## Description

I am looking for book call : Ross, Stephen, Westerfield, Randolph, Jaffe, Jeffrey, and Jordan, Bradford, Corporate

Ross, Stephen, Westerfield, Randolph, Jaffe, Jeffrey, and Jordan, Bradford, Corporate

Core Principles and Applications (5th edition), McGraw-Hill/Irwin,

ISBN: 9781259289903

(If you have the code I will pay more )

## Explanation & Answer

Hello I have tried and tried but all in vain ,I have attached 3rd edition. I know it might not help but just understand me .All the best and thank you for understanding me.for the sake of my account not to be banned I can honestly say I did not get the book.Thank you once again

C O R P O R AT E F I N A N C E

C O R E P R I N C I P L E S & A P P L I C AT I O N S

ros30689_fm_i-xxxiv.indd i

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The McGraw-Hill/Irwin Series in Finance, Insurance, and Real Estate

Stephen A. Ross

Franco Modigliani Professor of Finance

and Economics

Sloan School of Management

Massachusetts Institute of Technology

Consulting Editor

FINANCIAL MANAGEMENT

Adair

Excel Applications for Corporate Finance

First Edition

Block, Hirt, and Danielsen

Foundations of Financial Management

Fourteenth Edition

Brealey, Myers, and Allen

Principles of Corporate Finance

Tenth Edition

Brealey, Myers, and Allen

Principles of Corporate Finance, Concise

Second Edition

Brealey, Myers, and Marcus

Fundamentals of Corporate Finance

Sixth Edition

Brooks

FinGame Online 5.0

Bruner

Case Studies in Finance: Managing for

Corporate Value Creation

Sixth Edition

Chew

The New Corporate Finance: Where Theory

Meets Practice

Third Edition

Cornett, Adair, and Nofsinger

Finance: Applications and Theory

First Edition

DeMello

Cases in Finance

Second Edition

Grinblatt (editor)

Stephen A. Ross, Mentor: Influence through

Generations

Grinblatt and Titman

Financial Markets and Corporate Strategy

Second Edition

Higgins

Analysis for Financial Management

Ninth Edition

Kellison

Theory of Interest

Third Edition

ros30689_fm_i-xxxiv.indd ii

Kester, Ruback, and Tufano

Case Problems in Finance

Twelfth Edition

Rose and Marquis

Financial Institutions and Markets

Eleventh Edition

Ross, Westerfield, and Jaffe

Corporate Finance

Ninth Edition

Saunders and Cornett

Financial Institutions Management: A Risk

Management Approach

Seventh Edition

Ross, Westerfield, Jaffe, and Jordan

Corporate Finance: Core Principles and

Applications

Third Edition

Ross, Westerfield, and Jordan

Essentials of Corporate Finance

Seventh Edition

Ross, Westerfield, and Jordan

Fundamentals of Corporate Finance

Ninth Edition

Shefrin

Behavioral Corporate Finance: Decisions

that Create Value

First Edition

White

Financial Analysis with an Electronic

Calculator

Sixth Edition

INVESTMENTS

Bodie, Kane, and Marcus

Essentials of Investments

Eighth Edition

Bodie, Kane, and Marcus

Investments

Ninth Edition

Hirt and Block

Fundamentals of Investment Management

Ninth Edition

Hirschey and Nofsinger

Investments: Analysis and Behavior

Second Edition

Jordan and Miller

Fundamentals of Investments: Valuation

and Management

Fifth Edition

Stewart, Piros, and Heisler

Running Money: Professional Portfolio

Management

First Edition

Sundaram and Das

Derivatives: Principles and Practice

First Edition

FINANCIAL INSTITUTIONS AND MARKETS

Saunders and Cornett

Financial Markets and Institutions

Fourth Edition

INTERNATIONAL FINANCE

Eun and Resnick

International Financial Management

Fifth Edition

Kuemmerle

Case Studies in International

Entrepreneurship: Managing and Financing

Ventures in the Global Economy

First Edition

Robin

International Corporate Finance

First Edition

REAL ESTATE

Brueggeman and Fisher

Real Estate Finance and Investments

Fourteenth Edition

Ling and Archer

Real Estate Principles: A Value Approach

Third Edition

FINANCIAL PLANNING AND INSURANCE

Allen, Melone, Rosenbloom, and Mahoney

Retirement Plans: 401(k)s, IRAs, and Other

Deferred Compensation Approaches

Tenth Edition

Altfest

Personal Financial Planning

First Edition

Harrington and Niehaus

Risk Management and Insurance

Second Edition

Kapoor, Dlabay, and Hughes

Focus on Personal Finance: An Active

Approach to Help You Develop Successful

Financial Skills

Third Edition

Kapoor, Dlabay, and Hughes

Personal Finance

Ninth Edition

Rose and Hudgins

Bank Management and Financial Services

Eighth Edition

18/08/10 7:44 PM

THIRD EDITION

C O R P O R AT E F I N A N C E

C O R E P R I N C I P L E S & A P P L I C AT I O N S

Stephen A. Ross

Sloan School of Management

Massachusetts Institute of Technology

Randolph W. Westerfield

Marshall School of Business

University of Southern California

Jeffrey F. Jaffe

Wharton School of Business

University of Pennsylvania

Bradford D. Jordan

Gatton College of Business and Economics

University of Kentucky

ros30689_fm_i-xxxiv.indd iii

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CORPORATE FINANCE: CORE PRINCIPLES & APPLICATIONS

Published by McGraw-Hill/Irwin, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of

the Americas, New York, NY, 10020. Copyright © 2011, 2009, 2007 by The McGraw-Hill Companies, Inc.

All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means,

or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies,

Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for

distance learning.

Some ancillaries, including electronic and print components, may not be available to customers outside the

United States.

This book is printed on acid-free paper.

1 2 3 4 5 6 7 8 9 0 RJE/RJE 1 0 9 8 7 6 5 4 3 2 1 0

ISBN 978-0-07-353068-0

MHID 0-07-353068-9

Vice president and editor-in-chief: Brent Gordon

Publisher: Douglas Reiner

Executive editor: Michele Janicek

Director of development: Ann Torbert

Development editor II: Elizabeth Hughes

Vice president and director of marketing: Robin J. Zwettler

Senior marketing manager: Melissa S. Caughlin

Vice president of editing, design, and production: Sesha Bolisetty

Lead project manager: Christine A. Vaughan

Senior buyer: Carol A. Bielski

Senior designer: Mary Kazak Sander

Media project manager: Ron Nelms

Cover and interior design: Pam Verros

Cover image: Toyohiro Yamada, Tohoku Color Agency

Typeface: 10/12 Times New Roman

Compositor: MPS Limited, A Macmillan Company

Printer: R. R. Donnelley

Library of Congress Cataloging-in-Publication Data

Corporate finance : core principles & applications / Stephen A. Ross . . . [et al.]. — 3rd ed.

p. cm. — (The McGraw-Hill/Irwin series in finance, insurance, and real estate)

Includes index.

ISBN-13: 978-0-07-353068-0 (alk. paper)

ISBN-10: 0-07-353068-9 (alk. paper)

1. Corporations–Finance. I. Ross, Stephen A.

HG4026.C643 2011

658.15 —dc22

2010026731

www.mhhe.com

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To our family and friends with love

and gratitude.

—S.A.R.

ros30689_fm_i-xxxiv.indd v

R.W.W.

J.F.J.

B.D.J.

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ABOUT THE AUTHORS

Stephen A. Ross

SLOAN SCHOOL OF MANAGEMENT, MASSACHUSETTS INSTITUTE

OF TECHNOLOGY

Stephen A. Ross is the Franco Modigliani Professor of Financial Economics at

the Sloan School of Management, Massachusetts Institute of Technology. One

of the most widely published authors in finance and economics, Professor Ross

is recognized for his work in developing the Arbitrage Pricing Theory, as well as

for having made substantial contributions to the discipline through his research

in signaling, agency theory, option pricing, and the theory of the term structure

of interest rates, among other topics. A past president of the American Finance

Association, he currently serves as an associate editor of several academic and

practitioner journals. He is a trustee of CalTech.

Randolph W. Westerfield

MARSHALL SCHOOL OF BUSINESS, UNIVERSITY OF SOUTHERN CALIFORNIA

Randolph W. Westerfield is Dean Emeritus of the University of Southern

California’s Marshall School of Business and is the Charles B. Thornton Professor in Finance. Professor Westerfield came to USC from the Wharton School,

University of Pennsylvania, where he was the chairman of the finance department

and member of the finance faculty for 20 years. He is a member of several public company boards of directors including Health Management Associates, Inc.,

William Lyon Homes, and the Nicholas Applegate Growth Fund. His areas of

expertise include corporate financial policy, investment management, and stock

market price behavior.

ros30689_fm_i-xxxiv.indd vi

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Jeffrey F. Jaffe

WHARTON SCHOOL OF BUSINESS, UNIVERSITY OF PENNSYLVANIA

Jeffrey F. Jaffe has been a frequent contributor to finance and economic literature in such journals as the Quarterly Economic Journal, The Journal of Finance,

The Journal of Financial and Quantitative Analysis, The Journal of Financial

Economics, and The Financial Analysts Journal. His best known work concerns

insider trading, where he showed both that corporate insiders earn abnormal profits from their trades and that regulation has little effect on these profits. He has

also made contributions concerning initial public offerings, the regulation of utilities, the behavior of market makers, the fluctuation of gold prices, the theoretical

effect of inflation on the interest rate, the empirical effect of inflation on capital

asset prices, the relationship between small capitalization stocks and the January

effect, and the capital structure decision.

Bradford D. Jordan

GATTON COLLEGE OF BUSINESS AND ECONOMICS, UNIVERSITY OF KENTUCKY

Bradford D. Jordan is Professor of Finance and holder of the Richard W. and

Janis H. Furst Endowed Chair in Finance at the University of Kentucky. He has a

long-standing interest in both applied and theoretical issues in corporate finance

and has extensive experience teaching all levels of corporate finance and financial

management policy. Professor Jordan has published numerous articles in leading

journals on issues such as initial public offerings, capital structure, and the behavior of security prices. He is a past president of the Southern Finance Association,

and he is coauthor of Fundamentals of Investments: Valuation and Management,

5e, a leading investments text, also published by McGraw-Hill/Irwin.

ros30689_fm_i-xxxiv.indd vii

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FROM THE AUTHORS

IN THE BEGINNING…

It was probably inevitable that the four of us would collaborate on this project. Over the last 20 or so years, we have been

working as two separate “RWJ” teams. In that time, we managed (much to our own amazement) to coauthor two widely

adopted undergraduate texts and an equally successful graduate text, all in the corporate finance area. These three books

have collectively totaled more than 25 editions (and counting),

plus a variety of country-specific editions and international

editions, and they have been translated into at least a dozen

foreign languages.

Even so, we knew that there was a hole in our lineup at the

graduate (MBA) level. We’ve continued to see a need for a

concise, up-to-date, and to-the-point product, the majority of

which can be realistically covered in a typical single term or

course. As we began to develop this book, we realized (with

wry chuckles all around) that, between the four of us, we have

been teaching and researching finance principles for well

over a century. From our own very extensive experience with

this material, we recognized that corporate finance introductory classes often have students with extremely diverse educational and professional backgrounds. We also recognized

that this course is increasingly being delivered in alternative

formats ranging from traditional semester-long classes to

highly compressed modules, to purely online courses, taught

both synchronously and asynchronously.

OUR APPROACH

To achieve our objective of reaching out to the many different types of students and the varying course environments,

we worked to distill the subject of corporate finance down to

its core, while maintaining a decidedly modern approach. We

have always maintained that corporate finance can be viewed

as the working of a few very powerful intuitions. We also know

that understanding the “why” is just as important, if not more

so, than understanding the “how.” Throughout the development of this book, we continued to take a hard look at what

is truly relevant and useful. In doing so, we have worked to

downplay purely theoretical issues and minimize the use of extensive and elaborate calculations to illustrate points that are

either intuitively obvious or of limited practical use.

Perhaps more than anything, this book gave us the chance

to pool all that we have learned about what really works in

a corporate finance text. We have received an enormous

amount of feedback over the years. Based on that feedback,

the two key ingredients that we worked to blend together here

ros30689_fm_i-xxxiv.indd viii

are the careful attention to pedagogy and readability that we

have developed in our undergraduate books and the strong

emphasis on current thinking and research that we have

always stressed in our graduate book.

From the start, we knew we didn’t want this text to be encyclopedic. Our goal instead was to focus on what students

really need to carry away from a principles course. After much

debate and consultation with colleagues who regularly teach

this material, we settled on a total of 20 chapters. Chapter

length is typically 30 pages, so most of the book (and, thus,

most of the key concepts and applications) can be realistically

covered in a single term or module. Writing a book that strictly

focuses on core concepts and applications necessarily involves some picking and choosing, with regard to both topics

and depth of coverage. Throughout, we strike a balance by

introducing and covering the essentials, while leaving more

specialized topics to follow-up courses.

As in our other books, we treat net present value (NPV) as

the underlying and unifying concept in corporate finance. Many

texts stop well short of consistently integrating this basic principle. The simple, intuitive, and very powerful notion that NPV

represents the excess of market value over cost often is lost in

an overly mechanical approach that emphasizes computation

at the expense of comprehension. In contrast, every subject we

cover is firmly rooted in valuation, and care is taken throughout

to explain how particular decisions have valuation effects.

Also, students shouldn’t lose sight of the fact that financial

management is about management. We emphasize the role

of the financial manager as decision maker, and we stress

the need for managerial input and judgment. We consciously

avoid “black box” approaches to decisions, and where appropriate, the approximate, pragmatic nature of financial analysis

is made explicit, possible pitfalls are described, and limitations

are discussed.

NEW TO THE 3RD EDITION

With our first two editions of Corporate Finance: Core

Principles & Applications, we had the same hopes and fears

as any entrepreneurs. How would we be received in the market? Based on the very gratifying feedback we received, we

learned that many of you agreed with us concerning the need

for a focused, concise treatment of the major principles of corporate finance.

