now create equati

ribbon, you can then click Equation at the far r

in Figure 1-7.

Fig

URE 1-7

Equation editor templates.

For example, if you want to type an equation i

Large Operator options.

Sometimes you want a well-known equation (such a

your spreadsheet. After choosing Insert, click th

to import an already completed equation (such a

choosing Insert you select Symbol, you can ins

letter µ) into a cell.

improved Data Bars

Excel 2007 introduced using data bars as a meth

2010 data bars have been improved in two ways:

■

You can choose either Solid Fill or Gradien

■

Data bars recognize negative numbers.

Figure 1-8 shows an example of how the new dat

shading, and rows 12–17 contain solid shading. Y

in Chapter 24, “Conditional Formatting.”

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 1-8

Example of Excel 2010 data bars.

Paste Special Live Preview

If you right-click a range of cells and select P

of the Paste Special command), Excel 2010 brings u

choices, as shown in Figure 1-9.

Fig

URE 1-9

Paste Special live preview.

Clicking an option lets you see a preview of how y

that option.

Chapter 2

Range Names

Questions answered in this chapter:

■

I want to total sales in Arizona, California

use a formula to compute total sales in a f

SUM(A21:A25)

and still get the right answer

■

What does a formula like

Average(A:A)

do?

■

What is the difference between a name with w

scope?

■

I really am getting to like range names. I h

of the workbooks I have developed at the of

show up in my formulas. How can I make rece

previously created formulas?

■

How can I paste a list of all range names (

worksheet?

■

I am computing projected annual revenues as a m

a way to have the formula? look like

(1+growth

■

For each day of the week we are given the h

compute total salary for each

? day with the f

You have probably worked with worksheets. that u

Then you have to fnd out what’s contained in c

contain sales in each U.S. state, wouldn’t the f

In this chapter, I’ll teach you how to name in

how to use range names in formulas.

How Can i Create Named Ranges?

There are three ways to create named ranges:

■

By entering a range name in the Name box.

■

By clicking Create From Selection in the De

■

By clicking Name Manager or Defne Name in th

Formulas tab.

Microsoft Excel 2010: Data Analysis and Business Modeling

Using the Name Box to Create a Ra

The Name box (shown in Figure 2-1) is located di

the Name box, you need to display the Formula ba

box, simply select the cell or range of cells th

then type the range name you want to use. Press E

Clicking the Name arrow displays the range names d

display all the range names in a workbook by pre

dialog box. When you select a range name from th

the cells corresponding to that range name. This e

cell or range that you intended to name. Range n

Fig

URE 2-1

You can create a range name by selecting the cell r

range name in the Name box.

For example, suppose you want .

toSee

name

Figure

cell 2-2

fle Eastwest.xlsx. Simply select cell F3, type

select cell F4, type

west

in the Name box, and p

another cell, you see

. This

=east

means

instead

that of

whenever

=F3

you s

east

in a formula, Excel will insert whatever is i

Fig

URE 2-2

Naming cell F3

east

and cell F4

west.

Suppose you want to assign a rectangular

range o

Simply select the cell range A1:B4, type

Data

in th

formula such as

=AVERAGE(Data)

would average the c

Data.xlsx and Figure 2-3.

Fig

URE 2-3

Naming range A1:B4

Data.

Chapter

Range

Names

Sometimes you want to name a range of

rectangula

cells ma

ranges. For example, in Figure 2-4 and the fle

name

Noncontig

to the range consisting of cell

name, select any one of the three rectangles m

the Ctrl key, and then select the other two ra

key, type the name

Noncontig

in the Name box, a

formula will now refer to the contents of

- cell

ing the formula

=AVERAGE(Noncontig)

in cell E1

range add up to 57 and 57/12=4.75).

Fig

URE 2-4

Naming a noncontiguous range of cells.

Creating Named Ranges by Using t

Option

The worksheet States.xlsx contains sales durin

Figure 2-5 shows a subset of this data. We wou

with the correct state abbreviation. To do thi

Selection in the Defned Names group on the For

Left Column check box, as indicated in Figure 2

Fig

URE 2-5

By naming the cells that contain state sales with s

rather than the cell’s column letter and row number wh

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 2-6

Select Create From Selection.

Fig

URE 2-7

Select the Left Column check box.

Excel now knows to associate the names in the fr

cells in the second column of the selected

, B7 range

is named

, and

so on. Note that creating these rang

been incredibly tedious! Click the Name arrow to v

created.

Creating Range Names by Using the N

If you click Name Manager on the Formulas tab an

box shown in Figure 2-8 opens.

Fig

URE 2-8

The New Name dialog box before creating any range n

Suppose you want to assign the name

range1

(rang

cell range A2:B7. Simply type

range1

in the Name b

=A2:B7

in the Refers To area. The New Name dialo

OK, and you’re done.

Chapter

Range

Names

Fig

URE 2-9

New Name dialog box after creating a range name.

If you click the Scope arrow, you can select th

your workbook. I’ll discuss this decision late

Workbook. You can also add comments for any of y

The Name Manager

If you now click the Name arrow, the name

rang

appears in the Name box. In Excel 2010, there i

names. Simply open the Name Manager by selecti

Name Manager. You will now see a list of all r

xlsx, the Name Manager dialog box will look li

Fig

URE 2-10

Name Manager dialog box for States.xlsx.

Microsoft Excel 2010: Data Analysis and Business Modeling

To edit any range name, simply double-click the r

click Edit. Then you can change the name of the r

scope of the range.

To delete any subset of range names, frst select t

range names are listed consecutively, simply sel

want to delete, hold down the Shift key, and sel

range names are not listed consecutively, you ca

and then hold down the Ctrl key while you select th

press the Delete key to delete the selected rang

Now let’s look at some specifc examples of how t

Answers to This Chapter’s Quest

I want to total sales in Arizona, California,

. Can I

use a formula to compute total sales in a form s

SUM(A21:A25) and still get the right answer?

Let’s return to the fle States.xlsx, in which we a

name for the state’s sales. If you want to compu

Arkansas, you could clearly

. You

usecould

the formula

also point

SUM(

B8, and B9, and the formula would

. The be

latter

entered

formul

course, much easier to understand.

As another illustration of how to use range name

in Figure 2-11, which contains annual percentage r

rows are hidden in this fgure; the data ends in r

Fig

URE 2-11

Historical investment data.

Chapter

Range

Names

After selecting the cell range B7:D89 created

and choo

names in the top row of the range.

, theThe range

C8:C

T.Bills

, and the range

. Now

D8:D89

you

T.Bonds

no longer need to re

data is. For example, in

cell

(

youB91,

can after

press typin

F3 an

Name dialog box appears, as shown in Figure 2-

Fig

URE 2-12

You can add a range name to a formula by using t

Then you can select Stocks in the Paste Name l

parenthesis, the formula,

=AVERAGE(Stocks),

percent). The beauty of this approach is that e

you can work with the stock return data anywhe

I would be remiss if I did not mention the exc

you begin typing

, Excel

=Average(T

shows you a list of range n

with T. Then you can simply double-click T.Bil

What does a formula like Average(A:A) do?

If you use a column name (in the form A:A,

entire

C:C

column as a named range. For example, entering th

all numbers in column A. Using a range name fo

frequently enter new data into a column. For e

of a product, as new sales data is entered eac

monthly sales average. I caution you, however, t

in column A, you will get a circular reference

ing the average formula depends on the cell co

resolve circular references in Chapter 11, “Ci

=AVERAGE(1:1)

will average all numbers in row 1

What is the difference between a name with wor

scope?

The fle Sheetnames.xlsx will help you understa

have workbook scope and range names that have w

Microsoft Excel 2010: Data Analysis and Business Modeling

with the Name box, the names have workbook scope

Name box to assign the name

sales

to the cell ra

the numbers 1, 2, and 4, respectively. Then if y

any worksheet, you obtain an answer of 7. This i

workbook scope, so anywhere in the workbook wher

workbook scope) the name refers to cells E4:E6 o

the formula

=SUM(sales),

you will obtain 7 becau

sales

to cells E4:E6 of Sheet3.

Now suppose that you type 4, 5, and 6 in cells E

of Sheet2. Next you go to the Name Manager, give th

and defne the scope of this name as Sheet1. Then y

Manager, and give the name

jam

to cells E4:E6, a

The Name Manager dialog box now looks like Figur

Fig

URE 2-13

Name Manager dialog box with worksheet and workboo

Now, what if you enter the formula

=SUM(jam)

in e

total cells E4:E6 of Sheet1. Because those cells c

=Sum(jam)

will total cells E4:E6

. In of

Sheet3,

Sheet2,

however

yiel

formula

=SUM(jam)

will yield a

#NAME?

error beca

in Sheet3. If you enter anywhere in Sheet3

the f

nize the worksheet-level name that represents ce

3 + 4

Thus,

5 =12

prefacing a worksheet-level name by i

exclamation point (!) allows you to refer to a w

the sheet in which the range is defned.

Chapter

Range

Names

I really am getting. Itohave

likestarted

range names

defining ran

the workbooks I have developed

. However, at the

range

office

name

in my formulas

. How can I make recently created -range n

ated formulas?

Let’s look at the fle Applynames.xlsx. See Fig

Fig

URE 2-14

How to apply range names to formulas.

I entered the price of a product in cell F3, a

The unit cost and fxed cost are entered in

cel

ed in cell F7 with the

. Iformula

used Formulas,

=F4*(F3–F5)–F6

Create F

chose the Left Row option

, celltoF4

, name

cell

demand

cell

, cell

unit

F3 F6

pric

cos

cost

, and cell

. You

F7 would

proft

like these range names to s

formulas. To apply the range names, frst selec

applied (in this case, F4:F7). Now go to the D

the Defne Name arrow, and then click Apply Nam

and then click OK. Note that cell F4 now contai

contains the formula

=demand*(price–unitcost)–

, as you wanted.

By the way, if you want the range names to app

entire worksheet by clicking the Select All bu

headings.

How can I paste a list of all range names (and

Press F3 to display the Paste Name box, and th

Figure 2-12.) A list of range names and the ce

your

worksheet, beginning at the current cell l

I am computing projected annual revenues

. Is there

as a ma

way to have the formula look like (1+growth)*l

The fle Last year.xlsx contains the solution t

to compute revenues for 2012–2018 that grow at 1

million in 2011.

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 2-15

Creating a range name for

last year.

To begin, we use the Name. box

Now to

comes

namethe

cell

neat

B3 par

the cursor to B7 and bring up the New Name dialo

Defned Names group on the Formulas tab. Then fll i

in Figure 2-16.

Fig

URE 2-16

In any cell, this name refers to the cell above the a

Because we are in cell B7, Excel interprets this r

the current cell. Of course, this would not work i

signs. Now if we enter

lastyear*(1+growth)

in cell

and

copy

the formula

it down

to th

range B8:B13, each cell will contain the formula w

of the cell directly above the active cell.

For each day of the week we are given

. Canthe

we hourly w

compute total salary for each day with the formu

As shown in Figure 2-17 (see the fle Namedrows.x

row 13 contains hours worked each day.

Chapter

Range

Names

Fig

URE 2-17

In any cell, this name refers to the cell above t

You can simply select row 12 (by clicking on th

wage

. Then select row 13 and use the

. If

Name

youbox

nowte

in cell F14 the formula

wage*hours

and copy thi

that in each column Excel fnds the wage and ho

Remarks

■

Excel does not allow you to use the letters

■

If you use Create From Selection to create a

spaces, Excel inserts an underscore (_) to fl

Product 1

is created

Product_1

■

Range names cannot begin with numbers or lo

and

are not allowed as range names. Beca

a range name such as

cat1

is not permitted b

name a cell

, Excel

CAT1

tells you the name is invali

name the cell cat1_.

■

The only symbols allowed in range names are p

Problems

The fle Stock.xlsx contains monthly stock r

Name the ranges containing the monthly retu

average monthly return on each stock.

Open a worksheet and name the range containi

Given the latitude and longitude of any two c

the distance between the two cities. Defne r

of each city and ensure that these names sh

The fle Sharedata.xlsx contains the numbers o

price of each stock. Compute the value of th

shares*price

Create a range name that averages the last f

are listed in a single column.

Chapter 3

Lookup Functions

Questions answered in this chapter:

■

How do I write a formula to compute tax rat

■

Given a product ID, how can I look up the p

■

Suppose that a product’s price changes over ti

sold. How can I write a formula to compute th

Syntax of the Lookup Functions

Lookup functions enable you to “look up” value

2010 allows you to perform both vertical looku

horizontal lookups (by using the HLOOKUP functi

operation starts in the frst column of -a works

eration starts in the frst row of a worksheet r

lookup functions involve vertical lookups, I’l

VLOOKUP Syntax

The syntax of the VLOOKUP function is as follow

arguments.

VLOOKUP(lookup value,table range,column index,[range lookup])

■

Lookup value

is the value that you want to l

range.

■

Table range

is the range that contains the e

the frst column, in which you try and match th

in which you want to look up formula result

■

Column index

is the column number in the ta

lookup function is obtained.

■

Range lookup

is an optional argument. The p

specify an exact or approximate match.

- If th

ted, the frst column of the table range mus

range lookup

argument is

True

or omitted an

Microsoft Excel 2010: Data Analysis and Business Modeling

is found in the frst column of the table rang

the table in which the exact match is found. I

omitted and an exact match does not exist, Ex

in the frst column that is less than the look

False

and an exact match to the lookup value i

range, Excel bases the lookup on the row of th

found. If no exact match is obtained, Excel r

Note that a

range lookup

argument of

is equ

argument of

is equivalent to

False.

HLOOKUP Syntax

In an HLOOKUP function, Excel tries to locate th

column) of the table range. For an HLOOKUP functi

column

.to

row

Let’s explore some interesting examples of looku

Answers to This Chapter’s Quest

How do I write a formula to compute tax rates ba

The following example shows how a VLOOKUP functi

table range consists of numbers in ascending ord

income, as shown in the following table.

Income level Tax rate

$0–$9,999

15%

$10,000–$29,99390%

$30,000–$99,99394%

$100,000 and over

40%

To see an example of how to write a formula that c

open the fle Lookup.xlsx, shown in Figure 3-1.

Chapter

Lookup

Functions

Fig

URE 3-1

Using a lookup function to compute a tax rate. Th

range are sorted in ascending order.

I began by entering the relevant information (

I named the table. range

I recommend

D6:E9

lookup

that you always n

using as the table range. If you do so, you ne

table range, and when you copy any formula inv

will always be correct. To illustrate how the l

in the range D13:D17. By copying from E13:E17

, I

computed the tax rate for the income levels li

function worked in cells E13:E17. Note ,that

the be

answer always comes from the second column of th

■

In D13, the income of –$1,000 yields #N/A be

income level in the frst column of the tabl

associated with an income of –$1,000, simpl

–1,000 or smaller.

■

In D14, the income of $30,000 exactly match

range, so the function returns a tax rate o

■

In D15, the income level of $29,000 does not e

umn of the table range, which means the loo

less than $29,000 in the frst column of the r

returns the tax rate in column 2 of the tab

■

In D16, the income level of $98,000 does not y

of the table range. The lookup function sto

in the frst column of the table range. This r

range opposite $30,000—34 percent.

Microsoft Excel 2010: Data Analysis and Business Modeling

■

In D17, the income level of $104,000 does not y

of the table range. The lookup function stops a

in the frst column of the table range, which r

table range opposite $100,000—40 percent.

■

In F13:F17, I changed the value of the

range l

copied from F13 to F14:F17 the formula

. Cell F14

VLOOKU

sti

yields a 34 percent tax rate because the frst c

exact match to $30,000. All the other entries i

of the other incomes in D13:D17 have an exact m

table range.

Given a product ID, how can I look up the produc

Often, the frst column of a table range does not c

example, the frst column of the table range migh

In my experience teaching thousands of fnancial a

know how to deal with lookup functions when the fr

consist of numbers in ascending order. In these s

simple rule: use

False

as the value of the

range l

Here’s an example. In the fle Lookup.xlsx (see Fi

products, listed by their product ID code. How d

code and returns the product price?

Fig

URE 3-2

Looking up prices from product ID codes. When the t

enter

False

as the last argument in the lookup function f

Many people would enter the formula as

. I have in c

However, note that when you omit the fourth argu

value is assumed

. Because

to bethe

True

product IDs in the tab

are not listed in alphabetical order, an incorre

formula

VLOOKUP(H18,Lookup2,2,False)

the correct price

in cell

($5.20

I18

You would also use

False

in a formula designed t

employee’s last name or ID number.

Chapter

Lookup

Functions

By the way, you can see in Figure 3-2 that col

yob

uegin by selecting the columns you want to hi

In the Cells group, click Format, point to Hid

Hide Columns.

Suppose that a product’s. Iprice

know changes

the dateover

the

How can I write a formula to compute the produ

Suppose the price of a product depends on the d

a lookup function in a formula that will pick u

suppose the price of a product is as shown in th

Date sold

Price

January–April 200$

598

May–July 2005

$105

August–December 2005

$112

Let’s write a formula to determine the correct p

product is sold in the year 2005. For variety, w

dates when the price changes in the frst row o

shown in Figure 3-3.

Fig

URE 3-3

Using an HLOOKUP function to determine a price th

I copied from C8 to C9:C11 the .formula

This formula

HLOOKUP

to match the dates in column B with the frst r

1/1/05 and 4/30/05, the lookup function stops a

date between 5/01/05 and 7/31/05, the lookup s

and for any date later than 8/01/05, the looku

Microsoft Excel 2010: Data Analysis and Business Modeling

Problems

The fle Hr.xlsx gives employee ID codes, sala

formula that takes a given ID code and yields th

The fle Assign.xlsx gives the assignment of w

each worker for each group (on a scale from 0 t

gives the suitability of each worker for the g

You are thinking of advertising Microsoft pro

more ads, the price of each ad decreases as s

Number of ads

Price per ad

1–5

$12,000

6–10

$11,000

11–20

$10,000

21 and higher

$9,000

For example, if you buy 8 ads, you pay $11,00

$10,000 per ad. Write a formula that yields th

ads.

You are thinking of advertising Microsoft pro

You pay one price for the frst group of ads, b

decreases as shown in the following table.

Ad number

Price per ad

1–5

$12,000

6–10

$11,000

11–20

$10,000

21 or higher

$9,000

For example, if you buy 8 ads, you pay $12,00

for each of the next 3 ads. If you buy 14 ads

ads, $11,000 for each of the next 5 ads, and $

formula that yields the total cost of purchas

need at least three columns in your table ran

lookup functions.

Chapter

Lookup

Functions

The annual rate your bank charges you to bo

shown in the following table.

Duration of loanAnnual loan rate

1 year

5 years

10 years

30 years

10%

If you borrow money from the bank for any d

listed in the table, your rate is found by i

table. For example, let’s say you borrow mo

quarter of the way between 10 years and 30 y

culated as follows:

(9)

(10)

9.75%

Write a formula that returns the annual int

1 and 30 years.

The distance between any two U.S. cities (e

approximated by the formula

69 *

(lat1 - lat2)

+ (long1 - long2)

The fle Citydata.xlsx contains the latitude a

table that gives the distance between any t

In the fle Pinevalley.xlsx, the frst worksh

at Pine Valley University, the second works

the third worksheet contains the years of e

contains the salary, age, and experience fo

The fle Lookupmultiplecolumns.xlsx contains i

an electronics store. A salesperson’s name w

that can be copied from C17 to D17:F17 that w

to C17, TV sales to D17, printer sales to E1

Microsoft Excel 2010: Data Analysis and Business Modeling

The fle Grades.xlsx contains student’s grades o

follows:

Score

Grade

Below 60

61–69

70–79

80–89

90 and aboveA

Use Excel to return each student’s letter gra

10.

The fle Employees.xlsx contains the ranking e

scale) to three jobs. The fle also gives the j

formula to compute each worker’s ranking for th

11.

Suppose one dollar can be converted to 1,000 y

spreadsheet where the user can enter an amoun

spreadsheet converts dollars to the entered c

Chapter 4

The INDEX Function

Questions answered in this chapter:

■

I have a list of distances between U.S. citi

distance between, for example, Seattle and Mia

■

Is there a way I can write a formula that r

distances between each city and Seattle?

Syntax NDEX

of the

Function

The INDEX function allows you to return the en

numbers. The most commonly used syntax for the I

INDEX(Array,Row Number,Column Number)

To illustrate, the formula

INDEX(A1:D12,2,3)

column of the array A1:D12. This entry is the o

Answers to This Chapter’s Ques

I have a list of S..distances

cities

. How dobetween

I writeU a functio

distance between, for example, Seattle and Mia

The fle Index.xlsx (see Figure 4-1) contains th

C10:J17, which contains the

distances, is name

Fig

URE 4-1

You can use the INDEX function to calculate the d

Microsoft Excel 2010: Data Analysis and Business Modeling

Suppose that you want to enter the distance betw

distances from Boston are listed in

, and

the

- dis

frst row o

tances to Denver are listed in the fourth column o

INDEX(distances,1,4)

. The results show that Boston and Den

Similarly, to fnd the (much longer) distance bet

formula

INDEX(distances,6,8)

. Seattle and Miami are 3,389 miles a

Imagine that the Seattle Seahawks NFL team is em

games in Phoenix, Los Angeles (an exhibition agai

At the conclusion of the road trip, the Seahawks r

how many miles they travel on the trip? As you c

cities the

8-7-5-4-3-2-8

Seahawks

) in

visit

the (

order they are visited

in Seattle, and copy from D21 to D26

. The

the formula

in D21 computes the distance between Seattle and P

D22

computes the distance between Phoenix and Los A

travel a total of 7,112 miles on their road trip

that the Miami Heat travel more miles during the N

Fig

URE 4-2

Distances for a Seattle Seahawks road trip.

Is there a way I can write a formula that

- refere

tances between each city and Seattle?

The INDEX function makes it easy to reference an e

the row number to 0, the INDEX function referenc

number to 0, the INDEX function references the l

to total the distances from each listed city to S

formulas:

SUM(INDEX(distances,8,0))

SUM(INDEX(distances,0,8))

The frst formula totals the numbers in the eighth r

second formula totals the numbers in the eighth c

either case, you fnd that the total distance fro

you can see in Figure 4-1.

Chapter

The4 INDEX Function

Problems

Use the INDEX function to compute the dista

and the distance between Denver and Miami.

Use the INDEX function to compute the total d

Jerry Jones and the Dallas Cowboys are emba

Chicago, Denver, Los Angeles (an exhibition a

many miles will they travel on this road tr?

The fle Product.xlsx contains monthly sales f

to compute the sales of Product 2 in March. U

sales during April.

The fle Nbadistances.xlsx shows the distanc

you begin in Atlanta, visit the arenas in th

How far would you travel?

Use the INDEX function to solve problem 10 o

Chapter 5

The MATCH Function

Questions answered in this chapter:

■

Given monthly sales for several products, h

sales of a product during a specifc month? F

sell during June?

■

Given a list of baseball players’ salaries, h

with the highest salary? How about the play

■

Given the annual cash flows from an investme

returns the number of years required to pay b

Suppose you have a worksheet with fve thousand r

need to fnd the

, name

which

John

you

Doe

know appears somewhe

the list. Wouldn’t you like to know of a formu

name John Doe is located? The MATCH function e

frst occurrence of a match to a given text

- str

tion instead of a lookup function in situation

a range rather than the value in a particular c

Match(lookup value,lookup range,[match type])

In the explanation that follows, we’ll assume th

the same column. In this syntax:

■

Lookup value

is the value you’re trying to m

■

Lookup range

is the range you’re examining f

lookup range must be a row or column.

■

Match type=1

requires the lookup range to c

order. The MATCH function then returns the r

to the top of the lookup range) that contai

than or equal to the lookup value.

■

Match type=–1

requires the lookup range to c

order. The MATCH function returns the row lo

top of the lookup range) that contains the l

equal to the lookup value.

■

Match type=0

returns the row location in th

exact match to the lookup value. (I discuss h

Chapter 20, “COUNTIF, COUNTIFS, COUNT, COUNT

Microsoft Excel 2010: Data Analysis and Business Modeling

When no exact match exists

, Exceland

returns

match

the

type=0

error m

Most MATCH function applications

, but if

match

use

match

type ty

is n

match type=1

is assumed. Thus, use

match type

range are unsorted. This is the situation you u

The fle Matchex.xlsx, shown in Figure 5-1, contai

syntax.

Fig

URE 5-1

Using the MATCH function to locate the position of a v

In cell B13, the formula

MATCH(“Boston”,B4:B11,0

range B4:B11 contains

. Text

the

values must

Boston

be enclosed i

(

“

)

”

. In cell B14, the formula

MATCH(“Phoenix”,B4:

seventh cell in B4:B11) is the frst cell in the r

formula

MATCH(0,E4:E11,1)

returns 4 because the l

in the range E4:E11 is in cell E7 (the fourth ce

MATCH(–4,G4:G11,–1

) returns 7 because the last number th

in the range G4:G11 is contained in cell G10 (th

The MATCH function can also work with an inexact m

MATCH(“Pho*”,B4:B11,0)

returns 7. The asterisk i

Excel searches for the frst text string

. Incidentally

in the r

this same technique can be used with a lookup fu

exercise in Chapter 3, “Lookup Functions,”

) would the f

return the price of product X212 ($4.80).

If the lookup range is contained in a single row

match in the lookup range, moving from left to r

the MATCH function is often very useful when it i

as VLOOKUP, INDEX, or MAX.

Chapter

The5 MATCH Function

Answers to This Chapter’s Ques

Given monthly sales for several products, how d

of a product during a specific month? For-examp

ing June?

The fle Productlookup.xlsx (shown in Figure 5-

from January through June. How can you write a f

product during a specifc month? The trick is t

which the given product is located, and anothe

the given month is located. You can then use th

for the month.

Fig

URE 5-2

The MATCH function can be used in combination wit

I named the range B4:G7, which contains

. I entered

sales

th d

product I want to know about in cell A10

- and th

mula

MATCH(A10,A4:A7,0)

to determine which row n

sales fgures for the Kobe doll. Then, in cell D

determine which column number in the range

Sal

the row and column numbers that contain the sa

INDEX(Sales,C10,D10)

in cell E10 to yield the p

information on the INDEX function, see Chapter 4

Given a list of baseball players’ salaries, ho

with the highest salary? How about the player w

The fle Baseball.xlsx (see Figure 5-3) lists th

players during the 2001 season. The data- is not s

mula that returns the name of the player with th

with the ffth-highest salary.

To fnd the name of the player with the highest s

■

Use the MAX function to determine the value o

■

Use the MATCH function to determine the row th

highest salary.

Microsoft Excel 2010: Data Analysis and Business Modeling

■

Use a VLOOKUP function (keying off the data r

look up the player’s name.

I named the range C12:C412, which .includes

I named the p

range used in our VLOOKUP function

(range A12:C4

Fig

URE 5-3

This example uses the MAX, MATCH, and VLOOKUP funct

value in a list.

In cell C9, I fnd the highest player salary

. Next,($22 mi

in cell C8, I use the formula

MATCH(C9,Salaries,

player with the highest salary. I used

match typ

either ascending or descending order. Player num

cell C6, I use the function

VLOOKUP(C8,Lookup,2)

column of the lookup range. Not surprisingly, we fn

paid player in 2001.

To fnd the name of the player with the ffth-high

the ffth-largest number in an array. The LARGE f

LARGE function is.

LARGE(cell

When the LARGE

range,k)

function

is en

turns the

largest number in a cell range. Thus, the f

yields the ffth-largest salary ($12.6 million). P

is the player with the ffth-highest salary. (The

beginning of the season, Jeter was on the disabl

return the ffth-lowest salary.

Given the annual cash flows from an investment pr

returns the number of years required to pay back t

Chapter

The5 MATCH Function

The fle Payback.xlsx, shown in Figure 5-4, show

project over the next 15 years. We assume that i

of $100 million. During Year 1, the project ge

cash flows to grow at 10 percent per year. How m

back its investment?

The number of years required for a project to p

period.

In high-tech industries, the payback p

learn in Chapter 8, “Evaluating Investments

by U

back is flawed as a measure of investment quali

time.) For now, let’s concentrate on how to de

investment model.

Fig

URE 5-4

Using the MATCH function to calculate an investme

To determine the payback period for the projec

■

In column B, compute the cash flows for each y

■

In column C, compute the cumulative cash flow

Now you can use the MATCH )function

to determine

(with the

match

row

the frst year in which cumulative cash flow is p

period.

I gave the cells in B1:B3 the range names

list

ment) is entered in cell B5. Year 1 cash flow (

to B8:B20 the formula

B6*(1+Growth)

computes th

Microsoft Excel 2010: Data Analysis and Business Modeling

To compute the Year 0 cumulative cash flow, I use

you can calculate cumulative cash flow by using a f

flow=Year t–1 cumulative

cash

To implement

flow+Year

this

cash

relati

flow

copy from C6 to C7:C20

the formula

=C5+B6

To compute the payback period, use)the

to compute

MATCH fun

the last row of the range C5:C20 containing a va

you the payback period. For example, if the last r

0 is the sixth row in the range, that means the s

for the frst year the project is paid back. Beca

during Year 6. Therefore, the ,formula

yields in

the

- cell

payba

E2,

riod (6 years). If any cash flows after Year 0 ar

of cumulative cash flows would not be listed in a

Problems

Using the distances between U.S. cities given i

using the MATCH function to determine (based o

between any two of the cities.

The fle Matchtype1.xlsx lists in chronologica

transactions. Write a formula that yields the fr

date exceeds $10,000.

The fle Matchthemax.xlsx gives the product ID c

Use the MATCH function in a formula that yiel

with the largest unit sales.

The fle Buslist.xlsx gives the amount of time b

Street and Park Avenue in New York City. Writ

the frst bus, gives the amount of time you ha

arrive 12.4 minutes from now, and buses arriv

you wait

21–12.4=8.6

minutes for a bus.

The fle Salesdata.xlsx contains the number of c

Create a formula that returns the units sold by a g

Suppose the VLOOKUP function was removed from E

“get along” by using the MATCH and INDEX func

Chapter 6

Text Functions

Questions answered in this chapter:

■

I have a worksheet in which each cell contai

a product price. How can I put all the prod

IDs in column B, and all the prices in colu

■

Every day I receive data about total U.S. s

East, North, and South regional sales. How c

separate cells?

■

At the end of each school semester, my stud

a scale from 1 to 7. I know how many student

can I easily create a bar graph of my teachi

When someone sends you data or you download da

the way you want. For example, in sales data y

be in the same cell, but you need them to be i

data so that it appears in the format you need

Microsoft Excel text functions. In this chapte

text functions to magically manipulate your da

■

LEFT

■

RIGHT

■

MID

■

TRIM

■

LEN

■

FIND

■

REPT

■

CONCATENATE

■

REPLACE

■

VALUE

■

UPPER

■

LOWER

■

CHAR

Microsoft Excel 2010: Data Analysis and Business Modeling

Text Function Syntax

The fle Reggie.xlsx, shown in Figure 6-1, includ

to apply these functions to a specifc problem la

what each of the text functions does. Then we’ll c

fairly complex manipulations of data.

Fig

URE 6-1

Examples of text functions.

The LEFT Function

The function

text,k)

LEFT(

returns the frst

characters in a

contains the formula

. Excel

LEFT(A3,4)

returns

Regg

The RIGHT Function

The function

RIGHT(text,k)

returns the last

cell C4, the formula

RIGHT(A3,4)

returns

ller

The MID Function

The function

MID(text,k,m)

begins at character

characters. For example, the formula

MID(A3,2,5)

cell A3, the .

result being

eggie

The TRIM Function

The function

TRIM(text)

removes all spaces from a te

between words. For example, in cell C5 the formu

spaces between Reggie and .Miller

The TRIM

and function

yields

Regg

moves spaces at the beginning and end of the cel

Chapter

Text

6 Functions

The LEN Function

The function

LEN(text)

returns the number of c

For example, in cell C6, the formula

LEN(A3)

ters. In cell C7, the formula

LEN(C5)

returns 1

spaces removed, cell C5 contains two fewer cha

The FIND and SEARCH Functions

The function

text FIND(

to fnd,actual text,k)

returns th

the frst character of

. FIND

text

case

fnd

sensitive.

actual te

syntax as FIND, but it is not case sensitive. F

returns 15, the location of the frst

. (The

lowercase

upper

is ignored because FIND is case sensitive.) E

1 because SEARCH matches

to either a lowerca

Entering

FIND(“ “,A3,1)

in cell C9 returns 7 b

is the seventh character.

The REPT Function

The REPT function allows you to repeat a text s

REPT(text,

number of

. For

times)

example

REPT(“|”,3)

produce

The CONCATENATE and & Functions

The function

CONCATENATE(text1,text2, ...,te

into a single string. The & operator can be us

entering in cell&

”

C12

B“1

returns

the formula

Reggie

Entering

A1 Miller

in cell D

formula

CONCATENATE(A1,” “,B1)

yields the same r

The REPLACE Function

The function

oldREPLACE(

text,k,m,new text)

begins at cha

characters

. For

with

example,

new text

in cell C13, the f

replaces the third

and

) infourth

cell

. A3

This

characters

with

formula

(yiel

Miller

Microsoft Excel 2010: Data Analysis and Business Modeling

The VALUE Function

The function

text)

VALUE(

converts a text string that repre

example, entering in cell B15 the formula

VALUE(

to the numerical value 31. You can identify the v

justifed. Similarly, you can identify the value 3

justifed.

The UPPER and LOWER Functions

The function

UPPER(text)

changes

text

to all upp

UPPER(A1)

.yields

Similarly,

JAN

the function

LOWER(text)

contains

LOWER(A1)

JAN

. yields

jan

The CHAR Function

The function

number)

CHAR(

yields (for a number between 1 a

with that number. For example,

CHAR(65)

yields A

Answers to This Chapter’s Quest

You can see the power of text functions by using th

were sent to me by former students working for F

solving problems is to combine multiple text fun

I have a worksheet in which each cell contains a p

product . price

How can I put all the product descriptio

in column B, and all the prices in column C?

In this example, the product ID is always defned by th

always indicated in the last 8 characters (with t

The solution, contained in the fle Lenora.xlsx a

MID, VALUE, TRIM, and LEN functions.

It’s always a good idea to begin by trimming exc

from B4 to B5:B12 .the

Theformula

only excess

TRIM(A4)

spaces in co

the two spaces inserted after each price. To see thi

edit the cell. If you move to the end of the cel

using the TRIM function are shown in Figure 6-2. T

the two extra spaces at the end of cell A4, you c

to show that cell A4 contains 52 characters and c

Chapter

Text

6 Functions

Fig

URE 6-2

Using the TRIM function to trim away excess space

To capture the product ID, you need to extract th

do this, copy from C4 to .C5:C12

This formula

the formula

-extrac

most characters from the text in cell B4 and th

you can see in Figure 6-3.

Fig

URE 6-3

Using text functions to extract the product ID, p

To extract the product price, we know that the p

so we need to extract the rightmost six charac

D5:D12 the formula.

VALUE(RIGHT(B4,6))

used the VALUE function t

into a numerical value. If you don’t convert t

mathematical operations on the prices.

Extracting the product description is much tri

we begin our extraction with the thirteenth ch

from the end of the cell, we can get the

- data w

mula

MID(B4,13,LEN(B4)–6–12)

does the job.

LEN

in the trimmed text. This formula (MID for Mid

then extracts the number of characters equal t

the beginning (the product ID) and the 6 chara

only the product description.

Now suppose you are given the data with the pr

and the product description in column E. Can y

original text?

Text can easily be combined by using the CONCA

F5:F12 the formula

CONCATENATE(C4,E4,D4)

recov

can see in Figure 6-3.

Microsoft Excel 2010: Data Analysis and Business Modeling

The concatenation formula starts with the produc

description from cell E4. Finally, you add the p

entire text describing each computer! Concatenati

sign. You could recover the original product ID, p

with the formula

. Note

C4&E4&D4

that cell E4 contains- a spac

tion and a space after the product description. I

could use the formula

C4&” “&E4&” “&D4

to insert th

between each pair of quotation marks results in th

If the product IDs did not always contain 12 cha

information would fail. You could, however,

extr

tion to discover the location of the frst space. T

the LEFT function to extract all characters to th

next section shows how this approach works.

If the price did not always contain precisely si

little tricky. See Problem 15 for an example of h

Every day I receive

S.. sales,

data about

which

total

is computed

in a c

East, North, and South

. How can

regional

I extract

salesEast, North

separate cells?

This problem was sent to me by an employee in th

received a worksheet each day containing

, formula

and so on. She needed to extract each number int

she wanted to extract the frst number (East

sale

ber (North sales) to column D, and the third num

this problem challenging is that we don’t know th

the second and third numbers start in each cell. I

character. In cell A4, North sales begin with th

The data for this example is in the fle Salesstr

identify the locations of the different regions’ s

■

East sales are represented by every character t

■

North sales are represented by every characte

■

South sales are represented by every characte

By combining the FIND, LEFT, LEN, and MID functi

follows:

■

Use the Edit, Replace command to replace each e

the equal signs, select the range A3:A6. Then

Chapter

Text

6 Functions

click Find & Select, and then click Replace

and insert a space in the Replace With feld

formula into text by replacing the equal si

■

Use the FIND function to locate the two plu

Fig

URE 6-4

Extracting East, North, and South sales with a co

functions.

Begin by fnding the location of the frst plus s

to B4:B6 the formula

, you

FIND(“+”,A3,1)

can locate the frst plus s

fnd the second plus sign, begin one character a

C4:C6 the formula.

FIND(“+”,A3,B3+1)

To fnd East sales, you can use the LEFT functi

frst plus sign, copying from D3

. To

to extract

D4:D6 the

Norf

use the MID function to extract all the charac

character after the frst plus sign and extract th

2nd plus sign)–(Position

. If you

leave

1st plus

out

sign

the

)

–1,

sign. (Go ahead and check this.) So, to get No

MID(A3,B3+1,C3–B3–1)

To extract South sales, you use the RIGHT func

right of the second plus sign. South sales wil

(Total

characters in cell)

–

You

(Position

compute

the

2nd

total

plus

characters in each cell by copying

. Finally,

from F3 you

to Fc

obtain South sales by copying from .G3 to G4:G6 th

Extracting Data by Using the Tex

There is an easy way to extract East, North, a

without using text functions. Simply select

bon, in the Data Tools group, click Text To Co

in the dialog box as shown in Figure 6-5.

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 6-5

Convert Text To Columns Wizard.

Entering the plus sign in the Delimiters area di

breaking at each occurrence of the plus sign. Not

data at tabs, semicolons, commas, or spaces. Now c

your destination range (in the example, I chose c

in Figure 6-6.

Fig

URE 6-6

Results of Convert Text To Columns Wizard.

At the end of each school semester, my students e

scale from

. I 1know

to 7how many students gave

. How

me can

each p

I easily create a bar graph of my teaching evalu

The fle Repeatedhisto.xlsx contains my teaching e

7). Two people gave me scores of 1, three people g

REPT function, you can easily create a graph to s

to D5:D10 the formula

. This

=REPT(“|”,C4)

formula places

”

characters

in column D a

as the entry in column C. Figure 6-7 makes clear th

7s) and the relative rarity of poor scores (1s a

you to easily mimic a bar graph or histogram. Se

Histograms,” for further discussion of how to cr

Chapter

Text

6 Functions

Fig

URE 6-7

Using the REPT function to create a frequency gra

Problems

Cells B2:B5 of the workbook Showbiz.xlsx co

our favorite people. Use text functions to e

and each person’s street address to another

The workbook IDprice.xlsx contains the prod

text functions to put the product IDs and p

To Columns command on the Data tab on the ri

The workbook Quarterlygnpdata.xlsx contains q

(in billions of 1996 dollars). Extract this d

column contains the year, the second column c

third column contains the GNP value.

The fle Textstylesdata.xlsx contains inform

variety of shirts. For example, the frst shi

colon and the hyphen). Its color is 65, and i

style, color, and size of each shirt.

The fle Emailproblem.xlsx gives frst

employees.

and las

To create an e-mail address for each employe

the employee’s frst name by the employee’s l

end. Use text functions to effciently creat

The fle Lineupdata.xlsx gives the number

of mi

tions (lineups). (Lineup 1 played 10.4 minut

data into a form suitable for numerical cal

the number 10.4.

The fle Reversenames.xlsx gives the frst na

names of several people. Transform these na

followed by a comma, followed by the frst a

Gregory William Winston into Winston, Grego

The fle Incomefrequency.xlsx contains the d

graduates of Faber College. Summarize this d

Microsoft Excel 2010: Data Analysis and Business Modeling

Recall that

CHAR(65)

yields the letter A,

CHA

these facts to effciently populate cells B1:B

through Z.

10.

The fle Capitalizefrstletter.xlsx contains va

rain in Spain falls mainly in the plain.” Ens

capitalized.

11.

The fle Ageofmachine.xlsx contains data in th

S/N: 160768, vib roller,84” smooth drum,canopy A

Alabama

Each row refers to a machine purchase. Determi

12.

When downloading corporate data from the Secu

EDGAR site, you often obtain data for a compa

Cash and Cash Equivalents

$31,848

$ 3

How would you effciently extract the Cash and C

13.

The fle Lookuptwocolumns.xlsx gives the model

cars. Set up formulas that enable you to ente

its price.

14.

The fle Moviedata.xlsx contains the names of s

of copies of the movie DVD purchased by a loc

movie from this data.

15.

The fle Moviedata.xlsx contains the names of s

of copies of the movie DVD purchased by a loc

the number of copies purchased from this data

SUBSTITUTE function. The syntax of the SUBSTI

text,new_text,[instance_num])

. If _

instance

num

is omitted, every occur

text

is replaced

. If _

instance

num

by is

new_text

given, then only tha

old_text

new_text

replaced

. For example,

SUBSTITUTE(A4,1,2)

would

in cell A4 with a 2, but

SUBSTITUTE(A4,1,2,3)

a 1 in cell A4 with a 2.

16.

The fle Problem16data.xlsx contains the numbe

marketing questionnaire (1 = Very unlikely to b

product). Summarize this data graphically by u

summary look more appealing, you can go to th

Orientation in the Alignment group and make th

number, and increase the row height. Finally, i

so that you make the text of your graph verti

17.

The fle Problem17data.xlsx contains people’s n

functions to extract each person’s title and f

Chapter 7

Dates and Date Func

Questions answered in this chapter:

■

When I enter dates in Excel, I often see a n

as 1/4/2003. What does this number mean, an

■

Can I use a formula to automatically displa

■

How do I determine a date that is 50 workda

exclude holidays?

■

How do I determine the number of workdays b

■

I have 500 different dates entered in an Ex

extract from each date the month, year, day o

■

I am given the year, month, and day of the m

recover the actual date?

■

My business has purchased and sold machines

was purchased and the date the machine was s

months we kept these machines?

To illustrate the most commonly used month-day

suppose today is January 4, 2004. You can ente

■

1/4/2004

■

4-Jan-2004

■

January 4, 2004

■

1/4/04

If you enter only two digits to represent a ye

the digits represent years in the twentieth

sumes they represent years in the twenty-frst c

January 1, 2029, but 1/1/30 is treated as Janu

in the twenty-frst century increases by one.

Answers to This Chapter’s Ques

When I enter dates into Excel, I often see a n

as 1/4/2003 . What does this number mean, and h

Microsoft Excel 2010: Data Analysis and Business Modeling

The way Excel treats calendar dates is sometimes c

understanding that Excel can display a date in a v

can display a date

. A date

serial

in serial format, such a

integer that represents the number of days betwe

Both the current date and January 1, 1900

- are in

plays January 3, 1900, in serial format as the n

between January 1, 1900, and January 3, 1900 (in

Not

Excel assumes that 1900 was a leap year containin

contained only 365 days. For some fascinating inform

www.

joelonsoftware.com/items/2006/06/16.html

Figure 7-1 shows the worksheet named

Serial Form

given the dates shown in cells D5:D14 in serial f

D5 indicates a date that is 37,622 days after Ja

and day 37,622). To display these serial dates i

Select the cell range E5:E14, right-click the se

by the way, you can bring up the Format Cells dia

date format you want from the list shown in Figu

in date format, as you can see in Figure 7-1. If y

format, select E5:E14, right-click the selection

Fig

URE 7-1

Use the Format Cells command to change dates from s

format.

Simply changing the date format of a cell to Gen

Another way to obtain the date in serial

- format i

close the date in quotation marks. For example, i

Dates.xlsx, cell I5 contains. the

Excel

formula

yields

DATEVAL

37625

the serial format for January 4, 2003.

Chapter

Dates

and Date Functions

Fig

URE 7-2

Reformatting a serial number to month-day-year fo

Can I use a formula to automatically display t

Displaying today’s date with a formula is easy

Date Format

worksheet shown in Figure 7-3. Ent

display today’s date. I created this screenshot o

Fig

URE 7-3

Examples of date functions.

How do I determine a date that is 50 workdays a

exclude holidays?

The function

start_date

WORKDAY(

,#days,[holidays])

displays the d

of workdays (a workday is a nonweekend day) in

Holidays

is an optional argument for the functi

lation any dates that are listed in a cell ran

in cell D14 of the

Date Format

worksheet tells u

01/03/2003. If we believe that the only two ho

and Independence Day, we can change .

the

With

formul

thi

addition, Excel does not count 01/20/2003 in i

Microsoft Excel 2010: Data Analysis and Business Modeling

workday after 01/03/2003. Note that instead of r

can enter them directly in the WORKDAY formula w

enclosed in { }. For example,

WORKDAY(38500,10,{3

workday after the date with serial number 38500, i

Christmas of 2005.

Excel 2010 contains a new function, WORKDAY.INTL

defnition

workday.”

of a “ The syntax is

days,weekend,

WORKDAY.INTL(star

[holida

The third argument lets you specify the defnitio

codes to specify the defnition of a day off.

1 or omitted

Saturday, Sunday

Sunday, Monday

Monday, Tuesday

Tuesday, Wednesday

Wednesday, Thursday

Thursday, Friday

Friday, Saturday

Sunday only

Monday only

Tuesday only

Wednesday only

Thursday only

Friday only

Saturday only

For example, in sheet

Date Format

of the fle Dat

7-4) the date 100 workdays after 3/14/2011, with S

formula

WORKDAY.INTL(C23,100,2)

In cell C28 I computed the dat

3/14/2011 when only Sunday is a day off .

by using th

You can also enter

days

the

off”

defnition

with a of

string

“

of seven o

a one indicates a day off and the frst entry in th

and so on. Thus, in cells D26 and D27 I duplicat

WORKDAY.INTL(C23,100,”1000001”)

and

WORKDAY.INTL

respectively

How do I determine the number of workdays betwee

The key to solving this problem is to use the NE

function is

NETWORKDAYS(

start_date,end_date,[holidays])

where

holidays

is an o

argument identifying a cell range that lists the d

NETWORKDAYS function returns the number of worki

end_date

excluding weekends and any listed holid

NETWORKDAYS function, look at cell C18 in the

Chapter

Dates

and Date Functions

the formula

NETWORKDAYS(C14,C15)

. This formula yields the

num

tween 1/3/2003 and 8/4/2003, which is 152. The f

in cell C17 yields the number of workdays betw

Luther King Day and Independence

Day. The answ

Excel 2010 includes a new function, NETWORKDAY

function, allows you to customize the defnitio

the worksheet

Date Format

of the fle Dates.xls

between 3/14/2011 and 8/16/2012, when Sunday a

NETWORKDAYS.INTL(C23,C24,2)

(See Figure 7-4.) In cell D31 I c

with the formula

NETWORKDAYS.INTL(C23,C24,”100

Fig

URE 7-4

Examples of international date functions.

I have 500 different dates . entered

How do Iinwrite

an Excel

for w

will extract from each date the month, year, d

The

Date Format

worksheet of the fle Dates.xls

cell range B5:B10. In B5 and B7:B9, I used fou

In columns D:G, I extracted the year, month, da

date. By copying from D5 to

, ID6:D10

extracted

the formula

the ye

By copying from E5 to E6:E10

, I extracted

the formula

the

MONTH

month (

2=February, and so on) portion of each date. B

DAY(B5)

, I extracted the day of the month for eac

G6:G10 the formula

, I

WEEKDAY(B5,1)

extracted the day of the w

When the last argument of the WEEKDAY function i

so on. When the last argument is 2, then 1=Mon

argument is 3, then 0=Monday, 1=Tuesday, and s

I am given the year, month, and

. Is day

there

of an

theeasy

mon w

recover the actual date?

The DATE function, whose arguments

, returns

arethe

DATE(ye

date w

given year, month, and day of the month. In th

H5 to cells H6:H10 the formula

DATE(D5,E5,F5)

Microsoft Excel 2010: Data Analysis and Business Modeling

My business has purchased

. Forand

some,

sold

I have

machines

the date t

purchased and the date. Can

the Imachine

easily was

determine

sold

we kept these machines?

The DATEDIF function can easily determine the nu

or days between two dates. In fle Datedif.xlsx

(

chine was bought on 10/15/2006 and was sold on 4

years, months, or days was the machine kept? The s

DATEDIF(

startdate,enddate,time unit).

If the unit is w

complete years between the start and end dates; i

number of complete months between the start and e

“d,” you get the number of complete days between th

DATEDIF(D4,D5,”y”)

in cell D6 shows that the mac

formula

DATEDIF(D4,D5,”m”)

in cell D7 shows the m

Entering the formula

DATEDIF(D4,D5,”d”)

in cell D

complete days.

Fig

URE 7-5

Using the DATEDIF function.

Problems

What is the serial format for January 25, 200

What is the serial format for February 14, 19

To what actual date does a serial format of 4

Determine the day that occurs 74 workdays aft

excluding the current year’s Christmas, New Y

How many workdays (including holidays) are th

15, 2006?

How many workdays (including holidays but exc

Independence Day) are there between July 10, 2

Chapter

Dates

and Date Functions

Not

The fle Datep.xlsx contains several hundred d

problems.

Determine the month, year, day of the month

10.

Express each date in serial format.

11.

A project begins on December 4, 2005. The p

1, 2, and 3. Activity 2 can start the day a

day after Activity 2 fnishes. Set up a work

days) of the three activities and outputs b

activity is completed.

12.

We bought a stock on July 29, 2005, and

sol

change is closed on Labor Day, Christmas, a

when the stock market was open during the ti

13.

The fle Machinedates.xlsx contains dates on w

sold. Determine how many months and years e

14.

Given any date, fnd a way to have Excel comp

the date’s month.

15.

Given any date, fnd a way to have Excel comp

DATE(2005,13,1)

surprisingly, returns 1/1/2006.

16.

Given any date, how can you compute which d? F

day of the year will 4/15/2020 be? Hint: The f

serial number for day 0 of January 2020, an

17.

In the country of Fredonia, employees have T

200 workdays after 5/3/2013?

18.

In the country of Lower Ampere, employees h

Valentine’s Day is a holiday. How many workd

5/31/2015?

19.

Suppose the frst quarter of each year is Ja

June, and so on. Write a formula that retur

quarter.

20.

Using the defnitions of quarters given in P

for any given date the last day of the prev

21.

Set up a spreadsheet in which a person can e

spreadsheet returns the person’s actual age

Chapter 8

Evaluating Investme

Present Value Crite

Questions answered in this chapter:

■

What is net present value (NPV)?

■

How do I use the Excel NPV function?

■

How can I compute NPV when cash flows are re

the middle of a year?

■

How can I compute NPV when cash flows are re

Consider the following two investments, whose c

shown in Figure 8-1.

■

Investment 1 requires a cash outflow of $10,

now. One year from now, this investment will y

■

Investment 2 requires a cash outflow of $6,0

One year from now, this investment will yie

Which is the better investment? Investment 1 y

2 yields a total cash flow of $1,000. At frst g

wait a minute. Most of the cash outflow for Inv

most of the cash outflow for Investment 2 occur

doesn’t seem as costly as spending $1 today, s

appears. To determine which investment is bett

flows received at different points in time. Tha

proves useful.

Fig

URE 8-1

To determine which investment is better, you need t

Microsoft Excel 2010: Data Analysis and Business Modeling

Answers to This Chapter’s Quest

What is net present value?

The net present value (NPV) of a stream of cash fl

simply the value

measured

. Suppose

in today’s

you have

dollars

$1 today a

dollar at an annual interest ratedollars

percent.

in the fr

year,

dollars

(1+r)

in two years, and so on. You can s

$(1+r)

a year from now and

$(1+r)

two years from now. In general, y

is equal to

$(1+r)

years from now. As an equation, this c

follows:

$1 now=$(1+r)

received n years from now

If you divide both sides of this equation by

(1+

, you get the following im

1/(1+r)

now=$1 received n years from now

This result tells you how to compute (in today’s d

flows. You can convert any cash flow to today’s do

years from

cannow

be (

a fraction) by

1/(1+r)

You then add up the value of the cash flows (in t

Let’s assume

is equal to 0.2. You could calcul

considering as follows:

24,000

(1 + 0.20)

= $277.78

–14,000

(1 + 0.20)

= Investment1NPV = –10,000 +

8,000

(1 + 0.20)

= $–27.78

–1,000

(1 + 0.20)

= Investment2NPV = –6,000 +

On the basis of NPV, Investment 1 is superior to I

for Investment 2 exceeds total cash flow for Inve

because a greater proportion of Investment 1’s n

NPV criterion gives less weight to cash flows tha

, Investment 2 has a larger NPV because- when

counted as much, and NPV returns results similar t

according to total cash flow.

Chapter

Evaluating

Investments by Using

Net Present Value Criteria

Not

randomly chose the

, skirting

interestthe

rate

issue

r=0.2

of how t

appropriate

. You

value

need

of to

study fnance for at least a y

involved in determining

. The

appropriate valuefor

NPV is often called the company’s

cost of capital.

an annual cost of capital between 0.1 (10 percent) a

is chosen according to accepted fnance practices, p

company, projects with NPV<0 decrease the value of a

the value of a company unchanged. A company should (

invest in every available investment having positi

To determine the NPV of Investment 1 in -Excel, I f

terest rate (located in cell C3). I then copie

the NPV for Investment 1’s Year 1 and Year

2 c

mula

D5/(1+r_)^D$4

. The caret symbol (^), located over th

a number to a power. In cell A5, I computed th

each year’s cash flow with

. Tothe

determine

formulathe

SUM(C7:E

NPV f

copied the formulas from C7:E7 to C8:E8 and fr

How do I use the Excel NPV function?

The Excel NPV function uses .the

This

syntax

function

NPV(rat

NPV for the given rate of the cash flows-in the r

sumes that the frst cash flow is one period fro

NPV(r_,C5:E5)

will not determine the NPV for I

in cell C14) computes the NPV of the following s

from now, $24,000 two years from now, and –$14

Investment 1 (End of Year). The NPV of Investm

the actual cash NPV of Investment 1, I entered th

formula does not discount the Time 0 cash flow a

flow is already in today’s dollars), but frst m

multiplies the cash flow in E5 by

1/1.2

The formula in cell C11 yields the correct NPV o

How can I compute NPV when cash flows are recei

middle of a year?

To use the NPV function to compute the net pre

ways occur at the beginning of a year, you can u

NPV of Investment 1: separate out the Year 1 c

remaining cash flows. Alternatively,

$1 received

observe

at th

Microsoft Excel 2010: Data Analysis and Business Modeling

of year

is equivalent

) received to

at .$(1+

the

Remember

end of that

year in on

dollar will grow

). Thus,

by a factor

if you (1+

multiply the

- resul

tion

), (1+

you can convert the NPV of a sequence of y

sequence of cash flows received at the beginning o

of Investment 1 in cell D11

. Ofwith

course,

the formula

you again

(1+

of $277.78.

Now suppose the cash flows for an investment

occu

nization that receives monthly subscription reve

revenues received during a given year as a lump s

can you use the NPV function to determine the NP

For any, Year

1 + r

received at the end of Year

is equivalent to $

half a year $1 will grow by a factor of

1 + r

If you assume the cash flows for Investment 1 occ

the mid-year version of Investment 1. in

Youcell

obtain

C17 w

a value of $253.58.

How can I compute NPV when cash flows are receive

Cash flows often occur at irregular intervals, whi

of return (IRR) of these cash flows more diffcult

computing the NPV of irregularly timed cash flows a s

The XNPV function uses

rate,values,dates)

the. syntax

The frst

XNPV(

date listed m

the earliest, but other dates need not be listed i

computes the NPV of the given cash flows assuming th

sequence. For example, if the frst listed date i

dollars.

To illustrate the use of the XNPV function, look a

worksheet in the fle XNPV.xlsx, which is shown i

you paid out $900. Later you receive the followi

■

$300 on August 15, 2013

■

$400 on January 15, 2014

■

$200 on June 25, 2014

■

$100 on July 3, 2015

Chapter

Evaluating

Investments by Using

Net Present Value Criteria

If the annual interest rate is 10 percent, wha

the dates (in Excel date format) in D3:D7 and th

XNPV(A9,E3:E7,D3:D7)

in cell D11 computes the p

that is the frst date listed. This project wou

Fig

URE 8-2

Using the XNPV function.

The computations performed by the XNPV functio

Compute the number of years after April 8, 2

column F.) For example, August 15 is 0.3534 y

Discount cash flows at the rate

1/(1+rate)

years

after

For example, the August 15, 2013 cash flow i

(1 + 0.1)

3534

= 0.967

Sum up in cell E11 overall cash. flows:

(cash fl

Suppose that today’s date is actually July 11, 2

investment in today’s dollars? Simply add a row w

this row in the range for the XNPV function. (

NPV of the project in today’s dollars is $15.8

Fig

URE 8-3

NPV converted to today’s dollars.

I’ll close by noting that if a cash flow is lef

flow and the

Ifperiod

a cash flow is left blank, the XN

Microsoft Excel 2010: Data Analysis and Business Modeling

Problems

An NBA player is to receive a $1,000,000 signi

two years, and three years from now. Assuming

would he be better off receiving $6,000,000 t

A project has the following cash flows:

Now

One year from

Two now

years from

Threenow

years from now

–$4 million

$4 million $4 million –$3 million

If the company’s cost of capital is 15 percen

Beginning one month from now, a customer will p

month for the next fve years. Assuming all re

of a year, estimate the NPV

of these revenues

Beginning one month from now, a customer will p

provider for the next fve years. Assuming all r

middle of a year, use the XNPV function to ob

r=0.15

Consider the following set of cash flows over a f

these cash flows if

r=0.15

and cash flows occur a

Year

-$600

$550

-$680

$1,000

Solve Problem 5 assuming cash flows occur at th

Consider the following cash flows:

Date

Cash flow

12/15/01

–$1,000

1/11/02

$300

4/07/03

$600

7/15/04

$925

If today is November

, what

1, 2001,

is the

and

NPV

r=0.15

of these c

After earning an MBA, a student will begin wo

September 1, 2005. She expects to receive a 5 p

on September 1, 2035. If the cost of capital i

present value of her before-tax earnings.

Consider a 30-year bond that pays $50 at the e

of Year 30. If the appropriate discount rate i

this bond?

Chapter 9

Internal Rate of Re

Questions answered in this chapter:

■

How can I fnd the IRR of cash flows?

■

Does a project always have a unique IRR?

■

Are there conditions that guarantee a proje

■

If two projects each have a single IRR, how d

■

How can I fnd the IRR of irregularly spaced c

■

What is the MIRR and how do I compute it?

The net present

NPV) of

value

sequence

(

of cash flows

)

depe

used. For example, if you consider cash flows f

the fle IRR.xlsx, shown in ,Figure

Project

9-1),

2 has

youa fn

for

r=0.01

, Project 1 has a larger NPV. When you use N

can depend on the interest rate. It is the nat

in life down to a single number.

IRR) ofThe

a project

internal

isrs

interest rate that makes the NPV of the projec

IRR has a nice interpretation. For example, if a p

an annual rate of return of 15 percent on

- the c

ples, you’ll fnd that Project 1 has an IRR of 4

at Time 1 is yielding an annual rate of return o

might have more than one IRR or even no IRR. I

IRR is useless.

Fig

URE 9-1

Example of the IRR function.

Microsoft Excel 2010: Data Analysis and Business Modeling

Answers to This Chapter’s Quest

How can I find the IRR of cash flows?

The IRR function calculates internal rate of ret

IRR(range of cash

, where

flows,[guess])

is an optional argum

guess for a project’s IRR, Excel begins its calc

10 percent and then varies the estimate of the I

the project’s NPV equal 0 (the project’s IRR). I

the project’s NPV equal 0, Excel returns #NUM. I

compute Project 1’s IRR. Excel returns 47.5 perc

47.5 percent, Project 1 will have an NPV of 0. S

of 80.1 percent.

Even if the IRR function fnds an IRR, a project mi

whether a project has more than one IRR, you can v

(for example, from –90 percent to 90 percent).

I v

ing from B8 to B9:B17 the

. Because

formulaall

IRR($C$2:$I$2,

the guesses f

IRR yield 47.5 percent, I can be fairly confdent th

Similarly, I can be fairly confdent that Project 2 h

Does a project always have a unique IRR?

In the worksheet

Multiple IRR

in the fle IRR.xls

(cash flows of –20, 82, –60, 2) has two IRRs. I v

percent to 90 percent by copying from. C8 to C9:C

Fig

URE 9-2

Project with more than one IRR.

Note that when a guess is 30 percent or less, th

IRR is 216.1 percent. For both these interest ra

Chapter

Internal

Rate

of Return

In the worksheet

No IRR

in the fle IRR.xlsx

matter (s

what guess you use for Project 4’s IRR, you re

indicates that Project 4 has no IRR.

When a project has multiple IRRs or no IRR, th

Despite this problem, however, many companies s

investments.

Fig

URE 9-3

Project with no IRR.

Are there conditions that guarantee a project w

If a project’s sequence of cash flows contains e

guaranteed to have a unique IRR. For, example,

the sign fo

the cash flow sequence is – + + + + +. There is o

Time 2), so Project 2 must have a unique

, the

IRR. F

signs of the cash flows are – + – +. Because th

a unique IRR is not guaranteed., For

the Project

signs of4 th

flows are + – +. Because the signs of the -cash fl

teed in this case either. Most capital investm

a negative cash flow followed by a sequence of p

investment projects do have a unique IRR.

If two projects each have a single IRR, how do I u

If a project has a unique IRR, you can state th

company

if and only if

the project’s IRR excee

cost of capital for a company is 15 percent, b

value of the company.

Microsoft Excel 2010: Data Analysis and Business Modeling

Suppose two projects are under consideration

(both h

take at most one project. It’s tempting to belie

larger IRR. To illustrate that this belief can l

the

Which Project

worksheet in IRR.xlsx. Project 5 h

an IRR of 50 percent. If you rank projects based o

would choose Project 6. Remember, however, that a p

value the project adds to the company. Clearly, P

have a larger NPV than Project 6. Therefore, if o

it. IRR is problematic because it ignores the sc

than Project 5 on a per-dollar-invested basis,

able to the company than Project 6. IRR does not r

does.

Fig

URE 9-4

IRR can lead to an incorrect choice of which projec

How can I find the IRR of irregularly spaced cash fl

Cash flows occur on actual dates, notfunction

just at the s

has the syntax

XIRR(cash flow, dates, [guess]).

sequence of cash flows that occur on any set of i

function,

guess

is an optional argument. For an e

look at Figure 9-5 and worksheet

XIRR

of the fle I

Fig

URE 9-5

Example of the XIRR function.

The formula

XIRR(F4:F7,E4:E7)

in cell D9 shows th

What is the MIRR and how do I compute it?

In many situations the rate at which a company b

at which the company reinvests funds. IRR comput

which a company borrows and reinvests funds is e

at which we borrow money and the rate at which w

internal rate

MIRR)

offunction

return (computes a discount rat

Chapter

Internal

Rate

of Return

our cash flows (including paying back our loan a

rates) equal to 0. The syntax of MIRR is

MIRR(

rate).

A nice thing about MIRR is that it is a

fle IRR.xls contains an example of MIRR. Suppo

the following cash flows: Year 1: $39,000, Year 2

Year 5: $46,000. Assume you can borrow at 10 p

12percent per year.

After entering these values in cells E7:E12 of w

D15 with the formula

MIRR(E7:E12,E3,E4).

Thus, t

cell D16 I computed the actual IRR of 13.07 pe

Fig

URE 9-6

Example of the MIRR function.

I’ll close by noting that if a cash flow is lef

and the period.

If a cash flow is left blank, t

Problems

Compute all IRRs for the following sequence o

Year Y

1ear Y

2ear Y

3ear Y

4ear Y

5ear Y

6ear 7

–$10,000

$8,00$

01,500

–$1,500

Consider a project with the following cash fl

annual cost of capital is 20 percent, would y

Year 1

Year 2

Year 3

–$4,000 $2,000

$4,000

Microsoft Excel 2010: Data Analysis and Business Modeling

Find all IRRs for the following project:

Year 1

Year 2

Year 3

$100

–$300

$250

Find all IRRs for a project having the given c

1/10/2003

7/10/2003

5/25/2004

7/18/2004

3/20/2005

4/1/2005

1/10/2006

–$1,000

$900

$800

$700

$500

$350

Consider the following two projects, and

assu

cent. Find the IRR and NPV of each project. W

If the company can choose only a single proje

Year 1 Year 2 Year 3 Year 4

Project–$40

$130

$19

$26

Project–$80

$36

Twenty-fve-year-old Meg Prior is going to inv

the beginning of each of the next 40 years. A

years Meg will earn 15 percent on her investm

she retires, her investments will earn 5 perc

investments and her fnal retirement position. H

IRR? How would you interpret the unique IRR?

Give an intuitive explanation of why Project 6 (

fle IRR.xlsx) has an IRR of 50 percent.

Consider a project having the following cash fl

Year 1

Year 2

Year 3

–$70,000 $12,000

$15,000

Try to fnd the IRR of this project without si

is the IRR of this project? Does the project h

For the cash flows in Problem 1, assume you ca

invest profts at 15 percent per year. Compute th

10.

Suppose today that you paid $1,000 for the bo

“Evaluating Investments by Using Net Present V

bond’s IRR? A bond’s IRR is often called the

Chapter 10

More Excel Financia

Questions answered in this chapter:

■

You are buying a copier. Would you rather pa

years?

■

If at the end of each of the next 40 years I i

and earn 8 percent a year on my investments

■

I am borrowing $10,000 for 10 months with a

are my monthly payments? How much principal a

■

I want to borrow $80,000 and make monthly p

monthly payment I can afford is $1,000. Wha

afford?

■

If I borrow $100,000 at 8 percent interest a

many years will it take me to pay back the l

When we borrow money to buy a car or house, we a

deal. When we save for retirement, we are curi

retire. In our daily work and personal lives, f

Knowledge of the Excel PV, FV, PMT, PPMT, IPMT

functions makes it easy to answer these types o

Answers to This Chapter’s Ques

You are buying

. Would

a copier

you rather pay $11,000 toda

five years?

The key to answering this question is being ab

year. Assume the cost of capital is 12 percent p

answer this question, but the Excel PV functio

stream of cash flows that involves the same amo

is called. an

Assuming

annuity

that each period’s interest r

value an annuity by using the Excel PV functio

dollars of a series of future payments, under th

and a constant interest rate. The syntax

, of th

where,

pmt

fv,

and

type

are optional arguments.

Microsoft Excel 2010: Data Analysis and Business Modeling

Not

When working with Microsoft Excel fnancial functi

the signs of

pmt

future

(payment)

value):

and money

( received has a p

paid out has a negative sign.

■

Rate

is the interest rate per period.

percent

For exa

per year and the period

. If

is the

a year,

period

then

rate=

mon

rate=0.06/12=0.005

■

#per

is the number of periods in the

. Ifannuity. F

payments on the copier are made each

. Your

month

ratefo

must, of course, be

. That

consistent

is, if with

#per #per

implies a p

you must use a monthly interest rate; if

#per

annual interest rate.

■

Pmt

is the payment made each period.A For our c

payment has a negative sign, whereas money re

pmt

must be included.

■

is the cash balance (or future value) you wa

For our copier

. For example,

fv=0

if you want to hav

after the last payment,

. If youthen

want

fv=$500

to make an addi

at the end

fv=–$500

a. proble

is omitted, it is assu

■

Type

is either 0 or 1 and indicates when paym

equal to 0, payments are made at, the

payments

end ofare

made at the beginning of each period. Note th

and False instead of 0 in all functions discu

Figure 10-1 (see the worksheet

of fle the Exc

copier problem.

Fig

URE 10-1

Example of the PV function.

Chapter

10 Excel Financial

Functions

In cell B3 I computed the present value of pay

years with a 12 percent cost of capital by usi

returns an NPV of $10,814.33. By omitting the l

answer with the formula

=PV(0.12,5,–3000).

Thu

end of the year than to pay out $11,000 today.

If you make payments on the copier of $3,000 a

the NPV of the payments is computed in cell B4 w

Note that changing the last argument from a 0 t

year to beginning of year. You can see that th

Therefore, it’s better to pay $11,000 today th

Suppose you pay $3,000 at the end of each year a

at the end of Year 5. You can now fnd the

- pres

cluding a future value of $500 with the formul

and $500 cash flows have negative signs because y

value of all these payments is equal to $11,09

If at the end of each of the next 40 years I i

earn 8 percent a year on my investments, how m

In this situation we want to know the value of a

from now) and not today’s dollars. This is a j

FV function gives the future value of an inves

with a constant interest rate. The syntax

of th

where,

pmt

pv,

and

type

are

optional arguments

■

Rate

is the interest rate per

period. In ou

■

#Per

is the number of periods in the future a

computed.

#Per

is also the number of period

received. In our case,

#per

equals =40.

■

Pmt

is the payment made each period. In our c

sign indicates we are paying money into an a

included.

■

is the amount of money (in today’s dolla

$0. If today we owe someone $10,000, then

us $10,000 and we received it. If today we h

–$10,000 because we must have paid $10,000 i

is assumed to equal 0.

■

Type

is a 0 or 1 and indicates when payment

equals 0 or is omitted, then money is depos

type

is 0 or omitted.

then If

payments

type

equals

are made

or m

the beginning of the period.

Microsoft Excel 2010: Data Analysis and Business Modeling

In worksheet

of fle Excelfnfunctions.xlsx (se

=FV(0.08,40,–2000)

to fnd that in 40 years our n

that I entered a negative value for the annual p

into our account. You could obtain the same answ

arguments with the formula

FV(0.08,40,–2000,0,0)

If deposits were made at the beginning of each y

B4)

=FV(0.08,40,–2000,0,1)

would yield the value i

Fig

URE 10-2

Example of FV function.

Finally, suppose that in addition to investing $

years you initially have $30,000 to invest. If y

how much money will you have when you

question

retire in 4

bysetting

equal to –$30,000 in the FV functio

you have deposited, or paid, $30,000 into your a

=FV(0.08,40,–2000,–30000,0)

yields a future val

I am borrowing $10,000 for 10 months with

. Whatan

are

ann

my monthly payments? How much principal and inte

The Excel PMT function computes the periodic pay

constant payments and a constant interest rate. T

PMT(rate,#per,pv,[fv],[type])

where

and

type

are optional arg

■

Rate

is the per-period interest rate of the l

a period, so

rate

equals

0.08/12=0.006666667

■

#Per

is the number of payments made. In this c

Chapter

10 Excel Financial

Functions

■

is the present value of all the payments

case,

equals $10,000.

is positive bec

■

indicates the fnal loan balance you want t

our case

equals 0. If

is omitted, Exc

taken out a balloon loan for which you make p

at the conclusion of the loan you pay off th

payment. Then

equals –$1,000. The $1,000 i

■

Type

is a 0 or 1 and indicates when-payment

ted, then payments are made at the end of th

payments, so type is 0 or omitted. If

type

is deposited at the beginning of the period

In cell worksheet

G1 of

PMT

the

of the fle Excelfnfunctions.xl

computed

the monthly payment on a 10-month loan for

$10

est rate and end-of-month

=–PMT(0.08/12,10,10000

payments with the fo

monthly payment is $1,037.03. The PMT function by i

we are making payments to the company giving u

If you want to, you can use the Excel IPMT and P

interest paid each month toward the loan and th

month. (This is called the payment on the prin

Fig

URE 10-3

Examples of PMT, PPMT, CUMPRINC, CUMIPMT, and IP

To determine the interest paid each month, use th

function is

IPMT(rate,per,#per,pv,[fv],[type])

where

and

type

are opti

per

argument indicates the period number for w

Microsoft Excel 2010: Data Analysis and Business Modeling

arguments mean the same as they do for the PMT f

amount paid toward the principal eachsyntax

month you c

of the PPMT function is

PPMT(rate,per,#per,pv,[f

. The meaning of each a

the same as it is for the IPMT function. By copy

=–PPMT(0.08/12,C6,10,10000,0,0),

you can compute th

that is applied to the principal. For example, d

the principal. As expected, the amount paid towa

The minus sign is needed because the principal i

and PPMT will return a negative number. By copyi

=–IPMT(0.08/12,C6,10,10000,0,0)

you can compute the amount of i

For example, in Month 1 you pay $66.67 in intere

each month decreases.

Note that each month

(Interest Paid)+(Payment

Sometimes the total is off by a penny due to rou

You can also create the ending balances for each m

relationship

(Ending Month t Balance)=(Beginning M

toward Principal).

Note that in Month 1,

Beginnin

created each month’s beginning balance

)

(Beginning

by using th

Month t Balance)=(Ending

. Of

Month

course,

t–1

Ending

Balance)

Month 10 B

as it should.

Interest each month can be computed as

(Month t I

Month t

Balance)

For example, the Month 3 interest paym

=(0.0066667)*($8,052.80)

which equals $53.69.

Of course, the NPV of all payments is exactly $1

formula

NPV(0.08/12,E6:E15)

(See Figure 10-3.)

If the payments are made at the beginning of eac

is computed in cell D19 with the formula

=–PMT(0

argument to 1 changes each payment to the beginni

is getting her money earlier, monthly payments a

pays at the beginning of the month, the monthly p

Finally, suppose that you want to make a balloon p

months. If you make your monthly payments at the e

=–PMT(0.08/12,10,10000,–1000,0)

in cell D20 comp

monthly payment turns out to be $940. Because $1

with monthly payments, it makes sense that your n

original end-of-month payment of $1,037.03.

Chapter

10 Excel Financial

Functions

CUMPRINC and CUMIPMT Functions

You’ll often want to accumulate the interest o

CUMPRINC and CUMIPMT functions make this a sna

The CUMPRINC function computes the principal p

syntax of the CUMPRINC function is

CUMPRINC(ra

Rate

#per

, ,

and

type

have the same meanings as des

The CUMIPMT function computes the interest pai

syntax of the CUMIPMT function is

CUMIPMT(rate

Rate

#per

, ,

and

type

have the same meanings as des

cell F19 on the

PMT

worksheet, I computed the i

4 ($161.01) by using the formula

=CUMIPMT(0.08

puted the principal paid off in months 2 throu

=CUMPRINC(0.08/12,10,10000,2,4,0)

I want to borrow $80,000 and make

. The

monthly

maximum

paym

monthly payment I can

. What

afford

is the

is maximum

$1,000

intere

Given a borrowed amount, the length of a loan, a

function tells you the rate of the loan. The s

,[fv],[type],[guess])

where

type

and

guess

are optional

pmt

, ,

and

argumen

type

have the same meanings as previously desc

loan rate is. Usually

guess

can be omitted. En

Excelfnfunctions.xlsx) the formula

=RATE(120,–

monthly rate. I am assuming end-of-month payme

Fig

URE 10-4

Example of RATE function.

In cell D15 I verifed the RATE function calcul

yields $80,000.08. This shows that payments of $

months have a present value of $80,000.08.

Microsoft Excel 2010: Data Analysis and Business Modeling

If you could pay back $10,000 during month 120, t

be given by the formula

=RATE(120,–1000,80000,–1

. In cell D12, this f

a monthly rate of 0.818 percent.

If I borrow $100,000 at 8 percent interest and m

many years will it take me to pay back the loan?

Given the size of a loan, the payments each peri

tells you how many periods it takes to pay back a l

NPER(rate,pmt,pv,[fv],[type])

where

and

type

are optional arg

Assuming end-of-year payments, the formula

=NPER

worksheet

Nper

(in the fle Excelfnfunctions.xlsx

20 years of payments will not quite pay back the l

To verify the calculation, in cells D10 and D11 I u

$10,000 per year for 20 years pays back $98,181.

pays back $100,168.03.

Suppose that you are planning to pay back $40,00

How many years will it take to pay back the loan

=NPER(0.08,–10000,100000,–40000,0)

shows that i

loan. Thus, 15 years of payments will not quite p

slightly overpay the loan.

Fig

URE 10-5

Example of NPER function.

Chapter

10 Excel Financial

Functions

Problems

Unless otherwise mentioned, all payments are m

You have just won the lottery. At the end of e

a payment of $50,000. If the cost of capita

value of your lottery winnings?

perpetuity

is an annuity that is received f

beginning of each year I receive $14,000, w

an annual 10 percent cost of capital. (Hint

periods be many!)

I now have $250,000 in the bank. At the end o

$15,000. If I earn 8 percent per year on my i

20 years?

I deposit $2,000 per month (at the end

- of e

vestments earn 0.8 percent per month. I wou

much money should I deposit now?

An NBA player is receiving $15 million at th

can earn 6 percent per year on his investme

revenues?

At the end of each of the next 20 years I w

Years

Amounts

1–5

$200

6–10

$300

11–20

$400

Use the PV function to fnd the present valu

10 percent. Hint: Begin by computing the va

and then subtract the value of receiving $1

You are borrowing $200,000 on a 30-year mor

percent. Assuming end-of-month payments, de

payment each month, and amount paid toward p

Answer each question in Problem 7 assuming b

Use the FV function to determine the value t

you are earning 7 percent per year.

10.

You have a liability of $1,000,000 due in 1

year. What amount of money do you need to s

10 years to meet this liability?

Microsoft Excel 2010: Data Analysis and Business Modeling

11.

You are going to buy a new car. The cost of th

two payment plans:

❑

A 10 percent discount on the sales price of th

payments fnanced at 9 percent per year.

❑

No discount on the sales price of the car, f

fnanced at 2 percent per year.

If you believe your annual cost of capital is 9 p

deal? Assume all payments occur at the end of th

12.

I presently have $10,000 in the bank. At the b

am going to invest $4,000, and I expect to ea

How much money will I have in 20 years?

13.

balloon mortgage

requires you to pay off pa

period and then make a lump sum payment to pa

loan. Suppose you borrow $400,000 on a 20-yea

rate is .5 percent per month. Your end-of-mon

are required to pay off $300,000 of your loan

remaining $100,000. Determine your monthly pa

14.

An adjustable rate mortgage (ARM) ties monthl

U.S. T-Bill rate). Suppose you borrow $60,000 o

payments). The frst 12 payments are governed by th

In years 2–5, monthly payments are set at the y

percent. Suppose the T-Bill rates at the begi

Beginning ofT-Bill

year rate

10 percent

13 percent

15 percent

10 percent

Determine monthly payments during years 1–5 a

15.

Suppose you have borrowed money at a 14.4 per

monthly payments. If you have missed four con

should next month’s payment be to catch up?

16.

You want to replace a machine in 10 years and e

can earn 8 percent annually on your investmen

aside at the end of each year to cover the co

Chapter

10 Excel Financial

Functions

17.

You are buying a motorcycle. You pay $1,500 t

years. If the annual rate of interest is 18 p

motorcycle?

18.

Suppose the annual rate of interest is 10 p

$300 a month for a year, and $400 for two y

payments?

19.

You can invest $500 at the end of each six-m

to have $6,000 after fve years, what is the a

investments?

20.

I borrow $2,000 and make quarterly payments f

is 24 percent. What is the size of each pay

21.

I have borrowed $15,000. I am making 48 mon

interest is 9 percent. What is the total in

22.

I am borrowing $5,000 and plan to pay back th

annual rate of interest is 16.5 percent. Af

the period of the loan to two years total. W

second year of the loan?

23.

With an adjustable rate mortgage, you make m

interest rates at the beginning of each yeao

ARM. For the frst year, monthly payments ar

9 percent. In years 2–5, monthly payments w

rates +2 percent.

❑

Year 2: 10 percent

❑

Year 3: 13 percent

❑

Year 4: 15 percent

❑

Year 5: 10 percent

The catch is that the ARM contains a clause th

increase a maximum of 7.5 percent from one y

er for this provision, the borrower adjusts th

each year based on the difference between w

he should have paid. Determine monthly paym

24.

You have a choice of receiving $8,000 each y

you die, or receiving $10,000 each year beg

If you think you can earn an 8 percent annu

net the largest amount?

Microsoft Excel 2010: Data Analysis and Business Modeling

25.

You have just won the lottery and will receiv

interest would make these payments the equiva

26.

A bond pays a $50 coupon at the end of each o

value in 30 years. If you discount cash flows a

be a fair price for the bond?

27.

You have borrowed $100,000 on a 40-year mortg

annual interest rate is 16 percent. How much w

With four years left on the loan, how much wi

28.

I need to borrow $12,000. I can afford paymen

rate of interest is 4.5 percent. How many mon

29.

You are considering borrowing $50,000 on a 18

on the loan depends on your credit score in th

Write a formula that gives your monthly payme

30.

You are going to borrow $40,000 for a new car

payments and total interest paid for the foll

❑

48 month loan, 6.85% annual rate.

❑

60 month loan, 6.59% annual rate.

Chapter 11

Circular References

Questions answered in this chapter:

■

I often get a circular reference message fr

■

How can I resolve circular references?

When Microsoft Excel 2010 displays a message th

reference, it means there is a loop, or- depend

sheet. For example, a circular reference occur

D3, the value in cell D3 influences the value i

value in cell A1. Figure 11-1 illustrates the p

Fig

URE 11-1

A loop causing a circular reference.

As you’ll soon see, you can resolve circular r

and then clicking Options. Choose Formulas, an

check box.

Answers to This Chapter’s Ques

I often get a circular reference

. Does this

message

mean I’ve

frommE

A circular reference usually arises from a log

cells exhibit a looping relationship similar t

simple example of a problem that cannot easily b

reference.

A small company earns $1,500 in revenues and i

percent of their after-tax profts to charity. T

should they give to charity? The solution to thi

Circular.xlsx, shown in Figure 11-2.

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 11-2

A circular reference can occur when you’re calculat

I began by naming the cells in D3:D8 with the co

entered the frm’s revenue, tax rate, and- costs i

ity as 10 percent of after-tax proft, .I Then

entered i

I determined before-tax proft in cell D7

- by subtr

tion from revenues. The formula

. Finally,

cell D7

I is

compu

after-tax proft in cell D8 as

(1–tax_rate)*befor

Excel indicates a circular reference in cell D8 (

What’s going on?

Charity (cell D6) influences before-tax proft (

Before-tax proft (cell D7) influences after-ta

After-tax proft (cell D8) influences charity.

Thus, we have a loop of the form D6-D7-D8-D6 (in

Figure 11-2), which causes the circular referenc

we have done nothing wrong. Still, you can see f

incorrect answer for charitable contributions.

How can I resolve circular references?

Resolving a circular reference is easy. Simply c

and then click Options to open the Excel Options d

pane, and then select the Enable Iterative Calcu

section, as shown in Figure 11-3.

Chapter

Circular

References

Fig

URE 11-3

Use the Enable Iterative Calculation option to r

When you activate the Enable Iterative Calcula

reference has generated the following system o

Charity=0.1*(AfterTax Profit) BeforeTax Profit=Revenue–Charity–Costs AfterTax Profit=

(1–Tax rate)*(BeforeTax Profit)

The three unknowns

BeforeTax

are,

Charity

and

Proft

AfterTax

. When

Proft

you activ

Enable Iterative Calculation option, Excel

ite

erences, 100 iterations should be used) to see

circular reference. From one iteration to the n

by a complex mathematical

Gauss-Seidel

procedure

Iteration).

(

Exce

change in any worksheet cell from one iteratio

Change value (0.001 by default). You can reduc

number, such as 0.000001. If you do not reduce th

number, you might fnd Excel assigning a value o

equal 5, and this is annoying. Also, some comp

iterations

converging”

before “ to a resolution of the cir

circularity is almost instantly resolved, and y

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 11-4

Excel runs the calculations to resolve the circula

Note that the charitable contribution of $28.30 i

$283.01. All other cells in the worksheet are now c

Not

Excel’s iteration procedure is only guaranteed to w

equations. In other situations, convergence to a sol

example, resolving the circular references requires s

know Excel will fnd the correct answer.

Here’s one more example of a circular reference. I

entire column or row by name. For example, the f

column B. The formula

=AVERAGE(1:1)

averages all ce

you’re continually dumping new data (such

- as mon

mula always computes average sales, and you do n

is, of course, that if you enter this formula in th

a circular reference. By activating the Enable I

such as these are resolved quickly.

Problems

Before paying employee bonuses and state and f

of $60,000. The company pays employees- a bonu

its. State tax is 5 percent of profts (after b

profts (after bonuses and state tax are paid)

state tax, and federal tax.

On January 1, 2002, I have $500. At the end o

Each month’s interest is based on the average o

balances. How much money will I have after 12 m

My airplane is flying the following route: Hou

Houston. On each leg of the journey, the plan

lon) is

40–.02*(average

Here,

average

fuel en fuel

route)

en route

Chapter

Circular

References

fuel en route+fnal

. My

fuel

plane

begins

route)

in Houston w

The distance flown on each leg of the journe

Leg

Miles

Houston to Los Angeles

1,200

Los Angeles to Seattle

1,100

Seattle to Minneapolis

1,500

Minneapolis to Houston

1,400

How many gallons of fuel remain when I retu

A common method used to allocate costs to s

cost allocation

. This method can easily be-implem

erences. To illustrate, suppose Widgetco ha

and Consulting. Widgetco also has two produ

Widgetco has decided to allocate $600,000 o

department and $116,000 of the cost of oper

two divisions. The fraction of accounting a

company is as follows:

Accounting

Consulting

Division

Percentage of accounting

work done for other parts

of the company

20%

30%

50%

Percentage of consulting

work done for other parts

of the company

10%

80%

10%

How much of the accounting and consulting co

the company? You need to determine two

- quan

ing and total cost allocated to consulting. T

$600,000+.1*(total cost allocated to consult

work was done for the Accounting department

the total cost allocated to consulting. You s

allocation of both accounting and consultin

We start a year with $200 and receive $100 d

interest at the end of the year with the in

case we end the year with $320. Determine th

accrues on the average of

our starting and e

Chapter 12

IF Statements

Questions answered in this chapter:

■

If I order up to 500 units of a product, I p

1,200 units, I pay $2.70 per unit. If I ord

per unit. If I order more than 2,000 -units, I p

mula that expresses the purchase cost as a f

■

I just purchased 100 shares of stock at a c

the stock might decline in value, I purchas

option has an exercise price of $45 and cos

indicates the six-month percentage return o

future prices?

■

Many stock market analysts believe that mov

the market. A commonly suggested moving-ave

when the stock’s price moves above the aver

stock when the stock’s price moves below th

would this trading rule have performed agai

(S&P)?

■

In the game of craps, two dice are tossed. I

or 12, you lose. If the total of the dice o

game keeps going. How can I write a formula t

the frst roll?

■

In most pro forma fnancial statements, cash i

liabilities balance. I know that using debt a

set up a pro forma statement having debt as th

■

When I copy a VLOOKUP formula to determine s

a lot of #NA errors. Then when I average

cal answer because of the #NA errors. Can I e

space so I can compute average salary?

■

My worksheet contains quarterly revenues fo

revenue for each year and place it in the r

year?

■

IF statements can get rather large. How man

the maximum number of characters allowed in a

Microsoft Excel 2010: Data Analysis and Business Modeling

The situations listed above seem to have little, i

up Microsoft Excel 2010 models for each -of these s

ment. I believe that the IF formula is the singl

you conduct conditional tests on values and form

conditional logic provided by computing language

An IF formula begins with

. If

a the condition

suchis

astru

returns the frst value listed in the formula; oth

repeat the process. The easiest way to show you th

them to help answer each of this chapter’s questi

Answers to This Chapter’s Quest

If I order up to 500 units

00 perof

. If

unit

a Iproduct,

order from

I pay

501$ t

1200 units,

7.0 I

per

pay

. If

unit

I order from 1201 3

through

. 0 per

200

unit

. If I order more than

0. 0 per

2000

. How

units,

can I Iwrite

pay $2

a fo

expresses the purchase cost as a function of the n

You can fnd the solution to this question on the

Ifstatement.xlsx. The worksheet is shown in Figu

Fig

URE 12-1

You can use an IF formula to model quantity discoun

Suppose cell A9 contains our order quantity. You c

of the order quantity by implementing the follow

■

If A9 is less than or .equal to 500, the cost i

■

If A9 is from 501 through

1,200, the cost is

■

If A9 is from 1,201 through

2,000, the cost i

■

If A9 is more than. 2,000, the cost is

2*A9

Chapter

IF12

Statements

Begin by linking the range names in A2:A4 to c

D2:D5 to cells C2:C5. Then you can implement t

IF(A9<=_cut1,price1*A9,IF(A9<=_cut2,price2*A9,IF(A9<=_cut3,price3*A9,price4*A9)))

To understand how Excel computes a value from thi

evaluated from left to right. If the

cut1

),order

the cos

qua

given by.

price1*A9

If the order quantity is not less th

to see whether the order quantity is less than o

quantity is from 501 through 1,200, .

and

Next,

the th

formula checks whether the order quantity is l

order quantity is from 1,201 through 2,000,

Finally, if the order cost has not yet been co

price4*A9

. In each case, the IF formula returns the c

three other order quantities in cells A10:A12 a

each order quantity, the formula returns the c

An IF formula containing more than one

IF stat

I just purchased 100 shares of

. Tostock

hedgeatthe

a cost

ris o

stock might decline in value, I purchased

. Each opti

60 s

has an exercise price

. How

of can

$45 Iand

develop

costs a$5worksh

the six-month percentage return on my portfoli

Before tackling this problem, I want to review s

fnance. A European put option allows you to se

six months) a share of a stock for the exercis

six months is $45 or higher, the option has no v

stock in 6 months is below $45. Then you- can m

ately reselling the stock for $45. For example

can make a proft of $45–$37, or $8 per share, by b

put to resell the share for $45. You can see th

moves in a stock price. In this case, whenever th

puts start kicking in some value. This cushion

shares it owns. Note also that the percentage r

are paid by the stocks in the portfolio) is co

value

fnal

(

portfolio

–

initial

value

portfolio

) and dividing

value

that numbe

initial value.

With this background, let’s look at how the si

consisting of 60 puts and 100 shares of stock, v

and $65. You can fnd this solution on the

Hedg

worksheet is shown in Figure 12-2.

Microsoft Excel 2010: Data Analysis and Business Modeling

The labels in A2:A7 are linked to cells B2:B7. T

100($55)+60($5)

=$5,800, shown in cell B7. By copying fro

IF(A9<exprice,exprice–A9,0)*Nputs

compute the fnal value of the p

price is less than the exercise price, you

can v

Otherwise, each put will in six months have a va

the formula,

Nshares*A9

I compute the fnal value of the shar

D10:D18 the formula

((C9+B9)–startvalue)/startva

the hedged portfolio. Copying from E9 to E10:E18 th

(Nshares*pricenow)

computes the percentage retur

(that is, buy no puts).

Fig

URE 12-2

Hedging example that uses IF statements.

In Figure 12-2, you can see that if the stock pr

a larger expected return than the unhedged portf

not decrease, the unhedged portfolio has a large

of puts is often referred

to as

portfolio insura

Many stock market analysts believe that moving-a

the market

. A commonly suggested moving-average tradi

the stock’s price moves above the average of the p

when the stock’s price moves below the. How

average o

would this trading rule have performed against t

In this example, I’ll compare the performance of th

absence of transaction costs for buying and sell

strength of a moving-average trading rule

- is tha

ing-average trading rule lets you ride up with a b

destroys you.

Chapter

IF12

Statements

The data set contains the monthly value of the S

1871 through October, 2002. To track the perfo

strategy, I need to track the following inform

■

What is the average of the S&P 500 Index ov

■

Do I own stock at the beginning of each mon

■

Do I buy stock during the month?

■

Do I sell stock during the month?

■

What is the cash flow for the month (positiv

0 otherwise)?

The worksheet for this situation requires you t

columns A and B, as well as the headings in row 8

the fle Matradingrule.xlsx, move the cursor to c

click Freeze Panes in the Windows group. This p

Fig

URE 12-3

Freeze Panes options.

Here you choose the Freeze Panes option, which

as you scroll through the worksheet. The Freez

row visible while scrolling through the rest o

row is row 6, you see row 6 no matter how far d

Column option, you always see the leftmost col

Selecting Unfreeze Panes from the menu returns y

The fle Matradingrule.xlsx, shown in Figure 12

effectiveness of a moving-average strategy.

mulas, and some of the IF formulas require an

during a month if and only if I don’t own the s

current month’s price is higher than the 15-mo

frst month for which I can compute a 15-month m

calculations in row 24.