In developing the third edition, one of the things we focused on was extensive updating. We wanted to be as current

as possible throughout the book. As a result, we revamped,

18/08/10 7:44 PM

rewrote, or replaced essentially all of the chapter opening vignettes, in-chapter real-world examples, and The Real World

readings. We updated facts and figures throughout the book,

and we revised and expanded the already extensive end-ofchapter material.

A list of the most important revisions to the third edition

is below:

Overall:

Completely rewritten Chapter on Financial

Statements and Financial Models

Revised and updated data and figures

More Excel examples

All new chapter openers

All new problems at ends of chapters

Many new boxes

New chapter on Raising Capital

Completely rewritten International Corporate

Finance chapter

Updated real examples

Mergers and Acquisitions moved to online

Chapter 1:

New materials on corporate governance and

regulation, including Sarbanes-Oxley

Chapter 3:

Improved discussion of financial ratios

e.g. EBITDA and EV

More examples

Chapter 4:

New spreadsheet applications

Chapter 9:

New material on the full payout model

Chapter 10:

New material on global equity risk premiums

Update to 2009

New material on the global market collapse

Chapter 12:

New material on how to estimate the WACC

Updated examples

Chapter 13:

More material on bubbles

Changed Chapter title to underscore behavioral

challenges

Chapter 15:

Updated data on capital structure

ros30689_fm_i-xxxiv.indd ix

Our attention to updating and improving also extended to

the extensive collection of support and enrichment materials

that accompany the text. Working with many dedicated and

talented colleagues and professionals, we continue to provide

supplements that are unrivaled at the graduate level (a complete description appears in the following pages). Whether

you use just the textbook, or the book in conjunction with other

products, we believe you will be able to find a combination

that meets your current as well as your changing needs.

—Stephen A. Ross

—Randolph W. Westerfield

—Jeffrey F. Jaffe

—Bradford D. Jordan

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PEDAGOGY

Chapter Opening Case

Corporate Finance: Core

Principles & Applications

is rich in valuable learning

tools and support to help

students succeed in learning

the fundamentals of financial

management.

Each chapter begins with a recent real-world event to

introduce students to chapter concepts.

CHAPTER

4

Discounted Cash Flow

Valuation

OPENING CASE

PART TWO Valuation and Capital Budgeting

W

hat do Chris Iannetta, John Lackey, and Matt Holliday have in common? All

three are star athletes who signed big-money contracts during late 2009 or

early 2010. Their contract values were reported as $8.35 million, $82.5 million, and $120 million, respectively. But reported numbers can be misleading.

For example, catcher Chris Ianetta re-signed with the Colorado Rockies. His

deal called for salaries of $1.75 million, $2.55 million, and $3.55 million over the next three years,

respectively, with a contract buyout of $500,000 or a salary of $5,000,000 in four years. Not bad,

especially for someone who makes a living using the “tools of ignorance” (jock jargon for a catcher’s

equipment).

A closer look at the numbers shows that Chris, John, and Matt did pretty well, but nothing like the

quoted figures. Using Matt’s contract as an example, the value was reported to be $120 million, but it

was actually payable over several years. The terms called for a salary of $17 million per year for seven

years, then a club option for $17 million in 2017 or a club buyout of $1 million. However, of the $17 million annual salary, $2 million each year was to be deferred and paid annually from 2020 to 2029. Since

the payments are spread out over time, we must consider the time value of money, which means his

contract was worth less than reported. How much did he really get? This chapter gives you the “tools

of knowledge” to answer this question.

Explanatory Web Links

p

EXAMPLE

4.12

These Web links are provided in the

margins of the text. They are specifically

selected to accompany text material and

provide students and instructors with

a quick way to check for additional

information using the Internet.

If the stated annual rate of interest, 8 percent, is compounded quarterly, what is the effective annual

rate?

Using (4.7), we have

m

4

.08 ⫺ 1 ⫽ .0824 ⫽ 8.24%

⫺ 1 ⫽ 1 ⫹ ___

4

(

)

Referring back to our earlier example where C0 ⫽ $1,000 and r ⫽ 10%, we can generate the following table:

C0

COMPOUNDING

FR E Q U E N C Y ( m )

C1

$1,000

1,000

1,000

1,000

Yearly (m ⫽ 1)

Semiannually (m ⫽ 2)

Quarterly (m ⫽ 4)

Daily (m ⫽ 365)

$1,100.00

1,102.50

1,103.81

1,105.16

ros30689_fm_i-xxxiv.indd x

y

Online bond calculators

are available at

personal.ﬁdelity.com;

interest rate information

is available at money.

cnn.com/markets/

bondcenter and www.

bankrate.com.

This is just the amount of the discount.

What would the Xanth bond sell for if interest rates had dropped by 2 percent instead of

rising by 2 percent? As you might guess, the bond would sell for more than $1,000. Such a

bond is said to sell at a premium and is called a premium bond.

This case is just the opposite of that of a discount bond. The Xanth bond now has a

coupon rate of 8 percent when the market rate is only 6 percent. Investors are willing to

pay a premium to get this extra coupon amount. In this case, the relevant discount rate

is 6 percent, and there are nine years remaining. The present value of the $1,000 face

amount is:

Examples

Compounding Frequencies

( 1 ⫹ __mr )

,

Annuity present value $20 (1 1兾1.109)兾.10

$20 5.7590

$115.18

E FFE C T I V E A N N U A L

R AT E

r m

1 _

m 1

(

)

.10

.1025

.10381

.10516

Separate numbered and titled examples are extensively

integrated into the chapters. These examples provide

detailed applications and illustrations of the text

material in a step-by-step format. Each example is

completely self-contained, so students don’t have to

search for additional information.

8/19/10 12:59 PM

Figure 4.11 illustrates the relationship among annual, semiannual, and continuous compounding. Semiannual compounding gives rise to both a smoother curve and a higher ending value than does annual compounding. Continuous compounding has both the smoothest

curve and the highest ending value of all.

Figures and Tables

FIGURE 4.11

THE REAL WORLD

4

Interest

earned

3

2

4

Interest

earned

3

Dollars

4

Dollars

This text makes extensive use of real data

presented in various figures and tables.

Explanations in the narrative, examples,

and end-of-chapter problems refer to

many of these exhibits.

Dollars

Annual, Semiannual, and

Continuous Compounding

2

0

1

2

3

Years

4

5

0

Annual compounding

Interest

earned

2

1

1

1

3

1

2

3

Years

4

5

Semiannual compounding

0

1

2

3

Years

4

5

Continuous compounding

JACKPOT!

If you or someone you know is a regular lottery player, you probably already understand that you are 20 times more

likely to get struck by lightning than you are to win a big lottery jackpot. What are your odds of winning? Below you

will find a table with your chances of winning the Mega Millions Lottery compared to other events.

Odds of winning a Mega Millions jackpot

Odds of being killed by a venomous spider

Odds of being killed by a dog bite

Odds of being killed by lightning

Odds of being killed by drowning

Odds of being killed falling from a bed or other furniture

Odds of being killed in a car crash

The Real World

1:135,145,920*

1:57,018,763

1:11,403,753

1:6,479,405

1:690,300

1:388,411

1:6,029

By exploring information found in recent

publications and building upon concepts

learned in each chapter, these boxes work

through real-world issues relevant to the

surrounding text.

*Source: Virginia Lottery Web site. All other odds from the National Safety Council.

Sweepstakes may have different odds than lotteries, but these odds may not be much better. Probably the

largest advertised potential grand prize ever was Pepsi’s “Play for a Billion,” which, you guessed it, had a $1 billion

(billion!) prize. Not bad for a day’s work, but you still have to read the fine print. It turns out that the winner would

be paid $5 million per year for the next 20 years, $10 million per year for years 21 through 39, and a lump sum

$710 million in 40 years. From what you have learned, you know the value of the sweepstakes wasn’t even close to

$1 billion. In fact, at an interest rate of 10 percent, the present value is about $70.7 million.

In January 2010, a 59-year-old man and his 57-year-old wife in New York won the $162 million Mega Millions

jackpot. They were given the option of receiving the jackpot as $6.231 million immediately and $6.231 million per

year for the next 25 years, or $102 million immediately. So, what discount rate does this imply? After some computational effort, we find the interest rate is about 4.15 percent. Unfortunately for the winners, nearly $1 million was

placed in an escrow account over a dispute about the mismanagement of funds at a homeless shelter the couple

had previously operated.

Some lotteries make your decision a little tougher. The Ontario Lottery will pay you either $2,000 a week for the

rest of your life or $1.3 million now. (That’s in Canadian dollars or “loonies,” by the way.) Of course, there is the

chance you might die in the near future, so the lottery guarantees that your heirs will collect the $2,000 weekly

payments until the twentieth anniversary of the first payment, or until you would have turned 91, whichever comes

first. This payout scheme complicates your decision quite a bit. If you live for only the 20-year minimum, the breakeven interest rate between the two options is about 5.13 percent per year, compounded weekly. If you expect to

live longer than the 20-year minimum, you might be better off accepting $2,000 per week for life. Of course, if you

manage to invest the $1.3 million lump sum at a rate of return of about 8 percent per year (compounded weekly),

you can have your cake and eat it too because the investment will return $2,000 at the end of each week forever!

Taxes complicate the decision in this case because the lottery payments are all on an aftertax basis. Thus, the rates

of return in this example would have to be aftertax as well.

How to Calculate Present Values with

Multiple Future Cash Flows Using a

Spreadsheet

SPREADSHEET TECHNIQUES

We can set up a basic spreadsheet to calculate the present values of the individual cash flows as follows.

Notice that we have simply calculated the present values one at a time and added them up:

Spreadsheet Techniques

A

B

C

D

E

1

Using a spreadsheet to value multiple future cash flows

2

This feature helps students to improve their Excel

spreadsheet skills, particularly as they relate to

corporate finance. This feature appears in selfcontained sections and shows students how to set up

spreadsheets to analyze common financial problems—a

vital part of every business student’s education. For

even more help using Excel, students have access to

Excel Master, an in-depth online tutorial.

3

4

5

6

7

8

9

What is the present value of $200 in one year, $400 the next year, $600 the next year, and

$800 the last year if the discount rate is 12 percent?

10

11

12

13

14

15

16

17

18

19

20

21

22

Rate:

0.12

Year

Cash flows

1

2

3

4

$200

$400

$600

$800

Total PV:

Present values

$178.57

$318.88

$427.07

$508.41

$1,432.93

Formula used

=PV($B$7,A10,0,⫺B10)

=PV($B$7,A11,0,⫺B11)

=PV($B$7,A12,0,⫺B12)

=PV($B$7,A13,0,⫺B13)

=SUM(C10:C13)

Notice the negative signs inserted in the PV formulas. These just make the present values have

positive signs. Also, the discount rate in cell B7 is entered as $B$7 (an "absolute" reference)

because it is used over and over. We could have just entered ".12" instead, but our approach is more

flexible.

This real rate is the same as we had before. If we take another look at the Fisher effect, we

can rearrange things a little as follows:

1 R (1 r) (1 h)

Rrhrh

[5.3]

What this tells us is that the nominal rate has three components. First, there is the real rate

on the investment, r. Next, there is the compensation for the decrease in the value of the

money originally invested because of inﬂation, h. The third component represents compensation for the fact that the dollars earned on the investment are also worth less because of

the inﬂation.

This third component is usually small, so it is often dropped. The nominal rate is then

approximately equal to the real rate plus the inﬂation rate:

R 艐 rh

ros30689_fm_i-xxxiv.indd xi

Numbered Equations

Key equations are numbered within the

text and listed on the back end sheets for

easy reference.

[5.4]

8/19/10 12:59 PM

END-OF-CHAPTER

MATERIAL

The end-of-chapter material

reflects and builds on the

concepts learned from the

chapter and study features.

Summary and Conclusions

Each chapter ends with a numbered and concise, but

thorough, summary of the important ideas presented

in the chapter—helping students review the key points

and providing closure.

SUMMARY AND CONCLUSIONS

This chapter has explored bonds, bond yields, and interest rates. We saw that:

1. Determining bond prices and yields is an application of basic discounted cash ﬂow principles.

2. Bond values move in the direction opposite that of interest rates, leading to potential gains or

losses for bond investors.

3. Bonds have a variety of features spelled out in a document called the indenture.

4. Bonds are rated based on their default risk. Some bonds, such as Treasury bonds, have no risk

of default, whereas so-called junk bonds have substantial default risk.

5. A wide variety of bonds exist, many of which contain exotic or unusual features.

6. Almost all bond trading is OTC, with little or no market transparency in many cases. As a result,

bond price and volume information can be difﬁcult to ﬁnd for some types of bonds.

7. Bond yields and interest rates reﬂect the effect of six different things: the real interest rate and

ﬁve premiums that investors demand as compensation for inﬂation, interest rate risk, default

risk, taxability, and lack of liquidity.

CONCEPT QUESTIONS

Concept Questions

1. Treasury Bonds Is it true that a U.S. Treasury security is risk-free?

2. Interest Rate Risk Which has greater interest rate risk, a 30-year Treasury bond or a 30-year

BB corporate bond?

3. Treasury Pricing With regard to bid and ask prices on a Treasury bond, is it possible for the bid

price to be higher? Why or why not?

4. Yield to Maturity Treasury bid and ask quotes are sometimes given in terms of yields, so there

would be a bid yield and an ask yield. Which do you think would be larger? Explain.

5. Call Provisions A company is contemplating a long-term bond issue. It is debating whether

or not to include a call provision. What are the beneﬁts to the company from including a call

provision? What are the costs? How do these answers change for a put provision?

6. Coupon Rate How does a bond issuer decide on the appropriate coupon rate to set on its

bonds? Explain the difference between the coupon rate and the required return on a bond.

This end-of-chapter section facilitates your

students’ knowledge of key principles, as well

as their intuitive understanding of the chapter

concepts. The questions reinforce students’

critical-thinking skills and provide a review of

chapter material.

7. Real and Nominal Returns Are there any circumstances under which an investor might be

more concerned about the nominal return on an investment than the real return?

8. Bond Ratings Companies pay rating agencies such as Moody’s and S&P to rate their bonds,

and the costs can be substantial. However, companies are not required to have their bonds

rated in the ﬁrst place; doing so is strictly voluntary. Why do you think they do it?

9. Bond Ratings

U.S. Treasury bonds are not rated. Why? Often, junk bonds are not rated. Why?

Questions and Problems

Because solving problems is so critical to

students’ learning, we provide extensive end-ofchapter questions and problems. The questions

and problems are segregated into three learning

levels: Basic, Intermediate, and Challenge. All

problems are fully annotated so that students

and instructors can readily identify particular

types. Also, most of the problems are available

in McGraw-Hill’s Connect—see the next

section of this preface for more details.

ros30689_fm_i-xxxiv.indd xii

QUESTIONS AND PROBLEMS

1. Stock Values The Starr Co. just paid a dividend of $2.15 per share on its stock. The dividends

are expected to grow at a constant rate of 4 percent per year, indeﬁnitely. If investors require a

12 percent return on the stock, what is the current price? What will the price be in three years?

In 15 years?

Basic

(Questions 1–9)

2. Stock Values The next dividend payment by ZYX, Inc., will be $2.85 per share. The dividends

are anticipated to maintain a 4.5 percent growth rate, forever. If ZYX stock currently sells for

$84 per share, what is the required return?

3. Stock Values For the company in the previous problem, what is the dividend yield? What is the

expected capital gains yield?

4. Stock Values Mickelson Corporation will pay a $2.90 per share dividend next year. The

company pledges to increase its dividend by 4.75 percent per year, indeﬁnitely. If you require

an 11 percent return on your investment, how much will you pay for the company’s stock

today?

5. Stock Valuation Shelter, Inc., is expected to maintain a constant 5.2 percent growth rate in its

dividends, indeﬁnitely. If the company has a dividend yield of 4.4 percent, what is the required

return on the company’s stock?

6. Stock Valuation Suppose you know that a company’s stock currently sells for $73 per share

and the required return on the stock is 12 percent. You also know that the total return on the

stock is evenly divided between a capital gains yield and a dividend yield. If it’s the company’s

policy to always maintain a constant growth rate in its dividends, what is the current dividend

per share?

8/19/10 12:59 PM

What’s On the Web?

W H AT ’ S O N T H E W E B ?

1. Bond Quotes You can ﬁnd current bond prices at cxa.marketwatch.com/ﬁnra/BondCenter.

You want to ﬁnd the bond prices and yields for bonds issued by Georgia Paciﬁc. You can enter

the ticker symbol “GP” to do a search. What is the shortest maturity bond issued by Georgia

Paciﬁc that is outstanding? What is the longest maturity bond? What is the credit rating for

Georgia Paciﬁc’s bonds? Do all of the bonds have the same credit rating? Why do you think

this is?

Excel Problems

13. Nonconstant Dividends South Side Corporation is expected to pay the following dividends

over the next four years: $10, $8, $5, and $3. Afterward, the company pledges to maintain a constant 5 percent growth rate in dividends forever. If the required return on the stock is 13 percent,

what is the current share price?

Indicated by the Excel icon in the margin,

these problems are integrated in the

Questions and Problems section of almost

all chapters. Located on the book’s Web site,

Excel templates have been created for each

of these problems. Students can use the data

in the problem to work out the solution using

Excel skills.

14. Differential Growth Hughes Co. is growing quickly. Dividends are expected to grow at a

30 percent rate for the next three years, with the growth rate falling off to a constant 7 percent

thereafter. If the required return is 10 percent and the company just paid a $2.40 dividend, what

is the current share price?

15. Differential Growth Janicek Corp. is experiencing rapid growth. Dividends are expected to

grow at 27 percent per year during the next three years, 17 percent over the following year,

and then 7 percent per year indeﬁnitely. The required return on this stock is 12 percent, and the

stock currently sells for $65 per share. What is the projected dividend for the coming year?

16. Negative Growth Antiques R Us is a mature manufacturing ﬁrm. The company just paid a

$12 dividend, but management expects to reduce the payout by 4 percent per year, indeﬁnitely. If

you require a 9 percent return on this stock, what will you pay for a share today?

ros30689_fm_i-xxxiv.indd xiii

CLOSING CASE

S T O C K V A L U AT I O N AT R A G A N E N G I N E S

Larissa has been talking with the company’s directors about the future of East Coast Yachts. To this

point, the company has used outside suppliers for various key components of the company’s yachts,

including engines. Larissa has decided that East Coast Yachts should consider the purchase of an

engine manufacturer to allow East Coast Yachts to better integrate its supply chain and get more

control over engine features. After investigating several possible companies, Larissa feels that the

purchase of Ragan Engines, Inc., is a possibility. She has asked Dan Ervin to analyze Ragan’s value.

Ragan Engines, Inc., was founded nine years ago by a brother and sister—Carrington and

Genevieve Ragan—and has remained a privately owned company. The company manufactures

marine engines for a variety of applications. Ragan has experienced rapid growth because of a

proprietary technology that increases the fuel efﬁciency of its engines with very little sacriﬁce in

performance. The company is equally owned by Carrington and Genevieve. The original agreement

between the siblings gave each 125,000 shares of stock.

These end-of-chapter activities show

students how to use and learn from the vast

amount of financial resources available on

the Internet.

End-of-Chapter Cases

Located at the end of each chapter,

these mini-cases focus on common

company situations that embody

important corporate finance topics.

Each case presents a new scenario,

data, and a dilemma. Several questions

at the end of each case require students

to analyze and focus on all of the

material they learned in that chapter.

8/19/10 12:59 PM

COMPREHENSIVE TEACHING

DIGITAL SOLUTIONS

Online Learning Center (OLC): Online Support at www.mhhe.com/rwj

The Online Learning Center (OLC) contains FREE access to Web-based study and

teaching aids created for this text, all in one place!

INSTRUCTOR SUPPORT

ros30689_fm_i-xxxiv.indd xiv

■

Instructor’s Manual

prepared by David Diehl, Aurora University, and Joseph Smolira, Belmont

University

A great place to find new lecture ideas. The IM has three main sections. The first

section contains a chapter outline and other lecture materials. The annotated outline

for each chapter includes lecture tips, real-world tips, ethics notes, suggested

PowerPoint slides, and, when appropriate, a video synopsis. Detailed solutions for

all end-of-chapter problems appear in section three.

■

Test Bank

prepared by Bruce Costa, University of Montana

Great format for a better testing process. The Test Bank has 75–100 questions per

chapter that closely link with the text material and provide a variety of question

formats (multiple-choice questions problems and essay questions) and levels of difficulty (basic, intermediate, and challenge) to meet every instructor’s testing needs.

Problems are detailed enough to make them intuitive for students and solutions are

provided for the instructor.

■

Computerized Test Bank

Create your own tests in a snap! These additional questions are found in a computerized test bank utilizing McGraw-Hill’s EZ Test testing software to quickly create

customized exams. This user-friendly program allows instructors to sort questions

by format; edit existing questions or add new ones; and scramble questions for

multiple versions of the same test.

■

PowerPoint Presentation System

prepared by David Diehl, Aurora University

Customize our content for your course. This presentation has been thoroughly

revised to include more lecture-oriented slides, as well as exhibits and examples

both from the book and from outside sources. Applicable slides have Web links

that take you directly to specific Internet sites, or a spreadsheet link to show an

example in Excel. You can also go to the Notes Page function for more tips in

presenting the slides. This customizable format gives you the ability to edit, print,

or rearrange the complete presentation to meet your specific needs.

18/08/10 7:44 PM

AND LEARNING PACKAGE

Videos

Also available in DVD format. Current set of videos on hot topics! McGraw-Hill/Irwin

has produced a series of finance videos that are 10-minute case studies on topics such as

Financial Markets, Careers, Rightsizing, Capital Budgeting, EVA (Economic Value Added),

Mergers and Acquisitions, and Foreign Exchange. Discussion questions for these videos, as

well as video clips, are available in the Instructor’s Center at www.mhhe.com/rwj.

STUDENT SUPPORT

■

Narrated PowerPoint Examples

These in-depth slides are designed exclusively for students as part of the premium

content package of this book. Each chapter’s slides follow the chapter topics and provide steps and explanations showing how to solve key problems. Because each student

learns differently, a quick click on each slide will “talk through” its contents with you!

■

Interactive FinSims

Created by Eric Sandburg, Interactive Media, each module highlights a key concept

of the book and simulates how to solve its problems, asking the student to input

certain variables. This hands-on approach guides students through difficult and

important corporate finance topics.

■

Excel Master

Created by Brad Jordan and Joe Smolira, this extensive Excel tutorial is fully

integrated with the text. Learn Excel and corporate finance at the same time. For

more details about this exciting new feature see the inside cover of this book!

McGraw-Hill Investments Trader

Students receive free access to this Web-based portfolio simulation with a hypothetical

$100,000 brokerage account to buy and sell stocks and mutual funds. Students can use

the real data found at this site in conjunction with the chapters on investments. They

can also compete against other students around the United States. Please click on the

corresponding link found in the OLC for more details. This site is powered by Stock-Trak,

the leading provider of investment simulation services to the academic community.

■

And More!

Be sure to check out the other helpful features found on the OLC, including selfgrading quizzes and end-of-chapter problem Excel templates.

PACKAGE OPTIONS AVAILABLE

FOR PURCHASE & PACKAGING

You may also package either version of the text with a variety of additional learning tools

that are available for your students.

ros30689_fm_i-xxxiv.indd xv

18/08/10 7:44 PM

Solutions Manual

(ISBN 10: 0077316363/ISBN 13: 9780077316365)

Prepared by Joseph Smolira, Belmont University, this manual contains detailed, workedout solutions for all of the problems in the end-of-chapter material. It has also been

reviewed for accuracy by multiple sources. The Solutions Manual is also available for

purchase for your students.

FinGame Online 5.0

by LeRoy Brooks, John Carroll University

(ISBN 10: 0077219880/ISBN 13: 9780077219888)

Just $15.00 when packaged with this text. In this comprehensive simulation game,

students control a hypothetical company over numerous periods of operation. The game is

now tied to the text by exercises found on the Online Learning Center. As students make

major financial and operating decisions for their company, they will develop and enhance

their skills in financial management and financial accounting statement analysis.

Financial Analysis with an Electronic Calculator, Sixth Edition

by Mark A. White, University of Virginia, McIntire School of Commerce

(ISBN 10: 0073217093/ISBN 13: 9780073217093)

The information and procedures in this supplementary text enable students to master the

use of financial calculators and develop a working knowledge of financial mathematics

and problem solving. Complete instructions are included for solving all major problem

types on three popular models: HP 10B and 12C, TI BA II Plus, and TI-84. Hands-on

problems with detailed solutions allow students to practice the skills outlined in the text

and obtain instant reinforcement. Financial Analysis with an Electronic Calculator is a

self-contained supplement to the introductory financial management course.

McGRAW-HILL CONNECT FINANCE

Less Managing. More Teaching. Greater Learning.

McGraw-Hill’s Connect Finance is an online assignment and assessment solution that

connects students with the tools and resources they’ll need to achieve success.

Connect helps prepare students for their future by enabling faster learning, more

efficient studying, and higher retention of knowledge.

McGraw-Hill Connect Finance Features Connect Finance offers a number of

powerful tools and features to make managing assignments easier, so faculty can spend

more time teaching. With Connect Finance, students can engage with their coursework

anytime and anywhere, making the learning process more accessible and efficient.

Connect Finance offers you the features described below.

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Simple assignment management With Connect Finance, creating assignments is

easier than ever, so you can spend more time teaching and less time managing. The

assignment management function enables you to:

■

■

■

Create and deliver assignments easily with selectable end-of-chapter questions and

test bank items.

Streamline lesson planning, student progress reporting, and assignment grading to

make classroom management more efficient than ever.

Go paperless with online submission and grading of student assignments.

Smart grading When it comes to studying, time is precious. Connect Finance helps

students learn more efficiently by providing feedback and practice material when they

need it, where they need it. When it comes to teaching, your time is also precious. The

grading function enables you to:

■

■

■

Have assignments scored automatically, giving students immediate feedback on

their work and side-by-side comparisons with correct answers.

Access and review each response; manually change grades or leave comments for

students to review.

Reinforce classroom concepts with practice tests and instant quizzes.

Instructor library The Connect Finance Instructor Library is your repository for

additional resources to improve student engagement in and out of class. You can select

and use any asset that enhances your lecture.

Student study center The Connect Finance Student Study Center is the place for

students to access additional resources. The Student Study Center:

■

■

Offers students quick access to lectures, practice materials, and more.

Provides instant practice material and study questions, easily accessible on the go.

Student progress tracking Connect Finance keeps instructors informed about how

each student, section, and class is performing, allowing for more productive use of lecture

and office hours. The progress-tracking function enables you to:

■

■

View scored work immediately and track individual or group performance with

assignment and grade reports.

Access an instant view of student or class performance relative to learning

objectives.

Lecture capture through Tegrity Campus For an additional charge Lecture Capture

offers new ways for students to focus on the in-class discussion, knowing they can revisit

important topics later. This can be delivered through Connect or separately. See below for

more details.

ros30689_fm_i-xxxiv.indd xvii

18/08/10 7:44 PM

In short, Connect Finance offers you and your students powerful tools and features that

optimize your time and energies, enabling you to focus on course content, teaching, and

student learning. Connect Finance also offers a wealth of content resources for both

instructors and students. This state-of-the-art, thoroughly tested system supports you in

preparing students for the world that awaits.