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 12-4

Moving-average trading rule beats buy and hold.

Let’s assume I frst owned the stock in April 187

■

By copying from D24 to D25:D1590

, I compute

the formula

the

15-month moving average for each month.

Not

n easy way to copy the formula from D24 to D25:D

corner of cell D24 (the pointer appears as- a crossha

ton. Double-clicking copies the formula to all the c

to the left. This trick can also be used to copy for

■

By copying from E24 to E25:E1590 the formula

I determine for each month whether the S&P sh

Remember that I purchase the share only if I d

of the month and the current value of the S&P e

Notice the AND portion of the formula. It con

allowed) separated by a comma. If both conditi

Yes

; otherwise,

. For

it returns

an IF formula

to recognize

quotation marks (“ “) around the text.

■

By copying from F24 to F25:F1590 the formula

, I

determine for each month whether the S&P shar

I owned the S&P share at the beginning of the m

share is below the 15-month moving average. A

sell our S&P stock.

Chapter

IF12

Statements

■

During any month before October 2002, if I b

the cash flow is negative the value of the S

during the month, the cash flow equals the v. O

0. During October, 2002, I sell any S&P sha

by copying from G24 to G25:G1589 the formula

I record the cash flow for all months before O

formula

IF(C1590="yes",B1590,0)

gives me cr

beginning of the last month.

■

In cell G6, I compute total proft from the m

formula

SUM(G24:G1590)

. You can see that the 15-month m

earns a proft of $1,319.75.

■

The proft from buying and holding shares is s

the April, 1872 S&P value. I compute the pr

G7 with the formula

B1590–B24

As you can see, the buy and hold proft of $849

moving-average trading rule. Of course, this s

in buying and selling stocks. If transaction c

profts earned by the moving-average trading str

In the game of craps,

. Iftwo

thedice

total

areoftossed

the dice o

or 12, you

. If lose

the total of the dice on

. Otherwise,

first r

game keeps. How

going

can I write a formula to determi

the first roll?

The fact that you lose in craps if you throw a 2, 3

placing an OR formula within an IF formula. In c

Ifstatement.xlsx, shown in Figure 12-5, I ente

”lose”,IF(OR(A5=7,A5=11),”win”,”keep

. This formula is

going”))

then cop

The formula displays

lose

if a 2, 3, or -

12 is e

tered, and it displays

keep going

for any othe

Fig

URE 12-5

Using IF statements to model the frst roll in cr

In most pro forma financial statements, cash is u

liabilities

. I know

balance

that using debt as the

. Howplug

can w

set up a pro forma statement having debt as th

Microsoft Excel 2010: Data Analysis and Business Modeling

A pro forma is basically a prediction of a compa

construction of a company’s future balance sheet

provides a snapshot of the company’s assets and l

statement tells you how the company’s fnancial s

forma statements can help a company determine it

parts of models that stock analysts use to deter

the fle Proforma.xlsx, I generated the free cash fl

years. Figure 12-6 shows the balance sheet, and Fi

Fig

URE 12-6

Pro forma assumptions and balance sheet.

Fig

URE 12-7

Pro forma income statement.

Column D contains information about the company’

assumptions are as follows:

■

Sales growth (SG) is 2 percent per year.

■

Initial sales are $1,000.

■

Interest rate on debt is 10 percent.

Chapter

IF12

Statements

■

Dividend payout is 5 percent of net income.

■

The tax rate is 53 percent.

■

Cost of goods sold (COGS) is 75 percent of s

■

Depreciation is 10 percent of gross fxed as

■

Liquid assets earn 9 percent.

■

Current assets are 15 percent of sales.

■

Current liabilities are 7 percent of sales.

I assigned the names in the cell range C3:C10 t

each ,Year

basic

fnance and accounting imply the f

implemented in a series of formulas:

■

Formula 12.1:

Year t+1

sales=(Year

I computed sales

t sales)*

dur

copying from E28 to F28:H28

the formula

D28*

■

Formula 12.2:

Year t

COGS=COGS*(Year

Each year’s COGS

t sales

are c

copying from E29 to F29:H29

the formula

COG

■

Formula 12.3: If

Year

, Year

t assets>Year

debt must

liabil

be se

Year

total assets–Year t current

. Otherwise,

liabilities–Y

Year

0. I computed each year’s debt in E21:H21 wi

E24,0)

. If Year

total assets are greater than Y

debt to

Year t total assets–Year

. This equalizes

t current l

ances, assets and liabilities. Otherwise, y

cash and marketable securities are used to b

■

Formula 12.4:

Year t current liabilities=(CL

. In E20:H20, I u

the formula

$H$4*E28

to compute current lia

from E20 to F20:H20).

■

Formula 12.5:

Year t equity=Year

. In

E24:H24,

stock+Yea

I c

equity by copying from E24 to. F24:H24 the fo

■

Formula 12.6: If Year

debt is greater than 0

equals 0. Otherwise, Year

cash and

total

market

liabilities–Year t current

. In

assets–Year

E13:H13, I compu

t net f

and marketable securities for each year by c

IF(E21>0,0,MAX(0,E25–E14–E17))

. If Year

debt is greater th

cash and marketable securities to balance a

cash and marketable securities equal to 0. O

securities equal to

Year t total

assets–Year

This bala

t c

assets and liabilities if Year

assets (wi

than Year

liabilities. If debt does not ba

assets as the plug that does balance assets a

Microsoft Excel 2010: Data Analysis and Business Modeling

■

Formula 12.7:

Year t interest

. In E33,

expense=(Year

I compute in

t de

expense by using ,the

copying

formula

this

IRD*E21

formula again t

■

Formula 12.8:

Year t interest income=(Year

t c

In E32:H32, I compute interest income by copy

LAIR*E13

■

Formula 12.9:

Year t operating income=Year

. In

t s

E31:H31, operating income is computed by copy

E28–E29–E30

■

Formula 12.10:

Year t dividends=(Year

. In E39:H39,

net

copy

F39:H39 the formula

E36*DIV

to compute divide

■

Formula 12.11:

Year t+1 beginning retained

ear

I compute beginning retained earnings each ye

G38:H38 the.formula

E40

■

Formula 12.12:

Year t end of year retained eaY

earnings+Year t net

income–Year

In E40:H40,

dividends

compute ea

retained earnings by copying from .E40 to F40:

■

Formula 12.13:

Year t income before taxes=Year t o

expense+Year

cash

compute income before taxes by c

F34:H34 the formula

E31–E33+E32

■

Formula 12.14:

Year t taxes=(Year

. I compute

income

each yea

bef

in E35:H35 by copying from E35

to F35:H35 the f

■

Formula 12.15:

Year t net income after

taxes=

In E36:H36, I compute each year’s net income by c

formula .

E34–E35

■

Formula 12.16:

Year t gross fxed assets=Year t n

depreciation

. In cells E15:H15, I compute gross fxed a

formula .

E17+E16

■

Formula 12.17:

Year t depreciation=(Year

. For each year,

t net

I u

formula

DEP*E15

to compute depreciation, copy

■

Formula

Year

12.18:

t accumulated depreciation=Year t–

t depreciation

. For each year, I use the formula

D16+E

depreciation by copying the formula from E16 t

■

Formula 12.19:

Year t net fxed assets=Year t g

depreciation

. In row 17, to compute net fxed assets, I c

formula .

E15–E16

Chapter

IF12

Statements

■

Formula 12.20:

Year t total assets=Year t liq

and marketable

. By

securities

adding liquid assets, curre

compute total assets by copying from .

E18 to F

■

Formula 12.21:

Year t total liabilities=Year

equity

t c

By copying from E25 to F25:H25

, I the

compute

formula

tota

liabilities for each period. Each year will b

statements.

Formulas 12.3 and 12.6 require the use of IF s

circular references. (For more information abo

“Circular References.”) For example, the follow

■

Year

cash affects Year

total assets.

■

Year

total assets affect Year

debt.

■

Year

debt affects Year

cash.

Because the worksheet contains circular refere

Options, choose Formulas, and select the Enabl

explained in Chapter 11, this enables Excel to r

Year

, total assets in row 18 equal total liabili

formulas combined with circular references.

When I copy a VLOOKUP formula to determine sal

a lot of #N/A

. Then

errors

when I average the employee

cal answer because . of

Canthe

I easily

#N/A errors

replace the #N

space so I can compute average salary?

The fle Errortrap.xlsx (see Figure 12-8) contai

cell range D3:E7. In D11:D15 I have a list

of f

ing from E11 to E12:E15 the formula

. Unfortunately

=VLOOKUP(D

cells E13 and E14 Excel displays an #N/A error

#N/A error value when a formula cannot return a

have no listed salary, VLOOKUP cannot return a s

average salary in E16 with, the

I get

formula

an #N/A

=AVERAG

erro

I have taught go through and manually replace

erage formula will calculate properly (by igno

replacing errors with a character (such as a s

IFERROR(value,value_if_error)

The frst argument is the formula you want calc

value to insert in the cell if your formula re

are #DIV/0, #NAME, #NUM, #REF, #VALUE; more on th

copying from F11 to F12:F15 the formula

IFERRO

computes salary correctly for each actual empl

Microsoft Excel 2010: Data Analysis and Business Modeling

who are not actual employees. The formula

=AVERA

average salary for all listed employees.

Fig

URE 12-8

Error trapping formulas.

Excel 2010 contains a new function, the AGGREGAT

calculations and ignore rows that contain errors

AGGREGATE(

function number,

Function

option, number

array)

is a code b

that gives the function involved in your calcula

9 = SUM. See the Help topic on this function (ob

the Function Wizard) for a complete list of avai

that should be ignored in your calculations. (Se

error values are ignored.

Array

is simply the ra

in cell E18, the formula

AGGREGATE(1,6,E11:E15)

the listed salaries.

Option Behavior

0 or omitted

Ignore nested SUBTOTAL and AGGREGATE function

Ignore hidden rows and nested SUBTOTAL and AG

Ignore error values and nested SUBTOTAL and A

Ignore hidden rows, error values, and nested S

Ignore nothing

Ignore hidden rows

Ignore error values

Ignore hidden rows and error values

Chapter

IF12

Statements

The fle Errortypes.xlsx, shown in Figure 12-9, c

values.

Fig

URE 12-9

Examples of Excel error values.

■

In cell D3, the formula

=C3/B3

yields a #DI/

■

In cell D6, the formula

=C6+D6

yields a #VAL

appropriate type of data for the entered fo

■

In cell D7, the formula

=SUM(Sales)

returns a

name

Sales

referred to in the formula is not d

■

In cell D8, the formula

=SQRT(–1)

results in a

when you enter an unacceptable argument in a f

not have square roots, Excel displays the #

■

In cell C9, I entered the formula

SUM(A1:A3

a #REF! error because the cells that are re

longer in the worksheet.

The IFERROR function can be used to replace an

string.

My worksheet contains quarterly

. Can Irevenues

easily- compu

for W

enue for each year and place it in the row con

The fle Walmartrev.xlsx contains quarterly rev

Figure 12-10.) Rows 6, 10, 14, and so on contai

year. In each of these rows, I would like to c

In other rows, column E should be blank. I cou

and copy this formula to E10, then E14, then E

way. Using an IF statementROW

with

andtwo

)

,MOD

gives

neat me

Excel

an f

easy way to enter my formula once and then

copy th

ence)

yields the row of

ROW(A6)

reference.

yieldsThe

a 6;

functio

if yo

=ROW()

function would also yield a 6. The

- func

der when

number

. For

divided

example,

divisor

MOD(9,4)

yield

100

Microsoft Excel 2010: Data Analysis and Business Modeling

yields 0. Note that I want my formula to work on

divided by 4. Therefore, copying from E6 to E7:E

2,SUM(D6:D9),” “)

ensures that I add up revenues f

a remainder of 2 when divided by 4. This means th

frst quarter of each year, which is the goal.

Fig

URE 12-10

Summarizing Wal-Mart annual revenues.

IF statements can. How

get many

rather

IF large

statements can I n

the maximum number of characters allowed in an E

In Excel 2010, you can nest up to 64 IF statemen

you could nest a maximum of seven IF statements. I

contain up to 32,000 characters. Previous versio

a cell.

Problems

Suppose the price of a product will change at da

Date

Price

On or before February 15, 2004

From February 16, 2004, through

$9 April 10, 2005

From April 11, 2005, through $10

January 15, 2006

After January 15, 2006

$11

Write a formula that computes the price of th

is sold.

Chapter

IF12

Statements

101

The Blue Yonder Airline flight from Seattle t

The airline sold 270 tickets for the -

flight at a p

refundable. The variable cost of flying a pa

is $30 per passenger. If more than 250- peop

booked and Blue Yonder must pay overbooking c

each overbooked passenger. Develop a worksh

based on the number of customers who show u

A major drug company is trying to determine th

A unit of annual capacity can be built for a c

$12 and incurs variable costs of $2. The

sheet that computes the company’s 10-year p

level and the annual demand for the drug. A

each year. You can ignore the time value of m

The drug company is producing a new drug. T

assumptions:

❑

During Year 1, 100,000 units will be sold

❑

Sales will grow for three years and then d

❑

During the growth period, sales will grow a

the decline, sales will drop at a rate of 1

Develop a worksheet that takes values for Y

the length of the decline cycle, the growth r

decrease during the decline cycle and compu

You are bidding on a construction project. T

the project cost at $10,000. Four companies a

prepare the bid. Write a formula that (give

bid) computes your proft.

We are bidding on a valuable painting. The hi

the painting’s value at $10,000. Four compani

prepare the bid. Write a formula that (give

bid) determines whether we get the painting

A drug company believes its new drug will s

two competitors to enter the market. The ye

company expects to lose 30 percent of its m

competitor enters, the company expects to l

of the market is growing at 10 percent per y

two competitors enter, develop a worksheet th

years 2004–2013.

102

Microsoft Excel 2010: Data Analysis and Business Modeling

A clothing store has ordered 100,000 swimsuit

They plan to sell them until August 31 at a p

to $30. Given values for demand through Augus

worksheet to compute the proft from this orde

In a game of craps, on each roll of the dice a

the game has not ended and the current roll m

If the game has not ended and the current rol

continues. Develop a worksheet that tells you (

the status of the game after four dice rolls.

10.

On the S&P moving-average example, suppose we s

exceeds the 15-month moving average, but we s

5-month moving average. Is this strategy more p

price is less than the 15-month moving averag

11.

A European call option gives you the right to b

stock for a given exercise price. A

butterfly s

a low exercise price, buying one call option w

call options with an exercise price midway be

Here is an example of a butterfly spread: The c

six-month European call option for $9, buy a $

$4, and sell two $60 European call options fo

dollars, not percentage) for this transaction a

ranging from $40–$80. When a trader purchases a b

movement in the stock price during the next s

12.

Suppose a stock is currently selling for $32. Y

with an exercise price of $30 for $2.50 and s

an exercise price of $35 for $1. Compute

the p

tion of a six-month stock price ranging from $

spread

? How would you modify this?strategy to cr

13.

Let’s reconsider our pro forma example. Suppo

on our fnancial well-being. More specifcally,

est and taxes (EBIT) are negative, our intere

expense is more than 10 percent of EBIT and E

13 percent. Otherwise, our interest rate is 1

for this variable interest rate.

14.

Do this problem independently of Problem 13. S

equity ratio of 50 percent during each year. H

Hint: You must keep each year’s stock nonnega

marketable securities to balance assets and l

Chapter

IF12

Statements

103

15.

Martin Luther King Day occurs on the third M

computes (given the year) the date of Marti

day of the week for January 1 of the given y

16.

Thanksgiving occurs on the fourth Thursday i

computes (given the year) the date of Thank

week for November 1 of the given year.

17.

The frst quarter of the year is January–Mar

quarter, July–September; and the fourth qua

that returns (for any given date) the quart.

18.

Write a formula that returns a person’s age

19.

Labor Day is the frst Monday in September. W

of Labor Day for a given year.

20.

The fle Nancybonds.xlsx gives the bond rati

future month. You want to effciently count h

Unfortunately, each company is listed in mo

the data on the company name, how would you d

bonds?

21.

The fle Addresses.xlsx gives people’s names o

next line, and their city, state, and ZIP c

each person’s information on one line?

22.

The fle FormattingDDAnum.xlsx gives a bunch o

DDA1250045, and so on. A cell is properly f

DDA and the last seven characters are a num

cells are properly formatted.

23.

Suppose the number of Group 1 members is li

members is listed in cell B2, and the numbe

The total number of group members is always

bers, Group 2 has 30 members, and Group 3 h

each Group 1 member in column D, a 2 for ea

for each Group 3 member in column D. Thus, c

1 in D1:D50, a 2 in D51:D80 and a 3 in D81:D

24.

The fle Dividebyprice.xlsx contains units s

want to determine the average price for eac

there is no average price. Error-trap the fl

ucts with zero sales yield the message “No s

104

Microsoft Excel 2010: Data Analysis and Business Modeling

25.

The School of Fine Art has 100 lockers number

open. We begin by closing every locker whose n

“toggle” (toggling means opening a closed loc

locker whose number is divisible by 4; then w

divisible by 5,…, and fnally we toggle each l

How many lockers are now open?

26.

The fle Matchlist.xlsx contains a list of peo

and a list of people who bought it in March. D

customers purchased your product in March.

27.

Set up a “calendar worksheet” that takes a gi

the day of the week on which each day of the m

28.

Some rows of column C of fle Problem28data.xl

Create

formulas in column D that place an X in a row o

that row contains

the word

and

29.

Suppose you toss two 20-sided dice. The 400 p

(20,20). Use IF statements to systematically g

105

Chapter 13

Time and Time Funct

Questions answered in this chapter:

■

How do I enter times in Excel?

■

How do I enter a time and date in the same c

■

How does Excel do computations with times?

■

How can I have my worksheet always display th

■

How can I use the TIME function to create ti

■

How can I use the TIMEVALUE function to con

■

How do I extract the hour, minute, or secon

■

Given work starting and ending times, how d

employee worked?

■

I added up the total time an employee worke

What did I do wrong?

■

How can I easily create a sequence of regul

Recall from Chapter 7, “Dates and Date Functio

January 1, 1900, the serial number 1, January 2, 1

also assigns serial numbers to times (as a fra

midnight, so 3:00 A.M. has a serial number of .

has a serial number of .75, and so on. If you c

number is the number of days after January 1, 1

the given time. Thus, entering January 1, 2007

a serial number of 39083, whereas January 1, 2

39083.25.

Answers to This Chapter’s Ques

How do I enter times in Excel?

To indicate times, you enter a colon (:) after th

For example, in fle Time.xlsx (see Figure

- 13-1

ply 8:30 or as 8:30 A.M. In cell C3, I entered 8

also have entered 8:30 P.M. with 24-hour milit

PM. This represents 30 seconds after 3:10 P.M.

106

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 13-1

Examples of time formats.

How do I enter a time and date in the same cell?

Simply put a space after the date and enter the

entered January 1, 2007 5:35. Of course, this re

immediately reformatted this to 1/1/2007 5:35.

How does Excel do computations with times?

When Excel computes differences in times, the re

in the cell. Figure 13-2 displays the various Ex

Fig

URE 13-2

Excel time formats.

In the fle Time.xlsx (see Figure 13-2), I took th

in cells F5 and H5 with the formula

=C3–C2.

If y

these times are 12 hours apart and enters 12:00 P

want Excel to portray these times as .5 days apa

time difference to hours.) To make Excel show .5 i

In cell F7, I tried to subtract an earlier

time f

Because I did not reformat the cell, Excel displ

simply change the cell containing the formula to th

obtain the correct time difference, –.5 days.

Cells B17 and C17 give the start times for

two j

ish times for the jobs. (See Figure 13-3.) If yo

Chapter

Time

13 and Time Functions

107

complete each job, simply copy from B19 to C19 th

as Number. Thus, the frst job took 29.18 days, a

Fig

URE 13-3

Determining time needed to complete jobs.

How can I have my worksheet always display the c

The Excel formula

=NOW()

gives today’s date an

(see Figure 13-4) of fle Time.xlsx, entering

ated the screen capture at 21:50 P.M. on July 1

enter in cell H2 or I2 .the

Cell

formula

H2 is

=NOW()–TODA

formatted t

P.M.), whereas cell I2 is formatted to show a n

9:50 P.M. is 91 percent of the way between mid

day.

Fig

URE 13-4

Using the

Now()

and

Today()

functions.

How can I use the TIME function to create time

The TIME function has the .

syntax

Given

TIME(hour,min

an hour, min

seconds, the TIME function returns a time of d

exceeding 24 hours.

In cell A2 (see Figure 13-1), the formula

=TIM

=TIME(20,30,0)

yields 8:30 P.M. In cell A4, th

Finally, note that in cell A5 the formula

=TIM

yields 1:10:30 A.M.

Of course, if the number of seconds does not s

displays seconds.

How can I use the TIMEVALUE function to conver

The function TIMEVALUE has the syntax

=TIMEVAL

string that gives a time in a valid format. Th

between 0 and 1. (This means that the TIMEVALU

.) For

example, in cell A7 (see Figure 13-1), the for

because 8:30 A.M. is 35.4 percent of the way b

the next day.

108

Microsoft Excel 2010: Data Analysis and Business Modeling

How do I extract the hour, minute, or second fro

The Excel HOUR, MINUTE, and SECOND functions extr

a cell containing time. For example (as

- shown in Fi

mula

=HOUR(A4)

yields 15 (3:00 PM is 15:00 milit

=Minute(A4)

yields 10, whereas entering

=SECOND(

Given work starting and ending times, how do I d

employee worked?

In cells C10:D11 (see Figure 13-5), I entered th

ended work. We want to fgure out how long each o

is that Jane fnished work the day after she star

give the actual number of hours she worked. Copy

=IF(D10>C10,24*(D10–C10),24+24*(D10–C10))

yields th

formatted these cells as Number. If the fnish ti

start time from the fnish time and multiplying by 2

is before the start time, then

24*(fnish time–st

but adding 24 hours fxes things, assuming the en

worked 9 hours and Jack worked 8.5 hours.

Fig

URE 13-5

Computing length of time worked by employees.

I added up the total time an employee worked,

. What

did I do wrong?

In cells C31:D35 in Figure 13-6, I give the numb

worked on each day of her workweek. In cell D36, t

compute the total number of hours worked during th

wrong! With the format h:mm, Excel never yields a v

chose a format (38:48:00) that allows for more th

worked each day yields the correct number of hou

Fig

URE 13-6

Determining total hours worked during the week.

Chapter

Time

13 and Time Functions

109

How can I easily create a sequence of regularl

Suppose a doctor takes appointments from 8:00 A

How can I enter in different rows the list of p

great AutoFill feature. (See Figure 13-7.) Ent

in cells L15:L16. Now select cells L15:L16 and m

cell L16 until you see the black cross. Drag th

appointment time). From cells L15:L16, Excel h

times that are 20 minutes apart. Of course, en

using AutoFill will yield the sequence Monday, T

at Monday. Entering 1/1/2007 in one cell, 2/1/

and using AutoFill yields a sequence of dates, l

Fig

URE 13-7

Entering a sequence of times.

Problems

Write a formula that will return a time 18 h

The fle Marathon.xlsx gives marathon race ti

C refer to this data. Compute the average ti

How much faster was John than Jill?

How many total minutes did each runner ta

How many total seconds did each runner ta

The fle Jobshop.xlsx gives the start time a

required to complete each job. Determine th

111

Chapter 14

The Paste Special C

Questions answered in this chapter:

■

How can I move the results of calculations (

worksheet?

■

I have a list of names in a column. How can I m

column?

■

I’ve downloaded U.S. T-Bill interest rates f

5 when the interest rate is 5 percent, 8 wh

How can I easily divide my results by 100 s

is displayed as .05?

With the Paste Special command in Microsoft Ex

worksheet data. In this chapter, I’ll show how y

perform the following types of operations:

■

Paste only the values in cells (not the for) t

■

Transpose data in columns to rows and vice v

■

Transform a range of numbers by adding, sub

number in the range by a given constant.

Answers to This Chapter’s Ques

How can I move the results of calculations (no

worksheet?

In the

Paste Special Value

worksheet contains

the fl

the names, games, total points, and points per g

players from Bloomington, Indiana. In the cell r

to compute each child’s points per game, as sh

copy this data and the calculated points per g

calculations—to a different cell range (E13:H1

E4:H9, press Ctrl+C, and then move to the uppe

to copy the data (cell E13 in this example). N

target range, click Paste Special, and then fl

Figure 14-2. After clicking OK, the range E13:

the cell range E4:H9. You can check this by go

the formula that was used to compute Gregory’s a

112

Microsoft Excel 2010: Data Analysis and Business Modeling

use the Paste Special command, select Values, an

from which you copied the data, your formulas di

Fig

URE 14-1

Using the Paste Special command to paste only value

Fig

URE 14-2

The Paste Special dialog box with Values selected. S

any formulas.

I have a list of. names

How can

inIamake

column

the list appear i

column?

To realign data from a row to a column (or vice v

Special command with Transpose selected. Essentia

Special dialog box “flips” selected cells- around s

comes the frst column of the range you paste dat

at the

Paste Special Transpose

worksheet in the fl

Suppose that you want to list the players’ names i

select the range E5:E9, and then press Ctrl+C to c

Paste Special, and select Transpose in the Paste S

transposes the players’ names into one row.

Chapter

The

14Paste Special

113

Command

Fig

URE 14-3

Use the Transpose option in the Paste Special di

column or a column of data into a row.

Suppose you want to transpose the spreadsheet c

cell E17. Begin by selecting the range E4:H9. N

corner of the range where you want to put the tr

choose Paste Special, select Transpose, and th

is transposed (turned on its side), as shown i

smart enough to adjust the points-per-game for

now computed from data in the same column inst

Not

When you select Paste Special and click Paste L

linked to the original cells, and changes you make t

By changing the ,value

the value

in cell

in F5

cell

to F18

becomes 7 a

display Dan’s average as 4 points per game.

I’ve downloaded

S.. T-Bill

U interest rates

. The

from

data websit

displ

5 when the interest rate is 5 percent, 8.

when t

How can I easily divide my results by 100 so t

displayed

05? as

The

Paste Special Divide Before

worksheet in th

contains the annual rate of interest paid by th

January 1970 and February 1987. In January 197

was 8.01 percent. Suppose you want to earn ann

T-Bill rate. The formula to calculate

. It would

theberate

eas i

compute earned interest if the column of annua

The Operations area of the Paste Special dialo

each number in a range by a given number,

prov

est rate by 100. Here we want to divide each n

114

Microsoft Excel 2010: Data Analysis and Business Modeling

divisor (100). You can enter it anywhere in the w

F5 selected, press Ctrl+C. You will see the “mov

range of numbers you want to modify. To select a

press Ctrl+Shift and then the Down Arrow key. Thi

“tall” cell range. (To select a “wide” set of da

and then press Ctrl+Shift and the Right Arrow ke

and then select Divide in the Paste Special dial

Fig

URE 14-4

Data for using the Divide option in the Paste Spec

by a constant.

Fig

URE 14-5

You can apply an option in the Operation area of th

range of cells.

After you click OK, Excel divides each selected n

shown in Figure 14-6. If you had selected Add, D

Subtract, D10 would display –91.99; and if you h

Chapter

The

14Paste Special

115

Command

Fig

URE 14-6

Results of using the Divide option in the Paste S

Problems

The fle Mavs.xlsx contains statistics for th

basketball team. Player names are listed in c

row 3, and statistical results are listed i

player names are listed in the same row and a

same column.

Field goal percentage, free throw percentag

decimals. For example, Steve Nash made 91.9 p

as .919. Change the worksheet so that all s

from 1 through 100.

The fle Productpaste.xlsx contains data on q

data to another range so that quarterly sal

copied data to the original data so that yo

data range will reflect changes entered in r

The fle Productsalespaste.xlsx contains sal

of units). Convert this sales data to sales i

the Ctrl key (as explained in Chapter 2, “Ra

range of cells.

117

Chapter 15

Three-Dimensional F

Questions answered in this chapter:

■

Is there an easy way to setup a multiple-wo

worksheet

has a similar structure? Can I easily creat

worksheets?

■

In many business situations you have to set u

a similar format or structure. Here are som

■

You want to track your company’s sales in ea

worksheet and then summarize total sales in a s

■

You want to track your company’s sales for e

then summarize year-to-date sales in a summ

In this chapter, you will learn how to set up w

have a similar structure. In this chapter I al

you to easily write formulas to perform calcul

Answers to This Chapter’s Ques

Is there an easy way to setup a multiple-works

worksheet

has a similar structure? Can I easily create f

worksheets?

Let’s suppose you want to set up a workbook th

sales in each region (East, South, Midwest

and W

rize total sales in a summary worksheet. In ea

uct’s price, unit cost, and units sold as well a

worksheet you want to track just total proft a

worksheets to look like Figure 15-1.

Fig

URE 15-1

Sales in the East.

118

Microsoft Excel 2010: Data Analysis and Business Modeling

To set up this structure, you enter in cell C3 o

the unit cost, in cell C5 the units sold, and in c

compute the East region proft

. Of

with

course,

the formula

you wan

(

same structure in the worksheets for the other r

headings and formula in only one worksheet, and th

the other region’s worksheets.

To begin, open a blank workbook, which

clicking

by defaul

the Insert Worksheet icon to the right of the la

Shift+F11), insert two new worksheets so that yo

the frst four worksheets East, South, Midwest, a

All sales will be totaled in the Summary workshe

File tab and then choose General, you can change th

workbook by default.)

To set up the regional worksheets, select the fr

Shift key and select the last individual workshe

worksheet is duplicated in the other regional wo

Unit Cost

in cell B4,

Units Sold

in cell B5,

Fix

enter the formula

(C3-C4)*C5-C6

in cell C7. Now c

procedure. You will see that each regional works

the correct Proft formula in cell C7.

You are now ready to use three-dimensional formu

In cell C5, you will compute total units sold. R

region in cell C5. Move your cursor to cell C5 o

to compute total units sold. Type

=SUM(

and then m

want to total (cell C5 of sheet East). Next, hol

want to total (cell C5 of worksheet West). Lastl

and you will see entered in cell C5 of .the

This

Summa

formula is an example of a three-dimensional for

dimensions (rows and columns.) A three-dimension

across worksheets. This formula tells Excel to s

East worksheet and ending with the West workshee

have simply typed this formula in cell C5 of the S

and pasting it to cell C7 of the Summary workshe

(See Figure 15-2.)

In Chapter 47, “Consolidating Data,” you will le

can be used to summarize data from multiple work

Chapter

Three-Dimensional

119

Formulas

Fig

URE 15-2

Summarizing unit sales and proft.

Problems

You own six local coffee shops. The revenue

are given in the following table.

Shop

Revenues

Customer Count

$8,000

1,950

$7,000

1,800

$9,000

2,200

$8,400

2,000

$5,900

1,400

$10,100

2,500

Set up a workbook that makes it easy to ent

store and create a summary worksheet (using th

computes total weekly revenue and customer c

121

Chapter 16

The Auditing Tool

Questions answered in this chapter:

■

I’ve just been handed a fve thousand–row wo

value (NPV) of a new car. In the worksheet, m

about the annual percentage of the growth i

worksheet are affected by this assumption?

■

I think my fnancial analyst made an error c

cells in the worksheet model were used for thi

■

How does the auditing tool work when I’m wo

worksheet or workbook?

When we hear the

, we

word

often

structure

think about the stru

structure of a worksheet model refers to the wa

price, and unit cost) are used to compute outp

Microsoft Excel 2010 auditing tool provides an e

of a worksheet, which makes understanding the l

easier. To view the auditing options in Excel, d

view the Formula Auditing group. (See Figure 1

Fig

URE 16-1

The Formula Auditing toolbar.

In this chapter, I discuss the Trace Precedent

commands. I discuss the Evaluate Formula comma

Clicking Show Formulas serves as a switch that t

the display of the values that result from the f

between showing formulas in cells and showing th

By using the Watch Window you can select a cel

in the workbook, you will see how the value of th

selecting the Watch Window you can select Add W

Sheet 1). Now even if you are working in a dif

you how cell C3 of Sheet 1 changes.

Trace Precedents and Trace Dependents locate a

for worksheet cells or formulas. A

precedent

122

Microsoft Excel 2010: Data Analysis and Business Modeling

a selected formula’s value. For example, if you w

would make assumptions about the number of lette

mailing. Then you could compute the number

. Inof re

this case, the response rate and total letters m

formula used to compute total responses. A

depen

values can’t be computed without knowledge of a s

the cell containing the total number of response

response rate. Excel marks precedents and depend

Auditing tool. The Remove Arrows button clears th

Let’s apply the Auditing tool to some practical p

Answers to This Chapter’s Quest

I’ve just been handed a five thousand–row workshe

value (NPV) of

. Inathe

newworksheet,

car

my financial analy

about the annual percentage of . the

Which

growth

cells inthe p

worksheet are affected by this assumption?

The

Original Model

worksheet in the fle NPVaudit

the NPV of after-tax profts for a car expected t

years. (See Figure 16-2.) Price and cost- are in th

sumed for the analysis are given in cells C1:C8 (

B1:B8). I’ve assumed that the price of the produ

Which cells in the worksheet are dependents of thi

Fig

URE 16-2

You can use the Auditing tool to trace formulas in c

To answer this question, select cell C8 (the cel

growth), and then click the Trace Dependents but

Chapter

The

16Auditing

123

Tool

Formulas tab. Excel displays the set of arrows s

cells.

By clicking the Trace Dependents button

depend

once, E

on the price growth assumption. In Figure 16-3

Years 2–5 depend directly on this assumption. C

all formulas whose calculation requires the va

Figure 16-4.

Fig

URE 16-3

Tracing dependent cells.

Fig

URE 16-4

Clicking Trace Dependents repeatedly shows all t

assumption.

You can see that in addition to unit price in Y

Years 2–5 revenue, before-tax profts, tax paid

the arrows by clicking the Remove Arrows butto

124

Microsoft Excel 2010: Data Analysis and Business Modeling

I think my financial analyst made an error

. Which

in com

cells in the worksheet model were used for this c

Now we want to fnd the precedents for cell B15. T

compute Year 1 before-tax proft. Select cell B15

once. You’ll see the arrows shown in Figure 16-5

Fig

URE 16-5

Direct precedents for Year 1 before-tax proft.

As you can see, the cells directly needed to com

revenues and Year 1 cost. (Before-tax Year 1 pro

Repeatedly clicking the Trace Precedents button y

proft, as shown in Figure 16-6.

Fig

URE 16-6

Click Trace Precedents repeatedly to show all prec

Here the only input assumptions that influence Ye

Year 1 price, and Year 1 cost.

Chapter

The

16Auditing

125

Tool

How does the auditing tool work when I’m worki

worksheet or workbook?

Consider the simple worksheet model in the wor

in Figure 16-7. The formula in the

Proft

unit

works

sales*(price

–

variable

–

fxed

cost)

from information contained i

Fig

URE 16-7

Data for using the Auditing tool on multiple wor

Suppose you want to know the precedents of the p

worksheet, and then click Trace Precedents in th

tab. You’ll see a dotted line, an arrow, and th

Fig

URE 16-8

Results of tracing precedents with data on multi

The worksheet icon indicates that the preceden

worksheet. Double-clicking the dotted line dis

Figure 16-9.

Fig

URE 16-9

With the Go To dialog box, you can audit data in m

Now you can click any of the listed precedents (

will send you to the precedent you selected.

126

Microsoft Excel 2010: Data Analysis and Business Modeling

Problems

■

In the car NPV example, determine the followi

❑

The direct dependents and all dependents of th

❑

The direct dependents and all dependents of th

❑

The direct precedents and all precedents fo

❑

The direct precedents and all precedents fo

127

Chapter 17

Sensitivity Analysi

Questions answered in this chapter:

■

I’m thinking of starting a store in the loc

opening the store, I’m curious about how my p

depend on the price I charge and the unit c

■

I am going to build a new house. The amount o

15-year repayment period) depends on the pr

I’m also unsure about the annual interest r

how my monthly payments will depend on the a

interest rate?

■

A major Internet company is thinking of pur

retailer’s current annual revenues are $100 mi

Current projections indicate that the retai

year and its expenses are growing at 5 perc

be in error, however, and would like to know

revenue and expense growth, the number of y

Most worksheet models contain assumptions abou

model. In our lemonade example, the inputs inc

■

The price for which a glass of lemonade is s

■

The unit cost of producing a glass of lemon

■

The sensitivity of demand for lemonade to p

■

The annual fxed cost of running a lemonade s

Based on input assumptions, you can compute ou

example, the outputs of interest might include

■

Annual proft

■

Annual revenue

■

Annual variable cost

Despite best intentions, assumptions about inp

best guess about the variable cost of producin

possible that your assumption is in error.

Sen

outputs vary in response to changes to its inp

a change in product price affects yearly proft

Microsoft Excel 2010 lets you easily vary one o

128

Microsoft Excel 2010: Data Analysis and Business Modeling

With a

one-way

data table, you can determine how c

of outputs. With a

two-way

data table, you can d

a single output. This chapter’s three examples w

obtain meaningful sensitivity results.

Answers to This Chapter’s Quest

I’m thinking of starting a store in. Before

the local ma

opening the store, I’m curious about how my profi

depend on the price I charge

and the unit cost

The work required for this analysis is in the fl

17-4.) The input assumptions are given in the ra

lemonade (see the formula in. cell

(Chapter

D2) equals

79, “Esti

650

Demand Curve,” contains a discussion of how to e

names in C1:C7 to correspond to cells D1:D7.

I computed annual revenue in cell

. InD5

cell

with

D6,

theI fo

the annual variable cost with

. Finally,

the formula

in cell

unit_c

D7, I c

proft by using the formula .

revenue–fxed_cost–var

Fig

URE 17-1

The inputs that change the proftability of a lemona

Suppose that I want to know how changes in price (

in $0.25 increments) affect annual proft,

changing

revenu

only one input, a one-way data table will solve th

Figure 17-2.

Chapter

Sensitivity

Analysis

129

with Data Tables

Fig

URE 17-2

One-way data table with varying prices.

To set up a one-way data table, begin by listi

interest (ranging from $1.00 through $4.00 in $0

I moved over one column and up one row from th

formulas I want the data table to calculate. I e

formula for revenue in cell E10, and the formu

Now select the table range (C10:F23). The tabl

its last row is the row containing the last in

the column containing the inputs; its last col

After selecting the table range, display the Da

click What-If Analysis, and then click Data Ta

shown in Figure 17-3.

Fig

URE 17-3

Creating a data table.

For the column input cell, you use the cell in w

values listed in the frst column of the data t

inputs are prices, I chose D1 as the column in

one-way data table shown in Figure 17-4.

130

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 17-4

One-way data table with varying prices.

In the range D11:F11, proft, revenue, and variab

In cells D12:F12, proft, revenue, and variable c

through the range of prices. The proft-maximizin

price of $3.75 would produce an annual proft of $

and an annual variable cost of $14,062.50.

Suppose I want to determine how annual proft var

$5.00 (in $0.25 increments) and unit cost

varies f

ments). Because here I’m changing two inputs, I n

I list the values for one input down the frst co

H11:H25 for the price values) and the values for th

range. (In this example, the range I10:O10 holds th

table can have only one output cell, and the for

upper-left corner of the table range. Therefore, I p

Fig

URE 17-5

A two-way data table showing proft as a function of p

Chapter

Sensitivity

Analysis

131

with Data Tables

I select the table range (cells H10:O25) and d

click What-If Analysis and then click Data Tab

cell D3 (unit variable cost) is the row input c

frst column of the table range are used as pri

range are used as unit variable costs. After c

in Figure 17-5. As an example, in cell K19, wh

is $0.40, the annual proft equals $58,850.00. F

maximizing price. Note that as the unit cost i

as some of the cost increase is passed on to c

the proft-maximizing price in the data table i

price. When you learn about the Excel Solver i

the penny) the exact proft-maximizing price.

Here are some other notes on this problem:

■

As you change input values in a worksheet, t

change, too. For example, if you increased f

the data table would be reduced by $10,000.

■

You can’t delete or edit a portion of a dat

data table, select the table range, copy th

Special. Then choose Values from the -Paste S

ever, changes to your worksheet inputs no l

update.

■

When setting up a two-way data table, be ca

input cells. A mix-up will cause nonsensica

■

Most people set their worksheet calculation m

change in your worksheet will cause all you

you want this, but if your data tables

are l

credibly slow. If the constant recalculatio

click the File tab on the ribbon, click Opti

select Automatic Except For Data Tables. Wh

selected, all your data tables recalculate o

Alternatively, you can click the Calculatio

the Formulas tab) and then click Automatic E

I am going to build

. The aamount

new house

of money I need to b

repayment period) depends on the price

. I’m for

alsowhi

about the annual interest . rate

Can II’ll

determine

receivehow

wh m

payments will depend on the amount borrowed an

The real power of data tables becomes evident w

the Excel functions. In this example, we’ll us

amount borrowed and the annual interest rate) t

132

Microsoft Excel 2010: Data Analysis and Business Modeling

how the monthly payment varies as these inputs c

detail in Chapter 10, “More Excel Financial Func

Mortgagedt.xlst, shown in Figure 17-6.

Suppose you’re borrowing money on a 15-year mort

made at the end of each month. I’ve input the am

months in the mortgage (180) in D3, and annual i

names in cells C2:C4 with the cells D2:D4.

Based o

ment in D5 with the formula

-PMT(Annual_int_rate

Fig

URE 17-6

You can use a data table to determine how mortgage p

and the interest rate change.

You think that the amount borrowed will range (d

your current house) between $300,000 and $650,00

range between 5 percent and 8 percent. In prepar

the amounts borrowed in the range C8:C15 and pos

D7:J7. Cell C7 contains the output you want to r

Therefore, I set cell C7 equal to cell D5. Next I s

Analysis on the Data tab, and then click Data Ta

of the table range are amounts borrowed, the col

row of the table are annual interest rates, so o

see the data table shown in Figure 17-6. This ta

$400,000 at an annual rate of 6 percent, your mo

The data table also shows that at a low interest r

$50,000 in the amount borrowed raises the monthl

high interest rate (such as 8 percent), an incre

the monthly payment by about $478.

A major Internet company is thinking

. The

retailer’s

of purchasi

current annual revenues are $100 million,

. Current with e

projections indicate that the retailer’s revenue

its expenses are growing

. We at

know

5 percent

projections

per year

might b

however, and we would like to know, for a variet

and expense growth, the number of years

before t

Chapter

Sensitivity

Analysis

133

with Data Tables

We want to determine the number of years neede

in revenue from 10 percent through 50 percent a

percent through 20 percent. Let’s also assume th

we’ll say “cannot break even.” Our work is in th

17-8.

I chose to hide columns A and B and rows 16–18

cells in columns A and B (or select the column h

the Cells group, click Format, point to Hide & Un

16–18, select any cells in those rows (or sele

procedure, selecting Hide Rows. Of course, the

Rows and Unhide Columns. If you receive a work

and want to quickly unhide all of them, you ca

Select All button at the intersection of the c

Rows and/or Unhide Columns will unhide all hid

In row 11, I project the frm’s revenue out 13 y

rate assumed in E7) by copying from. F11

In row

to G11:

12, I

project the frm’s expenses out 13 years (based o

in E8) by copying from F12 to. G12:R12

(See Figure

the form

17-7

Fig

URE 17-7

You can use a data table to calculate how many y

We would like to use a two-way data table to d

revenues and expenses affects the years needed t

value always tells us the number of years need

during any of the next 13 years, this might se

I begin by using in row 13 an IF statement for e

during the year. The IF statement returns the n

year or 0 otherwise. I determine the year we b

all the numbers in row 13. Finally, I can use c

table.

I copy from cell F13 to G13:R13 the

. This

formula

reflects the fact that we break even for the fr

previous year, revenues are less than expenses

greater than expenses. If this is the case, th

entered.

134

Microsoft Excel 2010: Data Analysis and Business Modeling

Now, in cell E15 I can determine the breakeven y

IF(SUM(F13:R13)>0,SUM(F13:R13),”No

. If we do not break

BE”)

even dur

the formula enters the text string “No BE”.

I now enter the annual revenue growth rates (10 p

E21:E61. I enter annual expense growth rates (2 p

I ensure that the year-of-breakeven formula

is c

Next, I select the table range E20:X61, click Wh

Data Table. I select cell E7 (revenue growth rat

growth rate) as the row input cell. With these s

in Figure 17-8.

Fig

URE 17-8

A two-way data table.

Note, for example, that if expenses grow at 4 pe

revenue will result in breaking even in eight ye

revenue will result in breaking even in only two y

percent per year and revenues grow at 14 percent p

end of 13 years.

Problems

You’ve been assigned to analyze the proftabil

following assumptions have been made:

❑

Bill is receiving a one-time royalty paymen

❑

The fxed cost of producing the hardcover ve

❑

The variable cost of producing each hardcov

❑

The publisher’s net from book sales per har

❑

The publisher expects to sell 1 million har

❑

The fxed cost of producing the paperback is $

❑

The variable cost of producing each paperba

❑

The publisher’s net from book sales per pap

❑

Paperback sales will be double hardcover sa

Chapter

Sensitivity

Analysis

135

with Data Tables

Use this information to answer the followin

❑

Determine how the publisher’s before-tax p

from 100,000 through 1 million copies.

❑

Determine how the publisher’s before-tax p

from 100,000 through 1 million copies and th

sales varies from 1 through 2.4.

The annual demand for a product equals

500-

where

is the pr

product in dollars and

is hundreds of dol

annual fxed cost of selling the product

is $

ducing the product is $12. Determine a pric0

(within $100) that maximizes proft.

Reconsider our hedging example from Chapter 1

in six months that range from $20 through $

varying from 0 through 100 (in increments o

your portfolio.

For our mortgage example, suppose you know th

percent. Create a table that shows for amou

$600,000 (in $50,000 increments) the differ

20-year, and 30-year mortgage.

Currently, you sell 40,000 units of a produ

producing the product is $5. You are thinkin

percent. You are sure this will increase sa

percent. Perform a sensitivity analysis to s

the percentage increase in sales. Ignore fx

Let’s assume that at the end of each of the n

your retirement fund and earn the same inte

of money you will have at retirement change

from $5,000 through $25,000 and the rate of i

15 percent.

The

payback period

for a project is the num

profts to pay back the project’s initial in

investment at Time 0. The project yields pr

between $30 million and $100 million. Annua

through 25 percent a year. How does the proj

flow and cash flow growth rates?

A software development company is thinking o

Swahili. Currently, 200,000 units of the pr

each. Unit variable cost is $20. The fxed c

the product into Swahili will increase sale

136

Microsoft Excel 2010: Data Analysis and Business Modeling

unknown percentage over the current level of 2

proft resulting from the translation depends o

sales. You can ignore the time value of money a

The fle Citydistances.xlsx gives latitude and l

is also a formula that determines the distanc

latitude and longitude. Create a table that c

cities listed.

10.

You have begun saving for your child’s colleg

year, and want to know for annual rates of re

through 12 percent the amount of money you wi

for 10–15 years.

11.

If you earn interest at percentage rate

per y

per year, then in

years $1 will grow to

(1+(

dollars. Assuming a 10 p

annual interest rate, create a table showing th

years for daily, monthly, quarterly, and semia

12.

Assume I have $100 in the bank. Each year, I w

percent through 10 percent) of my original ba

percent through 10 percent per year, determin

run out of money. Hint: You should use the IF

because if my annual growth rate exceeds the w

money.

13.

If you earn interest at an annual rate of

become

(1+x)

dollars. For annual rates of interest f

determine the exact time (in years) in which $

14.

You are borrowing $200,000 and making payment

annual interest rate ranging from 5 percent th

10, 15, 20, 25, and 30 years, determine the t

15.

You are saving for your child’s college fund. Y

amount of money to the fund at the end of eac

$100,000. For annual investment returns rangi

and number of years investing varying from 5–

annual contribution.

16.

The fle Antitrustdata.xlsx gives the starting a

Determine the number of court cases active du

17.

You can retire at age 62 and receive $8,000 p

$10,000 per year. What is the difference (in t

as you vary the annual rate at which you disc

percent and vary age of death between 70 and 8

137

Chapter 18

The Goal Seek Comma

Questions answered in this chapter:

■

For a given price, how many glasses of lemo

per year to break even?

■

We want to pay off our mortgage in 15 years

bank told us we can afford monthly payments o

■

I always had trouble with “story problems” i

solving story problems easier?

The Goal Seek feature in Microsoft Excel 2010 e

worksheet input that makes the value of a give

example, in the lemonade store example in Chap

suppose you have fxed overhead costs, fxed per

this information, you can use Goal Seek to cal

need to sell to break even. Essentially, Goal S

worksheet

. To use Goal Seek, you need to provide E

■

Set Cell

Specifes that the cell contains the for

you’re seeking. In the lemonade example, th

proft.

■

To Value

Specifes the numerical value for the go

the lemonade example, because we want to de

the breakeven point, the To Value would be 0

■

By Changing

Specifes

Cell

the input cell that Excel c

calculates the goal defned in the To Value c

Changing Cell would contain annual lemonade s

Answers to This Chapter’s Ques

For a given price, how many glasses of lemonad

year to break even?

The work for this section is in the fle Lemona

Chapter 17, I’ve assumed an annual fxed cost o

Let’s assume a price of $3.00. The question is h

each year to break even.

138

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 18-1

We’ll use this data to set up the Goal Seek feature t

To start, insert any number for demand in cell D

tab, click Goal Seek. Now fll in the Goal Seek d

Fig

URE 18-2

The Goal Seek dialog box flled in with entries for a b

The dialog box indicates that I want to change c

(proft) hits a value of 0. After I click OK, I g

approximately 17,647 glasses of lemonade per yea

fnd the value I’m seeking, Excel varies the dema

low values) until it fnds a value that makes pro

solution, Goal Seek will still display only one a

We want to pay off our. The

mortgage

annual interest

15 years

. The rate i

bank told us we can afford . monthly

How muchpayments

can we borr

of $

You can begin to answer this question by setting u

payments on a 15-year loan (let’s assume payment

of the annual interest rate and a trial loan amo

Paymentgs.xlsx and in Figure 18-3.

In cell E6, the formula –PMT(annual_int_rate/12,

._borrowed)

computes th

payment associated with the amount borrowed, whi

Seek dialog box as shown in Figure 18-4 calculat

monthly payments equal to $2,000. With a limit o

borrow up to $237,007.03.

Chapter

The

18Goal Seek Command

139

Fig

URE 18-3

You can use data such as this with the Goal Seek f

borrow based on a set monthly payment.

Fig

URE 18-4

The Goal Seek dialog box set up to calculate the m

I always had trouble with “story

. Can

problems”

Excel make

in hs

story problems easier?

If you think back to high school algebra, most

variable (usually

) that

it solved

was called

particular

equati

solver, so it’s perfectly suited to solving st

problem:

Maria and Edmund have a lover’s quarrel while h

her Mazda Miata and drives 64 miles per hour t

hours after Maria leaves, Edmund jumps into hi

hour. How many miles will each person have trav

You can fnd the solution in the fle Maria.xlsx

Fig

URE 18-5

Goal Seek can help you solve story problems.

The Set Cell will be the difference between th

You can set this to a value of 0 by changing th

Edmund drives two hours less than Maria.

140

Microsoft Excel 2010: Data Analysis and Business Modeling

I entered a trial number of hours that Maria dri

names in the cell range C2:C8 with cells D2:D8. B

Maria, in cell D4 I entered

. the

In cells

formula

Time_Mar

and D7, I u

fact that

distance=speed*time

to compute the tot

difference between the distances traveled by Edm

the formula

Maria_distance–Edmund_distance

. Now I can fll in the Goal S

shown in Figure 18-6.

Fig

URE 18-6

The Goal Seek dialog box flled in to solve an alge

I change Maria’s hours of driving (cell D2) unti

by Edmund and Maria (cell D8) equals 0. As you c

Edmund 8 hours, they will each have driven a dis

Problems

From Problem 1 in Chapter 17, determine how m

break even.

From the car net present value (NPV) example i

what rate do annual sales need to grow for tot

What value of Year 1 unit cost would increase o

to $1 million?

In our mortgage example, suppose I need to bo

maximum payments are limited to $2,000 per mo

can I tolerate?

How could I use Goal Seek to determine a proj

At the end of each of the next 40 years, I’m g

fund. What rate of return on my investments d

available for retirement in 40 years?

I expect to earn 10 percent per year on my re

of the next 40 years, I want to put the

same a

folio. How much money do I need to put in eac

account when I retire?

Chapter

The

18Goal Seek Command

141

Consider two projects with the following ca

Year 1Year 2Year 3Year 4

Project 1 –$1,000

$400

$350

$400

Project 2 –$900 $100

$100

$1,000

For what rate of interest will Project 1 ha

that makes both projects have the same NPV.)

I am managing a conference at my college. M

10 speakers $700 each, and the college unio

and lodging costs. I am charging each confe

$900, which includes the conference fee and th

paid registrants need to attend for me to b

10.

I am buying 40 pounds of candy. Some of the c

sells for $6 per pound. How much candy at e

average cost of $7 per pound?

11.

Three electricians are wiring my new home. E

do the job. Electrician 2 by himself will

self will need 9 days to do the job. If all th

the job take to complete?

12.

To celebrate the Lewis and Clark Expedition

40 miles downstream in a canoe. The speed o

the trip takes me 5 hours total, how fast d

13.

In the NPV.xlsx fle in Chapter 8, “Evaluatin

Criteria,” we found that for high interest r

interest rates Project 2 has a larger NPV. F

have the same NPV?

143

Chapter 19

Using the Scenario M

Sensitivity Analysi

Question answered in this chapter:

■

I’d like to create best, worst, and most-lie

by varying the values of Year 1 sales, annu

tables for sensitivity analysis allow me to v

data table. Does Excel have a tool I can us

analysis?

You can use the Scenario Manager to perform se

input cells. With the Scenario Manager, you fr

vary. Next, you name your scenario and enter f

Finally, you select the output

) that cells

you want

(also

to cal

Manager then creates a beautiful report contai

cells for each scenario.

Answer to This Chapter’s Quest

I’d like to create best, worst, and most-likel

varying the values of Year 1 sales, . annual

Data tabl

sal

for sensitivity analysis allow me to vary . only o

Does Excel have a tool I can use to vary more t

Suppose you want to create the following three s

(NPV) of a car, using the example in Chapter 1

Year 1 sales

Annual salesYear

growth

1 sales price

Best case$20,000 20%

$10.00

Most likely

$10,000

case 10%

$7.50

Worst case$5,000 2%

$5.00

For each scenario, you want to look at the frm

work is in the fle NPVauditscenario.xlsx. Figu

in the

Original Model

worksheet), and Figure 1

the

Scenario Summary

worksheet).

144

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 19-1

The data on which the scenarios are based.

Fig

URE 19-2

The scenario summary report.

To begin defning the best-case scenario, display th

Manager on the What-If Analysis menu in the Data T

and fll in the Add Scenario dialog box as shown i

Chapter

Using

the Scenario Manager

145

for Sensitivity Analysis

Fig

URE 19-3

Data inputs for the best-case scenario.

Enter a name for the scenario (Best), and sele

that defne the scenario. After you click OK in th

Values dialog box with the input values that d

Fig

URE 19-4

Defning the input values for the best-case scena

By clicking Add in the Scenario Values dialog b

and worst-case scenarios. After entering data f

Values dialog box. The Scenario Manager dialog b

I created. When you click Summary in the Scena

result cells that will be displayed in scenari

Scenario Summary dialog box that I want the sc

after-tax proft (cells B17:F17) as well as tot

146

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 19-5

The Scenario Manager dialog box displays each scen

Fig

URE 19-6

Use the Scenario Summary dialog box to select the r

Because the result cells come from more than one r

B19 with a comma. (I could also have used the Ctr

After selecting Scenario Summary (instead

- of the P

ates the beautiful Scenario Summary report pictu

includes a column, ,labeled

for the

Current

values

Values

that were ori

worksheet. The worst case loses money (a loss of $

proftable (a proft of $226,892.67). Because the wo

the worst case loses money in each year.

Remarks

■

The Scenario PivotTable Report option on the S

the scenario results in a PivotTable format.

■

Suppose you select a scenario in the Scenario M

Show button. The input cells’ values for

the s

sheet, and Excel recalculates all formulas. T

of your scenarios.

Chapter

Using

the Scenario Manager

147

for Sensitivity Analysis

■

It’s hard to create a lot of scenarios with th

to input each individual scenario’s values.

“Introduction to Monte Carlo Simulation”) m

Using the Monte Carlo simulation method, yo

probability that the NPV of a project’s

cas

sure because it is the probability that the p

■

Clicking the minus (–) sign in row 5 of the S

Assumption cells and show only results. Cli) s

report.

■

Suppose you send a fle to several people, a

After each person returns the fle containin

the scenarios into one workbook by opening e

clicking the Merge button in the Scenario

book, and then selecting the workbooks cont

Excel merges the selected scenarios in the o

Problems

Delete the best-case scenario and run anoth

Add a scenario ,named

in which

High

Year

Price

1 price equal

inputs remain at their most-likely values.

For the lemonade stand example in Chapter 1, “

use the Scenario Manager to display a repor

scenarios:

Scenario

Price

Unit cost

Fixed cost

High cost/high $5.00

price

$1.00

$65,000.00

Medium cost/medium

$4.00price

$0.75

$45,000.00

Low cost/low price

$2.50

$0.40

$25,000.00

For the mortgage payment example in Chapter 1

a report tabulating monthly payments for th

Scenario

Amount borrowed

Annual rate

Number of monthly

payments

Lowest payment

$300,000

360

Most-likely $400,000

payment

240

Highest payment

$550,000

180

149

Chapter 20

The COUNTIF, COUNTI

COUNTA, and COUNTBL

Functions

Questions answered in this chapter:

■

Suppose I have a list of songs that were pl

singer, the date the song was played, and th

questions such as these about the songs in th

❑

How many were sung by each singer?

❑

How many were not sung by my favorite sin

❑

How many were at least four minutes long?

❑

How many were longer than the average len

❑

How many were sung by singers whose last n

❑

How many were sung by singers whose last n

❑

How many were played after June 15, 2005?

❑

How many were played before 2009?

❑

How many were exactly four minutes long?

❑

How many were sung by my favorite singer a

❑

How many were sung by my favorite singer a

In a more general context, how do I perform op

■

Count the number of cells in a range contai

■

Count the number of blank cells in a range.

■

Count the number of nonblank cells in a ran

You often need to count the number of cells in a r

example, if a worksheet contains information a

the number of sales transactions made by the s

sales transactions that

COUNTIF

occurred

function

after June

lets

ber of cells in a range that meet criteria tha

of the worksheet.

150

Microsoft Excel 2010: Data Analysis and Business Modeling

The syntax of the COUNTIF

range,criterion)

function

COUNTIF(

■

Range

is the range of cells in which you want t

■

Criterion

is a number, date, or expression th

in the range.

The syntax

COUNTIFS

COUNTIFS(range1,criterion1,range2,cri

COUNTIFS counts the number of rows for

, the

which the

range2

entry ,

meets

the

range_n

criterion2

entry

, and

meets

so on.

criterion

Thus,

COUNTIFS allows the criteria to involve more tha

column. Other functions that allow for multiple c

SUMIF, AVERAGEIF, SUMIFS, and AVERAGEIFS Functio

with Database Statistical Functions.”

The key to using the COUNTIF function

understanding

(and simil

the wide variety of criteria that Excel accepts. T

explained through the use of examples. In additi

provide examples of the COUNT, COUNTA, and COUNT

■

The COUNT function counts the number of cells i

■

The COUNTA function counts the number of nonb

■

The COUNTBLANK function counts the number of

As an illustration of how to use these functions

information for each song played on radio statio

■

The singer

■

The date the song was played

■

The length of the song

The fle Rock.xlsx, shown in Figure 20-1, shows a s

Chapter

The

20COUNTIF, COUNTIFS, COUNT, COUNTA,

151

and COUNTBLANK Functions

Fig

URE 20-1

The song database used for the COUNTIF examples.

Answers to This Chapter’s Ques

How many songs were sung by each singer?

To begin, I selected the frst row of the datab

whole database by pressing Ctrl+Shift+Down Arr

the Formulas tab, I clicked Create From Selecti

range D7:D957

, the

Song

range

Numb

,E7:E957

the range

Singer

, F7:F957

and the

Dat

G7:G957 .

Minutes

To determine how many songs were sung by e

C5 to C6:C12 the formula

. In

COUNTIF(Singer,B5)

cell C5, this formula

ber of cells in the range

Singer

that match th

114 songs sung by Eminem. Similarly, Cher sang 1

Figure 20-2. I could have also found the numbe

COUNTIF(Singer,”Eminem”)

. Note that you must enclose text s

marks (“ “) and that criteria are not case sen

Fig

URE 20-2

Using COUNTIF to determine how many songs were s

152

Microsoft Excel 2010: Data Analysis and Business Modeling

How many songs were not sung by Eminem?

To solve this problem, you need to know that Exc

as “not equal to.” The formula

, entered

COUNTIF(Singer,”<

cell C15, te

that 837 songs in the database were not sung by E

need to enclose

<>Eminem

in quotation

marks

)

beca

character combination as text and

Eminem

is, of c

result by using the formula

, which

COUNTIF(Singer,”<>”&B

uses

the

) symbol

ampersan

to concatenate the reference to cell B5 and the

Fig

URE 20-3

You can combine the COUNTIF function with the not-e

How many songs were at least four minutes long?

In cell C16, I computed the number of songs play

the formula

COUNTIF(Minutes,”>=4”)

. You need to enclose

>=4

in quot

the greater than

) character

or equal combination,

to, (is treated

as text

see that 477 songs lasted at least four minutes.

How many songs were longer than the average leng

To answer this question, I frst computed in cell G

formula

AVERAGE(Minutes)

. Then, in cell C17, I computed the n

longer than the average with the

. Iformula

can refer

COUNTIF

to a

cell (in this case G5) in the criteria by using th

longer than average, which matches the number of s

reason these numbers match is that I assumed the l

song to last at least 3.48 minutes, it has to la

How many songs were sung by singers whose last n

To answer this question, I used a wildcard chara

represents any sequence of characters. Thus, the f

picks up any song sung by a singer whose last na

sensitive.) Two hundred thirty-two songs were su

with S. This number is simply the total of the s

Spears

103+129=232

( ).

Chapter

The

20COUNTIF, COUNTIFS, COUNT, COUNTA,

153

and COUNTBLANK Functions

How many songs were sung by singers whose last n

In this example, I used the question mark (?) w

any character. Therefore, entering the formula

the number of songs sung by singers having six l

(Two singers have last names of six characters

sang a total

129+114=243

of 243

.)songs—

How many songs were played after June 15, 2005

The criteria you use with COUNTIF functions ha

serial number. (A later date is considered lar

COUNTIF(Date,”>6/15/2005”)

in cell C20 tells y

June 15, 2005.

How many songs were played before 2009?

Here, we want our criteria to pick up all date

in cell C21 the formula

COUNTIF(Date,”<=12/31/

. You can see that 951 s

turns out to be all the songs) were played bef

How many songs were exactly four minutes long?

In cell C22, I computed the number of songs la

COUNTIF(Minutes,4)

. This formula counts the number

- of c

ing a 4. As you can see, 247 songs lasted exac

shows that 230 songs lasted exactly fve minute

How many songs played were sung by Bruce Sprin

long?

We want to count each row where an entry in th

entry in the Minutes

. Sincecolumn

this question

involves m

is a job for the wonderful COUNTIFS function. S

=COUNTIFS(Singer,”Springsteen”,Minutes,4)

This formula counts any row in which

. Singer

Bruce

Springsteen sang 24 songs that were exactly fo

is “Thunder Road,” but that song is more than f

function wizard to input formulas involving th

can paste range names into your formula with th

How many songs played were sung by Madonna and w

Because we are dealing with multiple criteria,

C25 the formula

=COUNTIFS(Singer,”Madonna”,Min

in which Madonna sang a song that was from thr

154

Microsoft Excel 2010: Data Analysis and Business Modeling

the rows we want to count. It turns out that Mad

four minutes long. (My favorite one is “Crazy fo

How do I count the number of cells in a range co

The COUNT function counts the number of cells in a r

example, the formula

COUNT(B5:C14)

in cell C2 di

C5:C13) in the range B5:C14 contain numbers. (Se

How do I count the number of blank cells in a ra

The COUNTBLANK function counts the number of bla

formula

COUNTBLANK(B5:C14)

entered in cell C4 re

and C14) in the range B5:C14 contain blanks.

How do I count the number of nonblank cells in a r

The COUNTA function returns the number of nonbla

formula

COUNTA(B5:C14)

in cell C3 returns 18 bec

blank.

Remarks

In the remainder of the book I discuss alternati

or more criteria (such as how many Britney Spear

■

Database statistical functions are discussed i

Database Statistical Functions.”

■

Array formulas are discussed in Chapter 83, “

Problems

The following questions refer to the fle Rock.xl

How many songs were not sung by Britney Spear

How many songs were played before June 15, 20

How many songs were played between June 1, 20

difference between two COUNTIF functions.

How many songs were sung by singers whose las

How many songs were sung by singers

whose nam

Create a formula that always yields the numbe

TODAY() function.

Chapter

The

20COUNTIF, COUNTIFS, COUNT, COUNTA,

155

and COUNTBLANK Functions

For the cell range D4:G15, count the cells c

number of blank cells. Count the number of n

How many songs sung by Barry Manilow were p

How many songs at least four minutes long a

2007 or earlier?

10.

How many songs exactly three minutes long a

later than 2004?

11.

The fle NBA.xlsx contains the following inf

❑

Columns A and B contain the name of each N

each team. For example, Team 1 is Atlanta

❑

Column C contains the home team for each g

❑

Column D contains the visiting team for e

❑

Column E contains points scored by the ho

❑

Column F contains points scored by the vi

From this data, compute the number of games p

12.

The fle Matchthesecond.xlsx gives a list of n

than once. You need to determine the -row in w

rence of the name “Dave” occurs. Set -up a w

son’s name and a positive

) and returns

integer the

(such

rowasin

occurs th

fortime.

the

13.

The Numbers.xlsx

fle

contains a set of numbers.

between 1 and 12 inclusive.

157

Chapter 21

The SUMIF, AVERAGEI

AVERAGEIFS Function

Questions answered in this chapter:

■

I’m a sales manager for a makeup company an

transaction the following information: sale

total price received (or paid out for retur

❑

What is the total dollar amount of mercha

❑

How many units were returned?

❑

What is the total dollar amount of sales i

❑

How many units of lip gloss were sold? How m

bring in?

❑

What is the total dollar amount of sales m

salesperson?

❑

What is the average number of units sold i

salesperson?

❑

What is the total dollar amount of lipsti

❑

What is the average quantity (in units) o

salesperson?

❑

Among transactions involving at least 50 u

lipstick in each sale made by a specifc s

❑

Among transactions of more than $100, wha

sold by a specifc salesperson? What about t

If you want to sum all the entries in one colu

another column (or row), the SUMIF function ge

function

range,criterion,[sum

SUMIF(

range])

■

Range

is the range of cells that you want t

■

Criterion

is a number, date, or expression th

sum range is added.

■

Sum range

is the range of cells that are ad

be the same

range

158

Microsoft Excel 2010: Data Analysis and Business Modeling

The rules for criteria you can use with the SUMI

the COUNTIF function. For information about the C

COUNTIF, COUNTIFS, COUNT, COUNTA, and COUNTBLANK F

The AVERAGEIF function has the syntax.

AVERAGEIF(

AVERAGEIF averages the range of cells meeting a c

Microsoft Excel 2010 includes three functions (i

to flag rows that involve multiple criteria: COUNT

AVERAGEIFS. Other functions that you can use to d

are discussed in Chapter 45, “Summarizing Data w

functions (see Chapter 83, “Array Functions and F

calculations involving multiple criteria.

The syntax of SUMIFS is

SUMIFS(sumrange,range1,c

criterionN)

. SUMIFS sums up every entry in the

sumrang

range1

criterion2

(based

…

iterionNrange2

(based

) are on

all

rangeN

satisfed

similar fashion, the AVERAGEIFS function has the s

criterion1,range2,criterion2,…,rangeN,criterionN

. AVERAGEIFS averages every e

sumrange

for which

criterion1

criterion2

(based

…

iterionN

range1

ran

(based on

) are

rangeN

all satisfed.

Answers to This Chapter’s Quest

What is the total dollar amount of merchandise s

The work for the problems in this chapter is in th

subset of the data.

Fig

URE 21-1

Data we’ll use for SUMIF examples.

Chapter

The

21SUMIF, AVERAGEIF, SUMIFS, and

159

AVERAGEIFS Functions

As usual, I begin by labeling the data in colu

in cells G4:L4. For example, the range name

compute the total amount sold by each salesper

B5 to B6:B13 the formula

. This

SUMIF(Name,A5,Dollars

formula adds up e

Dollars column that contains the name

Emilee

sold $25,258.87 worth of makeup. Of course, th

would yield the same result.

Fig

URE 21-2

Results of SUMIF computations.

How many units were returned?

In cell B16, the formula

SUMIF(Units,”<0”,Unit

column (column K). The result is –922. Inserti

shows that 922 units were returned. (Recall th

from a SUMIF function, Excel assumes

. Therefore,

that

sum

the

formula –SUMIF(Units,”<0”) would also yield 92

What is the total dollar amount of sales in or a

In cell B17, the formula

SUMIF(Date,”>=1/1/200

column (column L) that contains a date on or a

shows that $157,854.32 worth of makeup was sol

How many units of lip gloss were sold? How muc

In cell B18, the formula

SUMIF(Product,”lip gl

that contains the text

lip gloss

in the Produc

160

Microsoft Excel 2010: Data Analysis and Business Modeling

units of lip gloss were sold. This is the net sa

gloss were returned are counted as negative sale

In a similar fashion, in cell B19 the formula

a net amount of $49,834.64 worth of lip gloss wa

associated with returns as negative revenue.

What is the total dollar amount of sales made by s

In cell B20, the formula

SUMIF(Name,”<>Jen”,Doll

transactions that do not have

Jen

in the Name co

Jen sold $211,786.51 worth of makeup.

What is the average number of units sold in each t

salesperson?

This is a job for the AVERAGEIF function. Enteri

=AVERAGEIF(Name,”Jen”,Units)

averages every entr

the Name column. Jen’s average transaction size wa

with the formula

=SUMIF(Name,”Jen”,Units)/COUNTI

What is the total dollar amount of lipstick sold b

This calculation

Name=”Jen”

involves two

andcriteria

Product=”lipstick

). Therefore,

(

you need to compute the quantity you’re looking f

=SUMIFS(Dollars,Name,”Jen”,Product,”lipstick”)

. The total dollar amount o

which Jen sold lipstick is $3,953.

What is the average quantity (in units) of lipst

This calculation requires the AVERAGEIFS functio

the formula

=AVERAGEIFS(Units,Name,”Zaret”,Produ

. For the sales tran

which Zaret sold lipstick, the average number of u

Among transactions involving at least 50 units, w

each sale made by Zaret?

Here again I used AVERAGEIFS, but I added a crit

transaction was at least 50. In cell B23, I ente

”Zaret”,Product,”lipstick”,Units,”>=50”)

. In all transactions in which Z

of lipstick, the average transaction size is 68 u

Among transactions of more than $100, what is th

Jen? What about transactions of less than $100?

Because the criteria

Product=lipstick

, and

Name=Jen

some statement about t

of each order, you need to use the SUMIFS functi

Chapter

The

21SUMIF, AVERAGEIF, SUMIFS, and

161

AVERAGEIFS Functions

in transactions in which Jen sold lipstick and th

formula

=SUMIFS(Dollars,Name,”Jen”,Product,”li

. Jen sold $3,5

worth of lipstick in such transactions. In lip

see in cell B25 (the formula is

=SUMIFS(Dollar

that the answer is $370. Note that

$370+$3,583

lipstick sales (computed in cell B21).

Problems

For each product, determine the total numbe

Determine the total revenue earned before D

Determine the total units sold by salespeop

Determine the total revenue earned by peopl

How many units were sold by people other th

How many units of makeup were sold from Jan

February 15, 2005?

The fle NBA.xlsx contains the following inf

❑

Columns A and B list the name of each NBA t

team. For example, team 1 is Atlanta, and s

❑

Column C lists the home team for each gam

❑

Column D lists the visiting team for each g

❑

Column E lists points scored by the home t

❑

Column F lists points scored by the visiti

From this data, compute for each team the a

per game and the average number of points th

The fle Toysrus.xlsx contains sales revenue (

for the years 1997–2001 and the frst two qu

seasonal index

for each quarter of the year

quarter were 80 percent of the overall aver

have a seasonal index of 0.8.

The fle Sumifrows.xlsx contains sales data d

fall quarters. Determine average sales duri

quarters.

10.

Again using the fle Makeup2007.xlsx, how muc

transactions involving at least 50 units of m

162

Microsoft Excel 2010: Data Analysis and Business Modeling

11.

How many units of lip gloss did Cici sell in 2

12.

What is the average number of units of founda

13.

What is the average dollar size of a foundati

2004?

14.

In transactions in which Ashley sold at least 4

amount?

15.

Create a table that contains sales of each pr

16.

Create a table that, when you enter a year in y

product by person during that year.

17.

For the fle Numbers.xlsx. fnd the total of al

18.

For the fle Numbers.xlsx fnd the average of a

163

Chapter 22

The OFFSET Function

Questions answered in this chapter:

■

How can I create a reference to a range of c

columns from a cell or another range of cel

■

How can I perform a lookup operation based o

range instead of the left-most column?

■

I often download software product sales inf

revenues from Iran as well as costs and uni

in the same location in the worksheet. Can I c

Iran’s revenues, costs, and units sold?

■

Each drug developed by my company goes thro

have a list of the cost by month for each d

each development stage. Can I create formul

cost incurred during each stage of developm

■

I run a small video store. In a worksheet, m

movie and the number of copies in stock. Un

in one cell for each movie. How can I extra

stock to a separate cell?

■

How does Excel’s Evaluate Formula feature w

■

How can I write a formula that always retur

■

How can I set up a range name that automati

■

I am charting my company’s monthly unit sal

recent month’s unit sales. I would like my c

way to accomplish this?

The OFFSET function is used to create a refere

rows and columns away from a cell or range of c

range of cells, you frst specify a reference c

columns away from the reference cell that you wa

using the OFFSET function, I can create a refe

three columns and begins two columns to the ri

can calculate the specifed number of rows and c

using other Excel functions.

The syntax of the OFFSET function is

OFFSET(re

moved,height,width)

164

Microsoft Excel 2010: Data Analysis and Business Modeling

■

Reference

is a cell or range of cells from whi

of cells, the cells must be adjacent to each oth

■

Rows moved

is the number of rows away from th

the range reference to start (the upper-left c

of rows moves you up from the reference; a po

For example, if

reference

equals C5 and

rows m

rows moved

equals +1, you move to row 6. If

■

Columns moved

is the number of columns away f

you want the range reference to start. A nega

from the reference; a positive number of colu

reference

equals C5 and

columns moved

equals –

moved

equals +1, you move to column D. If

colu

column C.

■

Height

and

width

are optional arguments that g

in the offset range. If

height

width

is omi

for which the value of

height

width

equals th

or range.

Answers to This Chapter’s Quest

How can I create a reference to a range of cells t

columns from a cell or another range of cells?

The fle Offsetexample.xlsx, shown in Figure 22-1

function in action.

Fig

URE 22-1

Using the OFFSET function.

Chapter

The

22OFFSET Function

165

For example, in cell B10, I entered the .formul

This formula begins in cell B7. It moves one r

brings us to cell C6. The formula now selects a r

which yields the range C6:C7. The SUM function a

2+6=8

. The other two examples shown in Figure 22

sections, I’ll show you how to apply the OFFSE

me by former students working at major U.S. co

How can I perform a lookup operation based on t

instead of the left-most column?

In Figure 22-2 (see the workbook Lefthandlooku

2003 Dallas Mavericks NBA basketball team and th

to fnd the player with a specifc feld goal per

using a VLOOKUP function. But

left-hand

what I lookup,”

really

waw

volves fnding the feld goal percentage for a p

can’t perform a left-hand lookup, but a left-h

and OFFSET functions.

Fig

URE 22-2

You can do a left-hand lookup by using the MATCH a

First, I enter the player’s name in cell D7. T

percentage column header) in the OFFSET functi

percentage, I need to move down to the row bel

This is a job for the MATCH function. The MATC

OFFSET(B7,MATCH(D7,$C$8:$C$22,0),0)

moves down t

player’s name and then moves over 0 columns. B

omitting the

height

and

width

arguments of the O

returned by this formula is also one cell. Thu

166

Microsoft Excel 2010: Data Analysis and Business Modeling

I often download software product. I

sales

need informat

to trac

revenues from Iran as well as costs and units so

the same location. Can

in the

I create

worksheet

a formula that wi

revenues, costs, and units sold?

The fle Asiansales.xlsx (see Figure 22-3) contai

variable cost for software sold to several countr

when you download the monthly fnancial reports, t

worksheet changes, so you need formulas that alwa

units sold, revenue, and variable cost.

Fig

URE 22-3

You can use the OFFSET function in calculations whe

in the same location in a worksheet.

By copying from D21 to E21:F21 the formula

OFFSE

you can compute the result you want. This- formul

tains the words

Country/Region

Then it moves over one column (

sold and down to the row containing the country l

D20 now refers to E20 and becomes a 2, so you mo

umn C to fnd revenue. In cell E21, the reference t

so you move three columns to the right of column C t

Each drug developed by my company goes. I

through

have

a list of the cost by month for each drug, and I a

opment stage took

. Can

forIeach

create

drug

formulas that comp

total cost incurred during each stage of develop

The fle Offsetcost.xlsx contains the monthly cos

each drug, the number of months required to comp

shown in Figure 22-4.

Chapter

The

22OFFSET Function

167

Fig

URE 22-4

Using the OFFSET function to compute development c

The goal is to determine for each drug the tot

phase. In cells D4:D6, I compute the total dev

compute Phase 1 costs for Drug 1 by using a ce

columns moved

equal to 0. Setting

height

equal t

width

equal to 1 captures all Phase 1 costs. I c

with the formula

SUM(OFFSET(D10,0,0,D1,1))

. Next, in cell D5, I comp

for Drug 1 by using the formula

. Note

SUM(OFFSET(D10

that I start w

reference of D10 (the frst month of costs) and m

length of Phase 1. This brings me to the begin

value in cell D2 ensures that I include all Ph

development costs for Drug 1 by using .the

In form

this

formula, I start from the frst month of sales a

the total time needed for Phases 1 and 2. This b

in cell D3, I total the number of rows

formulas

to capt

in D4:D6 to E4:H6, I can compute total costs f

example, for Drug 2, total Phase 1 costs equal $

Phase 3 costs equal $876.

I run a small

. In

video

a worksheet,

store

my accountant has l

movie and the number. Unfortunately,

of copies in stock

he combine

into one cell . for

How each

can Imovie

extract the number of c

stock to a separate cell?

The fle Movies.xlsx, shown in Figure 22-5, con

of copies in stock.

168

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 22-5

Movie example using the OFFSET function.

I want to extract the number of copies owned of e

of copies were listed to the left of a movie’s ti

the FIND function to locate the frst space and th

data to the left of the frst space. (See Chapter 6

use the LEFT and FIND functions, as well as othe

Unfortunately, this technique doesn’t work when th

the movie title. For a one-word movie title, for e

of the frst space, but for a four-word movie titl

fourth space.

One way to solve this problem is to click the Da

group, click Text To Columns to place each word i

separate columns. You can use the COUNTA functio

title, including the number of items as a word, f

function to locate the number of items.

To begin, insert enough columns to the

movies’

right of th

titles and the number of items to be extracted t

(

Raiders of the Lost Ark

requires six columns), a

the cell range C2:C12, and click Text To Columns o

Convert Text To Columns Wizard and use the space c

After selecting cell D2 as the destination cell, I h

of Figure 22-5.

Now I count the number of words in each movie’s c

word) by copying from A2 to A3:A12

. The results

the formula

are s

Figure 22-5.

Finally, copying from B2 to ,

B3:B12

I canthe

locate

formula

the n

copies of each movie in stock. This formula begi

title and moves over the number of columns equal t

Because the reference cell contains only one cel

of the OFFSET function so that the function uses o

number of copies) of the title cell.

Chapter

The

22OFFSET Function

169

How does Excel’s Evaluate Formula feature work

If you select any portion of a cell formula

createdan

by that portion of the formula. You must press E

debugging and understanding complex formulas

derstand what the OFFSET portion of the formul

the formulas in this chapter. For example, in th

Phase 1 cost with the formula

. If

=SUM(OFFSET(E10,

you move the cu

OFFSET(E10,0,0,E1,1),

highlight

and then

this

select

part F9,

of th

=SUM({135,120,58}),

which indicates that the O

the correct cells (D10:D12). Be sure you press

formula!

Another way to see how a complex formula works i

Move the cursor to E4 and click the Formulas t

group, click Evaluate Formula. (See Figure 22-

magnifying glass), and Excel simplifes the for

fnal result. After clicking Evaluate twice, th

know that in cell E4 you have selected the Pha

Fig

URE 22-6

Evaluate Formula dialog box.

How can I write a formula that always returns t

You often download new data into a worksheet. C

sales during

las most

therecent month? (See the fle Mos

170

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 22-7

Finding the last number in a column.

Simply enter in cell D4 the formula

OFFSET(B6,CO

This formula begins in cell B6 and moves down a n

numerical entries in column B. This takes you to th

selected because

1,1

returns only one cell.

How can I set up a range name that automatically i

Users of Excel often add rows or columns

create

of data t

a PivotTable or to perform another type of analy

of cells referred to in their formula and then r

dynamic range names and never have to update the r

PivotTable. The range will automatically update. H

The fle Dynamicrange.xlsx shows entries from an H

Fig

URE 22-8

Example of a dynamic range.

Currently, the data contains nine rows and four c

could create a range name that would automatical

when you add people or felds of information to th

Chapter

The

22OFFSET Function

171

To create a dynamic range, click the Formulas t

Name Manager. Then click New and defne a range a

Fig

URE 22-9

Creating a dynamic range.

The range starts in the upper-left corner: cel

cell A1. The selected range has

number of rows

number of columns=number

Thus,

nonblank

if you

entries

add pe

in r

felds, the formula will automatically expand t

so that the defned range will not shift if you m

To try this out, enter the formula

=SUM(data)

numbers in the range A1:D9 and yields $448,278

Now add to row 10,the

enter

name

Meredith

B10 a salary of $1

for Mistakes (add

), the

and word

in E10

Mistakes

enter 1,000. The f

includes the 10,000 and 1,000, and automatical

I am charting my company’s

. Eachmonthly Iunit

download

sales t

month’s unit

. I would

sales like my chart

. Is

to there

update

anauto

eas

accomplish this?

The workbook Chartdynamicrange.xlsx (see Figur

company’s product. As you can see, the units s

chart.

172

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 22-10

You can use the OFFSET function to update this cha

Beginning in row 19, you download new sales data

chart automatically includes the new data?

The key to updating the chart is to use the OFFS

for both the Months column and the Units

dynamic

Sold co

range for unit sales will automatically include a

months will include each month number. After cre

chart, replacing the data ranges used in the cha

updates as new data is entered.

To begin, click Defne Names on the Formulas tab o

dialog box. Create a range named

Units

by flling i

Fig

URE 22-11

Creating a dynamic range name for the units sold.

Entering

=OFFSET(‘dynamic range’!$C$3,0,0,COUNT(

dialog box creates a range one column wide begin

sales data point. The range will contain as many n

derived by the portion of the formula

. As

that

newreads

data

is entered into column C, the data is automatica

Chapter

The

22OFFSET Function

173

Next, create a dynamic range named Month for th

formula is shown in Figure 22-12.

Fig

URE 22-12

The formula used to defne a dynamic range named

Now go to the chart and click any point. In th

SERIES(‘dynamic range’!$C$2,’dynamic range’!$B

This formula is Excel’s version of the data or

the ranges $B$3:$B$18 and $C$3:$C18 with the d

SERIES(‘dynamic range’!$C$2,Chartdynamicrange.

Of course, if a blank space is listed above an

new data, and you’ll see that it is included i

Remarks

The Excel table feature makes it easy to set thi

automatically incorporate new data. See Chapte

Problems

The fle C22p1.xlsx contains data about unit s

1999–2003. Write a formula using the MATCH a

the sales of a given product during a given y

this problem without using the MATCH and OFF

174

Microsoft Excel 2010: Data Analysis and Business Modeling

A commonly suggested moving average trading r

moves above the average of the last

months a

below the average of the last

months. In Ch

for ,

D=15

this trading rule outperformed the Stan

amount. By combining a one-way data table with th

value of

that maximizes trading proft (excl

pertinent data in the fle Matradingrule.xlsx.

A commonly suggested moving average trading r

moves above the average of the last

months a

the average of the last

months. In Chapter 1

that for

, this

B=S=15

trading rule outperformed

the S

stantial amount. By combining a two-way data t

mine the values of

and

that maximize trad

You’ll fnd data for this problem in the fle M

The fle Lagged.xlsx contains data about the n

Army Recruiting during each of 60 consecutive

-month

lagged number of ads is defned to equal the n

months 7–60, you want to compute the 1-month l

6-month lagged values of the number of ads. U

compute these lagged values.

The fle Verizondata.xlsx gives sales of four d

regions. Determine an effcient method to ente

combinations, the region, type of phone, and s

This problem is a diffcult one. The fle Aging

claims projected to be received daily and the n

available. Each day, a worker can process up t

est claims in the system frst. Cells H6:AL6 c

system on January 1, before new claims arrive

of the claims. That is, for each day, how man

over 30-day old claims will be in the system.

Each row of the fle Tapesales.xlsx contains m

formula to determine sales for each tape duri

To obtain a golfer’s handicap, you average th

Then you subtract 80 and round to the nearest i

20 rounds adds up to 864, the handicap would b

golfer’s scores. Beginning in row 24, compute th

Assume that if the tenth best score in the la

all rounds including that score will be inclu

the Excel function

=ROUND(x,0)

will round

Chapter

The

22OFFSET Function

175

Each row of the fle Carsumdata.xlsx contain

plane) from January thru July. Suppose you e

worksheet. Write a formula that gives the t

month.

10.

The fle Verizon.xlsx contains monthly retur

function to extract all the January returns t

one column, and so on.

11.

The fle Casesensitive.xlsx contains product c

product codes are case sensitive. For examp

dag32. Write a formula that gives the produ

Hint: You might need to use the EXACT functi

yields True if cell1 and cell2 have exactly th

between

uppercase and lowercase letters.

12.

The fle Reversed.xlsx contains a column of n

“reverse” the numbers so that the number on b

13.

The fle Diagonal.xls contains a matrix of n

elements of the matrix in a single column.

14.

The fle Yeartodate.xlsx contains a company’

2008–2014. Write a formula that returns for

cumulative sales to date. For example, if y

year, your formula should compute total sal

15.

Show how you might create a graph of monthly s

six months of sales.

16.

The fle Transactiondata.xlsx contains sales tr

a drug company. Use the OFFSET function to m

division appear in a single row.

177

Chapter 23

The INDIRECT Functi

Questions answered in this chapter:

■

My worksheet formulas often contain referen

change these references in my formulas, can I p

that I can easily change my cell or range r

formulas?

■

Each worksheet in a workbook lists monthly s

easy way to write and copy a formula that l

worksheet?

■

Suppose I total the values in the .

range

If I A5:

ins

a blank row somewhere between rows 5 and 10

SUM(A5:A11)

. How can I write a formula so that w

rows 5 and 10, my formula still totals the v

■

How can I use the INDIRECT function in a fo

a formula in a worksheet?

■

My workbook contains sales in each country f

can I easily pool this data in a single sum

The INDIRECT function is probably one of the m

master. Knowing how to use the INDIRECT functi

seemingly unsolvable problems. Essentially, an

portion of a formula results in the immediate e

content of the cell. To illustrate the use of I

which is shown in Figure 23-1.

Fig

URE 23-1

A simple example of the INDIRECT function.

In cell C4, I entered. the

Excel

formula

returns

=INDIRECT(A4)

the value 6 b

reference to A4 is immediately replaced by the t

=B4

, which yields the value 6. Similarly, e

returns the value in cell B5, which is 9.

178

Microsoft Excel 2010: Data Analysis and Business Modeling

Answers to This Chapter’s Quest

My worksheet formulas often contain

. Rather

references

than t

change these references in my formulas, can I pl

that I can easily change my cell or

underlying

range refere

formulas?

In this example, the data we’ll use is contained i

Figure 23-2. The cell range B4:H16 lists monthly s

12-month period.

I currently calculate total sales of each produc

this calculation is to copy from.C18

Suppose,

to D18:H18

howevth

that you want to change which months are totaled

for months 3–12. You could change the formula in c

this formula to D18:H18, but using this approach i

the formula in C18 to D18:H18 and, without looki

rows are being added.

Fig

URE 23-2

You can use the INDIRECT function to change cell re

formulas themselves.

The INDIRECT function provides another approach. I p

and ending rows of our summation. Then, by using th

is change the starting and ending row references i

include the rows I want. Also, by looking at the v

which rows (months) are being added. All I need t

formula

SUM(INDIRECT(C$3&$D$2&’’:’’&C$3&$E$2))

If you want to see how Excel evaluates a referen

following trick. Click in part

) andofthen press

formula

F9.(fE

you the value of the selected portion of the for

Chapter

The

23INDIRECT Function

179

Be sure to press Esc to return to Excel. Every c

this formula is evaluated to equal the content

evaluated as 6, and

$E$2

is evaluated as- 16. W

enation symbol, Excel evaluates

, which

this formula

exactly wa

The formula in C18 returns

. Inthe

cell

value

D18,

38+91+…69

the for

SUM(D6:D16)

, which is the result you want. -Of cour

ing months 4 through 6, you simply enter 8 in D

returns

33+82+75=190

. (For information about using the a

see Chapter 6, “Text Functions.”)

Each worksheet in a workbook lists. Is

monthly

there sal

an e

way to write and copy a formula that lists eac

The fle Indirectmultisheet.xlsx (see Figure 23

worksheet, cell D1 contains data about the sal

Let’s suppose Sheet1 contains Month 1 sales, S

For example, sales in Month 1 equals 1, in Mon

Fig

URE 23-3

Monthly sales (Months 1–7) of a product listed b

Now suppose you want to compile a list of each m

tedious approach would be to list , Month

1 2

sale

sales with the ,

formula

and so

=Sheet2!D1

on, until you -list Mon

mula

=Sheet7!D1

. If you have 100 months of data, this a

much more elegant approach is to list Month 1 s

INDIRECT($C$10&D10&’’!D1’’)

. Excel

C$10

evaluates

as “Sheet”,

D10

as “

the text string “!D1”. The whole

, which,

formula

of is

cours

Month 1 sales, located in cell D1 of Sheet1. C

the entries in cell D1 of Sheets 2 through 7. W

the reference to D10 changes to D11, and cell E

Suppose I total the values in the range

. If A5:A10

I inse w

a blank row somewhere between rows

automatically

5 and 10, mt

180

Microsoft Excel 2010: Data Analysis and Business Modeling

SUM(A5:A11)

. How can I write a formula so that when I i

and 10, my formula still totals the values in th

The worksheet named

SUM(A5A10)

in the fle Indire

illustrates several ways to total the numbers in

traditional formula

, which

SUM(A5:A10)

yields.

6+7+8+9+1+2=33

Similarly, the formula

SUM($A$5:$A$10)

in cell E

however, if you insert a row between rows 5 and 1

in the range A5:A11.

Fig

URE 23-4

Several ways to sum the values in the cell range A5

With the INDIRECT function, you have at least tw

A5:A10. In cell F9, I entered .the

Because

formula

Excel

SUM(IN

tre

INDIRECT(‘’A5:A10’’) ’

,as

’

ifthe

youtext

insert

string

a row

‘’

in th

formula still totals the entries in the cell ran

Another way to use the INDIRECT function to tota

formula

SUM(INDIRECT(‘’A’’&C4&’’:A’’&D4))

, which is the formula entere

treats the reference to C4 as a 5 and the refere

SUM(A5:A10)

. Inserting a blank row between row 5 and r

because the reference to C4 is still treated as a 5

a 10. In Figure 23-5, you can see the sums calcu

is inserted below row 7. You can fnd this data o

Indirectinsertrow.xlsx.

As you can see, the classic SUM formulas, which d

changed to add up the entries in the range A5:A1

The two SUM formulas that do use the INDIRECT fu

the range A5:A10, so the value of 2 (now in cell A

sum. The SUM formulas that use the INDIRECT func

Chapter

The

23INDIRECT Function

181

Fig

URE 23-5

Results of SUM formulas after inserting a blank r

How can I use the INDIRECT function in a formu

formula in a worksheet?

Suppose you have named several ranges in a wor

sales. (See Figure 23-6 and the fle Indirectra

Quarter1

) contains fctitious frst-quarter sales of v

Fig

URE 23-6

Use the INDIRECT function to create a reference t

It would be great to write a formula that can e

sales of each product in each quarter

worksheet,

in a sin

as shown in H17:J20. You would formula

think you could e

=VLOOKUP(H$16,$G17,2,FALSE)

and then copy this f

Unfortunately, Excel does not recognize $G17 a

Rather, Excel just thinks $G17 is the text str

returns an #NA error. To remedy this problem, s

=VLOOKUP(H$16,INDIRECT($G17),2,FALSE)

and then

182

Microsoft Excel 2010: Data Analysis and Business Modeling

works perfectly!

INDIRECT($G17)

is evaluated as Q

name. You have now easily generated sales of all p

My workbook contains sales in each country

. How

for e

can I easily pool this data in a single summary wo

Cells E7:E9 of the fle Indirectconsolidate.xlsx c

each continent. Each continent has its own works

single sheet?

In the worksheet Summary, I created the summary s

Fig

URE 23-7

Use the INDIRECT function to create a summary of pr

I copied from cell E7 to

INDIRECT(E$6&”!”&$C7)

the range. E7:I9

This formula

the for

creates the ,

formula

which calculates

=LA!E7

car sales in Lati

picks off the sales for each type of product on e

In the worksheet

Another Summary

(see Figure 23-

a slightly different manner. I automated the gen

which I pull car, truck, and plane sales by copy

ADDRESS(ROW(),COLUMN()+2)

. This generates column E in the c

8 and 9. The function ROW() entered in -a cell re

tion COLUMN() entered by itself in a cell return

this case 3). When entered as part of the third a

COLUMN()+2

effectively returns the column label f

current cell (in this case column E.) Then I cop

INDIRECT(E$6&”!”&$C7)

Fig

URE 23-8

Use the INDIRECT function to create a summary of p

Chapter

The

23INDIRECT Function

183

Problems

The ADDRESS function yields the actual cell a

For example, the formula

ADDRESS(3,4)

yield

you entered the formula?

=INDIRECT(ADDRESS(3

The workbook P23_2.xlsx contains data for th

(East, West, North, and South). Use the IND

enable you to easily calculate the total sa

numbered products, such as Products 1–3, Pr

The fle P23_3.xlsx contains six worksheets. S

1–4. These sales are always listed in the r

effciently tabulate the sales of each produ

Write a formula that will total the entries i

or more columns between columns G and K.

The fle Marketbasketdata.xlsx contains sale

columns B through K indicates a purchased i

not purchased. In the Day Week column, a 1 m

a 2 means the transaction was on a Tuesday, a

calculate the percentage of transactions

calcu

in w

late the fraction of transactions taking pl

The fle Verizonindirectdata.xlsx contains e

rating for January–May. Set up a consolidati

person and then reports that person’s hours o

or her overall rating for the month.

185

Chapter 24

Conditional Formatt

Questions answered in this chapter:

■

How can I visually indicate whether recent te

global warming?

■

How does the Highlight Cells conditional fo

■

How do I check or customize my rules?

■

How do data bars work?

■

How do color scales work?

■

How do icon sets work?

■

How can I color-code monthly stock returns s

one color and every bad month in another?

■

Given quarterly corporate revenues, how can I i

increased over the previous quarter in one c

decreased from the previous quarter in anoth

■

Given a list of dates, how can I indicate w

■

Our basketball coach has given each player a r

player’s ability to play guard, forward, or c

indicates the ability of each player to pla

■

What does the Stop If True option in the Man

Conditional formatting lets you specify format

contents of the cell range. For example,- given e

tional formatting to display in red the names o

90. Basically, when you set up conditions to f

checks each cell in the range to determine whe

exam

)

score>90

is satisfed. Then Excel applies the f

to all the cells that satisfy the condition. I

conditions, the formatting of the cell remains

ting was completely revised and expanded. Exce

conditional formatting. In this chapter, I show y

features in Excel 2010.

186

Microsoft Excel 2010: Data Analysis and Business Modeling

To view the conditional formatting options, frst s

Then, on the Home tab, in the Styles group, clic

Figure 24-1) to open a menu of conditional forma

Fig

URE 24-1

Conditional formatting command.

Fig

URE 24-2

Conditional formatting options.

■

Highlight Cells

allows

Rules

you to assign a format to ce

of the following criteria:

❑

Are within a specifc numerical range

❑

Match a specifc text string

❑

Are within a specifc range of dates (relati

❑

Occur more than once (or only once) in the s

■

Top/Bottom

allows

Rules

you to assign a format to any o

❑

largest or smallest values in a range

❑

Top or bottom

percent of numbers in a ran

❑

Numbers above or below the average of all th

■

Data Bars, Color

con Scales,

Sets

allow you

and

easily identif

intermediate values in the selected range. La

numbers. With color scales you might, for exa

red and larger values in blue, with a smooth tr

increase from small to large. With icon sets, y

identify different ranges of values. For exam

Chapter

Conditional

Formatting

187

up to indicate a large value, pointing to th

pointing down to indicate a small value.

■

New Rule

allows you to create your own formula t

have a specifc format. For example, if a ce

could apply the color green to the cell. If th

you could apply the color red to the cell, a

■

Clear Rules

allows you to delete all conditional f

selected range or for the entire worksheet.

■

Manage Rules

allows you to view, edit, and delete

create new rules, or change the order in whi

rules you have set.

Answers to This Chapter’s Questi

How can I visually indicate whether recent tem

global warming?

This question offers a perfect opportunity for a

formatting rules. The fle Globalwarming.xlsx (

temperatures for the years 1856–2005. -

(I hid th

peratures are deviations from a base level of 1

occurred, you would expect the numbers in rece

in earlier years. To determine whether recent y

B3:B152 containing the temperatures. On the Ho

Conditional Formatting and then selected Top/B

and flled in the dialog box as shown in Figure 2

Fig

URE 24-3

Highlighting the ten highest temperatures in red

Not

licking the arrow shown on the right side of F

including Custom Format. Selecting this option dis

allows you to create a custom format that is appli

is satisfed.

188

Microsoft Excel 2010: Data Analysis and Business Modeling

Next I selected the range B3:B152 again and went b

I selected Bottom 10 Items and chose to highligh

can see in Figure 24-4 that the 10 highest tempe

the 10 lowest temperatures occurred before

1865. I

lighted the top 10 percent of the temperatures i

Finally,

column

in D I highlighted above-average tempera

temperatures in red. Note that all years earlier th

whereas all years from 1990 and later have had a

formatting is a powerful tool that can be used t

reasons) seems to have recently become warmer.

Fig

URE 24-4

Conditional formatting using Top/Bottom Rules.

How does the Highlights Cells conditional format

The fle Highlightcells.xlsx (see Figure 24-5) de

is used. For example, suppose you want to highli

Simply select the cell range C2:C11, click Condi

Home tab, click Highlight Cells Rules, click Dup

With Dark Red Text. Click OK to apply the rule s

(John and Josh) are highlighted in red.

Chapter

Conditional

Formatting

189

FigureUsing

24-5 the Highlight Cells Rules option.

Now suppose that you want to highlight in red a

text “Eric”. Simply select the cell range D2:D

Cells Rules, and then click Text That Contains

Red Fill With Dark Red Text on the right. As s

highlighted. (Erica, of course, contains the t

Suppose you have a list of dates (such as in E

contains yesterday’s date in green and any oth

the worksheet

Right Way

in the fle Highlightce

current date is September 24, 2010.

TODAY()–1

Note

, so

that c

cell E3 always display yesterday’s date. Cell E

I began by selecting the cell range I want to f

Occurring option and then selected the Yesterd

Text. Then I clicked Conditional Formatting, Hi

Occurring. In the A Date Occurring dialog box, t

Light Red Fill With Dark Red Text. Formatting r

created earlier (unless you change the order o

This explains why 9/23/2010 is formatted in re

How do I check or customize my rules?

After creating conditional formatting rules, y

Rules on the Conditional Formatting menu. For e

click Conditional Formatting, click Manage Rul

Figure 24-6. You can see that the Last 7 Days f

Yesterday

formatting rule.

190

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 24-6

Conditional Formatting Rules Manager dialog box.

In the Conditional Formatting Rules Manager dial

■

Create a rule by clicking the New Rule button

■

Edit or change a rule by clicking the Edit Ru

■

Delete a rule by selecting it and then clicki

■

Change the order of precedence by selecting a r

down arrow.

To illustrate the use of the Conditional Formatti

previous worksheet (simply right-click the

works

lect the Create A Copy check box) to the

Right W

I selected the Yesterday rule and clicked the up a

precedence than the Last 7 Days rule, so E3 will b

shows how the Conditional Formatting Rules Manag

shows that cell E3 is green and cell E4 is red a

Fig

URE 24-7

Now Yesterday has a higher priority than Last 7 day

Chapter

Conditional

Formatting

191

Fig

URE 24-8

After I change the precedence of rules, yesterda

How do data bars work?

When you have a long list of numbers, it’s nic

easily identify large and small numbers.

introduced

Data b

in Excel 2007) are perfect tools for displayin

Scalesiconsdatabars.xlsx illustrates the use o

Figure 24-9 shows the use of data bars. I bega

in D6:D15. I selected the data in D6:D15, clic

Data Bars. Next I selected blue data bars and c

format shown in column D of Figure 24-9. Cells c

blue bars. The default option is to associate th

in the selected range and the longest data bar w

column D, the size of the data bars is directl

bar for 4 is twice as large as the data bar fo

Fig

URE 24-9

Visually distinguishing numeric values by using d

192

Microsoft Excel 2010: Data Analysis and Business Modeling

If, after clicking Data Bars, you click More Rul

in Figure 24-10 is displayed. (You can also disp

and then clicking Edit Rule or by double-clickin

change the criteria used to assign the shortest a

assigned the shortest bar to the number 3 and th

Figure 24-9, all numbers in column E that are le

numbers that are greater than or equal to 8 have th

3 and 8 have graduated bars. Note that in the Ed

select the Show Bar Only check box to display on

conditionally formatted cells.

Fig

URE 24-10

Customizing your data bars.

Next, in column F, I chose to assign the shortes

the range F6:F15, and the longest bar to numbers i

numbers

<=1+.2(10–1)=2.8

have the shortest data b

have the longest data bar. Figure 24-9 shows tha

shortest data bar and the numbers 9 and 10 have th

In the cell range G6:G13, I associated the short

twentieth percentile of the data (1), and I asso

or above the ninetieth percentile of the data (9

whether your data bars begin at the right or lef

Chapter

Conditional

Formatting

193

Excel 2010 introduces solid shading for data b

associated with negative values so that they r

The fle Negativedatabars.xlsx and Figure 24-11 s

set containing negative numbers.

Fig

URE 24-11

Data bars for negative values with both solid an

How do color scales work?

Now let’s use color scales to summarize some d

a color scale uses cell shading to display the d

example of a three-color scale. (The fle Color

the use of a three-color scale. Note that I hi

76, right-click the selection, and then click

T-Bills, and T-Bonds in cells B8:D89. I then c

then More Rules to display the Edit Formatting R

Figure 24-13.

I chose the color red to indicate the lowest r

orange to indicate the return at the midpoint. A

color shading of each cell based on the value i

lowest return is shaded red. Note that 1931 an

for stocks. As the returns approach the fftieth p

yellow. Then, as the returns increase from the f

the cell color changes from yellow to green. M

with stocks because annual stock returns are m

variability causes large and small stock retur

returns for T-Bills or T-Bonds are yellow beca

investments means that intermediate returns oc

194

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 24-12

Three-color scales.

Fig

URE 24-13

Customizing a three-color scale.

I created some two-color scales in the fle Scale

I selected the range of cells and then clicked C

select the color combination you want from the g

More Rules.

I chose a two-color scale that indicates lower v

■

In the cell range D19:D28, I chose to make th

blue. As numbers increase, the cell shading b

Chapter

Conditional

Formatting

195

■

In the range E19:E28, I chose to make value

greater than or equal to 8 blue. For number

the cell shading becomes darker.

■

In the range F19:F28, I chose to make values i

white and numbers in the top 20 percent blu

cell shading becomes darker as numbers incr

■

In G19:G28, I chose to make values at or bel

and values at or above the eightieth percen

becomes darker as numbers increase.

Fig

URE 24-14

Two-color scales.

How do icon sets work?

You can also display numerical differences by u

Scalesiconsdatabars.xlsx.) An icon set consist

associate an icon with each value in a cell ra

for small numbers, an up arrow for large

numbe

ate values. The cell range E32:F41 contains tw

column, I used the red down arrow, the yellow h

Fig

URE 24-15

Using an icon set.

196

Microsoft Excel 2010: Data Analysis and Business Modeling

Here is how I assigned icons to a range of numer

■

After selecting the numbers in E32:E41, I cli

then clicked More Rules and chose the 3 Arrow

list. In column E, I want numbers less than 4 t

to 8 to display a horizontal arrow, and numbe

accomplish this goal, I set the options in th

in Figure 24-16.

■

In a similar fashion, I set up a formatting r

cells containing numbers in the

80th

)

, and

percenti

down

arrows are placed in cells containing

values

numbers i

(

)

. Figure 24-17 displays the needed formatti

Fig

URE 24-16

Assigning icons to numerical values.

Fig

URE 24-17

Assigning icons to percentile values.

Chapter

Conditional

Formatting

197

Optional settings include Reverse Icon Order, w

numbers and the icons on the right with larger n

the contents of the cell. In Excel 2010 -you ca

tomize icon sets. In the worksheet

Excel 2010 I

icons to summarize investment returns. The top thi

arrow, the bottom third of the returns contain a d

for the middle third of the returns. Figure 24

shows the dialog box (accessed from Manage Rul

customized the three gray arrow icon set by re

Fig

URE 24-18

Customized icon set with hidden icon.

Fig

URE 24-19

Dialog box for customizing and hiding icons.

198

Microsoft Excel 2010: Data Analysis and Business Modeling

How can I color-code monthly stock returns so th

color, and every bad month in another?

The fle Sandp.xlsx, shown in Figure 24-20, contai

Standard & Poor’s stock index. Suppose that you wa

which the S&P index went up by more than 3 perce

which it went down more than 3 percent.

I began by moving to cell C10 (the frst month co

monthly returns by pressing Ctrl+Shift+Down Arrow

Manage Rules, New Rule, and selected Format Only C

dialog box as shown in Figure 24-21. I told Exce

>0.03 and, after clicking Format, I selected the f

Notice that the lists for fonts and font size ar

change these attributes. The Fill tab provides th

and the Borders tab lets you create a border for

After clicking OK in the Format Cells dialog box

dialog box. You can now select New Rule again, a

all cells containing numbers that are less than –

When you click OK, all months with an S&P return th

C23, for example) are displayed in green, and al

–3percent (see cell C18) are displayed in red. Ce

either of these conditions maintain their origin

Fig

URE 24-20

Conditional formatting highlights returns in the S

Chapter

Conditional

Formatting

199

Fig

URE 24-21

Applying special formatting to S&P returns great

Fig

URE 24-22

Coloring stock returns less than 3 percent in re

Here are some useful tips concerning condition

■

To delete conditional formatting (or any for

select the range of cells, click Conditiona

Clear Rules From Selected Cells.

■

To select all the cells in a worksheet to w

F5 to display the Go To dialog box. In the d

Formats, and then click OK.

■

If you want to edit a conditional formattin

double-click the rule or click Edit Rules.

■

You can delete a specifc conditional format

the rule, and then clicking Delete Rule.

Notice that after both rules are defned, the r

created more recently than the green formattin

Manager dialog box, rules are listed in order o

matter which rule is listed frst because no ce

conflict, however, the rule listed frst takes p

formatting rules, select the rule and click th

the down arrow to move the rule down in preced

200

Microsoft Excel 2010: Data Analysis and Business Modeling

Given quarterly corporate revenues, how- can I in

creased over the previous quarter in one color, a

from the previous quarter in another color?

The fle Amazon.xlsx contains quarterly revenues (

years 1995–2009. (See Figure 24-23.) We want to hi

increased over the previous quarter in green and hi

decreased over the previous quarter in red.

Fig

URE 24-23

Highlighting increased sales in green and decrease

The Use A Formula option in the Conditional Form

you to specify a formula that defnes conditions th

to a cell. I’ll use this option in this section, b

look at how Excel evaluates some logical functio

xlsx.

What happens when you type a formula such as

=B3

number smaller than 2, Excel returns the value T

You can refer to the fle Logicalexamples.xlsx, s

this, including combinations of AND, OR, and NOT i

■

In cell B6,

OR(B3<3,

the formula

C3>5)=

returns the value Tr

conditions

B3<3 or C3>5

is true. Because the v

returns True.

■

In cell B7,

AND(B3=3,C3>5)

the formula

returns

. True

Because

B3=3

not equal to 3, Excel returns False. In cell B

returns True because

B3>3

and

C3>5

are both tr

■

In cell B9,

NOT(B3<2)

the formula

returns

True because

B3<2

a not-false value becomes True.

Chapter

Conditional

Formatting

201

Fig

URE 24-24

Logical functions.

Now let’s look at how the Use A Formula

format

option a

in a range of cells. Begin by selecting

apply athe ra

conditional format. Then click Conditional For

Conditional Formatting Rules Manager dialog bo

A Formula To Determine Which Cells To Format o

the

formula

). To

option

use the formula option, you ente

with an equals sign) that is true if and only i

assigned the chosen format. Your logical formu

the remainder of the selected range, so judici

that for each cell of the selected range the f

format to apply to the cell. Click Format, and th

After clicking OK in the Conditional Formattin

copied to the whole cell range. The formatting i

that satisfes the condition defned in the form

Returning to the fle Amazon.xlsx, let’s focus o

revenues increase. Basically, what you want to d

quarter to which you can compare the revenue f

if a cell’s value is larger than the cell abov

how to set up the rule.

Fig

URE 24-25

Conditional formatting settings that will displa

increased.

202

Microsoft Excel 2010: Data Analysis and Business Modeling

If you enter

=E6>E5

by pointing to the appropria

from the formula in the Conditional Formatting d

Probably the easiest way to insert or delete

dol

light a cell reference such as A3, pressing F4 i

order: A3, $A$3, A$3, $A3. Thus, if you start wi

to A$3. The formula in this example ensures that c

in that quarter exceed the previous quarter. Aft

which revenue increased are colored green. Notic

was copied in the usual

way, becoming

=E7>E6

To add the condition for formatting cells in whi

again, open the Conditional Formatting Rules Man

select Use A Formula To Determine Which Cells To F

then click Format. On the Fill tab, change the fl

Conditional Formatting Rules Manager dialog box n

Fig

URE 24-26

These conditions will display quarters in which re

which revenue decreased in red.

You can use the formula option with color scales

option when setting the criteria for your color s

Given a list of dates, how can I indicate weeken

The fle Weekendformatting.xlsx (see Figure 24-27

all Saturdays and Sundays in red. To do this, I f

cell D6 to D7:D69. Choosing

Type=2

for the WEEKD

a 2 for each Tuesday, and so on, so that the fun

each Sunday.

Chapter

Conditional

Formatting

203

Fig

URE 24-27

Using the WEEKDAY function to highlight weekend d

I now select the range D6:D69, click Condition

Rules. After clicking New Rule and the formula o

Figure 24-28.

Fig

URE 24-28

The Edit Formatting Rule dialog box set up to di

After I click OK, each date having its weekday e

colored red. The formula

=OR(D6=6,D6=7)

implie

red font color. Of course, I could have used F

to obtain the same formatting.

204

Microsoft Excel 2010: Data Analysis and Business Modeling

Our basketball coach has given each player a rat

player’s ability to play

. Can

guard,

I setforward,

up a worksheet

cent t

indicates the ability of each player to play the p

The fle Basketball.xlsx, shown in Figure 24-29, c

position and

1=Guard,

the position

2=Forward,

)( played

3=Center

by each player

here is to fll with red the cell containing the r

she’s assigned.

Fig

URE 24-29

This worksheet rates each player’s ability to play a p

Begin by selecting the range C3:E22, which contai

Formatting, Manage Rules. Then click New Rule, a

the dialog box as shown Figure 24-30.

Fig

URE 24-30

The Edit Formatting Rule dialog box set up to show p

Chapter

Conditional

Formatting

205

The formula

=$A3=C$1

compares the player’s ass

(1, 2, or 3) in row 1. If the player’s assigne

which is her guard rating, appears in red. Simi

her forward rating in column D appears in red. Fi

center rating in column E appears in red. Note th

the A and the 1 in the formula, it will not co

I also want to note that Excel 2010 allows con

reference data in other worksheets. In prior v

the worksheet where the format was placed.

What does the Stop If True option in t

Suppose that the Stop If True option is select

precedent rules are ignored. To illustrate the u

data bar format, but you don’t want data bars t

equal to 50. Simply use Manage Rules to add a f

only if the value

. Have

thecell

frstis

format

>=50

use an a

select Stop If True for that format. Now, for a

Excel will stop and not use the data bar forma

Problems

Using the data in the fle Sandp.xlsx, use c

situations:

❑

Format in bold each month in which the va

underline each month in which the value o

❑

Highlight in green each month in which th

2 percent.

❑

Highlight the largest S&P index value in r

Using the data in the fle Toysrusformat.xls

revenue has increased over at least the las

revenues in blue and frst-quarter revenues i

The fle Test.xlsx contains exam scores for s

A, the next 20 students receive a B, and al

A grades in red, the B grades in green, and th

LARGE(D4:D63,10)

gives you the tenth-highes

In the fle Weekendformatting.xlsx, highligh

days that occur in the frst 10 days of the m

206

Microsoft Excel 2010: Data Analysis and Business Modeling

Suppose each worker in Microsoft’s fnance dep

of four groups. The supervisor of each group h

and each worker has rated his satisfaction wi

Satissuper.xlsx.) Based on the group to which e

supervisor rating and the worker satisfaction r

The fle Varianceanalysis.xlsx contains monthl

sales. The sales variance for a month equals:

predictedsales

actualsales – predictedsales

Highlight in red all months with a favorable v

highlight in green all months with an unfavor

For our drug cost example from Chapter 22, “T

worksheet so that all Phase 1 costs are displ

in green, and all Phase 3 costs are displayed i

The fle Names.xlsx contains a list of names. Hi

names containing

in red.

The fle Duedates.xlsx contains due dates for v

invoices due by the end of the next month.

10.

In the fle Historicalinvest.xlsx, set up cond

10 percent of returns have an up arrow, 10 pe

have a horizontal arrow.

11.

The fle Nbasalaries.xlsx contains salaries of N

data bars to summarize this data. Players mak

shortest data bar, and players making more th

bar.

12.

Set up a three-color scale to summarize the N

bottom 10 percent of all salaries to green an

13.

Use fve icons to summarize the NBA player dat

million, $6 million, $9 million, and $12 mill

14.

How could you set things up so that no icons a

between $7 million and $8 million? Hint: Use th

15.

The fle Fractiondefective.xlsx contains the p

daily. A day’s production is considered accep

produced are defective. Highlight all accepta

worksheet, highlight all acceptable days with a r

option to ensure that no icon occurs in any c

Chapter

Conditional

Formatting

207

16.

Summarize global warming data with a three-

be blue, intermediate temperatures should b

should be red.

17.

Suppose you are saving for your child’s col

same amount of money to the fund at the end o

$100,000. For annual investment returns ran

number of years investing varying from 5 to 1

contribution. Suppose you are able to- save $

ting to highlight for each annual return ra

accumulate $100,000.

18.

The fle Amazon.xlsx contains quarterly reve

formatting to ensure that sales during each q

19.

Set up conditional formatting that colors th

alternating white and black coloring. Hint: T

a cell, and the COLUMN() function gives the c

20.

When students take Vivian’s accounting exam th

on a Scantron. Often they make a mistake. V

for the students in the class. She would li

entered by students that are not true alias

fle Scantrons.xlsx contains the necessary d

21.

The fle Top5.xlsx contains the revenues eac

highlight the companies that have the fve la

LARGE(B1:B50,5)

would return the ffth large

22.

The fle Threetimes.xlsx contains a list of n

appears at least three times.

23.

The fle GNP.xlsx contains quarterly U.S. gr

fact that data bars handle negative values t

growth rates.

24.

Using the data in the fle Globalwarmingtemp

temperatures) in which the temperature is a

209

Chapter 25

Sorting in Excel

Questions answered in this chapter

■

How can I sort sales transaction data so th

salesperson, then by product, then by units s

from oldest to most recent?

■

I have always wanted to sort my data based o

Excel 2010?

■

I love the great icon sets described in Cha

my data based on the icon in the cell?

■

My worksheet includes a column containing th

When I sort by this column, I get either Ap

(last month alphabetically) on top. How can I s

transactions are on top, followed by Februa

■

Can I sort data without using the Sort dial

Almost every user of Microsoft Excel has at on

alphabetically or by numerical value. Let’s lo

powerful sorting is in Excel 2010.

Answers to This Chapter’s Ques

How can I sort sales transaction data so that t

then by product, then by units sold, and finall

most recent?

JAC is a small company that sells makeup. The

xlsx fle in the Templates folder for this chap

transaction information:

■

Transaction number

■

Name of salesperson

■

Date of transaction

■

Product sold

210

Microsoft Excel 2010: Data Analysis and Business Modeling

■

Units sold

■

Dollars received

■

Location of transaction

Fig

URE 25-1

Sales transaction data before sorting.

I want to sort the data so that:

■

Transactions are listed alphabetically by sal

order so that all of Ashley’s transactions ar

■

Each person’s transactions are sorted by prod

will be followed by Ashley’s foundation trans

■

For each salesperson and product, transaction

descending order).

■

If a salesperson makes two or more sales of th

units, transactions are listed in chronologic

In versions of Excel before Excel 2007, it was d

Excel 2007 and Excel 2010 allow you to apply up t

data, I frst need

cell

to range

selectE3:K1894).

the data (Two easy wa

as follows:

■

Position the cursor in the upper-left corner o

Ctrl+Shift+Right Arrow followed by Ctrl+Shift+

■

Position the cursor anywhere in the cell rang

Chapter

Sorting

211

Excel

Next, on the Data tab, in the Sort & Filter gr

shown in Figure 25-2.

Fig

URE 25-2

Sort dialog box not yet flled in.

Because row 3 contains headings for the data c

check box. Now I select the following four cri

Sort by the Name column so that values (thi

Sort by the Product column so that values a

Sort by the Units column so that values are

Sort by the Date column so that values are i

newest.

The dialog box now looks like Figure 25-3.

Fig

URE 25-3

Sort dialog box set up for the sales sorting exa

The fnal result of our sort is shown in Figure 2

212

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 25-4

Sorted sales transaction data.

Note that all of Ashley’s transactions are liste

and so on. Eye liner transactions are listed fro

est. In the case of a tie (see rows 6 and 7), th

Using the Sort dialog box, you can easily

criteria

add so

(Delete Level), copy the settings that defne a l

whether your data has headers. By selecting Opti

sensitive or even sort data for which each data i

the more common situation in which each case is i

I have always wanted to sort my data

. Is this

basedpossib

on ce

Excel 2010?

In Excel 2010, sorting on cell or font color is s

Makeupsorttemp.xlsx fle. Several names in column F a

For example, Cici in cell F620 is highlighted in r

yellow. Suppose you want names with green fll on t

with the rest of the rows on the bottom. To sort th

range you want to sort (E3:K1894), click Sort, a

column, click the Sort On setting, and select Ce

color). For the frst level, select green from th

and select red for the third level. The -complete

sulting sort is shown in the

Colors

worksheet of th

Files folder for this chapter and shown in Figur

Chapter

Sorting

213

Excel

Fig

URE 25-5

Sort dialog box set up to sort by color.

Fig

URE 25-6

Results of sorting by color.

I love the great icon sets described

”. Can

in I

Chapte

sort m

data based on the icon in the cell?

To sort by icon, simply select Cell Icon from t

the Order list, choose the icon you want on to

My worksheet includes a column containing

the m

When I sort by this column, I get either April (

month alphabetically)

. How canon

I top

sort by this column s

are on top, followed by February, and so on?

The

Dates

worksheet in the Makeupsorttemp.xlsx fl

25-7.) I would like to sort the months- so that th

ning with January. I begin by selecting the ra

When selecting the order, I select Custom List a

214

Microsoft Excel 2010: Data Analysis and Business Modeling

January, February,

. Note that

March

you could also have sorte

completed dialog box is shown in Figure 25-8, wi

Note that in the Custom Lists dialog box you can c

select New List, under List Entries type the entr

click Add. Your new list is now included as a me

John, and Alan in List Entries (on different lin

would be listed frst, followed by John listings, w

Fig

URE 25-7

Months to be sorted.

Fig

URE 25-8

The Sort dialog box set up to sort by month.

Fig

URE 25-9

Months sorted in chronological order.

Chapter

Sorting

215

Excel

Can I sort data without using the Sort dialog b

Sometimes sorting data without using the Sort d

how this is done, suppose again that you want t

Makeup

worksheet in the Makeupsort.xlsx -fle so th

person, then by product, then by units sold, a

est to the most recent. To begin, select the l

the date column (G3:G1894). Next, in the Sort & Fi

To Z button (see Figure 25-10) and, with the E

so that all the columns are sorted. The Sort A T

smallest numbers or oldest dates are on top, a

Fig

URE 25-10

Sorting.

The Sort Z To A button, of course, sorts numer

recent dates are on top, and sorts text data s

Next, sort by the second least important colum

on top. Then sort from A to Z by Product, and fn

achieve the same results as shown in Figure 25

Problems

In the Makeupsort.xlsx fle, sort the sales d

product type, then by name, then by date of s

The Sortday.xlsx fle contains hours worked o

so that Monday data is followed by Tuesday d

The Sorticons.xlsx fle contains annual inve

indicate good years, a horizontal arrow

use

row used to indicate bad years. Sort the da

arrows on top, followed by horizontal arrow

The fle Makeupsortfont.xlsx contains our ma

blue, red, or brown font. Sort the data so th

dates, and then blue dates.

217

Chapter 26

Tables

Questions answered in this chapter:

■

I have entered in a worksheet the number of u

salesperson, and I can easily compute avera

create a nice format that is automatically c

easy way to automatically copy my formulas w

■

I have entered in my worksheet several year

line chart displaying the monthly variation i

add new gas price data, my chart automatica

■

For each sales transaction, I have the sale

the transaction. Can I easily summarize, fo

by Jen or Colleen?

■

How can I easily refer to portions of a tab

■

Do conditional formats automatically apply t

When most of us use Microsoft Excel, we often e

formulas, formats, and charts. What a drag! Now th

drudgery a thing of the past.

Answers to This Chapter’s Ques

I have entered in a worksheet the number of un

salesperson, and I can easily compute

. How average

can I

create a nice format that is automatically cop

way to automatically copy my formulas when new d

The fle Tableexampletemp.xlsx in the Templates f

contains units sold and revenue data for each o

will be added beginning in row 12. Also, in co

price

Units/Revenue

(

) earned by each salesperson. You

wou

mat for the data and have the formula for aver

data is added.

218

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 26-1

Data for creating a table.

Creating a table allows your analysis and format

add data. Begin by selecting the current range o

click Table on the Insert tab or press Ctrl+T. A

box, you will see that the table range (E5:G11) i

continue automatically whenever new data is ente

in a table, many styles and options are availabl

select a formatting style that will be applied a

Note that the column headings have arrows, as yo

work as flters that can be used to sort or flter th

chapter.)

Fig

URE 26-2

Table design options.

Fig

URE 26-3

Formatted table with flters.

The cells in the selected table (excluding

default.

the h

I changed the name to

Sales

in the Properties gr

Formulas tab and then click Name Manager, you ca

The beauty of this range name (and the table)

is th

clude new rows added to the bottom of the table a

table. In Chapter 22, “The OFFSET Function,” I u

range, but the new table capabilities make creati

Chapter

Tables

219

Suppose that in D15 you want to compute

total r

Excel

offers you the option to automatically comp

I implemented Autocomplete by double-clicking th

Autocomplete by moving the cursor to

Sales

and p

=SUM(Sales

and type an opening bracket ( [ ),

complete the formula with column headings from th

complete your formula as

=SUM(Sales[Revenue])

(See Figure 26-5.) (You will see an example of s

that begin with number signs (#) later in this c

Fig

URE 26-4

AutoComplete options for a table.

Fig

URE 26-5

Total revenue for original data.

If new rows of data are added, the data in the

formula. To illustrate this idea, you can add n

$5,000. As shown in Figure 26-6, the total rev

The formatting has been extended to row 12 as w

updated to include Amanda’s data. Even if data i

bottom), everything will be updated in a consi

220

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 26-6

New data added to table in row 12.

Now suppose that you want to compute in column H t

salesperson. Simply type

Unit Price

in H5 as the c

=SALES[

. In the AutoComplete list, click Revenue. T

Type a slash (/), and use Formula

formula

AutoComplete

=SALES[Revenue]}/Sales[Units].

An amazing thing h

the formula down to the bottom of the table in c

to any cell in column H, the formula appears as

=[@Revenue]/[@Units]

is a lot. easier

This formula

to understa

can b

interpreted as taking whatever is in the current r

by whatever is in the current row in the Units c

Fig

URE 26-7

Unit price formula autocopy.

If you click anywhere in a table, the Table Tool

offers choices including the following:

■

Change Table

Can

Name

be used to rename a table. I ch

(the default) to Sales.

■

Convert to

Converts

Range

the table range to normal c

structure.

■

Resize

Adds

Table

or subtracts rows and/or columns t

■

Remove Duplicates

Removes rows that contain duplicates

only the Name column in the Remove Duplicates d

not occur more than once. Checking both the N

no rows in the table will match both Name and Uni

Chapter

Tables

221

■

Header

Row

checked, displays the header row . I

displayed.

■

Total

Row

discuss the total row later in this c

■

First Column

If checked, applies a special format t

■

Last Column

If checked, assigns a special format t

■

Banded Rows

If checked, gives the even-numbered r

format than odd-numbered rows.

■

Banded Columns

If checked, gives odd-numbered colu

format than even-numbered columns.

■

Table Styles

Select from any of the table formats s

the table expands or contracts, the format w

I have entered in my worksheet several years o

line chart displaying the. Can

monthly

I setvariation

things upins p

add new gas price data, my chart automatically u

In the fle Gasprices507.xlsx, the worksheet

feet from July 2002 through December 2004. (Se

you can select B5:C34 (containing months and p

this range. Then you can create a line graph t

group on the Insert tab and selecting the four

is shown in Figure 26-9.

Fig

URE 26-8

Gas price data: 2002–2004.

222

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 26-9

Gas price line graph: 2002–2004 data.

Next, I copied this worksheet (by right-clicking th

Sheet, and then clicking Make A Copy) and added g

now extends to row 53.) I named

. Note the

newline

workshee

grap

worksheet automatically updates to include the n

Fig

URE 26-10

Gas price line graph: 2002–2006 data.

This example illustrates that if you create a ta

data will automatically be included in the chart

For each sales transaction I have the salesperso

transaction

. Can I easily summarize, for example, tota

Jen or Colleen?

The fle Tablemakeuptemp.xlsx contains sales tran

transaction, I have the following information: t

location, dollars, and units sold. If I format t

Units and Dollars columns and then use the flter a

subset of transactions I want. To begin, place th

a table by pressing Ctrl+T. Note that if you scr

Chapter

Tables

223

visible. With the cursor in the table, select th

group on the Design tab. By default, Excel wil

in cell K1895, which you can delete. Click the a

and then click Sum. This totals all entries in c

the total revenue is $239,012.67, and 78,707 u

Tablemakeuptotals.xlsx.)

Fig

URE 26-11

Makeup sales data.

Fig

URE 26-12

Total revenue and units sold.

To make the totals reflect only lipstick sales i

the arrow in F3 (to the right of the Name head

are selected. Then select the check boxes for

Next, click the Product arrow and select the l

arrow and select the East check box. Use the s

Product column and only East in the location c

224

Microsoft Excel 2010: Data Analysis and Business Modeling

fltering criteria in Figure 26-14 and in the fle

and Jennifer sold 497 units of lipstick in the E

feature makes it a snap to easily compute totals f

If you want, you can also copy the rows involvin

and paste them elsewhere.

Fig

URE 26-13

Selecting names from the table.

Fig

URE 26-14

Filtered subtotals for units and revenue.

Chapter

Tables

225

How can I easily refer to portions of a table i

The fle Tablestructure.xlsx shows many example

when you are working outside the table’s range

references.

(See Figure 26-15.) When you enter a t

makes the column names and the following table s

■

Table Name

All cells in the table, excluding the h

■

#AlAl

ll cells in the table, including the tot

■

#Dat

ll cells in the table except for the fr

■

#Headers

Just the header row.

■

#Totals

Just the total row. If there is no tota

■

#This

All

Row

table entries in the current row.

A column reference includes all cells in a tab

entries (if any).

Here are some examples of how table specifers c

■

In cell C15, the formula

=COUNTA(Table1[All#

entries.

■

In cell C16, the formula

=COUNTA([Table1])

tal rows are not counted. In cell C17, the f

because the cell range D5:H13 is referenced

■

In cell C18, the formula

=COUNTA(Table1[#Hea

row (D4:H4) is referenced.

■

In cell C19,

SUM(Table1[Q1])

the formula = yields 367 becaus

entries in E5:E13.

■

In cell C20, the formula

=SUM(Table1[#Totals

yields 1,340, which is the total sum of all t

■

In cell C21, the formula

=SUM(Table1[[Data#]

are in columns Q1:Q3, inclusive (cells E5:G1

include all data entries between and includ

the column name after the colon.

■

In cell B8, the formula

=SUM(Table1[#This Ro

(

41+28+49+40

Of course, all of these formulas are automatic

226

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 26-15

Structured references.

Do conditional formats automatically apply to ne

Yes, conditional formats will automatically incl

illustrate, I placed in worksheet

Original

of fl

highlight the three largest Q1 sales in -column E

lighted. In worksheet

, I added

Add

Biggersale

cell E14 the entry 9

largest entry in the column and is immediately hi

because it is no longer one of the three largest n

Fig

URE 26-16

Conditional formatting extends automatically to ne

Chapter

Tables

227

Problems

The fle Singers.xlsx contains a list of son

length of each song. Set up your worksheet t

sung by Eminem and the average length of ea

your formulas should automatically update.

In the fle Tableexample.xlsx, set things up s

to total revenue and units sold is included i

included, your ranks should automatically u

the RANK.EQ function. The syntax of the

. RAN

This function yields the rank of a number i1 b

number.

The fle Lookupdata.xlsx contains product co

that a product code can be entered and your w

Of course, when new products are introduced

The fle Productlookup.xlsx contains the pro

up a formula that returns the sale of any p

products are added to the data, your formul

products.

The fle Tablepie.xlsx contains sales inform

general store. You want to set up a pie char

product categories are added, the pie chart s

The fle Tablexnpvdata.xlsx lists cash flows r

formula to compute (as of January 5,annual

2007) t

discount rate of 10 percent. Of course, if n

should automatically include them.

The fle Nikedata.xlsx contains quarterly sa

sales that automatically includes new sales r

For the data in fle Tablemakeuptemp.xlsx, d

gloss or lipstick sold by Jen or Ashley in th

The fle Closest.xlsx contains people’s name

any number and fnds the person whose -salary i

sheet should accomplish this goal even if n

deleted from the list.

10.

The fle Adagency.xlsx contains salaries and a

a spreadsheet that will compute the average s

Of course, your calculations should automati

workers.

229

Chapter 27

Spin Buttons, Scrol

Buttons, Check Boxes

and Group List Boxes

Questions answered in this chapter:

■

I need to run a sensitivity analysis that h

sales growth, Year 1 price, and unit cost. I

and see the effect of the variation on the c

■

How do I set up a simple check box that tog

■

How can I set up my worksheet so that my su

choose whether we charge a high, low, or me

■

How can I create an easy way for a user of m

without having to type any text?

User forms enable a user of Microsoft Excel 20

to a worksheet. In this chapter, I show you how e

check boxes, option buttons, combo boxes, and l

Developer tab on the ribbon, click Insert in th

(not to be confused with ActiveX Controls, whi

Basic for Applications [VBA] programming langu

Not

o display the Developer tab, click the File ta

Ribbon, and then select Developer in the Main Tabs l

The user forms I discuss are shown in Figures 2

Controls.xlsx in the Practice fles folder for thi

Fig

URE 27-1

Spin button.

230

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 27-2

Scroll bar.

Fig

URE 27-3

Check box.

Fig

URE 27-4

Option button.

Fig

URE 27-5

Group box.

Fig

URE 27-6

Combo box.

Fig

URE 27-7

List box.

Answers to This Chapter’s Quest

I’ll begin by showing you how to use spin button

As I discussed in Chapter 19, “Using the Scenari

Scenario Manager lets you change a group of inpu

Unfortunately, the Scenario Manager requires you t

makes creating more than a few scenarios diffcul

four key inputs to the car net present value (NP

price, and Year1 cost. (See the fle NPVspinners.

the inputs change in the following ranges:

Chapter

Spin

27 Buttons, Scroll Bars, Option Buttons, Check

231

Boxes, Combo Boxes, and Group List Boxes

Input

Low value High value

Year 1 sales

$5,000

$30,000

Annual sales growth

50%

Year 1 price

$20

Year 1 cost

$15

Using the Scenario Manager to generate the sce

the given ranges would be very ,

time-consuming.

however, a us B

quickly generate a host of scenarios that vary e

spin button is a control that is linked to a s

the spin button, the value of the linked cell c

(such as one that calculates a car’s NPV) chan

I need to run a sensitivity analysis that has m

sales growth, Year 1 price,

. Is there

and Year

way1Iunit

can co

qui

inputs and see the effect of the variation on t

example?

Here’s how to create spin buttons that allow y

price, and Year1 cost within the ranges you wa

NPVspinnerstemp.xlsx in the Templates folder) i

Fig

URE 27-8

The Original Model worksheet without any spin bu

To create the spin buttons, select the rows in w

rows 2–5 in this example), and then increase

lecting Format, Row, and then Height. A row he

the spin button arrows. Alternatively, hold dow

that it fts the cell.

232

Microsoft Excel 2010: Data Analysis and Business Modeling

Display the User Forms menu by clicking Insert i

Click the spin button form control (shown in Fig

to appear in your worksheet (cell D2). You will s

anchors the spin button where you want it and al

button. To change the shape of a form control or t

the control and hold down the Ctrl key. When the p

drag the control to move it. When the pointer ap

the control to resize it.

A spin button now appears in cell D2. You can us

Year1 sales. Right-click the spin button, and on th

D3, and then click Paste. Also paste the spin bu

four spin buttons as shown in Figure 27-9.

Fig

URE 27-09

Spin buttons placed in worksheet cells.

Now you need to link each spin button to an inpu

C2, right-click the spin button in cell D2, and th

Control dialog box as shown in Figure 27-10.

Fig

URE 27-10

Use the Format Control dialog box to link Year1 sa

Chapter

Spin

27 Buttons, Scroll Bars, Option Buttons, Check

233

Boxes, Combo Boxes, and Group List Boxes

The current value is not important. The rest o

linked to the values in cell C2 (Year1 sales), t

value in C2 by 1,000, and that each click on th

1,000. When the value in C2 reaches 30,000, cl

the value in C2 reaches 5,000, clicking the dow

Next, use the Format Control dialog box to lin

C4). For the current value, I used 9. The mini

the incremental change is 1. Clicking the spin b

between $6 and $20 in $1 increments.

To link the spin button in cell D5 to Year1 co

the minimum value, 15 for the maximum value, a

spin button arrows in cell D5 changes Year1 co

Linking the spin button in cell D3 to control

Sales gr

to change sales growth to 0 percent, 1 percent

mum increment a spin button value can change i

button to a dummy value in cell E3 and place th

E3 varies from 1 to 50, sales growth varies be

shows how to link this spin button to cell E3. R

the number in cell E3 divided by 100.

Fig

URE 27-11

The Format Control dialog box settings that link t

By clicking a spin button arrow, you can easil

the values for the other inputs listed in the w

effect of the changes, you can select cell F9, c

234

Microsoft Excel 2010: Data Analysis and Business Modeling

click Freeze Panes again. This command freezes th

You can now use the scroll bars on the right of th

Figure 27-12.

Fig

URE 27-12

You can freeze panes to see the results of calcula

Given the values of the other inputs, clicking th

a 1-percent increase in sales growth is worth ab

normal state, click Freeze Panes on the View men

The scroll bar control is very similar to the sp

the cursor over the gray area in the middle of th

continuously change in value. By selecting

Forma

ing the value under Page Change in the Format Co

speed with which the linked cell changes.

How do I set up a simple check box that toggles

A check box is a form control that specifes a va

and False when the box is clear. Check boxes can b

a particular feature on or off. As an example, I w

conditional formatting feature on or off.

Suppose a worksheet contains monthly sales and y

green and the fve smallest sales in red. (See th

formula

=LARGE(Sales,5),

which computes the ffth

compute the ffth-smallest sales .value

(See with

Figure

the27f

Chapter

Spin

27 Buttons, Scroll Bars, Option Buttons, Check

235

Boxes, Combo Boxes, and Group List Boxes

Fig

URE 27-13

Using a check box to turn conditional formatting o

Next, you create a check box and confgure it t

Developer tab, click Insert and select the che

palette. Drag the check box to cell G9, and ch

Off. Then right-click the check box, click For

Figure 27-14.

Fig

URE 27-14

The Format Control dialog box for a check box.

Now, whenever you select the check box, True i

check box, False is placed in cell F1.

236

Microsoft Excel 2010: Data Analysis and Business Modeling

After selecting the cell range D4:D29, click Con

Home tab, and then click New Rule. Enter the for

color the top fve sales green and the portion

bottom fve s

of the formula ensures that the formatting can b

check box determines whether cell F1 is True or F

cells will not turn green or red.

Fig

URE 27-15

Format to turn fve largest cells green.

Fig

URE 27-16

Format to turn fve smallest cells red.

If you want, you can select cell F1 and change th

Chapter

Spin

27 Buttons, Scroll Bars, Option Buttons, Check

237

Boxes, Combo Boxes, and Group List Boxes

How can I set up my worksheet so that my suppl

choose whether we charge a high, low, or mediu

Let’s suppose that you can charge one of three p

These prices are listed in cells B7:B9 of the fl

lookup table to print the price if a user type

however, if the user can select an option butt

Price, and then have a formula automatically c

To use option buttons, you frst draw a group b

control from the User Forms menu. Then you dra

group box. Because you have three price levels

the group box. Right-click any option button, a

link any one of the option buttons to a cell. I l

the option buttons in the group box are -now li

tion button will enter a 1 in cell E4, selecti

E4, and selecting the third option button will e

Entering the

INDEX(A7:A9,E4,1)

formula

in cell E7 returns

ing to the selected option

VLOOKUP(E7,A7:B9,2,FA

button. In cell F7, t

computes the price corresponding to the select

Fig

URE 27-17

Using option buttons to select product price.

238

Microsoft Excel 2010: Data Analysis and Business Modeling

How can I create an easy way for a user of my sp

without having to type any text?

The fle Combobox.xlsx shows how to use a combo b

allow a user to easily

Data

select

validation

an itemalso

from

makes

lisi

ate drop-down boxes; see Chapter 40, “Validating Da

number of hours an employee worked on a given da

listed in cells G9:G15. A combo box or list box a

combo box or list box is linked to a cell (via F

box is selected, a 1 is placed in the linked cel

is entered in the linked cell, and so on. To set u

click Insert, and then drag a combo box from the F

B14.

Right-click the combo box and click Format Con

contains days of the week) and link cell A8. Now r

Control. Select the input range F9:F15 and link th

Tuesday from the combo box and Friday from the l

a 5 in A13.

In cell F3, the formula

=INDEX(F9:F15,A8,1)

list

combo box selection. In cell G3, the formula

=VL

number of hours worked for the day selected in th

formulas in F4 and G4 list the day of the week a

list box.

Fig

URE 27-18

Using combo boxes and list boxes.

Chapter

Spin

27 Buttons, Scroll Bars, Option Buttons, Check

239

Boxes, Combo Boxes, and Group List Boxes

Problems

Add a spin button for the car NPV example th

between 30 percent and 50 percent.

Add a spin button for the car NPV example th

between 5 percent and 20 percent.

The Format Control dialog box allows a mini

you fgure out a way to use a spin button to v

and 20 percent?

Using the lemonade example in Chapter 17, “S

create spin buttons that allow the inputs t

Input

Low value

High value

Price

$2.00

$5.00

Unit cost

$0.20

$1.00

Fixed cost

$20,000.00 $100,000.00

Using the mortgage payment example in Chapt, c

inputs to vary within the following ranges:

Input

Low value

High value

Amount borrowed $270,000

$800,000

Number of months 120

of payments360

Annual interest rate

10%

For the weekend example used in Chapter 24, “

box that turns conditional formatting on or o

In the fnancial formulas described in Chapt

used a last argument of 1 to indicate

- end o

ginning of month cash flows. Excel recognize

equivalent to 0. Set up a worksheet in whic

in a loan, principal, and annual interest r

check box to select whether the payments ar

The fle Quarterly.xlsx contains quarterly s

option buttons to select the quarter and a l

worksheet should then compute sales at a sp

240

Microsoft Excel 2010: Data Analysis and Business Modeling

Using the data for Problem 15 in Chapter 22, “

that lets you graph the last few months of sa

10.

The fle Suppliers.xlsx contains the unit pric

units purchased. Create a list box that allow

unit price and units purchased.

241

Chapter 28

An Introduction to O

with Excel Solver

In many situations, you want to fnd the best wa

to fnd the values of certain cells in a worksh

certain objective. The Microsoft Excel Solver h

the following:

■

How can a large drug company determine the m

plant that maximizes corporate proftability

■

If Microsoft produces Xbox consoles at thre

the cost of meeting demand for them?

■

What price for Xbox consoles and games will m

sales?

■

Microsoft would like to undertake 20 strate

skilled programmers for the next fve years. I

20 projects; which ones should it undertake

■

How do bookmakers fnd the best set of ratin

point spreads?

■

How should I allocate my retirement portfol

bonds, cash, and gold?

An optimization model has three parts: the tar

constraints. The

target cell

represents the ob

maximize the amount in the target cell. In the q

mix given earlier, the plant manager would pre

of the plant during each month. The cell that m

The target cells for each situation described a

Table 28-1.

Keep in mind, however, that in some situations y

example, Microsoft might have a secondary goal t

242

Microsoft Excel 2010: Data Analysis and Business Modeling

TABLE 28-1

List of Target Cells

Model

Maximize or Target

minimize

cell

Drug company product

Maximize

mix

Monthly proft

Xbox shipping

Minimize

Distribution costs

Xbox pricing

Maximize

Proft from Xbox consoles a

Microsoft project

Maximize

initiatives

Net present value (NPV) co

selected projects

NFL ratings

Minimize

Difference between scores p

ratings and actual game sc

Retirement portfolio

Minimize

Risk factor of portfolio

Changing cells

are the worksheet cells that you c

cell. In the drug company example, the plant man

each product during a month. The cells in

- which th

ing cells in this model. Table 28-2 lists

- the ap

els described at the beginning of the chapter, a

TABLE 28-2

List of Changing Cells

Model

Changing cells

Drug company product

Amount mix

of each product produced during t

Xbox shipping

Amount produced at each plant each mon

customer

Xbox pricing

Console and game prices

Microsoft program

Which

initiatives

projects are selected

NFL ratings

Team ratings

Retirement portfolio

Fraction of money invested in each ass

TABLE 28-3

List of Problem Constraints

Model

Constraints

Drug company product

Product mix uses no more resources tha

Do not produce more of a product than c

Xbox shipping

Do not ship more units eachcapacity

month from a p

Make sure that each customer receives t

consoles that they need

Xbox pricing

Prices can’t be too far out of line wi

Microsoft project

Projects

initiatives

selected can’t use more money o

than are available

NFL ratings

None

Retirement portfolio

Invest all our money somewhere (cash i

Obtain an expected return of at least 1

Chapter

An28

Introduction to Optimization

243

with Excel Solver

The best way to understand how to use Solver i

later chapters, you’ll learn how to use Solver t

this chapter as well as several other importan

To install Solver, click the File tab, click O

at the bottom of the dialog box, select Excel A

In check box in the Add-Ins dialog box, and cl

Solver by clicking Solver in the Analysis grou

Parameters dialog box. In the next few chapter

put the target cell, changing cells, and constr

Fig

URE 28-1

The Solver Parameters dialog box.

The Excel Solver has been greatly revamped and i

change is the presence of the Select A Solving M

appropriate solution engine for your optimizati

■

The Simplex LP engine is used to solve line

Chapters linear

29–32,optimization problem is

- one i

straints are all created by adding together

■

The GRG Nonlinear engine is used to solve o

cell and/or some of the constraints -

are not l

mon mathematical operations such as multipl

changing cells to a power, exponential or tr

so on. The GRG engine includes a powerful M

many problems that were solved incorrectly w

Chapters

33 through 35 discuss the GRG Non

244

Microsoft Excel 2010: Data Analysis and Business Modeling

■

The Evolutionary engine is used when your

tar

smooth functions that reference changing cell

slope abruptly changes. For example, when x = 0

abruptly changes from -1 to 1. If your Target c

COUNTIF, SUMIFS, COUNTIFS, AVERAGEIF, AVERAGEI

that reference the changing cells, then you a

Evolutionary engine probably has the best shot at f

optimization problem. The Evolutionary engine i

After you have input the target cell, changing c

answer this question, you need some background is

the changing cells that satisfes

feasible

solution

.the

Formodel’s

instance,

con

product mix that satisfes the following three col

■

Does not use more raw material or labor than i

■

Does not produce more of each product than is d

■

Does not produce a negative amount of any pro

Essentially, Solver searches all feasible soluti

cell value (the largest value for maximum

- optimi

tion). Such a solution. is

As called

you’ll an

see

optimal

in Chapter

solu

to Determine the Optimal Product Mix,” some Solv

some have a unique solution. Other Solver

models h

ber of) optimal solutions. In the next chapter, w

examining the drug company product mix problem.

Problems

For each situation described below, identify the t

I am borrowing $100,000 for a 15-year mortgag

percent. How can I determine my monthly mortg

How should an auto company allocate its adver

advertising formats?

How should cities transport students to more d

If a city has only one hospital, where should i

How should a drug company allocate its sales f

A drug company has $2 billion allocated to pu

companies should they buy?

The tax rate charged to a drug company depend

produced. How can a drug company determine wh

245

Chapter 29

Using Solver to Det

Optimal Product Mix

Questions answered in this chapter:

■

How can I determine the monthly product mix th

■

Does a Solver model always have a solution?

■

What does it mean if a Solver model yields th

Answers to This Chapter’s Ques

How can I determine the monthly product mix th

Companies often need to determine the quantity o

basis. In its simplest form, the product mix p

of each product that should be produced during a m

must usually adhere to the following constrain

■

Product mix can’t use more resources than a

■

There is a limited demand for each product. Y

product during a month than demand dictates b

wasted (for example, a perishable drug).

Let’s now solve the following example of the p

solution to this problem in the

Feasible Solut

Figure 29-1.

Fig

URE 29-1

A feasible product mix.

246

Microsoft Excel 2010: Data Analysis and Business Modeling

Let’s say you work for a drug company that produ

Production of each product requires labor and raw m

hours of labor needed to produce a pound of each p

raw material needed to produce a pound of each p

of Product 1 requires six hours of labor and 3.2 p

price per pound is given in row 6, the unit cost p

contribution per pound is given in row 9. For ex

incurs a unit cost of $5.70 per pound, and contr

demand for each drug is given in row 8. For exam

This month, 4,500 hours of labor and 1,600 pound

this company maximize its monthly proft?

If you knew nothing about the Excel Solver, you mi

a worksheet to track proft and resource usage as

could use trial and error to vary the product mi

or raw material than is available, and without p

use Solver in this process only at the trial-and-

tion engine that flawlessly performs the trial-an

A key to solving the product mix problem is to e

proft associated with any given product mix. An i

this computation is the SUMPRODUCT function. The S

corresponding values in cell ranges and returns th

in a SUMPRODUCT evaluation must have the same di

use SUMPRODUCT with two rows or two columns but n

As an example of how you can use the SUMPRODUCT f

let’s try to compute resource usage. Labor usage i

(Labor used per pound of drug 1)*(Drug 1 pounds produced)+(Labor

*(Drug 2 pounds produced) + ...(Labor used per pound of drug 6)*(Drug

You could compute labor usage in a more tedious f

G4+H2*H4+I2*I4

. Similarly, raw material usage could be c

F5+G2*G5+H2*H5+I2*I5

. However, entering these formulas in a w

time-consuming. Imagine how long it would take i

produced, for example, 50 products at its plant.

material usage is to copy from D14 to D15

. This

the fo

formula computes

D2*D4+E2*E4+F2*F4+G2*G4+H2*H4+I

Chapter

Using

Solver to Determine the

247

Optimal Product Mix

is much easier to enter. Notice that I use the $

the formula I still capture the product mix fr

material usage.

In a similar fashion, proft is determined by th

(Drug 1 profit per pound)*(Drug 1 pounds produced) + (Drug 2 profit per

*(Drug 2 pounds produced) + ...(Drug 6 profit per pound)*(Drug

Proft is easily computed in cell D12 with

the f

You now can identify the three components of th

■

Target

The

cell

goal is to maximize proft (comput

■

Changing

The

cells

number of pounds produced of eac

range D2:I2)

■

Constraints

You have the following constraints:

❑

Do not use more labor or raw material tha

D14:D15 (the resources used) must be less th

F14:F15 (the available resources).

❑

Do not produce more of a drug than is in d

D2:I2 (pounds produced of each drug) must b

for each drug (listed in cells D8:I8).

❑

You can’t produce a negative amount of an

I’ll show you how to enter the target cell, ch

you need to do is click the Solve button to fn

To begin, click the Data tab, and in the Analy

Not

s I explained in Chapter 28, “An Introduction t

installed by clicking the File tab, then Options, f

Add-ins and click Go. Select the Solver Add-In che

The Solver Parameters dialog box will appear, a

248

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 29-2

The Solver Parameters dialog box.

Click the Set Objective box, and then select the p

Variable Cells box, and then point to the range D

each drug. The dialog box should now look Figure 2

Fig

URE 29-3

The Solver Parameters dialog box with the target c

You’re now ready to add constraints to the model

Constraint dialog box, shown in Figure 29-4.

Chapter

Using

Solver to Determine the

249

Optimal Product Mix

Fig

URE 29-4

The Add Constraint dialog box.

To add the resource usage constraints, click th

D14:D15. Select <= from the middle list. Click th

range F14:F15. The Add Constraint dialog box s

Fig

URE 29-5

The Add Constraint dialog box with the resource u

You have now ensured that when Solver tries di

combinations that satisfy both D14<=F14 (labor u

and D15<=F15 (raw material used is less than

sidered. Click Add to enter the demand constrai

shown in Figure 29-6.

Fig

URE 29-6

The Add Constraint dialog box with the demand co

Adding these constraints ensures that when

Solv

ing cell values, only combinations that satisfr

■

D2<=D8 (the amount produced of Drug 1 is les

■

E2<=E8 (the amount produced of Drug 2 is les

■

F2<=F8 (the amount produced of Drug 3 is les

■

G2<=G8 (the amount produced of Drug 4 is les

■

H2<=H8 (the amount produced of Drug 5 is les

■

I2<=I8 (the amount produced of Drug 6 is les

250

Microsoft Excel 2010: Data Analysis and Business Modeling

Click OK in the Add Constraint dialog box. The S

Figure 29-7.

Fig

URE 29-7

The fnal Solver Parameters dialog box for the produ

Selecting the Make Unconstrained Variables Non-N

changing cells are forced to be greater than or e

Next choose Simplex LP from the Select A Solving M

engine because the product mix problem is a spec

model

. Essentially, a Solver model is linear under th

■

The target cell is computed by adding togethe

(changing cell)*(constant)

■

Each constraint satisfes the

linear model req

is evaluated by adding together the terms of th

comparing the sums to a constant.

Why is this Solver problem linear? Our target ce

(Drug 1 profit per pound)*(Drug 1 pounds produced) + (Drug 2 profit per

*(Drug 2 pounds produced) + ...(Drug 6 profit per pound)*(Drug

This computation follows a pattern in which the t

together terms of the form

(changing cell)*(cons

Chapter

Using

Solver to Determine the

251

Optimal Product Mix

Our labor constraint is evaluated by comparing th

pound of Drug 1)*(Drug 1 pounds produced) + (L

pounds

produced)+…(Labor used per pound of Drug 6)

available.

Therefore, the labor constraint is evaluated by a

(changing cell)*(constant)

and comparing the s

and the raw material constraint satisfy the li

The demand constraints take the form:

(Drug 1 produced)<=(Drug 1 Demand)

(Drug 2 produced)<=(Drug 2 Demand)

…

(Drug 6 produced)<=(Drug 6 Demand)

Each demand constraint also satisfes the linea

evaluated by adding together the terms of the f

the sums to a constant.

Knowing that the product mix model is a linear m

■

If a Solver model is linear and you select S

optimal solution to the Solver model. If a S

not fnd the optimal solution.

■

If a Solver model is linear and you select S

algorithm (the simplex method) to fnd the m

is linear and you do not select Simplex LP, S

GRG2 method) and might have diffculty fndin

After you click Solve, Solver calculates an op

model. As I stated in Chapter 28, an optimal s

set of changing cell values (pounds produced o

of all feasible solutions. Again, a feasible s

constraints. The changing cell values shown in Fi

production levels are non-negative, production l

usage does not exceed available resources.

Fig

URE 29-8

A feasible solution to the product mix problem f

252

Microsoft Excel 2010: Data Analysis and Business Modeling

The changing cell values shown in Figure 29-9 re

following reasons:

■

You produce more of Drug 5 than the demand fo

■

You use more labor than is available.

■

You use more raw material than is available.

Fig

URE 29-9

An infeasible solution to the product mix problem d

After you click Solve, Solver quickly fnds the o

need to select Keep Solver Solution to preserve th

Fig

URE 29-10

The optimal solution to the product mix problem.

Our drug company can maximize its monthly proft at a l

596.67 pounds of Drug 4, 1,084 pounds of Drug 5, a

determine whether you can achieve the maximum pr

can be sure of is that with your limited resourc

than $6,625.20 this month.

Does a Solver model always have a solution?

Suppose that demand for each product

must

be met

worksheet in the fle Prodmix.xlsx.) You then hav

D2:I2<=D8:I8 to D2:I2>=D8:I8. To do this, open S

then click Change. The Change Constraint dialog b

Chapter

Using

Solver to Determine the

253

Optimal Product Mix

Fig

URE 29-11

The Change Constraint dialog box.

Select >=, and then click OK. You’ve now ensur

values that meet all demands. When you click S

fnd a feasible solution.” This message does

not m

el, but rather that with limited resources, yo

simply telling you that if you want to meet de

labor, more raw materials, or more of both.

What does it mean if a Solver

Set Values

model Do

yields

Not Con

the r

Let’s see what happens if you allow unlimited d

negative quantities to be produced of each dru

Set Values Do Not Converge

worksheet in the fl

for this situation, open Solver and clear the

check box. In the Solver Parameters dialog box

and then click Delete to remove the constraint

sage “Set Cell Values Do Not Converge.” This m

maximized (as in this example), there are feas

values. (If the target cell is to be minimized

means there are feasible solutions with arbitr

byallowing negative production of a drug, you i

to produce arbitrarily large amounts of other d

allows you to make unlimited profts. In a real s

money. In short, if you see “Set Values Do Not C

Problems

Suppose our drug company can purchase up to 50

than current labor costs. How can it maximi

At a chip manufacturing plant, four technic

(Products 1, 2, and 3). This month, the chi

50 units of Product 2, and at most 50 units o

Products 1 and 3. Technician B can make only P

only Product 3. Technician D can make only P

254

Microsoft Excel 2010: Data Analysis and Business Modeling

products contribute the following proft: Prod

$10. The time (in hours) each technician need

Product

Technician

2.5

Cannot dC

oannot do

Cannot d3

o.5

Cannot d4

Cannot do

Each technician can work up to 120 hours per m

maximize its monthly proft? Assume a fraction

A computer manufacturing plant produces mice, k

The per-unit proft, per-unit labor usage, mon

usage are given in the following table:

Mice

KeyboardJ

soysticks

Proft/unit $8

$11

Labor usage/unit

.2 hour .3 hour .24 hour

Machine time/unit

.04 hour .055 hour.04 hour

Monthly demand

15,000

29,000

11,000

Each month, a total of 13,000 labor hours and 3

available. How can the manufacturer maximize i

plant?

Resolve our drug example assuming that a mini

drug must be met.

Jason makes diamond bracelets, necklaces, and e

of 160 hours per month. He has 800 ounces of d

ounces of diamonds required to produce each p

each product is unlimited, how can Jason maxi

Product Unit profit

Labor hoursOunces

per unit

of diamonds

per unit

Bracelet$300

.35

1.2

Necklace$200

.15

.75

Earrings$100

.05

In our product mix example, suppose that when

any product you must give a $1 per pound disc

How does this change the answer to the proble

255

Chapter 30

Using Solver to Sch

Workforce

Question answered in this chapter:

■

How can I effciently schedule my workforce t

Many organizations (such as banks, restaurants

their labor requirements are at different time

effciently schedule their workforce. You can u

solve workforce scheduling problems.

Answers to This Chapter’s Ques

How can I efficiently schedule my workforce to m

Bank 24 processes checks seven days a week. Th

process checks is shown in row 14 of the fle B

example, 13 workers are needed on Tuesday, 15 w

so on. All bank employees work fve consecutive d

employees Bank 24 can have and still meet its l

Fig

URE 30-1

The data we’ll use to work through the bank work

You begin by identifying the target cell, chan

model.

■

Target

Minimize

cell

total number of employees.

■

Changing

Number

cells

of employees who start work (

days) each day of the week. Each changing c

256

Microsoft Excel 2010: Data Analysis and Business Modeling

■

Constraints

For each day of the week, the number of e

must be greater than or equal to

Number

the number

employees

)

(

working

Needed employees

)

To set up the model for this problem,working

you need t

each day. I began by entering in the cell range A

employees who start their fve-day shift each day

that 1 employee begins work on Monday and works M

day’s required workers in the range C14:I14.

To track the number of employees working each da

range C5:I11. The value 1 indicates that the emp

designated in the cell’s row are working on the d

example, the 1 in cell G5 indicates that employe

working on Friday; the 0 in cell H5 indicates th

Monday are not working on Saturday.

By copying from C12 to

SUMPRODUCT($A$5:$A$11,C5:C11

D12:I12 the formula

, I compute

the number of employees working each day. For ex

A5+A8+A9+A10+A11

, which equals

(Number starting on Mo

Thursday)+(Number starting on Friday)+(Number st

Sunday)

. This total is indeed the number of people w

After computing the total number of

SUM(A5:A11)

employees

, I

in c

can enter a model in Solver as shown in Figure 3

Fig

URE 30-2

The Solver Parameters dialog box flled in to solve t

Chapter

Using

Solver to Schedule

257

Your Workforce

In the target cell (A3), I want to minimize th

C12:I12>=C14:I14

ensures that the number of em

as the number needed each day. The constraint

of employees beginning work each day is an int

in the Solver Parameters dialog box and flled i

Figure 30-3.

Fig

URE 30-3

This constraint defnes as an integer the number o

Note that this model is linear because

changing

the tar

cells, and the constraint is created by compar

the product of each changing cell times a cons

workers. Therefore I selected the Simplex

- LP e

ber of workers on a day, I checked the Make Un

After clicking Solve, I fnd the optimal soluti

A total of 20 employees is needed. One employe

four start on Thursday, one starts on Friday, t

Note that this model actually has multiple opti

the Solver again, you might very well fnd one o

Problems

Suppose Bank 24 had 22 employees and that t

that they would have the maximum number of w

workers be scheduled?

Suppose Bank 24 employees are paid $150 per d

work a day of overtime at a cost of $350. How s

258

Microsoft Excel 2010: Data Analysis and Business Modeling

The number of telephone reservation operators n

of day is as follows:

Time

Operators needed

Midnight–4 A.M.

4 A.M.–8 A.M.16

8 A.M.–Noon

Noon–4 P.M.

4 P.M.–8 P.M. 31

8 P.M.–Midnight

Each operator works one of the following six-

A.M.–noon, noon–6:00 P.M., 6:00 P.M.–midnight

operators needed?

Shown in Figure 30-4 are the number of people i

watch various TV shows and the cost (in thous

ad on each show. For example, it costs

. $160,0

The show is watched by 6 million males betwee

between 36 and 55, 1 million males over 55, 9 mi

million females between 36 and 55, and

2 mill

cludes the number of people in each group (in mi

ad. For example, the advertiser wants at leas

its ads. What is the cheapest way to meet the

Fig

URE 30-4

Data for Problem 4.

The Pine Valley Credit Union is trying to sch

8 A.M.– 6 P.M. and needs the following number o

Chapter

Using

Solver to Schedule

259

Your Workforce

NeededTime

8–9

9–10

10–11

11–12

12–1

1–2

2–3

3–4

4–5

5–6

Full-time tellers can work 8 A.M.–5 P.M. (w1 l

(with a 1 P.M.–2 P.M. lunch hour).

Part-time tellers work 10 A.M.–2 P.M. Full-ti

anp

dart-time tellers $60 per day. At most, fo

the credit union minimize their daily telle

261

Chapter 31

Using Solver to Sol

or Distribution Pro

Question answered in this chapter:

■

How can a drug company determine at which l

from which location it should ship drugs to c

Many companies manufacture products at )differe

and

ship their products to customers

). A natural

(often questi

called

the least expensive way to produce and ship pr

This type of problem is .

called

A transportation pro

up as a linear Solver model with the following s

■

Target

Minimize

cell

total production and shipping c

■

Changing

The

cells

amount produced at each supply p

demand point.

■

Constraints

The amount shipped from each supply p

Each demand point must receive its required d

non-negative.

Answer to This Chapter’s Quest

How can a drug company determine at which loca

which it should ship drugs to customers?

You can follow along with this problem by look

company produces a certain drug at its Los Ang

month, the Los Angeles plant can produce up to 1

produce up to 12,000 pounds, and New York

can p

pany must ship each month the number of pounds l

of the United States—East, Midwest, South,

and W

ample, the West region must receive at least 1

cost per pound of producing a drug at each pla

thceountry is given in cells B4:E6. For example

drug in Los Angeles and ship it to the Midwest r

region the quantity of the drug it needs?

262

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 31-1

Data for a transportation problem.

To express the target cell, you need to track tot

range B10:E12 trial values for shipments from ea

compute total shipping cost as follows:

(Amount sent from LA to East)*(Cost per pound of sending drug from

+(Amount sent from LAto Midwest)*(Cost per pound of sending drug

+(Amount sent from LA to South)*(Cost per pound of sending drug

+(Amount sent from LA to West)*(Cost per pound of sending drug

+...(Amount sent from New York City to West)

*(Cost per pound of sending drug from New York City to West)

The SUMPRODUCT function can multiply correspondi

rectangles (as long as the rectangles are the sa

I’ve named the cell range B4:E6

costs

. and the ch

Therefore, total shipping and production cost is c

SUMPRODUCT(costs,shipped)

To express the problem’s constraints,

supply

I frst com

point. By entering the formula

SUM(B10:E10)

in c

pounds shipped from Los Angeles as

(LA shipped t

(LA shipped to South)+(LA

. Copying

shipped

this formula

to West)

to F11:

total shipped from Atlanta and New York City. La

constraint

) that ensures that the amount shipped from e

plant’s capacity.

Next I compute the total received by each demand p

formula

SUM(B10:B12)

. This formula computes the total numb

East as

(Pounds shipped from LA to East)+(Pounds s

shipped from New

York

By copying

City to

this

East)

formula from B

Chapter

Using

Solver to Solve Transportation

263

or Distribution Problems

the pounds of the drug received by the Midwest

constraint (called

) that

demand

ensures

constraint

that each regi

the drug it requires.

Now I open the Solver Parameters dialog box (c

tab) and fll it in as shown in Figure 31-2.

Fig

URE 31-2

The Solver set up to solve our transportation pr

I want to minimize total shipping cost (comput

the number of pounds shipped from each plant t

amounts are listed in, the

consisting

range named

of cells

shipped

B10

F10:F12<=H10:H12 (the supply constraint) ensur

not exceed its capacity. The constraint B13:E1

that each region receives at least the amount o

This model is a linear Solver model because th

terms of the form

(changing cell)*(constant),

created by comparing the sum of changing cells t

I chose the Simplex LP engine. Clearly, shipme

Make Unconstrained Variables Non-Negative chec

After clicking Solve in the Solver Parameters d

solution shown earlier in Figure 31-1. The mini

264

Microsoft Excel 2010: Data Analysis and Business Modeling

$86,800. This minimum cost can be achieved if th

and shipping schedule:

■

Ship 10,000 pounds from Los Angeles to the We

■

Ship 3,000 pounds from Atlanta to the West re

to the Midwest region. Ship 6,000 pounds from A

■

Ship 9,000 pounds from New York City to the E

York City to the Midwest region.

Problems

The following table gives the distances betwe

and Miami. Each city requires 40,000 kilowatt h

Dallas, and Miami are capable of producing 70

kWh over 100 miles costs $4. From where shoul

meeting each city’s demand?

Boston ChicagoDallas Los Angeles

Miami

Chicago

983

1205

2112

1390

Dallas1815

1205

801

1332

Miami 1539

1390

1332

2757

Resolve this chapter’s example assuming that d

13,000.

Your company produces and sells drugs at seve

where to produce goods for each sales

- locatio

ability. The model here is similar to the mod

drugs should be produced. Use the following a

❑

You produce drugs at six locations and sell t

❑

The tax rate and variable production cost d

is produced. For example, any units produce

produce; profts from these goods are taxed a

❑

The sales price of each drug depends on whe

each product sold in Location 2 is sold for $

Production location

Sales price

$45 $40 $38 $36 $39 $34

Tax rate

31% 40% 20% 40% 35% 18%

Variable production

$7 cost

Chapter

Using

Solver to Solve Transportation

265

or Distribution Problems

❑

Each of the six plants can produce up to 6 mi

❑

The annual demand (in millions) for your p

Sales location

Demand

❑

The unit shipping cost depends on the pla

the location where the product is sold.

Sold S1old S2old S3old S4old S5old 6

Plant $13

Plant $25

$10

$11

Plant $34

Plant $45

Plant $6

Plant $67

$10

For example, if you produce a unit at Plant 1 a

it.

How can you maximize after-tax proft with y

Suppose that each day, northern, central, a

lion gallons of water. Also assume that nor

available 120 billion gallons of water, wher

of water available. The cost of shipping 1 b

regions is as follows:

NorthernCentral Southern

Northern

$5,000

$7,000

$10,000

Central

$7,000

$5,000

$6,000

Southern

$10,0000$6,000

$5,000

You will not be able to meet all demand for wa

of unmet demand incurs the following shorta

NorthernCentral Southern

Shortage cost/billion

gallons short

$6,000

$5,500

$9,000

How should California’s water be distribute

shortage costs?

267

Chapter 32

Using Solver for Ca

Question answered in this chapter:

■

How can a company use Solver to determine w

Each year, a company like Eli Lilly needs to d

like Microsoft, which software programs to dev

new consumer products to develop. The Solver i

make these decisions.

Answer to This Chapter’s Quest

How can a company use Solver to determine whic

Most corporations want to undertake projects th

(NPV), subject to limited resources (usually ca

opment company is trying to determine which of 2

The NPV (in millions of dollars) contributed by e

of dollars) and the number of programmers need

given on the

Basic Model

worksheet in the fle

example, Project 2 yields $908 million. It req

during Year 2, and $248 million during Year 3. P

Year 1, 86 programmers during Year 2, and 83 p

the capital (in millions of dollars) available d

indicate how many programmers are available. F

in capital and 900 programmers are available.

The company must decide whether it should unde

company can’t undertake a fraction of a softwa

allocated, for example, the company would have a n

$0 revenue!

The trick in modeling situations in which you e

binary changing

. A binary

cells

changing cell always equal

cell that corresponds to a project equals 1, y

corresponds to a project equals 0, you don’t d

of binary changing cells by adding a constrain

and then choose Bin from the list in the Add C

268

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 32-1

Data we will use with Solver to determine which pro

With this background, you’re ready to solve the s

always with a Solver model, you should begin by i

cells, and the constraints.

■

Target

Maximize

cell

the NPV generated by selected p

■

Changing

Look

cells

for a 0 or 1 binary changing cell f

these cells in the range A6:A25

). For (and

example,

nameda th

1 i

indicates that you undertake Project 1; a 0 i

Project 1.

■

Constraints

You need to ensure

t=1,

that

for

Year

each

capital

Year

less than or equal to Year

capital availabl

to Year

labor available.

As you can see, the worksheet must compute for a

capital used annually, and the programmers used e

SUMPRODUCT(doit,NPV)

to compute the total NPV ge

range name

NPV

refers to the range C6:C25.)

For e

mula picks up the NPV of the project, and for ev

does not pick up the NPV of the project.- Therefo

ects, and the target cell is linear because it i

form

(changing

cell)*(constant)

In a similar fashion, I compute th

the labor used each year by copying from .E2 to F

I now fll in the Solver Parameters dialog box as s

Chapter

Using

Solver for Capital

269

Budgeting

Fig

URE 32-2

Solver Parameters dialog box set up for the proj

The goal is to maximize the NPV of selected pr

named)

doit

are the binary changing cells for each p

ensures that during each year the capital and l

and labor available. To add the constraint tha

the Solver Parameters dialog box and then sele

Constraint dialog box. The Add Constraint dial

The goal is to maximize the NPV of selected pr

named)

doit

are the binary changing cells for each p

ensures that during each year the capital and l

and labor available. To add the constraint tha

the Solver Parameters dialog box and then sele

Constraint dialog box. The Add Constraint dial

Fig

URE 32-3

Use the Bin option in the Add Constraint dialog b

that display either a 0 or a 1.

270

Microsoft Excel 2010: Data Analysis and Business Modeling

This model is linear because the target cell is c

form

(changing cell)*(constant)

and because the r

by comparing the sum of

(changing cells)*(consta

Simplex LP engine.

With the Solver Parameters dialog box flled in, I c

in Figure 32-1. The company can obtain a maximum N

choosing Projects 2, 3, 6–10, 14–16, 19, and 20.

Handling Other Constraints

Sometimes project selection models have other co

select Project 3, you must also select Project 4

Project 3 but not Project 4, this tells you that th

solve this problem, simply add the constraint th

than or equal to the binary changing cell for Pr

You can fnd this example on the

If 3 then 4

work

shown in Figure 32-4. Cell L9 refers to the bina

to the binary value related to Project 4. By add

Project 3, L9 equals 1 and this constraint force

constraint must also leave the binary value in th

you do not select Project 3. If you do not selec

allows the Project 4 binary to equal 0 or 1, whi

is shown in Figure 32-4.

Fig

URE 32-4

New optimal solution for

if not Project 3 then Proj

Chapter

Using

Solver for Capital

271

Budgeting

Now suppose that you can do only four projects f

At Most 4 Of P1–P10

worksheet, shown in Figure 3

of the binary values associated with Projects

1 th

Then add the constraint L8<=L10, which ensures th

selected. The new optimal solution is shown in Fi

billion.

Fig

URE 32-5

Optimal solution when only 4 of 10 projects can b

Solving Binary and Integer Progr

Linear Solver models in which some or all chan

integer are usually harder to solve than linea

to be fractions. For this reason, analysts are o

binary or integer programming problem. If your S

want to consider adjusting the Integer Optimal

Solver Options dialog box. Tolerance

(See Figure

setting

32-6.)ofF 0

that Solver will stop the frst time it fnds a f

theoretical optimal target cell value. (The th

target value found when the binary and integer c

faced with a choice between fnding an answer w

fnding an optimal solution in two weeks of com

value is 1%, which means that Solver stops whe

of the theoretical optimal target cell value. W

example, I had the Integer Optimality set to 5

9269. When I changed the Integer Optimality va

value (9293).

272

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 32-6

Adjusting the Integer Optimality option.

Problems

A company has nine projects under considerati

the capital required by each project during th

table. (All numbers are in millions.) For exa

and require expenditures of $12 million durin

During Year 1, $50 million in capital is avai

during Year 2.

NPV

Year 1 expenditure

Year 2 expenditure

Project14

Project17

Project15

Project40

Project12

Project14

Project10

Project12

❑

If you can’t undertake a fraction of a proj

none of a project, how can you maximize NPV

Chapter

Using

Solver for Capital

273

Budgeting

❑

Suppose that if Project 4 is undertaken, P

you maximize NPV?

A publishing company is trying to determine w

year. The fle Pressdata.xlsx gives the foll

❑

Projected revenue and development costs (

❑

Pages in each book

❑

Whether the book is geared toward an audi

(indicated by a 1 in column E)

The company can publish books with a total o

publish at least four books geared toward s

maximize its proft?

In the equation SEND + MORE = MONEY each le

0-9. Which digit is associated with each le

Jill is trying to determine her class sched

of two seven-week half semesters. Jill

- must t

ter. There are fve time slots during each s

course twice. Jill has associated a value w

in the fle Classdata.xlsx. For example, cou

value of 5. Which courses should Jill take d

value from the semester’s courses?

275

Chapter 33

Using Solver for Fi

Questions answered in this chapter:

■

Can I use Solver to verify the accuracy of th

mortgage payments for a variable interest r

■

Can I use Solver to determine how much mone

The Solver feature in Microsoft Excel 2010 can b

planning problems. In many of these types of p

balance on a loan or the amount of money neede

example, consider a situation in which

noninterest

you bor

portion of each monthly payment reduces the un

following equation (which I’ll refer to as Equ

(Unpaid loan balance at end of period t)=(Unpaid loan balance at beginning of period t)

–[(Month t payment)–(Month t interest paid)]

Now suppose that you are saving for retirement

beginning of each period) (let’s

an amount

say of

periods

money eq

retirement account, and during the year, your r

areturn of some percentage. During retirement, y

of each year and your retirement fund still re

thfeollowingEquation

equation2)

( describes the relations

withdrawals, and return.

(Retirement savings at end of Year t+1) = (Retirement savings at end of Year t + retirement

contribution at beginning of Year t+1 – Year t+1 retirement withdrawal)

*(Investment return earned during Year t+1)

Combining basic relationships such as these wi

interesting fnancial planning problems.

Answers to This Chapter’s Ques

Can I use Solver to verify the accuracy of the E

mortgage payments for a variable interest rate

Recall that in Chapter 10, “More Excel Financia

(assuming payments occur at the end of a month

annual interest rate of 10 percent to be $1,03

276

Microsoft Excel 2010: Data Analysis and Business Modeling

our monthly payment? You’ll fnd the answer in th

Finmathsolver.xlsx, which is shown in Figure 33-

Fig

URE 33-1

Solver model for calculating the monthly payment fo

The key to this model is to use Equation 1 to tr

target cell is to minimize the monthly payment. T

The only constraint is that the ending balance i

I entered the beginning balance in cell B5. I en

I copied the monthly payment to the range C6:C14

occur at the end of each month, interest is incu

month. The monthly interest

) is

rate

computed

(I’ve in

named

D1 by

celd

the annual rate of 0.08 by 12. The interest paid e

cell D5 to D6:D14. the

Eachformula

month,

rate*B5

this formula comp

.006666*(month’s

beginning

By copying

balance)

the formula

(B5–(Pa

E5 to E6:E14, I use Equation 1 to compute each m

(Month t+1 beginning balance)=(Month

, each month’s

ending

beginnin

computed by copying from cell

B6 to B7:B14 the f

I am now ready to use Solver to determine the mo

Solver Parameters dialog box, take a look at Fig

The goal is to minimize the monthly payment (cel

same as the target cell. The only constraint is th

equal 0. Adding this constraint ensures that the l

engine and select the non-negative variables opti

$1,037.03, which matches the amount calculated by th

Chapter

Using

Solver for Financial

277

Planning

Fig

URE 33-2

Solver Parameters dialog box set up to determine m

This model is linear because the target cell e

created by adding multiples of changing cells.

I should mention that when Solver models invol

the Solver sometimes thinks models that

are

is good practice to check the Use Automatic Sc

should ensure that Solver properly recognizes l

Can I use Solver to determine how much money I n

By using Equation 2 (shown earlier in the chap

money a person needs to save for retirement. H

I am planning for my retirement, and at the be

39 years, I’m going to contribute some money t

increase my retirement contribution by $500. W

(at the beginning of each year) $100,000 per y

assumptions about the yields for my retirement i

■

During the frst 20 years of my investing, t

■

During all other years, my investments will e

278

Microsoft Excel 2010: Data Analysis and Business Modeling

I’ve assumed that all contributions and withdrawa

these assumptions, what is the least amount of m

enough to make my retirement withdrawals?

You can fnd the solution to this question on the

xlsx, shown in Figure 33-3. Note that I’ve hidde

This worksheet simply tracks my retirement balan

year, I earn the indicated interest rate on the r

value for my Year 1 payment in cell C6. Copying th

ensures that the retirement contribution increas

40. I entered in column D the assumed return on m

years. In cells E46:E65, I entered the annual $1

Copying the formula

(B6+C6–E6)*(1+D6)

from F6 to F

year’s ending retirement account balance. Copyin

computes the beginning balance for years 2 throu

is 0. Note that the value 6.8704E-07 in cell F65 i

result of a rounding error.

Fig

URE 33-3

Retirement planning data that can be set up for ana

The Solver Parameters dialog box for this model i

my Year 1 contribution (cell C6). The changing c

ensure that I never run out of money during reti

so that the ending balance for Years 41 through 6

Chapter

Using

Solver for Financial

279

Planning

Fig

URE 33-4

Solver Parameters dialog box set up for the reti

After choosing the Simplex LP engine and selec

Non-Negative option in the Solver Parameters d

Parameters dialog box and fnd that the frst ye

This model is linear because the target cell e

sreated by adding multiples of changing cells

investments is not the same each year, there i

solve this problem. Solver provides a general f

planning problems when mortgage rates or inves

Problems

I am borrowing $15,000 to buy a new car. I a

payments. The annual interest rate on the l

of mine, and he will allow me to make the mo

equal to one-half the payment for Months 31 th

each month?

Solve the retirement planning problem assumi

each year and contributions occur at the be

Solve our mortgage example assuming that pa

each month.

280

Microsoft Excel 2010: Data Analysis and Business Modeling

In the retirement-planning example, suppose th

and your salary increases 5 percent per year u

same percentage of your salary each year you w

should you save?

In the mortgage example, suppose that you wan

$50 each month. What should each month’s paym

Assume you want to take out a $300,000 loan o

month payments. The annual rate of interest i

need to make an ending balloon payment

of $40

come to increase, you want to structure the l

your monthly payments increase by 2 percent. D

monthly payment.

Blair’s mother is saving for Blair’s college e

made at the indicated times:

4 years from

5 years

now from

6 years

now

from

7 years

now

from now

$24,000

$26,000

$28,000

$30,000

The following investments are available:

❑

Today, one year from now, two years from now

years from now, she can invest money for on

return.

❑

Today, 2 years from now, and 4 years from n

years and receive a 14 percent return.

❑

Three years from now she can invest money f

percent return.

❑

Today she can invest money for seven years a

What is the minimum amount that Blair’s mothe

college education that ensures she can pay he

I owe $10,000 on one credit card that charges 1

on another credit card that charges 12 percen

is based on the month’s beginning balance. I c

$2,000 per month and the minimum monthly paym

the card’s unpaid balance at the beginning of th

cards in two years. What is the minimum amoun

281

Chapter 34

Using Solver to Rat

Question answered in this chapter:

■

Can I use Excel to set NFL point spreads?

Many of us follow basketball, football, hockey

on games in all these sports and others. For e

the Indianapolis Colts would win the 2010 Supe

Saints won the game. In this chapter, I’ll show th

were the better team and should have been favo

accurately estimate the relative ability of NF

Using a simple Solver model, you can generate r

the scores of the 2009 season. The work is in fl

You simply use the score of each game of the 2

cell for the Solver model is a rating for each t

For example, if the Indianapolis Colts have a r

of +7, the Jets are considered two points bett

With regard to the home-feld edge, in most yea

as well as professional basketball teams, tend t

home college basketball teams tend to win

- by a

ever, I will defne the home edge as a changing c

edge. You can defne the outcome of an NFL game t

the home team outscores the visitors and predi

following equation (which I’ll refer to as Equ

(Predicted points by which home team outscores v

(Away Team rating)

For example, if the home feld edge equals thre

Colts will be a

3+5–7

one-point

). If thefavorite

Jets host

(

the Colt

point favorite

3+7-5

). (The Tampa Bay-New England game wa

no home edge for this game.)

What target cell will yield reliable ratings? T

ratings and home-feld advantage that best pred

you want the prediction for each game to be as c

game. This suggests that you want to minimize th

(Predicted

. However,

outcome)

the problem with using

thi

tive prediction errors cancel each other out. F

282

Microsoft Excel 2010: Data Analysis and Business Modeling

margin by 50 points in one game and under predic

another game, the target cell would yield a valu

fact you were off by 50 points a game. You can r

over all games by using the formula

[(Actual Out

. Now positive

and negative errors will not cancel each other o

Answer to This Chapter’s Questi

Can I use Excel to set NFL point spreads?

Let’s now see how to determine accurate ratings f

2009 regular season. You can fnd the data for thi

which is shown in Figure 34-1.

Fig

URE 34-1

Data rating NFL teams that we’ll use with Solver.

To begin, I placed a trial home-feld advantage v

Starting in row 5, columns E and F contain the h

example, the frst game (listed in row 5) is Tenn

contains the home team’s score, and column H con

see, the Steelers beat the Titans 13-10. I can n

number of points by which the home team beats th

–

in cell I5. By pointing to the lower-right p

left mouse button, you can copy this formula dow

appears in row 260. (By the way, an easy way to s

Arrow. This key combination takes you to the las

In column J, I use Equation 1 to generate the pr

the frst game is computed in cell J5 as follows:

=$B$8+VLOOKUP(E5,$B$12:$C$43,2,FALSE)-VLOOKUP(F5

Chapter

Using

Solver to Rate

283

Sports Teams

This formula creates a prediction for the frst ga

home-team rating and then subtracting the visi

Ideleted the term $B$8 from the formula becaus

England-Tampa Bay game.) The term VLOOKUP(E5,$

home-team rating, and VLOOKUP(F5,$B$12:$C$43,2,

rating. (For more information about using look

Functions.”). In column K,

actual

I compute

score–predicted

)

the

for

squar

each game. Our squared error for the frst game i

= (I5-J5)^2.

After selecting the cell range I5

down to row 260.

Next I compute the target cell in cell K3 by s

SUM(J5:J260)

ou can enter a formula for a large column of nu

then selecting the frst cell in the range you want t

to enter the range from the cell you selected to t

closing parenthesis.

It is convenient to make the average team rati

better than average and a team with a negative r

average team rating in cell C10

. with the formu

I can now fll in the Solver Parameters dialog b

Fig

URE 34-2

Solver Parameters dialog box set up for NFL rati

284

Microsoft Excel 2010: Data Analysis and Business Modeling

I minimize the sum of the squared prediction err

changing each team’s rating (listed in cells C12

constraint

C10=0

ensures that the average team r

that the home team has an advantage of 2.26 poin

rated teams are shown in Figure 34-3. Remember th

are computed by Solver. In the template fle, you c

and Solver will still fnd the “best” ratings.

Fig

URE 34-3

Top 10 teams for the NFL 2009 season.

These ratings have the Saints around 5 points be

predicted (before the playoffs) that the Saints w

Why is our model not a linear Solver mo

This model is not linear because the target cel

(Home Team Rating+Home Field Edge–Visiting Team R

. Recall that for a S

model to be linear, the target cell must be cre

form

(changing

cell)*(constant)

This relationship doesn’t exist i

is not linear. Solver does obtain the correct a

model in which the target cell minimizes the su

GRG nonlinear engine because this model

is not l

ematical functions” such as IF statements. I di

Variables Non-Negative option because to have th

allow some of the team ratings to be negative.

Not

Recently, I found that the GRG Solver engine work

checked. I recommend that you go open the Options di

Scaling option.

Chapter

Using

Solver to Rate

285

Sports Teams

Problems

1–4.

The fles

.xlsx

Nfl0

= (1, 2, 3, 4) contain scores for e

the

200

NFL season. Rate the teams for each se

would you forecast to have made the Super B

For the 2004 season, devise a method to pre

Give each team an offensive rating and a de

Who had the best defense?

True or False? An NFL team could lose every ga

The fle Nba01_02.xlsx contains scores for e

season. Rate the teams.

The fle Nba02_03.xlsx contains scores for e

2002–2003 NBA season. Rate the teams.

The fle Worldball.xlsx contains all scores f

Championships. Rate the teams. Who were the b

10.