For more information about Connect, go to www.mcgrawhillconnect.com, or contact

your local McGraw-Hill sales representative.

TEGRITY CAMPUS: LECTURES 24/7

Tegrity Campus is a service that makes class time available 24/7

by automatically capturing every lecture in a searchable format

for students to review when they study and complete assignments. With a simple one-click

start-and-stop process, you capture all computer screens and corresponding audio. Students

can replay any part of any class with easy-to-use browser-based viewing on a PC or Mac.

Educators know that the more students can see, hear, and experience class resources,

the better they learn. In fact, studies prove it. With Tegrity Campus, students quickly

recall key moments by using Tegrity Campus’s unique search feature. This search helps

students efficiently find what they need, when they need it, across an entire semester

of class recordings. Help turn all your students’ study time into learning moments

immediately supported by your lecture.

To learn more about Tegrity watch a 2-minute Flash demo at http://tegritycampus.

mhhe.com.

McGRAW-HILL CUSTOMER CARE CONTACT INFORMATION

At McGraw-Hill, we understand that getting the most from new technology can be

challenging. That’s why our services don’t stop after you purchase our products. You can

e-mail our Product Specialists 24 hours a day to get product-training online. Or you can

search our knowledge bank of Frequently Asked Questions on our support Web site. For

Customer Support, call 800-331-5094, e-mail hmsupport@mcgraw-hill.com, or visit

www.mhhe.com/support. One of our Technical Support Analysts will be able to assist

you in a timely fashion.

ros30689_fm_i-xxxiv.indd xviii

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ACKNOWLEDGMENTS

To borrow a phrase, writing a finance textbook

is easy—all you do is sit down at a word processor and open a vein. We never would have completed this book without the incredible amount

of help and support we received from our colleagues, students, editors, family members, and

friends. We would like to thank, without implicating, all of you.

Clearly, our greatest debt is to our many colleagues (and their students). Needless to say,

without this support and feedback we would not

be publishing this text.

To the following reviewers we are grateful for

their many contributions:

Dean Baim, Pepperdine University

Madhulina Bandyopadhyay, University of

Wisconsin, Milwaukee

Peter Basciano, Augusta State University

Elizabeth Booth, Michigan State University

Christa Bouwman, Case Western Reserve

University

Bruce Costa, University of Montana

Isabelle Delalex, Pace University

David Diehl, Aurora University

Robert Duvic, University of Texas at Austin

Yee-Tien Fu, Stanford University

Janet Hamilton, Portland State University

Corrine Hasbany, Rivier College

Rodrigo Hernandez, Radford University

Vanessa Holmes, Penn State Worthington,

Scranton

Gary Kayakachoian, University of Rhode Island

Gregory Kivenzor, Oregon State University

V. Sivarama Krishnan, University of Central

Oklahoma

Sanjay Kudrimoti, Salem State College

Douglas Lamdin, University of Maryland

Baltimore County

Michael Madaris, William Carey University

Robert Nash, Wake Forest University

Ali Ozbeki, Oakland University

Deniz Ozenbas, Montclair State University

Chein-Chih Peng, Morehead State University

Jong Rhim, University of Southern Indiana

Atul Saxena, Georgia Gwinnett College

James Scott, Missouri State University

Michael Sullivan, University of Nevada,

Las Vegas

Alex Tang, Morgan State University

Antoinette Tessmer, Michigan State University

Charles Wellens, North Idaho College

J. Douglas Wellington, Husson University

Jill Wetmore, Saginaw Valley State University

Casey Whilhelm, North Idaho College

We owe a special thanks to Joseph Smolira

of Belmont University for his work on this book.

Joe worked closely with us to develop portions

of the Instructor’s Manual, along with the many

vignettes and real-world examples. In addition,

we would like to thank David Diehl, Aurora

University, for his work on the PowerPoint and

Instructor’s Manual, and Bruce Costa, University of Montana, for his revision of the Test

Bank.

The following doctoral students did outstanding work on this edition: Dane Makhoul and Tim

Riley. To them fell the unenviable task of technical

proofreading, and in particular, careful checking of each calculation throughout the text and

Instructor’s Manual.

Finally, in every phase of this project, we

have been privileged to have had the complete

and unwavering support of a great organization, McGraw-Hill/Irwin. We especially thank

the McGraw-Hill/Irwin sales organization. The

suggestions they provide, their professionalism

in assisting potential adopters, and the service

they provide have been a major factor in our

success.

We are deeply grateful to the select group of

professionals who served as our development

team on this edition: Michele Janicek, Executive

Editor; Elizabeth Hughes, Development Editor;

Melissa Caughlin, Marketing Manager; Christine

Vaughan, Lead Project Manager; Mary Sander,

Designer; Heather Burbridge, Senior Manager,

ACKNOWLEDGMENTS

ros30689_fm_i-xxxiv.indd xix

xix

18/08/10 7:44 PM

EDP; and Brian Nacik, Media Project Manager. Others at

McGraw-Hill/Irwin, too numerous to list here, have improved

the book in countless ways.

Finally, we wish to thank our families, Carol, Kate, Jon, Jan,

Mark, Lynne, and Susan, for their forbearance and help.

Throughout the development of this edition, we have taken

great care to discover and eliminate errors. Our goal is to provide the best textbook available on the subject. To ensure that

future editions are error-free, we gladly offer $10 per arithmetic error to the first individual reporting it as a modest token of

our appreciation. More than this, we would like to hear from

xx

instructors and students alike. Please write and tell us how to

make this a better text. Forward your comments to: Dr. Brad

Jordan, c/o Editorial–Finance, McGraw-Hill/Irwin, 1333 Burr

Ridge Parkway, Burr Ridge, IL 60527, or visit us online at www.

mhhe.com/rwj.

—Stephen A. Ross

—Randolph W. Westerfield

—Jeffrey F. Jaffe

—Bradford D. Jordan

ACKNOWLEDGMENTS

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BRIEF CONTENTS

PART ONE

PART TWO

OVERVIEW

CHAPTER ONE

Introduction to Corporate Finance

CHAPTER TWO

Financial Statements and Cash Flow

1

CHAPTER THREE

Financial Statements Analysis and Financial

Models 44

20

VALUATION AND CAPITAL BUDGETING

CHAPTER FOUR

Discounted Cash Flow Valuation

84

CHAPTER FIVE

Interest Rates and Bond Valuation

CHAPTER SIX

Stock Valuation 168

133

CHAPTER SEVEN

Net Present Value and Other Investment Rules

CHAPTER EIGHT

Making Capital Investment Decisions

CHAPTER NINE

Risk Analysis, Real Options, and Capital

Budgeting 267

199

236

PART THREE RISK AND RETURN

PART FOUR

CHAPTER TEN

Risk and Return Lessons from Market History

CHAPTER ELEVEN

Return and Risk: The Capital Asset Pricing

Model (CAPM) 321

CHAPTER TWELVE

Risk, Cost of Capital, and Capital Budgeting

363

CAPITAL STRUCTURE AND DIVIDEND POLICY

CHAPTER THIRTEEN

PART FIVE

293

Efficient Capital Markets and Behavioral

Challenges 395

CHAPTER FOURTEEN

Capital Structure: Basic Concepts

CHAPTER FIFTEEN

Capital Structure: Limits to the Use of Debt

430

CHAPTER SIXTEEN

Dividends and Other Payouts

459

490

SPECIAL TOPICS

CHAPTER SEVENTEEN

Options and Corporate Finance

CHAPTER EIGHTEEN

Short-Term Finance and Planning

527

568

CHAPTER NINETEEN

Raising Capital 601

CHAPTER TWENTY

International Corporate Finance

CHAPTER TWENTY ONE

Mergers and Acquisitions (Web only)

APPENDIX A

Mathematical Tables

APPENDIX B

Solutions to Selected End-of-Chapter Problems

APPENDIX C

Using the HP 10B and TI BA II Plus

Financial Calculators 677

Indexes

636

663

672

681

BRIEF CONTENTS

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CONTENTS

PART ONE

2.2

OVERVIEW

1.1

What Is Corporate Finance?

1

1

The Balance Sheet Model of the Firm

The Financial Manager

1.2

The Corporate Firm

4

The Corporation

5

4

The Importance of Cash Flows

1.4

The Goal of Financial Management

25

26

Net Working Capital

28

2.5

Financial Cash Flow

28

2.6

7

The Accounting Statement of Cash

Flows 31

10

Cash Flow from Operating

Activities 31

11

Cash Flow from Investing

Activities 32

10

A More General Goal

26

Cash Flow from Financing

Activities 33

12

The Agency Problem and Control

of the Corporation 12

Summary and Conclusions

Agency Relationships

Closing Case: Cash Flows at East Coast

Yachts 42

Management Goals

13

13

Do Managers Act in the Stockholders’

Interests? 14

34

CHAPTER THREE

Stakeholders 15

Financial Statements Analysis

and Financial Models 44

Regulation 15

3.1

Summary and Conclusions

19

3.2

46

Ratio Analysis 48

Short-Term Solvency or Liquidity

Measures 48

Financial Statements and Cash Flow 20

The Balance Sheet

20

Accounting Liquidity

Value versus Cost

45

Common-Size Income Statements

CHAPTER TWO

Debt versus Equity

44

Common-Size Balance Sheets

17

Closing Case: East Coast Yachts

Financial Statements Analysis

Standardizing Statements 45

The Securities Act of 1933 and the

Securities Exchange Act of 1934 16

2.1

Time and Costs

Taxes 25

2.4

7

The Goal of Financial Management

1.6

24

Average versus Marginal Tax Rates

1.3

1.5

Noncash Items

Corporate Tax Rates

4

A Corporation by Another Name . . .

Possible Goals

2.3

3

The Sole Proprietorship

The Partnership

2

23

Generally Accepted Accounting

Principles 24

CHAPTER ONE

Introduction to Corporate Finance

The Income Statement

21

22

22

Long-Term Solvency Measures

50

Asset Management or Turnover

Measures 51

Profitability Measures

Market Value Measures

53

54

CONTENTS

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3.3

The Du Pont Identity

57

CHAPTER FIVE

A Closer Look at ROE

57

Interest Rates and Bond Valuation

Problems with Financial Statement Analysis 59

3.4

3.5

5.1

Financial Models 61

133

Bond Features and Prices

134

A Simple Financial Planning Model

61

Bond Values and Yields

The Percentage of Sales Approach

62

Interest Rate Risk

External Financing and Growth

EFN and Growth

5.2

137

More on Bond Features

The Indenture

74

Closing Case: Ratios and Financial Planning

at East Coast Yachts 81

Security

145

Seniority

145

Repayment

CHAPTER FOUR

Discounted Cash Flow Valuation

4.1

Valuation: The One-Period Case

4.2

The Multiperiod Case

84

145

Present Value and Discounting

The Algebraic Formula

4.3

Simplifications

Perpetuity

101

150

151

Bond Markets 151

5.7

152

152

155

Inflation and Interest Rates

155

Real versus Nominal Rates

155

The Fisher Effect

103

156

Determinants of Bond Yields

157

The Term Structure of Interest Rates

104

Trick 2: Annuity Due

Conclusion

108

110

111

113

113

Stock Valuation

168

The Present Value of Common Stocks

Dividends versus Capital Gains

114

Summary and Conclusions

Closing Case: Financing East Coast Yachts’ Expansion

Plans with a Bond Issue 166

6.1

113

What Is a Firm Worth?

161

CHAPTER SIX

Loan Types and Loan Amortization

Interest-Only Loans

161

Summary and Conclusions

109

Trick 4: Equating Present Value of Two Annuities 110

Pure Discount Loans

157

Bond Yields and the Yield Curve: Putting It All

Together 159

Trick 3: The Infrequent Annuity

Amortized Loans

149

Floating-Rate Bonds

148

A Note on Bond Price Quotes

5.6

101

Trick 1: A Delayed Annuity

4.6

Zero Coupon Bonds

Bond Price Reporting

106

Growing Annuity

148

How Bonds Are Bought and Sold

103

Growing Perpetuity

Annuity

Government Bonds

Other Types of Bonds

5.5

96

Compounding over Many Years

4.5

Some Different Types of Bonds

Compounding Periods 97

Continuous Compounding

146

5.4

91

Distinction between Stated Annual Interest Rate

and Effective Annual Rate 99

4.4

Protective Covenants

88

92

146

Bond Ratings 147

84

The Power of Compounding: A Digression

143

5.3

88

Future Value and Compounding

141

144

The Call Provision

VALUATION AND CAPITAL BUDGETING

139

144

Terms of a Bond

Some Caveats Regarding Financial Planning Models 73

PART TWO

134

Long-Term Debt: The Basics

69

A Note about Sustainable Growth Rate Calculations 72

Summary and Conclusions

133

Finding the Yield to Maturity: More Trial and Error

66

67

Financial Policy and Growth

3.6

Bonds and Bond Valuation

Valuation of Different Types of Stocks

117

Case 1 (Zero Growth)

119

Closing Case: The MBA Decision

170

170

Case 2 (Constant Growth)

131

168

168

Case 3 (Differential Growth)

170

171

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6.2

Estimates of Parameters in the Dividend Discount

Model 173

Summary of Payback

204

7.3

The Discounted Payback Period Method

205

Where Does R Come From?

7.4

The Average Accounting Return Method

205

Total Payout

174

176

Defining the Rule

177

Growth Opportunities 177

Growth in Earnings and Dividends

versus Growth Opportunities 179

The No-Payout Firm

Price-Earnings Ratio 180

6.5

Some Features of Common and Preferred Stocks

Shareholder Rights

Proxy Voting

Other Rights

182

Problems with the IRR Approach

182

183

Problem 1: Investing or Financing?