Our method of rating teams works fne for fo

arise if you apply these methods to hockey o

287

Chapter 35

Warehouse Location a

GRG Multistart and E

Solver Engines

Questions answered in this chapter:

■

Where in the US should an Internet shipping c

minimize the total distance that packages a

■

Where in the U.S. should an Internet shippi

minimize the total distance that packages a

In Microsoft Excel 2010, the Solver has been b

this chapter (and Chapters 36 and 37) I will tr

can help you solve many important optimization p

Understanding

Rg Multistart

the g

and Evo

Solver Engines

As I pointed out in Chapter 28, “An Introducti

2010 Solver has three engines that it uses to s

Nonlinear, and Evolutionary. In the following s

latter two of these engines are used to solve o

How Does Solver Solve Linear Sol

As I pointed out in Chapters 28 through 33, a S

changing cells in the target cells and constrai

form

(changing

cells)*constants

For linear models, you should a

engine, which is designed to effciently fnd so

Solver can handle problems with up to 200 chan

Solver that can handle larger problems

are avai

288

Microsoft Excel 2010: Data Analysis and Business Modeling

How Does the GRG Nonlinear Engine So

Optimization Models?

If your target cell and/or any of your constrain

not of the form

(changing cell)*(constant)

you h

ing cells, references such as the following in th

model nonlinear:

■

sin x

■

If your nonlinear formulas involve ordinary math o

then proper use of the GRG Nonlinear engine shou

your Solver model. To illustrate how the GRG Non

maximize –x

+ 4x + 2. This function is graphed in Fig

Fig

URE 35-1

How the GRG Nonlinear engine maximizes a function.

You can see that this function is maximized

functionfor x = 2

has a slope of 0. The GRG Nonlinear engine solve

at which the slope of the function is 0. Similar

,the GRG

Nonlinear engine solves this problem by determini

x = 0. See Figure 35-2.

Chapter

Warehouse

Location and the GRG Multistart

289

and Evolutionary Solver Engines

Fig

URE 35-2

How the GRG Nonlinear engine minimizes a functio

Unfortunately, there are many functions that c

where the function’s slope equals 0. For examp

shown in Figure 35-3, when x ranges between -5 a

Fig

URE 35-3

Maximizing a function with multiple peaks.

You can see that this function has more than o

you will fnd the right solution to the problem (

near x = 5—you will fnd a solution of x = 5, w

(especially those with more than one changing c

it appears you have a major hurdle to clear. F

You can select Multistart after choosing Optio

When the Multistart option is selected, Excel c

best answer after beginning with these startin

multiple peak and valley problem.

By the way, pressing Esc stops the Solver. Als

works best when you place reasonable upper and l

example, you do not specify changing cell<100 mi

290

Microsoft Excel 2010: Data Analysis and Business Modeling

The GRG engine also runs into trouble if the tar

functions like MAX, MIN, ABS, IF, SUMIF, COUNTIF

involve changing cells. These functions create p

slope due to the fact that the slope changes

abr

tion problem requires you to model the value of a E

price. This call option lets you buy the stock f

thoeption, then the value of

. the

I graphed

call option

this relati

Figure 35-4. It is clear that when s = 40, the o

would break down.

Fig

URE 35-4

Option value has no slope for $40 stock price.

As Figure 35-5 shows, Solver models that include th

absolute value of a number is just the distance o

= 0. In Excel the function ABS(x) returns the ab

Fig

URE 35-5

Absolute value function has no slope for x = 0.

Chapter

Warehouse

Location and the GRG Multistart

291

and Evolutionary Solver Engines

Optimization problems in which the target cell a

for any changing cell values are called

nonsmo

Multistart option has diffculty with these typ

apply Solver’s Evolutionary engine. For nonlin

changing cells and 100 constraints.

How Does the Evolutionary Solver E

Optimization Problems?

The Evolutionary Solver in Excel 2010 is based o

by John Holland, a computer science professor a

Evolutionary Solver, begin by taking 50–100 po

the set of points that meet the constraints.)

Then,

the target cell is evaluated for each point. U

theory of evolution, you change the points in th

likelihood that future population members are l

that have a good target cell value. Because thi

and not on slopes, multiple peaks and valleys p

not have slopes (the so-called

nonsmooth

functi

The Evolutionary Solver engine (like the

- GRG M

sonable upper and lower bounds are placed on y

Evolutionary Solver engine, its best to choose O

change the mutation rate to .5. Also select th

increase the maximum time without improvement t

rate decreases the likelihood that the Solver g

maximum time without improvement to 3,600 seco

to improve the target cell for 3,600 seconds. T

your computer.

Now let’s use the Excel 2010 Solver to solve t

Answer to This Chapter’s Quest

Where in the US should an Internet shipping co

minimize the total distance that packages are s

The number of shipments (in thousands) made ea

Figure 35-6. (See the worksheet

One warehouse

292

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 35-6

Data for the single warehouse problem.

A key to this model is the following formula, whi

two U.S. cities having a latitude and longitude g

(

Lat

1 -

Lat

(

Long

1 -

Long

Distance

= 69

To begin, enter in cells F4:G4 trial values for th

Next, by copying from F7 to F8:F27 the

, you

formula

compute the approximate distance of each city fr

to G8:G27 the

E7*F7

formula

computes the distance traveled by

cell H5, the formula

SUM(G7:G27)

computes the tot

target cell is to minimize H5 by changing

engine,

F4:G4. A

the Solver Parameters dialog box appears as in Fi

After you click Solve, you’ll fnd that the wareh

latitude and 92.48 degrees longitude, which is n

Chapter

Warehouse

Location and the GRG Multistart

293

and Evolutionary Solver Engines

Fig

URE 35-7

Solver Parameters dialog box for the one warehou

Where in the US should an Internet shipping co

minimize the total distance that packages are s

The work for this problem is in the worksheet

shown in Figure 35-8.

Fig

URE 35-8

Model for locating two warehouses.

294

Microsoft Excel 2010: Data Analysis and Business Modeling

To begin, enter trial latitudes and longitudes f

from F7 to F8:F27 the formula

69*SQRT((C7-$F$4)^

distance of each city from Warehouse

formula

1. By copyi

69*SQRT((C7-$F$5)^2+(D7-$G$5)^2),

you compute the d

Warehouse 2. Since the shipments from each city w

you now compute the distance of each city to the c

H8:H27 the formula

MIN(F7,G7).

In I7:I27, you co

shipments by copying from I7 to I8:I27 the formu

distance traveled by shipments

with the formula

You’re now ready to use Solver to determine the o

the Solver Parameters dialog box is shown in Fig

Fig

URE 35-9

Solver set up for locating two warehouses.

Begin by selecting the GRG Nonlinear engine. The

each warehouse at 0 latitude and longitude. This s

the warehouses in Africa and it puts two warehou

we fnd Solver recommends locating both warehouse

a suboptimal solution. The problem is twofold: T

slopes, and perhaps our target cell, as a functi

peaks and valleys. If our target cell has multip

perhaps our poor starting solution is not near th

Chapter

Warehouse

Location and the GRG Multistart

295

and Evolutionary Solver Engines

solution. In situations in which you suspect m

to use the GRG Multistart option, which tries m

answer from each starting point. Most of the ti

will be the optimal solution to the problem. T

cells and run Solver using the GRG Multistart o

cells, I selected 0 and 90 degrees. This ensur

For the bounds on longitude changing cells, I c

location is west of Greenwich, England and eas

In the results, the average distance traveled p

warehouses are shown in cells F4:G5 of Figure 3

Kentucky, while Warehouse 2 is located near La

To confrm that Solver found the optimal soluti

and found no improvement in the optimal soluti

Suppose I had set an upper bound for longitude o

would have found that Solver recommends a long

bounds on a changing cell and the Solver force

a bound, then you should relax the bound.

Problems

Find the optimal solution to the warehouse p

Suppose you want to locate a single restroo

travel the smallest possible distance per d

work in four locations within the plant as d

Number of employees

Assume that employees always walk in a north

going to and from the restroom. Where shoul

Problem 2 if the company wants to locate tw

297

Chapter 36

Penalties and the E

Questions answered in this chapter:

■

What are the keys to successfully using the E

■

How can I use the Evolutionary Solver to as

job in one of four workgroups?

Answers to This Chapter’s Ques

What are the keys to successfully using the Ev

Previously I stated that the Evolutionary Solv

optimization problems in which the target cell a

functions such as IF, ABS, MAX, MIN, COUNTIF, C

and AVERAGEIFS. Before solving a problem with th

following in the Solver Parameters dialog box:

■

Click Options, select the Evolutionary tab, a

■

Change Maximum Time Without Improvement to 3

■

Place reasonable lower and upper bounds on y

Everything in life has an upside and a downsid

The upside of the Evolutionary Solver is -that i

side is that constraints that are not linear f

well. To handle most constraints with the Evol

cell to make violation of a constraint a bad thi

with any constraint violation. The chapter’s n

the Evolutionary Solver.

How can I use the Evolutionary Solver to assig

in one of four workgroups?

You need to assign 80 employees to four workgr

rated each employee’s competence on a 0 to 10 s

employee has rated his or her satisfaction with e

scale).

example,

For

Worker 1 has been given a 9 rati

Workgroup 4 a rating of 7.

298

Microsoft Excel 2010: Data Analysis and Business Modeling

The work for this question is in the fle Assign.

between 18 and 22 people to each workgroup. You c

important as employee satisfaction. How -can you a

mize total satisfaction and ensure that each div

Fig

URE 36-1

Data for job assignment problem.

In cells A3:A82 I entered trial assignments of w

to Workgroup 1, for example, is an okay starting s

formula

HLOOKUP(A3,Qual,B3+1)

enables you to loo

her assigned job. Note that

Qual

refers to the r

the formula

HLOOKUP(A3,Satis,B3+1)

enables you t

her assigned job.

Satis

is the range name for G2

To deal with the fact that each division needs b

count how many employees have been assigned to e

N6:N9 by copying from N6 to N7:N9

the

Next,

formula

in cell

O6:O9 you determine if a workgroup has the incor

from O6 to O7:O9 the formula

IF(OR(N6<18,N6>22),

Now I’ll show how to work on computing the targe

competence and total job quality by copying from K

To ensure that each workgroup will have between 1

target cell. I chose a penalty of 1,000 for each w

22 workers. There is no hard-and-fast rule to he

In this situation, the average rating is 5. This y

Therefore, it seems likely that putting the wron

beneft the target cell by more than 1,000, so su

which a workgroup has too many or too few worker

Chapter

Penalties

and the Evolutionary

299

Solver

too large (100,000) because it sometimes makes th

penalty is too small, Solver will not achieve th

In cell O10 I computed total number of divisio

workers with the

formula

Now we

SUM(O6:O9)

are fnally ready to c

in cell O12 by adding twice the total competen

a penalty of 1,000 for each group that does not h

fnal target cell is computed with the formula

You now can create the Solver model for this p

Solver because the COUNTIF functions are nonsm

model is shown in Figure 36-2.

Fig

URE 36-2

Solver model for worker assignment problem.

I maximize the weighted sum of workgroup and e

an incorrect number of workers in a workgroup (

assignment to be 1, 2, 3, or 4. The solution i

number of workers; average employee competence

tion is 6.3. Over all 80 workers, the average o

average for satisfaction ratings is 5, so cond

assignment.

If you had tried the GRG Nonlinear engine (eve

not have found the optimal solution because th

Another tip about using the Evolutionary Solve

and you will usually be rewarded by having Sol

300

Microsoft Excel 2010: Data Analysis and Business Modeling

Using Conditional Formatting to H

Ratings

You can use the conditional formatting feature t

(based on her assignment) competence and satisfa

cell range C3:J82. Then, select New Rule from Co

select the Use A Formula To Determine Which Cell

box as shown in Figure 36-3.

Fig

URE 36-3

Using conditional formatting to highlight worker q

This formula will enter in cell C3 a red format i

Workgroup 1. You can copy this formula across an

and satisfaction ratings are highlighted only fo

assigned.

Problems

Use the Evolutionary Solver to solve Problem 4 i

Budgeting.”

Solve the two warehouse problem in Chapter 35

Multistart and Evolutionary Solver Engines,” a

most 120,000 units.

Chapter

Penalties

and the Evolutionary

301

Solver

In the fctional state of Politicians Care A

districts. Each of 15 cities must be assign

must be assigned between 150,000 and 250,00

given below. Assign the cities to districts t

the Democrats.

City Rep

Dem

114

Solve the assignment of workers example ass

important as the bosses’ ratings.

303

Chapter 37

The Traveling Sales

Questions answered in this chapter:

■

How can I use Excel to solve sequencing pro

■

How can I use Excel to solve a traveling sa

Answers to This Chapter’s Ques

How can I use Excel to solve sequencing proble

Many business problems involve the choice of a

■

In what order should a print shop work on 1

jobs fail to meet their due dates? Problems o

problems.

■

A salesperson lives in Boston and wants to v

In which order should he visit the cities t

an example of the classic

traveling

salespe

Here are two other examples of a TSP:

■

A delivery driver needs to make twenty stop

packages to minimize her time on the road?

■

A robot must drill 10 holes to produce a si

drilling the holes minimizes the total time n

The new and improved Excel 2010 Solver makes t

Simply choose Evolutionary Solver, select your c

All Different option ensures that if you have 1

2, …10 to the changing cells with each value o

a range of

changing cells to be different, E

values 1,with

2, …,

each

possible value occurring ex

option to easily solve a traveling-salesperson p

How can I use Excel to solve a traveling sales

Let’s try and solve the following problem.

Willie Lowman is a salesman who lives in Bosto

Figure 37-1 and then return to Boston. In what o

the total distance he travels? Our work is in fl

304

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 37-1

Data for the TSP.

To model this problem in a spreadsheet, you shou

of the numbers 1 through 11 represents an order f

2-4-6-8-10-1-3-5-7-9-11 can be viewed as traveli

LA (City 5), and fnally to SF (City 10) before r

from the location of

×9

City

×8×7×6…

×2

×1

=there

3,628,800

are 10!

- possibl

= 10

ings for Willie to consider.

To begin you need to determine the total distanc

the cities. The INDEX function is perfect for thi

Function,” that the syntax

Range,

of the

row#,

INDEX

). Excel

column#

function

look i

in the range of cells named

Range

and picks out th

Range

. In this case, you can use the INDEX -functio

ing all cities.

I began by entering in the range F16:F26 an orde

Next, I named the range

, and G4:Q14

entered

distances

in cell G16 the f

INDEX(distances,F26,F16).

This formula determine

(in F26) and the frst city listed

INDEX(Distances,F16

(in F16). Next I e

in cell G17 and copy it to the range G18:G26. In G

between the frst and second city listed,

- and so o

tal distance traveled) in cell

G27 with the form

At this point, I’m ready to invoke the Evolution

then I click Add Constraint and select the range F

This ensures that Solver always keeps the changi

values 1, 2, up to 11. Each value will occur exa

shown in Figure 37-2. Before running Solver, I i

Chapter

The

37Traveling Salesperson

305

Problem

Fig

URE 37-2

Solver set up for a traveling salesperson proble

The minimum possible distance to travel

cities

is 8,9

are visited, simply begin in the row with a 1 (

and follow the cities in the listed sequence. T

Boston-NY-Pittsburgh-Chicago-Denver-Seattle-SF

are many other sequences for visiting the citi

distance of 8,995 miles.

Problems

A small job shop needs to schedule six jobs

complete each job are given below. In what o

minimize the total days the jobs are late?

Job

Processing Due

timedate(measured

from today)

306

Microsoft Excel 2010: Data Analysis and Business Modeling

The fle Nbamiles.xlsx contains the distance b

in New York and want to visit each arena once a

should you visit the cities to minimize total d

Suppose now that you live in Atlanta and are d

wants to return to his home. Each time you vi

home arena. In what order should you drop off th

distance traveled by the GMs.

In the Willy Lowman problem, suppose you

must

What is the solution to the problem?

307

Chapter 38

Importing Data from a T

Document

Question answered in this chapter:

■

How can I import data from a text fle into E

Jeff Sagarin, the creator of the

USA Today

bas

developed a system to rate NBA players for the

Cuban. Every day during the season, Jeff’s FOR

information, including ratings for each Dallas M

program produces this information in the form o

you can import a text fle into Microsoft Excel t

Answers to This Chapter’s Ques

How can I import data from a text file into Exc

You will likely often receive data in a Micros

need to import into Excel for numerical analys

should frst save it as a text fle. You can the

With the Text Import Wizard, you can break dat

the following approaches:

■

If you choose the

fxed-width

option, Excel g

into columns. You can easily modify Excel’s a

■

If you choose the

delimited

option, you pic

a space, or a plus sign), and Excel breaks th

the character you choose.

As an example, the fle Lineupsch38.docx (a sam

length of time each lineup played for Dallas i

The fle also contains the “rating” of the line

308

Microsoft Excel 2010: Data Analysis and Business Modeling

against Sacramento, the lineup of Bell, Finley, L

court together for 9.05 minutes and that the lin

minutes), worse than an average NBA lineup.

Bell

Finley

LaFrentz

Nash

Nowitzki

- 19.79

695# 9.05m SAC DAL* Finley

Nash

Nowitzki

Van Exel

Williams

- 11.63

695# 8.86m SAC DAL* Finley

LaFrentz

Nash

Nowitzki

Van Exel

102.98

695# 4.44m SAC DAL* Bradley

Nowitzki

Van Exel

- 44.26

695# 4.38m SAC DAL* Bradley

Nash

Nowitzki

Van

Williams

9.71

695# 3.05m SAC DAL* Bell

Finley

LaFrentz

Nowitzki

Van

121.50

695# 2.73m SAC DAL* Bell

LaFrentz

Nowitzki

Van Exel

Williams

39.35

695#

2.70m SAC DAL* Bradley

Finley

Nowitzki

Van Exel

Williams

86.87

695# 2.45m SAC DAL*

Bradley

Nash

Van Exel

Williams

Rigaudeau

- 54.55

695# 2.32m SAC DAL*

We’d like to import this lineup information into E

information would be listed in different columns

■

Each player’s name

■

Minutes played by the lineup

■

Rating of the lineup

The player Van Exel (his full name is Nick Van E

delimited option and use a space character to br

occupy two columns. For lineups that include Van E

in a different column than the column in which th

include Van Exel. To remedy this problem, I used th

each

occurrence of Van Exel to Exel. Now, when Exce

occurs, Van Exel will require only one column. T

the following.

Bell

Finley

LaFrentz

Nash

Nowitzki

- 19.79

695# 9.05m SAC DAL* Finley

Nash

Nowitzki

Exel

Williams

- 11.63

695# 8.86m SAC DAL* Finley

LaFrentz

Nash

Nowitzki

Exel

102.98

69 5# 4.44m SAC DAL* Bradley

Finley

Nash

Nowitzki

Exel

44.26

695# 4.38m SAC DAL* Bradley

Nash

Nowitzki

Exel

Williams

SAC DAL* Bell

Finley

LaFrentz

Nowitzki

Exel

- 121.50

695# 2.73m SAC DAL* Bell

LaFrentz

Nowitzki

Exel

Williams

39.35

69 5# 2.70m SAC DAL* Bradley

Exel

Williams

86.87

69 5# 2.45m SAC DAL* Bradley

Nash

Exel

Williams

Rigaudeau

54.55

695# 2.32m SAC DAL*

The trick to importing data from a Word or text fl

Wizard. As I mentioned earlier, you frst need to s

this example) as a text fle. To do this, simply o

Save As, and then select Plain Text in the Save A

select the Windows (Default) option, and then cl

the name Lineupsch38.txt. Close the Word documen

You’ll see step 1 of the Text Import Wizard, whi

Chapter

Importing

Data from a Text

309

File or Document

Fig

URE 38-1

Step 1 of the Text Import Wizard.

Clearly, in this case you want to select the D

However, let’s suppose that you choose Fixed W

appears, shown in Figure 38-2. As you can see, y

For many data import operations, changing colu

Fig

URE 38-2

Step 2 of the Text Import Wizard after selecting t

If you select Delimited in step 1, you’ll see th

shown in Figure 38-3. In this example, I’ve se

310

Microsoft Excel 2010: Data Analysis and Business Modeling

Consecutive Delimiters As One option ensures tha

column break. I recommend keeping Tab selected b

properly if Tab is cleared.

Fig

URE 38-3

Step 2 of the Text Import Wizard after selecting D

When you click Next, you’re sent to the third st

Figure 38-4. By selecting the General option as th

numerical data as numbers and other values as te

Fig

URE 38-4

Step 3 of the wizard, in which you can select a fo

Chapter

Importing

Data from a Text

311

File or Document

When you click Finish, the wizard imports the d

Fig

URE 38-5

Excel fle with lineup information.

Each player is listed in a separate column (co

lineup, column G contains the game number, col

lineup, and columns I and J list the two teams p

Excel workbook (.xlsx), you can use all -

of the a

formance of Dallas’s lineups. For example, you c

the team when Dirk Nowitzki is on or off the c

Problems

The fle Kingslineups.docx contains performa

Kings lineups. Import this data into Excel.

In the example discussed in the chapter, th

with .anModify

the fle so that the time playe

313

Chapter 39

Importing Data from t

Questions answered in this chapter:

■

Yahoo Finance provides analyst ratings (buy

import this information into Excel?

■

Is there a way I can download current stock p

We all know that the World Wide Web contains u

However, you can’t really do any sort of analy

to import the data into Microsoft Excel, which y

website where the data you want is located, co

an Excel worksheet. On the Data tab, in the Ge

the New Web Query dialog box appears, paste th

page appears, and you can select the data you wa

chapter’s frst question shows you how to imple

Answers to This Chapter’s Ques

Yahoo Finance provides analyst ratings

. How can

(buy,

I ims

this information into Excel?

The URL

http://fnance.yahoo.com/q/al?s=MSFT+An

analysts’ forecasts for the future price of Mi

can see that on August 2, 2010, 31 analysts pr

sell on August 2, 2011, for $33.35. The highes

was $24. It would be useful to import this dat

the data. You’ll fnd the web queries worksheet

used in thi

in the fle Webqueries.xlsx. When you open the W

“Security Warning: Data connections have been d

course, enable the content if you believe the s

314

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 39-1

Analyst forecast for Microsoft in August 2010. The W

easy to analyze on a website.

To import the data into Excel, copy the URL and th

the Data tab on the ribbon, and in the Get Exter

New Web Query dialog box appears, press Ctrl+V t

then click Go. The New Web Query dialog box disp

Fig

URE 39-2

New Web Query dialog box after choosing a URL.

You now click the arrow that points to the data y

case, you would click the arrow directly to the l

check mark. After clicking Import, you’ll

see th

cate to Excel where you want to place the data. I c

this example. After clicking OK, the analysts’ r

Figure 39-3.) Note that the numbers and labels a

Chapter

Importing

Data from

315

the Internet

Fig

URE 39-3

Analyst forecasts for Microsoft made on August 2

You can easily set your query to be refreshed o

right-click anywhere in the query results, sel

Refresh Control settings. As shown in Figure 3

every minute and be automatically refreshed wh

Fig

URE 39-4

Refresh settings for the web query.

To edit this query, simply right-click anywher

By clicking the Options button shown in the up

formatting of your query results. Of course,

ably see different information because analyst

future stock price for Microsoft.

Is there a way I can download current stock pr

Excel comes with a built-in web query that can b

about stocks. This web ,

query

which

ismeans

dynamic

that you

web

query to update stock information as it change

data you want to update and then, on the Data t

All. Let’s see how to download real-time stock i

MSFT) and International Business Machines (tic

316

Microsoft Excel 2010: Data Analysis and Business Modeling

Open or create a worksheet in Excel, and then di

Data group, double-click Existing Connections. N

MoneyCentral Investor

. Click

Stock

Open,

Quotes

and then use the I

to indicate where you want to place the data in th

Enter Parameter Value dialog box as shown in Fig

about Microsoft and IBM into Excel. Figure 39-6 (

fle Webqueries.xlsx) shows a sample of the downl

on August 2, 2010. Checking the options shown in Fi

changes to reflect the most current information.

Fig

URE 39-5

Use the Enter Parameter Value dialog box to designa

dynamic web query to download information.

Fig

URE 39-6

Downloaded information about Microsoft and IBM sto

Excel also ships with web queries designed to dow

information about major stock indexes. These que

information in real time unless you rerun the qu

Of course, you can create your own web queries. C

of this book. See Chapter 4 of

Data Analysis for M

S. Christian Albright, Wayne L. Winston, and Chr

introduction to creating web queries.

Chapter

Importing

Data from

317

the Internet

Problems

Download real-time information about Disney (

symbol GPS) into Excel.

Use the built-in web query designed to down

information into Excel.

Go to

NBA.com

and download the career stati

Go to

MLB.com

and download the career stati

Go to

NFL.com

and download the season stati

Go to

http://www.boxoffceguru.com/blockbust

moneymaking movies of all time into Excel.

Go to

http://money.cnn.com/magazines/fortune

information on the Fortune 500 into Excel.

Go to Fangraphs.com and download the latest C

(They are pretty sad!)

319

Chapter 40

Validating Data

Questions answered in this chapter:

■

I’m entering scores from professional baske

scores from 50 to 200 points per game. I on

points, which messed up my analysis. Is the

making this type of error?

■

I’m entering the date and amount of my busin

year, I often enter the previous year in th

up Excel to prevent me from making this typ

■

I’m entering a long list of numbers. Can I h

value?

■

My assistant needs to enter state abbreviati

sales transactions. Can we set up a list of s

that she’ll enter an incorrect abbreviation

A lot of our work often involves mind-numbing d

information into Microsoft Excel, it’s easy to m

Excel 2010 can greatly lessen the chances that y

validation, you begin by selecting the cell ra

Choose Data Validation on the Data tab, and th

chapter’s examples) that Excel uses to flag any

Answers to This Chapter’s Ques

I’m entering scores from professional

. I know basketba

that a t

scores from 50 to 200

. I once

points

entered

per game

1,000 point

which messed up. Is

my there

analysisway to have Excel pr

type of error?

Let’s suppose that you’re going to enter into c

home team, and in cells B2:B11, you’ll enter th

(You’ll fnd the work I did to solve this probl

that each value entered in the range A2:B11 is a w

Begin by selecting the range A2:B11, and then c

the Settings tab, select Whole Number from the A

dialog box as shown in Figure 40-1.

320

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 40-1

Use the Settings tab in the Data Validation dialog b

Excel’s default response to

) is

invalid

message

data (called

stating a

“

entered is not valid. A user has restricted valu

use the Error Alert tab in the Data Validation

ture of the error alert, including the icon, the ti

message itself. On the Input Message tab, you ca

the type of data that can be safely entered. The m

selected cell. For example, I entered an error a

between 50 and 200.” After typing a number that v

would then see the message shown in Figure 40-3.

Fig

URE 40-2

Error Alert tab options in the Data Validation dia

Fig

URE 40-3

Error alert for the basketball data validation exa

Chapter

Validating

321

Data

I’m entering the date and amount of. Early

my busines

year, I often enter the previous

. Is year

there

ina the

way dI c

up Excel to prevent me from making this type o

Suppose it is early in 2013 and you are enteri

fle Datedv.xlsx.) Simply select the range A2:A

Data tab. Fill in the Settings tab of the Data V

Then you will not be allowed to enter any date e

Fig

URE 40-4

Use settings such as these to ensure the validit

If you enter a date in this range that occurs e

about the error. For example, entering 1/15/20

defne.

I’m entering a long

. Canlist

I have

of numbers

Excel warn me if I e

value?

To unleash the full power of data validation, y

select Custom in the Allow list on the Setting

Figure 40-4), you use a formula to defne

valid d

tion works the same as a formula used for cond

Chapter 24, “Conditional Formatting.” You

- ente

tent of the frst cell in the selected range is v

dialog box, the formula is copied to the remai

in a cell in the selected range, Excel display

False for that value.

To illustrate the use of the Custom setting, l

entry in the cell range B2:B20 is a number. (S

this problem is using the Excel ISNUMBER functi

322

Microsoft Excel 2010: Data Analysis and Business Modeling

if the function refers to a cell that contains n

function refers to a cell that contains a nonnum

After selecting the cell range B2:B20 and placin

click Data Validation in the Data Tools group, a

Validation dialog box as shown in Figure 40-5.

Fig

URE 40-5

Use the ISNUMBER function to ensure that the data i

After clicking OK, you’ll receive an error promp

B2:B20. For example, if you type

John

in cell B3

If you click Data Validation while working in ce

displayed as .

=ISNUMBER(B3)

This demonstrates that the formul

in the correct fashion. Entering John in cell B3 c

receive the error alert.

My assistant needs to enter state abbreviations w

sales transactions

. Can we set up a list of state abbrevia

she’ll enter an incorrect abbreviation?

The key to this data validation problem is to us

a list of state abbreviations. See the fle State

and named the. range

Next,

abbrev

select the range in which y

(The example uses D5:D156.) After clicking Data V

Validation dialog box as shown in Figure 40-6.

Chapter

Validating

323

Data

Now, whenever you select a cell in thedisplays

range D

a list of state abbreviations, as shown in Fig

list are valid values in this range. If you do n

state abbreviation, you’ll receive an error me

(such as ALK for Alaska).

Fig

URE 40-6

The Data Validation dialog box can be used to de

Fig

URE 40-7

Drop-down list of state abbreviations.

Remarks

■

If you press F5, click Special in the Go To d

Excel selects all cells with data validatio

dialog box to select all cells containing c

■

In previous versions of Excel, if you wante

based on a data source list in a different w

(as I did in this chapter’s example) for the d

limitation has been removed.

324

Microsoft Excel 2010: Data Analysis and Business Modeling

■

If you use the dynamic-range technique descri

Function,” changes you make (adding or deleti

automatically reflected in the drop-down box. (

data source list as an Excel table (see Chapt

are reflected in the drop-down list, as long a

to type the table name.

■

Suppose you want to use a drop-down list to s

You want another drop-down list that you can u

sell at the selected store. The problem is th

sold at each store. How do you create such a n

are Target and CVS. Suppose you assign a rang

bars sold at Target, and a range name of

CVS

the drop-down list for store selection

- is in, f

propriate drop-down list in cell B20 by click

list selected the formula

. As I discussed

=INDIRECT(A20)

in Chapter 2

Function,” if A20 contains CVS, the list will k

bars sold at CVS, and so on. See Problem 11.

■

To clear data validation from a range, select th

Data tab, and then select Clear All.

■

If you have a long list, you probably want to i

start the range for your drop-down list in th

cells allowed), then Autocomplete will work. S

■

You can also use data validation to set up cr

(see Problem 4) or the time of day (see Probl

Problems

You are entering nonnegative whole numbers in th

validation setting that ensures that each entr

You are entering in the cell range C1:C15 the d

July 2004. Enter a data validation setting th

July 2004.

With the List option in the group of data val

error message if a value that is not included i

validating. Suppose you’re entering employee fr

Chapter

Validating

325

Data

The only employees of the company are Jen, G

option to ensure that no one misspells a fr

With the Text Length option in the group of d

an error message when the number of charact

you defne. Use the Text Length option to en

contain at most fve characters (including b

You are entering employee names in the cell r

ensure that no employee’s name is entered m

setting and the COUNTIF function.)

You are entering product ID codes in the ce

always end with .the

Usecharacters

data validation

xyz

to ens

code entered.ends

(Hint:

with

Use

xyz

the Custom setting a

Suppose you want every entry in the cell ra

numerical value. Use data validation to ens

an error. (Hint: Use the ISTEXT function.)

Set up a data validation procedure that ens

contain exactly two decimal places. (Hint: U

The fle Latitude.xlsx contains a formula to c

using their latitude and longitude. The fle a

various U.S. cities. Set up a drop-down lis

another city in cell Q2, the distance betwe

10.

Ensure that if new cities are added to the l

will include the new cities.

11.

The fle Candybardata.xlsx contains a list o

worksheet also contains the types of candy b

charged for each candy bar. Set up your wor

both the store and a candy bar from a drop-

in D19.

❑

Enable users to select a store from the d

❑

Set up a drop-down list in C13 to let use

containing only those candy bars sold at a s

function when defning the list.)

❑

If you change the store in B19, then C19 mi

sold at the newly selected store. Ensure th

selection above

if this is the case. For e

gumballs,

then C19 should

say

Make select

326

Microsoft Excel 2010: Data Analysis and Business Modeling

12.

You have a $100,000 expense budget. In column A

incurred. Set up a data validation criterion th

column E do not exceed your budget.

13.

Set up a data validation criterion that ensur

descending order.

14.

Set up data validation criteria that ensures th

on Monday through Friday. (Hint: The WEEKDAY f

Monday, etc.)

15.

Set up data validation criteria that ensures th

A1:A20 will be a morning time.

327

Chapter 41

Summarizing Data by U

Histograms

Questions answered in this chapter:

■

People often say that a picture is worth a t

picture (called

) that

histogram

summarizes the values in a da

■

What are some common shapes of histograms?

■

What can I learn by comparing histograms fr

The ability to summarize a large data set is i

summarize data in Microsoft

descriptive

Excel

, and

are

statistics

PivotTable

histogra

In this chapter, I discuss the use of histogra

statistics in Chapter 42, “Summarizing Data by U

Chapter 43, “Using PivotTables and Slicers to D

Answers to This Chapter’s Ques

People often say that a picture

. Can is

I use

worth

Excel

a tho

to c

picture (called a histogram) that summarizes t

A histogram is a commonly used tool to summari

how many observations (another

) fall in

term

various

for

data

range

example, a histogram created from monthly Cisc

monthly returns Cisco had from 0 percent throu

percent, and so on. The ranges in which

you gr

Let’s look at how to construct and interpret hi

returns for Cisco and GM stock in the years 19

other stocks) in the fle Stock.xlsx. Figure 41

worksheet). During March 1990, for example, Ci

328

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 41-1

Monthly stock returns.

When constructing histograms with Excel, you can l

defne the bin ranges yourself. If Excel defnes th

looking bin ranges, such as –12.53 percent to 4.

the ranges myself.

A good way to start defning bin ranges for a his

ranges as setting boundaries) is to divide the r

largest) into 8 to 15 equally spaced categories. A

–3p

0ercent through 40 percent, so I chose bin ran

percent,

–10

0 percent, and so on up to 40 per

To create bin ranges, I frst enter CSCO, .4, .3, .

in cells H54:H62. Next, on the Data tab on the r

Analysis to open the Data Analysis dialog box. T

Analysis ToolPak, which contains many of the sta

Not

f the Data Analysis command doesn’t appear on th

Options, and then click Add-Ins. In the Manage box, c

Add-Ins dialog box, select Analysis ToolPak, and the

ToolPak functions by clicking Data Analysis in the A

By clicking Histogram in the Data Analysis dialo

shown in Figure 41-2.

Chapter

Summarizing

Data by Using

329

Histograms

Fig

URE 41-2

Histogram dialog box for the Cisco histogram.

Here’s how to fll in the dialog box as it’s sh

■

Select the input range (F51:F181). (To selec

and then press Ctrl+Shift+Down Arrow. This t

This range includes all the data you want t

label CSCO from cell F51 because when you d

x-axis of the histogram is often labeled wi

■

The bin range (H54:H62) includes the bounda

of –30 percent through –20 percent, –20 per

30–40 percent.

■

I checked the Labels option because the frs

range contain labels.

■

I chose to create the histogram

in a new wo

■

Select Chart Output, or Excel will not crea

Click OK in the Histogram dialog box. The Cisc

Figure 41-3.

Fig

URE 41-3

Cisco histogram created by using an Excel Analys

When you create the histogram, you’ll see gaps b

right-click any bar on the graph and choose Fo

330

Microsoft Excel 2010: Data Analysis and Business Modeling

drag Gap Width to 0%. You might also see that a l

the labels do not appear, select the graph and d

the graph. You can also reduce the font size to m

right-click the graph axis, and then right-click F

change the title of the chart by selecting the t

made some of these changes, the histogram appear

Fig

URE 41-4

You can change the format of different elements in t

Notice that Cisco returns are most likely betwee

height of the bars drops off as the graph moves awa

the histogram, you also obtain the bin-range fre

Fig

URE 41-5

Cisco bin-range frequencies.

From the bin-range frequencies, you can learn, f

return was greater than –30 percent and less tha

monthly return was greater than –20 percent and l

What are some common shapes of histograms?

For most data

histogram

sets, created from the data will be c

following:

■

Symmetric

■

Skewed right (positively skewed)

■

Skewed left (negatively skewed)

■

Multiple peaks

Chapter

Summarizing

Data by Using

331

Histograms

Let’s look at each type in more detail. See th

■

Symmetric distribution

A histogram is symmetric if it h

approximately the same to the left of the p

(such as IQ tests) are often symmetric. For e

W42) might look like Figure 41-6. Notice tha

the peak bar are approximately the same, th

the peak bar are approximately the same, an

all people with an IQ greater than 95 and l

represents all people having an IQ less tha

Cisco monthly returns are approximately sym

Fig

URE 41-6

Symmetric histogram.

■

Skewed right (positively

A histogram

skewed)

is skewed right (

if it has a single peak and the values of th

the peak than to the left of the peak.- Many e

vidual income) exhibit a positive skew. Figu

positively skewed histogram created from a s

Fig

URE 41-7

A positively skewed histogram created from da

332

Microsoft Excel 2010: Data Analysis and Business Modeling

■

Skewed left (negatively

A histogram

skewed)

is skewed left (n

if it has a single peak and the values of the d

the peak than to the right of the peak. Days f

skewed. An example is shown in cell Q7

- of Fig

sents the number of women whose time from con

range. For example, two women gave birth fewe

Fig

URE 41-8

A negatively skewed histogram of data plotting d

■

Multiple

When

peaks

histogram exhibits multiple pe

from two or more populations are being graphe

diameter of elevator rails produced by two ma

Figure 41-9. See cell Q11 of the fle Twinpeaks

Fig

URE 41-9

A multiple-peak histogram.

In this histogram, the data clusters into two s

group of data corresponds to the elevator rai

assume that the diameter you want for an elev

that one machine is producing elevator rails th

machine is producing elevator rails that are t

interpretation of this histogram by constructi

produced by each machine. This example shows w

quality control.

Chapter

Summarizing

Data by Using

333

Histograms

What can I learn by comparing histograms from d

Analysts are often asked to compare different

how the monthly returns on GM and Cisco stock d

can construct a histogram for GM by using the s

one histogram above the other, as shown in Fig

fle Stock.xlsx.

Fig

URE 41-10

Using histograms that include the same bin range

By comparing these two histograms, you can draw t

■

Typically, Cisco performed better than GM. Y

Cisco is one bar to the right of the highes

ther to the right than the GM bars.

■

Cisco had more variability, or spread about t

bar contains 59 months, whereas Cisco’s pea

that for Cisco, more of the returns are out

Cisco return. Cisco returns are more spread o

In Chapter 42, we’ll look at more details abou

on Cisco and GM.

Problems

Use the data in Stock.xlsx to construct his

Use the data in Historicalinvest2009.xlsx t

stocks and bonds. Then compare the annual r

334

Microsoft Excel 2010: Data Analysis and Business Modeling

You are given (in the fle Deming.xlsx) the me

rods produced by Rodco, as reported -by the pr

ered

acceptable if it is at least 1 inch in diam

produced by Rodco has followed a symmetric hi

❑

Construct a histogram of these measurements

❑

Comment on any unusual aspects of the histo

Can you guess what might have caused any unus

(Hint:

One of quality-guru Edwards Deming’s 1

The fle Unemployment.xlsx contains monthly U.

histogram. Are unemployment rates symmetric o

The fle Teams.xlsx contains runs scored by ma

season. Create a histogram. Are runs scored s

The fle NFLpoints.xlsx contains points scored by N

histogram. Are points scored symmetric or ske

335

Chapter 42

Summarizing Data by U

Descriptive Statist

Questions answered in this chapter:

■

What defnes a typical value for a data set?

■

How can I measure how much a data set sprea

■

Together, what do the mean and standard dev

data?

■

How can I use descriptive statistics to com

■

For a given data point, can I easily fnd it

example, how can I fnd the ninetieth percen

■

How can I easily fnd the second largest or s

■

How can I rank numbers in a data set?

■

What is the trimmed mean of a data set?

■

When I select a range of cells, is there an e

describe the data in those cells?

■

Why do fnancial analysts often use the geom

return on a stock?

In Chapter 41, “Summarizing Data by Using Hist

sets by using histograms. In this chapter, I s

characteristics of the data, such as the mean, m

measures that Microsoft Excel 2010

. You

groups

can toge

obt

the descriptive statistics for a set of data by c

the Data tab and then selecting the Descriptiv

data and click OK, all the descriptive statisti

Answers to This Chapter’s Ques

What defines a typical value for a data set?

To illustrate the use of descriptive statistic

return data in the fle Stock.xlsx. To create a s

Data Analysis on the Analysis tab, and then se

Statistics dialog box as shown in Figure 42-1.

336

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 42-1

Descriptive Statistics dialog box.

The input range is the monthly Cisco and GM retu

(including the labels in row 51). I flled in the r

box as shown in Figure 42-1 for the following re

■

I selected Columns in the Grouped By options b

different column.

■

I selected Labels In First Row because the fr

and not data.

■

I selected cell I53 of the current worksheet a

■

By selecting Summary Statistics, I ensured th

descriptive statistics measures for both GM a

When you click OK, Excel calculates the descripti

Fig

URE 42-2

Descriptive statistics results for Cisco and GM st

Chapter

Summarizing

Data by Using

337

Descriptive Statistics

Now let’s interpret the descriptive statistics th

for Cisco’s monthly stock returns. The Descrip

central location: mean (or average), median, a

■

Mean

The mean of a data set is written as

observations in the sample. If the data val

,…,

, then the follow

equation calculates the mean.

∑

i – n

i – 1

x =

Here,

equals the number of observations i

is the

observati

in the sample. We fnd that Cisco’s mean month

It is always true that the sum of the devia

Thus, you can think of a data set’s mean as a “

without using the Descriptive Statistics op

by applying the AVERAGE function to the app

■

Median

The median of a sample is the “middle” o

from smallest to largest. If a sample contai

median is the observation that has as many o

a sample of nine, the median would be the f

When a sample includes an even number of ob

two middle observations. Essentially, the m

For example, the median monthly return on C

this information by using the MEDIAN functi

■

Mode

The mode is the most frequently occurrin

occurs more than once, the mode does not ex

more than once for the years 1990–2000, so th

mode was approximately 5.14 percent. In ver

could also use the MODE function to compute th

more than once, the MODE function returned #

The problem is that a data set canfunction

have mor

simply returned the frst mode it found. For thi

functions: MODE.SNGL and MODE.MULT (see the fl

MODE.SNGL performs exactly as the MODE func

versions. Earlier versions of Excel, howeve

MODE.MULT is an array function. You’ll learn m

“Array Functions and Formulas.” To use the M

function) you must frst select the range of c

Next, enter the function or formula. Finall

down the Ctrl key followed by the Shift key a

338

Microsoft Excel 2010: Data Analysis and Business Modeling

MODE.MULT function is that you do not know in a

has, so you do not know the correct size of th

The fle Modefunctions.xlsx (see Figure 42-3) s

involving modes.

Fig

URE 42-3

Examples of Excel’s MODE functions.

The data set displayed in Figure 42-3 has two m

“old school” MODE function with the formula M

mode it found (3). In cell F14 the

formula MO

After selecting the cell range E16:E17, I arr

and Excel returned both the modes (3 and 5). A

three-cell range), I array-entered the same f

because the data set had no third mode to fll th

range E20 and array-entered the same formula. B

single cell, Excel returned only the frst mod

The mode is rarely used as a measure of centr

however, that for a symmetric data set, the m

A natural question is whether the mean or med

location. Essentially, the mean is the best m

does not exhibit an excessive skew. Otherwise

sure of central location. If a data set is hi

In this case, the median is a better measure o

U.S. government reports median family income i

family income is highly positively skewed.

Chapter

Summarizing

Data by Using

339

Descriptive Statistics

The skewness measure reported by the Descri

data set is highly skewed.

❑

A skew greater than +1 indicates a high d

❑

A skew less than –1 indicates a high degr

❑

A skew between –1 and +1 inclusive indica

Thus, monthly returns of GM and Cisco exhib

Because the skewness measure for each data s

measure of a typical return than the median

compute the skew of a data set.

■

Kurtosis, which sounds like a disease, i

Kurtosis near 0 means

peakedness”

data set

exhibits

to the“ n

bell-shaped) curve. (I’ll discuss the norma

Variable.”) Positive kurtosis means that

a da

dom variable, whereas negative kurtosis mea

random variable. GM monthly returns are mor

Cisco monthly returns are less peaked than a n

How can I measure how much a data set spreads f

Let’s consider two investments that each yield a

deciding which investment you prefer, you’d li

the investment. The most important measures of th

its mean are sample variance, sample standard d

■

Sample variance and sample

The sample

standard

variance

deviati

is defned

by the following formula.

n – 1

∑

( x

– x )

i – n

i – 1

You can think of the sample variance as the a

its mean. Intuitively, it seems like you sh

squared deviation, but for technical

reason

Dividing the sum of the squared deviations by

an unbiased measure of the true variance of th

data is drawn.

The sample standard deviation

is just the s

Here is an example of these computations fo

3 – 1

[ ( 1 – 3 )

+ ( 3 – 3 )

+ ( 5 – 3 )

] = 4

340

Microsoft Excel 2010: Data Analysis and Business Modeling

We fnd that

s =

4 =

In the stock example, the sample standard dev

percent with a sample variance of 0.015%

. Naturally

is hard

, % to interpret

usually look at the sample standard deviation

8.97 percent.

In previous versions of Excel the sample varia

the VAR function, and the sample standard dev

function. You can still use these functions i

equivalent functions VAR.S and

.) STDEV.S.

The -new func

(The S s

tions VAR.P and STDEV.P compute the populatio

deviation. To compute a population variance o

in the denominator of the defnition of

■

RangT

he range of a data set is the largest

smallestnu

number. Here, the range in the monthly Cisco r

range for GM monthly returns is 52 percent.

Together, what do the mean and standard deviatio

Assuming that a histogram follows a Gaussian, or n

us the following:

■

Approximately 68 percent of all. observations a

■

Approximately 95 percent of all .observations a

■

Approximately 99.7 percent of all. observation

For example, you would expect that approximately 9

are from –19 percent through 30 percent, as show

Mean–2s=.056-2*(.122)=–19% and Mean+2s=.056+2*(.1

Any observation more than two standard deviation

For the Cisco data, 9 of 130 observations (or ro

In general, the rule of thumb is less accurate f

accurate for relatively symmetric data sets, eve

population.

Many valuable insights can be obtained by fnding c

to ensure that the causes of “good outliers” occ

outliers occur less frequently.

Chapter

Summarizing

Data by Using

341

Descriptive Statistics

Using Conditional Formatting to H

You’ll fnd that it is often useful to highligh

Figure 42-4 (see the

Stockprices

worksheet in th

Fig

URE 42-4

Outliers for Cisco highlighted with conditional f

For example, to highlight the outliers for the C

for an

mean–2s

outlier

) in (

cell J69 and the

mean+2s

upper

) incutoff

cell Jf

Next, select the entire range of Cisco returns (

range (F52), select Conditional Formatting on th

Formatting Rule dialog box, select Use A Formu

then fll in the rest of the dialog box as show

Fig

URE 42-5

Conditional formatting rules to select outliers, a

342

Microsoft Excel 2010: Data Analysis and Business Modeling

This condition ensures that

above

if cell

or F52

below

is eithe

monthly Cisco return, the format you select (a r

to cell F52. This formatting condition is automa

outliers show up in red.

How can I use descriptive statistics to compare d

You can use descriptive statistics to summarize th

example, between Cisco and GM monthly returns. L

and spread of a typical value, you can conclude th

■

Typically (looking at either the mean or the m

than GM.

■

Cisco monthly returns are more variable (look

range) than monthly GM returns.

■

Both Cisco and GM monthly returns exhibit sli

are more peaked than a normal curve, whereas C

than a normal curve.

For a given data point, can I easily find its per

example, how can I find the ninetieth percentile o

In previous versions of Excel, the PERCENTILE an

you wanted to determine an observation’s relativ

functions have been added in Excel 2010: PERCENT

INC, PERCENTRANK.EXC. The functions PERCENTILE.I

identical to the old PERCENTILE and PERCENTRANK

sions of Excel do not recognize these new functi

work are in the fle Percentile.xlsx, shown in Fi

Fig

URE 42-6

Examples of PERCENTILE and PERCENTRANK Functions.

Chapter

Summarizing

Data by Using

343

Descriptive Statistics

The PERCENTILE, PERCENTILE.INC, AND PERCENTILE

of a data set that you specify. The syntax of th

INC(

data,k

), which returns

th percentile

the

of the information i

data

Consider a data set consisting of

pieces of d

PERCENTILE.INC functions

th percentile

returned

(0<p<1)

the

as the

in the data set. For example, in H13, the form

ninetieth percentile of the data in C4:C18 as 1

That is, assuming the data is sorted in ascend

of the way between the thirteenth data point (

yields 136.

The PERCENTILE.EXC function

th percentile

computes

as the

(n+1)

data set. PERCENTILE.EXC computes the ninetieth p

is the 14.4 ranked item. That is, the ninetieth p

ascending order) is computed to be 40 percent o

point (140) and the ffteenth data point (300). T

can see that the two functions return drastica

to have been drawn by sampling from a large se

data you’ve seen, there is much more than a 10 p

be more than 136. After all, two of the 15 dat

reasonable to say that the ninetieth percentil

ninetieth percentile is 204 seems more reasona

function instead of the .INC function. Note

centile for 0 and 1. The .EXC stands for the f

the zero and one hundredth percentiles.

The PERCENTRANK, PERCENTRANK.INC, and PERCENTR

ranking of an observation relative to all valu

PERCENTRANK.EXC function, for

data,value

example,

)

The

is PERC

PERCENTRANK and PERCENTRANK.INC functions both c

th smallest number in. the

Thus,

data

as set

shown

as in

(k-1)/(n

cell E

or PERCENTILE.INC function yields a rank of 0 f

PERCENTRANK.EXC function th

computes

smallest

thedata

rank

. In

poin

of th

cell D4, the PERCENTRANK.EXC function returns a r

of 6.25 percent seems more realistic than a ra

to think that a value of 10 is the smallest da

was sampled.

Not

The PERCENTILE and PERCENTRANK functions are ea

PERCENTILE yields a value of the data, whereas PER

344

Microsoft Excel 2010: Data Analysis and Business Modeling

How can I easily find the second largest or secon

The formula

=LARGE(range,k)

th largest

returns

number the

in a

cell r

=SMALL(range,k)

th returns

smallestthe

number

in a cell range. F

Trimmean.xlsx, in cell F1, the formula

=LARGE(C4

in the cell range C4:C62 (99), whereas in cell F

second smallest number in the cell range C4:C62 (

Fig

URE 42-7

Examples of the LARGE and SMALL functions, the RAN

trimmed mean.

How can I rank numbers in a data set?

In previous versions of Excel, you used the RANK f

The syntax of the RANK

number,array,

function

0). Excel

is 2010

RANK(

includes a n

tion, RANK.EQ, which returns results identical t

rank of a number in a given array, where, the lar

the second largest

, and

number

so on.

is The

number,array,

ranksyntax

1) orRANK(

RANK.

EQ(

number,array,

1) results in assigning a rank of

to th

to the second smallest number, and so on. I

copying the formula

RANK.EQ(C4,$C$4,$C$62,0)

fro

of each test score. For example, the score of 10

scores of 98 in cells C21 and C22 tied for third hi

a 3 for both scores of 98.

Chapter

Summarizing

Data by Using

345

Descriptive Statistics

The new Excel 2010 function RANK.AVG

functions,

has the s

but in the case of ties, RANK.AVG returns the a

example, since the two scores of 98 ranked thi

I generated the average ranks by copying the f

to E5:E62.

What is the trimmed mean of a data set?

Extreme skewness in a data set can distort the m

people usually use median as a measure of the d

is unaffected by many changes in the data. For e

sets:

Set 1: –5, –3, 0, 1, 3, 5, 7, 9, 11, 13, 15

Set 2: –20, –18, –15, –10, –8, 5, 6, 7, 8, 9, 1

These data sets have the same median (5), but t

“typical” value than the frst. The Excel TRIMM

values than the AVERAGE function, but it is mo

median. The formula

=TRIMMEAN(range,percent)

deleting the data points at the top percent di

2. For example, applying the TRIMMEAN function w

after deleting the top 5 percent and bottom 5 p

Trimmean.xlsx, the formula

=TRIMMEAN(C4:C62,.1

C4:C62 after deleting the three highest and th

F4, formula

the

TRIMMEAN(C4:C62,.05)

computes the mean o

deleting the top and bottom scores. This- calcu

dicate the deletion of 1.48 of the largest obs

1.48 results

deleting only the top and bottom observa

When I select a range of cells, is there an ea

describes the data in those cells?

To see the solution to this question, select th

the lower-right corner of your screen, the Exc

describing the numbers in the selected cell ra

range C4:C36, the mean is 90.39, there are 33 n

est value is 100. If you right-click the statu

Fig

URE 42-8

Statistics shown on the status bar.

346

Microsoft Excel 2010: Data Analysis and Business Modeling

Why do financial analysts often use the geometric m

on a stock?

The fle Geommean.xlsx contains the annual return

Fig

URE 42-9

Geometric mean.

Cell C9 indicates that the average annual return o

annual return on Stock 2 is 10 percent. This wou

investment. If you think about it, however, what w

year you will lose 50 percent and the next gain 7

$1.00 becomes.

1(1.7)(.5)=.85

Because Stock 1 never loses money

the better investment. Using the geometric mean a

helps to correctly conclude that Stock 1 is the b

numbers is th

simply

root the

of the

product of the numbers

mean of 1 and 4 is the square root of 4 (2), whe

cube root of 8 (also 2). To use the geometric me

an investment, you add 1 to each annual return a

numbers. Then subtract 1 from this result to obt

return.

The formula

GEOMMEAN(range)

fnds the geometric mean of n

estimate the average annual return on each stock

Compute

1+each annual return

by copying

from C

Copy from C16 to D16 the formula

=GEOMEAN(C12

The annual average return on Stock 1 is estimate

return on Stock 2 is –7.8 percent. Note that if S

during two consecutive years, $1 becomes

1(1–.07

=.85

, which agrees with com

Chapter

Summarizing

Data by Using

347

Descriptive Statistics

Problems

Use the data in the fle Stock.xlsx to gener

stock.

Use your answer to Problem 1 to compare the m

City Power & Light produces voltage-regulati

equipment to Chicago. A voltage regulator i

voltage of 25–75 volts. The voltage held by e

each unit is shipped. The voltage is measur

sample of voltage measurements from each ci

❑

Using descriptive statistics, comment on w

held by units before and after shipment.

❑

What percentage of units are acceptable b

❑

Do you have any suggestions about how to i

Light’s regulators?

❑

Ten percent of all New York regulators ha

❑

Five percent of all New York regulators h

value?

In the fle Decadeincome.xlsx, you are given a s

1980 dollars) for a set of families sampled i

are representative of the whole United Stat

better off in 1990 than in 1980 because ave

Use descriptive statistics to compare the a

bonds. Use the data contained in the fle Hi

In 1970 and 1971, eligibility for the U.S. a

basis of a draft lottery number. The number wa

366 balls, one for each possible birth date

frst ball selected was given the number

days corresponded to the lowest numbers wer

contains the actual results of the 1970 and 1

drawing, January 1 received the number 305. U

that the 1970 draft lottery was not random a

the AVERAGE and MEDIAN functions to compute th

for each month.)

348

Microsoft Excel 2010: Data Analysis and Business Modeling

The fle Jordan.xlsx gives the starting salari

graduates from the University of North Caroli

“typical” starting salary for a geography maj

highest average starting salary in 1984 was g

player Michael Jordan was a geography major!

Use the LARGE or SMALL function to sort the a

Historicalinvest.xlsx. What advantage does thi

Sort button?

Compare the mean, median, and trimmed mean (tr

data) of the annual returns on stocks, T-Bill

Historicalinvest.xlsx.

10.

Use the geometric mean to estimate the mean a

T-Bills in the fle Historicalinvest.xlsx.

11.

The fle Dow.xlsx contains monthly returns on th

years. Use this data to determine the three s

returns.

12.

Using the Dow.xlsx data again, determine the th

variability.

13.

Using the Dow.xlsx data, determine the three s

14.

Using the Dow.xlsx data, how do the trimmed-m

returns) differ from the overall mean returns

15.

The fle Incomedata.xlsx contains incomes of a r

the years 1975, 1985, 1995, and 2005. Describ

over this time period.

16.

The fle Coltsdata.xlsx contains yards gained by t

rushing and passing play. Describe how the ou

plays differ.

349

Chapter 43

Using PivotTables a

Describe Data

Questions answered in this chapter:

■

What is a PivotTable?

■

How can I use a PivotTable to summarize groc

■

What PivotTable layouts are available in Exc

■

Why is a PivotTable called a PivotTable?

■

How can I easily change the format in a Piva

■

How can I collapse and expand felds?

■

How do I sort and flter PivotTable felds?

■

How do I summarize a PivotTable by using a P

■

How do I use the Report Filter section of th

■

How do Excel 2010 slicers work?

■

How do I add blank rows or hide subtotals ia

■

How do I apply conditional formatting to a P

■

How can I update my calculations when I add n

■

I work for a small travel agency for which I n

funds are limited, so I want to mail the br

on travel. From information in a random sam

age, and the amount these people spent on tr

determine how gender and age influence a per

conclude about the type of person to whom I s

■

I’m doing market research about Volvo Cross C

what factors influence the likelihood that a f

information in a large sample of families, I k

family income (high or low). How can I dete

the likelihood that a family will purchase a s

350

Microsoft Excel 2010: Data Analysis and Business Modeling

■

I work for a manufacturer that sells microchi

predicted sales for Canada, France, and the Uni

I’m also given the, variance,

between actual

difference

and budgete

For each month and each combination of countr

following data: actual revenue, budgeted reve

a percentage of annual revenue, and variance a

How can I display this information?

■

What is a calculated feld?

■

How do I use a report flter or slicer?

■

How do I group items in a PivotTable?

■

What is a calculated item?

■

What is “drilling down”?

■

I often have to use specifc data in a PivotTa

sales in France of Chip 1. Unfortunately, thi

added to my PivotTable. Does Excel have a fun

April’s Chip 1 sales in France from the Pivot

Answers to This Chapter’s Quest

What is a PivotTable?

In numerous business situations, you need to ana

important insights. Imagine that you sell differ

different points in time. You might have hundred

PivotTables let you quickly summarize your data i

for your grocery store data, you could use a Piv

■

Amount spent per year in each store on each p

■

Total spending at each store

■

Total spending for each year

In a travel agency, as another example, you migh

whether the average amount spent on travel is in

factors. In analyzing automobile purchases, you’

families that buy a station wagon to the fractio

wagon. For a microchip manufacturer, you’d like t

for example, during April, and so on. A PivotTab

can use to slice and dice data. The easiest way t

to walk through some carefully constructed examp

Chapter

Using

PivotTables and Slicers

351

to Describe Data

anintroductory example and then illustrate many a

subsequent examples.

Note

Excel 2010 contains

slicers

a new that

feature

make

called

it much eas

to examine your data from many perspectives. I dis

How can I use a PivotTable to summarize grocer

The

Data

worksheet in the fle Groceriespt.xlsx c

(See Figure 43-1.) Each row contains the numbe

store, as well as the month and year of the sa

or ice cream) is also included. You would like t

each product group and product at each store. Y

breakdown during any subset of months in a giv

during January–June).

Fig

URE 43-1

Data for the grocery PivotTable example.

Before creating a PivotTable, you must have he

that the grocery data contains headings (Year, M

Revenue) in row 2. Place your cursor anywhere i

the Tables group on the Insert tab. Excel open

Figure 43-2, and makes an assumption about you

guessed that the data range was C2:I924.) By s

also refer to a database as a source for a Piv

352

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 43-2

The Create PivotTable dialog box.

After you click OK, you see the PivotTable Field L

Fig

URE 43-3

The PivotTable Field List.

You fll in the PivotTable Field List

, into

by dragging

the boxe

zones

. This step is critical to ensuring that the P

data in the manner you want. The four zones are a

■

Row Labels

Fields dragged here are listed on the l

in which they are added to the box. For examp

felds Year, Group, Product, and Store, in tha

data frst by year, then for each product grou

within each group, and fnally each product by s

a different zone or reorder the felds within a z

zone or by clicking the arrow to the right of th

Chapter

Using

PivotTables and Slicers

353

to Describe Data

■

Column Labels

Fields dragged here have their valu

PivotTable. To start out this example, we ha

■

Values

Fields dragged here are summarized math

Units and Revenue (in that order) to this z

culation you want to perform on a feld. In thi

and Units should be summed, which happens t

method of calculation for a data feld to an a

click the data feld and choose Value Field S

Value Field Settings command later in the c

■

Report

Beginning

Filter

in Excel 2007,

Report Filte

Field area. For felds dragged to the Report Fi

the feld values so that the PivotTable shows c

this example, I dragged Month to the Report Fi

subset of months, for example January–June, a

those months. Slicers in Excel 2010 make re

The completed PivotTable Field List is shown i

in Figure 43-5 and in the

All Row Fields

works

you can see that 233,161 units were sold for $

ere is some advice about navigating workbooks (

many worksheets. In the lower-right corner of the E

names), you will see four arrows. Clicking the lef

clicking the right-most arrow shows the last works

one worksheet to the left or right.

Not

o see the feld list, you need to be in a feld i

list, right-click any cell in the PivotTable and s

Fig

URE 43-4

Completed PivotTable Field List.

354

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 43-5

The Grocery PivotTable in compact form.

What PivotTable layouts are available in Excel 2

The PivotTable layout shown in .Figure

In the43-5

compact

is caf

the row felds are shown one on top of another. T

anywhere within the table. On the Design tab, in th

choose one of the following: Show In Compact For

(see Figure 43-6 and the

Outline Form

worksheet)

the

Tabular Form

worksheet).

Fig

URE 43-6

The outline format.

Chapter

Using

PivotTables and Slicers

355

to Describe Data

Fig

URE 43-7

The tabular format.

Why is a PivotTable called a PivotTable?

You can easily pivot felds from a row to a col

For example, by dragging the Year feld to the C

layout shown in Figure 43-8. (See the

Years Co

Fig

URE 43-8

The Years feld pivoted to the column feld.

How can I easily change the format in a PivotT

If you want to change the format of an entire c

heading and select Number Format from the Valu

format you want. For example, in the

Formatted $

as currency by double-clicking the Sum Of Reve

You can also change the format of a value feld by c

356

Microsoft Excel 2010: Data Analysis and Business Modeling

feld in the PivotTable Field List. Select Value Fi

then you can reformat the column as you want it.

From any cell in a PivotTable, you can select th

PivotTable styles.

How can I collapse and expand fields?

Expanding and collapsing felds (a feature introd

PivotTables. In Figure 43-5, you see minus (–) s

the minus sign collapses a feld and changes the s

expands the feld. For example, if you click the mi

you will fnd that in each year, cereal is contra

longer listed. See Figure 43-9 and the

Cerealcol

A6 brings back the detailed or expanded view lis

Fig

URE 43-9

The cereal feld collapsed.

You can also expand or contract an entire feld. G

feld, and select PivotTable Tools Options on the r

the green Expand Entire Field button (labeled wi

Field button (labeled with a minus sign). (See Fi

Fig

URE 43-10

The Expand Entire Field and Contract Entire Field b

Chapter

Using

PivotTables and Slicers

357

to Describe Data

For example, suppose you simply want to see fo

Pick any cell containing a group’s name (for e

on the ribbon, and click the Collapse Entire Fi

Figure 43-11 (the

Groups Collapsed

worksheet). S

brings you back to the original view.

Fig

URE 43-11

The Group feld collapsed.

How do I sort and filter PivotTable fields?

In Figure 43-5, the products are listed alphab

chocolate

is the frst type of milk listed. If y

alphabetical order, simply move the cursor to a

in the

All Row Fields

worksheet) and click the d

entry in A5. You will see the list of fltering o

A would list

whole milk

frst for milk,

plums

Initially, our PivotTable displays results frs

to see the data for 2005 frst, move the cursor t

and choose Sort Smallest To Largest from the a

At the bottom of the fltering optionsproducts

dialog b

to be displayed. You may want to frst clear Se

want to show.

358

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 43-12

PivotTable fltering options for the Product feld.

For another example of fltering, look at the

Dat

shown in Figure 43-13. The worksheet data contai

customer number, the amount paid, and the quarte

received. After dragging Customer to the Row Lab

and Paid to the Values box, the PivotTable shown i

worksheet in the Pcustomers.xlsx fle.)

Fig

URE 43-13

The Customer PivotTable data.

Chapter

Using

PivotTables and Slicers

359

to Describe Data

Fig

URE 43-14

The Customer PivotTable.

Naturally, you might like to show a list of ju

simply click the Row Labels arrow and select

tain the layout shown in Figure 43-15 (see the

Clear Filter, you can return to the original l

Fig

URE 43-15

Top 10 customers.

Suppose you simply want to see the top custome

Select the Row Labels fltering icon, select Va

shown in Figure 43-16.

360

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 43-16

Confguring the Top 10 Filter dialog box to show cu

The resulting PivotTable is in the

Top half

work

see, the top 14 customers generate a little more th

Fig

URE 43-17

The top customers generating half of the revenues.

Now let’s suppose you want to sort your customer

worksheet.) Right-click anywhere in the Quarter

Largest To Smallest. (See Figure 43-18.) The res1

that Customer 13 paid the most in Quarter 1, Cus

Fig

URE 43-18

Sorting on the Quarter 1 column.

Chapter

Using

PivotTables and Slicers

361

to Describe Data

Fig

URE 43-19

Customers sorted on Quarter 1 revenue.

How do I summarize a PivotTable by using a Piv

Excel makes it easy to visually summarize

laying

Pivot

out the data the way you want it inexpand

PivotCha

felds. In the grocery example, suppose you wan

food group’s unit sales. (See the

Chart 1

work

move the Year feld to a column feld and delete Re

to collapse the entire Group feld in the Row L

PivotChart. Simply click anywhere inside the t

pick the chart type you want to create. I chos

the chart in Figure 43-20. The chart shows tha

in 2006.

362

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 43-20

PivotChart for unit group sales trend.

How do I use the Report Filter section of the Pi

Recall that I placed Months in the Report Filter s

report flter, suppose that you want to summarize s

clicking the Filter icon in cell B2 of the

First 6 m

This results in the PivotTable shown in Figure 4

sold by product, group, and year for the months J

Fig

URE 43-21

A PivotTable summarizing January–June sales.

Chapter

Using

PivotTables and Slicers

363

to Describe Data

How do Excel 2010 slicers work?

The problem with a report flter is that a view

cannot easily see that the table summarizes Ja

solves this problem. To create a slicer for an

PivotTable, place your cursor anywhere

ribbon’s

in the P

Insert tab. In the worksheet Slicers of the fl

menu. Then I selected the Month and Product fe

Using a given slicer, you can select any subse

table.In the Month slicer, I selected (one at a t

months January through June. I did nothing to th

January–June sales. The slicers are shown in Fi

Fig

URE 43-22

Example of slicers for the Month and Product fel

If you click in a slicer, you see formatting o

How do I add blank rows or hide subtotals in a P

If you want to add a blank row between each gr

on the ribbon, click Blank Rows, and then clic

to hide subtotals or grand totals, select Pivot

Grand Totals. After adding blank rows and hidi

rows no totals

worksheet, shown in Figure 43-2

you can select PivotTable Options to open the

box, you can replace empty cells by using any c

using a 0.

Fig

URE 43-23

Grocery PivotTable without totals.

364

Microsoft Excel 2010: Data Analysis and Business Modeling

How do I apply conditional formatting to a Pivot

Suppose you want to apply data bars to the Units c

problem you’ll encounter is that subtotals and g

make the other data bars smaller than apply

they shoul

to all product sales, not the subtotals and gran

workbook Groceriespt.xlsx.) To apply the data ba

by placing the cursor in a cell containing a pro

then select the Sum Of Units column data (the ce

Conditional Formatting followed by Data Bars, an

New Formatting Rule dialog box shown in Figure 4

Fig

URE 43-24

New Formatting Rule dialog box for using condition

By selecting All Cells Showing “Sum of Units” Va

data bars apply only to cells listing unit sales f

worksheet and Figure 43-25.

Chapter

Using

PivotTables and Slicers

365

to Describe Data

Fig

URE 43-25

Data bars for a PivotTable.

How can I update my calculations when I add ne

If the data in your original set of rows chang

data changes by right-clicking the table and s

after choosing Options.

If you want data you add to be automatically i

you refresh it, you should name your original d

(See Chapter 26, “Tables,” for more informatio

If you want to change the range of data used t

Change Data Source on the Options tab. You can a

by selecting Move PivotTable.

I work for a small travel agency for .which

I n

funds are limited, so I want to mail the broch

ontravel

. From information in a random sample of 9

age, and the amount these people

. How can

spent

I use

on trav

thi

determine how gender and age influence a person

conclude about the type of person to whom I sh

To understand this data, you need to break it d

■

Average amount spent on travel by gender

■

Average amount spent on travel for each age g

■

Average amount spent on travel by gender fo

366

Microsoft Excel 2010: Data Analysis and Business Modeling

The data is included on the

Data

worksheet in th

in Figure 43-26. For example, the frst person is a 4

Let’s frst get a breakdown of spending by gender

extracts the range A2:D927. After clicking OK, p

appears. Next, drag the Gender column to the Row L

Travel to the Values zone. This results in the P

You can tell from the heading Sum Of Amount Spen

total amount spent on travel, but you actually wa

men and women. To calculate these quantities, do

and then select Average from the Value Field Set

Fig

URE 43-26

Travel agency data showing amount spent on travel, a

Fig

URE 43-27

PivotTable summarizing the total travel expenditur

Fig

URE 43-28

You can select a different summary function in the

Chapter

Using

PivotTables and Slicers

367

to Describe Data

You now see the results shown in Figure 43-29.

Fig

URE 43-29

Average travel expenditures by gender.

On average, people spend $908.13 on travel. Wo

men spend $914.99. This PivotTable indicates

sity to travel. By clicking the Row Labels arr

Now you want to see how age influences travel s

PivotTable, simply click Gender in the Row Lab

remove it from the Row Labels area. Then, to b

row area. The PivotTable now appears as it’s s

Fig

URE 43-30

PivotTable showing the average travel expenditur

Age seems to have little effect on travel expe

in its present state. You need to group data by a

age, right-click anywhere in the Age column an

you can designate the interval by which to defn

you obtain the PivotTable shown in Figure 43-3

On average, 25–34 year olds spend $935.84 on tr

travel, and so on. This information is more us

ages tend to spend about the same amount on tr

determine who you should mail your brochure to

368

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 43-31

Use the Group And Show Detail command to group det

Finally, let’s get a breakdown of average travel s

separately. All you have to do is drag Gender to th

resulting in the PivotTable shown in Figure 43-3

Fig

URE 43-32

Age/gender breakdown of travel spending.

Now we’re cooking! You can see that as age incre

men spend less. Now you know who should get the b

men. As one of my students said, “That would be s

A graph provides a nice summary of this analysis

PivotTable and choosing PivotChart, select the f

is the chart shown in Figure 43-33. If you want t

Tools. Then, for example, if you choose Layout, y

make other changes.

Fig

URE 43-33

PivotChart for the age/gender travel expenditure b

Chapter

Using

PivotTables and Slicers

369

to Describe Data

Each age group spends approximately the same o

spend more than men. (If you want to use a dif

type by right-clicking the PivotChart and then c

Notice that the bars showing expenditures by m

representing the amount spent by women increas

that showed only gender and age data failed

to u

ple population are men and half are women, we f

people does not depend on the age. (Notice tha

age is approximately the same.) We also found th

women was approximately the same. You can see thi

blue and red bars have approximately equal

hei

ously across age and gender does a much better j

i’m doing market research about Volvo Cross Cou

what factors influence the likelihood that a fa

From information in a large sample of families

and the family income (high or low). How can i

influence the likelihood that a family will pur

In the fle Station.xlsx, you can fnd the follow

■

Is the family size large or small?

■

Is the family’s income high or low?

■

Did the family buy a station wagon? Yes or N

A sample of the data is shown in Figure 43-34 (

family listed is a small, high-income family th

Fig

URE 43-34

Data collected about income, family size, and th

370

Microsoft Excel 2010: Data Analysis and Business Modeling

You want to determine how family size and income i

will purchase a station wagon. The trick is to l

family size and how family size affects purchase

To begin, choose Insert Pivot Table, and then se

the PivotTable Field List, drag Family Size to th

Column Labels area, and any of the three felds t

shown in Figure 43-35 (see the

1st Table

- workshe

marize the data appropriately by counting the nu

example, 34 high-salary, large families did not b

large families did buy one.

Fig

URE 43-35

Summary of station wagon ownership by family size a

You would like to know for each row in the Pivot

purchased a station wagon. To display the data i

PivotTable data and then choose Value Field Setti

dialog box. In the dialog box, click Show Values A

Data As list. You now obtain the PivotTable show

Breakdown

worksheet.)

Fig

URE 43-36

Percentage breakdown of station wagon ownership by i

From Figure 43-36 you learn that for both large a

on whether the family purchases a station wagon. N

Chapter

Using

PivotTables and Slicers

371

to Describe Data

size affects the propensity to buy a station wa

To do this, move Salary above Family Size in th

shown in Figure 43-37 (see the Final Percent B

Fig

URE 43-37

Breakdown of station wagon ownership by family s

From this table, you learn that for high-incom

buy a station wagon than a small family. Simil

also more likely to purchase a wagon than a sm

has a much greater effect on the likelihood th

does income.

I work for a manufacturer that

. I’m given

sells monthly

microchip

predicted sales for Canada, France, and the Un

I’m also given the variance, or difference,

For each month and each combination of country a

following data: actual revenue, budgeted reven

percentage of annual revenue, and variance

. How as a p

can I display this information?

In this scenario, you are a fnance manager for a mi

products in different countries and at differe

your data in a format that’s easily understood

The fle Ptableexample.xlsx includes monthly ac

Chip 1, Chip 2, and Chip 3 in Canada, France, a

variance, or difference, between actual revenu

data is shown in Figure 43-38 (see the data wo

sales of Chip 1 totaled $4,000, although sales o

variance of –$1,454.

372

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 43-38

Chip data from different countries for different m

variance revenues.

For each month and each combination of country a

following data:

■

Actual revenue

■

Budgeted revenue

■

Actual variance

■

Actual revenue as a percentage of annual reve

■

Variance as a percentage of budgeted revenue

To begin, select a cell within the range of data y

frst row must include headings), and then choose I

determines that your data is in the range A1:F20

If you drag Month to the Row Labels area, Countr

to the Values area, for example, you obtain the t

feld you add to the Report Filter area (Product, f

by using values in that feld. By adding Product t

of only Chip 1 by month for each country. Given th

any combination of country and product, you shou

of the PivotTable and both Country and Product t

Revenue, and Budget to the Values zone. You have n

in Figure 43-39. (See the 1st Table worksheet.)

Chapter

Using

PivotTables and Slicers

373

to Describe Data

Fig

URE 43-39

Monthly summary of revenue, budget, and variance

For example, in January, total revenue was $87

actual sales fell $4,297 short of the forecast

You want to determine the percentage of revenu

Revenue from the feld list to the Values area o

column, and then choose Value Field Settings. I

Show Values As. In the Show Values As list, se

Of Revenue2, as shown in Figure 43-40.

Fig

URE 43-40

Creating each month’s percentage of annual reven

You now obtain the PivotTable shown in Figure 4

sales provided 8.53 percent of revenue. Total r

374

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 43-41

Monthly revenue breakdown.

What is a calculated field?

Now you want to determine for each month the var

do this, you can create

. Select

calculated

cell anywhere

feld

withi

PivotTable, and then choose Formulas on the Opti

display the Insert Calculated Field dialog box. A

your feld, and then enter your formula.You

Thecan

form

enter the formula yourself or use the list of fe

the formula. After clicking Add and then OK, you s

(See the

Calc Field

worksheet of the Ptableexamp

Fig

URE 43-42

Creating a calculated feld.

Chapter

Using

PivotTables and Slicers

375

to Describe Data

Fig

URE 43-43

The PivotTable with calculated feld for variance p

Thus, in January, sales were 4.7 percent lower th

Calculated Field dialog box again, you can mod

How do I

report

use afilter or slicer?

To see sales of Chip 2 in France, for example, y

Product and Country felds in the Report Filter a

would see the PivotTable shown in Figure 43-44

table with slicers (see the

Slicers

worksheet)

Fig

URE 43-44

Sales of Chip 2 in France.

In the worksheet

Slicers,

I used Slicers to cr

and selected Slicers from the Insert tab. Then I c

selecting the Product and Country felds. Selec

from the Country slicer yields the relevant co

in France. If you want to resize a slicer, hol

376

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 43-45

Sales of Chip 2 in France with slicers.

How do I group items in a PivotTable?

Often, you want to group headings in a PivotTabl

sales for January–March. To create a group, sele

the selection, and then choose Group And Show De

Group 1 to Jan-March, you obtain the PivotTable s

Fig

URE 43-46

Grouping items together for January, February, and M

Remarks About Grouping

■

You can disband a group by selecting Group An

■

You can group nonadjacent selections by holdi

nonadjacent rows or columns.

Chapter

Using

PivotTables and Slicers

377

to Describe Data

■

With numerical values or dates in a row fel

arbitrary intervals. For example, you can c

average income for all 25–34 year olds.

What is a calculated item?

A calculated item works just like a calculated f

rather than a column. To create a calculated i

of the PivotTable, not an item in the body

of th

lect Formulas, followed by Calculated Item. Se

chapter for an example of creating a calculate

example, you could not create a calculated ite

Revenue feld.

What is “drilling down”?

“Drilling down” is double-clicking a cell in a

summarized in that feld. For example, double-c

scenario displays the data that’s related to M

I often have to use specific data in a PivotTab

in France . of

Unfortunately,

Chip 1

this data moves arou

my PivotTable

. Does Excel have a function that enabl

sales in France from the PivotTable?

Yes, there is such a function. The GETPIVOTDAT

to extract sales of Chip 1 in France during Ap

worksheet in the fle Getpivotdata.xlsx. (See Fi

GETPIVOTDATA(A4,”April France Chip 1 Sum of Re

even if additional products, countries, and mo

also determine the resulting revenue by pointi

France (cell D24).

The frst argument for this function is in the c

(cell A4). You enclose in quotation marks (sep

defne the entry you want. The last entry must s

be listed in any order. Thus, the formula here m

corner is in cell A4, fnd the Sum of Revenue f

returns the correct answer even if the sales d

different location in the PivotTable.

378

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 43-47

Use the GETPIVOTDATA function to locate April Chip 1 S

If you want to simply return total revenue ($1,0

GETPIVOTDATA(A4,”Sum

of Revenue”)

Often, the GETPIVOTDATA function is a nuisance. I

to use it. Suppose you want to refer to data in c

your workbook. You would probably use the formul

Hopefully, this would extract B6, B7,…, B11 to th

GETPIVOTDATA option is active, you get a bunch o

the same cell. If you want to turn off GETPIVOTD

Select Formulas, and under Working With Formulas

PivotTable References. This ensures that clickin

rather than a GETPIVOTDATA function.

Finally, note that you can also combine the MATC

Chapter 5, “The MATCH Function,” and Chapter 22, “

extract various PivotTable entries.

Problems

Contoso, Ltd. produces microchips. Five types o

known to occur. Chips are manufactured by two o

machines (1–4). You are given data about a sa

the type of defect, the operator, machine num

occurred. Use this data to chart a course of a

possible, to improved product quality. You sh

defects with respect to type of defect, day o

working. You might even want to break down th

on. Assume that each operator and machine mad

fnd this data in the fle Contoso.xlsx.

Chapter

Using

PivotTables and Slicers

379

to Describe Data

You own a fast food restaurant and have don

better understand your customers. For a ran

the income, gender, and number of days per w

Use this information to determine how gende

with which a person goes out to eat fast fo

Students at the School of Fine Art apply to s

been assigned to determine whether the Scho

women in admitting students to the school o

data on the School of Fine Art’s students:

❑

Female or male

❑

Major applied for: English (Eng) or Scien

❑

Admit? Yes or No

Assuming that women are as equally qualifed f

indicate that the college discriminates agai

information. The data is in the fle Fineart

You have been assigned to evaluate the quali

at Emergency Room (ER) and Chicago Hope (CH

following patient data:

❑

Hospital (ER or CH).

❑

Risk category (high or low). High-risk pe

low-risk people.

❑

Patient outcome (live or die).

Use this data to determine which hospital i

attack patients. Hint: Use all the data. Th

You are given the monthly level of the Dow J

Does this data indicate any unusual seasona

extract the month (January, February,

TEXT(A4,”mmm”

and s

copied to any column. The data is in the fl

The fle Makeupdb.xlsx contains information a

each transaction, you are given the followi

❑

Name of salesperson

❑

Date of sale

❑

Product sold

❑

Units sold

❑

Transaction revenue

380

Microsoft Excel 2010: Data Analysis and Business Modeling

Create a PivotTable to compile the following i

❑

The number of sales transactions for each s

❑

For each salesperson, the total revenue by p

❑

Using your answer to the previous question, c

Jen’s lipstick sales.

❑

Total revenue generated by each salesperson b

❑

Total revenue by salesperson and year. (Hin

For the years 1985–1992, you are given monthl

money one year after the day they’re bought. I

are more volatile—tend to change more—when in

in the fle Intratevol-volatility.xlsx support thi

standard deviations.

For the grocery example, prepare a chart that s

sales at each store.

For the grocery example, create a calculate f

price received for each product.

10.

For the grocery example, create a PivotChart t

at each store for the years 2005 and 2006.

11.

For the data in the fle Calcitemdata.xlsx, cr

of dessert

cakes+puddings

() and

apples+grapes

fruits).(

12.

In the chip PivotTable example, create a Pivot

Chips 1 and 3 in France and the U.S.

13.

In the customer PivotTable example, show the t

bottom 5 customers in another table.

14.

The fle Ptablepartsdata.xlsx contains sales o

either Part (for

) or

computer

Comp (for

part

Create

computer

a PivotTable th

only sales of Parts. (Hint: Use a labels flte

15.

For the data in Problem 14, summarize the tot

16.

The fle Cigarettedata.xlsx contains the age o

smoke cigarettes or cigars, and whether they d

you conclude from this data?

17.

The fle Collegedata.xls tells you the

applied

followi

to graduate school at Kelley University: gend

rejected. If you construct the appropriate Pi

accepted than men. Do you think Kelley discri

381

Chapter 44

Sparklines

Questions answered in this chapter:

■

How can you graphically summarize daily cus

branches in a single cell?

■

How can you modify sparklines?

■

How can you summarize an NFL team’s sequence o

■

Do sparklines automatically update when new d

Sparklines are exciting graphics that can summ

The term

sparkline

was frst used by Edward

Tuf

tation of data and its analysis. Tufte describ

word-sized graphics.” Microsoft Excel 2010 mak

reside in a single cell.

Answers to This Chapter’s Ques

How can you graphically summarize daily custom

in a single cell?

The fle Sparklines.xlsx contains daily custome

state bank. See Figure 44-1.

Fig

URE 44-1

Data for sparklines.

Let’s say that you want to summarize the weekl

daily counts for each branch in a single cell. S

your

sparklines to go (I chose I8:I14), and then f

Sparklines group shown in Figure 44-2.

382

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 44-2

Sparkline choices.

Then fll in the dialog box below with the data o

Fig

URE 44-3

Creating line sparklines.

You now see a line graph (Figure 44-4) that summ

You can see this in the worksheet

Line Sparkline

Fig

URE 44-4

Line sparklines summarizing branch traffc.

You can see that for each branch, Monday and Fri

How can you modify sparklines?

If you click in any cell containing a sparkline, t

selecting the Design tab, you can make many chan

shown in Figure 44-5, I selected the high and low p

The resulting sparklines are shown in Figure 44-

Sparklines.xlsx.

Chapter

Sparklines

383

Fig

URE 44-5

Selecting high and low points to mark on sparkli

Fig

URE 44-6

High and low points marked on sparklines.

These sparklines make it clear that Friday is th

Wednesday is the least busy day.

From the Design tab you can make the following c

■

Change the type of sparkline (line, column, o

sparklines later in the chapter.

■

Use the Edit Data command to change the dat

also change the default setting so that hid

■

Select any combination of the high point, l

point to be marked.

■

Change the style or color associated with th

■

By selecting Axis, you can change the way th

example, you can make the x-axis or y-axis s

default is to base the scale for each axis o

is the scaling used in Figure 44-4. The Cus

lower limit for each axis.

■

When data points occur at irregularly space

Axis option so that the graphed points

- are s

tional to the differences in dates.

irregularly

Figure s

dates (see the worksheet

Date Axis

in the fl

is graphed as though the dates are spaced a

choosing the range C10:C13 to use as the dat

irregular date spacing.

384

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 44-7

Sparklines with a data axis.

You can also change line sparklines to column sp

selecting Column from the Sparklines Tools Desig

Column Sparkline

in the fle Sparklines.xlsx.

Fig

URE 44-8

Column sparkline graph.

How can you summarize an NFL team’s sequence of w

The fle Nflwinslosses.xlsx contains theduring

game by ga

the 2009 regular season. A subset of this data i

worksheet).

Fig

URE 44-9

Sparklines summarizing wins and losses for NFL tea

Chapter

Sparklines

385

A 1 denotes a win, and a –1 a loss. Each win/l

“up block” and any negative number as a “down b

create the win/loss sparklines, select the ran

range C8:C39), and then select Win/Loss from t

choose the data range E8:T39. The sparklines m

see the amazing starts of the Indianapolis Col

that the Tennessee Titans started poorly and th

well and then hit a rough patch. Win/loss spar

progress toward meeting quotas or goals. See P

Do Sparklines automatically update when new da

If you want your sparklines to automatically u

the data a table (see Chapter 26, “Tables”) or c

Chapter 22, “The OFFSET Function.”)

Problems

For the bank branch data, make your line sp

The data Dow.xlsx contains the values of th

2010. Create a line sparkline to show the up

Use win/loss sparklines to capture the mark

Dow.xlsx.

The fle Goals.xlsx shows the percentage amo

to meet their goals each month. Summarize thi

387

Chapter 45

Summarizing Data wi

Statistical Functio

Questions answered in this chapter

■

Joolas is a small makeup company that track

Excel 2010 worksheet. Often, they want to a

❑

How many dollars worth of lip gloss did J

❑

What was the average number of lipstick u

the East region?

❑

What was the total dollar amount of all m

region?

❑

How many dollars worth of lipstick were s

region?

❑

How many lipstick transactions were not i

❑

How many dollars worth of lipstick did Je

❑

How many units of makeup were sold for a p

❑

What is the total dollar amount each sale

❑

What helpful tricks can I use to set up c

■

I have a database that lists for each sales

product ID code. Given the date sold and th

way to extract the transaction’s revenue?

As you saw in Chapter 43, “Using PivotTables a

are a great tool for summarizing

PivotTable

data.

gives

Often,

you mh

information than you need.

Database statistica

“reporting” question without having to create a P

You are already familiar with functions such a

prefxing a

(which

) to

stands

thesefor

and

database

other functio

statistical functions. But what does the- DSUM f

tion can’t? Whereas the SUM function adds up e

enables you to specify (by using criteria) a s

388

Microsoft Excel 2010: Data Analysis and Business Modeling

example, suppose you have a sales database for a s

following information about each sales transacti

■

Name of salesperson

■

Transaction date

■

Product sold

■

Units sold

■

Dollars of revenue generated per transaction

■

Region of the country where the transaction t

You can fnd this data in the fle Makeupdb.xlsx, w

Fig

URE 45-1

We’ll use this data to describe how to work with da

Using the DSUM function with appropriate criteria

revenue generated only by transactions involving l

Essentially, the criteria you set up flags those r

Within these rows, the DSUM function acts like th

The syntax of the DSUM function is

DSUM(database

■

Database

is the cell range that makes up the d

labels for each column.

■

Field

is the column containing the values you wa

the feld by enclosing the column label in quot

designate the Dollars column by entering “Dol

by using the position of the column in the da

example, the makeup transaction database woul

Chapter

Summarizing

Data with Database

389

Statistical Functions

include the Transactions column as part of th

feld 1

and column

M as

feld 6

■

criterion

refers to a cell range that spe

operate. The frst row of a criteria range m

only exception to this

, which

rule is

I’ll

computed

discuss

cri

in th

ples in this chapter.) As the examples illus

understand that multiple criteria in the sa

different rows are joined by OR.

Now let’s go on to some examples that illustra

statistical functions.

Answers to This Chapter’s Ques

How many dollars’ worth of lip gloss did Jen s

In this example, you want to apply DSUM to col

the dollar volume for each transaction. (I gav

of the range H4:M1895.) The criteria range in O

Name equals Jen

and

Product equals lip gloss. T

the formula

DSUM(data,5,O4:P5)

calculates the t

You could have also entered the .formula

Jen sold

as $5,4

DSU

worth of lip gloss. In cell N6 you can fnd the s

Chapter 21, “The SUMIF, AVERAGEIF, SUMIFS, and A

SUMIFS(Dollars,Name,”Jen”,Product,”lip

gloss”

Fig

URE 45-2

Database statistical functions at work.

390

Microsoft Excel 2010: Data Analysis and Business Modeling

What was the average number of lipstick units so

region?

You can compute this number by entering .in cell N

Using 4 as the value for

feld

specifes the Units c

rows in the database in which Name equals Jen, P

East. Using DAVERAGE ensures that you average th

see that on average, Jen sold 42.25 units of lip

N9, you can calculate the same

AVERAGEIFS(Units,Name

answer by using th

Product,”lipstick”,Location,”east”)

What was the total dollar amount of all makeup s

In cell N11, you can compute the total dollars (

East by using the formula

. The

DSUM(data,5,O10:P12)

criteria in O10:P12 fl

East

by Emilee, because criteria in different r

programmers at Microsoft have ensured that this f

sales in the East. Here, you cannot use SUMIFS t

How many dollars’ worth of lipstick were sold by C

The formula

DSUM(data,5,O13:Q15)

in cell N14

generated

computes

through Colleen and Zaret’s sales ($1,073.20) in th

criteria that selects Colleen’s lipstick sales i

selects Zaret’s lipstick sales in the East. Reme

OR. In cell N15, the answer to this question is c

=SUMIFS(Dollars,Name,”Colleen”,Product,”lipstick”,Location,”east”)

+SUMIFS(Dollars,Name,”Zaret”,Product,”lipstick”,Location,”east”)

How many lipstick transactions were not in the E

In cell N17, you can compute the total number of l

region with the formula

. You

DCOUNT(data,4,O16:P17)

use DCOUNT in this p

you want to specify criteria by which the functi

lipstick sales and regions other than the East. E

range as “not East.” For this problem, using SUM

function for each region.

Because the COUNT function counts numbers, you n

numerical values. Column 4, the Units column, co

umn in the formula. The formula

DCOUNT(data,3,O1

no numbers in the database’s third column (which i

the formula

DCOUNTA(data,3,O16:P17)

would return th

counts text as well as numbers.

Chapter

Summarizing

Data with Database

391

Statistical Functions

How many dollars’ worth of lipstick did Jen se

The trick here is knowing how to flag only sale

row of your criteria range a reference to the

and

<1/1/2005

captures only the 2004 sales. Th

DSUM(data,5,O18:R19)

computes the total lipsti

2004, and before January 1, 2005. In cell N20, t

the formula

=SUMIFS(Dollars,Date,”>=1/1/2004”,

me,”Jen”).

How many units of makeup were20?

sold for a price o

This example involves

. Basically,

computed

computed

criteria

criteria fl

database on the basis of whether a computed co

question, you want to flag each row that contai

a computed criteria (see Figure 45-3), the lab

must not

be a column label. For example, you c

from row 4 of this worksheet. The computed cri

True based on the frst row of information in th

the average price is greater than or equal to $

your criteria range below a heading that is not a c

not satisfy this condition, you will see FALSE i

rows having a unit price that’s greater than o

DSUM(data,4,O21:O22)

computes the total number o

for which the unit price was greater than or e

formula

=(L5/K5)>=3.2

Fig

URE 45-3

Computed criteria.

What is the total dollar amount each salespers

For this problem, I’d like to use a DSUM functi

Name and Product columns. Using a data table,

I c

binations of Name and Product in the criteria r

Name and Product combination.

I begin by entering any name in cell X26 and a

Q25 the formula

DSUM(data,5,X25:Y26)

which computes total sales r

Betsy and eye liner. Next, I enter each salesp

product in the cell range R25:V25. Now select th

tab, in the Data Tools group, click What-If An

X26 as the column input cell and Y26 as the row i

392

Microsoft Excel 2010: Data Analysis and Business Modeling

in Figure 45-4. Each entry in the data table com

name/product combination because the data table c

X26 and the products to be placed in cell Y26. F

lipstick.

Fig

URE 45-4

Combining data tables with a DSUM function.

This example shows how combining data tables with d

quickly generate many statistics of interest. Not

from cell R37 to R37:V45

SUMIFS(Dollars,Name,$Q37,Produc

the formula

What helpful tricks can I use to set up criteria r

Here are some examples of little tricks that mig

range. Suppose the column label in the frst row o

containing text (for example, column H).

■

*Allie*

will flag records containing the text s

■

A?X

will flag a record if the record’s column H e

third character. (The second character can be a

■

<>*B*

will flag a record if column

H’s entry do

If a column (for example, column I) contains num

■

>100

will flag a record if column I contains a v

■

<>100

will flag a record if column I contains a v

■

>=1000

will flag a record if column I contains a v

I have a database that lists for each sales tran

product ID

. Given

code the date sold and the ID code fo

way to capture the transaction’s revenue?

The fle Dget.xlsx (see Figure 45-5) contains

product a d

ID codes for a series of sales transactions. If y

Chapter

Summarizing

Data with Database

393

Statistical Functions

for a transaction, how can you fnd the transac

simple. The syntax of the DGET function

. Given aiscell

DGE

for

database

and a value for

feld#

in the data

the range), the DGET function returns the entr

satisfying the criteria. If no record satisfes th

error message. If more than one record satisfe

#NUM! error message.

Suppose that you want to know the revenue for a tr

62426 that occurred on 1/9/2006. Assuming that th

the given date is unique, the formula (entered i

transaction’s revenue of $169. Note that I use

is listed in the frst column of the database (

The criteria range G5:H6 ensures that you fnd a t

1/9/2006.

Fig

URE 45-5

Using the DGET function.

Problems

How many units of lip gloss did Zaret sell d

Create a data table that contains each pers

How many units of lip gloss did Colleen sel

Using the data in fle Makeupdb.xlsx, create a d

unit revenue generated by each person for s

exceeded $3.30.

394

Microsoft Excel 2010: Data Analysis and Business Modeling

Use the data in the fle Sales.xlsx to determi

❑

Total dollar sales in the Midwest

❑

Total dollars that Heather sold in the East

❑

Total dollars that Heather sold or that wer

❑

Total dollars sold in the East by Heather o

❑

Number of transactions in the East region

❑

Number of transactions with greater than av

❑

Total sales not in the Midwest

The fle Housepricedata.xlsx contains the foll

❑

Square footage

❑

Price

❑

Number of bathrooms

❑

Number of bedrooms

Use this information to answer the following q

❑

What is the average price of all homes havi

bedrooms greater than or equal to six?

❑

How many homes sell for more than $300,000 a

bedrooms and bathrooms less than or equal t

❑

How many homes have at least three bathroom

bedrooms and bathrooms is less than or equa

❑

What is the highest price of a home

total

having a

number of bedrooms and bathrooms less than o

DMAX function to solve this problem.)

The fle Deciles.xlsx contains the unpaid bala

to compute the total unpaid balances in each d

395

Chapter 46

Filtering Data and R

Duplicates

Questions answered in this chapter:

Joolas is a small company that manufactures ma

transaction in a Microsoft Excel 2010 workshee

out,” a subset of their sales data. For exampl

that answer the following questions:

■

How can I identify all transactions in whic

■

How can I identify all transactions in whic

the East or South region?

■

How can I copy all transactions in which Ci

East or South region to a different workshe

■

How do I clear flters from a column or data

■

How can I identify all transactions that in

than 90 units?

■

How can I identify all sales occurring in 2

■

How can I identify all transactions in the l

months of 2006?

■

How can I identify all transactions for whi

■

How can I identify all transactions for whi

colored in red?

■

How can I identify all transactions in the

was the salesperson?

■

How can I easily obtain a complete list of s

■

How can I view every combination of salespe

the database?

■

If my data changes, how can I reapply the s

■

How can I extract all foundation transactio

Emilee or Jen was the salesperson and the a

Microsoft Excel 2010 has fltering capabilities th

snap. Excel also makes it easy to remove dupli

396

Microsoft Excel 2010: Data Analysis and Business Modeling

for this chapter in the fle Makeupflter.xlsx. Fo

(Figure 46-1 shows a subset of the data), you ha

■

Transaction number

■

Name of the salesperson

■

Date of the transaction

■

Product sold

■

Units sold

■

Dollar amount of the transaction

■

Transaction location

Fig

URE 46-1

Makeup sales data.

Each column (C through I) of our database

. Each row

(cell r

of the database that contains

. (Thus,data

the is

records

calledina o

contained in the cell range C4:I1894.) The frst r

For example, the name of the feld in column F is P

can query the database using AND criteria to ide

you can use queries of the form “Find all record

and

Field 2 satisfes certain conditions,

and

Fie

examples illustrate the capabilities of the Exce

Chapter

Filtering

Data and Removing

397

Duplicates

Answers to This Chapter’s Ques

How can I identify all transactions in which J

To begin, place your cursor anywhere in the da

group on the Data tab on the ribbon. As shown i

now has an arrow in the heading row (see the

Fig

URE 46-2

AutoFilter heading arrows.

After clicking the arrow for the Name column, y

You could choose Text Filters, which allows

son’s name (more on this later). For now, you ju

clear the Select All check box, then select th

see only those records for which Jen was the s

and select the lipstick check box. Then go to th

box. You now see only those transactions for w

Figure 46-4 and the

Lipstick Jen East

workshee

cone in the columns in which you set up flteri

398

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 46-3

Choices for fltering or sorting the Name column.

Fig

URE 46-4

Jen sells lipstick in the East region.

How can I identify all transactions in which Cic

East or South region?

You simply select Cici and Colleen from the Name c

the Product column list, and East and South from t

meeting this fltering criteria are shown in Figu

Masc

worksheet).

Chapter

Filtering

Data and Removing

399

Duplicates

Fig

URE 46-5

Transactions in which Cici or Colleen sold lipst

How can I copy all transactions in which Cici o

or South region to a different worksheet?

The trick here is to frst press F5, click Spec

Now when you copy your data, Excel includes on

selected by the fltering criteria). Select all th

lipstick, and mascara) and paste them into a b

worksheet in your workbook by right-clicking a

Worksheet, then clicking OK. The worksheet

Vis

Cici or Colleen sold lipstick or mascara in th

How do I clear filters from a column or databas

Clicking Filter on the Data tab removes all fl

you created a flter displays an option to clea

How can I identify all transactions that invol

90 units?

After clicking Filter on the Data tab, frst cl

shown in Figure 46-6.

400

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 46-6

Filtering options for a numerical column.

You can check any subset of numerical unit value

sales were –10 or –8 units). I clicked Number Fi

Fig

URE 46-7

Number Filters options.

Most of the options you see in the fgure are sel

Than option and then fll in the dialog box as sh

Chapter

Filtering

Data and Removing

401

Duplicates

Fig

URE 46-8

Selecting all records where units sold is greate

Next, go to the Dollars column and click to in

is greater than $280. You obtain the records s

dollars > $280

worksheet). Note that all selec

dollars greater than $280.

Fig

URE 46-9

Transactions where more than 90 units were sold f

How can I identify all sales occurring in 2005 o

After clicking Filter on the ribbon, click the a

choices in Figure 46-10.

402

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 46-10

Filtering options for the Date column.

After selecting 2005 and 2006, you see only thos

shown in Figure 46-11 (see the

Sales In 2005 And 2

Fig

URE 46-11

Sales during 2005 and 2006.

Note that you could also have selected Date Filt

Figure 46-12.

Chapter

Filtering

Data and Removing

403

Duplicates

Fig

URE 46-12

Date Filters options.

Most of these options are self-explanatory as w

select any range of dates as your fltering cri

How can I identify all transactions in the las

months of 2006?

After clicking the arrow for the Date column,

earlier. Clicking the + sign to the left of th

October through December of 2005 and then Janu

sales during those months. (See Figure 46-13 a

Fig

URE 46-13

All sales during October 2005–March 2006.

404

Microsoft Excel 2010: Data Analysis and Business Modeling

How can I identify all transactions for which th

Simply click the Name column arrow, and choose T

the dialog box shown in Figure 46-14, choose Beg

Fig

URE 46-14

Custom AutoFilter dialog box set up to select all r

begins with C.

How can I identify all transactions for which th

colored in red?

Click the Product column arrow, and then choose

color to use as a flter. As shown in Figure 46-1

the product is colored in red. Figure 46-16 show

worksheet).

Fig

URE 46-15

Dialog box for fltering by cell color.

Chapter

Filtering

Data and Removing

405

Duplicates

Fig

URE 46-16

All records where the product cell color is red.

How can I identify all transactions in the top 3

was the salesperson?

After clicking Filter on the ribbon, you click th

check boxes for Hallagan and Jen. Then you cli

Number Filters. From the Number Filters list, s

dialog box as shown in Figure 46-17. You have n

values in which Jen or Hallagan is the salespe

30 $s With Hallagan Or Jen

worksheet). Note th

or Jen as the salesperson. You can also select T

for any numerical column.

Fig

URE 46-17

Dialog box to select the top 30 records by dolla

Fig

URE 46-18

Top 30 records by dollar value for which Jen or H

How can I easily obtain a complete list of sal

Here we want a list of all the salespeople, wi

selecting Remove Duplicates on the Data tab on th

dialog box shown in Figure 46-19. After choosi

box, and then click OK. This setting flters th

salesperson’s name. See the results in Figure 4

worksheet.

406

Microsoft Excel 2010: Data Analysis and Business Modeling

Important

Because selecting Remove Duplicates removes so

making a copy of your data before selecting Remove D

Fig

URE 46-19

Remove Duplicates dialog box.

Fig

URE 46-20

List of salespersons’ names.

How can I view every combination of salesperson, p

the database?

Here again you need to click Remove Duplicates o

Remove Duplicates dialog box as shown in Figure 4

Chapter

Filtering

Data and Removing

407

Duplicates

Fig

URE 46-21

Finding unique salesperson, product, and locatio

Figure 46-22 lists the frst record for each co

occurring in the database (see the

Unique Name P

and eighty unique combinations occurred. Note th

because it included Zaret selling lip gloss in th

picked up this combination.

Fig

URE 46-22

List of unique salesperson, product, and locatio

If my data changes, how can I reapply the same fil

Simply right-click any cell in your fltered re

changes to your data are reflected in the flter

408

Microsoft Excel 2010: Data Analysis and Business Modeling

How can I extract all foundation transactions in t

Emilee or Jen was the salesperson and 20?

the averag

The AutoFilter feature (even with the Custom opti

columns. This means, for example, that you cannot f

by Jen during 2005

foundation sales by Zaret d

queries such as this one, you need to use the Ad

you set up a criteria range that specifes the re

described in detail in Chapter 45, “Summarizing Da

After specifying the criteria range, you tell Ex

to the current location or to a different locati

the frst six months of 2005 for which Emilee or J

average per-unit price was more than $3.20, you c

range O4:S6 in Figure 46-23. (See the

Jen + Emil

Fig

URE 46-23

Setting up a criteria range to use with an advance

In cells R5 and R6, I entered

. Recall

thefrom

formula

Chapter

=(L5/K

45 th

formula creates computed criteria that flags each r

than $3.20. Also remember that your heading for a

name. I used Price as the feld heading here. The c

Jen is the salesperson, the date is between 1/1/

foundation, and the per-unit price is more than $

in which Emilee is the salesperson, the date is b

sold is foundation, and the per-unit price is mo

exactly the records you want. Remember that crit

You can now select any cell within the database r

Filter group on the Data tab. Then fll in the dia

Fig

URE 46-24

Advanced Filter dialog box settings.

Chapter

Filtering

Data and Removing

409

Duplicates

With these settings, you are telling Excel to e

G4:M1895) that satisfy the criteria specifed i

range whose upper-left corner is cell O14. The r

O14:U18. Only the four records shown in Figure 4

+ Emilee

worksheet again).

Fig

URE 46-25

Advanced flter results.

If you select Unique Records Only in the Advan

are returned. For example, if Jen had another f

3/19/2005 for one unit for $4.88, only one of th

Problems

Find all transactions in which Hallagan sol

Find all transactions that rank in the top 5 p

Find the top 20 revenue-generating transacti

Find all transactions involving sales of at l

per-unit price was a maximum of $3.10.

Find all foundation transactions during the fr

per-unit price was larger than the average p

entire time period.

Find all transactions in which Zaret or Bet

Find all unique combinations of product and s

Find all of the top 30 sales (by units) occu

mascara.

Find all sales by Jen between August 10 and S

10.

Find all sales of lipstick sold by Colleen f

than the average number of units in a lipsti

11.

Find all unique combinations of name, produ

three months of 2006.

12.

Find all records in which the product cell i

411

Chapter 47

Consolidating Data

Question answered in this chapter:

■

My company sells products in several region

records of the number of units of each prod

February, and March. Is there an easy way t

combines each region’s sales and gives a ta

in the U.S. during each month?

A business analyst often receives worksheets th

monthly product sales) from different affliate

overall proftability, the analyst usually need

a single Microsoft Excel workbook. PivotTables b

be used to accomplish this goal, but the littl

tab on the ribbon) is another way to accomplis

that

changes in the individual worksheets are aut

worksheet.

Answer to This Chapter’s Quest

My company sells products in several

. Each regionske

records of the number of units of each product s

February, and

. Is March

there an easy

master

way workbook”

to create that

“ a

combines each region’s sales and gives a tally o

theS..U during each month?

The fle East.xlsx (shown in Figure 47-1) displ

eastern U.S. during January, February, and Mar

Figure 47-2) displays monthly unit sales of Pr

through March. Your need is to create a consol

product’s total sales by month.

412

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 47-1

East region sales during January–March.

Fig

URE 47-2

West region sales during January–March.

Before you use the Consolidate command, it’s hel

the screen. To do this, open both workbooks, cli

View tab, and select the Tiled option. Your scre

Chapter

Consolidating

413

Data

Fig

URE 47-3

East and West sales arranged on the same screen.

Now open a blank worksheet in a new workbook, a

In the blank worksheet, click Consolidate in th

see the Consolidate dialog box, shown in Figur

Fig

URE 47-4

Consolidate dialog box.

To consolidate the data from the East and West r

enter the ranges you want to consolidate in th

clicking Add after selecting each range. By se

boxes in the Use Labels In area, you ensure th

looking at labels in the top row and left colu

Data option enables changes in the selected ra

worksheet. Select Sum in the Function box beca

414

Microsoft Excel 2010: Data Analysis and Business Modeling

sales of each product by month. Selecting Count, f

transactions for each product during each month; s

sales transaction for each product during each m

flled out as shown in Figure 47-5.

After clicking OK, the new worksheet looks like th

Eastandwestconsolidated.xlsx.) You can see, for e

sold in February, 597 units of Product F were so

Fig

URE 47-5

Completed Consolidate dialog box.

Fig

URE 47-6

Total sales after consolidation.

Now go to cell C2 of East.xlsx and change the Fe

Notice that in the consolidated worksheet, the e

increased by 100 (from 1,317 to 1,417). This cha

Source Data option was selected in the Consolida

the 2 right below the workbook name in the conso

grouped the data to perform the consolidation.) T

Eastandwestconsolidated.xlsx.

Chapter

Consolidating

415

Data

If you frequently download new data to your so

West.xlsx), it’s a good idea to name the range

is automatically included in the consolidation

rows below the current data set. When you popu

picks up the new data when it performs the con

data range a dynamic range (see Chapter 22, “T

Problems

The following problems refer to the data in fl

contains the unit sales, dollar revenues, and p

month.

Create a consolidated worksheet that gives th

each product by region.

Create a consolidated worksheet that gives th

product by region from the standpoint of re

417

Chapter 48

Creating Subtotals

Questions answered in this chapter:

■

Is there an easy way to set up a worksheet t

by region?

■

Can I also obtain a breakdown by salesperso

Joolas is a small company that manufactures ma

name of the salesperson, the location of the tr

the revenue. The managers want answers to ques

chapter.

PivotTables can be used to slice and dice data i

an easier way to summarize a list or a databas

you might want to create a summary of sales re

by product, and a summary of sales revenue by s

in which specifc data is listed, the Subtotal c

on the basis of the values in the column. For e

location, you can calculate total revenue and u

just below the last row for that region. As an

product, you can use the Subtotal command to c

each product and display the totals below the r

section, we’ll look at some specifc examples.

Answers to This Chapter’s Ques

Is there an easy way to set up a worksheet to c

region?

The data for this question is in the fle Makeu

subset of the data as it appears after sorting th

To calculate revenue and units sold by region, p

and then click Subtotal in the Outline group o

the values as shown in Figure 48-2.

By selecting Location from the At Each

created

Change I

at each point in which the value in the Locati

different regions. Selecting Sum from the Use F

and dollars for each different region. By sele

418

Microsoft Excel 2010: Data Analysis and Business Modeling

Subtotal To area, you indicate that subtotals sh

these columns. The Replace Current Subtotals opti

computed subtotals. Because you haven’t created a

this option is selected for this example. If the

Excel inserts a page break after each subtotal. S

causes Excel to place subtotals below the data. I

created above the data used for the computation. C

from the list.

Fig

URE 48-1

After sorting a list by the values in a specifc co

data.

Fig

URE 48-2

Subtotal dialog box.

Chapter

Creating

Subtotals

419

A sample of the subtotals results is shown in Fi

sold in the East region, earning revenue of $5

Fig

URE 48-3

Subtotals for each region.

Notice that in the left corner of the window, b

1, 2, and 3 appear. Clicking the largest numbe

you click the 2 button, you see just the subtot

the 1 button yields the Grand Total, as shown i

number reduces the level of detail shown.

Fig

URE 48-4

When you create subtotals, Excel adds buttons th

both subtotals and details.

Fig

URE 48-5

Displaying the overall total without any detail.

420

Microsoft Excel 2010: Data Analysis and Business Modeling

Can I also obtain a breakdown by salesperson of s

If you want to, you can nest subtotals. In other wo

sales by each salesperson in each region, or you c

each salesperson sold of each product in each re

Todemonstrate the creation of nested subtotals, l

salesperson in each region.

To begin, you must sort your data frst by Locati

breakdown for each salesperson of units sold and r

frst by Name and then by Location, you would get a b

for each salesperson by region. After sorting th

the subtotals by region. Then you click Subtotal a

Figure 48-6.

Fig

URE 48-6

Creating nested subtotals.

You now want a breakdown by Name. Clearing the Re

that you will not replace your regional breakdow

by each salesperson in each region as shown in Fi

Chapter

Creating

Subtotals

421

Fig

URE 48-7

Nested subtotals.

Problems

You can fnd the data for this chapter’s proble

Subtotal command for the following computation

Find the units sold and revenue for each sa

Find the number of sales transactions for e

Find the largest transaction (in terms of r

Find the average dollar amount per transacti

Display a breakdown of units sold and reven

results for each product by region.

423

Chapter 49

Estimating Straight L

Relationships

Questions answered in this chapter:

■

How can I determine the relationship betwee

monthly

operating costs?

■

How accurately does this relationship explai

operating costs?

■

How accurate are my predictions likely to b

■

When estimating a straight line relationshi

slope and intercept of the line that best f

Suppose you manage a plant that manufactures s

tells you how many refrigerators to produce ea

to forecast your monthly operating costs and n

focus of this chapter.

Every business analyst should have the ability t

business variables. In Microsoft Excel, the tr

as in Chapter 50, “Modeling Exponential Growth

often helpful in determining the relationship

lysts try to predict is

. The

called

variable

the

dependent

you use f

called the

independent

. Here are

variable

some examples of busi

want to estimate.

Independent variableDependent variable

Units produced by plant

Monthly

in a cost

monthof operating plan

Dollars spent on advertising

Monthly sales

in a month

Number of employees

Annual travel expenses

Company revenue

Number of employees (headcount

Monthly return on theMonthly

stock market

return on a stock (for e

Square feet in home

Value of home

The frst step in determining how two variables a

using the Scatter Chart option) so that the in

424

Microsoft Excel 2010: Data Analysis and Business Modeling

dependent variable is on the y-axis. With the ch

points are then displayed in blue), click Trendl

Layout tab, and then click More Trendline Option

You’ll see the Format Trendline dialog box, whic

Fig

URE 49-1

Format Trendline options.

If your graph indicates that a straight line is a r

option. If the graph indicates that the dependen

the Exponential (and perhaps Power) option proba

that the dependent variable increases at a decre

decreases at a decreasing rate, the Power option i

In this chapter, I’ll focus on the Linear option

option, and in Chapter 51, I’ll cover the Power o

to Understand Time Series,” I’ll discuss the mov

Products by Using Tie-Ins,” I’ll discuss the pol

value in this discussion, so I won’t address it.

Chapter

Estimating

Straight

425

Line Relationships

Answers to This Chapter’s Ques

How can I determine the relationship between m

operating costs?

The fle Costestimate.xlsx, shown in Figure 49-

the monthly plant operating cost for a 14-month p

monthly operating costs from units produced, w

operating budget and better understand the cos

Fig

URE 49-2

Plant operating data.

Begin by creating an XY chart (or a scatter pl

produced) on the x-axis and the dependent varia

column of data that you want to display on the x

umn of data you want to display on the y-axis. T

range C2:D16 (including the labels in cells C2 a

on the Insert tab, and

Scatter

select

With

theOnly

frstMarkers)

option (a

You’ll see the graph shown in Figure 49-3.

Fig

URE 49-3

Scatter plot of operating cost vs. units produce

426

Microsoft Excel 2010: Data Analysis and Business Modeling

If you want to modify this chart, you can click a

Tools contextual tab. Using the commands on the

■

Change the chart type.

■

Change the source data.

■

Change the style of the chart.

■

Move the chart.

Using the commands on the Chart Tools Layout tab, y

■

Add a chart title.

■

Add axis labels.

■

Add labels to each point that give the x and y c

■

Add gridlines to the chart.

Looking at the scatter plot, it seems reasonable th

exists between units produced and monthly operati

that best fts the points by adding a trendline t

and then click a data point. All the data points a

point. Right-click, and then click Add Trendline

the Linear option, and then select the Display E

Value On Chart check boxes, as shown in Figure 4

Fig

URE 49-4

Selecting trendline options.

Chapter

Estimating

Straight

427

Line Relationships

After clicking Close, you’ll see the results s

the chart and labels for the x-axis and y-axis by s

and then Axis Titles in the Labels group on th

Fig

URE 49-5

Completed trend curve.

If you want to add more decimal points to the v

trendline equation, and after selecting Layout f

Now after selecting Number, you can choose the n

How does Excel determine the best ftting line?

all lines that could be drawn) the sum of the s

line. The vertical distance from

, or

each

residual

. The

point

line

to th

created by Excel is called

. You minimize

the

least-squares

the

errors

sum

- rath

er than the sum of the errors because

negative

in simpl

errors can cancel each other out. For example, a p

100 units below the line cancel each other if y

the fact that your predictions for each point a

ftting line.

Thus, Excel calculates that the best ftting str

from monthly units produced as follows:

(Monthly operating cost)=37,894.0956+64.2687(Units produced)

By copying the*

C3+37894.

formula

0956

64.2687

from cell E3 to the ce

compute the predicted cost for each observed d

produced, the predicted cost is $123,118. (See Fi

You should not use a least-squares line to pre

lie outside the range for which you have data. T

428

Microsoft Excel 2010: Data Analysis and Business Modeling

to predict monthly plant operating costs during m

approximately 450 and 1,300 units.

The intercept of this line is $37,894.10,So,

which c

even if the plant does not produce any refrigera

that the plant will still incur costs of $37,894

each extra refrigerator produced increases month

producing a refrigerator is estimated to be $64.

In cells F3:F16, I computed the errors (or resid

each data point as the amount by which the point v

month, error equals the observed cost minus the p

the formula

D3-E3

computes the error for each da

is above the least-squares line, and a negative e

least-squares line. In cell F1, I computed the s

for any least-squares line, the sum of the error

rounded the equation to four decimal points.) Th

least-squares line has the intuitively satisfyin

How accurately does this relationship explain th

cost?

Clearly, each month both the operating

question

cost and th

is, What percentage of the monthly variation in

variation in units produced? The answer to this q

value (0.69 shown i

Figure 49-5). You can state that the linear rela

monthly operating costs. This implies that 31 pe

costs is explained by other factors. Using

multi

you can try to determine other factors that influ

People always ask, what is a good R

value? There is really no defni

question. With one independent variable, of cour

value indicates a b

the data than a smaller R

value. A better measure of the accur

standard error

which

the

I’ll

regression

describe in the next s

How accurate are my predictions likely to be?

When you ft a line to points, you obtain

measuresstand

the “spread” of the points around the least-squa

with a least-squares line can be computed with th

function

yrange

is,

xrange

STEYX(

), where

yrange

contains the value

variable, and

xrange

contains the values of the i

the standard error of the cost estimate line in th

STEYX(D3:D16,C3:C16)

. The result is shown in Figure 49-6.

Chapter

Estimating

Straight

429

Line Relationships

Approximately 68 percent of the points should b

(SER) of the least-squares line, and about 95 p

of the least-squares line. These measures are r

thumb that I described in Chapter 42, “Summari

In this example, the absolute value of around 6

or smaller, and the absolute value of around 9

2*13,772

) or smaller. Looking at the errors in col

71 percent, of the points are within one SER o

the points are within two standard SER of the l

two SER from the least-squares

. Looking

line

foriscauses

calledo a

often help you improve the operation of -your b

tual operating costs are $30,000 higher than a

side. If you could ascertain the cause of this hi

you would clearly improve plant effciency. Simi

are $30,000 less than expected. If you could a

ensure it occurred more often, you would impro

Fig

URE 49-6

Computation of slope, intercept, RSQ, and standa

When estimating a straight line relationship, w

and intercept of the line that best fits the da

The Excel

yrange

SLOPE(

xrange

) and INTERCEPT(

yrange

xrange

) functions return th

and intercept, respectively, of the least-squa

SLOPE(D3:D16,C3:C16)

(see Figure 49-6) returns th

Entering in cell I2 the formula

INTERCEPT(D3:D

of the least-squares

yrange

line.

xrange

)By

function

the way,returns

the RSQth

value

associated with a least-squares line. So, ente

returns the R

value of 0.6882 for the least-squares l

Problems

The fle Delldata.xlsx contains monthly returns f

Dell stock. The

beta

of a stock is defned as th

the monthly return for a stock from the monthl

Estimate the beta of Dell.

Interpret the meaning of Dell’s beta.

430

Microsoft Excel 2010: Data Analysis and Business Modeling

If you believe a recession is coming, would y

beta stock?

During a month in which the market goes up 5 p

Dell’s stock price will increase between whic

The fle Housedata.xlsx gives the square footage a

Bellevue, Washington.

You are going to build a 500-square-foot addi

think your home value will increase as a resu

What percentage of the variation in home valu

A 3,000-square-foot house is selling for $500

real estate values in Bellevue? What might ca

We know that 32 degrees Fahrenheit is equival

degrees Fahrenheit is equivalent to 100

degre

mine the relationship between Fahrenheit and C

your initial chart, before clicking Finish, y

not rows, because with only two data points, E

different rows.

The fle Betadata.xlsx contains the monthly re

as well as the monthly returns on Cinergy, De

Estimate the beta of each stock.

10.

The fle Electiondata.xlsx contains, for sever

Republicans gained from voting machines

(coun

age Republicans gained from absentee ballots (

that during an election, Republicans obtained 4

and 62 percent of the absentee ballot votes. T

What do you think?

431

Chapter 50

Modeling Exponentia

Question answered in this chapter:

■

How can I model the growth of a company’s r

If you want to value a company, it’s important t

Although the future might not be like the past

corporation by studying the company’s revenue

lysts like to ft a trend curve to recent reven

on the x-axis (for example, the frst year of d

and so on), and on the y-axis, you plot the co

Usually, the relationship between time and rev

straight line always has the same slope, which i

(in this case, the year) is increased by 1, th

increases by the same amount. For most compani

percentage each year. If this is the case,

as r

enue also increases. After all, revenue growth o

grows by $100,000. Revenue growth of 10 percen

by $10 million. This analysis implies that a t

more steeply and have an increasing slope. The

as the independent variable increases by 1, th

percentage. This relationship is exactly what y

The equation for the exponential function is

. Here,

is the value o

variable (in this example, the year), whereas

case, annual revenue). The value

(approximat

you select Exponential from Excel’s trendline o

that best ft the data. Let’s look at an exampl

Answers to This Chapter’s Ques

How can I model the growth of a company’s reve

The fle Ciscoexpo.xlsx, shown in Figure 50-1, c

1990 through 1999. All revenues are in million

revenues were $103.47 million.

432

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 50-1

Cisco’s annual revenues for the years 1990 through 1

To ft an exponential curve to this data, begin by s

the Insert tab, in the Charts group, click Scatt

Only Markers) creates the chart shown in Figure 50

Fig

URE 50-2

Scatter plot for the Cisco trend curve.

Fitting a straight line to this data would be ri

increasing, as in this example, an exponential g

data.

To obtain the exponential curve that best fts thi

turn blue), and then click Add Trendline. In the

Exponential option in the Trendline Options area

Chart and Display R-Squared Value On Chart check b

trend curve shown in Figure 50-3.

The estimate of Cisco’s revenue in year

(remem

from the following formula

Estimated Revenue=58.552664e

569367x

Chapter

Modeling

Exponential

433

Growth

I computed estimated revenue in the cell range C

formula

=58.552664

EXP(0.569367

A4)

. For example, the estimate o

(year 10) is $17.389 billion.

Fig

URE 50-3

Exponential trend curve for Cisco revenues.

Notice that most of the data points are -very c

tern indicates that exponential growth does a g

during the 1990s. The fact that the R

value (0.98) is very close to 1 i

visual evidence of a good ft.

Remember that whenever

increases by 1, the e

by the same percentage. You can verify this

mated revenue to the previous year’s estimated r

D5 to D6:D13

=C5/C4

the

. You’ll

formulafnd that the estimate o

percent per year, which is the best estimate o

through 1999.

Of course, to use this estimated annual revenu

to ask yourself whether it’s likely that this g

that exponential growth cannot continue foreve

trend curve to forecast revenues for 2005 (yea

be $530 billion. If this estimate were realize

enues of the world’s largest company (Walmart)

that during its early years, the revenue growth f

growth. After a while, the growth rate slows d

this fact during the late 1990s, the Internet s

during 1999, Cisco’s actual revenue fell well s

This fact may well have indicated the start of th

late 2000.

434

Microsoft Excel 2010: Data Analysis and Business Modeling

By the way, why must you

? use

If you

x=1

used

,instead

Excel

x=1990

would

x=19

to juggle numbers around the size of e

1990

. A number this large causes E

diffculty.

Problems

The fle Exponentialdata.xlsx contains annual sal

Use this data to work through the frst fve probl

For each company, ft an exponential trend cur

For which company does exponential growth hav

growth?

For each company, estimate the annual percent

For each company, use your trend curve to pre

The fle Impalas.xlxs contains the price of 20

2010. From this data, what can you conclude a

grows older?

435

Chapter 51

The Power Curve

Questions answered in this chapter:

■

As my company produces more of a product, i

effciently. Can I model the relationship be

to produce a unit?

A power curve is calculated with the equation

. In the equation,

Using a trend curve, you can determine the val

ft a scatter plot diagram. In most situations,

slope of the power curve

, as

depends

follows:

on the value o

■

For ,

b>1

increases as

increases, and the sl

increases.

■

For

0<b<1

increases as

increases, and the s

increases.

■

For ,

b=1

the power curve is a straight line.

■

For ,

b<0

decreases as

increases, and the pow

Here are examples of different relationships th

examples are contained in the fle Powerexample

If you are trying to predict total production c

fnd a relationship similar to that shown

in Fi

tioned previously, the

withcost

thisofvalue

production

incre

units produced. The slope becomes steeper, whi

more to produce. This relationship might occur b

overtime labor, which costs more than regular l

Fig

URE 51-1

Predicting cost as a function of the number of u

436

Microsoft Excel 2010: Data Analysis and Business Modeling

If you are trying to predict sales as a function o

curve similar to that shown in Figure 51-2.

Fig

URE 51-2

Plotting sales as a function of advertising.

Here,

equals 0.5, which is between 0 and 1. Wh

with increased advertising but at a decreasing r

model the idea of diminishing return—that each a

provide less beneft.

If you are trying to predict the time needed to p

the number of units produced to date, you often f

Figure 51-3.

Here you fnd that

equals –0.1. Because

is le

unit decreases, but the rate

learning”—slows

of decrease—that

down.

is T

relationship means that during the early stages o

time occur. As you make more of a product, howev

rate. The relationship between cumulative units p

last unit is called the

learning

experience

Fig

URE 51-3

Plotting the time needed to produce a unit based on c

Chapter

The

51Power Curve

437

A power curve has the following properties:

■

Property

increases by 1 percent,

increas

■

Property

Whenever

doubles,

increases by the s

Suppose that demand for a product as a functio

–2

Property 1 then implies that a 1 percent incre

of price) by 2 percent. In this case, the expo

elasticity

. I will discuss elasticity further in Cha

background, let’s take a look

at how to ft a p

Answer to This Chapter’s Quest

As my company produces more of a product, it l

efficiently

. Can I model the relationship between un

produce a unit?

The fle Fax.xlsx contains data about the numbe

(in 1982 dollars) of producing the “last” fax m

example, 70,000 fax machines were produced, an

was $3,416. The data is shown in Figure 51-4.

Fig

URE 51-4

Data used to plot the learning curve for produci

Because a learning curve tries to predict eith

from data about cumulative production, -I’ve ca

ber of fax machines produced by the end of eac

the number of fax machines produced in 1982. B

SUM($B$4:B4)

, I compute cumulative fax machine produ

You can now create a scatter plot that shows c

unit cost on the y-axis. After creating the ch

points will be displayed in blue), then right-

Trendline dialog box, select the Power option a

438

Microsoft Excel 2010: Data Analysis and Business Modeling

Chart and the Display R-Squared Value On Chart c

obtain the chart shown in Figure 51-5. The curve d

fts the data.

Fig

URE 51-5

Learning curve for producing fax machines.

The power curve predicts the cost of producing a f

Cost of producing fax machine=65,259(cumulative units produced)

-.2533

Notice that most data points are near the ftted p

value is near

indicating that the power curve fts the data wel

By copying from cell E4*

C4^–0.2533

to E5:E10

, you the

compute

formula

the

predicted cost for the last fax machine produced d

which is located over the 6 key, is used to rais

If you estimated that 1,000,000 fax machines wer

total 1989 production (2,744,000) in cell C11, y

to predict that the last fax machine produced in 1

Remember that Property 2 of the power curve stat

the same percentage. By entering twice cumulativ

your forecast formula in E10 to cell E12, you’ll fn

reduces the predicted cost to 83.8 percent of it

reason, the current learning curve is known as a

double units produced, the labor required to mak

If a curve gets steeper, the exponential curve mi

does. A natural question is which curve fts the d

be answered simply by eyeballing the curves

and c

ter ft. More precisely, you could compute the Su

(obtained by adding up for each data point the sq

value) and choose the curve with the smaller SSE

Chapter

The

51Power Curve

439

The learning curve was discovered in 1936 at W

Ohio, when it was found that whenever the cumu

doubled, the time required to make each airpla

Wikipedia

gives the following learning curve e

■

Aerospace: 85 percent

■

Shipbuilding: 80–85 percent

■

Complex machine tools for new models: 75–85 p

■

Repetitive electronics manufacturing: 90–95 p

■

Repetitive machining or punch-press operati

■

Repetitive electrical operations: 75–85 per

■

Repetitive welding operations: 90 percent

■

Raw materials: 93–96 percent

■

Purchased parts: 85–88 percent

Problems

Use the fax machine data to model the relati

produced and total production cost.

Use the fax machine data to model the relati

produced and average production cost per ma

A marketing director estimates that total s

as shown in the following table. Estimate th

and predict demand for a $46 price. A 1 per

by what percentage?

Price

Demand

$30.00

300

$40.00

200

$50.00

110

$60.00

440

Microsoft Excel 2010: Data Analysis and Business Modeling

The brand manager for a new drug believes tha

function of the number of sales calls on doct

Estimate sales of the drug if 80,000 sales ca

Sales calls

Units sold

50,000

25,000

100,000

52,000

150,000

68,000

200,000

77,000

The time needed to produce each of the frst te

Unit

Hours

1,000

800

730

630

600

560

500

510

Estimate the total number of hours needed to p

441

Chapter 52

Using Correlations t

Relationships

Questions answered in this chapter:

■

How are monthly stock returns for Microsoft

Trend curves are a great help in understanding h

however, you need to understand how more than t

correlation between any pair of variables can p

move up and down in value together.

The correlation (usually

) betweendenoted

two variables

by)

(call

unit th

measure of the strength of the

. The

linear

correlation b

any two variables is always between –1 -and +1. A

pute the correlation between two variables isn

correlation between the variables is.

A correlation near +1 means that

and

have a s

is, when

is larger than average,

tends to b

than average,

also tends to be smaller than a

data, there will be a straight line with a pos

points. As an example, for

x=units

the data

produced

shown in

andFi

production

and

cost)

have a correlation of +0.90. (

Figures 52-1 through 52-3.)

Fig

URE 52-1

A correlation near +1, indicating that two varia

442

Microsoft Excel 2010: Data Analysis and Business Modeling

On the other

correlation

hand, a near –1 means that there i

relationship .between

That is,

and

when

y x

is larger than av

than average, and when

is smaller than average

When a straight line is applied to the data, the l

jobftting

the points. As an example, for the dat

correlation of –0.90.

Fig

URE 52-2

A correlation near –1, indicating that two variable

A correlation near 0 means that

and

have a w

whether

is larger or smaller than its mean tel

or smaller than its mean. Figure 52-3

)

shows

a gr

years of sales

). Years

experience

of experience

(

and unit sale

In this data set, the average experience is 10 y

than 10 years of sales experience, his or her sa

that when a person has fewer than 10 years of sa

Although experience and sales have little or no l

relationship (see the ftted curve) between years o

not measure the strength of nonlinear relationshi

Fig

URE 52-3

A correlation of 0, indicating a weak linear relati

Chapter

Using

Correlations to Summarize

443

Relationships

Answer to This Chapter’s Quest

How are monthly stock returns for Microsoft, G

The fle Stockcorrel.xlsx (see Figure 52-4) show

Intel, GM, and Cisco during the 1990s. You can u

movements in these stocks are related.

To fnd the correlations between each pair of s

on the Data tab, and then select the Correlati

(as described in Chapters 41 and 42) before yo

the Correlation dialog box as shown in Figure 5

Fig

URE 52-4

Monthly stock returns during the 1990s.

Fig

URE 52-5

Correlation dialog box.

444

Microsoft Excel 2010: Data Analysis and Business Modeling

The easiest way to enter the input range is to s

then press Ctrl+Shift+Right Arrow, followed by C

First Row option if the frst row of the input ra

upper-left cell of the output range. After click

Fig

URE 52-6

Stock return correlations.

The correlation between Cisco and Microsoft

is 0

tion between GM and Microsoft is 0.069. The anal

Microsoft are most closely tied together. Becaus

stocks is around 0.5, these stocks exhibit a mod

if one stock does better than average, it is lik

do better than average. Because Cisco, Intel, an

technology spending, their fairly strong correla

monthly returns on Microsoft and GM are virtuall

that when Microsoft stock does better than avera

will do better or worse than average. Again, thi

really a high-tech company and is more susceptib

Filling In the Correlation Matrix

As you can see in this example, Excel left some e

example, the correlation between Microsoft

and G

tween GE and Microsoft) is omitted. If you want t

click the matrix, and then click Copy. Right-cli

click Paste Special. In the Paste Special dialog b

its side. Now right-click the flipped data, and c

matrix, and click Paste Special again. In the Pa

then click OK. The transposed data is copied to th

not copy the blank cells from the transposed dat

Figure 52-7.

Chapter

Using

Correlations to Summarize

445

Relationships

Fig

URE 52-7

The complete correlation matrix.

Using the CORREL Function

As an alternative to using the Correlation opti

CORREL function. For example, entering in cell I

confrms that the correlation between monthly r

(shown in column E) is 0.159.

Relationship Between Correlation a

In Chapter 49, “Estimating Straight Line Relati

value for unit

produced and monthly operating cost of 0.688. H

between units produced and monthly operating c

data is simply

value

for the trendline, where you choose the sign f

of the slope of the trendline. Thus the correl

operating cost for the data in Chapter 49 is

.688 = + .829

Correlation and Regression Towar

You have probablyregression

heard the toward

phrase the

“ statement

mean.” E

means that the predicted value of a dependent v

average value than the independent variable. M

446

Microsoft Excel 2010: Data Analysis and Business Modeling

dependent variable

from

. If

independent

standard

variabl

devia

average, then your prediction for

will be

r=correlation

between

Because

and

between -1 and +1, t

standard deviations away

. This

from

is the mean

real than

defnitio

toward the mean.” See Problem 5 for an -interesti

sion toward the mean.

Problems

The data for the following problems is in fle Ch

The

Problem 1

worksheet contains the number o

outdoor lot and in the parking garage near th

Business. Find and interpret the correlation b

outdoor lot and in the parking garage.

The

Problem 2

worksheet contains daily sales v

printer cartridges, and school supplies. Find a

these quantities.

The

Problem 3

worksheet contains annual retur

and interpret the correlations between the an

investments.

Here are two more problems:

The fle Dow.xlsx contains the monthly returns b

Dow Jones Index. Find the correlations betwee

conditional formatting to highlight the three s

(Of course, you should not highlight a stock a

NFL teams play 16 games during the regular se

of the number of games won by all teams

is 2, a

ber of games a team wins in two consecutive s

during a season, what is your best prediction f

next season?

447

Chapter 53

Introduction to Mul

Questions answered in this chapter:

■

Our factory manufactures three products. How c

factory based on the number of units produc

■

How accurate are my forecasts for predictin

■

I know how to use the Data Analysis command t

a way to run the regression without using thi

results in the same worksheet as the data?

Answers to This Chapter’s Ques

Our factory manufactures

. How can

three

I predict

productsthe cos

factory based on the number of units produced?

In Chapters 49 through 51, I described how to u

to predict one, variable

or the

dependent

(called

variable) fro

or the

independent

variable). However, you oft

variable (called the

1,2,

independent

…

)

predict

variables

the value

variable. In these cases, you can use either th

Analysis feature or the LINEST function to esti

Multiple regression assumes that

1,2,

the

… has

relations

the

following form:

Y=Constant+B1X1+B2X2+...BnXn

Excel calculates ,the

values

… to make

Constant

the prediction

equation as accurate (in the sense of minimizi

following example illustrates how multiple reg

The

Data

worksheet in the fle Mrcostest.xlsx (

plant over 19 months, as well as the number of u

produced during each month.

448

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 53-1

Data for predicting monthly operating costs.

You would like to fnd the best forecast for month

form (which I’ll refer to as Form 1):

Monthly operating cost=Constant+B1

(Units A produced)+B2

(Units B produced)

+B3

(Units C produced)

The Excel Data Analysis feature can fnd the equa

Click Data Analysis in the Analysis group on the Da

the Regression dialog box as shown in Figure 53-

Not

f you haven’t previously installed the Analysis T

and then click Add-Ins. With Excel Add-ins selected i

Analysis ToolPak box, and then click OK.

Fig

URE 53-2

Regression dialog box.

Chapter

Introduction

to Multiple

449

Regression

■

Input Y Range (B3:B22 in this example) contai

(including the Cost label) that you want to p

■

Input X Range (C3:E22) contains the data or i

A Made, B Made, and C Made) that you want t

of 15 independent variables, which must be i

■

Because both the Input X and Input Y ranges i

box.

■

I chose to place the output .

in a new worksh

■

Selecting the Residuals check box causes Ex

prediction from Form 1 and the residual, whi

predicted cost.

After clicking OK in the Regression dialog box

and 53-4. (See the

Regression

worksheet.)

Fig

URE 53-3

Original multiple regression output.

Fig

URE 53-4

Original multiple regression residual output.

450

Microsoft Excel 2010: Data Analysis and Business Modeling

What is the best prediction equation? You’ll fnd i

summary output) that the best equation of Form 1 t

is the following:

Predicted monthly cost=35,102.90+2.07(AMade)+4.18(BMade)+4.79(CMade)

A natural question is, Which of our independent v

cost? After all, if you choose the number of gam

one-month period as an independent variable, you w

have little effect on predicting monthly operati

independent variable has a

p-value

between 0 and 1

p-value (see column E) of less than or equal to 0

the dependent variable. Thus, the smaller the p-

independent variable. Our three independent varia

0.025 (for B Made), and 0.017 (for C Made). Thes

■

When you use B Made and C Made to predict mon

percent chance (1–0.23) that A Made adds pred

■

When you use A Made and C Made to predict mon

percent chance (1–0.025) that B Made adds pre

■

When you use A Made and B Made to predict mon

percent chance (1–0.017) that C Made adds pre

Our p-values indicate that A Made does not add m

C Made, which means that if you know B -

Made and C M

erating cost about as well as you can if you inc

Therefore, you can opt to delete A Made as an in

and C Made for your prediction. I copied the dat

deleted the A Made column (column C). I then adju

In the worksheet

, youtitled

can see

NoA

the regression output s

Figure 53-6.

Fig

URE 53-5

Multiple regression output with A Made data remove

Chapter

Introduction

to Multiple

451

Regression

Fig

URE 53-6

Residual output calculated when A Made data is r

You can see that A Made and B Made each have v

respectively). These values indicate that both th

predictive power. Using the new coeffcients in c

operating cost using the following equation:

Predicted monthly operating cost=35,475.3+5.32(BMade)+5.42(CMade)

How accurate are my forecasts for predicting m

In the regression output in cell B5 of the

NoA

equals 0.61

value such as this one means that together, B M

of the variation in monthly operating costs. N

included A Made as an independent variable, R2 e

of A Made as an independent variable explains o

operating costs. Having such a minor differenc

A Made as an independent variable.

In the regression output in cell B7 in the

NoA

regression with B Made and C Made as independe

about 68 percent of your multiple regression f

error, and 95 percent to be accurate within tw

fromactual

the

value by more than two standard err

your

forecasted operating cost

2*1274

is ),

in you

error

consider

by mor th

observation to be an outlier.

In the Residual portion of the output, shown e

observation the predicted cost and the residua

predicted cost. For the frst observation, for e

residual of $1,057.95 indicates that the predi

452

Microsoft Excel 2010: Data Analysis and Business Modeling

I know how to use the Data Analysis. command

Is thereto

a r

to run the regression without using this command a

the same worksheet as the data?

The Excel LINEST function can be used to insert th

into a workbook. To use the LINEST function when th

by selecting a blank cell range consisting of fv

LINEST to deposit the results. In the

A Removed

The syntax of the LINEST

(KnownYs,KnownXs,True,True).

function is LINEST

argument is changed to False, Excel estimates th

Changing the fourth argument to False causes the L

computations and return only the multiple regres

With the upper-left cell of the target range sel

of the size you want (in this case, the cell ran

=LINEST(B4:B22,C4:D22,True,True)

. At this point,

do not

press Ent

function (see Chapter 83, “Array Formulas and Fu

functions), so you must

frst

hold down Ctrl+Shif

work correctly. After using this key combination

(See the

A Removed

worksheet.)

Fig

URE 53-7

Using the LINEST function to calculate a multiple r

In row 5, you fnd the prediction equation (coeff

intercept) of

Predicted monthly cost=35,475.3+5.

Row 6 contain

standard errors for each coeffcient estimate, bu

the

value

of 0.61, and cell G7 contains the regr

9 contain information (F statistic, degrees of f

squares residual) that is less important.

Not

oblems that you can work with to learn more abo

the end of Chapter 55.

453

Chapter 54

Incorporating Quali

into Multiple Regres

Questions answered in this chapter:

■

How can I predict quarterly U.S. auto sales

■

How can I predict U.S. presidential electio

■

Is there an Excel function I can use to eas

equation?

In the frst example of multiple regression in C

Regression,” I forecasted the monthly cost of p

of each product manufactured at the plant. Bec

a product produced at a plant, you can refer t

and Product C as

quantitative

. In many

independent

situations,

varia

dent variables can’t be easily quantifed. In thi

qualitative factors such as seasonality, gende

multiple regression

analysis

Answers to This Chapter’s Ques

How can I predict

S.. auto

quarterly

sales? U

Suppose you want to predict quarterly U.S. aut

the year impacts auto sales. We’ll use the dat

shown in Figure 54-1. Sales are listed in thou

454

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 54-1

Auto sales data.

You might be tempted to defne an independent var

quarter, 2 during the second quarter, and so on.

fourth quarter to have four times the effect of th

quarter of the year is a.

qualitative

To model a qualitative

independent

variable, you create an independent variable cal

qualitative variable’s possible values. -(It is a

ple, I chose to omit Quarter 4.) The

qualitative

dummy varia

variable occurs. Thus, we’ll have a dummy variab

with the following properties:

■

Quarter 1 dummy variable equals 1 if the quar

■

Quarter 2 dummy variable equals 1 if the quar

■

Quarter 3 dummy variable equals 1 if the quar

A Quarter 4 observation will be identifed by the f

through Quarter 3 equal 0. You can see why you d

In fact, if you include a dummy variable- for Qua

gression, Microsoft Excel returns an error messa

relationship exists between any set of independe

ematical equivalent of dividing by 0 (an impossi

In this example, if you include a Quarter 4 dumm

following exact linear relationship:

(Quarter 1 Dummy)+(Quarter 2 Dummy)+(Quarter 3 Dummy)+(Quarter 4 Dummy)=1

Chapter

Incorporating

Qualitative Factors

455

into Multiple Regression

Not

n exact linear relationship

0,1,occurs

… such

if that

therefor

each data

0 +

point

c c

+ N…

= 0.1Here,

through

are

the values of t

independent variables.

To create the dummy variable for Quarter 1, I c

IF(B12=1,1,0)

. This formula places a 1 in column G wh

a 0 in column G whenever the quarter is not th

dummy variables for Quarter 2 (in H12:H42) and Q

of the formulas in Figure 54-2.

Fig

URE 54-2

Using dummy variables to track the quarter in wh

In addition to seasonality, we’d like to use m

product (GNP, in billions of 1986 dollars), in

car sales. Suppose, for example, that you are tr

of 1979. Because values for GNP, interest rate

beginning of the second quarter in 1979, you c

rate, and unemployment rate to predict Quarter 2 1

ues for GNP, interest rate, and unemployment r

By copying from J12 to, J12:L42

you create

the the

formula

lagged

=D1

frst of our macroeconomic independent variable

GNP, unemployment rate, and interest rate for th

You can now run the multiple regression by cli

selecting Regression in the Data Analysis dial

G11:L42 as the Input X Range, select the label

456

Microsoft Excel 2010: Data Analysis and Business Modeling

the Residuals check box. After clicking OK, you o

Regression

worksheet and in Figures 54-3 through 5

Fig

URE 54-3

Summary output and ANOVA table for auto sales data

In Figure 54-4, you can

equation

see that

1) used

the equation

to predict

( q

sales is as follows:

Predicted quarterly sales=3154.7+156.833Q1+379.784Q2+203.03 6Q3+.174(LAGGNP

–93.83(LAGUNEMP)–73.91(LAGINT)

Also in Figure 54-4, you see that each independe

to 0.15. You can conclude that all independent v

auto sales. You interpret all coeffcients in a r

that each coeffcient gives the effect of the ind

effects of all other variables in the regression

Fig

URE 54-4

Coeffcient information for auto sales regression.

Here’s an interpretation of each coeffcient:

■

A $1 billion increase in last quarter’s GNP i

■

An increase of 1 percent in last quarter’s un

sales by 93,832.

■

An increase of 1 percent in last quarter’s in

by 73,917.

Chapter

Incorporating

Qualitative Factors

457

into Multiple Regression

To interpret the coeffcients of the dummy varia

effect of seasonality relative to the value le

■

In Quarter 1, car sales exceed Quarter 4 ca

■

In Quarter 2, car sales exceed Quarter 4 ca

■

In Quarter 3, car sales exceed Quarter 4 ca

You fnd that car sales are highest during the s

and summer are coming) and lowest during the thi

why buy a new car when winter salting will rui

From the Summary output shown in Figure 54-3, y

■

The variation in the independent variables (

explains 78 percent of the variation in the d

■

The standard error of regression is 190,524 c

of your forecasts to be accurate within 190

forecasts to be accurate

2*190,524

within 381,048 car

■

There are 31 observations used to ft the re

The only quantity of interest in the ANOVA tab

(0.00000068). This measure implies that there a

together, all of the independent variables are u

be quite sure that the independent variables a

Figure 54-5 shows, for each observation, the p

the second quarter of 1979 (observation 1), pr

thousand and the residual

2910–2728.6

).isNote

181,400

that cars

no residu

(

381,000 in absolute value, so you have no outl

Fig

URE 54-5

Residuals for the auto sales data.

458

Microsoft Excel 2010: Data Analysis and Business Modeling

How can I S..predict

presidential

elections?

When asked which factors drive presidential elec

said, “It’s the economy, stupid.” Yale economist R

in thinking that the state of the economy

has a l

tial elections. Fair’s dependent variable (see th

shown in Figure 54-6) for each election (1880 th

party vote (ignoring votes received by third par

party. He tried to predict the incumbent party’s p

independent variables such as:

■

Party in power. In our data, I use 1 to denot

and 0 to denote when the Democratic party was i

■

Percentage growth in GNP during the frst nine m

■

Absolute value of the inflation rate during th

You use the absolute value because either a p

■

Number of quarters during the last four years i

Strong economic growth is defned as growth at a

■

Length of time an incumbent party has been in o

in offce, 1 for two terms, 1.25 for three ter

terms or more. This defnition implies that ea

less influence on the election results than th

■

Elections during wartime. The elections in 19

and 1948 (World War II was still underway in 1

(Elections held during the Vietnam War were n

During wartime years, the variables related t

were deemed irrelevant and were set to 0.

■

The current president running for re-election

1; otherwise, this variable is set to- 0. In 1

dent running for re-election because he was n

vice-president.

Not

The data comes from Roy Fair’s excellent book

Pre

Things

(Stanford University Press, 2002).

Chapter

Incorporating

Qualitative Factors

459

into Multiple Regression

Fig

URE 54-6

Presidential election data.

I’ve attempted to use the data from the electi

multiple regression equation that can be used t

saved the 2008

validation

election point.”

as a “

When ftting a r

a good idea to hold back some of your data for u

Holding back data allows you to determine wheth

job of forecasting data it hasn’t seen. Any fo

seen should not be used to predict the future.

To run the regression, click Data Analysis in th

select the Regression tool in the Data Analysi

Range and C16:I48 as the Input X Range. I also s

labels). I placed the output in the

Results

Fig

URE 54-7

Regression output for predicting presidential el

460

Microsoft Excel 2010: Data Analysis and Business Modeling

In Figure 54-7, you can see that War? and Presid

0.15. Therefore, you should rerun the regression w

The results of this regression. are

In this

shownworkshee

in work

remaining independent variables have p-values le

fnal prediction equation. From the coeffcients s

that the best equation to predict

equation

elections

2):

is g

Predicted presidential election percentage=51.69+.53GROWTH-.80ABSINF+.58GOODQUARTERS

-3.48DURATION+3.18REP

Fig

URE 54-8

Final presidential election equation.

The coeffcients of the independent variables can b

for all other independent variables used in equa

■

A 1 percent increase in the annual GNP growth r

0.53 percent to the incumbent party.

■

A 1 percent deviation from the ideal (0 perce

0.80 percent of the vote.

■

Every good quarter of growth during an incumb

someday soon) vote by 0.58 percent.

■

Relative to having one term in offce, the sec

incumbent’s vote by 3.48 percent, and each la

by 0.25*(3.48 percent)=0.87 percent.

■

A Republican has a 3.18 percent edge over a D

Sixty-three percent of the variation in the perc

presidential election is explained by our indepe

percent indicates that about 95 percent of our f

Chapter

Incorporating

Qualitative Factors

461

into Multiple Regression

From the residuals, shown in Figure 54-9, you c

1892 and 1904 elections. In 1892 the incumbent c

much worse than expected, while in 1904 the in

performed much better than expected.

Fig

URE 54-9

Residuals from the presidential election equatio

Is there an Excel function I can use to easily m

equation?

It’s tedious to make forecasts using an equati

function makes it easy to generate forecasts f

to run a regression with the Data Analysis com

To illustrate the use of the TREND function, I

1880 through 2008 elections using data from on

by selecting the cell range (in this example, H

you want your forecasts to go. With the pointe

the formula

TREND(B17:B48,C17:G48,C17:G49)

. Next, press Ctrl+Shift+E

(see Figure 54-10) the forecast for each electi

forecast for the 2008 election (using data onl

receive 50.9 percent of the vote. This is fair

462

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 54-10

Residuals from presidential election equation.

The TREND function is an.example

I’ll provide

of an

array

fun

discussion of array functions in Chapter 83, “Ar

some background about array functions:

■

Before entering an array function, you must a

want the results of the array function to be l

■

Instead of pressing Enter to perform the calc

complete the entry of an array function.

■

After entering an array function, you’ll see a c

select a cell in which the array function’s r

the results in the cell were computed with an a

■

You can’t modify data in any part of a range c

Not

oblems that you can work with to learn more abo

the end of Chapter 55.

463

Chapter 55

Modeling Nonlineari

Interactions

Questions answered in this chapter:

■

What does it mean when we say that an indep

a dependent variable?

■

What does it mean when we say that the effe

dependent variable interact?

■

How can I test for the presence of nonlinea

Answers to This Chapter’s Ques

What does it mean when we say that an independ

dependent variable?

An independent variable often influences a depe

relationship. For example, if you try to predi

Sales=500–10

Price,

price influences sales linearly. T

in price will (at any price level) reduce sale

price were governed by an *

Price–.40

equation

Price

such as

Sal

, price and s

would be related nonlinearly. As shown in Figu

decreases in demand (see the

Nonlinearity

work

the change in the dependent variable caused by a u

is not constant, there is a nonlinear relation

variables.

Fig

URE 55-1

Nonlinear relationship between demand and price.

464

Microsoft Excel 2010: Data Analysis and Business Modeling

What does it mean when we say that the effects o

dependent variable interact?

If the effect of one independent variable on a d

of another independent variable, you can say tha

interaction

. For example, suppose you try to predict s

on advertising. If the effect of changing the le

price is small and small when the price is high, p

effect of changing the level of advertising doll

price do not exhibit any interaction.

How can I test for the presence of nonlinearity a

To see whether an independent variable has a non

simply add an independent variable to the

- regres

dent variable. If the squared term has a low p-v

nonlinear relationship.

To check whether two independent variables exhib

the regression that equals the product of the in

p-value (less than 0.15), you have evidence of i

To illustrate, let’s try to determine how gender a

manufacturing company. For each employee, you ar

fnd the information in the

Data

worksheet in the fl

■

Annual salary (in thousands of dollars)

■

Years of experience working in the manufactur

■

Gender (1=female, 0=male)

We’ll use this data to predict salary (the depen

and gender. To test whether years of experience h

term Experience Squared by copying

. To

from

test

D2 wheth

to D3

experience and gender have a signifcant interacti

by copying from E2 to

.E3:E98

I ran the

a regression

formula

with a

A1:A98 and an Input X Range of B1:E98. After sel

dialog box and clicking OK, I got the results sh

Chapter

Modeling

Nonlinearities

465

and Interactions

Fig

URE 55-2

Data for predicting salary based on gender and e

Fig

URE 55-3

Regression results that test for nonlinearity an

You can see that gender is insignifcant (its p

independent variables are signifcant (meaning th

0.15). You can delete the insignifcant gender v

I copied the data into a new worksheet called

click Move Or Copy, and then select the Create A C

column, you obtain the regression results incl

shown in Figure 55-4.

466

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 55-4

Regression results after deleting insignifcant gen

All independent variables are now signifcant (ha

Therefore, you can predict salary (in thousands o

(equation 1):

Predicted salary=59.06+.78(EXP)-.033EXP

–2.07(EXP*GENDER)

The negative EXP

term indicates that each additional yea

salary, which means that experience has a nonlin

that after 13 years of experience, each addition

Remember that gender equals 1 for a woman and 0 f

gender in equation 1, a woman’s salary can be pr

Predicted salary=59.06+78EXP-.033EXP

–2.07(EXP*1)=59.06-.033EXP2–1.29EXP

For a man (substituting

), the following

gender=0

equation can be u

Predicted salary=59.06+.78EXP-.033EXP

–2.07(EXP*0)=59.06+.78EXP-.033EXP

Thus, the interaction between gender and experie

experience benefts a woman an average of 0.78–(

indicates that women are not being treated fairl

Chapter

Modeling

Nonlinearities

467

and Interactions

Problems for Chapters 53 Throug

Fizzy Drugs wants to optimize the yield from a

thinks that the number of pounds produced each ti

of the container used, the pressure, and the t

effect of changing one variable might depend o

the process container must be between 1.3 and 1

4 and 4.5 mm, and temperature must be between 2

patiently set up experiments at the lower and u

obtain the data shown in the fle Fizzy.xlsx.

Determine the relationship between yield, s

Discuss the interactions between pressure, s

What settings for temperature, size, and pr

Here are additional multiple regression proble

For 12 straight weeks, you have observed th

tomatoes at Mr. D’s Supermarket. (See the fl

of the following:

❑

Was a promotional notice for canned tomat

❑

Was a coupon for canned tomatoes given to e

❑

Was a price reduction (none, 1, or 2 cent

Use this data to determine how the above fa

canned tomatoes during a week in which you u

and reduce price by 1 cent.

The fle Countryregion.xlsx contains the fol

countries:

❑

Infant mortality rate

❑

Adult literacy rate

❑

Percentage of students fnishing primary s

❑

Per capita GNP

Use this data to develop an equation that c

there any outliers in this set of data? Int

what value should 95 percent of your predic

468

Microsoft Excel 2010: Data Analysis and Business Modeling

The fle Baseball96.xlsx gives runs scored, si

bases stolen for each major league baseball t

to determine the effects of singles, doubles, a

The fle Cardata.xlsx provides the following i

❑

Cylinders

❑

Displacement

❑

Horsepower

❑

Weight

❑

Acceleration

❑

Miles per gallon (MPG)

Determine an equation that can be used to pre

independent variables are not signifcant?

The fle Priceads.xlsx contains weekly unit sa

and advertising expenditures. Explain how adv

sales.

The fle Teams.xlsx contains runs scored, hit-

triples, and home runs for major league baseb

❑

Use this data to build a model that predict

based on the team’s hitting statistics.

❑

How accurate is this model for predicting h

a season?

❑

Suppose a team had a positive residual exce

standard error. What might cause such a res

10.

A hitter’s on-base percentage (OPS) is calcul

hits/(at bats + hit-by-pitcher + walks+ sacri

(SLG) is total bases (home runs gets credit f

and singles, 1) divided by at bats. The fle O

league teams during the 2000–2006 seasons.

Use this data to build a model that can be us

team’s OBP and SLG.

❑

Would you recommend a team use this model o

predict runs scored?

❑

How could this model be used to evaluate in

❑

Why might you be skeptical if this model wa

of a truly great hitter like Albert Pujols o

Chapter

Modeling

Nonlinearities

469

and Interactions

11.

The fle NFlinfo.xlsx contains the following d

seasons:

❑

Margin = Number of points by which a team o

❑

NYP/A = Yards gained passing per pass att

❑

YR/A = Yard gained per rushing attempt.

❑

DNYP/A = Yards gained passing by opponent

❑

DYR/A = Yards gained rushing by opponents p

❑

TO = Turnovers by team.

❑

DTO = Turnovers by a team’s opponents.

Does this data indicate that passing or rus

success?

Around how many points does a turnover cost a te

Many football fans believe you need a good r

Does this data give any support to that vie

12.

The fle Qbinfo.xlsx lists the famous quarte

the 2009 season. The quarterback rating is b

percentage, percentage of passes that resul

and percentage of passes that are intercept

❑

Develop a formula to predict a quarterbac

❑

How accurate are your predictions?

471

Chapter 56

Analysis of Varianc

ANOVA

Questions answered in this chapter:

■

The owner of my company, which publishes com

the position of our books in the computer b

More specifcally, does it really matter whe

or middle of the computer book section?

■

If I am determining whether populations hav

technique called?

analysis of variance

■

How can I use the results of one-way ANOVA f

Data analysts often have data about several di

determine whether the data about the groups di

■

Is there a signifcant difference in the len

the hospital after they give birth?

■

Does the production yield for a new drug de

in which the drug is produced is large, sma

■

Does the drop in blood pressure attained af

drug taken?

When you’re trying to determine whether the me

one factor are signifcantly different, one-way a

tool to use. In the examples given above, the f

the drug, respectively. In analyzing the data, y

■

Null hypothesis

, which indicates that the means of a

■

Alternative

, which

hypothesis

indicates that there is a s

between the groups’ means.

To test these hypotheses in Microsoft Excel, y

in the Data Analysis dialog box. If the p-valu

or equal to 0.15), you can conclude that the a

signifcantly different). If the p-value is gre

populations have identical means). Let’s look a

472

Microsoft Excel 2010: Data Analysis and Business Modeling

Answers to This Chapter’s Quest

The owner of my company, which publishes compute

the position of our books in the computer

book s

More specifically, does it really matter whether t

middle of the computer book section?

The publishing company wants to know whether its b

in the front, back, or middle of the computer bo

monitored at 12 different stores. At fve stores, t

stores, in the back; and at three stores, in the mi

Signif

worksheet in the fle Onewayanova.xlsx, whi

indicate that the location of the books has a si

Fig

URE 56-1

Book sales data.

You can assume that the 12 stores have similar s

same size. This assumption allows you to use one

most one factor (the position of the display in th

(If the stores were different sizes, you would n

which I’ll discuss in Chapter 57, “Randomized Bl

To analyze the data,

Data

on Analysis,

the Data tab,

and then

clickselec

Fill in the dialog box as shown in Figure 56-2.

Fig

URE 56-2

Anova: Single Factor dialog box.

Chapter

Analysis

of Variance:

473

One-Way ANOVA

I used the following confgurations:

■

The data for our input range, including lab

■

Select the Labels In First Row option becau

labels.

■

I selected the Columns option because the d

■

I selected C12 as the upper-left cell of th

■

The selected alpha value is not important. Y

After clicking OK, you obtain the results show

Fig

URE 56-3

One-way ANOVA results.

In cells F16:F18, you see average sales depend

display is at the front of the computer book s

is at the back of the section, sales average 1

average 1,100. Because the p-value of 0.003 (i

that these means are signifcantly different.

If I am determining whether populations have s

technique called analysis of variance?

Suppose that the data in our book sales study i

Insig

, shown in Figure 56-4 (and also in the fle O

ANOVA on this data, you obtain the results show

Fig

URE 56-4

Book store data for which the null hypothesis is a

474

Microsoft Excel 2010: Data Analysis and Business Modeling

Note that the mean sales for each part of the st

.66 indicates that you should accept the null hy

display in the computer book section doesn’t aff

that in the second data set, you have much more v

position in the computer book section. In the fr

when the display is at the front is between 700 a

variation in sales is between 200 and 2,000. The v

is measured by the sum of the squares of data wi

D24 in the frst data set and in cell F24 in the s

of data within groups is only 22, whereas in the s

groups is 574! This large variation within the d

variation between the groups (store positions)

clude for the second data set that the differenc

signifcant.

Fig

URE 56-5

Anova results accepting the null hypothesis.

How can I use the results of a one-way ANOVA for f

If there is a signifcant difference between grou

simply the group’s mean. Therefore, in the frst d

■

Sales when the display is at the front of the c

per week.

■

Sales when the display is at the back will be 1

■

Sales when the display is in the middle will b

If there is no signifcant difference between the g

observation is simply the overall mean. Thus, in th

of 1,117, independent of where the books are pla

Chapter

Analysis

of Variance:

475

One-Way ANOVA

You can also estimate the accuracy of your for

MS (mean square) is the standard deviation of th

shown in Figure 56-6, the standard deviation o

Signif

worksheet again). By the rule of thumb, t

■

During 68 percent of all the weeks in-which b

puter section, sales will be between 900–151

■

During 95 percent of all weeks in which boo

book section, sales will be between 900–2(1

books.

Fig

URE 56-6

Computation of forecast standard deviation.

Problems

You can fnd the data for the following problem

For patients of four cardiologists, you are g

in the hospital after open-heart surgery.

❑

Is there evidence that the doctors have d

❑

You are 95 percent sure that a patient

of D

tween what range of days?

476

Microsoft Excel 2010: Data Analysis and Business Modeling

A drug can be produced by using a 400-degree, 3

are given the pounds of the drug yielded when v

temperatures.

❑

Does temperature appear to influence the pro

❑

What is the range of pounds of the product t

produced with a 200-degree oven?

❑

If you believe that pressure within the con

does this analysis remain valid?

477

Chapter 57

Randomized Blocks a

ANOVA

Questions answered in this chapter:

■

I am trying to analyze the effectiveness of m

addition to a sales representative’s effecti

sells depends on the district to which he o

district assignments of my representatives i

■

Based on my knowledge of sales representati

How accurate are my sales forecasts?

■

How can I determine whether varying the pri

the sales of a video game? How can I determi

signifcantly?

■

How can I interpret the effects of price an

absence of signifcant interaction between p

In many sets of data, two factors can influence a

examples.

Factors

Dependent variable

Sales representative andSales

district assignment

Product price and advertising

Sales expenditure

Temperature and pressureProduction yield

Surgeon and brand of stent

Health

usedof patient after ope

When two factors might influence a dependent va

analysis of variance (ANOVA) can be used to de

signifcant influence on the dependent variable.

termine whether two factors exhibit a signifca

trying to predict sales by using product price a

interact signifcantly if the effect of adverti

In a randomized block model, you observe each p

once. You can’t test for interactions in a ran

model, you observe each combination of

). factors th

In this case,

must be greater than 1. In a t

for interactions.

478

Microsoft Excel 2010: Data Analysis and Business Modeling

Answers to This Chapter’s Quest

I am trying to analyze the . effectiveness

The problem isofthat

my si

addition to a sales representative’s effectivene

depends on the district to. How

which

canheI incorporate

she is as t

assignments of my representatives into my analys

Suppose you want to determine how a sales repres

representative is assigned influence product sale

you can have each of four sales reps spend a mon

resulting sales

Randomized

are given

worksheet

Blocks

in the

Twowayanova.xlsx

in the fle

shown in Figure 57-1. For example, Rep

assigned

1 soldto

20 u

District 4.

Fig

URE 57-1

Data for the randomized blocks example.

This model is called a

two-way ANOVA without rep

sales representative) can potentially influence s

pairing each representative with each district. T

design because you’d like to randomize (chronolo

to districts. In other words, you’d like

to ensu

signed to District 1 is equally likely to be the fr

randomization hopefully lessens the effect of ti

better over time) on your analysis; in a sense, y

you try to compare sales representatives.

To analyze this data in Microsoft Excel, click Da

the Anova: Two-Factor Without Replication option

Figure 57-2.

I used the following information to set up this a

■

The input range data is in cells C5:G10.

■

I selected Labels because the frst row of the i

■

I entered B12 as the upper-left cell of the o

■

The alpha value is not important. You can use th

Chapter

Randomized

Blocks and Two-Way

479

ANOVA

Fig

URE 57-2

Anova: Two-Factor Without Replication dialog box f

The output you obtain is shown in Figure 57-3. (

by the Excel Data Analysis feature. I entered f

chapter.)

Fig

URE 57-3

Randomized blocks output.

To determine whether the row factor (districts

a signifcant effect on sales, just look at the p

than .15), the factor has a signifcant effect o

umn p-value (.024) are both less than .15, so b

signifcant effect on sales.

480

Microsoft Excel 2010: Data Analysis and Business Modeling

Based on my knowledge of sales representatives a

How accurate are my sales forecasts?

How should you predict product sales? You can pr

equation 1, shown here:

Predicted sales=Overall average+(Rep effect)+(District effect)

In this equation,

Rep effect

equals 0 if the sal

factor is signifcant,

Rep effect

equals the mean f

Likewise,

District effect

equals 0 if the distri

signifcant,

District effect

equals the mean for th

I computed the overall average (17.6) in

. The

cell G1

representative and district effects are computed by c

formula

E15–$G$12

. As an example, you can compute predic

as 17.6–2.85+3.6=18.35. This value is computed i

G12+G16+G24

. If the district effect is signifcant an

predicted sales for Rep 4 in District 2 would be 1

Fig

URE 57-4

Forecast for sales in District 2 by sales Rep 4.

As in one-way ANOVA, the standard deviation of th

mean square error shown in cell E31. I computed thi

formula

SQRT(E31)

. Thus, you can be 95 percent sure that i

monthly sales will be between 18.35–2(3.99)=10.3

computed in cell D39 and *

E32

D40 and

with

E32

D38+2

,the

respectively

formulas

How can I determine whether varying the price an

the sales of a video game? How can I determine w

significantly?

When you have more than one observation for each c

factors, you have a two-factor ANOVA

with

replic

Excel requires that you have the same number of o

combination.

In addition to testing for the signifcance of th

signifcant interaction between them. For example

advertising affect sales, an interaction between p

Chapter

Randomized

Blocks and Two-Way

481

ANOVA

effect of an advertising change would depend o

of a price change would depend on the advertis

and advertising would mean that the effect of a p

of advertising.

As an example of two-factor ANOVA with replica

price and advertising level affect the monthly s

No Interaction

worksheet in the fle Twowayanov

Figure 57-5. During the three months in which a

for

example, 21, 20, and 16 units were sold.

Fig

URE 57-5

Video game sales data; no interaction.

Notice that for each price/advertising combina

In cell D1, I computed the overall average (25

AVERAGE(D4:F12)

. In cells G4, G7, and G10, I computed

ing. For example, the effect of having a low l

advertising minus the overall average. In cell G

–5.59 with the formula

. In

AVERAGE(D4:F6)–$D$1

a similar fashion, I c

each price level by copying from D13 to

. E13:F1

To analyze this data, click Data Analysis on th

Factor With Replication in the Data Analysis d

Figure 57-6.

Fig

URE 57-6

Anova: Two-Factor With Replication dialog box fo

with replication.

482

Microsoft Excel 2010: Data Analysis and Business Modeling

I used the following information to set up the a

■

The input range data, including labels, is in C

Excel requires a label for each level of the c

in the input range. Thus, I entered Low, Mediu

the possible price levels. Excel also require

the frst column of the input range. These lab

thbeeginning of the data for each level. Thus, I p

medium, and high levels of advertising in cel

■

In the Rows Per Sample box, I entered 3 becau

combination of price and advertising level.

■

The upper-left cell of our output range is B1

The only important portion of the output is the A

Fig

URE 57-7

Two-way ANOVA with replication output; no interacti

As with randomized blocks, an effect (including

that’s less than .15. Here, Sample (this is the r

in the row labeled Columns) are highly -signifcan

tion. (The interaction p-value is .79!) Therefor

influence sales and that the effect of advertisin

Figure 57-8 graphically demonstrates the fact th

signifcant interaction. (See the

Graph No Intera

Fig

URE 57-8

Price and advertising do not interact in this data s

Chapter

Randomized

Blocks and Two-Way

483

ANOVA

Notice that as advertising increases, sales in

price level is low, medium, or high.

How can I interpret the effects of price and a

of significant interaction between price and ad

In the absence of a signifcant interaction, yo

replication in the same way that you do in a t

the

equation

to use

2):

(

Predicted sales=Overall average+[Row or advertising effect(if significant)]

+[Column or price effect(if significant)]

This analysis assumes that price and advertisi

are highly seasonal, seasonality would need to b

seasonality in Chapter 59, “Winters’s Method,” a

of Special Events.”) For example, when price i

sales are given by 25.037+(–1.814)+(–8.704)=14

the

Two Way ANOVA No Interaction

worksheet agai

see that the overall average is equal to 25.03

and the high price effect =–8.704.

Fig

URE 57-9

Forecasts for sales with high price and medium a

The standard deviation of the forecast errors e

within error.

29.78 = 5.46

You can be 95 percent sure that the forecast i

you are 95 percent sure that sales during a mo

will be between 3.60 and 25.43 units.

484

Microsoft Excel 2010: Data Analysis and Business Modeling

In the

Two Way ANOVA with Interaction

worksheet, I c

example to the data shown in Figure 57-10. After r

ANOVA with replication, I obtained the results s

Fig

URE 57-10

Sales data with interaction between price and adve

Fig

URE 57-11

Output for the two-factor ANOVA with interaction.

In this data set, the p-value for interaction is .

.15) for interaction,

you do not even check p-va

forecast sales for any price and advertising com

observations involving that price and advertisin

for sales during a month with high advertising a

34 + 40 + 32

106

= 35.555

units

The standard deviation of forecast errors is agai

(

17.11 = 4.14)

Thus, you can be 95 percent sure that the sales

Chapter

Randomized

Blocks and Two-Way

485

ANOVA

Figure 57-12 illustrates why this data exhibit

advertising. For a low and medium price, incre

is high, increased advertising has no effect o

equation 2 to forecast sales when a signifcant i

talk about an advertising effect when the effe

Fig

URE 57-12

Price and advertising exhibit a signifcant inter

Problems

The data for the following problems is in the fl

You believe that pressure (high, medium, or l

low) influence the yield of a production

pro

swers to the following problems:

❑

Use the data in the

Problem 1

worksheet t

pressure influence the yield of the proces

❑

With high pressure and low temperature, y

yield will be in what range?

You are trying to determine how the particu

sales calls (one, three, or fve) made to a d

dollars) that each doctor prescribes of

you

sheet to determine the answers to the follow

❑

How do the representative and number of s

❑

If Rep 3 makes fve sales calls to a docto

prescriptions within what range of dollar

Answer the questions in Problem 2 by using th

The fle Coupondata.xlsx contains informatio

when a coupon was given out (or not) and ad

paper. Describe how the coupon and advertis

487

Chapter 58

Using Moving Averag

Understand Time Ser

Question answered in this chapter:

■

I’m trying to analyze the upward trend in q

1996. Fourth quarter sales in the U.S. are u

sales during the frst quarter of the

- follow

ward trend in sales. Is there any way that I c

revenues?

Answers to This Chapter’s Ques

Time series data simply displays the same quan

example, the data in the fle Amazon.xlsx, a su

the time series for quarterly revenues in mill

the time interval from the fourth quarter of 1

To graph this time series, select the range C2

frst quarter is Quarter 1 and the last is Quar

millions of dollars). Then choose Chart on the I

the

Scatter

chart type

with. Smooth

(

Lines and Marker

in Figure 58-2.

Fig

URE 58-1

Quarterly revenues for Amazon sales.

488

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 58-2

Time series plot of quarterly toy revenues.

There is an upward trend in revenues, but the fa

revenues during the frst three quarters of each y

there are four quarters per year, it would be ni

last four quarters. This is. called

Using a four-quarte

perio

inaverage smooths out the seasonal influence beca

point for each quarter. Such a graph is called a

average “moves” over time. Moving average graphs a

helps you get a better idea of what is going on w

To create a moving average graph of quarterly re

graph, and then click a data point until all the d

any point, click Add Trendline, and then select t

equal to 4. Microsoft Excel now creates the four

shown in Figure 58-3. (See the fle Amazonma.xlsx

For each quarter, Excel plots the average of the c

Of course, for a four-quarter moving average, th

fourth data point. The moving average curve make

had a steady upward trend. In fact the slope of th

be increasing. In all likelihood , the slope of thi

off, resulting in a graph that looks like an S c

curves, but the Excel 2010 Solver can be used to f

Chapter

Using

Moving Averages to Understand

489

Time Series

Fig

URE 58-3

Four-quarter moving average trend curve.

Problem

■

The fle Ch58data.xlsx contains quarterly re

four-quarter moving average trend curve for e

you learn from each trend curve.

491

Chapter 59

Winters’s Method

You often need to predict future values of a t

product revenues. This is usually diffcult

series

bec

are constantly changing. Smoothing or adaptive m

forecasting future values of a time

powerful

series. In thi

smoothing method:

’s method.

Winters

To help you understand h

works, I’ll use it to forecast monthly housing s

simply the number of new homes whose constructi

describing the three key characteristics of a t

Time Series Characteristics

The behavior of most time series can be explai

base, trend, and seasonality.

■

The

base

of a series describes the series’ c

For example, suppose the base level for U.S

can believe that if the current month were a

of the year, 160,000 housing starts would o

■

The

trend

of a time series is the percentag

trend of 1.02 means that you estimate that h

each month.

■

The

seasonality

(index) for a periodtypical

tells y

month you can expect housing starts to be. F

index is .8, then December housing starts a

the June seasonal index is 1.3, then June h

typical month.

Parameter Defnitions

paAfter observing

, you will

monthhave

used all data obse

to estimate the following quantities of intere

■

=Level of series

■

=Trend of series

■

=Seasonal index for current month

492

Microsoft Excel 2010: Data Analysis and Business Modeling

The key to Winters’s method is the following thr

, and S

. In the following

, ,

bet

and

formulas,

gam

are

alp

called

. You

smoothin

choose the values of these parameters to optimiz

equals the number of periods

=12 months,

in a seasonal

for example)

cycle

a (

equals

the observed value of

. the time series at time

■

Formula 1:

=alp(x

–c

)+(1–alp)(L

t–1

–1

)

■

Formula 2:

=bet(L

–1

)+(1–bet)T

t–1

■

Formula 3:

=gam(x

)+(1–gam)s

t-c

Formula 1 indicates that the new base estimate i

observation (deseasonalized) and the last period

Formula 2 indicates that the new trend estimate i

current base to the last period’s base

period’s

(this is a c

trend. Formula 3 indicates that you update your s

average of the estimate of the seasonal index ba

estimate. Note that larger values of the smoothi

weight on the current observation.

You can defne

t,k

as your

)forecast

after period

(

This

for the

results

period

in th

formula

t,k

t*(

t+k–c

. (I refer to this as formula 4.)

This formula frst uses the current trend estimat

the resulting base estimate for period

t+k

is ad

nitializing Winters’s Method

To start Winters’s method, you must have initial e

seasonal indexes. I used monthly housing

initialize

starts f

Winters’s method. Then I chose smoothing paramet

forecasts for the years 1988 through 1996. See Fi

are the steps I followed.

Chapter

Winters’s

Method

493

Fig

URE 59-1

Initialization of Winters’s method.

Step

estimated, for example, the January seas

January

housing starts for 1986 and 1987 divided by th

for 1986 and 1987. Therefore, copying from G14 t

=AVERAGE(B2,B14)/AVERAGE($B$2:$B$25)

generates th

For example, the January estimate is 0.75 and th

Step

estimate the average monthly trend, I t

starts divided by the 1986 mean starts. I comp

with the formula

=(J1/J2)^(1/12).

Step

Going

into January 1987, I estimated the b

December 1987 value. This was computed

in C25 w

Estimating the Smoothing Const

Now I’m ready to estimate smoothing constants. I

in column D, the series trend; and in column

pute the forecast for next month, and in colum

for each month. Finally, I use the Solver to c

minimize the sum of the absolute percentage er

Step

G11:I11, I enter trial values (between 0 a

Step

C26:C119, I compute the updated series

to C27:C119 the formula

=alp*(B26/G14)+(1–alp)

494

Microsoft Excel 2010: Data Analysis and Business Modeling

Step

D26:D119, I use formula 2 to update the s

D27:D119 the formula

=bet*(C26/C25)+(1–bet)*D25

Step

G26:G119, I use formula 3 to update the s

G27:G119 the formula

=gam*(B26/C26)+(1–gam)*G14

Step

E26:E119, I use formula 4 to compute the f

copying from E26 to E27:E119

the formula

=(C25*D

Step

F26:F119, I compute the absolute percenta

from F26 to F27:F119 the. formula

=ABS(B26-E26)/B

Step

compute the average absolute percentage er

in F21 with the formula

=AVERAGE(F26:F119)

Step

Now

I use Solver to determine smoothing para

average absolute percentage error. The Solver Pa

Fig

URE 59-2

Solver Parameters dialog box for Winters’s model.

I used smoothing parameters (G11:I11) to minimiz

(cell F21). The Solver ensures that you fnd the b

Smoothing constants must be,between

bet=.01

, and 0

gam=.27

and 1. Her

minimizes the average absolute percentage error. Y

for the smoothing constants, but you should obtai

(MAPE) close to 7.3 percent. In this example, th

constants that give forecasts having approximate

forecasts are off by an average of 7.3 percent.

Chapter

Winters’s

Method

495

Remarks

■

Instead of choosing smoothing parameters to o

could, for example, choose to optimize the a

in forecasting total housing starts for the n

■

If at the end of month

you want to foreca

simply add

t,1

t,2

t,3

t,4

. If you want, you could choose s

minimize the absolute percentage error incu

Problems

All the data for the following problems is in th

Use Winters’s method to forecast one-quarte

Use Winters’s method to forecast total reve

Home Depot.

497

Chapter 60

Ratio-to-Moving-Ave

Method

Questions answered in this chapter:

■

What is the trend of a time series?

■

How do I defne seasonal indexes for a time s

■

Is there an easy way to incorporate trend a

product sales?

Often you need a simple, accurate method to pr

corporation or future monthly sales of a produ

provides an accurate, easy-to-use forecasting m

In the fle Ratioma.xlsx, you are given sales o

in Figure 60-1 in rows 5 through 24), and you wa

quarters (quarters 21-24). This time series ha

Answers to This Chapter’s Ques

What is the trend of a time series?

A trend of 10 units per quarter means, for exa

per quarter, while a trend of -5 units per qua

units per quarter.

How do I define seasonal indexes for a time ser

We know that Walmart sees a large increase in i

of the holiday season.) If you do not recogniz

good forecasts of quarterly Walmart revenues. T

better understand a company’s sales pattern. T

revenues are as follows:

■

Quarter 1 (January through March): .90

■

Quarter 2 (April through June): .98

■

Quarter 3 (July through September): .96

■

Quarter 4 (October through December): 1.16

498

Microsoft Excel 2010: Data Analysis and Business Modeling

These indexes imply, for example, that sales dur

higher than sales during an average quarter.

Sea

To see whether you understand seasonal

question:

indexes, t

Suppose that during Quarter 4 of 2013 Walmart ha

1 of 2014 Walmart has sales of $180 billion. Are thi

The key idea here is to

deseasonalize

sales and e

average quarter. For example, the Quarter 4 2013 s

$172.4 billion in an average quarter,selling

and the Qu

180/.9 = $200 billion in an average quarter. Thu

decreased 10 percent, sales appear to be increas

quarter. This simple example shows how important i

product’s seasonal indexes.

Is there an easy way to incorporate trend and se

product sales?

Now let’s turn to the simple ratio-to-moving-ave

enables you to easily estimate a time series’ tr

to generate forecasts of future values of the ti

shown in Figure 60-1 and the fle Ratioma.xlsx.

Fig

URE 60-1

Data for the ratio-to-moving-average example.

You begin by trying to estimate the deseasonaliz

(using centered moving averages). Then you can f

estimates (in column G). Next you determine the s

you estimate the future level of the series by e

future sales by reseasonalizing the trend line e

Chapter

Ratio-to-Moving-Average

499

Forecast Method

■

Calculating moving

To begin,

averages

compute aaverage

four-quar

(four quarters eliminates seasonality)

for e

ter, the current quarter, and the next two q

the formula

AVERAGE(E5:E8)

. For example, for Quarter 2, t

.25*(24+44+61+79) = 52.

■

Calculating centered

The moving

averages

for Qu

centered at Quarter 2.5, while the moving a

3.5. Averaging these two moving averages gi

estimates the level of the process at the e

formula

AVERAGE(F6:F7)

gives you an estimat

series—without seasonality!

■

Fitting a trend line to the

You

centered

use the centere

moving a

averages to ft a trend line that can be use

In F1, I use the formula

SLOPE(G7:G22,B7:B22

in cell F2 I use the formula

INTERCEPT(G7:G2

trend line. You can now estimate the level o

6.94t+ 30.17. Copying from G25 to G26:G28 th

computes

estimated

the

level of the series from Qu

■

Computing the seasonal

Recall that

indexes

a seasonal index o

means sales in that quarter are twice sales d

index of .5 for a quarter means that sales d

quarter. To determine the seasonal indexes, b

for which you have sales

actual

. To

sales/cente

do this, co

cell H7 to H8:H22. the

You’ll

formula

see,

=E7/G7

for example, t

quarter, sales were 77, 71, 90, and 89 perce

seasonal index for Quarter 1 as the average o

calculate the initial seasonal index estima

AVERAGEIF($D$7:$D$22,J3,$H$7:$H$22)

. This formula averages th

have for Quarter 1 seasonality.

Unfortunately, the seasonal indexes do not a

seasonal indexes average to 1, copy from L3 t

K3/AVERAGE($K$3:$K$6)

■

Forecasting sales during

To create

Quarters

the sales

21–24

fore

quarter, you simply multiply the trend line e

G) by the appropriate seasonal index. Copyi

VLOOKUP(D25,season,3)*G25

computes the fnal f

500

Microsoft Excel 2010: Data Analysis and Business Modeling

If you think the trend of the

series’

has changed r

trend based on more recent data. For

moving

example, yo

averages for Quarters 13–18 to get a more recent t

SLOPE(G17:G22,B17:B22)

. This yields an estimated trend of 8

to forecast Quarter 22 sales, for example, you w

you have (from Quarter 18) of 160.13 and add 4(8

Quarter 22. Then multiplying by the Quarter 2 se

for Quarter 22 sales of (160.13+4(8.09))*(.933) = 1

Problem

The fle Walmartdata.xlsx contains quarterly r

1994–2009. Use the ratio-to-moving-average me

Quarters 3 and 4 in 2009 and Quarters 1 and 2 o

a trend estimate that you use in your forecas

501

Chapter 61

Forecasting in the P

Special Events

Questions answered in this chapter:

■

How can I determine whether specifc factors i

■

How can I evaluate forecast accuracy?

■

How can I check whether my forecast errors a

For a student project, a class and I attempted t

the Eastland Plaza Branch of the Indiana Unive

with the branch manager made it clear that the f

customers:

■

Month of the year

■

Day of the week

■

Whether the day was a faculty or staff payd

■

Whether the day before or the day after was a h

Answers to This Chapter’s Ques

How can I determine whether specific factors in

The data collected is contained in the

Origina

shown in Figure 61-1. If you try to run a regr

(as

described in Chapter 54, “Incorporating Qual

the dependent variable would be the number of c

column E). You would need 19 independent varia

■

Eleven to account for the month (12 months mi

■

Four to account for the day of the week (5 b

■

Two to account for the types of paydays that o

■

Two to account for whether a particular day f

Microsoft Excel 2010 allows only 15 independen

in trouble.

502

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 61-1

Data used to predict credit union customer traffc.

When a regression forecasting model requires mor

can use the Excel Solver to estimate the coeffci

also use Excel to compute the R-squared values b

traffc and the standard deviation for the foreca

forecasting equation by using a lookup table to l

other factors. Then I used Solver to choose the c

yields the minimum sum of squared errors. (Each d

forecasted customers.) Here are the particulars.

I began by creating indicator variables (in colu

staff payday (SP), faculty payday (FAC), before a h

Figure 61-1.) For example, in cells G4, H4, and J

staff payday, faculty payday, and after a holida

was not before a holiday.

The forecast is defned by a constant (which help

more accurate) and effects for each day of the w

payday, a day occurring before a holiday, and a da

values for all these parameters (the Solver chan

Figure 61-2. Solver will then choose values that m

day, the forecast of customer count will be gene

Predicted customer count=Constant+(Month effect)+(Day of week effect)

+(Staff payday effect, if any)+(Faculty payday effect, if any)+

(Before holiday effect, if any)+(After holiday effect, if any)

Chapter

Forecasting

in the Presence

503

of Special Events

Using this model, you can compute a forecast f

K4 to K5:K257 the following formula:

$O$26+VLOOKUP(B4,$N$14:$O$25,2)+VLOOKUP(D4,$N$4:$O$8,2) +G4*$O$9+H4*$O$10+I4*$O$11+J4*$O$12

Cell O26 picks up the constant term.

VLOOKUP(B

coeffcient for the current month, and

VLOOKUP(

week coeffcient for the current week.

G4*$O$9+

the effects (if any) when the current day is c

By copying from L4 to L5:L257

, I compute

the formula

the squared

(E4-

day. Then, in cell L2, I compute the sum

. of sq

Fig

URE 61-2

Changing cells and customer forecasts.

In cell R4, I average the day of the week

chan

and in cell R5, I average the month changing

. Later,

I’ll constrain the average month and day of th

month or day of the week with a positive effec

and a month or day of the week with a negative e

count.

You can use the Solver settings shown in Figur

minimize the sum of squared errors.

504

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 61-3

Solver Parameters dialog box for determining forec

The Solver model changes the coeffcients for the m

and the constant to minimize the sum of square e

the week and month effect to equal 0. Using the S

obtained. For example, Friday is the busiest day o

A staff payday raises the forecast (all

) byelse

397 bei

customers.