NPV Rule

185

185

General Rules

185

214

The Scale Problem

186

186

217

Redeeming Qualities of IRR

A Test

187

7.7

187

219

219

The Profitability Index

220

Calculation of Profitability Index

188

7.8

Stock Market Reporting

220

Application of the Profitability Index

189

189

The Practice of Capital Budgeting

Summary and Conclusions

Closing Case: Stock Valuation at Ragan Engines

197

220

222

224

Closing Case: Bullock Gold Mining

192

235

CHAPTER EIGHT

Making Capital Investment Decisions

CHAPTER SEVEN

Net Present Value and Other Investment

Rules 199

7.1

Why Use Net Present Value?

199

7.2

The Payback Period Method

202

8.1

Incremental Cash Flows

Sunk Costs

203

Problem 1: Timing of Cash Flows within the Payback

Period 203

237

238

Allocated Costs

8.2

236

237

Opportunity Costs

Side Effects

236

236

Cash Flows—Not Accounting Income

202

Problems with the Payback Method

215

215

The Timing Problem

186

NASDAQ Operations

214

Problems Specific to Mutually Exclusive Projects

186

Organization of the NYSE

Defining the Rule

213

The Guarantee against Multiple IRRs

Dealers and Brokers

Summary and Conclusions

212

213

Modified IRR

Is Preferred Stock Really Debt?

ECNs

212

Problem 2: Multiple Rates of Return

185

Floor Activity

210

Two General Problems Affecting Both Independent

and Mutually Exclusive Projects 211

Cumulative and Noncumulative Dividends

Operations

207

Definition of Independent and Mutually Exclusive

Projects 210

184

The Stock Markets

207

The Internal Rate of Return

182

Preferred Stock Features

Members

207

7.6

Dividends 184

Stated Value

206

Step 2: Determining Average Investment

7.5

183

Classes of Stock

Step 1: Determining Average Net Income

Step 3: Determining AAR

179

Common Stock Features

205

Analyzing the Average Accounting Return Method 207

6.4

6.6

204

Where Does g Come From? 173

A Healthy Sense of Skepticism

6.3

Managerial Perspective

238

The Baldwin Company: An Example

An Analysis of the Project

Problem 2: Payments after the Payback Period 203

Investments 240

Problem 3: Arbitrary Standard for Payback

Period 204

Income and Taxes

Salvage Value

239

240

241

242

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Cash Flow

PART THREE

243

Net Present Value

243

Which Set of Books?

243

CHAPTER TEN

A Note on Net Working Capital

A Note on Depreciation

Interest Expense

8.3

8.4

8.5

Risk and Return Lessons from Market

History 293

243

244

10.1

245

Returns 293

Dollar Returns

Inflation and Capital Budgeting

245

Discounting: Nominal or Real?

246

The Bottom-Up Approach

249

The Top-Down Approach

249

The Tax Shield Approach

249

248

Holding Period Returns

10.3

Return Statistics

10.4

Average Stock Returns and Risk-Free

Returns 304

10.5

Risk Statistics

Variance

Investments of Unequal Lives: The Equivalent Annual

Cost Method 250

The General Decision to Replace

252

297

303

306

306

Normal Distribution and Its Implications

for Standard Deviation 307

10.6

The U.S. Equity Risk Premium: Historical and

International Perspectives 3 0 8

10.7

2008: A Year of Financial Crisis

10.8

More on Average Returns

254

Closing Cases: Expansion at East Coast Yachts 265

Bethesda Mining Company 265

295

10.2

250

Summary and Conclusions

293

Percentage Returns

Alternative Definitions of Operating Cash Flow

Conclusion

RISK AND RETURN

311

312

Arithmetic versus Geometric Averages

CHAPTER NINE

Risk Analysis, Real Options, and Capital

Budgeting 267

9.1

9.2

Summary and Conclusions

269

CHAPTER ELEVEN

Sensitivity Analysis and Scenario Analysis 270

Costs

Return and Risk: The Capital Asset Pricing

Model (CAPM) 321

270

271

Break-Even Analysis

Accounting Profit

Present Value

9.3

273

11.1

Individual Securities

273

11.2

Expected Return, Variance, and Covariance

Monte Carlo Simulation

Covariance and Correlation

276

11.3

276

Step 3: The Computer Draws One Outcome

Step 4: Repeat the Procedure

Step 5: Calculate NPV

The Return and Risk for Portfolios

The Variance

278

326

326

The Diversification Effect

280

The Efficient Set

329

329

The Two-Asset Case

282

329

The Efficient Set for Many Securities

283

Closing Case: Bunyan Lumber, LLC

11.5

291

327

328

An Extension to Many Assets

11.4

327

327

Standard Deviation of a Portfolio

278

279

The Option to Abandon

Summary and Conclusions

322

Variance and Standard Deviation of a Portfolio

278

Real Options 279

The Option to Expand

322

323

The Expected Return on a Portfolio

Step 2: Specify a Distribution for Each Variable

in the Model 276

Timing Options

321

Expected Return and Variance

275

Step 1: Specify the Basic Model

9.4

315

Closing Case: A Job at East Coast Yachts,

Part 1 319

Sensitivity Analysis, Scenario Analysis, and

Break-Even Analysis 269

Revenues

313

Arithmetic Average Return or Geometric

Average Return? 314

Decision Trees 267

Warning

312

Calculating Geometric Average Returns

Riskless Borrowing and Lending

The Optimal Portfolio

333

334

336

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11.6

12.6

Announcements, Surprises, and Expected

Returns 338

Announcements and News

339

Risk: Systematic and Unsystematic

340

12.7

Cost of Capital for Divisions and Projects 377

Systematic and Unsystematic Risk

340

12.8

Cost of Fixed Income Securities

Cost of Debt

Diversification and Portfolio Risk

12.9

The Principle of Diversification

Diversification and Systematic Risk

Market Equilibrium

Eastman’s Cost of Equity

343

Eastman’s Cost of Debt

343

Eastman’s WACC

344

Definition of the Market Equilibrium Portfolio

A Test

The Basic Approach

Summary and Conclusions

11.10 Relationship between Risk and Expected

Return (CAPM) 349

350

Closing Case: A Job at East Coast Yachts, Part 2

PART FOUR

361

CHAPTER TWELVE

Risk, Cost of Capital, and Capital Budgeting

12.1

The Cost of Equity Capital

12.2

Estimating the Cost of Equity Capital with

the CAPM 364

363

363

13.1

Can Financing Decisions Create

Value? 395

13.2

A Description of Efficient Capital

Markets 397

Foundations of Market Efficiency

Real-World Betas

369

Stability of Beta

Independent Deviations from Rationality

12.4

12.5

Arbitrage

13.3

The Different Types of Efficiency

372

Beta and Covariance

372

The Efficacy of Dart Throwing

Determinants of Beta

373

Price Fluctuations

Operating Leverage

13.4

373

373

The Evidence

The Weak Form

403

403

Stockholder Disinterest

373

Financial Leverage and Beta

401

Some Common Misconceptions about

the Efficient Market Hypothesis 402

Beta and Covariance

Cyclicality of Revenues

400

400

The Semistrong and Strong Forms

370

399

400

The Weak Form

369

Using an Industry Beta

399

Rationality 399

367

Method 2: Using the Dividend Discount Model

(DDM) 367

368

CAPITAL STRUCTURE

AND DIVIDEND POLICY

Efficient Capital Markets and Behavioral

Challenges 395

367

Estimation of Beta

387

387

CHAPTER THIRTEEN

367

Method 1: Using Historical Data

12.3

386

Closing Case: The Cost of Capital for Goff

Computer, Inc. 394

352

Market Risk Premium

385

349

Expected Return on Individual Security

The Risk-Free Rate

384

Internal Equity and Flotation Costs

349

Summary and Conclusions

383

385

Flotation Costs and NPV

347

Expected Return on Market

380

12.11 Flotation Costs and the Weighted Average Cost

of Capital 385

344

Definition of Risk When Investors Hold

the Market Portfolio 345

The Formula for Beta

379

The Weighted Average Cost of Capital

12.10 Estimating Eastman Chemical’s Cost

of Capital 383

341

Diversification and Unsystematic Risk

378

378

Cost of Preferred Stock

341

The Effect of Diversification: Another Lesson

from Market History 341

11.9

375

Can a Low-Dividend or a No-Dividend Stock

Have a High Cost of Capital? 376

Systematic and Unsystematic Components

of Return 340

11.8

375

Comparison of DDM and CAPM

Expected and Unexpected Returns 338

11.7

Dividend Discount Model

403

403

404

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The Semistrong Form

Event Studies

405

The Weighted Average Cost of Capital RWACC

and Corporate Taxes 449

406

The Record of Mutual Funds

The Strong Form

13.5

Stock Price and Leverage under Corporate

Taxes 449

407

408

Summary and Conclusions

The Behavioral Challenge to Market

Efficiency 409

Rationality 409

Independent Deviations from

Rationality 409

Arbitrage

CHAPTER FIFTEEN

Capital Structure: Limits to the Use

of Debt 459

410

13.6

Empirical Challenges to Market Efficiency

13.7

Reviewing the Differences

13.8

410

15.1

416

Representativeness 416

Indirect Bankruptcy Costs

Conservatism 416

Agency Costs

Implications for Corporate Finance

2. The Timing Decision

417

4. Information in Market Prices

Summary and Conclusions

420

420

The Capital Structure Question and the Pie

Theory 430

14.2

Maximizing Firm Value versus Maximizing

Stockholder Interests 431

14.3

Financial Leverage and Firm Value:

An Example 433

The Choice between Debt and Equity

A Key Assumption

Protective Covenants

464

Consolidation of Debt

465

463

464

Pie Again

465

15.4

Signaling

468

15.5

Shirking, Perquisites, and Bad Investments: A Note

on Agency Cost of Equity 469

Effect of Agency Costs of Equity on

Debt-Equity Financing 471

430

14.1

Can Costs of Debt Be Reduced?

Integration of Tax Effects and Financial

Distress Costs 465

CHAPTER FOURTEEN

Leverage and Returns to Shareholders

460

461

15.3

422

Closing Case: Your 401(K) Account at East Coast

Yachts 428

Capital Structure: Basic Concepts

459

460

Summary of Selfish Strategies

15.2

417

3. Speculation and Efficient Markets

Free Cash Flow

15.6

471

The Pecking-Order Theory

472

Rules of the Pecking Order

473

Rule #1 Use Internal Financing

473

Rule #2 Issue Safe Securities First

435

474

Implications 474

433

15.7

Growth and the Debt-Equity Ratio

No Growth

437

Growth

475

475

475

Modigliani and Miller: Proposition II

(No Taxes) 437

15.8

How Firms Establish Capital Structure

Risk to Equityholders Rises with Leverage 437

15.9

A Quick Look at the Bankruptcy Process

Proposition II: Required Return to Equityholders

Rises with Leverage 438

MM: An Interpretation

14.5

Costs of Financial Distress

Direct Bankruptcy Costs

1. Accounting Choices, Financial Choices,

and Market Efficiency 417

14.4

451

Closing Case: Stephenson Real Estate

Recapitalization 458

Taxes

443

481

482

482

483

Financial Management and the Bankruptcy

Process 483

444

Present Value of the Tax Shield

Value of the Levered Firm

Bankruptcy Liquidation

Bankruptcy Reorganization

444

The Basic Insight

Liquidation and Reorganization

477

446

446

Expected Return and Leverage under Corporate

Taxes 448

Agreements to Avoid Bankruptcy

Summary and Conclusions

484

484

Closing Case: McKenzie Corporation’s Capital

Budgeting 489

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CHAPTER SIXTEEN

Value of Stock Splits and Stock Dividends

Dividends and Other Payouts

490

The Benchmark Case

16.1

Different Types of Dividends

490

16.2

Standard Method of Cash Dividend Payment

16.3

The Benchmark Case: An Illustration of the

Irrelevance of Dividend Policy 493

516

Popular Trading Range

491

Reverse Splits

516

517

517

Summary and Conclusions

518

Closing Case: Electronic Timing, Inc.

525

Current Policy: Dividends Set Equal to Cash Flow 493

Alternative Policy: Initial Dividend Is Greater than Cash

Flow 494

PART FIVE

The Indifference Proposition

CHAPTER SEVENTEEN

Homemade Dividends

494

Options and Corporate Finance

494

17.1

Options

17.2

Call Options

Dividend versus Repurchase: Conceptual Example 498

17.3

Put Options

Dividends versus Repurchases: Real-World

Considerations 499

17.4

Selling Options

17.5

Option Quotes

17.6

Combinations of Options

17.7

Valuing Options

A Test

496

Dividends and Investment Policy

16.4

Repurchase of Stock

1. Flexibility

497

499

500

4. Repurchase as Investment

5. Taxes

500

500

500

Firms without Sufficient Cash to Pay a Dividend

501

533

536

Upper Bound

536

536

The Factors Determining Call Option

Values 536

502

Exercise Price

503

Desire for Current Income

Stock Price

503

536

537

537

The Key Factor: The Variability of the

Underlying Asset 538

504

505

The Interest Rate

Information Content of Dividends and Dividend

Signaling 506

The Clientele Effect: a Resolution of Real-World

Factors? 507

539

A Quick Discussion of Factors Determining

Put Option Values 539

17.8

An Option Pricing Formula

A Two-State Option Model

What We Know and Do Not Know about Dividend

Policy 508

Determining the Delta

540

541

541

Dividends and Dividend Payers

508

Determining the Amount of Borrowing

Corporations Smooth Dividends

510

Risk-Neutral Valuation

542

The Black–Scholes Model

543

Payouts Provide Information to the Market

Putting It All Together

511

511

17.9

Some Survey Evidence on Dividends

16.9

532

Real-World Factors Favoring a High-Dividend Policy 503

Agency Costs

529

531

Expiration Date

Behavioral Finance

16.8

529

Lower Bound 536

Personal Taxes, Issuance Costs, and Dividends

Summary on Personal Taxes

16.7

528

Bounding the Value of a Call

Firms with Sufficient Cash to Pay a Dividend

16.6

527

The Value of a Put Option at Expiration

499

3. Offset to Dilution

527

The Value of a Call Option at Expiration 528

497

2. Executive Compensation

16.5

SPECIAL TOPICS

514

Stock Dividends and Stock Splits 515

Some Details on Stock Splits and Stock Dividends 515

Example of a Small Stock Dividend

Example of a Stock Split

515

516

Example of a Large Stock Dividend

516

Stocks and Bonds as Options

547

The Firm Expressed in Terms of Call Options

The Stockholders

548

The Bondholders

549

The Firm Expressed in Terms of Put Options

The Stockholders

550

The Bondholders

550

542

548

550

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A Resolution of the Two Views

A Note on Loan Guarantees

550

18.6

552

Summary and Conclusions

553

Options and Capital Budgeting

591

CHAPTER NINETEEN

554

17.11 Investment in Real Projects and Options

Summary and Conclusions

590

Closing Case: Keafer Manufacturing Working Capital

Management 599

17.10 Options and Corporate Decisions: Some

Applications 552

Mergers and Diversification

A Short-Term Financial Plan

Raising Capital

556

19.1

558

601

The Financing Life Cycle of a Firm: Early-Stage

Financing and Venture Capital 602

Closing Case: Exotic Cuisines Employee Stock

Options 567

Venture Capital

CHAPTER EIGHTEEN

Choosing a Venture Capitalist

Short-Term Finance and Planning

Conclusion

Tracing Cash and Net Working Capital

18.2

The Operating Cycle and the Cash Cycle 570

569

Defining the Operating and Cash Cycles

The Operating Cycle

The Cash Cycle

Some Venture Capital Realities

568

18.1

571

571

19.3

Alternative Issue Methods

19.4

Underwriters

The Operating Cycle and the Firm’s Organization Chart 573

The Operating Cycle

576

The Green Shoe Provision

577

The Aftermarket

Lockup Agreements

The Quiet Period

19.5

Which Financing Policy Is Best?