How can I evaluate forecast accuracy?

To evaluate the accuracy of the forecast,

between

you co

thfeorecasts and the actual customer count in cel

RSQ(E4:E257,K4:K257)

. This formula computes the percentage o

customer count that is explained by the forecasti

explain 77 percent of the daily variation in cus

You compute the error for each day in column M by c

formula.

E4–K4

A close approximation to the standard e

standard deviation of the errors. This value is c

STDEVS(M4:M257)

. Thus, approximately 68 percent of the f

within 163 customers, 95 percent accurate within 3

Let’s try and spot any outliers. Recall that an o

of a forecast error exceeds two times the standa

M4:M257, and then click Conditional Formatting o

and in the New Formatting Rule dialog box, choos

Chapter

Forecasting

in the Presence

505

of Special Events

To Format. Fill in the rule description in the d

information about conditional formatting, see C

Fig

URE 61-4

Using conditional formatting to spot forecast ou

After choosing a format with a red font, the c

red any error that exceeds

2*(standard deviati

outliers, you can see that the model often und

three days of the month. Also, during the seco

overforecasts, and the day before spring break

To remedy this problem, in the

1st Three Days

of the frst three days of the month and for sp

added trial values for these new effects in ce

following formula:

$O$25+VLOOKUP(B4,$N$13:$O$24,2)+VLOOKUP(D4,$N$4:$O$8,2)+G4*$O$9+H4*$O$10+I4*$O$11+J4*$O$12

+IF(C4=1,$O$26,IF(C4=2,$O$27,IF(C4=3,$O$28,0)))

I include the effects of the frst three days o

IF(C4=2,$O$27,IF(C4=3,$O$28,0)))

picks up the e

I manually entered the spring break coeffcient

added

+O29

to the formula, and

in cells K53:K5

After including the new changing cells in the S

Figure 61-5. Notice that the frst three days o

(probably because of government support and So

break reduces customer count. Figure 61-5 also s

accuracy. The R squared value (RSQ) has improv

reduced to 122 customers.

506

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 61-5

Forecast parameters and forecasts including spring b

By looking at the forecast errors for the week 1

see that the model has greatly overforecasted th

It also underforecasted customer counts for the w

of the forecast errors

) also

(often

shows

called

the following:

residuals

■

Thanksgiving is different from a normal holid

than expected the day after Thanksgiving.

■

The day before Good Friday is really busy bec

■

Tax day (April 16) is also busier than expect

■

The week before Indiana University starts fal

probably because many staff and faculty take a “

hectic onrush of the fall semester.

Fig

URE 61-6

Errors for Christmas week.

Chapter

Forecasting

in the Presence

507

of Special Events

In the

Christmas week

worksheet, I added chang

factors. After adding the new parameters as ch

are shown in Figure 61-7. The RSQ is up to 92 p

98.61 customers! Note that the post-Christmas w

359, the day before Thanksgiving added 607 cus

customer count by 161, and so on.

Fig

URE 61-7

Final forecast parameters.

Notice also how the forecasting model is impro

something in common (like being the frst three d

factor as an independent variable and your for

How can I check whether my forecast errors are r

A good forecasting method should create foreca

random errors, I mean that your errors exhibit n

random, the sign of your errors should change

(

mately half the time. Therefore, a commonly

cast errors is to look at the number of sign c

nonrandomness of the errors is indicated if yo

n – 1

–

or more than

n – 1

508

Microsoft Excel 2010: Data Analysis and Business Modeling

changes in sign. In the

Christmas week

worksheet

the number of sign changes in the residuals by c

IF(M5*M4<0,1,0)

. A sign change in the residuals occurs i

consecutive residuals is negative. Therefore, thi

sign of the residuals occurs. There were 125 cha

254 = 110.6

254 – 1

–

changes in sign as the cutoff for nonrandom resi

A similar analysis was performed to predict dail

restaurant chain. The special factors correspond

Sunday (the day of the NFL’s Super Bowl) was the l

Mother’s Day were the busiest. Also, Saturday wa

Friday was the busiest day of the week for lunch

Problems

How can you use the techniques outlined in thi

pens at Staples?

If you had several years of data, how would y

509

Chapter 62

An Introduction to R

Variables

Questions answered in this chapter:

■

What is a random variable?

■

What is a discrete random variable?

■

What are the mean, variance, and standard d

■

What is a continuous random variable?

■

What is a probability density function?

■

What are independent random variables?

In today’s world, the only thing that’s certai

In the next nine chapters, I’ll give you some p

incorporate uncertainty in business models. Th

snderstanding how to use random variables.

Answers to This Chapter’s Ques

What is a random variable?

Any situation whose outcome is

. The

uncertain

value of

is ca

variable is based on the (uncertain) outcome o

of dice is an experiment, and a random variabl

shown on each die. In this case, the random va

so on up to 12. As another example, consider th

console, for which a random variable might be d

product.

What is a discrete random variable?

A random variable is discrete if it can assume a f

some examples of discrete random variables:

■

Number of potential competitors for your pr

■

Number of aces drawn in a fve-card poker ha

■

Number of car accidents you have (hopefully z

510

Microsoft Excel 2010: Data Analysis and Business Modeling

■

Number of dots showing on a die

■

Number of free throws out of 12 that Phoenix S

basketball game

What are the mean, variance, and standard deviat

In Chapter 42, “Summarizing Data by Using Descri

variance, and standard deviation for a data set. I

(often denoted by µ) is the average value of the r

performed an experiment many times. The mean of a r

as the random variable’s

expected

value. The var

)

is the average value of the squared deviatio

you would expect if you performed an experiment m

random variable (often denoted by σ) is simply t

sets, the mean of a random variable is a summary m

variable, whereas the variance and standard devia

variable about its mean.

As an example of how to compute the mean, varian

variable, suppose you believe that the return on th

governed by the following probabilities:

Probability

Market return

.40

+20 percent

.30

0 percent

.30

-20 percent

Hand calculations show the following:

µ=.40*(.20)+.30*(.00)+.30*(–.20)=.02 or 2 percent

=.4*(.20–.02)

+.30*(.0–.02)

+.30*(–.20–.02)

=.0276

Then

=.166

or 16.6 percent.

In the fle Meanvariance.xlsx (shown in Figure 62

Chapter

An62

Introduction to Random

511

Variables

Fig

URE 62-1

Computing the mean, standard deviation, and vari

I computed the mean of the market return in ce

SUMPRODUCT(B4:B6,C4:C6)

. This formula multiplies each val

probability and sums up the products.

To compute the variance of the market return, I d

value of the random variable from its mean by c

(B4–$C$9)^2

. Then, in cell C10, I computed the

varia

age squared deviation from the mean with

the f

Finally, I computed the standard deviation of th

SQRT(C10)

What is a continuous random variable?

A continuous random variable is a random varia

or, to all intents and purposes, an infnite nu

continuous random variables:

■

Price of Microsoft stock one year from now

■

Market share for a new product

■

Market size for a new product

■

Cost of developing a new product

■

Newborn baby’s weight

■

Person’s IQ

■

Dirk Nowitzki’s three-point shooting percen

What is a probability density function?

A discrete random variable can be specifed

by a l

rence for each value of the random variable.

sume an infnite number of values, you can’t li

of a continuous random variable. A continuous r

its

probability

. For

density

example,

function

the probability de

chosen person’s IQ is shown in Figure 62-2.

512

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 62-2

Probability density function for IQs.

A probability density function (pdf) has the fol

■

The value of the pdf is always greater than o

■

The area under the pdf equals 1.

■

The height of the density function for a valu

the likelihood that the random

. For

variable

example,

assum

the h

of the density for an IQ of 83 is roughly hal

This tells you that IQs near 83 are approxima

because the density peaks at 100, IQs around 1

■

The probability that a continuous random varia

the corresponding area under the density func

having IQs from 80 through 100 is simply the a

100.

■

We note that a discrete random variable which a

as a continuous random variable. (See Chapter 6

example, while the number of half gallons

of mi

cery store is discrete, it proves more conveni

as a continuous random variable.

What are independent random variables?

A set of random variables are independent if know

tells you nothing about the values of the other r

games won by the Indiana University football

tea

centage return on Microsoft during the same year

not change your view of how Microsoft stock did d

Chapter

An62

Introduction to Random

513

Variables

On the other hand, the returns on Microsoft st

are told that Microsoft stock had a high retur

were high, which tells you that Intel probably h

Problems

Identify the following random variables as d

❑

Number of games the Seattle Seahawks win n

❑

Number that comes up when spinning a roul

❑

Unit sales of Tablet PCs next year

❑

Length of time that a light bulb lasts be

Compute the mean, variance, and standard de

when a die is tossed.

Determine whether the following random varia

❑

Daily temperature and sales at an ice cre

❑

Suit and number of a card drawn from a de

❑

Inflation and return on the stock market

❑

Price charged for and the number of units s

The current price of a company’s stock is $

takeover is successful, the company’s stock p

is unsuccessful, the stock price will drop t

probability of a successful takeover that w

stock today. Assume your goal is to maximiz

Seek command, which is discussed in detail i

When a roulette wheel is spun, the possible o

bet on a number coming up you win $35 if you

otherwise. What is the mean and standard de

of the game?

515

Chapter 63

The Binomial, Hyperg

Negative Binomial R

Questions answered in this chapter:

■

What is a binomial random variable?

■

How do I use the BINOM.DIST function to com

■

If equal numbers of people prefer Coke to P

people whether they prefer Coke to Pepsi, w

people prefer Coke to Pepsi and the probabi

Coke to Pepsi?

■

Of all the elevator rails my company produc

are about to ship a batch of 10,000 elevatoo d

the batch is acceptable, the customer will r

check whether each sampled rail is defectiv

tive, the customer will accept the batch. H

batch will be accepted?

■

Airlines do not like flights with empty seat

ticket purchasers show up for a flight. If th

what is the probability that the flight will b

■

The local Village Deli knows that 1,000 cus

20 percent order the specialty vegetarian s

How many should the deli make if they want t

of vegetarian sandwiches?

■

What is the hypergeometric random variable?

■

What is the negative binomial random variab

Answers to This Chapter’s Ques

What is a binomial random variable?

binomial random variable

is a discrete rando

situation in which all three of the following a

■

independent trials occur.

516

Microsoft Excel 2010: Data Analysis and Business Modeling

■

Each trial results in one of two outcomes: su

■

In each trial, the

) probability

remains constant.

of success (

In such a situation, the binomial random variabl

related to the number of successes in a given nu

variable denoting the number of successes occurr

probability of success

. Here on

areeach

sometrial

examples

in whi

random variable is relevant.

■

Coke or

Assume

Pepsi

that equal numbers of people pr

to Coke. You ask 100 people whether they pref

probability that exactly 60 people prefer Cok

through 60 people prefer Coke to Pepsi. In thi

variable defned by the following:

❑

Trial: survey individuals

❑

Success: prefer Coke

❑

equals 0.50

❑

equals 100

Let

equal the number of people sampled who p

probability

=60 and

thatalso

the probability

that

≤

■

Elevator

rails

all the elevator rails you -produce, 3 p

tive. You are about to ship a batch of 10,000 e

whether the batch is acceptable, the customer w

rails and check whether each sampled rail is d

defective, the customer will accept the batch

that the batch will be accepted.

You have a binomial random variable defned by th

❑

Trial: look at a sampled rail

❑

Success: rail is defective

❑

equals 0.03

❑

equals 100

Let

equal the number of defective rails in th

that

≤ 2

■

Airline overbooking

Airlines don’t like flights with emp

average, 95 percent of all ticket purchasers s

tickets for a 100-seat flight, what is the pro

Chapter

The

63Binomial, Hypergeometric, and Negative

517

Binomial Random Variables

You have a binomial random variable defned by th

❑

Trial: individual ticket holders

❑

Success: ticket holder shows up

❑

equals 0.95

❑

equals 105

Let

equal the number of ticket holders wh

probability that

≥ 101.

How do I useD. IST

the function

BINOM

to compute binomial p

Microsoft Excel 2010 includes the BINOM.DIST f

binomial probabilities. If you want to compute th

binomial random variable having

trials with p

DIST(x,n,

. If

p,1)

you want to compute the probability o

random variable having

trials with probabili

Entering 1 as the last argument of BINOM.DIST y

0 yields

probability

the “

mass function” for any parti

of True can be used instead of a 1, and a last a

Previous versions of Excel will not recognize th

Excel you can use the BINOMDIST function, whic

DIST function. Let’s use the BINOM.DIST functi

You’ll fnd the data and analysis in the fle Bi

Figure 63-1.

Fig

URE 63-1

Using the binomial random variable.

518

Microsoft Excel 2010: Data Analysis and Business Modeling

If equal numbers of people prefer Coke to Pepsi a

whether they prefer Coke to Pepsi, what is the p

Coke to Pepsi and the probability that between 4

You have

=100

and

=0.5.

You seek the

=60 probability

and the probabilit

that

≤

, ≤

where

equals the number of people who p

the probability

=60 by that

entering

the formula

. Excel

BINOM.DIST(

return

the value 0.011.

To use the BINOM.DIST function to ,compute

you canthe

note

that the probability that

≤

equals the p

that .

Thus,

≤

you can obtain the probability that f

by entering the formula

BINOM.DIST(60,100,0.5,1)

Excel return

the value 0.9648. So, if Coke and Pepsi -

are equa

ple of 100 people, Coke or Pepsi would be more th

people shows Coke or Pepsi to be more than 10 pe

that Coke and Pepsi are equally preferred.

Of all the elevator rails my company produces,

. We

3 p

are about to ship a batch of 10,000

. To determine

elevatorwhet

rai

batch is acceptable, the customer will randomly c

whether each sampled

. Ifrail

two is

or defective

fewer sampled rail

customer will accept

. How can

theIbatch

determine the probabil

accepted?

If you let

equal the number of defective rails i

variable

=100

with

and

=0.03.

n p

You seek the probability that

the formula

BINOM.DIST(2,100,0.03,1)

Excel returns the value 0.42 T

accepted 42 percent of the time.

Really, your chance of success is not exactly 3 p

10 rails are defective, the chance the next rail i

frst 10 rails are not defective, the chance the n

the probability of success on the eleventh

trial i

cess on one of the frst 10 trials. Despite this f

as an approximation when a sample is drawn and th

the total population. Here, the population equal

probabilities involving sampling from a -fnite po

geometric random variable, which I’ll discuss la

Airlines do not like . flights

Supposewith

that,

empty

on average

seats

, 9

ticket purchasers . show

If the

up airline

for a flight

sells 105 tick

what is the probability that the flight will be o

Chapter

The

63Binomial, Hypergeometric, and Negative

519

Binomial Random Variables

Let

equal the number of ticket holders

=105 and

who s

=0.95. You seek the

≥

101

.probability

Note that the

that

≤

101

probability

equals

1 minus the probability

≤

So, to that

compute

the probabili

booked, you enter in cell C10 the

. Excel

formula

yields

1–BI

which means there is a 39.2 percent chance tha

The local Village Deli knows that 1,000

. On average

custom

20 percent order the specialty

. These vegetarian

sandwiches

. Howsand

are p

many should the deli make if they want to have a 5 p

vegetarian sandwiches?

In Excel 2010 the function BINOM.INV,

trials,

probability

with the s

success,

alpha

determines the smallest number

for w

than or equal to

successes

. In earlier

is at

versions

least

alpha

of Ex

CRITBINOM(

trials, probability

) yielded

of success,

the same

alpha

results a

example,

trials

equals 1,000,

probability of s

in Figure 63-2, if the deli orders 221 sandwic

than or equal to 221 is at least 0.95. Also, t

demanded is less than 0.95.

Fig

URE 63-2

Example of BINOM.INV function.

What is the hypergeometric random variable?

The

hypergeometric random variable

governs a s

■

An urn contains

balls.

■

Each ball is one of two types (called succe

■

There are

successes in the urn.

■

A sample of size

is drawn from the urn.

520

Microsoft Excel 2010: Data Analysis and Business Modeling

Let’s look at an example in the fle Hypergeom.di

Excel 2010 formula

HYPERGEOM.DIST(x,n,s,N,0)

giv

are drawn from an urn containing

balls, of whi

formula

HYPERGEOM.DIST(x,n,s,N,1)

gives the prob

balls are drawn from an urn containing

with the BINOM.DIST function, True can be used t

For example, suppose that 40 of the Fortune 500 c

CEOs are analogous

N=500

to the

) and

balls

the in

40 the

women

urn

are

( rep

of the

successes in the urn. Then, copying fro

DIST(C8,Sample_size,Population_women,Population_

of 10 Fortune 500 companies will have 0, 1, 2,…, 1

10,

Population_women

equals 40, and

Population_s

Finding a woman CEO is a success. In the sample o

of 0.431 that no women CEOs will be in the sampl

approximated this probability with

, yielding

the formula

0.434

which is very close to the true probability of 0

that at most 2 of the 10 people in the sample wo

HYPGEOM.DIST(2,Sample_Size,Population_women,Popu

Thus there is a 9

percent chance that at most two people in the sa

obtained this answer by adding together the shad

Fig

URE 63-3

Using the hypergeometric random variable.

What is the negative binomial random variable?

The

negative binomial random variable

applies

to th

dom variable, but the negative binomial random v

occurring th

before

success.

the

NEGBINOM.DIST(f,s,p,0)

Thus

gives th

exactly

failures

thwill

success

occur

when

before

the probability

the

each trial, and

=NEGBINOM.DIST(f,s,p,1)

-gives th

cur before

th success

the

when the probability of succes

Chapter

The

63Binomial, Hypergeometric, and Negative

521

Binomial Random Variables

consider a baseball team that wins 40 percent o

and Figure 63-4). Copying from E9 to E34 the f

the probability of 0, 1, 2,…, 25 losses occurr

equals a game won. For example, there is a 19.

one game before winning two games. In cell G10 I u

NEGBINOM.DIST(3,2,0.4,TRUE)

to compute the chance that

occur

at m

before our team wins two games (0.663). Of cou

simply adding up the shaded cells (E9:E12).

Fig

URE 63-4

Using the negative binomial random variable.

Problems

Suppose that, on average, 4 percent of all C

are defective. The company has adopted the f

each shipment, and accept the shipment if n

determine the following:

❑

What fraction of shipments will be accept

❑

If the policy changes so that a shipment i

sample is defective, what fraction of shi

❑

What is the probability that a sample siz

CD drives?

522

Microsoft Excel 2010: Data Analysis and Business Modeling

Using the airline overbooking data:

❑

Determine how the probability of overbookin

sold varies from 100 through 115. Hint: Use a o

❑

Show how the probability of overbooking var

varies from 100 through 115, and the probab

varies from 80 percent through 95 percent. Hi

Suppose that during each year, a given

beating

mutual f

the Standard & Poor’s 500 Stock Index (S&P In

what is the probability that at least 10 fund

out of 10 years?

Professional basketball player Steve Nash is a 9

❑

If he shoots 100 free throws, what is the p

15 shots?

❑

How good a foul shooter would Steve Nash be i

of making fewer than 90 free throws out of 1

When tested for extra sensory perception (ESP

shape of a card from a 25-card deck. The deck c

shapes. If a person identifes 12 cards correc

Suppose that in a group of 100 people, 20 hav

select 30 people, what is the chance that at l

A student is selling magazines for a school f

that a given house will buy a magazine. He ne

probability that he will need to visit 5, 6, 7

Use the BINOM.DIST function to verify that th

answer to our Village Deli example.

In the seventeenth century, French mathematic

were inspired to formulate the modern probabi

”Problem of the Points.” Here is a simple exa

coins. Fermat wins a point if a head is tosse

If Pascal is ahead 8-7 and the frst player wi

Pascal will win?

523

Chapter 64

The Poisson and Exp

Random Variable

Questions answered in this chapter:

■

What is the Poisson random variable?

■

How do I compute probabilities for the Pois

■

If the number of customers arriving at a ba

variable, what random variable governs the ti

Answers to This Chapter’s Ques

What is the Poisson random variable?

The

Poisson random variable

is a discrete rand

probabilities for situations in which events (

placed for a product) have a small probability o

specifcally, during a short

, either

time zero

interval,

or oneden

the probability of one event occurring during a s

.lHere, λ is the mean number of occurrences p

Situations in which the Poisson random variabl

■

Number of units of a product demanded durin

■

Number of deaths per year by horse kick in th

■

Number of car accidents you have during a y.

■

Number of copies of

The Seat of the Soul

■

Number of workers’ compensation claims fled a

■

Number of defects in 100 yards of string. (

524

Microsoft Excel 2010: Data Analysis and Business Modeling

How do I compute probabilities for the Poisson r

You can use the Microsoft Excel 2010 POISSON.DIS

involving the Poisson random variable. In earlie

yielded POISSON probabilities. Just

, theremember

mean of tha

Poisson random

. The

variable

syntaxisof

the POISSON function i

POISSON.DIST(x,Lambda,True

calculates the p

with a mean equal to

Lambda

is less than or equa

POISSON.DIST(x,Lambda,False

calculates the p

with a mean equal to

Lambda

is equal to

Here are some examples of how to compute probabi

can fnd these examples in the fle Poisson.xlsx, s

Fig

URE 64-1

Using the Poisson random variable.

Suppose that my consulting business receives an a

a two-hour period, I want to determine the follow

■

The probability that exactly 60 calls will be r

■

The probability that the number of calls rece

than or equal to 60

■

The probability that from 50 through 100 call

During a two-hour period, the mean probability

number of cal

(0.05) that exactly 60 calls will be received in th

POISSON.DIST(60,C2,False)

In cell C5, I fnd the probability (

be received in two hours with the

. Informula

cell C6,

POISSO

probability (0.916) that from 50 through 100 cal

formula

POISSON.DIST(100,C2,True)–POISSON.DIST(4

Not

ou can always use 1 instead of True as an argume

Chapter

The

64Poisson and Exponential

525

Random Variable

If the number of customers arriving at

variable,

bank i

what random variable governs the time between a

The time between arrivals can be any value, whi

continuous random variable. If an average of a

arrivals follows an exponential random variabl

f(t)=le

-lt

. This random variable has a mean, or av

graph of the exponential pdf is shown in Figur

this example in the

Density

worksheet in the fl

Fig

URE 64-2

Exponential probability density function.

Recall from Chapter 62, “An Introduction to Ra

variable, the height of the pdf for a number

assumes a .

value

You can

nearsee

in Figure 64-2 that ex

arrivals (for example, less than 0.05 hours) a

drops off sharply.

Even though the average time between arrivals i

chance that the time between arrivals will be a

EXPON.DIST(x,1/mean,True or 1)

will give the p

with a given

mean

will assume

. Thus,

a value

the less

second

thaa

to the EXPON.DIST function is the rate per tim

to compute the probability that the time betwe

copied from cell D5 to D7 the formula

. In earlier

1–EXPON.r

of Excel, the EXPONDIST function yields the sa

Note that I frst converted minutes to hours (5

mean time between arrivals is 0.033 hours,

so I e

In short, I entered the arrival rate per time u

526

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 64-3

Computations of exponential probabilities.

Problems

Beer drinkers order an average of 40 pitchers o

Bloomington, Indiana.

❑

What is the probability that at least 100 p

period?

❑

What is the chance that the time between or

less?

Suppose that teenage drivers have an average o

❑

What is the probability that a teenager wil

during a year?

❑

What is the probability that the time betwe

I am next in line at a fast food restaurant i

the time to serve a customer follows an expon

minutes. What is the chance that I will have t

Since 1900 a fraction (.00124) of all major l

no-hitters. A team plays 162 games in a seaso

two or more no-hitters during a season?

527

Chapter 65

The Normal Random V

Questions answered in this chapter:

■

What are the properties of the normal rando

■

How do I use Excel to fnd probabilities for th

■

Can I use Excel to fnd percentiles for norm

■

Why is the normal random variable appropria

Answers to This Chapter’s Ques

What are the properties of the normal random v

In Chapter 62, “An Introduction to Random Varia

variables can be used to model quantities such a

■

Price of Microsoft stock one year from now

■

Market share for a new product

■

Market size for a new product

■

Cost of developing a new product

■

Newborn baby’s weight

■

A person’s IQ

Remember that if a discrete random variable (s

caa

nssume many possible values, you can approxi

random variable as well. As I described in Cha

hasprobability density function (pdf). The pdf f

negative function with

the

and following

are arbitrary

propertie

num

■

The area under the pdf is 1.

■

The probability

equals

that

the

probability

. This probability

that

X≤a

by the area under .

the pdf to the left of

■

The probability

equals

that

the

probability

. This probability

that

X≥b

the area under the

. pdf to the right of

■

The probability that

a<X<b

equals

. This the

probabilit

area under the pdf

between

and

528

Microsoft Excel 2010: Data Analysis and Business Modeling

Thus, the area under a continuous random variabl

larger the value of, thedensity

more likely

function

the random

a value

. near

For example,

if the density function of a r

density function of the random variable at 5, th

take on a value near 20 than a value near 5.

For a continuous random variable, the probabilit

example, some people are from 5.99999 feet throu

exactly 6 feet tall. This explains why you can r

or equal to sign (≤) in the probability statemen

Figure 65-1 displays the pdf for

X=IQ

of a rando

is 1. If you want to fnd the probability-that a p

ply fnd the area to the left of 90. If you want t

95 through 120, you fnd the area under the pdf f

probability that a person’s IQ is more than 130, y

to the right of 130. (See the

IQ Density

workshe

Fig

URE 65-1

IQ pdf.

Actually, the density plotted in Figure. 65-1

The is a

normal random variable is specifed by its mean a

random variable with µ=100 and σ=15. This is the p

random variable has the following properties:

■

The most likely value of a normal random varia

at 100 in Figure 65-1).

■

As the value

of the random variable moves a

random variable is near

sharply decreases.

■

The normal random variable is symmetric about i

as likely as IQs near 120.

Chapter

The

65Normal Random

529

Variable

■

A normal random variable has 68 percent of i

percent within 2σ of its mean, and 99.7 per

should remind you of the rule of thumb I de

by Using Descriptive Statistics.” In fact, t

that data is “sampled”, from

whicha explains

normal distrib

why th

does not work as well when the data fails t

For a larger σ, a normal random variable

pattern

is mo

is illustrated in Figures 65-2 and 65-3. (See th

Normalexamples.xlsx.)

Fig

URE 65-2

Normal random variable pdf with a mean equal to 6

Fig

URE 65-3

Normal random variable pdf with a mean equal to 6

How do I use Excel to find probabilities for th

Consider a normal random variable

with a mea

for any number

, you want to fnd the probabil

cumulative

. To

function

use Microsoft Excel 2010 to fnd th

formula

NORM.DIST(x,µ,

,1)

. Of course, the fourth argument o

530

Microsoft Excel 2010: Data Analysis and Business Modeling

The argument

tells Excel to compute the normal c

function

, Excel

returns the actual value of the no

statistical functions (like NORM.DIST) have

been m

vide better accuracy than their counterparts (li

You can use the NORM.DIST function to answer man

probabilities. You can fnd examples in the

Norma

Normalexamples.xlsx, which is shown in Figure 65

Fig

URE 65-4

Calculating normal probability.

■

What fraction ofQ people

of less

have

Let

than

90?

equal

the IQ o

randomly chosen person. Then

<90,

you which

seek the

is equa

pro

to the probability

90. Therefore,

that

X≤

you can enter into c

worksheet the formula,

NORM.DIST(90,100,15,1)

and Excel returns 0.25

percent of all people have an IQ less than 90

■

What fraction ofQs

all

from

people

95 through

have

When fnding

120?

the probability

, youthat

use

a≤X≤b

the form

(area- under the n

tion to the

)–(area

leftunder

normal density

)

. Thus,

function

you

can fnd the probability that

a≤X≤b

–

enterin

NORM.DIST(a,µ,s,1)

This fact is illustrated in Figure 6

area is

)–(area

to left

)to

. You

left

can

answer the questi

from 95 through 120 by entering into cell C4 o

NORMDIST(120,100,15,1)–NORMDIST(95,100,15,1)

. Excel returns the pro

so 53.9 percent of all people have an IQ from 9

Probability a<=X<=b

Fig

URE 65-5

Calculating the probability that

. a random varia

■

What fraction ofQs

all

of people

at least

have

fnd

130?

the

probabili

≥

, note in Figure 65-6≥

that

equals

the

1–probability

. You

can compute the ≥probability

by entering

that

the

formula

,1)

1–N

Chapter

The

65Normal Random

531

Variable

You seek the probability

≥130. This equals

that

1–probabilit

You enter i

C5 of the worksheet

Normal

the .formula

Excel retur

1–NO

0.023, so you know that 2.3 percent of peop

Probability X>=b

Fig

URE 65-6

Calculating that the probability random varia

Can I use Excel to find percentiles for normal r

Consider a given normal random variable

with m

situations, you want to answer questions such a

■

A drug manufacturer believes that next year

will be normally distributed, with mean equ

sigma equal to 5 million DOT. How many units o

year if the company wants to have only a 1 p

■

Family income in Bloomington, Indiana, is n

to $30,000 and sigma equal to $8,000. The p

Bloomington are eligible for federal aid. W

In the frst example, you want to determine the ni

antidepressant. That is, you seek the number

demand will exceed

and a 99 percent

. Inchance

the sec

example, you want the tenth percentile of fami

the number

such that there is only a 10 perc

and a 90 percent chance .that family income w

Suppose you want

th percentile

to fnd the (expressed as a de

variable

with a mean and a standard deviatio

NORM.INV(p,µ,

)

into Excel. This formula returns a nu

that

X≤x

equals the specifed percentile. You n

exercises on the

Normal

worksheet in the fle N

For the drug manufacturing example, let

equa

value

such that≥

the

equals

probability

0.01 or that

the probabi

Again, you seek the ninety-ninth percentile

of d

ing in cell C7 the formula

. Excel

NORM.INV(0.99,60,5)

returns 71.63, so th

produce 71,630,000 DOT. This assumes, of cours

no supply of the drug on hand. If, for example

DOT, they would need to produce 61,630,000 DOT d

532

Microsoft Excel 2010: Data Analysis and Business Modeling

To determine the cutoff for federal family,

aid, if

you seek a value of

such that the probability th

percentile of Bloomington family income. You fnd thi

INV(0.10,30000,8000)

Excel returns $19,747.59, so aid sho

incomes smaller than $19,749.59.

Why is the normal random variable appropriate in m

A well-known mathematical result called the

Cent

together many (usually at least 30 is suffcient) i

is normally distributed. This result holds true e

normally distributed. Many quantities (such as m

ing together many independent random variables, w

variable occurs often in the real world. Here ar

the Central Limit Theorem.

■

The total demand for pizzas during a month at a s

even if the daily demand for pizzas is not.

■

The amount of money you win if you play craps 1

even though the amount of money you win on ea

Another important mathematical result shows how t

deviations of sums of independent random

- variabl

dent random variables

,…,

where mean

=µ

, and standard deviation

=σ

then the

following are true:

Mean

(

+…

)=µ

+µ

+…

Variance

+…

(

)

+...?

Standard

deviation

+…

(

...?

Note that 1 is true even when the random variabl

through 3 with the Central Limit Theorem,

you ca

lems, such as the demand for pizza. Our pizza so

the fle Normalexamples.xlsx, which is shown in Fi

Fig

URE 65-7

Using the Central Limit Theorem.

Chapter

The

65Normal Random

533

Variable

Even though the daily demand for frozen pizzas i

the Central Limit Theorem that the 30-day dema

Given this, 1 through 3 above imply the follow

■

From 1, the mean of a 30-day

demand equals

■

From 2, the variance of a 30-day demand equ

=4,320

■

From 3, the standard deviation

4320 = 65.73

of a 30-day d

Thus, the 30-day demand for pizzas can be mode

with a mean of 1,350 and a standard deviation o

ity that at least 1,400 pizzas are sold as the p

least 1,399.5 (note that a demand of 1,399.6, f

formula

1–NORM.DIST(1399.5,D7,D9,TRUE)

fnd the probability tha

period for at least 1,400 pizzas is 22.6 perce

The number of pizzas that you must stock to ha

of pizzas is just the ninety-ninth percentile o

ninety-ninth percentile of the demand distribu

NORM.INV(0.99,D7,D9)

Therefore, at the beginning of a m

of pizzas up to 1,503 if you want to have only a 1 p

Problems

Suppose you can set the mean number of ounc

actual number of ounces has a standard devia

❑

If you set the mean at 12.03 ounces, and a s

least 12 ounces, what fraction of cans is a

❑

What fraction of cans have less than 12.1 o

❑

What should you set the mean to if you wa

contain at most 12 ounces? Hint: Use the G

Annual demand for a drug is normally distri

standard deviation of 10,000 units.

❑

What is the probability that annual deman

❑

If you want to have only a 5 percent chan

level should you set annual production?

534

Microsoft Excel 2010: Data Analysis and Business Modeling

The probability of winning a game of craps is 0

bet the same amount on each game, what is the p

determining the mean and standard deviation o

use the Central Limit Theorem.

Weekly sales of Volvo’s Cross Country station wa

mean of 1,000 and standard deviation of 250.

❑

What is the probability that during a week, f

wagons are sold?

❑

There is a 1 percent chance that fewer than w

sold during a week?

535

Chapter 66

Weibull and Beta Di

Modeling Machine Li

of a Project

Questions answered in this chapter:

■

How can I estimate the probability that a m

20 hours?

■

How can I estimate the probability that han

than 200 hours?

The

Weibull random variable

is a continuous ra

lifetime of a machine. If you have data about h

past, you can estimate

alpha

the

and

) two

that

beta

parameters

defne a Weibu

(

variable. You can then use the WEIBULL.DIST fu

probabilities of interest, such as an estimate o

The

Beta random variable

is a continuous rando

duration of an activity. Given estimates of th

duration, and the standard deviation of the du

Excel 2010 to determine probabilities of inter

Answers to This Chapter’s Ques

How can I estimate the probability that a mach

20 hours?

Suppose you have observed the lifetime of seve

the machines is contained in the fle Weibulles

Fig

URE 66-1

Machine lifetime data.

536

Microsoft Excel 2010: Data Analysis and Business Modeling

Reliability engineers have found that the Weibul

modeling machine lifetimes. The Weibull random v

alpha

and

. Based

beta

on the data, you can determine (u

functions in cells B13 and B14) that, on average

deviation of 7.40 hours. By copying these values t

with the settings shown in Figure 66-2, you can f

that the Weibull random variable will have a mea

In this case,

alpha

equals 2.725 and

beta

equals 2

value you enter for

alpha

and

beta

in cells E2 a

mean (computed in cell E6) and standard deviatio

varies

alpha

and

beta

until the mean and standar

the mean and standard deviation of machine

lifeti

mend using the Multistart option for the GRG Non

best with upper and lower bounds on the changing c

and

beta

will always work. I tried. an

If upper

the Solve

boun

makes

alpha

beta

bump up against your upper b

Fig

URE 66-2

Solver settings for determining parameters for a W

Chapter

Weibull

and Beta Distributions: Modeling

537

Machine Life and Duration of a Project

Fig

URE 66-3

Estimates of

alpha

and

beta

for a Weibull random v

Here’s the syntax of the WEIBULL.DIST function

WEIBULL.DIST(x,alpha,beta,Cumulative)

When

Cumulative

equals True, this formula

randomresu

variable with parameters

alpha

. Changing

and

beta

True

is les

False yields the height of the Weibull probabi

Chapter 62, “An Introduction to Random Variabl

of a continuous random variable indicates the l

value .near

Thus,

if the Weibull density for 20 hou

hours, you would know that a machine is twice a

than to work for 10 hours before failing.

Befo

abilities of interest, I’ll note that in prior v

the same

results as WEIBULL.DIST.

■

What is the probability that a machine

This

will l

probability (41.7 percent) is computed in ce

1–WEIBULL.DIST(20,alpha,beta,1)

Essentially, this formula c

the Weibull pdf to the right of 20 hours by s

20 hours.

■

What is the probability that a machine will l

hours?

This probability (66.9 percent) is comp

WEIBULL.DISTL(30,alpha,beta,TRUE)–WEIBULL.D

This formu

fnds the area under the Weibull pdf from 15 th

area to the left of 30 hours minus the area t

the probability of a machine working withou

probability of a machine working without fai

you are left with the probability that a ma

through 30 hours.

538

Microsoft Excel 2010: Data Analysis and Business Modeling

How can I estimate the probability that hanging d

200 hours?

Since the development of the Polaris missile in th

activity durations with the Beta random variable

need to specify a minimum value,

alpha

maximum

and

beta

value

The data in the fle Beta.xlsx (see Figure 66-4) c

Beta distribution.

Fig

URE 66-4

Determining probabilities with the Beta random var

Suppose that you believe that the time needed to h

between 0 and 600 hours. These are your minimum a

C7 and C8. The cell range F8:F22 contains the le

buildings of a similar size. In cell F5, I used th

(78.49 hours) needed to hang drywall in these

15 b

tion to determine the standard deviation (47.97 h

in these buildings. Any choice of values of

alph

distribution’s pdf and the mean and standard dev

variable. If you can choose

alpha

and

beta

value

of the drywall installation times computed

from t

pha

and

beta

values will yield probabilities con

the mean and standard deviation for the drywall i

worksheet computes values for

alpha

(2.20)

ensurein ce

that the mean and standard deviation of the Beta r

standard deviation of the data.

Chapter

Weibull

and Beta Distributions: Modeling

539

Machine Life and Duration of a Project

The function

BETA.DIST(x,alpha,beta, True or 1

a Beta random variable ranging

, withfrom

parameters

lower

, thro

alp

assumes a value less

. The

than

last

ortwo

equal

parameters

are o

omitted, Excel assumes

lower

equals 0 and

uppe

BETA.DIST(x,alpha,beta,False or 0,lower,upper)

following

a Beta distribution. You can now use the BETA.

interest.

To compute the probability that hanging drywal

the formula in cell C15,

1–BETA.DIST(200,alpha

The result i

percent. This formula simply computes the prob

200 hours as

1–probability dry walling

takes l

The probability that hanging drywall will take a

computed with the formula in cell C16,

. And

BETA.DI

to compute the probability that the task

will t

cent), in cell C17 I used the formula

BETA.DIS

DIST(30,alpha,beta,True,

. This formula

lower,upper)

computes the pr

takes from 30 through 150 hours as the probabi

to 150 hours minus the probability that dry wa

The difference between these probabilities cou

from 30 through 150 hours.

Problems

The data for this chapter’s problems is contai

In the

Problem 1

worksheet, you are given d

lifetime.

❑

What is the probability that the machine w

❑

What is the probability that the machine w

❑

What is the probability that the machine w

You need to clean your house today. In the

data about how long it has taken to clean y

at noon, what are the chances that you’ll b.

a movie?

541

Chapter 67

Making Probability S

Forecasts

Questions answered in this chapter:

■

On what basis do we evaluate forecasts?

■

If a drug company forecasts that it will se

the chance it will sell more than 65 million u

Each day we are constantly inundated by foreca

■

The government predicts the GNP will grow by 4 p

■

The Eli Lilly marketing department predicts th

given drug will be 400,000,000 DOT (days of th

■

A Wall Street guru predicts the Dow will go u

■

The bookmakers forecast that the Indiana Pa

in the opening game of the 2015 NBA season.

Although the forecasts we receive may be the b

incorrect. For example, the bookmaker’s predic

is incorrect unless the Pacers win by exactly s

forecast) implies a distribution for the quanti

forecast and fnd a random variable that correc

point forecast? The key to putting a distributi

historical data about the accuracy of past for

with regard to the forecast for the Dow Industr

years the forecast made in January of each yea

the actual change in the Dow for each of the 1

542

Microsoft Excel 2010: Data Analysis and Business Modeling

Answers to This Chapter’s Quest

On what basis do we evaluate forecasts?

You can begin by seeing whether

. For

past

each

forecast,

forecasts

past

youe

determine the actual value/forecasted value. The

are

unbiased

, this average should be around 1. Any sig

signifcant bias. For example, if

actual

the average

results of

tena

be around twice the forecast.

automatically

To correct for

double

a b y

forecast. If the average of actual/forecasted is .

actual forecast, so

automatically

eliminate bias

halve

youyour

should

eliminate forecast bias, you look at the standar

unbiased forecast

following

and use

normal

the random variable t

being forecasted:

■

Mean = the unbiased forecast

■

Standard deviation = (unbiased forecast)*(sta

associated with the unbiased forecasts).

The standard deviation of the percentage errors m

Clearly, a smaller standard deviation of percent

standard deviation.

The fle Drugfore.xlsx (see Figure 67-1) illustra

accuracy. The fle contains actual and forecasted s

2005–2012. I’ll frst show that these forecasts a

Fig

URE 67-1

Correcting for forecast bias and measuring forecas

Chapter

Making

Probability Statements

543

from Forecasts

To begin, in cells F5:F12 I check for bias by c

sales. To do this, I copy from

F5 to F6:F12 th

Next, in cell F2, I compute the bias of the or

forecasted value with the

I fnd

formula

that

AVERAGE(F5:F

actual sale

8 percent under forecast. To correct past bias

from G5 to G6:G12 .the

In H5:H12

formula

$F$2*E5

compute each yea

for the unbiased forecast by copying. from

As you

H5 ct

see, for example, 2005 actual sales were 16 pe

2011 actual sales were 19 percent larger than th

Now I evaluate the accuracy of the forecast er

deviation of the percentage errors

. I fnd

with the

stan

deviation of past unbiased forecasts has been a

If a drug company forecasts it will sell 60 mi

chance it will sell more than 65 million units o

Forecast errors often follow a normal random v

you can assume forecast errors follow a normal r

■

Mean = the unbiased forecast.

■

Standard deviation = (unbiased forecast)*(s

associated with the unbiased forecasts).

In our example, this means that you should mod

variable with mean = 60(.918) = 55.08 million a

million. You can now use the Excel NORM.DIST f

(see Figure 65-2) the chance of selling at lea

1-NORM.DIST(65,F15,F16,TRUE)

There is a 5.7 percent chance o

units of the drug.

Fig

URE 67-2

Chance of selling more than 65 million units of d

544

Microsoft Excel 2010: Data Analysis and Business Modeling

Problems

In Game 7 of the Boston Celtics-Los Angeles L

favored by seven points. Looking at -past NBA g

ers’ forecasts are unbiased. Also, the standa

past NBA games is 12 points. Before the game, w

probability that the Lakers would win the gam

A leading cell phone company forecasts that i

bestselling phone. In the past, actual sales h

having a standard deviation equal to 10 perce

chances that less than 2.5 million phones wil

The fle USC.xlsx contains the USC football te

2005–2009 and the bookmaker’s forecast (befor

victory. Does this data indicate that the boo

favored by 10 points, estimate the chance tha

545

Chapter 68

Using the Lognormal R

Variable to Model S

Questions answered in this chapter:

■

What is the lognormal random variable?

■

Is there a reason stock prices might follow a l

■

How can I model the future price of any sto

■

How can I compute the probability that Micr

from now?

Many people are interested in modeling the fut

oil or wheat, or a future exchange rate. For th

has been the random variable most often used t

learn about why the lognormal random variable i

how to determine the appropriate lognormal par

by showing how the Excel LOGNORM.DIST and LOGN

calculate probabilities that involve the futur

Answers to This Chapter’s Ques

What is a lognormal random variable?

A random variable Y follows a lognormal random v

variable. When using the Excel LOGNORM.DIST an

random variable Y is characterized by two para

value of ln Y, and a standard deviation Sigma e

Is there a reason stock prices might follow a l

Let Y equal the price of a stock

days from n

equal

the percentage change in.the

Then

stock’s

Y = P*X

price dur

*…

X. Because th

logarithm of a product is the sum of the logar

+ ln X

+… ln X

. Suppose the changes in prices on differe

Recall from Chapter 65, “The Normal Random

Var

plies that the sum of many independent random v

even if the individual random variables are not n

likely to be a normal random variable, and thi

546

Microsoft Excel 2010: Data Analysis and Business Modeling

How can I model the future price of any stock as a l

At the close of trading on August 26, 2010, the p

you are interested in modeling the price -of Micr

dom variable. How can you estimate Mu

available

and Sigma? L

on the Internet to help you model the future pri

provides an estimate of a stock’s annual volatil

surrogate for a stock’s riskiness or variability

Microsoft’s implied volatility (see Figure 68-1) wa

a decimal, you write Sigma_ = .2718. (The method u

discussed in Chapter 74, “Pricing Stock Options.

Fig

URE 68-1

Implied volatility for Microsoft stock.

From the Investment section of fnance.yahoo.com, y

analysts for the price of Microsoft in a year, s

Fig

URE 68-2

Analyst’s forecasts for Microsoft stock price in o

Let S equal today’s stock price, and S

equal the estimated mean price i

a surrogate for the annual mean return on the st

S).

You know that S equals $24.10 and S

equals $33.06. Therefore (as c

fle Lognormal.xlsx; see Figure 68-3),

Mu_ = ln (

Chapter

Using

the Lognormal Random Variable

547

to Model Stock Prices

Fig

URE 68-3

Using the Lognormal to model the price of Micros

If you want to model the price of Microsoft st

= Mean of ln of Microsoft stock price in

= Standard deviati

Microsoft stock price in

years. It turns out th

= ln S +t(Mu_-.5Sigma_^2) and Sigma = Sigma_

For six months t =.5 years. In cell E9, I comp

ln(24.10)+..5*(.322

)

3.324815.

In cell E10 I computed Sigma

= (.2718)*

.5=

.192192.

Therefore, you can model the price of Microsof

variable with Mu = 3.324815 and Sigma = .19219

How can I compute the probability that Microso

from now?

The Excel 2010 function

x, Mean,

LOGNORM.DIST(

Sigma,

) computes

True

the

that a lognormal random variable with paramete

Changing True or 1 to False or 0, .returns the h

In previous versions of Excel, the function LO

LOGNORM.DIST. In cell F13, I determine the cha

will exceed $38. This is calculated

, so Iby

formula

use

1 –

the

Pro

1-LOGNORM.DIST(38,F9,F10,True)

There is only a 5.2 percent c

Microsoft will sell for more than $38 in six m

In cell F14 I determine the chance that a shar

$20 in six months with the formula

. There

LOGNORM.DIS

is a 4.3 p

chance that a share of Microsoft will sell for $

548

Microsoft Excel 2010: Data Analysis and Business Modeling

Suppose you want to determine the median price o

price

such

that there is a 50 percent chance that t

will be less

than

. In or

cell

equal

F15 to

I fnd

the median pric

formula

LOGNORM.INV(0.5,F9,F10)

The median price in six months i

Remarks

■

In Chapter 74, I discuss the famous Black-Sch

Scholes formula assumes that the price of a s

variable.

■

In recent years it has become apparent that f

extremely high or low values more often than th

This has caused analysts to search for other r

used to model future stock prices. For more d

best-selling book

. Also,

The Black

in Chapter

Swan

71, “Simulati

Asset Allocation Modeling,” I discuss an alte

that does not assume that future stock prices f

Problems

Suppose a stock sells for $30 today. The annual v

analysts predict the expected price of the stock i

answer Questions 1–3.

What is the probability that in two years the s

You are 95 percent sure that the price of the s

two values? Hint: Use .025 and .975 as the fr

function.

549

Chapter 69

Introduction to Mon

Simulation

Questions answered in this chapter:

■

Who uses Monte Carlo simulation?

■

What happens when I type

=RAND()

in a cell?

■

How can I simulate values of a discrete ran

■

How can I simulate values of a normal rando

■

How can a greeting card company determine h

Data analysts would like to accurately estimat

example, what is the probability that a new pr

present value (NPV)? What is the risk factor o

simulation enables you to model situations tha

on a computer thousands of times.

Not

The term

Monte Carlo simulation

comesduring

from the c

the 1930s and 1940s to estimate the probability th

bomb to detonate would work successfully. The phys

gambling, so they gave the simulations

the code na

In the next fve chapters, I provide some examp

to perform Monte Carlo simulations.

Answers to This Chapter’s Ques

Who uses Monte Carlo simulation?

Many companies use Monte Carlo simulation as a

process. Here are some examples.

■

General Motors, Proctor and Gamble, Pfzer, B

simulation to estimate both the average ret

At GM, this information was used by former C

products came to market.

550

Microsoft Excel 2010: Data Analysis and Business Modeling

■

GM uses simulation for activities such as for

predicting structural and purchasing costs,

ent kinds of risk (such as interest rate chan

■

Lilly uses simulation to determine the optima

■

Proctor and Gamble uses simulation to model a

risk.

■

Sears uses simulation to determine how many u

ordered from suppliers—for example, the numbe

should be ordered this year.

■

Oil and drug companies use simulation to valu

option to expand, contract, or postpone a proj

■

Financial planners use Monte Carlo simulation t

strategies for their clients’ retirement.

What happens when I type =RAND() in a cell?

When you type the formula

=RAND()

in a cell, you g

assume any value between 0 and 1. Thus, around 2

number less than or equal to 0.25; around 10 per

that is at least 0.90, and so on. To demonstrate h

the fle Randdemo.xlsx, shown in Figure 69-1.

Fig

URE 69-1

Demonstrating the RAND function.

Chapter

Introduction

to Monte

551

Carlo Simulation

Not

When you open the

Sheet1

worksheet in the fle R

random numbers shown in Figure 69-1. The RAND func

generates when a worksheet is opened or when new i

The

Frozen

worksheet has its values fxed to corres

I copied from cell C3 to. C4:C402

I named the formula

range

Then, in column F, I tracked the average of th

COUNTIF function to determine the fractions th

0.50 and 0.75, and 0.75 and 1. When you press th

culated. Notice that the average of the 400 nu

around 25 percent of the results are in interv

the defnition of a random number. Also note

ent cells are independent. For example, if the r

number (for example, 0.99), that tells you nothi

numbers generated.

How can I simulate values of a discrete random v

Suppose the demand for a calendar is governed by th

Demand

Probability

10,000

0.10

20,000

0.35

40,000

0.3

69,000

0.25

How can you have Excel play out, or simulate, t

trick is to associate each possible value of th

calendars. The following assignment ensures th

of the time, and so on.

Demand

Random number assigned

10,000

Less than 0.10

20,000

Greater than or equal to 0.10, and less t

40,000

Greater than or equal to 0.45, and less t

69,000

Greater than or equal to 0.75

To demonstrate the simulation of demand, look a

Discretesim.xlsx (or its

Frozen

version shown i

552

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 69-2

Simulating a discrete random variable.

The key to this simulation is to use a random nu

range F2:G5 (named

). Random

lookup

numbers greater than or eq

will yield a demand of 10,000; random numbers gr

0.45 will yield a demand of 20,000; random numbe

than 0.75 will yield a demand of 40,000; and ran

will yield a demand of 69,000. I generated 400 r

C4:C402 the formula

. I then

RAND()

generated 400 trials, or i

by copying from B3 to B4:B402 .the

This formula

VLOOKU

ens

that any random number less than 0.10 generates a d

between 0.10 and 0.45 generates a demand of 20,0

I used the COUNTIF function to determine the fra

demand. When I press F9 to recalculate the rando

close to the assumed demand probabilities.

How can I simulate values of a normal random var

If you type in any cell the ,formula

you will

NORM.INV(ran

simulated

generate a

value of a normal random variable having

sigma

. I’ve

a mean

illustrated this procedure in the

Sim

worksheet i

the

Frozen

version).

Chapter

Introduction

to Monte

553

Carlo Simulation

Fig

URE 69-3

Simulating a normal random variable.

Let’s suppose you want to simulate 400 trials f

of 40,000 and a standard deviation of 10,000. (

named these cells

, respectively.)

mean

and

sigma

Copying the fo

C5:C403 generates 400 different random numbers

NORM.INV(C4,mean,sigma)

generates 400 differen

able with a mean of 40,000 and a standard devia

to recalculate the random numbers, the mean re

deviation close to 10,000.

Essentially, for, athe

random

formula

number

NORM.INV(p,mean,s

th percentile of a normal random variable

sigma

. with a m

For example, the random number 0.87 in cell C4 (

approximately the eighty-seventh percentile of a n

40,000 and a standard deviation of 10,000.

554

Microsoft Excel 2010: Data Analysis and Business Modeling

How can a greeting card company determine how ma

In this section, I’ll demonstrate how Monte Carl

making tool. Suppose that the demand for a Valen

following discrete random variable:

Demand

Probability

10,000

0.10

20,000

0.35

40,000

0.3

69,000

0.25

The greeting card sells for $4.00, and the varia

Leftover cards must be disposed of at a cost of $0

printed?

Basically, you simulate each possible production q

many times (for example, one thousand iterations

yields the maximum average proft over the one th

for this section in the

Sim

worksheet in the fle

Figure 69-4). I assigned the range names in cell

range G3:H6 the

. The

name

sales

lookup

price and cost paramete

Fig

URE 69-4

Valentine’s Day card simulation.

I then enter a trial production quantity (40,000 i

random number in cell C2. with

As previously

the formula

describe

=RAND(

demand for the card in cell C3 with

. (In the

formula

VLOOKU

formula,

rand

is the cell name assigned to cell C3

The number of units sold is the smaller of the p

compute revenue with the formula

. In

MIN(produced,de

cell C9, I c

total production cost with the

formula

produced*

Chapter

Introduction

to Monte

555

Carlo Simulation

If more cards are produced than are in demand, t

production minus demand; otherwise no units ar

cell C10 with the formula

unit_disp_cost*IF(pr

. Finally,

in cell C11, I compute proft as

revenue–

total

It would be nice to have an effcient way to pr

for each production quantity and tally the exp

one in which a two-way data table comes to the r

with Data Tables,” for details about data tabl

shown in Figure 69-5.

Fig

URE 69-5

Two-way data table for greeting card simulation.

In the cell range A16:A1015, I entered the num

trials). One easy way to create these values i

and then on the Home tab in the Editing group, c

select Series to display the Series dialog box

enter a step value of 1 and a stop value of 1,

option, and then click OK. The numbers 1 throu

in cell A16.

556

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 69-6

Using the Series dialog box to fll in the trial num

Next I enter the possible production quantities (

B15:E15. I want to calculate proft for each tria

production quantity. I refer to the formula for p

cell of the data table

(A15) by entering

=C11

You can now trick Excel into simulating one thou

production quantity. Select the table range (A15

on the Data tab, click What If Analysis, and the

table, choose the production quantity (cell C1) a

(I chose cell I14) as the column input cell. Aft

demand values for each order quantity.

To understand why this works, consider the value

C16:C1015. For each of these cells, Excel uses a v

input cell value of 1 is placed in a blank cell, a

The corresponding proft is then recorded in cell C

is placed in a blank cell, and the random number i

proft is entered in cell C17.

By copying from cell B13 to C13:E13

, you the

can formula

compute

average simulated proft for each production quan

the formula

STDEV(B16:B1015)

, you can compute the standard dev

profts for each order quantity. Each time you pr

are simulated for each order quantity. Producing 4

expected proft, so producing 40,000 cards appear

Chapter

Introduction

to Monte

557

Carlo Simulation

The Impact of Risk on Our Decisi

If you produce 20,000 instead of 40,000 cards, t

percent, but risk (as measured by the standard d

Therefore, if you are extremely averse to risk

decision. Incidentally, producing 10,000 cards a

because if you produce 10,000 cards, you will a

Not

n this workbook I set the Calculation option t

Calculation command in the Calculation group on th

data table does not recalculate unless you press F

table will slow down your work if it recalculates

sheet. Note that in this example, whenever you pre

because each time you press F9, a different sequen

to generate demands for each order quantity.

Confidence Interval for Mean Profi

A natural question to ask in this situation is

that the true mean proft will fall? This inter

for mean

. A

proft

95 percent confdence interval for th

computed by the following formula:

Mean Profit

1.96 *

profitst.dev

number iterations

In cell J11, I computed the lower limit for th

when 40,000 calendars are produced with

. In the

cellfo

J12, I computed the upper limit for the 95 per

D13+1.96*D14/SQRT(1000)

These calculations are shown in Fi

Fig

URE 69-7

Ninety-fve percent confdence interval for mean p

You can be 95 percent sure that your mean prof

between $55,076 and $61,008.

558

Microsoft Excel 2010: Data Analysis and Business Modeling

Problems

An auto dealer believes that demand for 2015 m

with a mean of 200 and a standard deviation o

$25,000, and he sells an Envoy for $40,000. H

can be sold for $30,000. He is considering or

Envoys. How many should he order?

A small supermarket is trying to determine how m

should order each week. The owner believes th

following discrete random variable:

Demand

Probability

0.10

0.20

0.30

0.25

0.15

The supermarket pays $1.00 for each copy of

copy can be returned for $0.50. How many copi

559

Chapter 70

Calculating an Opti

Questions answered in this chapter:

■

How do I simulate a binomial random variabl

■

How can I determine whether a continuous ra

normal random variable?

■

How can I use simulation to determine the o

When bidding against competitors on a project, t

the number of competitors and the bids submitt

you’ll make a lot of money on each project, bu

low, you’ll work on lots of projects but make v

bid is somewhere in the middle. Monte Carlo si

the bid that maximizes expected proft.

Answers to This Chapter’s Ques

How do I simulate a binomial random variable?

The formula

BINOM.INV(n,p,rand())

simulates th

trials, each of which has .a As

probability

explained of

in suc

“Introduction to Monte Carlo Simulation,” the R

likely to assume any value between 0 and 1. As s

Figure 70-1), when you press F9, the formula

simulates the number of free throws that Steve

makes in 100 attempts. The formula

BINOM.INV(1

ber of heads tossed in 100 tosses of a fair co

simulates the number of competitors entering th

three possible entrants and each competitor is a

entering the market. Of course,

in D3:D5, I en

560

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 70-1

Simulating a binomial random variable.

How can I determine whether a continuous random v

normal random variable?

Let’s suppose that you think the most likely bid by a c

normal probability density function (pdf)

is sym

mine whether a normal random variable can be use

to test for symmetry about the bid’s mean. If th

the mean of $50,000, bids of $40,000 and $60,000

be approximately equally likely. If the symmetry a

model each competitor’s bid as a normal random v

How can you estimate the standard deviation of e

rule of thumb discussed in Chapter 42, “Summariz

that data sets with symmetric histograms have ro

standard deviations of the mean. Similarly, a no

probability of being within two standard deviati

percent sure that a competitor’s bid will be bet

2*(standard deviation of competitor’s bid)

equal

competitor’s bid equals $10,000.

If the symmetry assumption is reasonable, you ca

formula

NORM.INV(rand(),50000,10000)

(See Chapter 69 for details a

normal random variables using the NORM.INV functi

How can I use simulation to determine the optima

Let’s assume that you’re bidding on a constructi

complete. It costs $1,000 to prepare your bid. Y

estimate that there is a 50-percent chance that e

competitor places a bid, its bid is assumed to f

equal to $50,000 and a standard deviation equal t

preparing bids that are exact multiples of $5,00

Chapter

Calculating

an Optimal

561

Bid

proft? Remember, the low bid wins! You’ll fnd th

Bidsim.xlsx, shown in Figures 70-2 and 70-3.

Fig

URE 70-2

Bidding simulation model.

Fig

URE 70-3

Bidding simulation data table.

Your strategy should be as follows:

■

Generate the number of bidders.

■

For each potential bidder who actually bids

model the bid. If a potential bidder does n

$100,000) to ensure that they do not win th

■

Determine whether you are the low bidder.

562

Microsoft Excel 2010: Data Analysis and Business Modeling

■

If you are the low bidder, you earn a proft e

$1,000 (the cost of making the bid). If you a

cost of the bid.

■

Use a two-way data table to simulate each pos

$35,000, … $60,000) one thousand times, and th

expected proft.

To begin, I assigned the names in the cell range D

E3 the number of bidders with

. the

Cellformula

F3 contains

BINOM.

formula. Next I determine which of the potential b

E10:E14 the formula

IF(D9<=Number_bidders,”yes”,

I then generate a bid for each bidder copying

(nonbidder

from cell F9 to F10:F14 the formula

IF(E9=”yes”,

Each cell in the cell range G9:G14 contains the R

whether I am the low bidder and win the project w

IF(mybid<=MIN(F9:F14),”yes”,”no”)

. In cell D19, I compute proft wi

IF(D17=”yes”,mybid–costproject–cost_

bid,–cost_bid)

recognizing that I recei

amount of the bid and pay project costs if I win th

Now I can use a two-way data table (shown in Fig

between $30,000 and $60,000. I copy the.proft to c

Then I select the table range D22:K1022. On the Da

What-If Analysis and then click Data Table to sp

column input cell is any blank cell in the works

of the bid). Clicking OK in the Data Table dialo

thousand times.

Copying from E21 to F21:K21 the formula

AVERAGE(

each bid. Each time I press F9, I see that the m

by bidding $40,000.

Problems

How would the optimal bid change if you had 1

Suppose you are bidding for an oil including

well that y

the cost of developing and mining the oil) in p

against you, and each competitor’s bid is ass

with a mean of $30 million and a standard dev

(within $1 million)?

Chapter

Calculating

an Optimal

563

Bid

A commonly used continuous random variable i

uniform random variable—written

is equally likely

U(a,b)—

-to as

tween two given.numbers

Explain

why

andthe

formula

a+(

used to simulate

U(a,b)

Investor Peter Fischer is bidding to take o

equally likely to be worth any amount betwe

company itself knows its true value. Peter i

immediately estimate the frm’s value at 50 p

should Peter bid per share for this company

Seattle Mariner baseball player Ichiro Suzu

contract. Salary arbitration in Major Leagu

submits a salary that he thinks he should b

(without seeing the salaries submitted by th

The player is then paid the submitted salar

For example, suppose Ichiro submits a -$12 mi

mit a $7 million offer. If the arbitrator sa

$12 million, whereas if the arbitrator says a f

$7 million. Assume that the arbitrator’s es

between $8 and $11 million, and the team’s

tween $6 million and $9 million. Within $1 mi

565

Chapter 71

Simulating Stock Pr

Allocation Modeling

Questions answered in this chapter:

■

I recently bought 100 shares of GE stock. W

year this investment will return more than 1

■

I’m trying to determine how to allocate my i

T-Bills, and bonds. What asset allocation o

expected return of at least 10 percent and mi

The last few years have shown that future retu

Chapter 68, I showed how to use the lognormal r

Many fnancial experts have been critical of us

stock prices because the lognormal underestima

called

black

“ swans”). In this chapter, I’ll explai

uncertainty in future investment returns.. This a

Essentially, bootstrapping simulates future in

will be similar to the past. For example, if y

year, you can assume that each month’s percent

one of, for example, the percentage changes fo

you to easily generate thousands of scenarios f

addition to scenarios that assume that future v

threecent past, you can easily adjust bootstrap

investments will be less or more favorable tha

After you’ve generated future scenarios for in

the Microsoft Excel Solver to work out the ass

allocate your investments to attain the level o

risk?

The following two examples demonstrate the sim

approach.

566

Microsoft Excel 2010: Data Analysis and Business Modeling

Answers to This Chapter’s Quest

I recently bought 100

. What

is the

of GE

probability

stock

tha

year this investment will return more than 10 pe

Let’s suppose that GE stock is currently selling f

returns on GE (as well as for Microsoft and Inte

July 2002 is included in the fle Gesim.xlsx, show

ending on August 2, 2002 (basically, this is Jul

include dividends (if any) paid by each company.

Fig

URE 71-1

GE, Microsoft, and Intel stock data.

The price of GE stock in one year is uncertain, s

of variation in the price of GE stock one

year f

ply estimates a return on GE during each

- of the n

turn

during each month is equally likely to be any o

In other words, the return on GE next month is e

the cell range F5:F64. To implement this idea, y

choose a “scenario” for each of the next 12 month

for next month, you use the return for GE in cel

the range, as next month’s return. The results a

values because the RANDBETWEEN function automati

you open the worksheet.)

Chapter

Simulating

Stock Prices and

567

Asset Allocation Modeling

To begin, you enter GE’s current price

generate

per sha

a scenario for each of the next 12 months by c

RANDBETWEEN(1,60)

. Next you use a lookup table to obt

scenario. To do this, you simply copy from

L6 t

As the formula indicates, the

, with

range

theB5:F64

returns

isfn

the ffth column of the lookup range. In the sc

for example, that the return for GE twelve mon

data point, that is, a -10.9 percent return. (

Figure 71-1.)

Fig

URE 71-2

Simulating GE stock price in one year.

Copying from M6 to M7:M17 the formula

(1+L6)*J

price. The formula takes the form.

(1+

Finally,

month’s

from J7 to J8:J17 the formula

=M6

computes the b

the previous month’s ending price.

You can now use a data table to generate one th

year and the one-year percentage return on you

Figure 71-3. In cell J19, you copy

. In

the

cell

ending

K19,py

enter the formula

(M17–$J$6)/$J$6

Ending

to compute

GE price

Beginning GE price)/Beginning

GE price

568

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 71-3

Data table for GE simulation.

Next, select the table range (J19:K1019), click W

Data tab, and then select Data Table. You set up a

cell as the column input cell. After you click O

one thousand scenarios for GE’s stock price

in o

book has been set to Automatic Except For Tables o

dialog box. You need to press F9 if you want to s

In cells M20:M24, I used the COUNTIF function (s

COUNT, COUNTA, and COUNTBLANK Functions”) to sum

occur in one year. For example, in cell M20, I c

one year with the formula

COUNTIF(returns,”<0”)/

(I named the range con

one thousand simulated

.) The

returns

simulation

Returns

indicates th

for 1997–2002, there is roughly a 40-percent cha

during the next year. You can also see the follow

■

There is a 45-percent probability that return

■

There is a 15-percent probability that return

■

There is a 12-percent chance that the investm

■

There is a 28-percent chance that the investm

■

The average return for the next year will be a

Many pundits believe that future stock returns w

Suppose you feel that in the next year, GE will p

than it performed during the 1997–2002 period

corporate this assumption into a simulation by c

M17 to

(1+L17)*J17–0.05*J6

This simply reduces the ending GE p

price, which reduces your returns for the next y

the fle Gesimless5.xlsx, shown in Figure 71-4.

Chapter

Simulating

Stock Prices and

569

Asset Allocation Modeling

Fig

URE 71-4

Pessimistic view of the future.

Note that the estimate is now a 50-percent cha

during the next year. The average is not exactl

because each time you run one thousand iterati

I’m trying to determine how to allocate my inv

and bonds

. What asset allocation over a five-year p

expected return of at least 8 percent and mini

A key decision made by individuals, mutual fun

allocate assets between different asset classe

for these asset classes. A reasonable approach t

generate one thousand simulated values for th

then use the Excel Solver to determine an asse

minimizes risk. As an example, suppose you are g

bonds during the period 1973–2009. You are inv

based on the historical data, you want to know w

(as measured by standard deviation) of annual r

of at least 10 percent. You can see this data i

(Not all the data is shown.)

Fig

URE 71-5

Historical returns on stocks, T-Bills, and bonds

570

Microsoft Excel 2010: Data Analysis and Business Modeling

To begin, you use bootstrapping to generate one th

T-Bills, and bonds in fve years. Assume that eac

(See Figure 71-6.)

For each asset class, you enter an initial unit p

copying from K10 to K11:K14 the, formula

you generate

RANDBETW

scenario for each of the next fve years. For exa

similar to 1985; the following year will be simi

L10:N14 the formula

H10*(1+VLOOKUP($K10,lookup,L

for each asset class. For stocks, for example, t

(Ending year t stock value)=(Beginning year t stock value)*(1+Year

Fig

URE 71-6

Simulating fve-year returns on stocks, T-Bills, an

Copying from H11 to H11:J14 the formula

=L10

com

the beginning of each successive year.

You can now use a one-way data table to generate o

stocks, T-Bills, and bonds in fve years.-Begin by c

set class to cells I16:K16. Next select the tabl

Data tab, and then click Data Table. Use any bla

one-way data table. After clicking OK in the Dat

simulated values for the value of stocks, T-Bill

note that this approach models the fact that

sto

dently. In each of the fve years, the stock, T-B

the same row of data. This enables the -

bootstrap

dence of returns on these asset classes that has b

Problem 7 at the end of this chapter for concret

models the interdependence between the returns o

Chapter

Simulating

Stock Prices and

571

Asset Allocation Modeling

With this setup, we’re ready to fnd the optima

Assetallocationopt.xlsx, shown in Figure 71-7. T

fve-year asset values and paste them into a bl

In cells C2:E2, I enter trial fractions of our a

respectively. In cell F2, I add these asset

Later, I’ll add the constraint

F2=1

to the Sol

of our money in one of the three asset classes

Fig

URE 71-7

Optimal asset allocation model.

Next I want to determine the fnal portfolio

calculatio

I can use a formula such as

(Final portfolio v

(Final value of T-bills)+(Final

. Copying from

value

cell

bonds

to F

SUMPRODUCT(C4:E4,$C$2:$E$2)

determines the fna

The next step is to determine the annual retur

scenario that Excel generated. Note that

(1+ A

equals

(Final portf

(Initial portfolio

. Because

value)

the initial portfolio valu

Annual return

equals

(Final portfolio value)

–

By copying from cell G4 to G5:G1003

, I compute

the formul

the an

return for each scenario during the fve-year s

G4:G1003 (which contains the simulated annual r

annual return in cell I3 with the formula

AVER

annual returns in cell I4 .with the formula

STD

Now I’m ready to use Solver to determine the s

expected annual return of at least 8 percent y

annual returns. The Solver Parameters dialog b

in Figure 71-8.

572

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 71-8

Solver Parameters dialog box set up for our asset a

■

I try to minimize the standard deviation of th

■

The changing cells are the asset allocation w

■

I must allocate 100 percent of the

F2=1

money I ha

■

The expected annual return

I3>=0.08

must

be at least 8 p

■

I assume that no short sales are allowed, whi

the money in each asset class to be nonnegati

Make Unconstrained Variables Non-Negative che

■

The minimum risk asset allocation is 24.3 per

bonds. This portfolio yields an expected annu

standard deviation of 2.3 percent.

Suppose you believe that the next 5 years will, o

are 5 percent worse than they’ve been for the la

expectations into the simulation. (See Problem 4 at th

Chapter

Simulating

Stock Prices and

573

Asset Allocation Modeling

Problems

Problems 1-3 utilize data in the fle Gesim.xls

Assume that the current price of Microsoft s

probability that in two years the price of Mi

Solve Problem 1 again, but this time with th

years, Microsoft will on average perform 6 p

during the 1997–2002 period for which you hv

Assume that the current price of Intel is $

during the next three years, you will earn at l

year period) on a purchase of Intel stock?

Problems 4 through 7 utilize data in the fl

Suppose you believe that over the next fve y

5 percent worse per year, on average,- than th

tion between stocks, T-Bills, and bonds tha

6 percent yet minimizes risk.

Suppose you believe that it is two times mo

the next fve years will be more like the pe

For example, the chance that next year will b

that next year will be like 1980. This beli

more weight to the recent past. How would y

optimization model?

Many mutual funds and investors hedge

purchasing

the r

put options. (See Chapter 74, “Pricing Stock O

options.) How could an asset allocation mod

hedging strategy that uses puts?

Determine the correlations (based on the 19

stocks, T-Bills, and bonds. Then determine th

scenarios created by bootstrapping) between th

assets. Does it appear that the bootstrappi

between the returns on stocks, T-Bills, and b

575

Chapter 72

Fun and Games: Simu

Gambling and Sporti

Probabilities

Questions answered in this chapter:

■

What is the probability of winning at craps

■

In fve-card draw poker, what is the probabi

■

Going into the NCAA basketball Final Four, w

winning the tournament?

Gambling and following sporting events are pop

are exciting because you never know what’s goi

powerful tool that you can use to approximate g

Essentially, you estimate probability by playi

multiple times. If, for example, you have Micr

times and you win 4,900 times, you would estim

equal 4900/10,000, or 49 percent. If you play o

times and Syracuse wins 300 of the iterations, y

winning the championship as 300/1,000, or 30 p

Answers to This Chapter’s Ques

What is the probability of winning at craps?

In the game of craps, a player rolls two dice. I

If the combination is 7 or 11, thenumber,

player wins

the

player continues rolling the dice until he or s

frst roll (called

) or rolls

the 7.

point

If the player rolls th

wins. If the player rolls 7 before rolling

the p

tions, you can show that the probability of a p

Excel to simulate the game of craps many times (

probability.

In this example, it is crucial to keep in mind th

will take. I will show that the chance of a ga

576

Microsoft Excel 2010: Data Analysis and Business Modeling

highly unlikely, so we’ll play out 50 rolls of th

as follows:

■

0 equals the game is lost.

■

1 equals the game is won.

■

2 equals the game continues.

The output cell keeps track of the status of the g

indicate a win and 0 to indicate a loss. You can r

shown in Figure 72-1.

Fig

URE 72-1

Simulating a game of craps.

In cell B2, I used the RANDBETWEEN function to g

frst roll by using the.formula

The

RANDBETWEEN(1,6)

function e

that each of its arguments is equally likely, so e

1, 2, 3, 4, 5, or 6. Copying this formula to the r

Figure 72-1, I hid rolls 8 through 48.)

In the cell range B4:AY4, I compute the total di

copying from B4 to C4:AY4

. Inthe

cell

formula

B5, Istatus

SUM(B2:B3)

determine th

after the frst roll with the formula

IF(OR(B4=2,

Remember that a roll of 2, 3, or 12 results in a l

results in a win (1); and any other roll results i

Chapter

Fun

72and Games: Simulating Gambling

577

and Sporting Event Probabilities

In cell C5, I compute the status of the game a

IF(OR(B5=0,B5=1),B5,IF(C4=$B4,1,IF(C4=7,0,2)))

. If the game ends on the fr

the status of the game. If a roll makes our po

a loss. Otherwise, the game continues. I added a

($B4) in this formula to ensure that each roll tr

Copying this formula from C5 to D5:AY5 records th

The game result is in cell AY5, which is copie

a one-way data table to play out the game of c

the formula

, which

=C6

tracks the fnal outcome of the g

select the table range (D9:E2009), click What-

tab, and then click Data Table. I choose a one

input cell. After I press F9, Excel simulates th

In cell E8, I can compute the fraction of the s

AVERAGE(E10:E2009)

. For the two thousand iterations, I w

I had run more trials (for example, 10,000 ite

probability of winning at craps (49.3%). For i

see Chapter 17, “Sensitivity Analysis with Dat

In five-card draw poker, what is the probabilit

An ordinary deck of cards contains four cards o

so on, up to four kings. To estimate the proba

can assign the value 1 to an ace, 2 to a deuce

assigned the value 11, a queen is assigned 12, a

In fve-card draw poker, you are dealt fve card

use simulation to estimate the probability of g

have three of one type of card and no pairs. (

is a full house.) To simulate the fve cards dr

Poker.xlsx, shown in Figure 72-2.)

■

Associate a random number with each card in th

■

The fve cards chosen will be the fve cards a

numbers, which gives each card an equal cha

■

Count how many of each card (ace through kin

578

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 72-2

Estimating the probability that you’ll draw three o

To begin, I list in cells D3:D54 all the cards i

four 13s. Then I copy from cell E3random

to E4:E54 the R

number with each card in the deck. Copying from C

RANK.EQ(E3,$E$3:$E$54,1)

gives the rank (ordered f

random number. For example, in Figure 72-2, you c

is associated with the fourteenth smallest rando

the worksheet because the random numbers are aut

the worksheet.)

The syntax of the RANK.EQ

number,array,1

function

). If is

the

orRANK.EQ(

last arg

the RANK.EQ function is 1, the function returns th

smallest number receiving a rank of 1, the secon

the last argument of the RANK.EQ function

is 0, t

ber in the array with the largest number receivi

receiving a rank of 2, and so on.

In ranking random numbers, no ties can occur (be

match 16 digits).

Chapter

Fun

72and Games: Simulating Gambling

579

and Sporting Event Probabilities

Suppose, for example, that you are ranking the n

argument of the RANK.EQ function was 1. Excel wo

Number

Rank (smallest number has rank of 1)

Because 3 is the second smallest number, 3 wou

also be assigned a rank of 2. Because 4 is the f

a rank of 4. Understanding the treatment of ti

complete Problem 1 at the end of the chapter.

By copying from cell B3 to B4:B7 ,

the

you

formula

can draw

fve cards from the deck. This formula draws th

random numbers. (The lookup table.)

range

I used

C3:D54

FAL h

the VLOOKUP function because the ranks need not b

Having assigned the range name

Drawn

to the dr

J3 to J4:J15 the formula

COUNTIF(drawn,I3)

cou

drawn. In cell J17, I determine whether the ha

(AND(MAX(J3:J15)=3,COUNTIF(J3:J15,2)=0),1,0)

. This formula returns a 1 i

hand has three of one kind and no pairs.

I now use a one-way data table to simulate fou

the results of cell

J17

with

I select

the formula

the table ra

clicking What-If Analysis in the Data Tools gr

Table, I set up a one-way data table by selecti

I click OK, Excel simulates four thousand poke

probability of three of a kind. with

I estimate

the formul

the c

of three of a kind at 1.9 percent. (Using basi

probability of drawing three of a kind is 2.1 p

Going into the 2003 NCAA men’s basketball Fina

team winning the tournament?

You can rate college basketball teams using th

“Using Solver to Rate Sports Teams,” but it is d

highly respected Sagarin ratings (available

) alwaysat

gives up-to-date ratings for all college baske

Four, the Sagarin ratings of the four teams we

Kansas, 92.76; Marquette (led by Dwayne Wade

), 8

tion, you can play out the Final Four several th

team will win.

580

Microsoft Excel 2010: Data Analysis and Business Modeling

The mean prediction for the number of points by w

rating–underdog

. In the

rating

Final Four, there is no home t

would add fve points to the home team’s rating. (

is four points, and in college and professional f

you can use the NORM.INV function to simulate th

“The Normal Random Variable,” for a discussion o

a normal random variable.)

I calculated the likely outcome of the 2003 Fina

Figure 72-3. The semifnals pitted Kansas against M

Fig

URE 72-3

Simulating the outcome of the NCAA 2003 Final Four.

To begin, I enter each team’s name and rating in th

I use the RAND function to enter a random number f

in cell F8 I enter a random number for the Syrac

always relative to the top team listed.

In cell E4, I determine the outcome of the Kansa

Kansas) with the formula

. Note

NORM.INV(F4,D4–D5,10)

that Kansas is favo

points. In cell E8, I determine the outcome of th

of Syracuse) with the formula

. (The

NORM.INV(F8,D8–D9,

standard deviatio

winning margin of college basketball games is 10 p

In cells G5 and G6, I ensure that the winner of e

semifnal outcome of greater than 0 causes

bottom

the to

listed team wins. Thus, in cell G5, I enter the w

Chapter

Fun

72and Games: Simulating Gambling

581

and Sporting Event Probabilities

IF(E4>0,”KU”,

. In

“MARQ”)

cell G6, I enter the winner of th

formula

IF(E8>0,”SYR”,”TEX”)

In cell H5, I enter a random number that is us

championship game. Copying from I5 to I6 the f

obtains the rating for each team in the champi

outcome of the championship game (from the ref

cell G5) with the formula

. Finally,

NORM.INV(H5,I5–I6,10

in cell K5, I d

champion with the formula

IF(J5>0,G5,G6)

Now I can use a one-way data table in the usua

thousand times. The simulated winners are in th

to K13:K15 the formula

COUNTIF($M$12:$M$2011,J

ability for each team winning: 38 percent for K

Texas, and 14 percent for Marquette. These pro

following formula:

prob team wins

prob team loses

Odds against team winning

For example, the odds against Kansas are 1.63 t

(1 – 0.38)/0.38 = 1.63

This means that if you placed $1 on Kansas to w

Kansas championship, the bet is fair. Of cours

ensure that he makes money. (See Problem 6 at t

This methodology can easily be extended to sim

IF statements to ensure that each winner advan

team’s rating. See the fle Ncaa2003.xlsx-for a s

sis gave Syracuse (the eventual winner) a 4-pe

In this worksheet, I used comments to explain m

Here is some background about using comments:

■

To insert a comment in a cell, frst select th

group, click New Comment, and then type you

mark in the upper-right corner of any cell c

■

To edit a comment, right-click the cell cont

Comment.

■

To make a comment always visible, right-clic

Clicking Hide Comment when the comment is d

pointer is in the cell containing the comme

582

Microsoft Excel 2010: Data Analysis and Business Modeling

■

If you want to print your comments, click the P

small arrow in the bottom-right corner of the g

the Page Setup dialog box. In the Comments bo

whether you want comments printed as displaye

sheet.

Fig

URE 72-4

Comments in a worksheet.

Problems

Suppose 30 people are in a room. What is the p

have the same birthday?

What is the probability of getting dealt one p

What is the probability of getting dealt two p

In the game of keno, 80 balls (numbered 1 thr

are randomly drawn. Before the 20 balls

- are d

bers. If at least 5 of the numbers are drawn, t

winning?

Going into the 2003 NBA fnals, the rating sys

San Antonio Spurs three points higher than th

team wins four games. The frst two games were a

Jersey, and the fnal two games were scheduled f

ity that San Antonio will win the series?

What odds should the bookmaker give on

- Kansas w

maker wants to earn an average of 10 cents pe

What is the probability of getting dealt a flu

If you break a 1-inch stick in two places tha

smaller sticks. What are the chances that the th

Suppose each hitter on a baseball team has a 50

run and a 50-percent chance of striking out. O

score in an inning?

583

Chapter 73

Using Resampling to A

Question answered in this chapter:

■

I produced nine batches of a product by usi

by using a low temperature. What is the pro

the high temperature?

Data analysts often need to address questions s

■

What is the probability that a new teaching t

■

What is the probability that aspirin reduce

■

What is the probability that Machine 1 is th

You can use a simple yet powerful technique kn

data. To make statistical inferences by using r

by sampling with replacement from your data. S

that the same data point can be chosen more th

on the results of this repeated sampling. A ke

RANDBETWEEN function. Entering

a,b

) the

yields

function

with

ability any integer between

and

(inclusive

likely to yield one of the numbers 1 through 9

Answer to This Chapter’s Quest

I produced nine batches of a product by using a h

using a low temperature

. What is the probability that the p

high temperature?

The fle Resampleyield.xlsx, shown in Figure 73

batches of a product manufactured at a high te

at a low temperature.

The mean yield at a high temperature is 39.74, a

32.27. This difference does not prove, however

ter than mean yield at a low temperature. You wa

probability that yield at a high temperature i

this question, you can randomly generate nine i

resampling of the high-temperature yields. For e

4, the resampled data for high-temperature yie

Next you randomly generate seven integers betw

584

Microsoft Excel 2010: Data Analysis and Business Modeling

the low-temperature yields. You can then check th

temperature mean is larger than the low-temperat

repeat this process several hundred times. (I re

In the resampled data, the fraction of the time th

the low-temperature mean estimates the probabili

superior to the low-temperature process.

Fig

URE 73-1

Product yields at high and low temperature.

To begin, you generate a resampling of the high-

to C17:C24 the formula RANDBETWEEN(1,9), as show

can be chosen more than once or not chosen at al

formula VLOOKUP(C16,lookup,2)—the range

generates

C4:E13 h

the yields corresponding to the random resamplin

resampling from the low-temperature yields. Copy

RANDBETWEEN(1,7)

generates a resampling of seven o

low-temperature data. Copying from F16 to F17:F2

generates the seven actual resampled low-tempera

Fig

URE 73-2

Implementation of resampling.

In cell D26, I compute the mean of the resampled hi

formula

AVERAGE(D16:D24)

. Similarly, in cell F26 I compute th

Chapter

Using

Resampling to

585

Analyze Data

low-

temperature yields with the

. Informula

cell D29,

AVERAGE(

- I det

er the resampled mean for high temperature is l

temperature with the.formula

IF(D26>F26,1,0)

To replay the resampling 400 times, you can us

numbers 1 through 400 in the cell range C32:43

Carlo Simulation,” for an explanation of how t

list of iteration values.) By typing =D29 in c

high-temperature mean is larger than low-tempe

table. After selecting the table range (C31:D4

What-If Analysis menu in the Data Tools group o

worksheet as the column input cell. You have n

the resampling 400 times. Each iteration with a v

high temperature has the larger mean. Each ite

for which low temperature has a larger mean. I

that high-temperature yield has a larger

. mean by u

In Figure 73-2, the resampling indicates a 92-

a larger mean than low temperature. Of course, p

of 400

resamplings and give you a slightly differe

temperature yield is superior to low-temperatu

Problems

You are testing a new flu drug. Out of 24 flu v

better and 4 felt worse. Out of 9 flu victim

3 felt worse. What is the probability that th

A talk on the dangers of high cholesterol wa

cholesterol was tested both before and afte

What is the probability that the talk cause

that reduced their cholesterol?

Cholesterol before

Cholesterol after

220

210

195

198

250

210

200

199

220

224

260

212

175

179

198

184

586

Microsoft Excel 2010: Data Analysis and Business Modeling

The

beta

of a stock is simply the slope of th

monthly return on the stock from the monthly r

(S&P) 500 index. A

beta

that is larger than 1 i

the market, whereas a

beta

of less than 1 ind

market. The fle Betaresampling.xlsx contains m

Microsoft (MSFT), Pfzer (PFE), other stocks,

mine the probability that Microsoft has a low

the Excel SLOPE function to estimate the

beta

The fle Lawdata.xlsx gives the LSAT scores an

students. Based on this data you are 95 perce

score and GPA is between which two values?

587

Chapter 74

Pricing Stock Optio

Questions answered in this chapter:

■

What are call and put options?

■

What is the difference between an American a

■

As a function of the stock price on the exe

European calls and puts?

■

What parameters determine the value of an o

■

How can I estimate the volatility of a stoc

■

How can I use Excel to implement the Black-

■

How do changes in key parameters change the v

■

How can I use the Black-Scholes formula to e

■

I don’t want somebody changing my neat opti

the formulas in my worksheet so that nobody c

■

How can I use option pricing to help my com

During the early 1970s, economists Fischer Bla

the Black-Scholes option-pricing formula, whic

call or put option. Scholes and Merton were awa

their efforts. (Black died before 1997, and No

work of these economists revolutionized corpor

to their important work.

Not

or an excellent technical discussion of option

Investment Science

(Oxford University Press, 1997)

Answers to This Chapter’s Ques

What are call and put options?

call option

gives the owner of the option th

the

exercise

. A

put

price

option

gives the owner of the o

for the exercise price.

588

Microsoft Excel 2010: Data Analysis and Business Modeling

What is the difference between an American and a E

American

option can be exercised on or before a d

referred to as ).

theA

expiration

European

option

date

can be exerci

date.

As a function of the stock price on the exercise d

European calls and puts?

Let’s look at cash flows from a six-month Europea

exercise price of $110. Let

equal the price of I

call option on these shares. is

With

$0 aifvalue

P≤110

ofand

you would not exercise the option. If

is great

to buy stock for $110 and ,immediately

thereby earning

sell

the

a pro

Figure 74-1 shows the payoff from this call opti

dollar by which the stock price exceeds the exer

be written as

. Notice

Max(0,P–110)

that the call option graph i

worksheet in the fle Optionfgures.xlsx) has a sl

exercise price. Its slope is 1 for a value of

Fig

URE 74-1

Cash flows from a call option.

You can show that if a stock pays no dividends, i

call option early. Therefore, for stock that doe

European call option both have the same value.

Now let’s look at cash flows from a six-month Eur

exercise price of $110. Let

equal the price of I

option ≥

110

$0and

–

110

if.

P<110

For a value of

below $110, y

of stock for

and immediately sell .the

If stock

is fo

larger than $110, it would not be proftable to b

would not exercise the option to sell the stock f

Chapter

Pricing

Stock

589

Options

Figure 74-2 displays the payoff from this put o

Optionfgures.xlsx). In short, a put option pay

below the exercise price. A put. payoff

Note that

can the

be ws

of the put payoff is –1 for a value of

less th

payoff is 0 for a value of

greater than the e

Fig

URE 74-2

Cash flows from a put option.

An American put option can be exercised early, s

option cannot be determined without knowledge o

expiration date.

What parameters determine the value of an opti

In their derivation of the Black-Scholes optio

showed that the value of a call or put option d

■

Current stock price.

■

The option’s exercise price.

■

Time (in years) until the option ).

expires (r

■

Interest rate (per year on a compounded bas

throughout the duration of the investment.

For

example, if three-month T-Bills are paying 5 p

ln(1+0.05)

(Calculating the logarithm transform

pounded rate.) Compound interest simply mea

interest on your interest.

■

Annual rate (as a percentage of the stock p

pays 2 percent of its value each year in di

590

Microsoft Excel 2010: Data Analysis and Business Modeling

■

Stock

volatility

(measured on an annual basis

percent means that (approximately) the standa

changes in the stock’s price is expected to b

bubble of the late 1990s, the volatility of m

I’ll show you two ways to estimate this impor

The Black-Scholes pricing formula requires that th

random variable. See Chapter 68, “Using the Logn

Prices,” for further discussion of the lognormal r

How can I estimate the volatility of a stock bas

To estimate the volatility of a stock based on d

proceed as follows:

■

Determine the monthly return on the stock for a p

■

Determine for each month

ln(1+monthly return)

■

Determine the standard deviation

. This calculation

ln(1+month

the monthly volatility.

■

Multiply the monthly

volatility

convert monthly

volatili

volatility.

This procedure is illustrated in the fle Dellvol

of Dell stock using monthly prices from the peri

Figure 74-3, in which I’ve hidden several rows o

Fig

URE 74-3

Computing the historical volatility for Dell.

Copying from cell C2 to C3:C154 the formula

(B2–

Dell stock. Then copying from D2 to D3:D154 the f

1+month’s

. Next

return

I compute

ln(1+ month’s return)

E2 to E3:E154 the

, and

formula

I compute

LN(D2)

the monthly volati

formula

STDEV.S(E2:E154)

Finally, I compute an estimate of D

the formula.

SQRT(12)*H3

Dell’s annual volatility is estimat

Chapter

Pricing

Stock

591

Options

How can I use Excel to implement the Black-Sch

To apply the Black-Scholes formula in Microsof

following parameters:

■

=Today’s stock price

■

=Duration of the option (in years)

■

=Exercise price

■

=Annual risk-free rate (This rate is assume

■

σ=Annual volatility of stock

■

=Percentage of stock value paid annually in d

Given these input values, the Black-Scholes pr

as follows:

Defne

(

)+(

–

)

and

–

Then the call price C is given by

C = Se

–yt

(

)

– Xe

–rt

(

)

Here,

N(x)

is the probability that a normal ra

to 1 is less .than

For or

example,

equal to

N(–1)=.16,N(0)=.5,

A normal random variable with a mean of 0 and a s

standard

normal

The cumulative normal probability can b

NORM.S.DIST function. Entering

NORM.S.DIST(x, T

standard normal random variable

. For example,

is less than

entero

NORM.S.DIST(–1,True)

in a cell will yield 0.16

with a mean of 0 and a standard deviation of 1 h

less than –1.

The price of a European put

can be written a

P = Se

–yt

(

)

–

– Xe

–rt

(

)

–

592

Microsoft Excel 2010: Data Analysis and Business Modeling

In the fle Bstemp.xlsx (see Figure 74-4), I crea

European call or put option. Enter the parameter v

a European call in D13 and a European put in D14

Fig

URE 74-4

Valuing European calls and puts.

Not

aluing American options is beyond the scope of t

refer to Luenberger’s excellent textbook.

As an example, suppose that Cisco stock sells fo

a seven-year European call option. Assume that th

percent, and the risk-free rate during the seven

year. Compounded, this translates

. Cisco does

to not

ln(1+.05)=.

pay div

annual dividend rate is 0. The value of the call o

put option with an exercise price of $24 would b

How do changes in key parameters change the valu

■

In general, the effect of changing an input p

given in the following table:

ParameterEuropean call American

put

American

call

put

Stock pric+

Exercise price

Time to expiration

Volatility+

Risk-free +

rate

Dividends-

An increase in today’s stock price always inc

value of a put.

Chapter

Pricing

Stock

593

Options

■

An increase in the exercise price always in

value of a call.

■

An increase in the duration of an option al

option. In the presence of dividends, an in

increase or decrease the value of a Europea

■

An increase in volatility always increases o

■

An increase in the risk-free rate increases th

to increase the growth rate of the stock pr

more than cancels out the fact that the opti

higher interest rate. An increase in the ri

because the higher growth rate of the stock t

future payoffs from the put are worth less. Ag

not affect current stock prices, but they d

■

Dividends tend to reduce the growth rate of a s

reduce the value of a call and increase the v

Using one-way and two-way data tables (see Cha

Tables,” for details about how to work with da

specifc effects of parameter changes on the va

How can I use the Black-Scholes formula to est

Earlier in this chapter, I showed how to use hi

volatility. The problem with a historical

backward.

vola

What you really want is an estimate of a stock

volatility

approach simply estimates a stock’s v

the Black-Scholes price match the option’s mar

the volatility value implied by the option’s m

You can easily use the Goal Seek command and th

compute an implied volatility. On July 22, 200

2003 call option with a $17.50 exercise price wa

October 18 (89 days in the future). Thus, the o

Cisco does not expect to pay dividends, and I’

acorresponding risk-free

. To

rate

determine

ln(1+.05)=0.0

the volati

implied by this option price, you enter the re

Ciscoimpvol.xlsx, which is shown in Figure 74-

594

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 74-5

Using implied volatility to estimate Cisco’s volati

Next you use the Goal Seek dialog box (see Figur

in cell B10) that makes the call price (the form

Fig

URE 74-6

Goal Seek settings to fnd implied volatility.