Cash Outflows

583

18.5

583

584

The Cash Balance

585

Short-Term Borrowing

Unsecured Loans

585

Letters of Credit

586

587

614

19.6

What CFOs Say about the IPO Process

19.7

CEOs and the Value of the Firm

19.8

The Cost of Issuing Securities

19.9

Rights

588

Commercial Paper

588

616

617

618

622

622

623

Effect of Rights Offering on Price of Stock

Effects on Shareholders

587

The Rights Puzzle

625

626

19.10 Dilution 626

Dilution of Proportionate Ownership

588

626

Dilution of Value: Book versus Market Values

Understanding Trade Credit Terms

589

623

623

625

The Underwriting Arrangements

Inventory Loans

Cash Discounts

610

Number of Rights Needed to Purchase a Share

586

587

Accounts Receivable Financing

Trade Credit

609

Why Does Underpricing Exist?

Subscription Price

Cost of a Compensating Balance

Secured Loans

IPOs and Underpricing

The Mechanics of a Rights Offering

586

Compensating Balances

609

IPO Underpricing: The 1999–2000 Experience 611

Current Assets and Liabilities in Practice 583

Sales and Cash Collections

608

609

Evidence on Underpricing

582

608

609

Alternative Financing Policies for Current Assets 578

578

607

607

Dutch Auction Underwriting

The Size of the Firm’s Investment in Current Assets 577

The Cash Budget

607

Best Efforts Underwriting

Different Policies for Financing Current Assets 580

18.4

607

Firm Commitment Underwriting

574

Some Aspects of Short-Term Financial Policy

An Ideal Case

606

607

Types of Underwriting

574

575

Interpreting the Cash Cycle

18.3

603

Selling Securities to the Public: The Basic

Procedure 603

Choosing an Underwriter

Calculating the Operating and Cash Cycles

603

603

19.2

571

The Cash Cycle

602

588

A Misconception

626

627

The Correct Arguments

628

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19.11 Issuing Long-Term Debt

628

20.6

Exchange Rate Risk

653

19.12 Shelf Registration 629

Short-Run Exposure

653

Summary and Conclusions

Long-Run Exposure

654

630

Closing Case: East Coast Yachts Goes Public

634

Translation Exposure

CHAPTER TWENTY

International Corporate Finance

20.7

636

Terminology

637

20.2

Foreign Exchange Markets and Exchange Rates

Exchange Rates

Types of Transactions

642

Purchasing Power Parity

643

Relative Purchasing Power Parity

645

Solutions to Selected End-of-Chapter

Problems 672

647

Interest Rate Parity, Unbiased Forward Rates, and the

International Fisher Effect 647

Covered Interest Arbitrage

647

648

Forward Rates and Future Spot Rates

Using the HP 10B and TI BA II Plus Financial

Calculators 677

681

COMPANY INDEX

650

The International Fisher Effect

International Capital Budgeting

APPENDIX C

NAME INDEX

649

650

Uncovered Interest Parity

SUBJECT INDEX

683

685

650

651

Method 1: The Home Currency Approach

Method 2: The Foreign Currency Approach

Unremitted Cash Flows

663

APPENDIX B

645

Putting It All Together

Closing Case: East Coast Yachts Goes

International 662

Mathematical Tables

643

645

Interest Rate Parity

657

Mergers and Acquisitions (Web only)

641

Currency Appreciation and Depreciation

20.5

656

APPENDIX A

Absolute Purchasing Power Parity

The Basic Idea

656

CHAPTER TWENTY ONE

639

Cross-Rates and Triangle Arbitrage

20.4

638

639

Exchange Rate Quotations

The Result

Political Risk

Summary and Conclusions

20.1

20.3

655

Managing Exchange Rate Risk

652

652

653

CONTENTS

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LIST OF BOXES

THE REAL WORLD BOXES

CHAPTER 1

Sarbanes-Oxley 16

CHAPTER 2

Putting a Spin on Cash Flows

CHAPTER 3

What’s in a Ratio?

CHAPTER 4

Jackpot!

CHAPTER 5

Beauty Is in the Eye of the Bondholder

150

CHAPTER 6

How Fast Is Too Fast? 176

The Wild, Wild West of Stock Trading

190

32

60

100

CHAPTER 9

When Things Go Wrong . . .

270

CHAPTER 11

Beta, Beta, Who’s Got the Beta?

348

CHAPTER 12

The Cost of Capital, Texas Style

382

CHAPTER 13

Can Stock Market Investors Add and Subtract?

CHAPTER 16

Stock Buybacks: No End in Sight

CHAPTER 18

A Look at Operating and Cash Cycles

CHAPTER 19

IPO Underpricing around the World

Anatomy of an IPO 620

CHAPTER 20

McPricing

412

504

572

612

644

LIST OF BOXES

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Introduction to Corporate

Finance

CHAPTER

1

I

n 2008 and 2009, the U.S. government set up the $700 billion Troubled Asset Relief Program

(TARP) to help companies avoid bankruptcy due to the severe financial turmoil. The loans to

companies such as Bank of America and General Motors created unique governance problems. One such that received special attention was executive compensation. In June 2009,

Kenneth Feinberg was appointed as a Special Master for Compensation (better known as the

“Pay Czar”) and given broad powers over executive compensation for firms participating in the

TARP program.

In October 2009, Mr. Feinberg capped the salaries at the seven largest TARP companies at

PART ONE Overview

OPENING CASE

$500,000. This group’s annualized total pay would be 50 percent lower than a year before through

reduced bonuses and options. Interestingly, 80 of the 136 employees affected actually had their base

salaries increased, including an average base salary increase of about 87 percent at Citigroup.

Some outside experts argued that the pay cuts were overstated. Many employees continued to

receive seven-figure pay packages, including one who received $9.9 million. Of the 136 employees

whose paychecks were reviewed, 29 were on track to collect total 2009 pay of at least $5 million. The

discrepancy arose because the pay cut calculation depended in part on departures of certain highly

paid employees from the previous year.

The Pay Czar’s role in setting compensation limits is an unusual case in the U.S. of direct government involvement in corporate decisions. Understanding how a corporation sets executive pay, and

the role of shareholders in that process, takes us into issues involving the corporate form of organization, corporate goals, and corporate control, all of which we cover in this chapter.

1.1

W H AT I S C O R P O R AT E F I N A N C E ?

Suppose you decide to start a firm to make tennis balls. To do this you hire managers

to buy raw materials, and you assemble a workforce that will produce and sell finished

tennis balls. In the language of finance, you make an investment in assets such as inventory,

machinery, land, and labor. The amount of cash you invest in assets must be matched by an

equal amount of cash raised by financing. When you begin to sell tennis balls, your firm

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will generate cash. This is the basis of value creation. The purpose of the firm is to create

value for you, the owner. The value is reflected in the framework of the simple balance

sheet model of the firm.

The Balance Sheet Model of the Firm

Suppose we take a financial snapshot of the firm and its activities at a single point in time.

Figure 1.1 shows a graphic conceptualization of the balance sheet, and it will help introduce you to corporate finance.

The assets of the firm are on the left side of the balance sheet. These assets can be

thought of as current and fixed. Fixed assets are those that will last a long time, such as

buildings. Some fixed assets are tangible, such as machinery and equipment. Other fixed

assets are intangible, such as patents and trademarks. The other category of assets, current

assets, comprises those that have short lives, such as inventory. The tennis balls that your

firm has made, but has not yet sold, are part of its inventory. Unless you have overproduced,

they will leave the firm shortly.

Before a company can invest in an asset, it must obtain financing, which means that it

must raise the money to pay for the investment. The forms of financing are represented

on the right side of the balance sheet. A firm will issue (sell) pieces of paper called debt

(loan agreements) or equity shares (stock certificates). Just as assets are classified as longlived or short-lived, so too are liabilities. A short-term debt is called a current liability.

Short-term debt represents loans and other obligations that must be repaid within one year.

Long-term debt is debt that does not have to be repaid within one year. Shareholders’ equity

represents the difference between the value of the assets and the debt of the firm. In this

sense, it is a residual claim on the firm’s assets.

From the balance sheet model of the firm, it is easy to see why finance can be thought of

as the study of the following three questions:

1. In what long-lived assets should the firm invest? This question concerns the left side

of the balance sheet. Of course the types and proportions of assets the firm needs

tend to be set by the nature of the business. We use the term capital budgeting to

describe the process of making and managing expenditures on long-lived assets.

FIGURE 1.1

The Balance Sheet

Model of the Firm

Net

working

capital

Current assets

Current

liabilities

Long-term

debt

Fixed assets

1. Tangible fixed

assets

2. Intangible fixed

assets

Total Value of Assets

2

Shareholders’

equity

=

Total Value of the Firm to Investors

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2. How can the firm raise cash for required capital expenditures? This question

concerns the right side of the balance sheet. The answer to this question involves

the firm’s capital structure, which represents the proportions of the firm’s

financing from current liabilities, long-term debt, and equity.

3. How should short-term operating cash flows be managed? This question concerns the

upper portion of the balance sheet. There is often a mismatch between the timing of

cash inflows and cash outflows during operating activities. Furthermore, the amount

and timing of operating cash flows are not known with certainty. Financial managers must attempt to manage the gaps in cash flow. From a balance sheet perspective,

short-term management of cash flow is associated with a firm’s net working capital.

Net working capital is defined as current assets minus current liabilities. From a

financial perspective, short-term cash flow problems come from the mismatching

of cash inflows and outflows. This is the subject of short-term finance.

The Financial Manager

In large firms, the finance activity is usually associated with a top officer of the firm,

such as the vice president and chief financial officer, and some lesser officers. Figure 1.2

FIGURE 1.2

Hypothetical Organization

Chart

Board of Directors

Chairman of the Board and

Chief Executive Officer (CEO)

President and Chief

Operations Officer (COO)

Vice President and Chief

Financial Officer (CFO)

Treasurer

Controller

Cash Manager

Credit Manager

Tax Manager

Cost Accounting

Manager

Capital

Expenditures

Financial

Planning

Financial

Accounting

Manager

Information

Systems

Manager

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For current issues

facing CFOs, see

www.cfo.com.

depicts a general organizational structure emphasizing the finance activity within the firm.

Reporting to the chief financial officer are the treasurer and the controller. The treasurer is

responsible for handling cash flows, managing capital expenditure decisions, and making

financial plans. The controller handles the accounting function, which includes taxes, cost

and financial accounting, and information systems.

1.2

T H E C O R P O R AT E F I R M

The firm is a way of organizing the economic activity of many individuals. A basic problem

of the firm is how to raise cash. The corporate form of business—that is, organizing the

firm as a corporation—is the standard method for solving problems encountered in raising large amounts of cash. However, businesses can take other forms. In this section we

consider the three basic legal forms of organizing firms, and we see how firms go about the

task of raising large amounts of money under each form.

The Sole Proprietorship

For more about small

business organization,

see the “Business and

Human Resources”

section at

www.nolo.com.

A sole proprietorship is a business owned by one person. Suppose you decide to start a

business to produce mousetraps. Going into business is simple: You announce to all who

will listen, “Today, I am going to build a better mousetrap.”

Most large cities require that you obtain a business license. Afterward, you can begin to

hire as many people as you need and borrow whatever money you need. At year-end all the

profits and the losses will be yours.

Here are some factors that are important in considering a sole proprietorship:

1. The sole proprietorship is the cheapest business to form. No formal charter is

required, and few government regulations must be satisfied for most industries.

2. A sole proprietorship pays no corporate income taxes. All profits of the business

are taxed as individual income.

3. The sole proprietorship has unlimited liability for business debts and obligations.

No distinction is made between personal and business assets.

4. The life of the sole proprietorship is limited by the life of the sole proprietor.

5. Because the only money invested in the firm is the proprietor’s, the equity

money that can be raised by the sole proprietor is limited to the proprietor’s

personal wealth.

The Partnership

Any two or more people can get together and form a partnership. Partnerships fall into

two categories: (1) general partnerships and (2) limited partnerships.