This option implies an annual volatility for Cis

Not

The Web site

www.Ivolatility.com

provides an esti

historical or implied.

I don’t want somebody changing my

. How

neat

canoption-pr

I protec

formulas in my worksheet so that nobody can chan

I’m sure that you have sent a worksheet to someo

constructed formulas. Sometimes you want to prot

only enter input data but not modify the workshe

how to protect all the formulas in the Black-Sch

Bstempprotected.xlsx.)

I begin by unlocking all the cells in the worksh

First, click the gray box in the upper-left corn

headings intersect (next to the A and the 1). Af

make affect the entire worksheet. For example, i

box, all the cells in the worksheet will use the b

Chapter

Pricing

Stock

595

Options

After selecting the entire worksheet, click th

on the Home tab. This displays the Format Cell

Protection tab, clear the Locked check box, as s

all cells in the worksheet are unlocked, which m

you can still access these cells.

Fig

URE 74-7

Format Cells dialog box.

Next, select all the formulas in the worksheet

dialog box. Click Special, select Formulas, an

again, and on the Protection tab, select the L

formulas.

Now you can protect the worksheet, which will p

Click Protect Sheet in the Changes group on th

select the Select Unlocked Cells check box, as s

of a template to select unlocked cells, but th

Fig

URE 74-8

Allowing user to access unlocked cells.

596

Microsoft Excel 2010: Data Analysis and Business Modeling

Now, when you click any formula, you cannot see o

try to mess up a formula! The fnal result of prot

Bstempprotected.xlsx.

How can I use option pricing to help my company m

Option pricing can be used to improve a company’

making process. The use of option pricing to eva

real options

. The idea of real options is credited to J

offcer of Merck. Essentially, real options let y

which is often missed by traditional capital bud

thceoncepts of real options.

Not

Refer to Luenberger’s book for a more detailed di

Let’s say that you own an oil well. Today, your b

$50 million. In fve years (if you own the well), y

well, at a cost of $70 million. A wildcatter is w

Should you sell the well?

Of course, the value of the oil in fve years mig

of the oil would increase by 5 percent a year, t

fve years. Traditional capital budgeting says th

develop it is more than the value of the oil in th

of the oil in the well will be different because m

change. There’s a chance that the oil will be wo

worth $80 million in fve years, developing the w

Essentially, you own a fve-year European call op

the well in fve years is the same as the payoff o

of $50 million, an exercise price of assume

$70 million

an annual volatility similar to the volatility o

30percent). If you use a T-Bill rate of 5 percent

percent, in the fle Oilwell.xlsx (see Figure 74-

option is $11.47 million, which means that you s

Of course, you do not know the actual volatility f

a one-way data table to determine how the value o

Chapter

Pricing

Stock

597

Options

estimate. (See Figure 74-9.) From the data tab

volatility is at least 27 percent, your oil we

Fig

URE 74-9

Oil well real options.

As a second example, consider a biotech drug c

major pharmaceutical frm. The biotech company c

is million.

$50

Of course, the value of the drug mi

price drop, the biotech company wants the drug t

in fve years. If an insurance company wants to u

to charge?

Essentially, the biotech company is asking for a p

$1 million by which the value of the drug in f

to a fve-year put option on the value of the d

the annual volatility on comparable drug stock

shown in Figure 74-10), the value of this opti

referred to as an,

abandonment

but it is equivalent

option

to a p

a one-way data table, shown in Figure 74-10, t

option depends on the assumed volatility, rang

598

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 74-10

Calculating an abandonment option.

Problems

Use the monthly stock returns in the fle Vola

volatility for Intel, Microsoft, and GE.

A stock is selling today for $42. The stock h

annual risk-free rate is 10 percent.

❑

What is a fair price for a six-month Europe

$40?

❑

How much does the current stock price have t

call option to break even in six months?

❑

What is a fair price for a six-month Europe

$40?

❑

How much does the current stock price have t

put option to break even in six months?

❑

What level of volatility would make the $40 c

Goal Seek command.)

Chapter

Pricing

Stock

599

Options

On September 25, 2000, JDS Uniphase stock s

day, a $100 European put expiring on January 2

implied volatility for JDS Uniphase stock b

percent.

On August 9, 2002, Microsoft stock was sell

call option expiring on January 17, 2003, wa

estimate the implied volatility for Microso

You have an option to buy a new plane in thr

estimate of the value of the plane is $21 mi

the plane’s value is 25 percent, and the ri-

buy the plane worth?

The current price of copper is 95 cents per p

prices is 20 percent, and the risk-free rat

(if you want it) to spend $1.25 million to mi

can be sold at whatever the copper price is i

pound of copper from the ground. What is th

You own the rights to a biotech drug. Your b

these rights is $50 million. Assuming that t

90 percent and the risk-free rate is 5 perc

rights to the drug fve years from now for $

Merck is debating whether to invest in a pi

estimates that the worth of the project is –

gives Merck the option to own, if it wants t

available in four years. If Merck does not p

own the bigger project. The bigger project w

from now. Currently, Merck estimates the ne

from the bigger project to be $597 million. A

that the annual volatility for the bigger p

(This is the problem that started the whole f

Develop a worksheet that uses the following i

❑

Annual fxed cost

❑

Unit cost

❑

Unit price

❑

Annual demand=

10,000–100*(price)

Protect the cells used to compute annual de

601

Chapter 75

Determining Custome

Questions answered in this chapter:

■

A credit-card company currently has an 80-p

company’s proftability improve if the reten

■

A long-distance phone company gives the com

switch. How large an incentive should it gi

Many companies undervalue their customers. Whe

look at the net present value (NPV) of the lon

the customer. (For detailed information about n

Investments by Using Net Present Value Criteria

a customer often causes a company to make poor d

cut its customer service staff by 10 percent t

service quality might cause them to lose much m

which would, of course, result in the company b

examples show how to compute customer value.

Answers to This Chapter’s Ques

A credit-card company currently. How

has will

an 80-perc

the

company’s profitability improve if the retentio

This example is based on a discussion in Frede

Effect

(Harvard Business School Press, 2001). Y

fle Loyalty.xlsx, shown in Figure 75-1. Reichh

customer based on the number of years the cust

the frst year a customer has the credit card, t

the result of customer acquisition costs and th

During each successive year, the proft generat

who has owned a card for 20 or more years gene

The credit-card company wants to determine how th

company’s retention rate. Currently, the compa

means that at the end of each year, 20 percent (

card. (I refer to the 20 percent of customers

.) The

credit-card company wants to determine the lon

rates of 80 percent, 85 percent, 90 percent, 9

602

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 75-1

Value of a credit-card customer.

To determine the long-term value of a customer, y

100 customers. (A

cohort

is a group of individua

size 100 is arbitrary here, but round numbers ma

yod

uetermine how many of these customers are stil

(Customers around for year t+1)=(Retention

. You can

rate)

assume that customers quit only at the end of ea

to determine the total NPV (assuming a 15-percen

nal cohort of 100 customers. The 15-percent disc

from now is worth the same as

$1.00/$1.15

of pro

the number of customers in the original cohort (

customer.

I frst assign the names in the cell range B6:B7 t

number of original customers (100) in cell C9. C

the formula

retention_rate*C9

generates the numb

example, 80 customers will be present in Year 2.

I compute the proft earned each year by multiply

each customer’s proft. To make this calculation, c

C9*B9

. In cell E4, I compute the average NPV gener

formula

(1+Interest_rate)*NPV(Interest_rate,D9:D

. I am assuming cash flow

beginning of the year and a 15-percent annual di

that reads

NPV(Interest_rate,D9:D38)

computes th

customer assuming end-of-year cash flows. Multipl

end-of-year cash flow NPV to a beginning-of-year N

Chapter

Determining

Customer

603

Value

With an 80-percent retention rate, the average c

the value of an individual customer varies with a c

way data table. I enter the relevant annual re

enter the formula I want the data table

=E4

. cal

Next, I select the table range (F8:G13) and th

command on the Data tab. After entering a colu

culations shown in Figure 75-1. Notice that in

90 percent nearly doubles the value of each cu

to these customers and against pinching pennie

Understanding the value of a customer gives mo

to increase their proftability.

A long-distance phone company gives the compet

switch

. How large an incentive should it give?

Let’s say that you work for a phone company in w

spends $400 per year and the company generates a 1

spent. At the end of each year, 50 percent

of th

tition, and without any incentives, 30 percent o

company. You’re considering giving the competi

switch companies. How large an incentive can y

The key to analyzing this problem (which you c

Figure 75-2) is to look at the NPV for two sit

■

Situation 1: 100 customers begin with the c

■

Situation 2: You pay the 100 customers who a

to switch to your company.

Following through each situation for a period o

Goal Seek command to determine the dollar amou

company that makes you indifferent about the f

■

Situation 1: You have just

each

paid to

100

switch

unloyal

to c

company.

■

Situation 2: The market consists of 100 unl

Assume that the analysis begins on June 30, 20

companies at most once per year. I assigned th

The key step in the analysis is to realize tha

.3*(year t competitor customers)+.5*(year

Similarly

(yeartt+1

ourcc

competition)=.7*(year t competition

customers)

604

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 75-2

Phone incentive analysis.

Next I enter 100 in cell D9 (customers with us) a

competition). This customer alignment correspond

is offered to 100 customers. I’m assuming that c

with the company for at least one year. Copying f

(1–probleave)*D9+probcome*E9

generates the numbe

(Years 2022 through 2029 are hidden in Figure 75

formula

probleave*D9+(1–probcome)*E9

calculates th

competition during each year.

In cell F9, I generate the proft earned during th

D9*annrevenue*proftmargin–switch_fee*100

. Note that I have subtracte

paying the 100 customers with the competition to s

the formula

D10*annrevenue*proftmargin

generates p

D5, I compute the NPV of the profts associated w

XNPV(0.1,F9:F28,B9:B28)

(See Chapter 8 for a discussion of th

In a similar fashion, in the cell range G8:I28 I g

100 customers who were originally with the compe

customers will have switched (even without incen

between the NPV with the incentive and the NPV w

Finally, I use the Goal Seek command to vary the s

to 0. The Goal Seek dialog box is shown in Figur

NPV of the two situations identical. Therefore, y

customer to switch and still have increased prof

Chapter

Determining

Customer

605

Value

Fig

URE 75-3

Goal Seek settings to determine the maximum ince

Problems

Whirlswim Appliance is considering giving e

each VCR purchased. The company estimates th

an average of $2.50 for each VCR sold today (

market consists of 72,000 consumers whose l

86,000 consumers whose last purchase was

cent of all consumers purchase a VCR. If th

60-percent chance that their next purchase w

was not a Whirlswim, there is a 30-percent c

Whirlswim. A purchase during the current

tion to proft (and maintenance cost per

pur

cent per year. Profts (over a 30-year horizo

Suppose that you provide free maintenance. I

Whirlswim, the probability that the custome

increase by an unknown amount between 0 per

give free maintenance and the customer’s

ability that their next purchase is a Whirl

between 0 percent and 10 percent. Do you re

maintenance policy?

Mr. D’s Supermarket is determined to please i

card. Currently, 30 percent of all shoppers a

shops at Mr. D’s 80 percent of the time. An u

percent of the time. A typical customer spe

on a 4-percent proft margin.

The customer advantage card will cost Mr. D

believe Mr. D’s share of loyal customers wil

2 percent and 10 percent. You also believe

tomer shops at Mr. D’s will increase by an u

percent. Should Mr. D’s adopt a customer ads a

card if its proft margin is 8 percent inste

607

Chapter 76

The Economic Order Qu

Inventory Model

Questions answered in this chapter:

■

An electronics store sells 10,000 cell phon

a supply of cell phones, the store incurs a

each cell phone, and the cost of holding a c

to be $20. When the store orders cell phone

■

A computer manufacturing plant produces 10,

each server is $2,000. The cost to set up a p

cost to hold a server in inventory for a ye

servers per year if it wants to. When the p

should it produce?

When a store orders an item repeatedly, a natu

order each time? If the store orders too many i

costs. If the store orders too few items, it i

must be a happy medium that minimizes the sum o

Similarly, consider a manufacturing plant that p

size minimizes the sum of annual inventory and s

chapter show how to use the economic order qua

F. Harris of Westinghouse Corporation) to answ

Answers to This Chapter’s Ques

An electronics store sells

. Each

10,000

time

cell

an order

phonesi p

supply of cell phones, an . order

The store

cost pays

$100

is fi

phone, and the cost of holding a cell phone

in i

When the store orders cell phones, how large a

The size of an order that minimizes the sum of a

determined after the following parameters are k

■

=Cost per order

■

=Cost of holding one unit in inventory for a y

■

=Annual demand for product

608

Microsoft Excel 2010: Data Analysis and Business Modeling

You can follow an example of how to work with th

worksheet in the fle Eoq.xlsx, which is shown in Fi

Fig

URE 76-1

EOQ template.

equals order size,.

annual

. (Throughout

inventory

this

cost

exam

this equation as Equation 1.) We derive

.Equation

1 b

will be half the maximum inventory level.

5, note

To see w

that you can compute the average inventory level f

of orders). At the beginning of a cycle,

. At an

theorde

end of the cycle, you are out of stock, and the i

at a constant rate, the average inventory level d

Maximum

inventory level will equal

becau

instant that the inventory level is reduced to 0

Because

D/q

orders are placed per .year,

(I refer

annual

to othi

equation as Equation 2.) Using calculus or the E

of inventory and ordering costs is minimized for a v

quantity (EOQ), which is calculated using the fo

Equation 3.)

EOQ=

From this formula, you can see the following:

■

An increase in demand or ordering cost will i

■

An increase in holding cost will decrease the E

In the fle Eoq.xlsx, I use Equation 3 to determi

cost in cell C6 by using Equation 1. I determine

2. Notice that for EOQ, the annual ordering cost e

always be the case. In cell C8, I determine the t

which does not depend on my ordering

strategy) w

Of course, you can use one-way and two-way data t

the EOQ and various,costs

.dIn

this

variations

example,

0 D=10,000

cel

Chapter

The

76Economic Order Quantity

609

Inventory Model

phones per=

$20

year,

perand

cell

phones. Inserting thes

following:

■

Each order should be for 100 cell phones.

■

Annual holding and ordering costs each equa

holding costs equal to annual ordering cost

■

Total annual costs (exclusive of purchasing c

When you are working with EOQ, keep the follow

■

The presence of quantity discounts invalida

cost then depends on the order size.

■

The EOQ assumes that demand occurs at a rel

The EOQ should not be used for products for w

■

Annual holding cost is usually assumed to b

product’s unit purchasing cost.

■

I’ve included (in the EOQ

Protected

workshe

worksheet in which all formulas are protect

can change the formulas. See Chapter 74, “P

about how to protect a worksheet.

More Info

For more information about inventory modelin

book

Operations Research: Applications and Algorit

A computer manufacturing plant produces

. The cost10,000

to pr s

each server. The

is $2,000

cost to set up a production ru

to hold a server in inventory

. The plant

forcan year

produce

is $50

year if it

. When

wants

the

toplant produces servers, how l

With the EOQ model, you assume an order arrive

company manufactures a product instead of orde

cannot arrive instantaneously. In such situati

order quantity, you need to determine the- cost

duces a product internally instead of purchasi

minimizes costs depends on the following param

■

=Cost of setting up a batch for production

■

=Cost of holding each unit in inventory for a y

■

=Annual demand for the product

■

=Annual rate at which the product can be pr

capacity to produce 25,000 servers per year

610

Microsoft Excel 2010: Data Analysis and Business Modeling

equals the size of each production batch, t

0.5*(q/R)*(R–D)*h

(I refer to this equation as Equation 4

batch takes

q/R

years to produce, and during a p

rate .

ofThe

R–D

maximum inventory level, which occurs a

calculated .

asThe

(q/R)*(R–D)

average inventory level

will th

Because

D/q

batches are produced per year, annua

to as Equation 5). Using calculus or the Excel S

minimizes the sum of annual setup and production

(which I refer to as Equation 6). This model is c

(

R–D

)

KDR

EOB=

From this formula, you can determine the followi

■

An increase in

will increase the EOB.

■

An increase in

will decrease the EOB.

In the

Cont Rate EOQ

worksheet in the fle Contra

determine the EOB, annual setup, and holding cos

Fig

URE 76-2

Template for computing EOB.

For this =$200,

example,

=$500,

=10,000

units=

25,000

per year,

units

andper

After entering these parameter values in the cel

■

The batch size that minimizes costs is 115.47 s

produce 115 or 116 servers in each batch.

■

The annual holding cost and setup costs equal $

set annual holding cost equal to annual setup c

■

Total annual cost (exclusive of variable prod

■

86.6 batches per year will be produced.

Chapter

The

76Economic Order Quantity

611

Inventory Model

When you are working with the EOB model, keep th

■

If the unit variable cost of producing a pr

model is invalid.

■

The EOB assumes that demand occurs at a rel

The EOB should not be used for products for w

■

The annual holding cost is usually assumed t

of a product’s unit purchasing cost.

■

I’ve included (in the

Protected

worksheet i

EOB worksheet in which all formulas are prot

about how to protect a worksheet.

Problems

An appliance store sells plasma TVs. Annual d

cost to carry a TV in inventory for one yea

plasma TVs is $400.

❑

How many TVs should be ordered each time a

❑

How many orders per year should be placed

❑

What are the annual inventory and orderin

Suppose that the Waterford Crystalpitchers

company c

per day. Further suppose that the plant is o

demand is for 20,000 pitchers. The cost to h

be $10, and the cost to set up the facility t

❑

What batch size would you recommend for i

❑

How many batches per year should be produ

❑

What are the annual setup and inventory c

613

Chapter 77

Inventory Modeling w

Demand

Questions answered in this chapter:

■

At what inventory level should I place an o

holding, ordering, and shortage costs?

■

What does the term

95-percent service level

In Chapter 76, “The Economic Order Quantity In

economic order quantity (EOQ) to determine an o

batch size. The examples assumed that demand o

demand occurred at a rate of, for example, 1,2

equal 100 units. As long as demand occurs at a r

approximation of the cost-minimizing order qua

In reality, demand during any time period is u

question is how low to let the inventory level g

at which an order should be. placed

Clearly,

is called

high rth

will decrease shortage costs and increase hold

increase shortage costs and decrease holding c

sum of shortage and holding costs is minimized

to determine a reorder point that minimizes ex

based on the following two assumptions:

■

Each unit you are short is back ordered by a c

cost

. This cost is primarily a measure of the c

receipt of an ordered item.

■

Each unit you are short results in a lost s

The lost sales cost includes the proft lost f

included in c

The second example shows how to determine the o

level

approach.

95-percent

For example,

service

level means th

at a level ensuring that, on average, 95 perce

diffcult to determine the cost of a shortage i

case. For that reason, most companies set reor

614

Microsoft Excel 2010: Data Analysis and Business Modeling

Not

n this book’s companion Web site, for the back-o

I’ve included a worksheet named

Protected

in which a

back-ordered and lost-sales cases. You can use these w

Answers to This Chapter’s Quest

At what inventory level should I place an order if m

ordering, and shortage costs?

As I indicated in Chapter 76, the EOQ depends on th

■

=Cost per order .

■

=Cost of holding one unit in inventory for a y

■

=Annual demand for the product. Because deman

for the expected annual demand for the produc

The Back-Order Case

See the fle Reorderpoint_backorder.xlsx, shown i

example. Let’s frst suppose that each shortage r

words, a shortage does not result in any lost de

short incurs a cost

. In this case, the reorder point depen

■

EOQ

is the economic order quantity (the quanti

■

is the cost per order

■

is the annual holding cost per unit

■

is the mean annual demand

■

SOC

is the cost per unit short

■

annsig

is the standard deviation of annual de

■

meanLT

is the average

; that is,

lead

the

time

average time bet

and the time the order is received

■

sigmaLT

is the standard deviation of lead tim

Say that a department store wants to determine a

electric mixers. They have the following informa

■

It costs $50 to place an order for mixers.

■

It costs $10 to hold a mixer in inventory for a y

Chapter

Inventory

Modeling with

615

Uncertain Demand

Fig

URE 77-1

Determining reorder point when shortages are bac

■

On average, the store sells 1,000 mixers pe

■

All customers who try to purchase a mixer w

a later date and buy a mixer when the mixer i

$20 for each unit it is short.

■

The annual demand for mixers (based on hist

40.8.

■

Lead time is always two weeks (0.038 years)

After you

enter

and

in cells C2:C4, the spreads

C5. After you

annsig

,enter

meanLT

, and

SOC sigmaLT

in cells -C7:C10

putes in cell C14 the reorder point that minimi

shortage costs (51.63 mixers). Thus, the depar

its stock decreases to 51.62 (or 52) mixers.

The

safety stock level

associated with a given r

demand

. The department store maintains a safety s

computed in cell C15. Essentially, the safety s

holding costs. A higher level of safety stock w

The Lost-Sales Case

Now suppose that each shortage results in a lo

is usually estimated as the back-order penalty p

Suppose that the department store earns a $20 p

shortage cost for the

$20

lost-sales

proft+$20

case ).

back-o

then $

In the fle Reorderpoint_lostsales.xlsx, shown i

estimate the reorder point for the lost-sales c

the lost-sales cost of $40, I fnd that the opti

place an order when inventory is down to 54.23 mi

and 2.4 percent of the store’s demand for mixe

616

Microsoft Excel 2010: Data Analysis and Business Modeling

of a lost sale has increased the reorder point a

happens because the increased cost of a shortage (

eager to avoid shortages.

Fig

URE 77-2

Determining reorder point when sales will be lost.

Increased uncertainty greatly increases the reor

if the standard deviation for lead time is one we

point increases to 79.50 mixers, and the safety s

which our lead time was known with certainty.

What does the term 95-percent service level mean

As stated earlier in the chapter, a

95-percent s

95 percent of your demand to be met on time. Bec

and/or the penalty that results from a lost sale i

stock levels for products by setting a service l

(shown in Figure 77-3), you can determine the re

level you want.

Fig

URE 77-3

Determination of reorder point using the service l

Chapter

Inventory

Modeling with

617

Uncertain Demand

As an example, consider a pharmacy that is try

for a drug it stocks. The pharmacy would like t

time. The following parameters are relevant.

■

Each order for the drug costs $50.

■

The cost to hold a unit of the drug in inve

■

Average demand per year for the drug is 1,0

■

The standard deviation of annual demand is 6

■

The time required to receive a shipment of th

(0.083 years).

You enter the service level you want (0.95) in c

and C7:C9. To determine the reorder point yiel

the Data Analysis group on the Data tab.- The S

order point until the percentage of demand met o

Under Options, choose the Multistart setting. (

GRG Multistart and Evolutionary Solver Engines

reorder point (to keep the Solver from trying a n

of 10,000 (fairly arbitrary) on the reorder po

bound, you should relax the bound. As you can s

order 100 units of the drug whenever its inven

point corresponds to a safety stock level of 6

Fig

URE 77-4

Solver Parameters dialog box for determining the r

618

Microsoft Excel 2010: Data Analysis and Business Modeling

In the following table, I’ve listed the reorder p

service levels between 80 percent and 99 percent

Service-levelReorder

percentage

point/units

Safety stock/units

65.34

-17.99

71.85

-11.48

79.57

-3.76

90.23

6.90

108.44

25.11

Notice that moving from an 80-percent service le

the reorder point by almost 67 percent!

- Also not

vice level with a reorder point less than the me

in Figure 77-3). A 90-percent service level resu

possible because shortages occur only during the l

small portion of a year.

Problems

When working with Problems 1 and 2, assume that a r

bottles of wine per year. The standard deviation o

bottles. The annual holding cost for a bottle of w

wine, and it takes an average of three weeks (wi

wine to arrive.

Assume that when the restaurant is out of win

lost goodwill. Also, the restaurant earns a p

optimal ordering policy for the wine.

Determine an inventory policy for wine that y

A reorder point policy is often

. How referred

can a reorder

to a p

policy be implemented in a situation in which t

619

Chapter 78

Queuing Theory: The M

of Waiting in Line

Questions answered in this chapter:

■

What factors affect the number of people an

■

What conditions should be met before analyz

present or the average time spent in a queu

■

Why does variability degrade the performanc

■

Can I easily determine the average time a p

in line at a bank?

We have all spent a lot of time waiting in lin

in service capacity can often greatly reduce th

a business, ensuring that your customers

do not s

tant. Therefore, business people need to under

referred to as

. In

queuing

this chapter,

theory

I’ll show you h

capacity needed to provide adequate service.

Answers to This Chapter’s Ques

What factors affect the number of people and t

In this chapter, I’ll address queuing problems i

for the frst available service person. (To kee

servers

.) This model is a fairly accurate represen

wait at a bank, at an airport security line, o

customers wait in one line started about 1970, w

that although waiting in one line does not red

it does reduce the variability of the time the

Three main factors influence the time you spend i

■

The number of

Clearly,

servers

the more servers, the l

spend in line, and fewer people on average w

■

The mean and the standard deviation

The

time

the t

between arrivals is

. called

If the average

interarrival tim

the number of arrivals decreases, which res

620

Microsoft Excel 2010: Data Analysis and Business Modeling

a queuing system. As you’ll soon interarrival

see, an incr

times increases the average time a customer s

average number of customers present.

■

The mean and the standard deviation of the ti

service

If the average service time increases, yo

time a customer spends in the system and in th

you’ll see, an increase in the standard devia

time a customer spends in a queuing system an

present.

What conditions should be met before analyzing t

or the average time spent in a queuing system?

When analyzing the time people spend waiting in l

state

characteristics of a system. Essentially, s

for a long time. More specifcally, analysts woul

quantities in the steady state:

■

=Average time a customer spends in the syste

■

=Average time a customer spends waiting in l

■

=Average number of customers present in the s

■

=Average number of customers waiting in line

By the way, it is always true that

L=(1/mean int

=(1/mean interarr

time)*W

To discuss the steady state of a queuing system m

■

The mean and standard deviation of both the i

changes little over time. The technical phras

service times is

stationary

over time.

■

(1/mean service time)*(number of

. I’ll

servers)>(1/(

refer to thi

equation as Equation 1.

Essentially, if Equation 1 is true, you can serv

For example, if mean service time equals 2 minut

interarrival time equals 1 minute (or 1/60 of an h

30*(number

servers)>60

, or that the number of servers must b

for a steady state to exist. If you cannot serve c

you fall behind and never catch up, resulting in a

Chapter

Queuing

Theory: The Mathematics

621

of Waiting in Line

Why does variability degrade the performance o

To see why variability degrades the performanc

system in which customers arrive every 2 minut

There will never be more than one customer in th

arrive every 2 minutes, but half of all servic

Even though arrivals are totally predictable,

tually the server falls behind and a line form

3.5 minute service times, after 12 minutes, fo

the following table.

Time

Event

Present after event

0 minutes Arrival

1 person

2 minutes Arrival

2 people

3.5 minutesService completed

1 person

4 minutes Arrival

2 people

6 minutes Arrival

3 people

7 minutes Service completed

2 people

8 minutes Arrival

3 people

10 minutes Arrival

4 people

10.5 minutes

Service completed

3 people

12 minutesArrival

4 people

Can I easily determine the average time a pers

line at a bank?

The

Model

worksheet in the fle Queuingtemplate

to determine approximate

, ,

and

values

for

(usually within 10 per

value). The worksheet is shown in Figure 78-1.

Fig

URE 78-1

Queuing template.

622

Microsoft Excel 2010: Data Analysis and Business Modeling

After you enter the following data, the template c

. dThe

parameter

in cells B6:B9 can easily be estimated by using p

■

Number of servers (cell B5)

■

Mean interarrival time (cell B6)

■

Mean service time (cell B7)

■

Standard deviation of interarrival times (cel

■

Standard deviation of service times (cell B9)

Here’s an example of the template in action. You wa

characteristics of an airline security line duri

number of agents working. In the

Queuing Data

shown in Figure 78-2, I’ve tabulated interarriva

been hidden.)

Fig

URE 78-2

Airline interarrival and service times.

By copying from cell B1 to ,C1you

thefnd

formula

the mean

AVERAG

int

time is 12.864 seconds and the mean service

time i

vice time is almost six times as large as mean i

to guarantee a steady state. Copying from cell B

you that the standard deviation of the interarri

deviation of the service times is 48.051 seconds

Chapter

Queuing

Theory: The Mathematics

623

of Waiting in Line

Returning to the queuing template in the

Model

B6:B9 and enter six servers in cell B5, you fn

236 people will be in line (cell B19). You’ve p

I used a one-way data table (shown in Figure 7

of agents affects the system’s performance. In c

to consider (6 through 10). In (

cell

=B19

), G9,

and Iinente

H9,

I enter the formula

(

=B18

). to

Next,

compute

I select

the table r

click Data Table from the What-If Analysis men

number of servers) as the row input cell, I ob

that adding just one ticket agent to the origi

of customers present in line from 236 to fewer th

customer’s average time in the system from 3,0

minutes). This example shows that a small incr

performance of a queuing system.

Fig

URE 78-3

Sensitivity analysis for an airport security lin

In cells F16:K22, I used a two-way data table t

the system

) to (changes in the number of servers an

The row input cell is B5, and the column input c

increase in the standard deviation of service ti

29 percent increase in the mean time in the sy

Not

Readers who are interested in a more extensive d

refer to my book

Operations Research: Applications a

624

Microsoft Excel 2010: Data Analysis and Business Modeling

Problems

A bank has six tellers. Use the following inform

■

Mean service time equals 1 minute.

■

Mean interarrival time equals 25 seconds.

■

Standard deviation of service times equals 1 mi

■

Standard deviation of interarrival times equal

Determine the average time a customer waits i

On average, how many customers are present in th

Would you recommend adding more tellers?

Suppose it costs $20 per hour to have a telle

at $15 per hour. How many tellers should you h

Thirty women work on the ffth floor of a busin

the restroom three times a day (the offce is o

takes 180 seconds on average, with a standard d

standard deviation of time between arrivals t

toilets would you recommend for the woman’s r

625

Chapter 79

Estimating a Demand C

Questions answered in this chapter:

■

What do I need to know to price a product?

■

What is the meaning ?of

elasticity of demand

■

Is there any easy way to estimate a demand c

■

What does a demand curve tell us about a cu

product?

Every business must determine a price for each o

diffcult. In Chapter 80, “Pricing Products by U

by Using Subjectively Determined Demand,” I’ll d

you in pricing a product to maximize proftabil

the excellent book

, by

Power

Robert

Pricing

J. Dolan and Hermann

Answers to This Chapter’s Qu

What do i need to know to price a product?

Let’s consider a product such as a candy bar. I

you need to know two things:

■

The variable cost of producing each

unit of th

■

The product’s

demand

curve. Simply

tells

put,

you

a th

of a product a customer will demand at

each p

per unit, the demand curve

, which

gives

equals

you athe

numb

of the product that will

. Ofbecourse,

demanded frm’s

at prid

constantly changing and often depends on fa

the state of the economy and a competitor’s p

After you know

and the demand curve,

isthe

simpl

(p–UC)*D(p)

. After you have,an

which

equation

givesfor

the

D(p)

quantit

demanded for each price, you can use the Micro

maximizing price, which I’ll show you how to d

626

Microsoft Excel 2010: Data Analysis and Business Modeling

What is the meaning of

elasticity of demand

Given a demand curve, the

price elasticity

for d

demand resulting from a 1 percent increase in pr

demand is price elastic. When demand is price el

elasticity is less than 1 percent, demand is pri

price cut decreases revenue. Here are some obser

■

Salt, 0.1 (very inelastic)

■

Coffee, 0.25 (inelastic)

■

Legal fees, 0.4 (inelastic)

■

TV sets, 1.2 (slightly elastic)

■

Restaurant meals, 2.3 (elastic)

■

Foreign travel, 4.0 (very elastic)

A 1-percent decrease in the cost of foreign trav

increase in demand for foreign travel.

is there any easy way to estimate a demand curve

Using

to represent the quantity demanded of a p

forms for estimating demand curves are as follow

■

Linear demand

In this

curve

case, demand follows a str

form

q=a–bp

. For example,

q=10–p

is a linear demand c

determined by using a method that I’ll descri

curve is linear, the elasticity is constantly c

■

Power demand

curve

this situation, the demand curv

curve of the form

q=ap

b<0

. (See Chapter 51, “The Power

Cur

tion.) Again,

and

can be determined by th

The equation

q=100p

-2

is an example of a power demand cu

a power curve, for any price the elasticity e

q=100p

the price elasticity of demand always e

Suppose that a product’s demand curve follows a l

the current price and demand for a product and th

determining the product’s demand curve is a simp

A product is currently selling for $100 and dema

elasticity for demand is 2. Assuming the demand c

equation of the demand curve. The solution is in th

Figure 79-1.

Chapter

Estimating

a Demand

627

Curve

Fig

URE 79-1

Fitting a linear demand curve.

Given two points, you know that a unique strai

you actually know two points on the demand

. Because

cur

elasticity of demand equals 2, a 1-percent inc

in demand. Thus, if

p=101

(a 1-percent increas

units) to 490. Thus

p=101

and

q=490

is a secon

use the Excel trendline to fnd the straight li

(101,490).

You begin by entering these points in the work

Figure 79-1. Then you select the range D4:E6, a

Insert tab, choose Scatter, Scatter With Strai

chart, you see the graph has a positive slope. T

demand, which cannot be correct. The problem

sumes that the data points you want to graph a

To be sure that Excel understands that the ind

the graph, and on the ribbon, click the Design t

Switch Row/Column in the Data section of the D

Data button, you can change the source data th

one of the points, click Add Trendline, and th

On Chart options. After clicking OK in the Add T

line plot, complete with the equation shown

in Fi

mand, the equation for the

. demand

This equation

curve is

means

q=1

increase in price costs you 10 units of demand

values of

because for large values demand.

a l

628

Microsoft Excel 2010: Data Analysis and Business Modeling

For prices near the current price, however, the l

approximation of the product’s true demand curve

As a second example, let’s again assume that a p

demand equals 500 units. The product’s price ela

power demand curve to this information. See the fl

Fig

URE 79-2

Power demand curve.

In cell E3, I enter

. Then,

a trial

in cell

value

D5, for

I enter

the c

elasticity of demand equals 2, we know that the d

where

is unknown. In cell E5, I enter the demand for a p

in cell E3, with

. Nowthe

I can

formula

use the

a*D5^-2

Goal Seek c

see Chapter 18, “The Goal Seek Command”)- to dete

mand for price $100 equal to 500 units. I simply s

E3. I fnd that a value for

of 5 million yields a d

demand curve (graphed in Figure 79-2) is given by

For any price, th

elasticity of demand on this demand curve equals 2

What does a demand curve tell us about a custome

product?

Let’s suppose you are trying to sell a software p

equal the number of copies of the program the co

charged for the software. Suppose you have estim

is given .

byClearly,

q=400–p

your customer is willing to p

of the software program. Locked inside this dema

the company is willing to pay for each unit of th

maximizing proftability of sales.

Chapter

Estimating

a Demand

629

Curve

Let’s rewrite the demand

. Thus,

curve

,when

p=$399

,as

q=1

and

p=400–q

so on. Now l

try and fgure out the value the customer- attac

gram. Assuming that the customer is rational, t

value of the unit exceeds your price. At a pri

cannot be worth $400. At a price of $399, howe

frst unit must be worth something between $399 a

thceustomer does not purchase the second unit. A

is purchasing two units, so the customer does p

customer values the second unit somewhere betw

It can be shown that the bestthapproximation

unit purchased

of by

th th

customer is the price that

. For

makes

example,

demand by

equal

setti

0.5, the value of the .frst

Similarly,

unit is

, by

400–0.5=$39

thesetting

value o

second unit is.

400–1.5=$398.50

Problems

Suppose you are charging $60 for a board ga

thousand copies during the last year. Elasti

Use this information to determine a linear a

For each of your answers in Problem 1, dete

two thousandth unit purchased of your game.

631

Chapter 80

Pricing Products by U

Question answered in this chapter:

■

How does the fact that customers buy razor b

proft-maximizing price of razors?

Certain consumer product purchases frequently r

tie-ins

. Here are some examples:

Original purchasTie-in product

Razor

Razor blades

Men’s suit

Shirt and/or tie

Personal computerSoftware training manual

Video game console

Video game

Using the techniques I described in Chapter 79

determine a demand curve for the product that’

Microsoft Excel Solver to determine the origin

proft earned from the original and the tie-in p

this analysis is done.

Answer to This Chapter’s Que

How does the fact that customers buy razor bla

proft-maximizing price of razors?

Suppose that you’re currently charging $5.00 f

Assume that the variable cost of producing a r

elasticity of demand for razors is 2. What pri

Let’s assume (incorrectly) that no purchasers o

demand curve (assuming a linear demand curve) a

data and the chart on the

No Blades

worksheet i

on the demand curve are price=$5.00, demand=6 mi

of 1 percent), demand=5.88 million (2 percent l

inserting a linear trendline as shown in Chapt

y=18–2.4x

Because

equals price and

equals dem

razors as follows:

demand

(in millions)=18–2.4

632

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 80-1

Determining the proft-maximizing price for razors.

I associate the names in cell C6 and the range C

enter a trial price in D9 and determine

formula

demand f

18-2.4*price

Then I determine in cell D11 the proft fo

demand*(price–unit_cost)

Next, I use Solver to determine the proft-maximi

is shown in Figure 80-2.

Fig

URE 80-2

Solver Parameters dialog box set up for maximizing r

I maximize the proft cell (cell D11) by changing th

because the target cell multiplies together two q

Chapter

Pricing

Products by

633

Using Tie-Ins

depending on the changing cell. Solver fnds th

(Maximum proft is $18.15 million.)

Now let’s suppose that the average purchaser o

$0.15 of proft per blade purchased. How does thi

razor? Assume that the price of a blade is fxe

blade price changes.) The analysis is in the

Fig

URE 80-3

Price for razors with blade proft included.

I used the Create From Selection command in th

tab to associate the names in cells C6:C11 with c

Demand

Not

Astute readers will recall that I also .named ce

What does Excel do when you use the range name

Dem

the cell named

Demand

in the current worksheet. In o

Demand

in the

Blades

worksheet, Excel refers to ce

the

No Blades

worksheet.

In cells D7 and D8, I entered the relevant inf

trial price for razors, and in D10 I.computed

Next,

in cell D11, I computed total proft from razor

demand*(price–unit_cost)+demand*blades_per_raz

. Notice that

demand*blades_per_razor*proft_per_blade

is the p

The Solver setup is exactly as was shown

maximize

earli

the proft. Of course, now the proft formula in

shows that proft is maximized by charging

razor.only $

This price results from making so much money f

634

Microsoft Excel 2010: Data Analysis and Business Modeling

ensuring that many people have razors even thoug

companies do not understand the importance of th

them to overprice their primary product and not m

Problems

Not

n all of the following problems, assume a linear d

You are trying to determine the proft-maximiz

Currently, you are charging $180 and selling 2 mi

produce a console, and price elasticity of de

you charge for a console?

Now assume that, on average, a purchaser of y

games and you earn $10 proft on each video ga

consoles?

In the razor and blade example, suppose the c

charge $0.35 for a blade, a customer buys an a

elasticity of demand for blades is 3. What pr

blade?

You are managing a movie theater that can han

week. The current demand, price, and elastici

candy are given in Figure 80-4. The theater k

cost per ticket, popcorn sales, candy sales, a

linear demand curves, how can the theater max

fraction of patrons who purchase the given fo

Fig

URE 80-4

Movie problem data.

A prescription drug is produced in the United S

of the drug costs $60 to produce. In the Germ

150 euros per unit. The current exchange rate i

demand for the drug is 100 units, and the esti

demand curve, determine the appropriate sales p

635

Chapter 81

Pricing Products by U

Subjectively Determ

Questions answered in this chapter:

■

Sometimes I don’t know the price elasticity f

believe a linear or power demand curve is r

and use Solver to determine a proft-maximiz

■

How can a small drugstore determine the pro

Answer to This Chapter’s Que

Sometimes i don’t know the price

n other

elasticity

situations

believe a linear or power demand curve is rele

curve and use Solver to determine a proft-maxi

In situations when you don’t know the price el

rely on a linear or power demand curve, a good wa

is to identify the lowest price and highest

timate the product’s demand with the high pric

the high and low prices. Given these three poi

use the Microsoft Excel trendline feature to f

formula (which I’ll call Equation 1):

Demand=a(price)

+b(price)+c

For any three specifed points

and

the

exist

demandtha

Equation 1 exactly ft the three specifed point

demand curve, it seems reasonable to believe

sentation of demand for other prices. You can th

maximum proft, which is given by. the

The formula

followin

(

example shows how this process works.

How can a small drugstore determine the proft-

Let’s suppose that a drugstore pays $0.90 for e

considering charging from $1.50 through $2.50 f

price of $1.50, it will sell 60 units per week

a price of $2.00, the store thinks it will sel

per week. What price should the store charge f

636

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 81-1

Lipstick pricing model.

You begin by entering the three points with whic

range E3:F6. After selecting E3:F6, click the Ch

select the frst option for a Scatter chart. You c

Trendline. In the Format Trendline dialog box (s

2 in the Order box (to obtain a quadratic curve o

option Display Equation On Chart.

Fig

URE 81-2

Confguring the Format Trendline dialog box for sele

Chapter

Pricing

Products by Using Subjectively

637

Determined Demand

Excel creates the chart shown in Figure 81-1. T

Demand=–44*Price

+136*Price–45

Next, you insert a trial price in cell I2. You c

cell I3 with the formula

–44*price^2+136*price

named.)cell

ThenI2

-you

Price

pute weekly proft from lipstick sales in

. cell I

(Cell E2 is ,

named

and cell

Unit_Cost

I3 .)

is Then

named

you

Demand

use Solve

the price that maximizes proft. The Solver Par

Note that I constrain the price to be from the l

($1.50 through $2.50). If you allow Solver to c

demand curve might slope upward, which implies th

demand. This result is unreasonable, which is w

Fig

URE 81-3

Confguring the Solver Parameters dialog box to c

The result is that the drugstore should charge $

49.4 units per week and a weekly proft of $56.

The approach to pricing outlined in this chapt

price elasticity. Inherently, the Solver

- consi

mines the proft-maximizing price. This approac

that sell thousands of different products. The o

product is its variable cost and the three giv

638

Microsoft Excel 2010: Data Analysis and Business Modeling

Problems

Suppose it costs $250 to produce a video game c

$400 is under consideration. Estimated demand f

following table.

Price

Demand (in millions)

$200

$300

0.9

$400

0.2

What price should you charge for a game conso

This problem uses the demand information give

an average of 10 video games. You earn $10 pr

you charge for the game console?

You are trying to determine the correct

variable

price f

cost of printing and distributing a copy of th

of charging from $0.50 through $1.30 per copy

magazine are shown in the following table.

Price

Demand (in millions)

$0.50

$0.90

1.2

$1.30

0.3

In addition to sales revenue from the magazin

copies sold for each of the 20 pages of adver

should you charge for the magazine?

639

Chapter 82

Nonlinear Pricing

Questions answered in this chapter:

■

What is linear pricing?

■

What is nonlinear pricing?

■

What is bundling, and how can it increase p

■

How can I fnd a proft-maximizing nonlinear p

Answers to This Chapter’s Qu

What is linear pricing?

In Chapter 80, “Pricing Products by Using Tie-

Using Subjectively Determined Demand,” I show h

for a product. In those chapters’ examples, how

matter how many units a customer purchases, th

unit. This model is known as

linear pricing

function of

namely,.

cost

You will

of x

see

units=(unit

in this c

pricing

can often greatly increase a company’s p

What is nonlinear pricing?

nonlinear pricing

scheme simply means that th

function

. Weofhave

all encountered nonlinear pric

■

Quantity discounts

The frst fve units might cost $20 e

$12 each. Quantity discounts are commonly u

computers. An example of the cost of purcha

Pricing Examples

worksheet in the fle Nlp.x

that the graph has a slope of 20 for fve or f

more than fve units purchased.

640

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 82-1

Cost of quantity discount plan.

■

Two-part

When

tariff

you join a country club,

joining

you usu

the club and then a fee for each round of gol

club charges a membership fee of $500 per yea

This type of pricing strategy

. For thiscalled

pricing

two

pol

of purchasing a given number of rounds of gol

the

Nonlinear Pricing Examples

worksheet in N

of 520 from zero through one unit purchased a

purchased. Because a straight line must alway

two-part tariff is highly nonlinear.

Fig

URE 82-2

Cost of two-part tariff.

What is bundling, and how can it increase profta

Price bundling involves offering a customer a se

of the products’ individual prices. To analyze w

how a rational consumer makes decisions.- For eac

nal consumer looks at the value of what you are s

Chapter

Nonlinear

Pricing

641

it. This yields the

consumer surplus

of the pu

consumer surplus of each available option is n

the product combination having the largest con

So how can bundling increase your proftability

printers and have two customers. The values ea

a printer are shown here:

Customer Computer value

Printer value

$1,000

$500

$1,000

You only offer the computer and printer for sa

and for a computer, you will sell one printer

enue. Now suppose that you offer the printer a

customer buys both the computer and the printe

bundling the computer and printer, you can extr

Bundling works best if customer valuations

for th

lated. In this example, the negative correlati

results because the customer who places a high v

a computer, and the customer who places a low v

a computer.

When you go to a theme park such as Disneyland

buy a ticket to enter the theme park or you do

because the consumer does not have the option o

ucts. This approach reduces lines (imagine a l

To see why this bundling approach increases pr

and that the number of rides the customer want

that is calculated as

(Number

. From

the

rides)=20–2*(

discussion o

curves in Chapter 79, “Estimating a Demand Cur

gives th

to ride

the

is the price that

. Thus,

makes you

demand

knowe th

i–0.5=20–2*(value of ride

that

or,

(value

solving

.for

ride

The frst ride is worth $9.75, the second ride i

which is worth $0.25.

Assume you charge a constant price per ride an

You seek the proft-maximizing linear pricing s

Nlp.xlsx, shown in Figure 82-3, I show how to d

642

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 82-3

Proft-maximizing linear pricing scheme.

I associate the range names in C8:C10 with cells D

compute the number of ride tickets purchased

. Then Iin c

compute the proft in cell D12 with

. Ithe

canformula

now use

Solver to maximize the value in D12 (proft) by c

in eight ride tickets being purchased, and I ear

Now let’s pretend that you’re like Disneyland an

customer. You set a price equal to the sum of th

($9.75+$9.25+…$0.75+$0.25=$100.00)

The customer values all 20 ri

the customer will buy a park entry ticket for $1

$2.00(20)=$60.00

, which almost doubles your proft from l

How can i fnd a proft-maximizing nonlinear prici

In this section, I’ll show how you can determine a

plan for the amusement park example. I’ll procee

■

Hypothesize trial values for the fxed fee and th

■

Determine the value the customer associates

■

Determine the cumulative value associated with b

■

Determine the price charged for

rides:

Fixe

■

Determine the consumer surplus for buying

■

Determine the maximum consumer surplus.

■

Determine the number of units purchased. If th

negative, no units are purchased. Otherwise, I

number of units yielding the maximum surplus.

■

Use a VLOOKUP function to look up revenue cor

purchased.

■

Compute proft as

revenue–costs

■

Use a two-way data table to determine a proft

The work for this approach is in the

Two-Part Ta

shown in Figure 82-4.

Chapter

Nonlinear

Pricing

643

To begin, I named

, and cell

. I F2

entered

Fixed

trial values f

price per ride in cells F2 and F3. Next, I det

ride by copying from cell E6.to

I fnd

E7:E25

that the

for

places a value of $9.75 on the frst ride, $9.2

Fig

URE 82-4

Determination of optimal two-part tariff.

To compute the cumulative value of the frst

SUM($E$6:E6)

. This formula adds up all values in col

row. By copying from G6 to G7:G25 ,the

I compute

formula th

cost of

rides. For example, the cost of fve r

Recall that the consumer surplus for.

rides e

copying from cell H6 to the, range

I compute

H7:H25

the

con

er’s

surplus for purchasing any number of rides. F

purchasing fve rides is –$24.75, which is the r

In cell H4, I compute the maximum consumer

sur

Remember that if the maximum consumer surplus i

Otherwise, the consumer will purchase -the numb

sumer surplus. Therefore, entering in cell

, I I1 th

determine the number of units purchased (in thi

fnds the number of rows I need to move down in th

the maximum surplus.

I now name the range

. I D5:G25

can then

as look

Lookup

total r

umn of this range based on the number of units p

I1). The total revenue is computed in cell

. I2 w

Notice that if no rides are purchased, I earn n

644

Microsoft Excel 2010: Data Analysis and Business Modeling

rides purchased in cell

. In

I3cell

withJ6,

theIformula

compute

I1*C

pro

costs with the

formula

I2–I3

Now I can use a two-way data table to determine th

fee and price per ride. The data table is shown i

hidden.) In setting up the data table, I vary th

values in the range K10:K60) and vary the price p

in L9:BE9). I recomputed proft

in cell K9 with th

I select the table range (cells K9:BE60), and th

click What-If Analysis and then select Data Tabl

and the row input cell is F3 (the price per ride

the proft for each fxed fee and price per ride c

Fig

URE 82-5

Two-way data table computing optimal two-part tari

To highlight the proft-maximizing two-part tarif

range L10:BE60. Click Conditional Formatting on th

then click Top 10 Items. Then change the 10 in th

proft is formatted. Here, a fxed fee of $56.00 a

$63.50, which almost doubles the proft from line

per ride of $2.30 also yields a proft of $63.50.

Because a quantity-discount plan involves selecti

low price), you cannot use a data table to deter

plan. You might think you could use a Solver mod

Chapter

Nonlinear

Pricing

645

price, and low price) to determine a proft-max

Excel 2010, the Solver often had diffculty det

cell is computed by using formulas containing I

the quantity-discount problem with ease, even w

xlsx (see Figure 82-6) I used the Evolutionary S

quantity-discount plan. I assumed that all uni

at a high price (called HP) and that the remai

The only change in the spreadsheet setup is in c

names in E1:E3, I compute the amount a person w

by copying from G6 to G7:G25 the formula

. The

IF(D6

Solver Parameters dialog box setup is shown in Fi

“Warehouse Location and the GRG Multistart and E

Evolutionary Solver here because the model use

cells. I also changed the Mutation Rate under E

Iconstrained the cutoff point to be an integer a

changing cells. Of course, if Solver had chose

upper bound on the price changing cells.

The Solver found a maximum proft of $63.97, ob

units purchased and $1.84 for the remaining uni

run Solver longer, it would have found the tru

Fig

URE 82-6

Use of Solver to fnd the proft-maximizing quanti

646

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 82-7

Solver settings for maximizing a quantity-discount p

Problems

You own a small country club and have three t

of golf they play during a month as shown in th

Round . noCustomer Customer

type 1

Customer

type 2

type 3

$60

$50

$40

$50

$45

$30

$40

$30

$20

$30

$15

$10

$20

$10

Find a proft-maximizing two-part tariff.

Suppose you are going to offer a pure bundle. F

fve rounds of golf for $60 per month. The mem

than the pure bundle. What pure bundle maximi

647

Chapter 83

Array Formulas and F

Questions answered in this chapter:

■

What is an array formula?

■

How do I interpret formulas such ?

(D2:D7)*

■

I have a list of names in one column. These n

transpose the listed names to one row so th

are reflected in the new row?

■

I have a list of monthly stock returns. Is th

from –30 percent through –20 percent, –10 p

will automatically update if I change the o

■

Can I write one formula that will sum up th

■

Is there a way to look at two lists of name

lists?

■

Can I write a formula that averages all num

value?

■

I have a sales database for a small makeup c

units sold, and dollar amount for every

tra

cal functions or COUNTIFS, SUMIFS, and AVER

also use array functions to summarize the d

units of makeup a salesperson sold, how man

many units were sold by a specifc salespers

■

What are array constants and how can I use th

■

How do I edit array formulas?

■

Given quarterly revenues for a toy store, c

store’s revenues?

■

Given a list of transactions in different c

a transaction in each country?

Answers to This Chapter’s Qu

What is an array formula?

Array formulas often provide a shortcut or mor

calculations with

array

Microsoft

formula

result

Excel.

can return

An either

648

Microsoft Excel 2010: Data Analysis and Business Modeling

range of cells. Array formulas perform

array

operation

arguments

. Each array argument used in an array form

number of rows and columns.

When you enter an array formula, you must frst s

place the array formula’s results. Then,

- after e

lected range,

you must

. If

press

you fail

Ctrl+Shift+Enter

to press Ctrl+, y

incorrect or nonsensical results. I refer to the p

pressing Ctrl+Shift+Enter as

array-entering

a fo

Excel also contains a

. variety

In Chapter

array

42, “Summarizin

functions

Descriptive Statistics,” I discuss the array fun

(LINEST and TREND) in Chapter 53, “Introduction t

“Incorporating Qualitative Factors into Multiple Re

use an array function you must frst select the r

placed. Then, after entering the function in the fr

press Ctrl+Shift+Enter. In this chapter, I’ll in

TRANSPOSE, FREQUENCY, and LOGEST.

As you’ll see, you cannot delete any part of a c

an array formula. Also, you cannot paste an arra

blank cells and array formulas. For example, if y

you want to copy it to the cell range C10:J15, y

range because the range contains both blank cell

around this diffculty, copy the formula from C10 t

C10:J10 to C11:J15.

The best way to learn how array formulas and fun

so let’s get started.

How do i interpret formulas such as ?

(D2:D7)*(E2:

In the

Total Wages

worksheet in the fle Arrays.x

the hourly wage rates for six employees, as you c

Fig

URE 83-1

Using array formulas to compute hourly wages.

Chapter

Array

Formulas and

649

Functions

If you want to compute each person’s total wag

the formula

. There

D3*E3

is certainly nothing wrong with th

formula provides a more elegant solution. Begi

want to compute each person’s total

(D2:D7*E2:E7)

earnings.

, and

press Ctrl+Shift+Enter. You will see that each p

Also, if you look at the Formula bar, you’ll

The curly brackets are the way Excel tells you th

enter the curly brackets that show up at the b

indicate that a formula is an array formula in thi

To see how this formula works, click in the Fo

then press F9. You

, which

will see

is the

{3;4;5;8;6;7}

way Excel crea

as an array. Now select E2:E7 in the Formula b

{6;7;8;9;10;11}

, which is the way Excel creates an arra

inclusion of the asterisk (*) tells Excel to m

Because the cell ranges being multiplied inclu

items, and because you selected a range of six c

its own cell. Had you selected a range of only f

be displayed.

Suppose you want to compute the total wages ea

is to use the formula

=SUMPRODUCT(D2:D7,E2:E7)

. Again, however, let’s tr

array formula to compute total wages. Begin by s

to place the result. Then

SUM(D2:D7*E2:E7)

enter .

inAfter

cell pressi

G2 the f

Ctrl+Shift+Enter, you obtain

(3)(6)+(4)(7)+(5)

. To see how thi

formula works, select the

D2:D7*E2:E7

portion i

see

SUM({18;28;40;83;60;77})

, which shows that Excel created a s

element ,

iswhose

3*6(18)

second ,element

and so is

on,

4*7(28)

until the l

7*11

. Excel

(77)

then adds up the values in the ar

i have a list of names in one column.

s thereThese

an easy

na w

to transpose the listed names to one row so th

names are reflected in the new row?

In the

Transpose

worksheet in the fle Arrays.x

names in cells A4:A8. The goal is to list thes

knew that the original list of names would nev

by copying the cell range and then using the T

box. (See Chapter 14, “The Paste Special Comma

in column A change, the names in row 3 would n

Special, Transpose. What you need in this situ

650

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 83-2

Using the TRANSPOSE function.

The TRANSPOSE function is an array function that c

columns, and vice versa. To begin using TRANSPOS

C3:G3, where you want the transposed list of nam

enter the formula .

=TRANSPOSE(A4:A8)

The list of names is now disp

importantly, if you change any of the names in A

the transposed range.

i have a list of monthly

s therestock

a wayreturns.

to determine th

returns from –30 percent through –20 percent, –1

on that will automatically update if i change th

This problem is a job for the FREQUENCY array fu

how many values in an array

) occur

(called

withinthe

given

data

value

arr

by a bin array). The syntax of

data

the FREQUENCY

bin

array

fun

To illustrate the use of the FREQUENCY function, l

Arrays.xlsx fle, shown in Figure 83-3. I’ve list

the cell range A4:A77.

I found in cells A1 and A2 (using the MIN and MA

percent through 53 percent. Based on this inform

C7:C17, starting at –0.4 and ending at 0.6. Now I s

results of the FREQUENCY function to be placed. I

of data points less than or equal to –0.4, D8 wi

than –0.4 and less than or equal to –0.3, and so o

than 0.5 and less than or equal to 0.6, and cell D

greater than 0.6.

Chapter

Array

Formulas and

651

Functions

Fig

URE 83-3

Using the FREQUENCY function.

I enter the formula

=FREQUENCY(A4:A77,C7:C17)

and then press Ctrl+Shi

formula tells Excel to count the number of dat

each of the bin ranges defned in C7:C17. The r

–0.4 and less than or equal to –0.3. Thirteen r

equal to 0.2. If you change any of the data po

the FREQUENCY function in cells D7:D17 will re

Can i write one formula that will sum up the s

In the cell range A4:A10 in the

Sum Up 2nd Dig

seven integers. (See Figure 83-4.) I would lik

digit of each number. I could obtain this sum by c

VALUE(MID(A4,2,1))

. This formula returns (as a numerica

A4. Then I could add up the range B4:B10 and o

Fig

URE 83-4

Summing second digits in a set of integers.

652

Microsoft Excel 2010: Data Analysis and Business Modeling

An array function makes this process much easier

formula

=SUM(VALUE(MID(A4:A10,2,1))

. Your array formula will retur

To see what this formula does, highlight

MID(A4:

F9. You will see

{“4”;”5”;”6”;”6”;”0”;”3”;”3”}

. This string of values shows th

an array consisting of the second digit (viewed a

portion of the formula changes these text string

by the SUM portion of the formula.

Notice that in cell A11, I entered a number with o

second digit, the MID portion

. How

of can

our you

formula

modify

retthi

formula to account for the possible inclusion of o

E8 the formula

{SUM(IF(LEN(A4:A11)>=2,VALUE(MID(

. This formula rep

any one-digit integer with a 0, so you still obt

is there a way to look at two lists of names and d

lists?

In the

Matching Names

worksheet in the fle Array

columns D and E), as you can see in Figure 83-5. H

on List 1 also appear on List 2. To accomplish thi

enter in cell C5 the formula

. This

={MATCH(D5:D28,E5:E

formula loops th

C5:C28. In cell C5, the formula verifes whether th

match exists, the formula returns the position o

the formula returns

#NA

(for not available). Simi

the second name on List 1 has a match. You see, f

the second list but Harrington does (frst matche

Fig

URE 83-5

Finding duplicates in two lists.

Chapter

Array

Formulas and

653

Functions

To enter Yes for each name in List 1 with a ma

namweithout a match, select the cell range B5:B

{IF(ISERROR(C5:C28),”No”,”Yes”)}

in cell B5. T

containing the #NA message and Yes for all cel

=ISERROR(x)

yields True if the formula

evalu

Can i write a formula that averages all number

to the list’s median value?

In the

Average Those > Median

worksheet in the A

range D5:D785)(named

contains

Prices

a list of prices. I’d l

at least as large as the median price. In cell F

Median(prices)

. In cell F3, I compute the average of n

median by entering the formula

=SUMIF(prices,”

This formula adds up all prices that are at le

divides by the number of prices that are at le

prices at least as large as the median price i

Fig

URE 83-6

Averaging prices at least as large as the median p

An easier approach is to select cell F6 and ar

DIAN(prices),prices,””))}

. This formula creates an array that c

price is greater than or equal to the median p

gives you the results you want.

654

Microsoft Excel 2010: Data Analysis and Business Modeling

i have a sales database for a small makeup compa

product, units sold, and dollar amount for every t

database statistical

FS,

functions

SUM

FS, andgE

AVERA

iFS COUNT

to summa

rize this data, but can i also use array functio

questions such as how many units of makeup a sal

lipstick were sold, and how many units were sold by a s

lipstick?

The Makeuparray.xlsx fle contains a list of 1,90

company. For each transaction, the transaction

uct sold, units sold, and dollar volume are list

Fig

URE 83-7

Makeup database.

This data can easily be summarized by using data

in Chapter 46, “Summarizing Data with Database S

COUNTIFS and SUMIFS functions. (See Chapter 20, “

COUNTA, and COUNTBLANK Functions,” and Chapter 2

and AVERAGEIFS Functions”). As you’ll see in thi

powerful alternative to these functions.

How many units of makeup

You can

did

easily

Jen

question

sell?

answer

using

bythis

the

SUMIF function. In this worksheet, I named the c

M5:M1904.

Units

I entered in cell E7 the formula

SUMIF(

units sold by Jen. The total is 9,537 units. You c

in cell E6 the formula

=SUM(IF(J5:J1904=”Jen”,M5

. This formula create

that contains the units sold for a transaction m

Therefore, summing this array also yields the nu

see in Figure 83-8.

Chapter

Array

Formulas and

655

Functions

Fig

URE 83-8

Summarizing data with array formulas.

How many units of lipstick

This question

did Jen

requires

sell?

a cr

two columns (Name and Product). You could answ

statistical function

DSUM(J4:N1904,4,E9:F10)

formula

, which

is entered in c

formula shows that Jen sold 1,299 units of lip

the array formula

=SUM((J5:J1904=”jen”)*(L5:L190

entered in cell F6,

To understand this formula, you need to know a b

formula that reads

(J5:J1904=”jen”)

creates a B

equals

Jen,

the array includes the value True, a

equal

Jen,

the array contains False. Similarly

creates a Boolean array with a True correspond

the word

lipstick

and a False corresponding to e

Boolean arrays are multiplied, another array i

■

True*True=1

■

True*False=0

■

False*True=0

■

False*False=0

In short, multiplying Boolean arrays mimics th

Boolean arrays by the values in the range M5:M

Jen sold lipstick, this array contains the uni

Summing this array yields Jen’s total lipstick s

■

How many units were sold

cell

Jen

G7,

or were

I used

lip

statistical function

=DSUM(J4:N1904,4,E12:F

Jen or that were lipstick total 17,061. In c

656

Microsoft Excel 2010: Data Analysis and Business Modeling

were sold by Jen or that were lipstick by arr

”jen”)+(L5:L1904=”lipstick”),1,0)*M5:M1904)}

Again, the portion of this formula that reads

two Boolean arrays. The frst array contains True i

sensitive) is the salesperson. The second array c

lipstick. When Boolean arrays are added, the fol

■

False+True=1

■

True+True=1

■

True+False=1

■

False+False=0

In short, adding Boolean arrays mimics the OR op

array in which each row where Jen is the salespe

number of units sold multiplied by 1. In any oth

by 0. The same result is obtained as with the da

Can I summarize the number of units

salesperson?

Array

each prod

formulas make answering a question such as this a s

salesperson’s name in the

product

cell range

name A17:A25

in the cell

and er

B16:F16. Now you array-enter in cell B17 the for

*($L$5:$L$1904=B$16)*$M$5:$M$1904)}.

This formula counts only units of eye liner sold by A

formula to C17:F17, I compute the units of

each p

mulas in C17:F17 to C18:C25 and compute the numb

salesperson. Notice that I add a dollar sign to A i

pull the person’s name, and I add a dollar sign t

always pull the product.

Not

Astute readers might ask why I simply didn’t sele

in one step to fll in the table. Remember that you c

that contains both blank cells and array formulas, w

C17:F17 and then dragged it down to complete the tab

What are array constants and how can i use them?

You can create your own arrays and use them in a

values in curly brackets, { }. You need to enclo

You can also include the logical values True and F

symbols such as dollar signs or commas are not a

Chapter

Array

Formulas and

657

Functions

As an example of how an array constant might b

worksheet in the Arrays.xlsx fle, shown in Fig

Fig

URE 83-9

Creating second and fourth powers of sales.

In this worksheet, you’re given sales during s

month the second, third, and fourth power of s

where you want the resulting computation to be p

=C4:C9^{2,3,4}

. In the cell range D4:D9, this formula l

in C4:C9. In the cell range E4:E9, the formula l

Finally, in the cell range F4:F9, the formula l

to the fourth power. The array constant {2,3,4

power values.

How do i edit array formulas?

Suppose you have an array formula that creates r

move, or delete the results. You cannot edit a s

formula, however, you can begin by selecting a

in the array. By pressing F2 to edit a cell in th

making the changes, press Ctrl+Shift+Enter to e

array will reflect your changes.

given quarterly revenues for a toy store, can

the store’s revenues?

The Toysrustrend.xlsx fle, shown in Figure 83-

of dollars) for a toy store during the years 1

trend in revenues as well as the seasonality a

January–March; second quarter equals April–Jun

fourth Quarter equals October–December). A tre

means that sales are increasing at 1 percent p

of 0.80, for example, means that sales during Q

average quarter.

The trick to solving this problem is to use th

to predict a variable

1,from

2,…,

, independent

and

you believe

varia

values

,1,

2,…,

b a

the relationship

1,2,…,

between

given

and

(b2)

(bn)

. (I’ll call this Equation 1.)

658

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 83-10

Toy revenue trend and seasonality estimation.

The LOGEST function is used

1,2,…,

determine

that best

values

ft thi

to the observed data. To use the LOGEST function t

following:

■

equals quarterly revenues.

■

1 equals the quarter number (listed in chrono

Quarter 1, the next quarter is Quarter 2, and s

■

2 equals 1 if the quarter is the frst quarter o

■

3 equals 1 if the quarter is the second quart

■

4 equals 1 if the quarter is the third quarte

You need to choose one quarter to leave out of th

quarter.) This approach is similar to the one us

model you choose to estimate is then

y=a(b1)

(b2)

(b3)

(b4)

. When the LOGEST fu

determines,1,

values

and

4ofthat

best ft the data, the v

follows:

■

is a constant used to scale the forecasts.

■

1 is a constant that represents the average p

store sales.

■

2 is a constant that measures the ratio of fr

(fourth quarter) sales.

■

3 is a constant that measures the ratio of se

quarter’s sales.

■

4 is a constant that measures the ratio of thi

sales.

Chapter

Array

Formulas and

659

Functions

To begin, I created the dummy variables for Qu

from G6 to G6:I27 the. formula

Remember

IF($D6=G$4,1,0)

that a fourth q

Excel because all three dummy variables equal 0 d

can leave out the dummy variable for this quar

I now select the cell range K6:O6, where I wan

The constant

will be placed in the right-mos

ing to the ordering of the independent variabl

the constant, then the Quarter 1 coeffcient, a

The syntax I use for the

LOGEST

range,x

function

range,True,Tr

. After is

arra

entering in cell K6 the formula

=LOGEST(E6:E27

estimates shown in Figure 83-11. The equation t

follows:

4219.57*(1.0086)

quarter

numb

*(.435)

Q1dummy

*(.426)

Q2dummy

*(.468)

Q3dummy

Fig

URE 83-11

LOGEST estimates trend and seasonality.

During the frst quarter, the Q1 dummy equals 1 a

that any number raised to the power 0 equals

enues are predicted to equal

4219.57*(1.0086)

quarter

*(.435)

number

During a second quarter, the Q1 dummy and the Q

dummy equals 1. During this quarter, quarterly r

4219.57*(1.0086)

quarter number

*(.426)

During a third quarter, the Q

dummy equal 0 and the Q3 dummy equals 1. Quart

predicted to equal

4219.57*(1.0086)

quarter

*(.468)

number

. Finally, during a fo

Q1, Q2, and Q3 dummies equal 0. During this qu

equal

4219.57*(1.0086)

quarter

number

660

Microsoft Excel 2010: Data Analysis and Business Modeling

In summary, I have estimated a quarterly upward tr

3.6 percent annually). After adjusting for the tr

■

Quarter 1 revenues average 43.5 percent of Qu

■

Quarter 2 revenues average 42.6 percent of Qu

■

Quarter 3 revenues average 46.8 percent of Qu

To create a seasonal index for each quarter, you g

of 1, and fnd that an average quarter has a weig

Figure 83-11):

= .582

.435 + .426 + .468 + 1

Then you can compute the relative seasonal index f

to L4:M4 the formula

. The Quarter

K6/$K$2

4 seasonality is comp

formula

. After

1/K2

adjusting for the trend, I can con

■

Quarter 1 sales are 80 percent of a typical q

■

Quarter 2 sales are 73 percent of a typical q

■

Quarter 3 sales are 75 percent of a typical q

■

Quarter 4 sales are 172 percent of a typical q

Suppose you want to generate the forecast for ea

equation (Equation 1). You can use the Excel GRO

GROWTH function is an array function

known ys,known

with the

xs,n

xs,True

). This formula gives sthe

when

predictions

Equation 1for

is the

ft n

data contained in the ranges .specifed

Thus, selecting

known

J6:J27 and array-entering in cell J6 the formula

generates forecasts from Equation 1 for each qua

Quarter 4 of 1997 using Equation 1 is $4.366 bil

given a list of transactions in different countr

of a transaction in each country?

The fle Medians.xlsx (see Figure 83-12) contains th

transactions in France, the U.S., and Canada. He

of the transactions in each country. Suppose, fo

size of a transaction in the U.S. An easy way to d

only the U.S. revenues and replaces other revenu

Excel compute the median of this new array. Afte

andaming the data in column D

Revenue,

you can a

=MEDIAN(IF(Country=F5,Revenue,””))

in cell G5 to r

containing a non-U.S. transaction by a blank spa

Chapter

Array

Formulas and

661

Functions

transactions ($6,376.50). Copying this formula f

transaction size for Canada and France.

Fig

URE 83-12

Finding median transaction size in each country.

Problems

All data for Problems 1 through 5 is in the Ch

The

Duplicate

worksheet contains two lists o

number of names appearing on both lists.

The

Find Errors

worksheet contains some cal

the number of cells containing errors. (Hin

formula.)

The

Sales

worksheet contains 48 months of s

to add (beginning with Month 3) every ffth m

to use the Excel

(number,divisor)

MOD function. MOD

yields the r

number is divided by the divisor. For examp

Use an array function to compute the third, f

sales.

The

Product

worksheet contains sales during A

through 7. Sales for each month are listed i

that sales for each month are listed in the s

are reflected in the new arrangement you hav

662

Microsoft Excel 2010: Data Analysis and Business Modeling

Use the data in the Historicalinvest.xlsx fle t

which stock, bond, and T-Bill returns are fro

percent through –10 percent, and so on.

matrix is a rectangular array of nu

For example,

1 2 3

4 5 6

7 8 9

is a 3-by-3 matrix. Consider two matrices, A a

columns in matrix A equals the number of rows i

matrix A by matrix B. (The

.) The

product

entry is

in written

row I a a

J of

is computed by applying the SUMPRODUC

umn J of B.

will have as many rows as A an

MMULfTunction is an array function with which y

the MMULT function to multiply the following m

1 2 3

4 5 6

7 7 0

1 2 3

1 2 0

3 3 0

and

A square matrix has the same number of rows a

suppose there exists a matrix B whereby

entry equals 1 and all other entries equal 0. Y

A. The Excel array function MINVERSE fnds the i

MINVERSE function to fnd the inverse for matr

Suppose you have invested a fraction

of your money

=1,2,…,

investment

Also, suppose the standard deviation of the a

and the correlation between the annual per

investment

is ñ

You would like to know the variance a

annual percentage return on your portfolio. T

matrix multiplication. Create the following th

❑

Matrix 1 equals a th

1 by

entrymatrix

whose

❑

Matrix 2 equals an

matrix whose entr

❑

Matrix 3 is a

byentry

1 matrix

whose

The variance of the annual percentage return o

(Matrix 1)*(Matrix

. The

2)*(Matrix

data in Historicalinvest.x

on stocks, bonds, and T-Bills. Use the MMULT a

Chapter

Array

Formulas and

663

Functions

(based on the given historical data) the va

that invests 50 percent in stocks, 25 perce

Problems 10 through 13 use the data in the

10.

How many dollars’ worth of lip gloss did Je

11.

What was the average number of lipstick uni

12.

How many dollars of sales were made by Emil

13.

How many dollars’ worth of lipstick were so

14.

Use the data in the Chapter58data.xlsx fle t

components of the quarterly revenues of For

15.

In the toy store example (using the Toysrustr

to forecast quarterly revenues for 2002.

16.

The Lillydata.xlsx fle contains information f

used to gather insights to aid in designing a n

(six from Lilly and nine from other -compani

pare fve sets of four potential Lilly produ

competitor’s drug is chosen over the four l

For example, in the frst scenario, the seco

that reduced blood pressure 18 points, resu

for $16.

The range I5:N21 contains the choices each e

For example, the frst expert (who worked fo

faced with Scenario 1 and chose the frst li

this information to answer the following:

❑

Enter a formula that can be copied from I

each scenario and option in I2:M5.

❑

Enter an array formula in I23 that can be c

that calculates for each question- the fre

ken down by Lilly and non-Lilly experts. T

responded 1, three responded 2, and two r

17.

The Arrayexam1data.xlsx fle contains sales by c

sales down on a quarterly basis by using ar

I want the data summarized (using only arra

shown in Figure 83-13.

664

Microsoft Excel 2010: Data Analysis and Business Modeling

Fig

URE 83-13

Format for Problem 17 answer.

For example, L7 should contain Quarter 1 (Jan

so on. Verify your answer with a PivotTable.

18.

Explain why array-entering the formula

=SUM(1

number of unique entries in the range Info. A

Unique.xlsx fle and verify that it returns th

19.

The Salaries.xlsx fle contains the salaries o

adds the four largest player salaries.

- Hint: U

tion with the LARGE function. Then generalize y

anp

yositive integer

and your formula will add th

contains an

, when

integer

you array-enter a ,

formula

Excel

ROW

will create an array constant {1,2,…,n}.

665

Chapter 84

PowerPivot

Questions answered in this chapter:

■

How do I read data into PowerPivot?

■

How do I use PowerPivot to create a PivotTab

■

How can I use slicers with PowerPivot?

■

What are DAX functions?

Microsoft PowerPivot for Excel 2010 is an add-i

for large data sets—up to 100,000,000 rows of d

from a variety of sources. For example, some o

Access database, some from a text fle, some fr

imported from a website. In this chapter, I pr

complete explanation of how PowerPivot works, I h

for Excel 2010: Give Your Data Meaning

(Micros

Ferrari.

You can download PowerPivot

. Afrom

separate

www.powerpivo

version o

is available for 32-bit and 64-bit versions

of E

able, so be sure you download the correct vers

Answers to This Chapter’s Ques

How do I read data into PowerPivot?

After you install PowerPivot, you see a PowerP

tab displays the options shown in Figure 84-1.

Fig

URE 84-1

PowerPivot options.

666

Microsoft Excel 2010: Data Analysis and Business Modeling

Clicking the PowerPivot Window button in the Lau

and displays the Home tab, part of which is show

PowerPivot window’s Home tab does not concern us

Fig

URE 84-2

The PowerPivot window Home tab.

If you installed PowerPivot after October 2010, y

external data from the Windows Azure Datamarket. T

PowerPivot analyses on a variety of interesting d

For example, you can download game-by-game stati

down how each team performed rushing and passing a

On the Home tab, you can import data from multip

PowerPivot will accept input from an Access or Mi

you select From Report, PowerPivot will accept i

Services report. Selecting From Data Feeds allow

an Atom feed.

Not

or more information on Atom feeds, see

social.te

articles/ssrs-2008-r2-atom-data-feeds-for-powerpivot

From Text allows you to import data from a text fl

read data from the previously described sources a

types of databases, such as Oracle and Teradata.

After copying data from Excel, you can select Pa

To illustrate how to download data from multiple s

fle Storesales.txt, in which I’ve listed sales tr

shown in Figure 84-3.

You can see that for each transaction, I am give

date, units sold, and revenue. I want to summari

store is listed in a different fle, States.xlsx. T

Chapter

PowerPivot

667

Fig

URE 84-3

Sales data to be imported into PowerPivot.

Fig

URE 84-4

Location of each store.

I want to create a PivotTable that lets me sli

did selling each product in each state. To beg

PowerPivot Window in the Launch group (as show

the Home tab in the PowerPivot window. Because I wa

Text on the Home tab. As shown in Figure 84-5, I c

668

Microsoft Excel 2010: Data Analysis and Business Modeling

Because the frst row of data contains column hea

Headers option. In the Column Separator list, I s

fle are not separated by spaces or a character, s

Finish imports the text fle’s data into PowerPiv

Fig

URE 84-5

Setting up a text fle import for PowerPivot.

Figure 84-6 shows the result after the text data i

the data is shown. At the bottom you can see a t

Storesales.txt.

Fig

URE 84-6

Subset of the data imported from Storesales.txt.

Next, I want to import the fle States.xlsx so th

store is located. To import States.xlsx, I retur

Chapter

PowerPivot

669

upper-left corner of the PowerPivot ribbon. Th

data I need. Now, I select Paste on the Home t

Preview dialog box shown in Figure 84-7 appear

Fig

URE 84-7

Paste Preview dialog box.

After I select Use First Row As Column Headers a

imported into PowerPivot, as shown in Figure 8

a tab appears for each data source used to imp

States.xlsx as Table, but you can easily chang

Fig

URE 84-8

Data from two sources is now imported into Power

670

Microsoft Excel 2010: Data Analysis and Business Modeling

Recall that I want to analyze sales in different s

PowerPivot does not know that the listing of sto

to the stores listed in the text fle. To remedy thi

between the two data sources. To create this rel

PowerPivot window (see Figure 84-2) to display th

Fig

URE 84-9

PowerPivot Design tab.

On the Design tab, I click Create Relationship t

Filling in the dialog box as shown ensures that P

in each data source refer to the same set of sto

that Stores 19 and 20 in the fle Storesales.txt a

Fig

URE 84-10

Creating a relationship between two data sources.

How do I use PowerPivot to create a PivotTable?

Now, I’m ready to use PowerPivot to summarize ou

I display the Home tab in the PowerPivot window a

The Create PivotTable dialog box appears and pro

location in the current worksheet. I choose a ne

displayed, shown in Figure 84-11.

Chapter

PowerPivot

671

Fig

URE 84-11

PowerPivot Field List.

When I click Table, the feld list shows all th

Table data. The goal is to get a breakdown by s

sold. To summarize revenue and units sold, I d

area. Next, I drag State to the Row Labels are

arrange the PivotTable felds as shown in Figur

PivotTable are selected.

Fig

URE 84-12

Assignment of felds to create a PivotTable repor

672

Microsoft Excel 2010: Data Analysis and Business Modeling

The portion of the PivotTable involving CDs, DVD

can see, 3,881 DVDs were sold in Illinois (ILL) f

Fig

URE 84-13

PivotTable breaking down product sales by state.

How can I use slicers with PowerPivot?

In Chapter 43, “Using PivotTables and slicers

Slicers to D

to reveal details and different perspectives in y

nicer in PowerPivot PivotTables. Here, I’ll

crea

set of products and stores. To do this, I place P

Store in the Slicers Vertical area in the PowerP

in Figure 84-14. (See the fle Pivotwithslicers.x

down the Ctrl key as you click to select any sub

the Ctrl key also enables you to resize the slic

the total revenue and units sold of DVDs and foo

through 11 are all in Illinois or Michigan, thes

PivotTable.

If I had created the Product

slicer w

ality, all six products would be listed in a sin

PowerPivot Product slicer looks much nicer.

Fig

URE 84-14

Product and store slicers.

Chapter

PowerPivot

673

What are DAX functions?

Recall from Chapter 43 that you can generate n

calculated items or calculated felds. After yo

use the DAX (short for Data Analysis Expressio

columns that make your PivotTables much more m

Not

full discussion of DAX is beyond the scope of t

Excel 2010: Give Your Data Meaning

includes an exc

language.

To illustrate a DAX formula, I’ll show how to p

for each sales transaction in a separate colum

PowerPivot window and select the frst blank co

PowerPivot ribbon brings up a list of DAX func

and DAY) are virtually identical to ordinary E

of DAX functions shown in Figure 84-15. These a

example, the DISTINCT function can return a li

criterion.

Fig

URE 84-15

Listing of DAX functions.

To place the year, month, and day of the month f

move to the frst cell of the .frst

Thenblank

you are

column

pr a

with the columns from the PowerPivot data sour

Select the date column, and enter

. The

thecolumn

formula

is n

populated with the year of each sales transacti

674

Microsoft Excel 2010: Data Analysis and Business Modeling

rename the column Year. In the next column I com

the formula

=MONTH(storesales[Date])

. In the next column I compute th

with the formula

=DAY(storesales[Date])

. After I rename these columns M

Month, the data is arranged as shown in Figure 8

Fig

URE 84-16

Year, Month, and Day Of Month columns created with D

Now I can create a variety of informative PivotT

each state by year. (See Problem 1.)

Problem

Summarize total sales in each state by year.

Summarize total revenue by store and create a s

675

Index

Symbols

& function, 41, 44

A Date Occurring option, 189

A Removed

worksheet, 452

abandonment options, 597–598.

See

also

stock options

absolute percentage error

computing, 494

minimizing, 494

absolute value function, 290

ABS(x) function, 290

accuracy of predictions, 428–429

Active Field group, 356

activity durations, modeling,

538–539

actual text argument, 41

Adagency.xlsx fle, 227

adaptive forecasting methods, 491

Add Biggersale

worksheet, 226

Add Constraint dialog box, 248–249

Bin option, 267, 269

for workforce scheduling

problem, 257

Add Scenario dialog box, 144–145

Add To Quick Access Toolbar

command, 3

Add Trendline command, 424, 426

Add Watch command, 121

add-ins, Analysis ToolPak, 328

Add-Ins dialog box, 243

ADDRESS function, 182, 183

Addresses.xlsx fle, 103

adjustable rate mortgages (ARMs),

78–79

Advanced Filter dialog box, 408

Unique Records Only option, 409

Advanced Filter feature, 408

after-tax profts, 82

AGGREGATE function, 6, 98

ignoring, 98

Agingdata.xlsx fle, 174

airport security queuing times,

621–623

Albright, S. Christian, 316

algebra story problems, solving,

139–140

All Cells Showing “Sum of Units”

Values For “Product” option,

364

All Different option, 303

All Row Fields

worksheet, 353, 357

alpha

parameter, 536

alphabetical sorting, 210

alternative hypothesis, 471

Amazonma.xlsx fle, 488

Amazon.xlsx fle, 200, 207, 487

American stock options, 588.

See

also

stock options

amount borrowed, calculating with

Goal Seek command, 138–139

ampersand (&), for concatenation,

41, 42, 152, 179

analysis, automatically updating,

218

Analysis group

Data Analysis option, 328, 443

Descriptive Statistics option, 335

Solver, 243

Trendline option, 424

analysis of variance.

See

ANOVA

Analysis ToolPak, 328

Correlation option, 443

installing, 448

Analysts Forecasts

worksheet, 313

AND operator, 91–92, 396

AutoFilter feature with, 408

evaluation of, 200

multiplying Boolean arrays and,

655

angle brackets (<>), 152

annual holding costs, 610–611.

See

also

inventory modeling

determining, 608

annual ordering costs.

See

also

inventory modeling

determining, 608

annual payments

negative value for, 72

valuing per year, 69–71

annual returns

estimating, 346

of stock dividends, 589

annual revenue, computing, 128

annual setup costs, 610

annuities

defned, 69

number of periods in, 70

value in future dollars, 71–72

valuing, 69–71

Another Summary

worksheet, 182

ANOVA, 456

accuracy of forecasts, 475

alpha value, 473, 478

alternative hypothesis, 471

forecasting with, 474–475

input range, 473, 478, 482

interactions, testing for, 4

null hypothesis, 471

null hypothesis, accepting

one-way, 471–476

output range, 473, 478, 482

prediction equations, 483

signifcance measures, 457

two-factor with interactio

two-factor with replicatio

two-way, 477–486

two-way without replicatio

Anova: Single Factor dialog b

Labels In First Row option7

Anova: Single Factor option

Anthony, Carmelo, 579

Antitrustdata.xlsx fle, 136

Apply Names command, 17

arguments

True and 1, 524

unacceptable, 99

Arrange All command, 412

array arguments

in AGGREGATE function, 98

defned, 648

array constants, 656–657

array formulas

asterisk in, 649

cell ranges containing, 64

curly brackets ({}) for, 64

defned, 647–648

dollar sign ($) in, 656

dummy variables for, 659

editing, 657

entering, 648

interpreting, 648–649

lists, matching items in, 6

median, averaging numbers

larger than, 653

median transaction size, f

660–661

pasting, 656

powers of sales, 657

summarizing data with, 654

summing second digits in se

integers, 651–652

trends, estimating with, 6

value ranges, counting valu

650–651

array functions, 462, 648

cell ranges containing, 64

FREQUENCY function, 650–65

GROWTH function, 660

LINEST function, 452, 648

LOGEST function, 657–660

676

array functions

continued

)

(

MINVERSE function, 662

MMULT function, 662

MODE.MULT function, 337–338,

648

TRANSPOSE function, 649–650

TREND function, 462, 648

array-entering a formula, 648

Arrayexam1data.xlsx fle, 663

arrays, 647–664

bin arrays, 650

Boolean arrays, 655–656

creating, 656–657

data arrays, 650–651

quotation marks (“ “) for text, 656

ranking numbers in, 344

Arrays.xlsx fle, 648

arrivals, mean and standard

deviation between, 619

ASCII characters, 42

Asiansales.xlsx fle, 166

Asselallsim.xlsx fle, 573

asset allocation, 565, 569–572

Assetallocationopt.xlsx fle, 571

Assetallsim.xlsx fle, 569

assets

balancing with liabilities, 95

total, computing, 97

Assign.xlsx fle, 26, 298

Assumption cells, hiding, 147

asterisks (*), 152

for multiplication, 649

as wildcard character, 34

At Most 4 Of P1–P10 worksheet, 271

Atom feeds, importing data from,

666

auditing tool, 121–126

precedents and dependents, 122

Audittwosheets.xlsx fle, 125

AutoComplete feature, 15, 219–220

with data validation, 324

table names options, 225

autocopy feature, 220

AutoFill feature, for time interval

creation, 109

AutoFilter feature

heading arrows, 397

querying databases with, 396

automated formulas, 182

Automatic Except For Data Tables

option, 131

Automatic Except For Tables option,

557

automatic updating

of line graphs, 222

with new data, 218–219

Automatic worksheet calculation

modes, 131

Auto.xlsx fle, 453

AVERAGE function, 152, 337

extreme values and, 345

Average Those > Median

worksheet,

653

AVERAGEIF function, 158, 160

AVERAGEIFS function, 158, 160, 390

averages

of all numbers greater than

median, 653

based on criteria, 158

Axis Titles command, 427

back-order case, 613–615

balance paid, calculating, 73–74

balance sheets, defned, 94

balloon mortgages, 78

balloon payments, 73, 74

Banded Columns option, 221

Banded Rows option, 221

Bar Direction list, 192

base of natural logarithms, 431

base of time series, 491

estimating, 493

Baseball96.xlsx fle, 468

Basic Model

worksheet, 267

Basketball.xlsx fle, 204

best-case scenarios, calculating,

143–147

beta parameter, 536

Beta random variable, 535, 538–539

Betadata.xlsx fle, 430

BETA.DIST function, 539

Beta.xlsx fle, 538

Bezos.xlsx fle, 133

bias, in forecasts, 542

bids

mean proft, calculating, 562

modeling as normal random

variables, 560–561

optimizing, 559–563

symmetry assumption, 560

Bidsim.xlsx fle, 561

bin arrays, 650

bin ranges, 327

creating, 328

defning, 328, 329

bin-range frequencies, 330

binary changing cells, 267, 269

binary programming problems,

solving, 271–272

BINOM.DIST function, 517–519

binomial random variables, 515–519

BINOM.DIST function, 517

BINOM.INV function, 519

negative, 520–521

simulating, 559–560

Binomialexamples.xlsx fle

Binomialsim.xlsx fle, 559

BINOM.INV function, 519, 5

562

Black, Fischer, 587

Black-Scholes option-pric

formula, 548, 587–599

implementing in Excel, 5

input values, 591

requirements of, 590

volatility, estimating, 5

593–594

Black Swan, The

(Taleb), 5

black swans, 565

Blades

worksheet, 633

blank cells, counting, 15

blank rows

adding to PivotTables, 3

inserting, totaling valu

Blank rows no totals

work

Boolean arrays, 655–656

adding, 656

multiplying, 655

bootstrapping, 565

asset allocation, 569–57

future investment return

566–567

interdependence of retur

asset classes, 570

simulated values, genera

Borders tab, 198

borrow amount, calculatin

Goal Seek command, 138–

borrow rate vs. reinvest r

break points, creating, m

deleting, 309

breakeven analysis, with G

command, 137–138

breakeven point, calculat

133–134

Bstempprotected.xlsx fle, 5

Bstemp.xlsx fle, 592, 594

bundling, 640–642.

See

also

product pricing

pure bundling, 641

business variables.

See

also

correlations; tren

trend curves

estimating relationships a

423

butterfly spreads, 102

buy-and-hold strategy vs. m

average trading rule, 9

By Changing Cell, defned, 1

By Changing Variable Cell

array functions (continued)

677

C22p1.xlsx fle, 173

Calc Field

worksheet, 374

calculated felds and items, 374–375,

377

creating with DAX functions,

673–674

Calculation group, 557

Calculation Options button, 131

Calculation Options command, 131

calculation results, moving, 111–112

call options.

See also

stock options

cash flows from, 588

defned, 587

dividends, exercising option and,

588

graphs of, 588

Call

worksheet, 588

Candybardata.xlsx fle, 325

Capbudget.xlsx fle, 267

capital, cost of, 59

capital budgeting.

See also

project

selection problems

option pricing and, 596–598

capital investment projects, unique

IRR of, 65

carat symbol [^], 438

Cardata.xlsx fle, 468

Carville, James, 458

Casesensitive.xlsx fle, 175

cash, computing, 95

cash balances, 70

cash flows

beginning-of-year, caluclating,

59–60

buying and selling stock shares,

calculating, 37–38

from call options, 588

discounting, 59, 61

free cash flows, 94

irregular, calculating, 60–61

irregular dates, calculating IRR

of, 66–67

IRR, fnding, 64–65

mid-year, calculating, 60

nonnegative NPV, 147

NPV of, 63

from put options, 588–589

sequence of cash flows, 65

cash outflows, annuities, 69

cell addresses, automated

generation of, 182

cell formats.

See also

conditional

formatting; formatting

Gradient Fill option, 191

cell ranges.

See also

named ranges;

range names

array formulas and functions in,

648

assigning names, 95

blank cells, counting, 150, 154

cells with numbers, counting,

150, 154

conditional formatting of,

185–207

counting cells in, 149–150

for data consolidation, 413

descriptive statistics on, 345

for DSUM function, 389

th largest/smallest number in,

344

listing in single row, 649–650

naming, 151

nonblank cells, counting, 150, 154

noncontiguous, selecting, 115

referencing, 163–175

selecting, 114, 210

totaling numbers in, 180

transposing, 650

validating data in, 319–320

Cell Reference box, 249

cell references

changing without changing

formulas, 178–179

equal to content of cell, 177.

See

also

INDIRECT function

Excel evaluation of, 178–179

cell values.

See also

numerical data;

percentiles; values

hiding, 192, 197

moving, 111–112

cells.

See also

input cells

binary changing cells, 267

border for, 198

changing cells, 241.

See

also

changing cells

conditional formatting of,

185–207

with conditional formatting,

selecting, 199

extracting data from, 167–168

linking, 113

linking combo and list boxes to,

238

linking option buttons to, 237

missing from worksheet, 99

reference cells, 163

shading, 193–195, 198

sorting on color, 212–213

target cells, 241.