In a general partnership all partners agree to provide some fraction of the work and

cash and to share the profits and losses. Each partner is liable for all of the debts of

the partnership. A partnership agreement specifies the nature of the arrangement. The

partnership agreement may be an oral agreement or a formal document setting forth the

understanding.

Limited partnerships permit the liability of some of the partners to be limited to the

amount of cash each has contributed to the partnership. Limited partnerships usually

require that (1) at least one partner be a general partner and (2) the limited partners do

not participate in managing the business. Here are some things that are important when

considering a partnership:

1. Partnerships are usually inexpensive and easy to form. Written documents are

required in complicated arrangements. Business licenses and filing fees may

be necessary.

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2. General partners have unlimited liability for all debts. The liability of limited

partners is usually limited to the contribution each has made to the partnership.

If one general partner is unable to meet his or her commitment, the shortfall

must be made up by the other general partners.

3. The general partnership is terminated when a general partner dies or withdraws

(but this is not so for a limited partner). It is difficult for a partnership to transfer

ownership without dissolving. Usually all general partners must agree. However,

limited partners may sell their interest in a business.

4. It is difficult for a partnership to raise large amounts of cash. Equity contributions

are usually limited to a partner’s ability and desire to contribute to the partnership. Many companies, such as Apple Computer, start life as a proprietorship or

partnership, but at some point they choose to convert to corporate form.

5. Income from a partnership is taxed as personal income to the partners.

6. Management control resides with the general partners. Usually a majority vote is

required on important matters, such as the amount of profit to be retained in the

business.

It is difficult for large business organizations to exist as sole proprietorships or partnerships. The main advantage to a sole proprietorship or partnership is the cost of getting

started. Afterward, the disadvantages, which may become severe, are (1) unlimited liability,

(2) limited life of the enterprise, and (3) difficulty of transferring ownership. These three

disadvantages lead to (4) difficulty in raising cash.

The Corporation

Of the forms of business enterprises, the corporation is by far the most important. It is a

distinct legal entity. As such, a corporation can have a name and enjoy many of the legal

powers of natural persons. For example, corporations can acquire and exchange property.

Corporations can enter contracts and may sue and be sued. For jurisdictional purposes the

corporation is a citizen of its state of incorporation (it cannot vote, however).

Starting a corporation is more complicated than starting a proprietorship or partnership.

The incorporators must prepare articles of incorporation and a set of bylaws. The articles

of incorporation must include the following:

1.

2.

3.

4.

Name of the corporation.

Intended life of the corporation (it may be forever).

Business purpose.

Number of shares of stock that the corporation is authorized to issue, with a

statement of limitations and rights of different classes of shares.

5. Nature of the rights granted to shareholders.

6. Number of members of the initial board of directors.

The bylaws are the rules to be used by the corporation to regulate its own existence,

and they concern its shareholders, directors, and officers. Bylaws range from the briefest possible statement of rules for the corporation’s management to hundreds of pages

of text.

In its simplest form, the corporation comprises three sets of distinct interests: the shareholders (the owners), the directors, and the corporation officers (the top management).

Traditionally, the shareholders control the corporation’s direction, policies, and activities.

The shareholders elect a board of directors, who in turn select top management. Members

of top management serve as corporate officers and manage the operations of the corporation

in the best interest of the shareholders. In closely held corporations with few shareholders,

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there may be a large overlap among the shareholders, the directors, and the top management.

However, in larger corporations, the shareholders, directors, and the top management are

likely to be distinct groups.

The potential separation of ownership from management gives the corporation several

advantages over proprietorships and partnerships:

1. Because ownership in a corporation is represented by shares of stock, ownership

can be readily transferred to new owners. Because the corporation exists independently of those who own its shares, there is no limit to the transferability of

shares as there is in partnerships.

2. The corporation has unlimited life. Because the corporation is separate from its

owners, the death or withdrawal of an owner does not affect the corporation’s

legal existence. The corporation can continue on after the original owners have

withdrawn.

3. The shareholders’ liability is limited to the amount invested in the ownership

shares. For example, if a shareholder purchased $1,000 in shares of a corporation, the potential loss would be $1,000. In a partnership, a general partner with

a $1,000 contribution could lose the $1,000 plus any other indebtedness of the

partnership.

Limited liability, ease of ownership transfer, and perpetual succession are the major

advantages of the corporate form of business organization. These give the corporation an

enhanced ability to raise cash.

There is, however, one great disadvantage to incorporation. The federal government

taxes corporate income (the states do as well). This tax is in addition to the personal income tax that shareholders pay on dividend income they receive. This is double taxation

for shareholders when compared to taxation on proprietorships and partnerships. Table 1.1

summarizes our discussion of partnerships and corporations.

Today all 50 states have enacted laws allowing for the creation of a relatively new

form of business organization, the limited liability company (LLC). The goal of this

TABLE 1.1

A Comparison of Partnerships and Corporations

CORPORAT I O N

6

PA R T N E R S H I P

Liquidity and

marketability

Shares can be exchanged without termination of

the corporation. Common stock can be listed on a

stock exchange.

Units are subject to substantial restrictions on transferability.

There is usually no established trading market for partnership units.

Voting rights

Usually each share of common stock entitles the

holder to one vote per share on matters requiring a

vote and on the election of the directors. Directors

determine top management.

Some voting rights by limited partners. However, general

partners have exclusive control and management of

operations.

Taxation

Corporations have double taxation: Corporate

income is taxable, and dividends to shareholders

are also taxable.

Partnerships are not taxable. Partners pay personal taxes on

partnership profits.

Reinvestment and

dividend payout

Corporations have broad latitude on dividend

payout decisions.

Partnerships are generally prohibited from reinvesting

partnership profits. All profits are distributed to partners.

Liability

Shareholders are not personally liable for

obligations of the corporation.

Limited partners are not liable for obligations of partnerships.

General partners may have unlimited liability.

Continuity of

existence

Corporations may have a perpetual life.

Partnerships have limited life.

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TABLE 1.2

International Corporations

T Y P E O F C O M PA N Y

COM PANY

COU N T RY O F O R I G I N

I N O R I G I N A L LA N G U A G E

I N T E R P R ETATION

Bayerische

Motoren Werke (BMW) AG

Germany

Aktiengesellschaft

Corporation

Dornier GmBH

Germany

Gesellschaft mit

Beschränkter Haftung

Limited liability company

Rolls-Royce PLC

United Kingdom

Public limited company

Public Ltd. Company

Shell UK Ltd.

United Kingdom

Limited

Corporation

Unilever NV

Netherlands

Naamloze Vennootschap

Joint stock company

Fiat SpA

Italy

Società per Azioni

Joint stock company

Volvo AB

Sweden

Aktiebolag

Joint stock company

Peugeot SA

France

Société Anonyme

Joint stock company

entity is to operate and be taxed like a partnership but retain limited liability for owners,

so an LLC is essentially a hybrid of partnership and corporation. Although states have

differing definitions for LLCs, the more important scorekeeper is the Internal Revenue

Service (IRS). The IRS will consider an LLC a corporation, thereby subjecting it to

double taxation, unless it meets certain specific criteria. In essence, an LLC cannot be

too corporation-like, or it will be treated as one by the IRS. LLCs have become common.

For example, Goldman, Sachs and Co., one of Wall Street’s last remaining partnerships,

decided to convert from a private partnership to an LLC (it later “went public,” becoming a publicly held corporation). Large accounting firms and law firms by the score have

converted to LLCs.

To find out more about

LLCs, visit

www.incorporate.com.

A Corporation by Another Name . . .

The corporate form of organization has many variations around the world. The exact laws

and regulations differ from country to country, of course, but the essential features of public ownership and limited liability remain. These firms are often called joint stock companies, public limited companies, or limited liability companies, depending on the specific

nature of the firm and the country of origin.

Table 1.2 gives the names of a few well-known international corporations, their countries of origin, and a translation of the abbreviation that follows each company name.

1.3

T H E I M P O R TA N C E O F C A S H F L O W S

The most important job of a financial manager is to create value from the firm’s capital

budgeting, financing, and net working capital activities. How do financial managers create

value? The answer is that the firm should create more cash flow than it uses.

The cash flows paid to bondholders and stockholders of the firm should be greater

than the cash flows put into the firm by the bondholders and stockholders. To see

how this is done, we can trace the cash flows from the firm to the financial markets and

back again.

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FIGURE 1.3

Cash Flows between the Firm and the Financial Markets

Cash for securities issued by the firm (A)

Firm invests

in assets

(B)

Current assets

Fixed assets

Total Value of Assets

Financial

markets

Retained cash

flows (E)

Cash flow from

firm (C)

Short-term debt

Long-term debt

Equity shares

Dividends and

debt payments (F )

Ta xes

Total Value of the Firm

to Investors in

the Financial Markets

Government

(D)

The interplay of the firm’s activities with the financial markets is illustrated in Figure 1.3.

The arrows in Figure 1.3 trace cash flow from the firm to the financial markets and back

again. Suppose we begin with the firm’s financing activities. To raise money, the firm sells

debt and equity shares to investors in the financial markets. This results in cash flows from

the financial markets to the firm (A). This cash is invested in the investment activities (assets) of the firm (B) by the firm’s management. The cash generated by the firm (C) is paid to

shareholders and bondholders (F). The shareholders receive cash in the form of dividends;

the bondholders who lent funds to the firm receive interest and, when the initial loan is repaid, principal. Not all of the firm’s cash is paid out. Some is retained (E), and some is paid

to the government as taxes (D).

Over time, if the cash paid to shareholders and bondholders (F) is greater than the cash

raised in the financial markets (A), value will be created.

EXAMPLE

1.1

Identification of Cash Flows Unfortunately, it is sometimes not easy to observe cash flows

directly. Much of the information we obtain is in the form of accounting statements, and

much of the work of financial analysis is to extract cash flow information from accounting

statements. The following example illustrates how this is done.

Accounting Profit versus Cash Flows

The Midland Company refines and trades gold. At the end of the year, it sold 2,500 ounces of gold for

$1 million. The company had acquired the gold for $900,000 at the beginning of the year. The company

paid cash for the gold when it was purchased. Unfortunately it has yet to collect from the customer to

(continued)

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whom the gold was sold. The following is a standard accounting of Midland’s financial circumstances

at year-end:

T HE M I D LA N D C O M PA N Y

A c c o u n t i n g Vi e w

Income Statement

Ye a r E n d e d D e c e m b e r 31

Sales

⫺Costs

Profit

$1,000,000

⫺900,000

$ 100,000

By generally accepted accounting principles (GAAP), the sale is recorded even though the customer has

yet to pay. It is assumed that the customer will pay soon. From the accounting perspective, Midland seems

to be profitable. However, the perspective of corporate finance is different. It focuses on cash flows:

T HE M I D LA N D C O M PA N Y

Fi n a n c i a l Vi e w

Income Statement

Ye a r E n d e d D e c e m b e r 31

Cash inflow

Cash outflow

$

0

⫺900,000

⫺$ 900,000

The perspective of corporate finance is interested in whether cash flows are being created by the

gold trading operations of Midland. Value creation depends on cash flows. For Midland, value creation

depends on whether and when it actually receives $1 million.

EXAMPLE

1.2

Timing of Cash Flows The value of an investment made by a firm depends on the timing

of cash flows. One of the most important principles of finance is that individuals prefer to

receive cash flows earlier rather than later. One dollar received today is worth more than

one dollar received next year.

C a s h F l o w Ti m i n g

The Midland Company is attempting to choose between two proposals for new products. Both proposals will provide additional cash flows over a four-year period and will initially cost $10,000. The cash

flows from the proposals are as follows:

YE AR

1

2

3

4

Total

NE W P R O D U C T A

$

0

0

0

20,000

$20,000

NEW PRODUCT B

$ 4,000

4,000

4,000

4,000

$16,000

At first it appears that new product A would be best. However, the cash flows from proposal B come

earlier than those of A. Without more information, we cannot decide which set of cash flows would

create the most value for the bondholders and shareholders. It depends on whether the value of getting cash from B up front outweighs the extra total cash from A. Bond and stock prices reflect this

preference for earlier cash, and we will see how to use them to decide between A and B.

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EXAMPLE

1.3

Risk of Cash Flows The firm must consider risk. The amount and timing of cash flows are

not usually known with certainty. Most investors have an aversion to risk.

Risk

The Midland Company is considering expanding operations overseas. It is evaluating Europe and

Japan as possible sites. Europe is considered to be relatively safe, whereas operating in Japan is

seen as very risky. In both cases the company would close down operations after one year.

After doing a complete financial analysis, Midland has come up with the following cash flows of

the alternative plans for expansion under three scenarios—pessimistic, most likely, and optimistic:

Europe

Japan

PESSIMISTIC

MOST LIKELY

OPTIMISTIC

$75,000

0

$100,000

150,000

$125,000

200,000

If we ignore the pessimistic scenario, perhaps Japan is the best alternative. When we take the pessimistic scenario into account, the choice is unclear. Japan appears to be riskier, but it also offers a

higher expected level of cash flow. What is risk and how can it be defined? We must try to answer this

important question. Corporate finance cannot avoid coping with risky alternatives, and much of our

book is devoted to developing methods for evaluating risky opportunities.

1.4

THE GOAL OF FINANCIAL MANAGEMENT

Assuming that we restrict our discussion to for-profit businesses, the goal of financial management is to make money or add value for the owners. This goal is a little vague, of course,

so we examine some different ways of formulating it to come up with a more precise definition. Such a definition is important because it leads to an objective basis for making and

evaluating financial decisions.

Possible Goals

If we were to consider possible financial goals, we might come up with some ideas like the

following:

■

■

■

■

■

■

■

Survive.

Avoid financial distress and bankruptcy.

Beat the competition.

Maximize sales or market share.

Minimize costs.

Maximize profits.

Maintain steady earnings growth.

These are only a few of the goals we could list. Furthermore, each of these possibilities

presents problems as a goal for the financial manager.