See also

target

cells

unlocking, 594–595

user access to, 595

Cells group, 25

Format command, 133

centered moving averages

calculating, 499

trend lines, ftting to, 499

Central Limit Theorem, 532–

545

Central Limit

worksheet, 53

central location

mean, 337–338

median, 337–338

mode, 337–338

Cerealcollapse

worksheet, 3

ceteris

paribus

456

Ch52data.xlsx fle, 446

Ch57.xlsx fle, 485

Ch58data.xlsx fle, 489

Ch66data.xlsx fle, 539

Change Constraint dialog bo

252–253

Change Data Source command, 3

change in sign in cash flow

sequences, 65

Change Table Name command, 2

Changes group, 595

changing cells, 241–242

all different values, 303

binary changing cells, 267

binary, integer vs. fracti

bounds on, 295, 297

for fnancial planning probl

276

new parameters as, 505, 50

in project selection probl

for sports teams ratings, 2

for transportation problem

Chapter56data.xlsx fle, 475

Chapter58data.xlsx fle, 663

Chapter83data.xlsx fle, 661

CHAR function, 42

characters in text strings

counting, 41

extracting, 42–44

returning, 40

charitable contributions, c

81–82

Chart 1

worksheet, 361

Chart Output command, 329

Chart Title command, 427

Chart Tools Design tab, 426

Chart Tools Layout tab, 426

Chartdynamicrange.xlsx fle,

171–172

charts

dynamic updates, 171–173

source data for, 627

tables for data in, 222

Charts group Line option, 2

Charts group Line option

678

check boxes, 230

Christmas week worksheet, 507

chronological sorting, 210, 212,

213–214

churn rate, 601

Cici Colleen Lipstick And

Masc

worksheet, 398

Cigarettedata.xlsx fle, 380

circular references, 81–85

for cost allocation to support

departments, 85

with IF formulas, 97

iterations, 83

Maximum Change setting, 83

resolving, 15, 82–84

Ciscoexpo.xlsx fle, 431

Ciscoimpvol.xlsx fle, 593

Citydata.xlsx fle, 27

Citydistances.xlsx fle, 19, 136

Citypower.xlsx fle, 347

Classdata.xlsx fle, 273

Clear Filter command, 359

Clear Rules command, 187

Clear Rules From Selected Cells

option, 199

Closest.xlsx fle, 227

coeffcients, interpretation of, 456,

460

COGS, computing, 95

cohorts, defned, 602

Collegedata.xls fle, 380

colons in times, 105

color, sorting on, 212–213

color coding, 198–199

color scales, 186, 193–195

color combinations, 194

formula option with, 202

Color Scales option, 186–187

Colors

worksheet, 212

Colorscaleinvestment.xlsx fle, 193

Coltsdata.xlsx fle, 348

COLUMN function, 182, 207

column headings flter arrows, 218

column index

argument of

VLOOKUP function, 21

column labels, returning, 182

Column Labels zone, 353

column names in formulas, 15

column numbers, returning, 182

Column Separator list, 668

Column Sparkline

worksheet, 384

columns

breaking data into, 307–311

break points, 309

Delimited and Fixed-Width

options, 307–309

extracting text to, 46–47

flling with data, 555–556

fltering criteria for, 397

flters, clearing, 399

hiding, 25, 133

last number in, fnding, 169–170

referencing with INDEX function,

referring to by name, 84

separating data into, 168

transposing data to rows, 112–113

visibility of, 91

columns moved

argument of OFFSET

function, 164, 167

combo boxes, 230, 238

Combobox.xlsx fle, 238

commands,

See also specifc

command names

grouping, 2–3

from previous Excel versions, 3

commas, breaking data at, 46

comments

editing, 581

inserting, 581

printing, 582

showing and hiding, 581

compact form PivotTables, 354.

See

also

PivotTables

company values, 59

complex formulas, evaluating, 169

compound interest, 589

computed criteria, 389, 391–392,

408

CONCATENATE function, 41, 43–44

concatenation, ampersand (&) for,

152

Cond form

worksheet, 364

conditional formatting, 185–207,

300

based on formulas, 200–205

border on cells, 198

Clear Rules From Selected Cells

option, 199

color coding options, 198–199

color scales, 193–195

conditions, defning, 200–202

data bars, 191–195

deleting, 199

Format Only Cells That Contain

option, 198, 203

formatting options, 186–187

Highlight Cells feature, 188–189

highlighting dates, 189

highlighting text that contains

option, 189

icon sets, 195–197

More Rules option, 192

of new table data, 226

other worksheets, refere

205

of outliers, 341–342

for PivotTables, 364–365

rules, customizing, 189–

See also

rules for cond

formatting

selecting cells with, 19

shading cells, 198

Stop If True option, 205

toggling on and off, 234

top/bottom rules, 187–18

of weekend dates, 202–20

Conditional Formatting ar

Conditional Formatting me

Conditional Formatting Ru

Manager dialog box, 190

order of rules, 199

Use A Formula option, 20

Use A Formula To Determi

Which Cells To Format o

201

conditional tests, on val

formulas, 88.

See also

statements

confdence interval for me

557–558

Connections group Refresh A

option, 315

Consolidate command, 411

Consolidate dialog box, 4

Create Links To Source D

option, 413

Function box options, 41

Use Labels area, 413

consolidation, 411–415

grouping data for, 414

updating with new data, 4

constants

data ranges, dividing by

in forecasting equations

constraints, 241–242

adding, 249

changing, 252–253

for fnancial planning pr

276

in linear problems, comp

251

in project selection pro

in transportation proble

with Evolutionary Solver

consumer decision making,

640–641

consumer product valuatio

641–643

consumer surplus, 641

determining, 642–643

check boxes

679

Cont Rate EOQ

worksheet, 610

content, enabling, 313

continuous random variables, 511

Beta random variable, 535

discrete random variables,

modeling as, 512

modeling as normal random

variables, 560

modeling quantities with, 527

probability density functions,

511–512, 527

time between arrivals, 525–526

Weibull random variable, 535

Contoso.xlsx fle, 378

Contract Entire Field button,

356–357

Contrateeoq.xlsx fle, 610

controls.

See also

form controls

adding, 229

Controls group Insert option, 229

Controls.xlsx fle, 229

conventions for signs of

pmt

and

convergence to solution, 83–84

Convert Text To Columns Wizard,

168

Convert to Range command, 220

copying

fltered data, 399

formulas, 92

CORREL function, 445

Correlation dialog box, 443

Labels In First Row option, 444

correlation matrices, flling in,

444–445

Correlationexamples.xlsx fle, 441

correlations

defned, 441

input range, 444

interpretation of, 441–442

negative, 442

positive, 441

R2 values and, 445

regression toward the mean and,

445–446

among variables, 441–446

zero correlation, 442

cost of capital, 59

IRR in excess of, 65–66

Costestimate.xlsx fle, 425, 428

costs

allocating, 85

based on order quantity, 88–89

as function of units produced, 435

of production, 625

unit costs, 625, 639

COUNT function, 150, 154

COUNTA function, 150, 154, 168

COUNTBLANK function, 150, 154

COUNTIF function, 149–150, 551

counting cells based on criteria,

151–153

summarizing range of returns

with, 568

syntax, 150

COUNTIFS function, 150, 153, 158

Countryregion.xlsx fle, 467

Coupondata.xlsx fle, 486

craps

game status, determining,

576–577

modeling frst roll, 93

probability of winning at, 575–577

Craps

worksheet, 93

Craps.xlsx fle, 576

Create A Copy option, 190, 465

Create From Selection command,

633

range names, creating with, 11–12

Create Links To Source Data option,

413–414

Create PivotTable dialog box,

351–352, 670

Create Relationship command, 670

Creating Powers

worksheet, 657

Creditunion.xlsx fle, 501

CRITBINOM function, 519

criteria

case sensitivity, 151

dates as, 153

multiple, 150, 153

multiple,

flagging rows with, 158

for sorting, 210–212

summing based on, 157

text in quotation marks, 151

wildcard characters in, 152

criteria ranges

advanced flters and, 408

AND criteria in, 389

date references, 391

exclusion criteria, 390

multicolumn, 391

numerical values in columns, 392

text in columns, 392

tips for, 392

criterion

argument

of COUNTIF function, 150

of DSUM function, 389

of SUMIF function, 157

criterion_n

argument of COUNTIFS

function, 150

criterion1

argument of SUMIFS

function, 158

Ctrl key, 376

resizing slicers with, 672

selecting with, 115, 672

Ctrl+Shift+Enter key combina

648

Cuban, Mark, 307

CUMIPMT function, 75

CUMPRINC function, 75

cumulative value, 642

curly brackets ({}) for arr

649, 656

currency exchange rate quer

current time, displaying, 1

Current Values column, 146

Custom AutoFilter dialog bo

Custom Filter option, 403

Custom Format option, 187

custom formats.

See

conditional

also

formatting

creating, 187

Custom Lists dialog box sor

options, 214

custom sort orders, 214

customer value, 601–605, 64

churn rate, 601

loyalty incentives, calcul

603–605

retention rates, 601–603, 6

Customize Ribbon command, 2

Customize Ribbon page, 1–2

Customize the Quick Access T

page, 3

Dallas Mavericks, 307

data.

See also

new data

breaking into columns, 307–

consolidating, 411–415

copying, 399

deseasonalizing, 498–499

fltering, 357–361.

See

also

PivotTables

histograms from, 327–334

importing, 666

importing from Internet, 3

importing in text fles, 30

location, changes in, 166

making inferences from, 58

in multiple worksheets, 12

reading into PowerPivot, 66

realigning from column to r

and row to column, 112–113

refreshing, 315

sample standard deviation,

339–340

sample variance, 339

sorting, 357–361.

See

also

PivotTables

summarizing, 46–47

data

680

data

continued

( )

summarizing across worksheets,

117–119

summarizing in single worksheet,

182

summarizing with descriptive

statistics, 335–348

summarizing with slicers, 4

sum of squares, 474

time series data, 487–489

from Windows Azure Datamarket,

666

Data Analysis dialog box, 328–329

Anova: Single Factor option, 471,

472

Anova: Two-Factor Without

Replication option, 478

Anova: Two-Factor With

Replication option, 481

Histogram option, 328

Regression option, 455

Residuals option, 456

Rows Per Sample option, 482

Data Analysis Expressions (DAX)

functions, 673–674

Data Analysis for Managers with

Microsoft Excel

(Albright,

Winston, and Zappe), 316

data arrays, 650

changing data points in, 651

data bars, 186, 191–195

Bar Direction list, 192

Excel 2010 improvements, 7–8

formula option with, 202

orientation of, 193

for PivotTable data, 364

shading, 7

size of, 191, 192

solid shading, 193

Data Bars option, 186–187, 191,

207–208

data changes, watching, 121

Data Consolidate command, 118

data feeds, importing data from,

666

data formatting, 39–40.

See also

conditional formatting

data manipulation with Paste

Special command, 111–115

Data named ranges, 10

data points

in bin ranges, counting, 651

in data arrays, changing, 651

errors and residuals for, 428

graphing, 423–424

validation points, 459

Data Range Properties options, 315

data ranges.

See also

cell ranges

dividing by a constant, 113–115

select all data in, 114

data sets

comparing, 333, 342

kurtosis, 339

large, 665

mean, 337, 340

median, 337

mode, 337–338

range of, 340

ranking numbers in, 344–345

relative position in, 342–343

skewness measures, 339

spread of, 339–340

standard deviation, 340

summarizing, 193–195

trimmed mean, 345

data sources

multiple, 665–666

relationships among, 670

Data Table dialog box, 129

data tables, 127

automatic recalculation of, 131

bids, simulating in, 562

column input cells, 562

with database statistical functions,

391–392

EOQ sensitivity, 608

Excel functions and, 131–132

one-way, 128–130.

See also

one-

way data tables

for parameter changes in stock

options, 593

recalculating, 557

row and column input cells, 131

row input cells, 562

saving values in, 131

setting up, 129

two-way, 130–131, 131–134,

555–556.

See also

two-way data

tables

Data Tools group

Scenario Manager, 144

Text To Columns option, 45, 168

What-If Analysis option, 129

data validation, 238, 319–326

Autocomplete feature with, 324

clearing, 324

error alerts, 320

formulas for, 321–322

INDIRECT function with, 324

length of text criteria, 324

list validation criteria, 322–324

selecting all cells with, 323

time of day criteria, 324

Data Validation dialog box, 319–320

Custom setting, 321–322

Error Alert tab, 320

Input Message tab, 320

Settings tab, 320

database

argument of DSUM

function, 388

database statistical func

387–394

computed criteria, 389, 3

criteria ranges, 389.

also

criteria ranges

data tables with, 391–39

date criteria, 391

DAVERAGE function, 390

DCOUNTA function, 390

DCOUNT function, 390

DGET function, 393–394

DSUM function, 387–389

exclusion criteria, 390

multicolumn criteria ran

391–392

OR operations, 390

summarizing data with, 6

databases

duplicates, removing fro

405–406

extracting records, 408

feld names, 396

felds, 396

flters, clearing, 399

importing data from, 666

querying with AutoFilter

records in, 396

selecting all, 151

date and time

in same cell, 106

serial number for, 105

Date Axis

worksheet, 383

Date Filters options, 402

DATE function, 53

date functions, 49–55

DATEDIF function, 54

DATE function, 53

DATEVALUE function, 50

DAY function, 53

MONTH function, 53

NETWORKDAYS function, 52

NETWORKDAYS.INTL functio

TODAY() function, 51

WEEKDAY function, 53

WORKDAY function, 51–52

WORKDAY.INTL function, 5

YEAR function, 53

DATEDIF function, 54

Datedv.xlsx fle, 321

Datelookup.xlsx fle, 25

dates, 49–55

as criteria, 153

extracting year, month, d

data (

continued

)

681

formatting conditionally, 202–203

grouping, 377

holidays, 51–52

month-day-year formats, 49–50

serial format, 50–51

today’s date, displaying, 51

validating, 321

weekend dates, 202–203

workdays, defning, 52

dates

argument, 60–61

Dates

worksheet, 213

DATEVALUE function, 50

DAVERAGE function, 390

DAX functions, 673–674

DAY function, 53

days

counting, 54

selecting without typing, 238

sorting chronologically, 214

#days

argument, 51

days

argument, 52

days off, defning, 52–53

DCOUNTA function, 390

DCOUNT function, 390

debt

computing, 95

in pro forma statements, 93–97

debugging formulas, 169

Decadeincome.xlsx fle, 347

Deciles.xlsx fle, 394

Defne Names command, 172

Defned Names group, 17

Create From Selection option, 151

Name Manager option, 171

Delete Rule command, 190, 199

Delimited option, 307, 309

delimiters for columns, 309–310

delimiting characters, 168

Delldata.xlsx fle, 429

Dellvol.xlsx fle, 590

demand

constant rate, inventory modeling

and, 607–611

economic order batch and, 611

economic order quantity and, 609

elasticity of, 626

meeting with limited resources,

253

95-percent service level and, 616

and price, nonlinear relationship,

463

production and, 245

simulating, 551–552, 554

uncertain, inventory modeling

with, 613–618

unlimited, 253

demand constraints, 251

demand curves, 625–629

customer willingness to pay and,

628–629

defned, 625

determining, 631

determining for unknown

elasticity, 635

estimating, 626–628

linear and power curves, 626–628

quadratic, 635

demand points, 261

total product received by,

calculating, 262–263

Deming, Edwards, 334

Deming.xlsx fle, 334

dependencies between cells, 81

dependent variables, 423

multiple factor effects on, 477

nonlinear effects on, 463

regression toward the mean,

445–446

dependents

defned, 122

tracing, 122–123

deposits

at beginning or end of period,

71–72

future value of, 72

depreciation

accumulated, computing, 96

computing, 96

descriptive statistics, 327, 335–348

on cell ranges, 345

central location measures,

337–338

comparing data sets with, 342

condition formatting for outliers,

341–342

geometric mean, 346

grouping settings, 336

input range, 336

kurtosis, 339

labels, 336

large and small numbers, fnding,

344

percentile rankings, 342–343

ranking numbers, 344–345

skewness measures, 339

spread of data, 339–340

summary statistics, 336

Descriptive Statistics dialog box,

335–336

deseasonalizing, 498, 499

Design tab, 218, 670

Table Style Options group, 223

Developer tab, displaying, 229

development costs, OFFSET function

for, 167

DGET function, 393–394

Dget.xlsx fle, 392

Diagonal.xls fle, 175

Dif option, 303–305

discount rate, 602

NPV to zero, 66–67

discounts, quantity discoun

discrete random variables, 5

binomial random variables,

515–517

modeling as continuous rand

variables, 512

simulating values of, 551–5

Discretesim.xlsx fle, 551

dispersion measures, 339–34

Display Equation On Chart o

426, 636

Display R-Squared Value On C

option, 426

distances, calculating, 29–

DISTINCT function, 673

distribution problems, 261–

#DIV/0! error, 99

Dividebyprice.xlsx fle, 103

dividend rate, 589

dividends

computing, 96

exercising call options and

stock price and, 593

Dolan, Robert J., 625

dollar sign ($), 247, 577

in array formulas, 656

inserting and deleting, 20

use of, 201

double-clicking to copy for

Dow.xlsx fle, 348, 379, 385

D prefx, 387–388

Draftlottery.xlsx fle, 347

drilling down in PivotTables

drop-down lists, 238

for data validation, 322–32

Drugabandon.xlsx fle, 597

Drugfore.xlsx fle, 542

DSUM function, 387–388, 390

multicolumn criteria range,

391–392

syntax, 388–389

Duedates.xlsx fle, 206

dummy variables, 454–458

for array formulas, 659

interpretation of, 457

duplicates

fnding with array formulas

652–653

formatting conditionally, 1

removing, 405–406

removing from tables, 220

duration of activity, model

duration of activity, modeling

682

duration of stock options, 589

increases in, 593

dynamic range names, 170–171.

See

also

range names

creating, 172

dynamic ranges, creating, 170–171,

172–173, 218

dynamic updates of charts, 171–173

dynamic web queries, 315–316

value (base of natural logarithms),

431

Eastandwestconsolidated.xlsx fle,

414

Eastwest.xlsx fle, 10

East.xlsx fle, 411

economic order batch (EOB),

610–611

annual holding costs, 611

batch size and, 611

demand and, 611

economic order quantity (EOQ), 608

demand and, 609

quantity discounts and, 609

economic order quantity formula,

607–611

economy, effect on elections, 458

Edit Comment command, 581

Edit Data command, 383

Edit Formatting Rule dialog box,

193, 203, 204

icon set options, 196

Reverse Icon Order option, 197

Show Bar Only option, 192

Show Icon Only option, 197

Edit Query command, 315

Edit Rule button, 190

Edit, Replace command, 44

effciency, outliers and, 429

elasticity of demand, 626

Electiondata.xlsx fle, 430

elections

data on, 459

predicting, 458–461

employees

length of time worked,

computing, 108

total hours worked, computing,

108

Employees.xlsx fle, 28

Enable Iterative Calculations option,

81–84, 97

end_date argument, 52

enddate argument, 54

ending balances, calculating, 74

Enter Parameter Value dialog box,

316

EOB, 610–611

EOQ, 608–609

EOQ

worksheet, 608

Eoq.xlsx fle, 608

Equation 1, 275

for loan payment calculations, 276

for sports teams ratings, 282–283

Equation 2, 275

for retirement planning, 278

equation editor, 7

equation editor templates, 7

equation solver, 137–141.

See

also

Goal Seek command

equations

creating in Excel, 7

importing, 7

iteration procedure for linear

equations, 83–84

equity, computing, 95

error alerts, 320

error values, 97

examples of, 99

ignoring, 98

errors

data validation feature and, 319

ignoring rows with, 98

replacing with spaces, 97–99

Errortrap.xlsx fle, 97

Errortypes.xlsx fle, 99

Esc button, 169

Esc key, 289

estimation.

See also

forecasts and

forecasting

standard error of regression,

428–429

of straight-line relationships,

423–430

European stock options, 588.

See

also

stock options

call options, 102

put options, 89–90

valuing, 592

Evaluate button, 169

Evaluate Formula command, 169

Evolutionary Solver engine, 244, 291

constraints, 297

cutoff points, 645

for job assignment problems,

297–300

keys to using, 297

penalties with, 297–300

for proft-maximizing quantity-

discount plan, 645

for sequencing problems,

303–306

EXACT function, 175

Excel 2010, new features, 1

Excel 2010 Icons

workshee

Excel fles, importing dat

666, 668–669

Excel icon, 668

Excel NPV function, 59

Excel Options dialog box, 8

Excel Solver.

See

Solver

excess production, 245

exclamation point (!), 16

exercise date, defned, 58

exercise price

defned, 587

increases in, 593

option value and, 589

Existing Connections opti

Expand Entire Field butto

expected values, 510

expenditures, sorting by g

366

experience curves, 436

modeling, 437–439

experiments.

See also

pro

succes

defned, 509

expiration date, defned, 5

EXPON.DIST function, 525

EXPONDIST function, 525

exponential functions, eq

for, 431

exponential growth, model

431–434

exponential probabilities

exponential trendlines, 4

431–434

ft of, 433

Exponentialdata.xlsx fle, 4

extracting data, 42–44, 4

from cells, 167–168

Text To Columns Wizard, 4

extracting records, 408

F. Harris of Westinghouse

Corporation, 607

F3 key, 153

F4 key, 202

F5 key, 199, 323, 399, 59

F9 key, 131, 178–179, 233

for data tables, 557

multiple presses of, 555

factors

effect on data, 471

mulitple, 477

Fair, Roy, 458

Fairmodel.xlsx fle, 458

duration of stock options

683

favorite rating–underdog rating of

sports teams, 580

Fax.xlsx fle, 437

Feasible Solution

worksheet, 245

feasible solutions, 244

to product mix model, 251

features, toggling on and off,

234–236

feeds, importing data from, 666

Ferrari, Alberto, 665

feld

argument of DSUM function,

388–389

feld names, 396

felds, database, 396

felds in PivotTables, 352

calculated felds, 374–375

collapsing and expanding,

356–357

sorting and fltering, 357–361

File Conversion dialog box

(Microsoft Word), 308

File menu, 6

File tab, 5–6

Fill command, 555

Fill tab, 198

Filter By Color option, 404

Filter By Color

worksheet, 404

Filter By Months

worksheet, 403

Filter command, 399

fltering, 395–409.

See also

sorting

Advanced Filter feature, 408

clearing flters, 399

by color, 404

copying data to new worksheets,

399

Date Filters options, 402–403

Date options, 401–402

duplicates, removing, 405–406

Greater Than option, 400–401

by months, 403

by name, 404

numerical data, 399–400

reapplying flters, 407

text flters, 397

top 10 values, 359

top records, 405

for unique combinations,

406–407

Final Four basketball tournament,

simulating, 579–582

Final Percent Breakdown

worksheet,

371

Final Table

worksheet, 368

Final4sim.xlsx fle, 580

FinalRegression

worksheet, 465

fnance.yahoo.com, 546

fnancial decision making, option

pricing and, 596–598

fnancial functions, author’s

conventions, 70

fnancial future, predictions of, 94

fnancial planning problems,

275–280

changing cells, 276

constraints, 276

retirement funds, 275

target cells, 276

FIND function, 41, 44, 45, 168

case sensitivity, 41

Find & Select command, 45

Finearts.xlsx fle, 379

Finmathsolver.xlsx fle, 276

First Column option, 221

1st Percent Breakdown

worksheet,

370

First 6 months

worksheet, 362

1st Table

worksheet, 370, 372

1st Three Days

worksheet, 505

fxed assets

gross, computing, 96

net, computing, 96

Fixed Width option, 307, 309

Fizzy.xlsx fle, 467

font color, sorting on, 212–213

Font dialog box launcher, 595

forecast errors, 506–507

random variables and, 543

forecasts and forecasting

accuracy of, 451, 460, 475, 480,

484, 504–507, 542

bias in, 542

evaluating, 542–543

forecast errors, examining,

506–507

forecast errors, random, 507

formulas, 492

future values, 491

GROWTH function for, 660

historical data about, 541

lagged values and, 455

mean of, 542

from multiple regression, 461–462

with one-way ANOVA, 474–475

optimizing, 492

outliers in, 504–505

parameters settings, 503–504

point forecasts, 541

presidential elections, 458–461

ratio-to-moving-average method,

497–500

sales, 483

scale constant, 658

special events, accounting for,

501–504, 504–506

standard deviation of, 542

Winters’s method, 491–495

form controls

check boxes, 234–236

combo boxes, 238

displaying, 229

list boxes, 238

option buttons, 237

resizing, 232

scroll bars, 234

shapes, changing, 232

spin buttons, 231–234

Format Cells, General comma

Format Cells dialog box, 18, 5

opening, 50

Format command, 133, 198

Format Control command, 232

Format Control dialog box, 23

minimum values, 239

Page Change option, 234

Format Only Cells That Cont

option, 198, 203

Format Trendline dialog box4

Display Equation On Chart o

426, 636

Display R-Squared Value On C

option, 426

Exponential option, 432

Linear option, 426

Polynomial option, 636

Power option, 437–438

Format Visibility options, 1

Formatted $s

worksheet, 355

formatting, 39–40

automatically updating, 218

conditional formatting, 18

deleting, 199

in PivotTables, changing, 3

of query results, 315

tables, 218

Formula Auditing group, 121

Evaluate Formula option, 169

Trace Dependents button, 1

Trace Precedents button, 12

Formula AutoComplete featur

219–220

formulas

array-entering a formula, 6

array formulas, 647–648.

also

array formulas

autocompleting, 219

autocopying, 220

automating, 182

column names in, 15

for columns of numbers, 283

for conditional formatting,

200–205

conditional tests on, 88.

also

IF statements

copying, 92, 99–100

formulas

684

formulas

continued

)(

for data validation, 321–322

DAX functions, 673–674

deleting, 112

dollar sign in, 577

evaluating parts of, 169

protecting from changes, 594–

596, 609

range names, applying to, 17

range names in, 14–15, 153

selecting all, 595

table specifers in, 225

three-dimensional, 117–119

and values, toggling between, 121

four-period moving averages,

488–489

Fractiondefective.xlsx fle, 206

fractions, time displayed as, 107

free cash flows (FCFs), 94

Freeze First Column option, 91

Freeze Panes command, 91,

233–234

Freeze Top Row option, 91

FREQUENCY function, 650–651

frequency graphs, 46–47

frequency of values in value ranges,

650–651

Frequency

worksheet, 650

From Web option, 313–314

Fruitlist.xlsx fle, 324

function number, 98

Function Wizard, 153

Help On This Function, 98

functions

DAX functions, 673–674

maximizing and minimizing,

288–289

new in Excel 2010, 6

nonsmooth functions, 291

future dollars, annuity values in,

71–72

future payments, value in today’s

dollars, 69–71

future values, 70

forecasting, 491

in PV function, 70

sign conventions, 70

argument of PMT function, 73

FV function, 71–72

syntax, 71

fx button, 673

gambling

craps, probability of winning at,

575–577

poker, probability of getting a

particular hand, 577–579

Gasprices507.xlsx fle, 221

Gauss-Seidel Iteration, 83

Gaussian histograms, 340

geometric mean, 346

GEOMMEAN function, 346

Geommean.xlsx fle, 346

Gesimless5.xlsx fle, 568

Gesim.xlsx fle, 566, 573

Get External Data group

Existing Connections option, 316

From Web option, 313–314

GETPIVOTDATA function, 377–378

turning off, 378

GetPivotData Function For

PivotTable References option,

378

Getpivotdata.xlsx fle, 377

Globalwarmingtemp.xlsx fle, 207

Globalwarming.xlsx fle, 187

GNP.xlsx fle, 207

Goal Seek command, 137–141

amount borrowed, calculating,

138–139

implied volatility, calculating, 593

loyalty incentives, calculating,

603–605

story problems, solving with,

139–140

Goal Seek dialog box, 138, 594

Goals.xlsx fle, 385

Golfdata.xlsx fle, 174

Go To dialog box, 125, 595

Conditional Formats option, 199

Special option, 323

Grades.xlsx fle, 28

Gradient Fill option, 191

Grand Total, displaying, 419

Graph No Interaction

worksheet,

482

graphics, sparklines, 381–385

graphs.

See also

histograms

creating, 46–47

of data points, 423–424

moving average graphs, 488–489

of time series, 487

greater than or equal to (>=)

operator, 152

GRG Nonlinear engine, 243

maximizing and minimizing

functions with, 288–289

Multistart option, 289, 295

for nonlinear optimization

models, 288–291

for warehouse location problems,

292, 294–295

GRG2 method, 251

Groceriespt.xlsx fle, 351

Grocery.xlsx fle, 467

gross fxed assets, comput

group boxes, 230

drawing, 237

grouping

dates, 377

nonadjacent selections, 3

numerical values, 377

Grouping dialog box, 367

groups

disbanding, 376

in PivotTables, creating

Groups Collapsed

workshee

groups within tabs, 2

growth, modeling, 431–434

GROWTH function, 660

guess

argument, 66

for IRR, 64

in RATE function, 75

varying, 64

Harrison, Benjamin, 461

Header Row option, 221

header rows, displaying, 2

heading arrows, in AutoFi

headings, for PivotTable d

Hedging

worksheet, 89–90

height

argument of OFFSET

function, 164, 167

Help On This Function opt

hidden rows, ignoring, 98

Hide Columns command, 25, 1

Hide Rows command, 133

hiding

cell values, 197

columns, 133

icons, 197

rows, 133, 193

High Low

worksheet, 382

highest value

fnding, 35–36

formatting conditionally

Highlight Cells condition

formatting feature, 186

Highlight Cells Rules opt

188

A Date Occurring option, 1

Text That Contains optio

Highlightcells.xlsx fle, 1

Histogram dialog box, 328

histograms, 327–334

bin-range frequencies, 3

bin ranges, 327–328, 329

comparing data sets with

gaps between bars, 329–3

formulas ()

continued

685

histograms

continued

) (

Gaussian, 340

input range, 329

labels, 329–330

shapes of, 330–332

title of, 330

Histograms

worksheet, 333

Historicalinvest2009.xlsx fle, 333

Historicalinvest.xls fle, 197

Historicalinvest.xlsx fle, 14, 206,

348, 662

HLOOKUP function, 21

example, 25

syntax, 22

holding costs.

See also

inventory

modeling

assumptions about, 613

minimizing, 614–616

holidays, 51–52

holidays

argument, 51, 52

Holland, John, 291

horizontal lookups, 21

Hospital.xlsx fle, 379

hour, extracting from times, 108

HOUR funtion, 108

Housedata.xlsx fle, 430

Housepricedata.xlsx fle, 394

House2.xlsx fle, 492

housing starts, forecasting, 491–495

Hr.xlsx fle, 26

HYPERGEOM.DIST function, 520

Hypergeom.dist.xlsx fle, 520

hypergeometric random variables,

519–520

icon sets, 186–187, 195–197

formula option with, 202

icons, customizing, 197

Icon Styles list, 196

Icon Sets option, 186–187

Icon Styles list, 196

icons

cell values, associating with,

195–197

hiding, 197

sorting on, 213

If 3 then 4

worksheet, 270

IF statements, 87–104

for breakeven analysis, 133–134

circular references with, 97

conditions on, 88, 92

craps, modeling frst roll, 93

errors, ignoring, 97

Evolutionary Solver for, 645

with MOD function, 99–100

nesting, 89, 100

order of evaluation, 89

OR formulas in, 93

for percentage return on

portfolio, 89–90

for quantity discounts, 88–89, 645

with ROW function, 99–100

sports winners, advancing with,

580–581

text in, 92

IFERROR function, 97–99, 99, 136

Impalas.xlxs fle, 434

implied volatility approach, 593

Import Data dialog box, 314

importing

data, 666

data from Internet, 313–317

queries, refreshing, 315

text fles, 307–311

Word documents, 307

income before taxes, computing, 96

income statements, defned, 94

Incomedata.xlsx fle, 348

independent random variables,

512–513

mean, variance, and standard

deviations of, 532–533

independent variables, 423

allowed number, 501

coeffcients, estimating, 502

coeffcients, intrepreting, 456, 460

defning, 458

dropping from analysis, 450, 460,

465

dummy variables, 454–458

interactions between, 464–467

multiple, 447–452

nonlinear effect on dependent

variables, 463

predictive power, 450–451, 457

p-values, 450

qualitative, 453–462

quantitative, 453

INDEX function, 29–31, 237

distances, calculating with, 29–30

referencing columns and rows

with, 30

syntax, 29

for total distance traveled, 304

Index.xlsx fle, 29

indicator variables, 502

INDIRECT function, 177–183

blank rows and, 180

changing cell references in

formulas, 178–179

with data validation, 324

for summarizing data in sin

worksheet, 182

listing entries in one work

179

range names, referencing,

181–182

totaling values in original r

180

Indirectconsolidate.xlsx fl

Indirectinsertrow.xlsx fle, 1

Indirectmultisheet.xlsx fle

Indirectrange.xlsx fle, 181

Indirectsimpleex.xlsx fle, 1

inexact matches, 34

infeasible solutions to pro

model, 252

inferences from data, 583–5

input assumptions, 121

changes, analyzing effects o

127–136

dependents on, 122–123

listed inputs, 129

outputs of interest, 127

input cells

spin buttons, linking to, 23

varying, 143–147

input values

changes in two values, 131–

changing, 131

Insert Blank Line After Eac

option, 363

Insert Calculated Field dia

374

Insert Field button, 374

Insert Worksheet command, 1

Insig

worksheet, 473

Integer Optimality setting, 2

integer programming problem

271–272

integers, 152

summing second digits in se

651–652

interactions

in ANOVA analysis, 482, 484

defned, 464

prediction equations and, 4

testing for, 464, 477, 480–

Interactions.xlsx fle, 463, 4

interarrival times, 619

mean and standard deviatio

619, 622

stationary, 620

INTERCEPT function, 429

intercept of least-squares l

interdependence between ret

570

interest expense, computing

686

interest income, computing, 96

interest paid

calculating, 73–74

cumulative, 75

interest rate, 63

annual, 59

calculating, 75–76, 113–114

computing, 276

IRR and, 63

NPV of zero and, 64

risk-free rate, 589, 593

internal rate of return.

See

IRR

Internet, importing data from,

313–317

invalid data.

See also

data validation

error alerts, 320

flagging, 319

inventory costs

annual, 609

minimizing, 607–609

inventory levels

average, 608

average, production, 610

inventory modeling

economic order batch, 609–611

economic order quantity,

607–609

reorder point, 613

safety stock levels, 615

with uncertain demand, 613–618

investment evaluation

net present value criteria, 57–63

with payback period, 37

Investment Science

(Luenberger),

587

investments

future scenarios, generating, 565

future value of, 71–72

IPMT function, 73–74

syntax, 73

IQ Density

worksheet, 528

IRR

borrow and reinvest rates and,

66–67

calculating, 60–61

cash flows on irregular dates,

calculating, 66–67

cost of capital, in excess of, 65–66

defned, 63

fnding, 64–65

multiple, 64

no IRR, 65

scale of project and, 66

unique, 63–65

unique, guarantee of, 65

using, 65–66

IRR function, 63

cash flow left blank, 67

IRR, fnding, 64

syntax of, 64

ISNUMBER function, 321–322

iteration procedure, 83–84

Ivolatility.com, 546

Jen + Emilee

worksheet, 408

job assignment problems, 297–300

job shop scheduling problems, 303

Jobshop.xlsx fle, 109

Jordan.xlsx fle, 348

justifcation of text, 42

Keep Solver Solution command, 252

Kingslineups.docx fle, 311

th-largest/smallest number, 344

fnding, 36

kurtosis, 339

labor

length of time worked, 108

for production, 246

scheduling problems, 255–259

usage calculations, 246–247

lagged values, 455

Lagged.xlsx fle, 174

LARGE function, 207, 344

functionality of, 36

syntax of, 36

largest values, associating data bars

with, 191–192

Last Column option, 221

last number in column, returning,

169–170

Last year.xlsx fle, 17

Latitude.xlsx fle, 325

Launch group, 666

Lawdata.xlsx fle, 586

Layout Group Report Layout option,

354

layout method, 3

leap year bug, 50

learning curves, 436

estimates for various industries,

439

modeling, 437–439

learning rates, 436

least-squares lines, 427

intercept of, 429

slope of, 429

standard error of, 428–4

LEFT function, 40, 43, 45

left-hand lookups, 165

Lefthandlookup.xlsx fle, 1

Lemonadegs.xlsx fle, 137

Lemonade.xlsx fle, 128

LEN function, 41, 43

length of time worked, co

108

level of time series, 491

updating, 493

Lewent, Judy, 596

liabilities

balancing with assets, 9

computing, 95

total, computing, 97

Lillydata.xlsx fle, 663

linear demand curves, 626

linear equations, iterati

procedure, 83–84

linear model requirement, 2

linear models

Solver solutions for, 28

very large and small num

and, 277

linear optimization probl

250

project selection proble

270

transportation problems, 2

workforce scheduling pro

257

linear pricing.

See also

pricing

defned, 639

proft-maximizing price, 6

linear relationships

dummy variables for, 454

exact, 454–455

strength of, 441.

See

also

correlations

linear trendlines, 424

estimating, 423–430

Linearft.xlsx fle, 626

line graphs

automatically updating, 2

creating, 221

Line Sparkline

worksheet, 3

LINEST function, 447, 452

Lineupsch38.docx fle, 307

Lineupsch38.txt fle, 308

linking range names, 89

Lipstick Jen East

workshe

Lipstickprice.xlsx fle, 6

interest income, computing

687

list boxes, 230, 238

List validation criteria, 322–324

listed inputs, 129

lists

items in, selecting, 238

matching items in, 652–653

lists that change, TRANSPOSE

function for, 649–650

loan balances, fnal, 73

loan payments, calculating, 72–74

loans

amount of, 73

interest paid, 276

monthly payments, calculating

with Solver, 275–277

unpaid balances, 275

Locked option, 595

LOGEST function, 657–660

syntax, 659

logical functions

copying, 201–202

evaluation of, 200–201

Logicalexamples.xlsx fle, 200

lognormal random variables

for Black-Scholes pricing formula,

590

stock price modeling with, 545–

548, 565

LOGNORM.DIST function, 545, 547

LOGNORM.INV function, 545, 548

LOGNORMDIST returns, 547

lookup functions, 21–28

fnding values based on date, 25

fnding values based on ID

numbers, 24–25

frst column in ascending order,

22–24

frst column not in ascending

order, 24–25

left-hand lookups, 165

table ranges, naming, 23

VLOOKUP function, 21–22

wildcard characters and, 34

lookup ranges, 33

single-row, 34

unsorted values, 34

lookup value

argument of VLOOKUP

function, 21

lookup values, 33

exact matches to, 33

values greater than or equal to, 33

values less than or equal to, 33

Lookupdata.xlsx fle, 227

Lookupmultiplecolumns.xlsx fle, 27

Lookup.xlsx fle, 22

loops between cells, 81

lost-sales case, 613–616

LOWER function, 42

lowest values, formatting

conditionally, 188

Loyalty Effect, The

(Reichheld), 601

Loyalty.xlsx fle, 601

Luenberger, David G., 587

matrixes, 662

Macdonalds.xlsx fle, 379

machine lifetimes, modeling,

535–537

Make Unconstrained Variables Non-

Negative option, 250, 253, 257,

572

Makeup

worksheet, 209, 212–213

Makeuparray.xlsx fle, 654

Makeupdb.xlsx fle, 379, 388, 393,

663

Makeupflter.xlsx fle, 396

Makeupsortfont.xlsx fle, 215

Makeupsorttemp.xlsx fle, 209, 212,

213

Makeupsort.xlsx fle, 212

Makeupsubtotals.xlsx fle, 417

Makeup2007.xlsx fle, 158, 161

Manage Rules command, 187,

189–191

Manage Rules dialog box Stop If

True option, 205

managerial flexibility, valuing, 596

MAPE, 494

Marathon.xlsx fle, 109

Maria.xlsx fle, 139

marketable securities, computing,

Marketbasketdata.xlsx fle, 183

master workbooks, creating,

411–415

MATCH function, 33–38

functionality of, 33

inexact matches, 34

th value, determining, 35–36

OFFSET function with, 165–166

with other functions, 35

payback period, calculating,

37–38

in PivotTables, 378

syntax of, 33

for units purchased, 642–643

wildcard characters and, 34

match type=0

argument, 33–34, 36

match type=–1

argument, 33

match type=1

argument, 33, 37, 38

Matching Names

worksheet, 652

Matchlist.xlsx fle, 104

Matchthesecond.xlsx fle, 15

mathematical operations, so

optimization problems wit

243

Matradingrule.xlsx fle, 91–

matrices

multiplying, 662

square matrices, 662

MAX function, 35

Maximum Change setting, 83

Maximum Time Without

Improvement option, 297

mean, 337–338

analysis of variance, 471–4

of forecasts, 542

geometric means, 346

of random variables, 510

of resampled data, 584

signifcant differences amo

trimmed means, 344–345

mean absolute percentage er

(MAPE), 494

Meanvariance.xlsx fle, 510

median, 337–338

averaging numbers larger t

653

calculating using array for

660–661

in skewed data sets, 345

MEDIAN function, 337

Medians.xlsx fle, 660

Merton, Robert, 587

Microsoft PowerPivot for Ex

Give Your Data Meaning

(Ru

and Ferrari), 665, 673

Microsoft SQL Server Report

Services, 666

Microsoft Word equation edi

MID function, 40, 43, 45

military time, 105–106

minute, extracting from tim

MINUTE funtion, 108

MINVERSE function, 662

MIRR function, 66–67

syntax of, 67

MIRR

worksheet, 67

MMULT function, 662

MOD function, 99–100

mode, 337–338

MODE function, 337–338

MODE.MULT function, 337–338

MODE.SNGL function, 337–338

Modefunctions.xlsx fle, 337

Model

worksheet, 621

modeling.

See

Solver

activity durations, 538–53

modeling

688

modeling

continued

(

)

growth of revenue, 431–434

machine lifetimes, 535–537

stock prices, 545–548

uncertain events with Monte

Carlo simulation, 549–558

modifed internal rate of return

(MIRR), 66–67

money deposited

at beginning or end of period,

71–72

future value of, 72

money owed, value of, 71

Monte Carlo simulations, 147,

549–558

annual return, calculating, 571

assumptions, incorporating, 568

of binomial random variables,

559–560

confdence interval for mean

proft, 557–558

continuous random variable,

modeling as normal random

variables, 560

of craps game, 575–577

for decision making, 554–556

of demand, 551–552

fnal asset position for each

scenario, 571

for gambling and sporting event

simulations, 575

optimal bids, calculating with,

559–563

probability of getting a particular

poker hand, 577–579

RAND funciton, 550–551

random variables, simulating

values of, 551–553

risk and, 557

sports teams, rating, 579–582

users of, 549–550

month-day-year formats, 49

MONTH function, 53

monthly fxed costs, 428

monthly payments

amount borrowed based on,

138–139

calculating, 73–74

months

counting, 54

sorting chronologically, 213

More Rules option, 192

mortgage payments

changes based on input changes,

131–132

determining with Solver, 275–277

Mortgagedt.xlst fle, 132

mortgages

adjustable rate mortgages, 78–79

amount borrowed, calculating,

138–139

balloon mortgages, 78

most-likely scenarios, calculating,

143–147

Move Or Copy command, 190, 465

Move PivotTable command, 365

Movies.xlsx fle, 167–168

moving average graphs, 488–489

Moving Average option, 488

moving-average trading rules,

90–93, 174

moving averages

calculating, 499

centered, calculating, 499

four-period moving averages,

488–489

four-quarter, 499

moving cell values, 111–112

Mrcostest.xlsx fle, 447

MSFT and IBM

worksheet, 316

MSN MoneyCentral Investor Stock

Quotes query, 316

multiple criteria

flagging rows with, 158

functions allowing for, 150

Multiple IRR

worksheet, 64

multiple peaks histograms, 332

multiple regression, 428, 447–452

accuracy of predictions, 451–452

coeffcients, interpreting, 456

dummy variables, interpreting,

457

forecasts from, 461–462

independent variables, deleting

from analysis, 450

independent variables, predictive

power, 450

input ranges, 449

interactions, checking for,

464–466

lagged values, 455

LINEST function, calculating with,

452

nonlinear effects, checking for,

464–466

outliers, 451, 461

output location, 449

prediction equation 1, 456, 466

prediction equation 2, 460

presidential elections, predicting

with, 458–461

qualitative factors in, 453–462

residuals, 449, 451, 457

results, inserting in workbook, 452

for sales forecasts, 453–457

standard error, 451

validation points, 459

Multistart option, 243, 289, 295

mutation rate, 291, 297

increasing, 304

My Data Has Headers optio

My Table Has Headers opti

#NA (not available), 34, 9

Name arrow, 10

Name box

defned, 10

range names, creating in

workbook scope names, 16

#NAME? errors, 99

Name Duplicates Removed

worksheet, 405–406

Name Manager, 171, 218

range names, creating wi

named ranges.

See also

range names

column names as, 15

creating, 9–12

Namedrows.xlsx fle, 18

Names.xlsx fle, 206

Nancybonds.xlsx fle, 103

Nash, Steve, 559

navigating workbooks, 353

NBA players, rating, 307

Nbadistances.xlsx fle, 31

Nbadvl.xlsx fle, 319

Nbamiles.xlsx fle, 306

Nbasalaries.xlsx fle, 206

NBA.xlsx fle, 161

Nba01_02.xlsx fle, 285

Nba02_03.xlsx fle, 285

Ncaa2003.xlsx fle, 581

negative binomial random v

520–521

negative numbers in data b

negative production, 253

negative values, data bar

negatively skewed histogr

NEGBINOM.DIST function, 5

Negbinom.dist.xlsx fle, 5

nested IF formulas, 89, 1

Nestedsubtotals.xlsx fle, 4

net fxed assets, computin

net income, computing, 96

net present value (NPV).

NETWORKDAYS function, 52–

NETWORKDAYS.INTL function

New Comment command, 581

new data

automatic updating on, 2

222

conditional formatting o

formatting style for, 21

updating with, 171–173

New Data

worksheet, 222

modeling ()

continued

689

New Formatting Rule dialog box,

192

for PivotTables, 364

Use A Formula To Determine

Which Cells To Format option,

341

New Group button, 2

New Name dialog box, 12, 12–13,

18, 172

New Rule button, 190

New Rule command, 187

New Tab button, 2

new text

argument, 41

New Web Query dialog box,

313–314

NFL point spreads, setting, 281–285

NFLpoints.xlsx fle, 334

Nfl2009april2010.xlsx fle, 281, 282

Nflwinslosses.xlsx fle, 384

Nfl0x.xlsx fle, 285

Nikedata.xlsx fle, 227

95-percent service level, 616–618

defned, 613

Nlp.xlsx fle, 639

No Blades

worksheet, 631

No Feasible Solution

worksheet, 252

No IRR

worksheet, 65

NoA

worksheet, 450–451

nonadjacent selections, grouping,

376

nonblank cells, counting, 150, 154

Noncontig.xlsx fle, 11

nonlinear effects, 463

checking for, 464

nonlinear optimization models, GRG

Nonlinear engine for, 288–291

nonlinear pricing, 639–646.

See

also

product pricing

defned, 639

quantity discounts, 639

two-part tariffs, 640

Nonlinear Pricing Examples

worksheet, 639

Nonlinearity

worksheet, 463

nonsmooth functions, 291.

See

also

Evolutionary Solver engine

defned, 244

solving, 244

nonsmooth optimization problems,

291.

See also

Evolutionary

Solver engine

NORM.DIST function, 529–530, 543

NORM.INV function, 531–532,

552–553, 560

for sports simulations, 580–581

NORM.S.DIST function, for

cumulative normal probability,

591

normal cumulative functions, 529

normal random variables, 527–534

continuous random variables,

modeling as, 560

larger σ, 529

percentiles for, 531–532

properties of, 528–529

simulating values of, 552–553

standard normals, 591

Normalexamples.xlsx fle, 528, 530

not equal to angle brackets (<>),

152

NOT function, evaluation of, 200

NOW() function, 107

NPER function, 76

NPV

beginning-of-year cash flows,

59–60

calculating, 58–59

of customers, 602

defnition of, 57–59

end-of-year cash flow, converting

to beginning-of-year, 602

interest rate and, 63

irregular cash flows, 60–61

maximizing, 267, 269

mid-year cash flows, 60

nonnegative

cash flows, 147

NPV function, 59

of payments, 71

in today’s dollars, 61

XNPV function, 60–61

zero value, 63, 64

NPVauditscenario.xlsx fle, 143

NPVaudit.xlsx fle, 122

NPVspinnerstemp.xlsx fle, 231

NPV.xlsx fle, 141

null hypothesis, 471

accepting, 473

#NUM! error messages, 61, 67, 99,

393

for no IRR, 64, 65

number

argument, 42

Number Filters option, 400

Number format for time formulas,

106–107

number of periods, 70

number of times

argument, 41

Numberdv.xlsx fle, 321

numbers

extracting into separate cells,

44–45

position in range, 33

ranking, 578

text strings, converting from,

42, 43

Numbers.xlsx fle, 155, 162

numerical data

counting cells with, 154

fltering, 399–400

grouping, 377

icons, associating with, 19

ranking, 344–345

sorting, 215

treating as numbers, 310

validating, 321–322

visually distinguishing, 19

Obama, Barack, 461

odds, translating probabili

581

Offce button, 5

OFFSET function, 163–175

cells, extracting data fro

167–168

changes in data location, 1

dynamic updates with, 172,

171–173

evaluating parts of, 169

last number in column, fndi

170

for left-hand lookups, 165

MATCH function with, 165–16

in PivotTables, 378

syntax, 163–164

Offsetcost.xlsx fle, 166, 1

Offsetexample.xlsx fle, 164

Oilwell.xlsx fle, 596

old text

argument, 41

One warehouse

worksheet, 29

one-way analysis of varianc

471–476

one-way data tables.

See al

tables; two-way data tabl

for customer valuation, 603

for option pricing, 596–597

for resampling data, 585

setting up, 568

simulating craps in, 577

OnePrice

worksheet, 641

Onewayanova.xlsx fle, 472

operating costs

forecasting, 448–451

monthly variation in, 428

vs. production, 425–428

operating income, computing

Operations Research: Applic

and Algorithms

(Winston), 6

optimal bids, calculating, 5

optimal solutions, 244

multiple, 257

to product mix model, 251

optimal solutions

690

optimization.

See also

Solver

defned, 241

linear optimization problem, 243

solution engines, 243–244

solution types, 244

optimization models, parts of, 241

optimization problems

nonlinear optimization problems,

288–290

nonsmooth optimization

problems, 291

option

argument of AGGREGATE

function, 98

option buttons, 230, 237

linking to cells, 237

option pricing

Black-Scholes formula, 548,

587–599

for capital budgeting and

fnancial decision making,

596–598

Optionbuttons.xlsx fle, 237

Optionfgures.xlsx fle, 588

options.

See

stock options

Options dialog box Use Automatic

Scaling option, 277

OR operator

adding Boolean arrays and, 656

with DSUM function, 390

evaluation of, 200

in IF formulas, 93

order quantity, discounts on, 88–89

ordering costs

assumptions about, 613

minimizing, 607–609, 614–616

Original Model

worksheet, 122, 143,

231

Original

worksheet, 221

outliers, 340

common factors of, 507

effciency and, 429

in forecasts, 504–505

formatting conditionally, 341–342

in multiple regression analysis,

451, 461

outline form PivotTables, 354

Outline Form

worksheet, 354

Outline group Subtotal command,

417

outputs of interest, sensitivity

analysis on, 127–136

p-values

alternative hypothesis and, 471

independent variables, dropping,

460

interactions and, 464

low values, 484

in multiple regression analysis,

450

null hypothesis and, 471

signifcance of, 456, 465–466, 479

Page Setup dialog box, 582

parameter values, 122

Parameters dialog box, 494

Paste Link option, 113

Paste List button, 17

Paste Name dialog box, 15, 17

Paste Preview dialog box, 669

Paste Special command, 111–115

live preview, 8

pasting only values, 111–112

Paste Special dialog box, 111–112

Divide option, 114

Operations area, 113–114

Paste Link option, 113

Skip Blanks option, 444

Transpose option, 112–113, 444,

649

Values option, 112

Paste Special Divide Before

worksheet, 113

Paste Special Transpose

worksheet,

112

Paste Special Value

worksheet, 111

Pastespecial.xlsx fle, 111

payback period, 135

calculating, 37–38

Paymentgs.xlsx fle, 138

payments

balloon payments, 73

at beginning or end of period, 71,

73, 74

future value of, 69–71

loan payments, calculating, 72–74

number of, 72

number of periods of, 76

present value of, 71, 73

on principal, calculating, 73–74

sign conventions, 70

type of, 70

payoffs

for call options, 588

for put options, 589

peakedness of data, 339

penalties with Evolutionary Solver,

297–300

#per

argument, 70

in FV function, 71

in IPMT function, 73

in PMT function, 72

percentage errors, standard

deviation of, 542

percentage return on port

89–90

PERCENTILE function, 342–

percentile rankings, 342–

PERCENTILE.EXC function, 6

342–343

PERCENTILE.INC function, 3

percentiles

icons, associating with, 1

for normal random variab

531–532

Percentile.xlsx fle, 342

PERCENTRANK function, 342

PERCENTRANK.EXC function,

342–343

performance, automatic

recalculation and, 131

periodic payments, calcul

72–74

periods

number of, calculating, 7

payback periods, 135

payments made at end or

beginning of, 70–71, 73

in PV function, 70

Phoneloyalty.xlsx fle, 60

Pinevalley.xlsx fle, 27

PivotCharts, 361–362

chart types, changing, 3

Column Graphs option, 36

editing, 368

Line Graph option, 361

PivotTable Field List, 35

PivotTable Options dialog b

PivotTable Tools Design o

PivotTable Tools Options c

356

PivotTables, 4, 327, 349–

blank rows, adding, 363

calculated felds, 374–37

calculated items, 377

Clear Filter command, 35

Column Labels zone, 353

conditional formatting f

364–365

creating with PowerPivot

670–672

vs. database statistical f

387

data source, changing, 3

description of, 350–351

drilling down in, 377

dynamic range names in, 1

empty cells, replacing, 3

external data source for

extracting entries, 378

felds, 352

felds, arranging, 671

optimization

691

PivotTables

continued

) (

felds, collapsing and expanding,

356–357

felds, pivoting, 355

felds, sorting and fltering, 357–

361, 372

formatting, changing, 355–356

GETPIVOTDATA function, 377–378

grouping items in, 376

grouping results, 367

headings, 351

layouts, 354

locating and returning data,

377–378

percentages, displaying data as,

370

PivotCharts, summarizing with,

361–362.

See also

PivotCharts

PowerPivot add-on, 5

removing row labels from, 367

report flters, 362, 375–376

Report Filter zone, 353

Row Labels zone, 352

scenario results as, 146

Show Field List command, 353

slicers.

See

slicers

sorting data by two variables, 368

standard deviations in, 380

styles, 356

totals, hiding, 363

updating, 365

Values zone, 353

variables, influence on each other,

369–371

zones, 352–353

Pivotwithslicers.xlsx fle, 672

plus sign (+), 232

pmt

argument

in FV function, 71

in PV function, 70

PMT By Solver

worksheet, 276

PMT function, 72–74

accuracy of, 275–277

syntax, 72

PMT

worksheet, 75

point forecasts, 541.

See

also

forecasts and forecasting

probability statements about, 541

point spreads, setting, 281–285

POISSON function, 524

Poisson random variable, 523–526

time between arrivals, 525–526

POISSON.DIST function, 524

Poisson.xlsx fle, 524

poker, probability of getting a

particular hand, 577–579

population standard deviation, 340

population variance, 340

populations, 291

portfolio insurance, 90

portfolios, percentage return on,

89–90

positive values, data bars for, 193

positively skewed histograms, 331

power curves, 424, 435–440

ft of, 438

production costs as function of

units produced, 435

properties of, 437

sales as function of advertising

expenditures, 436

slope of, 435

steepness of, 438

time for production as funtion of

cumulative production, 436

power demand curves, 626

Power Pricing

(Dolan and Simon),

625

Powerexamples.xlsx fle, 435

Powerft.xlsx fle, 628

PowerPivot, 5, 665–674

DAX functions, 673–674

downloading, 665

importing data into, 666

inserting data in, 666

options for, 665

PivotTables, creating, 670–672

reading data into, 665–670

slicers with, 672

PowerPivot Design tab, 670

PowerPivot Field List, 670–671

Slicers Horizontal and Vertical

felds, 672

PowerPivot Home tab, 666, 667

Paste Preview dialog box, 669

PivotTable option, 670

PowerPivot tab, 665

Excel icon, 669

fx button, 673

PowerPivot window Design option,

670

PowerPivot Window button, 666

powers of sales, 657

PPMT function, 73–74

syntax, 74

precedence of conditional

formatting rules, 190–191, 199

precedents

with data on multiple worksheets,

125

defned, 121–122

tracing, 124–125

Predicting Presidential Elections and

Other Things

(Fair), 458

prediction equations, 502

equation 1, 466

equation 2, 483, 485

ft of, 456, 460

interactions and, 485

predictions.

See also

forec

forecasting

accuracy of, 428–429

presidential elections, 45

sales, 453–457

of time series future value

two-factors with replicati

480–485

presidential elections, pre

458–461

Pressdata.xlsx fle, 273

price

and demand, nonlinear

relationship, 463

of products.

See

product p

proft-maximizing price.

See

proft-maximizing pric

price bundling, 640–642

price cuts, price elasticit

price elasticity

defned, 626

unknown, 635

Priceads.xlsx fle, 468

pricing products.

See

produ

pricing

principal payments, 73–74

cumulative, 75

Print menu, 6

printing comments, 582

pro forma statements

debt as plug, 93–97

defned, 94

probabilities

with Beta random variable,

538–539

of lognormal random variab

with parameters Mean and

Sigma is less than or equa

, 547

resampling data for, 583–5

that

equals

and always e

0, 528

translating to odds, 581

probability density functio

511–512

of continuous random variab

527–528

exponential, 525

height of, 512

normal, 560

probability mass functions, 5

probability of occurrences

exponential probabilities,

in short interval, 523–526

probability of occurrences

692

probability of success

calculating, 516–518

of failuers

th success,

before

520

of greater than

, 518

or less than

of less than

, 519

or equal to

with small sample size, 518–519

probability statements from point

forecasts, 541–544

Prodmix.xlsx fle, 245

production

batch sizes, optimizing, 609–611

economic order batch size model,

610

monthly variation in, 428

negative, 253

vs. operating costs, 425–428

setup costs, 610

simulating levels of, 554–556

production costs

computing, 643–644

as function of units produced, 435

variable, 625

product mix optimization problems,

245–254

changing cells, 247

constraints, 245, 247

feasible solutions, 251

infeasible solutions, 252

SUMPRODUCT evaluations,

246–247

target cells, 247

product pricing

bundling, 640–642

demand curve and, 625

factors affecting, 625

nonlinear pricing, 639–646

proft-maximizing price, 631–633,

635–638, 641–642

quantity discounts, 639

for subjective demand, 635–638

with tie-ins, 631–634

two-part tariffs, 640

with variable cost and three

points on demand curve,

635–638

product sales. fnding, 35

Productlookup.xlsx fle, 227

Productpaste.xlsx fle, 115

products

cumulative value associated with,

642

demand curve, 625

fxed fee for, 643–644

price charged for, 642–644.

See

also

product pricing

unit value, 629

Productsalespaste.xlsx fle, 115

Product.xlsx fle, 31

proft

computing, 128, 642, 644

confdence interval for, 557–558

formula for, 247

maximizing, 245–252

transaction cost impact on, 93

Proft

worksheet, 125

proft-maximizing price

fnding, 631–633, 635–638,

641–642

two-part tariff price, 642–646

proftability

of customers, 601–605

customer value and, 603

loyalty incentives and, 603–605

price bundling and, 640–642

product pricing and, 625

tie-ins and, 631–634

Proforma.xlsx fle, 94

project durations, modeling,

538–539

project selection problems, 267–273

additional constraints, 270–271

changing cells, 268

constraints in, 268

linear model, 268, 270

target cells, 268

projects

scale of, 66

value, adding, 66

Protect Sheet command, 595

Protect Sheet dialog box, 595

Ptable

worksheet, 358

Ptableexample.xlsx fle, 371, 374

Ptablepartsdata.xlsx fle, 380

Ptcustomers.xlsx fle, 358

P23_2.xlsx workbook, 183

purchases, consumer surplus, 641

pure bundling, 641

put options, 89–90.

See also

stock

options

cash flows from, 588–589

defned, 587

graphing, 589

argument

in FV function, 71

in PMT function, 73

PV function, 69–71

syntax, 69

Qd.xlsx fle, 645

quadratic demand curves, 635

qualitative factors

modeling, 454

in multiple regression, 453–462

quantitative independent v

453

Quantity Discount

workshe

quantity discounts, 639

computing with Solver, 6

modeling, 88–89

Quarterly.xlsx fle, 239, 4

queries

editing, 315

refreshing and updating, 3

query results, formatting

question mark (?) wildcar

character, 153

Queuing Data

worksheet, 6

queuing systems

conditions of, 620

infnite lines, 620

interarrival time, mean a

standard deviation, 619

queuing template, 621–62

servers, number of, 619

service capacity, 623

service time, mean and s

deviation, 620

steady state, 620

time in, factors affecti

variability and, 621

queuing theory, 619–624

Queuingtemplate.xlsx fle, 6

Quick Access Toolbar, 2–3

position of, 3

quotation marks (“ “)

for array text, 656

for text in criteria, 15

for PivotTable headings, 3

for text, 34, 92

R-squared values, computi

RAND function, 550–551

recalculation of numbers

=RAND() formula, 550–551

RANDBETWEEN function, 566

576

resampling with, 583–585

Randdemo.xlsx fle, 550

random numbers

generating, 550–551

ranking, 578–579

recalculating, 551

random variables, 509–513

Beta random variable, 53

538–539

binomial, 515–517, 559–5

continuous, 511

discrete, 509–510

expected values, 510

probability of success

693

random variables

continued

)

(

forecast errors and, 543

hypergeometric, 519–520

independent, 512–513

lognormal random variables,

545–548

mean and standard deviation of,

552–553

mean of, 510

negative binomial, 520–521

NEGBINOM.DIST function, 520

normal, 527–534

Poisson random variable, 523–526

probability density functions,

511–512

simulating values of, 551–553

standard deviation of, 510–511

uniform random variables, 563

values of, 509

variance of, 510–511

Weibull random variable, 535–537

random variation, smoothing, 488

randomization in ANOVA analyses,

478

randomized block models, 477,

478–479

Randomized Blocks

worksheet, 478

randomness of forecast errors, 507

range

argument

of COUNTIF function, 150

of SUMIF function, 157

range lookup

argument of

VLOOKUP function, 21–22, 24

range names, 9–19, 159.

See

also

named ranges

for cell above active cell, 18–19

comments for, 13

disallowed letters, 19

displaying, 10

dynamic, 170–171

editing and deleting, 13–14

in formulas, 14–15, 153

formulas, applying to, 17

for rectangular cell ranges, 10

linking, 89

Name box, creating with, 10–11

new data in, 218

for noncontinguous cells, 11

pasting into worksheets, 17

permitted name types, 19

referencing, 181–182

scope of, 15–16

spaces and underscores in, 19

symbols in, 19

undefned, 99

references in worksheets, 633

range of cells.

See

cell ranges

range of data set, 340

range_n

argument of COUNTIFS

function, 150

range1

argument of SUMIFS

function, 158

ranges, position of number in, 33

RANK function, 344

RANK.AVG function, 344

RANK.EQ function, 227, 344,

578–579

syntax, 578

ranking numbers, 344–345,

578–579

ranking projects on IRR, 66

rate

argument, 60–61

in FV function, 71

in PMT function, 72

in PV function, 70

RATE function, 75–76

rate indexes, 78

rate of loan, 75–76.

See also

interest

rate

ratio-to-moving-average

forecasting method, 497–500

Ratioma.xlsx fle, 497, 498

raw materials

for production, 246

usage calculations, 246–247

Razorsandblades.xlsx fle, 631

real options, 596.

See also

stock

options

realigning data, 112–113

Reapply command, 407

reciprocal cost allocation method,

records, database, 396

#REF! errors, 99

reference

argument of OFFSET

function, 164

reference cells, 163

references to cell ranges, 163–175.

See also

cell ranges

Refresh command, 365

Refresh Control settings, 315

refunds, counting, 160

regression analysis.

See

multiple

regression

Regression dialog box, 448

regression equations.

See

also

prediction equations

validating, 459

regression toward the mean,

445–446

Regression

worksheet, 449, 456

Regressionfnal

worksheet, 460

Reichheld, Frederick, 601

reinvest rate vs. borrow rate, 66–67

remainders, yielding, 99–100

Remove Arrows button, 122

Remove Duplicates command, 2

Remove Duplicates dialog bo

405–406

Remove From Quick Access Too

command, 3

Rename button, 2

reorder point

back-order case, 614–615

defned, 613

lost-sales case, 615–616

95 percent service level, 6

616–618

safety stock level, 615

two-bin policy, 618

uncertainty and, 616

variables affecting, 614

Reorderpoint_backorder.xlsx f

614

Reorderpoint_lostsales.xlsx f

Replace All command, 45

Replace Current Subtotals o

418

REPLACE function, 41

Report Filter zone, 353

report flters, 362, 372, 37

Report Layout option, 354

reports, importing data fro

REPT function, 41, 46–47

Required Bounds On Variable

check box, 291

Resampleyield.xlsx fle, 583

resampling, 583–586

mean of resampled data, 58

replaying, 585

residuals

calculating, 457

examining, 506–507

random, 507

Resize Table command, 220

resource usage

calculating, 246–247

for production, 246

result cells, 143

choosing, 145

results

editing, moving, deleting, 6

moving, 111–112

returning in one or multipl

647–648

selecting display range, 6

retained earnings, beginnin

ending, 96

retention rates, customer, 6

Retire

worksheet, 278

retirement funds, relations

among contributions,

withdrawals, and return, 2

retirement funds, relationship among contributions

694

retirement planning, using Solver

for, 277–279

revenue

calculating, 99–100, 643–644

computing, 128

determining by month, 373

modeling growth of, 431–434

summarizing by two variables,

372

revenue trends, estimating with

array formulas, 657–660

Reverse Icon Order option, 197

Reversed.xlsx fle, 175

ribbon

customizing, 1–2

PowerPivot tab, 665

RIGHT function, 40, 45

Right Way

worksheet, 189

risk, decision making and, 557

risk-free rate, 589

increases in, 593

Rock.xlsx fle, 150–151, 154

Roosevelt, Theodore, 461

rounding errors in IPMT function, 74

ROW function, 99–100, 182, 207

Row Inserted

worksheet, 180

Row Labels zone, 352

row location, returning, 33

row numbers, returning, 182

row of reference, 99

rows

adding together, 387–388

errors in, ignoring, 98

height, increasing, 231

hiding, 133, 193

inserting, totaling values and, 180

listing cell ranges in, 649–650

with multiple criteria, flagging,

158

new, in tables, 219

referencing with INDEX function,

referring to by name, 84

subsets of, 224

transposing data to columns,

112–113

visibility of, 91

rows moved

argument of OFFSET

function, 164, 167

RSQ function, 504

R2 values, 428

correlations and, 445

interpreting, 451

rules for conditional formatting,

186–187.

See also

conditional

formatting

creating, 187, 190

criteria for, 192

deleting, 187, 190, 199

editing, 190, 199

managing, 187, 189–191

order of, 199

precedence of, 190, 199

Stop If True option, 205

top/bottom rules, 187–188

viewing, 189

Russo, Marco, 665

S curves, 488

safety stock levels, 615

service levels and, 616

Sagarin, Jeff, 307

Sagarin ratings, 579

Salaries.xlsx fle, 664

sales

computing, 95

deseasonalizing, 498

effects on, checking for, 472–473

as function of advertising

expenditures, 436

predicting, 453–457, 480

seasonality of, 497–498

sales forecasts, 497–500.

See also

forecasts and forecasting

with ratio-to-moving-average

method, 499–500

Sales > 90 units dollars > $280

worksheet, 401

Sales In 2005 And 2006

worksheet,

402

Sales.xlsx fle, 394

sample standard deviation, 339–340

sample variance, 339–340

sampling with replacement, 583

Sandp.xlsx fle, 198, 205

Satissuper.xlsx fle, 206

scale of projects, IRR and, 66

Scalesiconsdatabars.xlsx fle, 191,

194, 195

Scatter Chart option, 423

scatter plots

creating, 425

for linear demand curves, 627

modifying, 426

for power curves, 437–438

for time series, 487

for trend curves, 432

Scatter With Only Markers option,

425

Scatter with Smooth Lines and

Markers option, 487

Scatter With Straight Lines option,

627

Scenario Manager, 230–231

for sensitivity analysis

starting, 144

Scenario Manager dialog b

145–146

Merge button, 147

Show button, 146

Summary option, 145

Scenario PivotTable Repor

146

Scenario Summary dialog b

145–146

Scenario Summary option, 1

Scenario Summary reports

Assumption cells, hiding a

showing, 147

Current Values column, 1

Scenario Summary

workshee

Scenario Values dialog bo

scenarios, 145–149

creating, 230–231

input data, 144

listing, 145–146

merging into one workboo

Monte Carlo simulation, 1

showing, 146

summary report, 144, 145

Scenario PivotTable Repo

option, 146

scheduling, Solver optimi

255–259

Scholes, Myron, 587

Scope arrow, 13

scroll bar controls, 230, 23

SEARCH function, 41

seasonal indexes, 491, 65

creating, 660

defning, 497–498

estimating with ratio-to

average method, 498–500

estimating with Winters’

493

updating, 494

seasonality.

See also

sea

indexes

defned, 491

estimating with array fo

657–660

modeling, 454–455

predicting effect of, 45

removing from estimates, 4

smoothing, 488–489

SECOND funtion, 108

2nd Table

worksheet, 373

seconds (time)

displaying, 107

extracting from times, 1

retirement planning

695

Select A Solving Method list,

243–244

Simplex LP, 250

Select All button, 133

select all data in a range, 114

Select Unlocked Cells option, 595

selecting

cell ranges, 210

lists items, 238

with option buttons, 237

sort criteria, 211

table specifers, 225

semicolons, breaking data at, 46

sensitivity analysis, 127–136

of queuing system components,

623

Scenario Manager for, 143–147

sequence of cash flows, one change

in sign in, 65

sequence of times, entering, 109

sequencing problems, solving, 303

serial format dates, 50–51

serial numbers

for date and time, 105

for times, 105

Series dialog box, 555–556

servers (in queuing system), number

of, 619, 622, 623.

See also

queuing systems

service times.

See also

queuing

systems

mean and standard deviation of,

620, 622

stationary, 620

Servicelevelreorder.xlsx fle, 616

Set Cell, defned, 137

Set Objective box, 248

Set Values Do Not Converge

message, 253

Set Values Do Not Converge

worksheet, 253

Sharedata.xlsx fle, 19

Sheetnames.xlsx fle, 15

shipping costs, calculating, 262

shortage costs

assumptions about, 613

minimizing, 614–616

Show Bar Only option, 192

Show Field List command, 353

Show Formulas command, 121

Show/Hide Comments command,

581

Show Icon Only option, 197

sign changes, 507

Signif

worksheet, 472, 475

Simon, Hermann, 625

Simplex LP engine, 243, 287

for product mix problems,

250–251

simplex method, 251

simulation.

See also

Monte Carlo

simulations

of values for stocks, 570

Singers.xlsx fle, 227

single-row lookup ranges, 34

single warehouse problem, 291–293

SKEW function, 339

skewed left histograms, 332

skewed right histograms, 331

skewness, 339

mean of data and, 345

slashes (/), 220

slicers, 4, 351, 353, 363

creating, 375–376

with PowerPivot, 672

resizing, 672

Slicers

worksheet, 375

SLOPE function, 429

slope of least-squares lines, 429

SMALL function, 36, 344

smallest values, associating with

data bars, 191–192

smoothing constants, 492

estimating, 493–494

smoothing methods, Winters’s

method, 491–495

solution engines, 243–244

solutions

feasible, 244, 251

no feasible solutions, 252–253

optimal, 244, 251, 257

Solver

for asset allocation problems,

571–572

binary changing cells, 267

for distribution problems,

261–265

errors in model, 253

Esc key, 289

feasible solutions, 244

for fnancial planning, 275–280

forecast parameters settings,

503–504

functionality of, 241

installing, 243

linear problems, 251

mortgage payments, determining

with, 275–277

new capabilities, 5

no feasible solutions, 252–253

optimal solutions, 244

Parameters dialog box, 494

price, constraining, 637

product mix problems, 245–254

proft-maximizing price, fnd

632–633, 637

project selection problems

267–273

for quantity-discount prob

644–645

resolving incorrect proble

previous versions, 243

for retirement planning, 27

running, 243

scheduling problems, 255–25

Select A Solving Method li

243–244

for sequencing problems, 3

service level reorder poin

calculation, 617–618

for single warehouse probl

291–293

solution engines, 243–244

for sports teams ratings, 2

tolerance settings, 271–272

for transportation problem

261–265

for two warehouses problem

293–295

very large and small numbe

and, 277

Weibull random variable par

settings, 536

Solver Options dialog box I

Optimality setting, 271

Solver Parameters dialog bo

247–248

for asset allocation model

571–572

By Changing Variable Cells b

248

changing and target cells,

defning, 248

for Evolutionary Solver pr

297

for proft-maximizing quanti

discounts, 646

Make Unconstrained Variable

Non-Negative check box, 2

253, 257, 572

for maximizing proft, 632, 6

for mortgage payment probl

276–277

for one warehouse problem,

292–293

for product mix problem, 25

for project selection prob

268–269

for reorder point calculat

for retirement planning pr

278

Set Objective box, 248

Set Objective box

696

Solver Parameters dialog box

(

continued

)

for sports teams ratings, 283

for traveling salesperson problem,

304–305

for two warehouses problem, 294

for workforce scheduling

problem, 256

Sort A To Z button, 215

Sort & Filter group

Advanced option, 408

Filter option, 397

Sort button, 211

sort criteria, 210–212

managing, 212

selecting, 211

Sort dialog box, 211

Add Level option, 212

Cell Color option, 212

Cell Icon option, 213

criteria management, 212

Font Color option, 212

not using, 215

Sortday.xlsx fle, 215

Sorted q1

worksheet, 360

Sorticons.xlsx fle, 215

sorting, 209–215.

See also

fltering

by age, 367

alphabetically, 210

A-to-Z order, 210

on cell or font color, 212–213

chronologically, 210, 212, 213–214

criteria, 210

custom sort orders, 214

by gender, 366

on icons, 213

largest to smallest, 360

My Data Has Headers option, 211

numerical values, 215

reverse alphabetical order, 357

smallest to largest, 357

subtotals for, 417–420

on two values, 368

without Sort dialog box, 215

spaces

breaking data at, 46

as column delimiters, 309–310

errors, replacing with, 97–99

inserting, 44

removing from text strings, 40

trimming excess, 42

Sparkline Tools Design tab, 382–383

sparklines, 4, 381–385

automatically updating with new

data, 385

axes for, 383

converting type of, 384

data for, 381–383

irregularly spaced data, 383

modifying, 382–384

win/loss sparklines, 384–385

Sparklines group Line option,

381–382

Sparklines.xlsx fle, 381

special events, forecasting, 501–504

spin buttons, 229, 231–234

anchoring, 232

copying and pasting, 232

creating, 231–232

linking to input cells, 232–233

minimum increment, 233

row height for, 231

shape, changing, 232

sports teams ratings, 281–285,

579–582

changing cells, 281

favorite rating–underdog rating,

580

home-feld edge, 281–282, 284

squared errors, 282, 284

target cells, 281

spread of data, 339–340

square matrices, 662

squared errors, 282–283

standard deviation, 340

estimating, 560

of forecast errors, 480

of forecasts, 542

PivotTables and, 380

of random variables, 510–511

standard error of regression,

428–429

calculating, 457

standard normals, 591

start_date

argument, 51, 52

startdate

argument, 54

Statedv.xlsx fle, 322

States.xlsx fle, 11, 668

Station.xlsx fle, 369

statistical inferences, 583

status bar, 345

STDEV function, 340

STDEV.S function, 340

steady state, quantities in, 620

STEYX function, 428–429

stock indexes, queries about, 316

stock market

moving-average trading rules,

90–93

trends, following, 90–93

stock options.

See also

call options;

put options

abandonment options, 597–598

American vs. European, 588

duration of, 589

exercise (expiration) date, 588

exercise price, 587

implied volatility appro

input values, changes in

option-pricing formula, 5

real options, 596

risk-free rate, 589

value parameters, 589–59

valuing, 592

volatility of, 590

stock prices

bootstrapping, 565–568

downloading, 315–317

downward moves in, 89–90

implied volatility, 546

increases in, 592

median price, predicting

modeling, 545–548

one-year returns, calcul

stock option value and, 5

stock volatility, 590

estimating, 590

Stockcorrel.xlsx fle, 443

Stockprices

worksheet, 32

stocks

average return on, 346

butterfly spreads, 102

European put options, 89

Stock.xlsx fle, 19, 327, 3

Stop If True option, 205

Storesales.txt fle, 666

story problems, solving w

Seek, 139–140

straight-line relationshi

estimating, 423–430

INTERCEPT function, 429

SLOPE function, 429

structure of worksheets, 1

structured references, 22

Styles group Conditional F

arrow, 186

subjective demand, produc

for, 635–638

subsets of data, identify

also

fltering

SUBSTITUTE function, 48

Subtotal command, 417

Subtotal dialog box, 417–

Add Subtotal To area, 41

At Each Change In list, 4

Page Break Between Group

option, 418

Replace Current Subtotal

418, 420

Summary Below Data check b

418

Use Function box, 417

SUBTOTAL function, ignori

Solver Parameters dialog

)

box (

continued

697

subtotals, 417–421

below data, 418

buttons to display, 419

hiding, 363

nesting, 420–421

page break after, 418

removing, 418

SUM function.

See also

summing

with INDIRECT function, 180

sum of squared errors

computing, 438, 503

minimizing, 503–504

sum of squares, 474

sum range

argument

ommitting, 159

of SUMIF function, 157

Sum Up 2nd Digit

worksheet, 651

SUMIF function, 157–158, 654

criteria for, 158–160

criteria rules, 158

Sumifrows.xlsx fle, 161

SUMIFS function, 158, 160–161,

389, 392

Sumindirect.xlsx fle, 178

summarizing data

with array formulas, 654–656

column and row data, 381–385

with database statistical functions,

387–394, 654

with descriptive statistics,

335–348

with histograms, 327–334

with PivotTables.

See

PivotTables

with PowerPivot slisers, 672

with slicers, 4

subtotals, 417–421

summary worksheets, pooling data

in, 182

summing

based on criteria, 157

blank rows and, 180

second digits in set of integers,

651–652

SUMPRODUCT function, 246–247,

256, 262

sumrange

argument of SUMIFS

function, 158

Suppliers.xlsx fle, 240

supply points, 261

total product shipped from,

calculating, 262

support department costs,

allocating, 85

Suzuki, Ichiro, 563

symbols

in range names, 19

ranges of values, identifying with,

186, 195–197

symmetric distributions, 331

symmetry assumption, 560

tab order, 2

table range

argument of VLOOKUP

function, 21

table ranges, 129

Table Style Options group Total Row

option, 223

Table Styles option, 221

Table Tools tab, 220–221

Banded Columns option, 221

Banded Rows option, 221

Change Table Name command,

220

Convert to Range command, 220

First Column option, 221

Header Row option, 221

Last Column option, 221

Remove Duplicates command,

220

Resize Table command, 220

Table Styles option, 221

Total Row option, 221

Tableexampletemp.xlsx fle, 217

Tableexample.xlsx fle, 227

Tablemakeupfnal.xlsx fle, 224

Tablemakeuptemp.xlsx fle, 222

Tablepie.xlsx fle, 227

tables, 217–227.

See also

PivotTables

autocomplete options, 219

autocopying formulas in, 220

banded columns and rows, 221

for chart data, 222

conditional formatting of new

data, 226

creating, 218

design options, 218

duplicates, removing, 220

dynamic data and, 173

flter arrows, 223–224

frst column formatting, 221

header rows, 221, 222

last column formatting, 221

My Table Has Headers option, 218

naming, 218

parts of, referring to, 225–226

renaming, 220

resizing, 220

structured references, 225–226

table formats, 221

table range, converting to normal

cells, 220

table specifers, 225

totals, fltering, 223–224

totals rows, 222–224

Tables group PivotTable opti

Tablestructure.xlsx fle, 22

Tablexnpvdata.xlsx fle, 227

tabs

breaking data at, 46

customizing, 1–2

groups within, 2

renaming, 2

tabular form PivotTables, 35

Tabular Form

worksheet, 354

Taleb, Nicholas, 548

Tapesales.xlsx fle, 174

target cells, 241

in capital budgeting probl

268

in fnancial planning proble

276

in linear problems, comput

250

multiple, 241–242

penalizing, 297, 298–299

in sports teams ratings, 21

theoretical optimal value o

in transportation problems

tax rates, computing, 22–24

Teams.xlsx fle, 334, 468

technology companies, reven

growth of, 433

Test.xlsx fle, 205

text

combining, 43–44

fnding, 41

in IF statements, 92

justifcation of, 42

lowercase, 42

numbers, converting to, 43

quotation marks around, 34

151–152

replacing, 41

spaces, trimming from, 42

uppercase, 42

uppercase and lowercase

conversions, 42

text

argument, 40, 42

text fles

importing, 307–311

importing data from, 666–6

Text Filters command, 397

text functions

CHAR function, 42

CONCATENATE funtion, 41

FIND function, 41

formatting data with, 39–4

& function, 41

LEFT function, 40

LEN function, 41

LOWER function, 42

MID function, 40

text functions

698

text functions

continued

)

(

REPLACE function, 41

REPT function, 41

RIGHT function, 40

SEARCH function, 41

syntax, 40

TRIM function, 40

UPPER function, 42

VALUE function, 42

Text Import Wizard, 307–309

Treat Consecutive Delimiters As

One option, 310

text strings

characters, extracting from, 42–44

characters in, calculating, 41

converting to times, 107

characters, returning, 40

numbers, converting to, 42

repeating, 41

spaces, removing from, 40

Text That Contains option, 189

Text To Columns command, 168

Text To Columns Wizard, 45–47

text to fnd

argument, 41

3 Arrows (Colored) icon set option,

196

three-color scales, 193–194

three-dimensional formulas,

117–119

Threetimes.xlsx fle, 207

tie-ins, 631–634

Tiled view, 412–413

time and time functions, 105–109

computations with, 106–107

current time, displaying, 107

and dates in same cell, 106

effect of, 478

entering in cells, 105–106

extracting time units from, 108

formats for, 105–106

as function of cumulative

production, 436

length of time worked,

computing, 108

seconds,

displaying, 107

serial numbers for, 105

text strings, converting to, 107

time intervals, creating, 109

time of day, 107

total hours worked, computing,

108

time between arrivals, 525–526

time differences, calculating,

106–107

time format

displaying seconds, 107

h:mm, 108

TIME function, 107

time intervals, creating, 109

time series, 487–489

characteristics of, 491

forecasting future values with

ratio-to-moving-average

method, 498–500

forecasting future values with

Winters’s method, 491–495

graphing, 487

parameter defnitions, 491–492

seasonality of.

See

seasonal

indexes

trend of, 497

time unit

argument, 54

timetext

argument of TIMEVALUE

function, 107

TIMEVALUE function, 107

Time.xlsx fle, 105

To Value, defned, 137

TODAY function, 51, 107, 189

today’s date, displaying, 51

today’s time, displaying, 107

toggle switches, check box controls

for, 234–236

Tolerance setting, 271

Tool tabs, 2

Top/Bottom conditional formatting

rules, 187–188

Top/Bottom Rules option, 186, 187

Top5.xlsx fle, 207

Top half

worksheet, 360

top row, freezing in place, 91

Top 10 cus

worksheet, 359

Top 30 $s With Hallagan Or Jen

worksheet, 405

total assets, computing, 97

total hours worked, computing, 108

total liabilities, computing, 97

Total Row option, 221

Total Wages

worksheet, 648

totals

fltering, 223–224

hiding, 363

totals rows, 222–224

Toysrusformat.xlsx fle, 205

Toysrustrend.xlsx fle, 657, 663

Toysrus.xlsx fle, 161

Trace Dependents command,

121–123

Trace Precedents command, 121–

122, 124–125

transaction costs, impact on profts,

Transactiondata.xlsx fle, 175

transactions, median size of,

660–661

transportation problems, 261–265

changing cells, 261

constraints, 261

demand constraints, 263

demand points, 261

linear models, 261, 263

shipping costs, calculat

supply constraints, 262–

supply points, 261

target cells, 261

total product received,

calculating, 262–263

total product shipped, c

262

Transport.xlsx fle, 261

TRANSPOSE function, 649–

Transpose

worksheet, 649

transposing data from col

to row and row to colum

112–113

Traveldata.xlsx fle, 366

traveling salesperson pro

(TSPs), 303–305

total distance traveled, 3

Treat Consecutive Delimit

option, 310

TREND function, 461–462, 6

Trendline option, 424

trendlines and trend curv

calculation of, 427

centered moving averages

to, 499

decimal places to displa

errors and residuals, 42

exponential, linear, and p

424

exponential trendlines, 4

formatting options, 426

four-quarter moving aver

488–489

intercept of, 428

least-squares lines, 427

linear, estimating, 423–

power curves, 435–440

production vs. operating c

425–428

for revenue growth, 431

S curves, 488

trends, estimating with a

formulas, 657–660

trends of time series, 49

defned, 497

estimating with ratio-to

average method, 498–500

estimating with Winters’

493

updating, 494

trial-and-error searches, 2

TRIM function, 40, 42

TRIMMEAN function, 345

text functions (

continued

)

699

Trimmean.xlsx fle, 344

trimmed means, 344–345

trimming excess spaces, 42

Tsp.xlsx fle, 303

Tufte, Edward, 381

two-bin policy, 618

two-color scales, 194–195

two-factor ANOVA

with interaction, 484

with replication, 480–481

Two-Part Tariff

worksheet, 642

two-part tariffs, 640

determining, 642–646

two warehouses problem, 293–295

Two warehouses

worksheet, 293

two-way analysis of variance,

477–486

Two Way ANOVA No Interaction

worksheet, 481

Two Way ANOVA with Interaction

worksheet, 484

two-way ANOVA without

replication, 478

two-way data tables, 555–556.

See

also

data tables

bids, simulating in, 562

for proft-maximizing two-part

tariffs, 644

Twowayanova.xlsx fle, 478, 481

type

argument

in FV function, 71

in PMT function, 73

in PV function, 70

uncertain events, modeling,

549–558

uncertainty

in future investment returns,

estimating, 565

reorder point and, 616

underscore (_) in range names, 19

Unemployment.xlsx fle, 334

Unfreeze Panes command, 91, 234

Unhide Columns command, 133

Unhide command, 193

Unhide Rows command, 133

uniform random variables, 563

Unique Name Product Location

worksheet, 407

Unique Records Only option, 409

Unique.xlsx fle, 664

unit cost (UC), 625

nonlinear, 639–640

unit value, approximation of, 629

units sold

averaging, 390

summing, 654–655

unsorted values in lookup range, 34

updates, dynamic, 171–173

UPPER function, 42

USC.xlsx fle, 544

Use A Formula To Determine Which

Cells To Format option, 200–

202, 341

Use An External Data Source option,

351

Use Automatic Scaling option, 277

Use First Row As Column Headers

option, 668–669

user forms, accessing, 229

User Forms menu, 232

Valentine.xlsx fle, 554

validation points, 459

valuation analyses, modeling

growth, 431–434

#VALUE error messages, 99, 393,

652

Value Field Settings dialog box, 370

Number Format option, 355

Show Values As setting, 373

summary functions in, 366

VALUE function, 42, 43

value ranges, counting values in,

650–651

values.

See also

cell values; numbers;

numerical data; percentiles

changing with spin buttons, 231

color coding, 198–199

conditional tests on, 88.

See

also

IF statements

deseasonalizing, 498

expected values, 510

and formulas, toggling between,

121

moving, 111–112

probability mass function of, 517

values

argument, 60–61

Values zone, 353

Van Exel, Nick, 308

VAR function, 340

variable costs, 428

computing, 128

of production, 625

variables

correlations among, 441–446

dependent and independent, 423

dummy variables, 454–458

estimating exponential

relationships among, 431–434

estimating straight-line

relationships among, 423–430

estimating trend relations

among, 435–440

indicator variables, 502

influence on each other, 369

random variables.

See

rand

variables

relationship among multipl

independent variables and

dependent variable, 447–4

variance of random variable

510–511

Varianceanalysis.xlsx fle, 2

VAR.S function, 340

Verizondata.xlsx fle, 174

Verizonindirectdata.xlsx fl

Verizon.xlsx fle, 175

vertical lookups, 21

Visible Cells Copied

worksh

Visible Cells Only option, 3

VLOOKUP function, 21, 36, 1

fnding team ratings with, 5

#N/A errors and, 97–99

for simulated card draw, 57

syntax, 21–22

volatility, 590

estimating, 590, 593–594

implied volatility, 593

increases in, 593

option pricing and, 597

Volatility.xlsx fle, 598

Wade, Dwayne, 579

wages, computing with array

formulas, 648–649

Waggoner, Rick, 549

waiting in line.

See also

systems

calculating, 621–623

factors affecting time wai

619–620

Walmartdata.xlsx fle, 500

Walmartrev.xlsx fle, 99–100

Warehouseloc.xlsx fle, 291

Watch Window, use of, 121

web queries, built-in, 315–

Webqueries.xlsx fle, 313, 3

WEEKDAY function, 53, 202–20

weekend

argument, 52

weekend dates, formatting

conditionally, 202–203

Weekendformatting.xlsx fle, 2

205

Weibull random variable, 53

alpha parameter, 536

beta parameter, 536

density, 537

Weibull random variable

700

WEIBULL.DIST function, 535, 537

WEIBULLDIST function, 537

Weibullest.xlsx fle, 535

West.xlsx fle, 411

What If Analysis, 129, 556

What-If Analysis group Goal Seek

button, 138

Which Project

worksheet, 66

whole numbers, validating, 319–320

width

argument of OFFSET function,

164, 167

wildcard characters

asterisk (*), 34, 152

in criteria, 152–153

question mark (?), 153

win/loss sparklines, 384–385

Win Loss

worksheet, 384

Window group Arrange All option,

412

Windows Azure Datamarket, 666

Winston, Wayne, 316, 609

Winters’s method, 491–495

initializing, 492–493

smoothing parameters, 492

Within Groups MS, 475

Word documents

importing, 307

saving as text fles, 308–309

workbook scope names, 15–16

workbooks

navigating, 353

range names, displaying, 10

scenarios, merging in, 147

viewing in tiled format, 412

worksheets, inserting, 118

WORKDAY.INTL function, 6, 52

workdays

counting, 51–53

defning, 52

WORKDAY(start_date,#days,

[holidays]) function, 51–52

worker assignment problems,

297–300

workforce scheduling problems,

255–259

changing cells, 255

constraints, 256

target cells, 255

worksheet calculation modes,

Automatic, 131

worksheet FV, 72

worksheet Nper, 76

worksheet PMT, 73

worksheet PV, 70

worksheet scope names, 15–16

worksheet Sheet1, 81

worksheets

consolidating data in, 411–415

controls, adding to, 229

copying, 190

copying data into, 465

creating, 399

default number of, 118

duplicating formulas among, 118

inserting, 118

listing entries from other

worksheets, 179

looking up values in, 21–28

protecting from changes,

594–596

range name references

in, 633

range names, applying to, 17

selecting, 133

setup, similar, 117–118

structure of, 121

summarizing data across, 1

Worldball.xlsx fle, 285

worst-case scenarios, cal

143–147

Wright-Patterson Air Forc

439

XIRR function, 66–67

syntax, 66

XIRR

worksheet, 66

XNPV function, 60–61

XY charts

creating, 425

labels and titles for, 4

modifying, 426

YEAR function, 53

years, counting, 54

Years Column

worksheet, 3

Yeartodate.xlsx fle, 175

Zappe, Christopher, 316

zones in PivotTables, 352

WEiBULL.DiST function

703

About the Author

Wayne Winston, professor of operations and dec

and an Eli Lilly & Co. faculty fellow, develop

Excel with a comprehensive understanding of sp

years, Wayne has taught Excel modeling to thou

as Microsoft, Eli Lilly, Cisco, eBay, the U.S. A

He has won more than 25 teaching awards. Wayne a

NBA team. His book on math and sports,

Mathlet

University Press. Wayne is a two time

Jeopardy

How To

Download

Your eBoo

Please

note

This access code is non-transferable and is void if altered or r

sold or redeemed for cash, credit, or refund.

RVBJZXW

Your access code:

Microsoft® Excel® 2010: Data Analysis and

Business Modeling

To download your eBook, go to

http://go.microsoft.com/FWLink/?Linkid=224345

and follow the instructions.

Thank you for purchasing this Microsoft Press

title. Your companion PDF eBook is r

download from O’Reilly Media, offcial distributor o

Your PDF eBook allows you to:

•Search

the full text

•

Copy and paste

Best yet, you will be notifed about

free updates to your eBook.

If you ever lose your eBook fle, you

can download it again just by logging

in to your account.

Need help? Please contact:

mspbooksupport@oreilly.com

or call 800-889-8969.

Please note: You will be asked to create a

free online account and enter the access

code below.