For example, it’s easy to increase market share or unit sales: All we have to do is lower

our prices or relax our credit terms. Similarly, we can always cut costs simply by doing

away with things such as research and development. We can avoid bankruptcy by never

borrowing any money or never taking any risks, and so on. It’s not clear that any of these

actions are in the stockholders’ best interests.

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Profit maximization would probably be the most commonly cited goal, but even this is

not a precise objective. Do we mean profits this year? If so, then we should note that actions

such as deferring maintenance, letting inventories run down, and taking other short-run

cost-cutting measures will tend to increase profits now, but these activities aren’t necessarily desirable.

The goal of maximizing profits may refer to some sort of “long-run” or “average”

profits, but it’s still unclear exactly what this means. First, do we mean something like

accounting net income or earnings per share? As we will see in more detail in the next

chapter, these accounting numbers may have little to do with what is good or bad for

the firm. We are actually more interested in cash flows. Second, what do we mean by the

long run? As a famous economist once remarked, in the long run, we’re all dead! More

to the point, this goal doesn’t tell us what the appropriate trade-off is between current

and future profits.

The goals we’ve listed here are all different, but they tend to fall into two classes. The

first of these relates to profitability. The goals involving sales, market share, and cost control all relate, at least potentially, to different ways of earning or increasing profits. The

goals in the second group, involving bankruptcy avoidance, stability, and safety, relate in

some way to controlling risk. Unfortunately, these two types of goals are somewhat contradictory. The pursuit of profit normally involves some element of risk, so it isn’t really

possible to maximize both safety and profit. What we need, therefore, is a goal that encompasses both factors.

The Goal of Financial Management

The financial manager in a corporation makes decisions for the stockholders of the firm.

So, instead of listing possible goals for the financial manager, we really need to answer a

more fundamental question: From the stockholders’ point of view, what is a good financial

management decision?

If we assume that stockholders buy stock because they seek to gain financially, then

the answer is obvious: Good decisions increase the value of the stock, and poor decisions

decrease the value of the stock.

From our observations, it follows that the financial manager acts in the shareholders’

best interests by making decisions that increase the value of the stock. The appropriate goal

for the financial manager can thus be stated quite easily:

The goal of financial management is to maximize the current value per share of the

existing stock.

The goal of maximizing the value of the stock avoids the problems associated with

the different goals we listed earlier. There is no ambiguity in the criterion, and there is

no short-run versus long-run issue. We explicitly mean that our goal is to maximize the

current stock value.

If this goal seems a little strong or one-dimensional to you, keep in mind that the stockholders in a firm are residual owners. By this we mean that they are entitled only to what

is left after employees, suppliers, and creditors (and everyone else with legitimate claims)

are paid their due. If any of these groups go unpaid, the stockholders get nothing. So if the

stockholders are winning in the sense that the leftover, residual portion is growing, it must

be true that everyone else is winning also.

Because the goal of financial management is to maximize the value of the stock, we

need to learn how to identify investments and financing arrangements that favorably impact

the value of the stock. This is precisely what we will be studying. In the previous section we

emphasized the importance of cash flows in value creation. In fact, we could have defined

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corporate finance as the study of the relationship between business decisions, cash flows,

and the value of the stock in the business.

A More General Goal

Business ethics are

considered at

www.business-ethics.

com.

If our goal is as stated in the preceding section (to maximize the value of the stock), an

obvious question comes up: What is the appropriate goal when the firm has no traded

stock? Corporations are certainly not the only type of business; and the stock in many

corporations rarely changes hands, so it’s difficult to say what the value per share is at any

particular time.

As long as we are considering for-profit businesses, only a slight modification is needed.

The total value of the stock in a corporation is simply equal to the value of the owners’

equity. Therefore, a more general way of stating our goal is as follows: Maximize the value

of the existing owners’ equity.

With this in mind, we don’t care whether the business is a proprietorship, a partnership, or a corporation. For each of these, good financial decisions increase the value of

the owners’ equity, and poor financial decisions decrease it. In fact, although we choose to

focus on corporations in the chapters ahead, the principles we develop apply to all forms of

business. Many of them even apply to the not-for-profit sector.

Finally, our goal does not imply that the financial manager should take illegal or unethical actions in the hope of increasing the value of the equity in the firm. What we mean

is that the financial manager best serves the owners of the business by identifying goods

and services that add value to the firm because they are desired and valued in the free

marketplace.

1.5 THE AGENCY PROBLEM AND CONTROL

O F T H E C O R P O R AT I O N

The processes, policies, laws, and institutions that direct a company’s actions are all

included under the broad category of corporate governance. Corporate governance can also

include the relationships among various stakeholders including shareholders, management,

employees, the board of directors, suppliers, and the community at large, among others. As

such, corporate governance is a wide-ranging topic.

We’ve seen that the financial manager acts in the best interests of the stockholders by

taking actions that increase the value of the stock. However, in large corporations, ownership can be spread over a huge number of stockholders. This dispersion of ownership

arguably means that management effectively controls the firm. In this case, will management necessarily act in the best interests of the stockholders? Put another way, might not

management pursue its own goals at the stockholders’ expense?

Corporate governance varies quite a bit around the world. For example, in most countries other than the U.S. and the U.K., publicly traded companies are usually controlled by

one or more large shareholders. Moreover, in countries with limited shareholder protection, when compared to countries with strong shareholder protection like the U.S. and the

U.K., large shareholders may have a greater opportunity to take advantage of minority

shareholders. Research shows that a country’s investor protection framework is important

to understanding a firms’ cash holdings and dividend payouts. For example, studies find

that shareholders do not highly value cash holdings in firms in countries with low investor

protection when compared to firms in the U.S. where investor protection is high.1

1

See, for example, “Investor Protection and Corporate Valuation,” by Rafael La Porta, Florencio Lopez-De-Silanes, Andrei Shleifer,

and Robert Vishny, Journal of Finance 57 (2002), pp. 1147–1170; and “Cash Holdings, Dividend Policy, and Corporate Governance:

A Cross-Country Analysis,” by Lee Pinkowitz, René M. Stulz, and Rohan Williamson, Journal of Applied Corporate Finance, Vol. 19,

No. 1 (2007), pp. 81–87.

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In the basic corporate governance setup, the shareholders elect the board of directors

who in turn appoint the top corporate managers, such as the CEO. The CEO is usually a

member of the board of directors. One aspect of corporate governance that has received

attention recently concerns the chair of a firm’s board of directors. In a large number of

U.S. corporations, the CEO and the board chair are the same person. An argument can be

made that combining the CEO and board chair positions can contribute to poor corporate governance. When comparing the corporate governance of the U.S. and the U.K., an

edge is often given to the U.K. in governance partially because over 90 percent of U.K.

companies are chaired by outside directors rather than the CEO.2 This is a contentious

issue confronting many U.S. corporations. For example, in May 2008, 19 institutional

investors, including some of ExxonMobil’s largest shareholders and members of the

founding Rockefeller family, supported a resolution to split the jobs of CEO and board

chair. About 40 percent of the shareholders voted for the split.

Agency Relationships

The relationship between stockholders and management is called an agency relationship.

Such a relationship exists whenever someone (the principal) hires another (the agent) to

represent his or her interests. For example, you might hire someone (an agent) to sell a car

that you own while you are away at school. In all such relationships there is a possibility

of a conflict of interest between the principal and the agent. Such a conflict is called an

agency problem.

Suppose you hire someone to sell your car and you agree to pay that person a flat fee

when he or she sells the car. The agent’s incentive in this case is to make the sale, not necessarily to get you the best price. If you offer a commission of, say, 10 percent of the sales

price instead of a flat fee, then this problem might not exist. This example illustrates that the

way in which an agent is compensated is one factor that affects agency problems.

Management Goals

To see how management and stockholder interests might differ, imagine that a firm is considering a new investment. The new investment is expected to favorably impact the share

value, but it is also a relatively risky venture. The owners of the firm will wish to take the

investment (because the stock value will rise), but management may not because there is

the possibility that things will turn out badly and management jobs will be lost. If management does not take the investment, then the stockholders may lose a valuable opportunity.

This is one example of an agency cost.

More generally, the term agency costs refers to the costs of the conflict of interest between stockholders and management. These costs can be indirect or direct. An indirect

agency cost is a lost opportunity, such as the one we have just described.

Direct agency costs come in two forms. The first type is a corporate expenditure that

benefits management but costs the stockholders. Perhaps the purchase of a luxurious

and unneeded corporate jet would fall under this heading. The second type of direct

agency cost is an expense that arises from the need to monitor management actions. Paying outside auditors to assess the accuracy of financial statement information could be

one example.

It is sometimes argued that, left to themselves, managers would tend to maximize the

amount of resources over which they have control or, more generally, corporate power or

wealth. This goal could lead to an overemphasis on corporate size or growth. For example,

cases in which management is accused of overpaying to buy up another company just to

2

“U.S. Corporate Governance: Accomplishments and Failings, a Discussion with Michael Jensen and Robert Monks” (moderated

by Ralph Walkling), Journal of Applied Corporate Finance , Vol. 20, No. 1 (Winter 2008), pp. 28–46.

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increase the size of the business or to demonstrate corporate power are not uncommon.

Obviously, if overpayment does take place, such a purchase does not benefit the stockholders of the purchasing company.

Our discussion indicates that management may tend to overemphasize organizational

survival to protect job security. Also, management may dislike outside interference, so

independence and corporate self-sufficiency may be important goals.

Do Managers Act in the Stockholders’ Interests?

Whether managers will, in fact, act in the best interests of stockholders depends on

two factors. First, how closely are management goals aligned with stockholder goals?

This question relates, at least in part, to the way managers are compensated. Second,

can managers be replaced if they do not pursue stockholder goals? This issue relates

to control of the firm. As we will discuss, there are a number of reasons to think that,

even in the largest firms, management has a significant incentive to act in the interests

of stockholders.

Managerial Compensation Management will frequently have a significant economic incentive to increase share value for two reasons. First, managerial compensation, particularly at the top, is usually tied to financial performance in general and often to share value

in particular. For example, managers are frequently given the option to buy stock at a

bargain price. The more the stock is worth, the more valuable is this option. In fact, options

are often used to motivate employees of all types, not just top management. According to

The New York Times, in 2009, Alan Mulally, CEO of Ford Motor, made $1,400,003 in salary

and $16 million in bonuses tied to financial performance. As mentioned, many firms also

give managers an ownership stake in the company by granting stock or stock options. In

2009, the total compensation of Jay L. Johnson, CEO of General Dynamics, was reported

by The New York Times to be $12.8 million. His base salary was $1.1 million with bonuses

of $2.5 million, stock option grants of $5.8 million, and restricted stock grants of

$2.9 million. Although there are many critics of the high level of CEO compensation, from

the stockholders’ point of view, sensitivity of compensation to firm performance is usually

more important.

The second incentive managers have relates to job prospects. Better performers within

the firm will tend to get promoted. More generally, managers who are successful in pursuing stockholder goals will be in greater demand in the labor market and thus command

higher salaries.

In fact, managers who are successful in pursuing stockholder goals can reap enormous

rewards. For example, the best-paid executive in 2008 was Larry Ellison, the CEO of Oracle;

according to The New York Times, he made about $84.5 million. By way of comparison,

J. K. Rowling made $300 million and Rachael Ray made about $18 million. Over the

period of 2004–2008, Ellison made $944 million.3

Control of the firm ultimately rests with stockholders. They elect the

board of directors, who, in turn, hire and fire management.

An important mechanism by which unhappy stockholders can replace existing management is called a proxy fight. A proxy is the authority to vote someone else’s stock. A

proxy fight develops when a group solicits proxies in order to replace the existing board

and thereby replace existing management. In 2002, the proposed merger between HP and

Compaq triggered one of the most widely followed, bitterly contested, and expensive proxy

fights in history, with an estimated price tag of well over $100 million.

Control of the Firm

3

This raises the issue of the level of top management pay and its relationship to other employees. According to The New York

Times, the average CEO compensation was greater than 180 times the average employee compensation in 2007 and only 90 times

in 1994. However, there is no precise formula that governs the gap between top management compensation and that of employees.

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Another way that management can be replaced is by takeover. Firms that are poorly

managed are more attractive as acquisitions than well-managed firms because a greater

profit potential exists. Thus, avoiding a takeover by another firm gives management another

incentive to act in the stockholders’ interests. Unhappy prominent shareholders can suggest different business strategies to a firm’s top management. This was the case with Carl

Icahn and Motorola. Carl Icahn specializes in takeovers. His stake in Motorola reached

7.6 percent ownership in 2008, so he was a particularly important and unhappy shareholder.

This large stake made the threat of a shareholder vote for new board membership and a

takeover more credible. His advice was for Motorola to split its poorly performing handset

mobile phone unit from its home and networks business and create two publicly traded

companies—a strategy the company adopted.

Until recently, proxy fights were fairly rare. For example, from January to October 2009, only 75 proxy contests occurred in the U.S. As the HP/Compaq proxy fight

shows, expenses in a proxy fight can become large, and the cost is often the reason given

for so few proxy fights. Also, outsiders waging the proxy fight must cover their own

expenses, while the current directors use company finances to back their bid to retain

board seats. In October 2009, HealthSouth became the first company to adopt a corporate

bylaw that would reimburse proxy contestants for “reasonable” costs, provided that they

had won at least 40 percent of the votes cast. Although not yet approved by the Securities

and Exchange Commission, these “proxy access” rules are likely to result in more proxy

contests.

The available theory and evidence are consistent with the view that stockholders control the firm and that stockholder wealth maximization is the relevant goal of the

corporation. Even so, there will undoubtedly be times when management goals are pursued

at the expense of the stockholders, at least temporarily.

Conclusion

Stakeholders

Our discussion thus far implies that management and stockholders are the only parties with

an interest in the firm’s decisions. This is an oversimplification, of course. Employees, customers, suppliers, and even the government all have a financial interest in the firm.

Taken together, these various groups are called stakeholders in the firm. In general, a

stakeholder is someone other than a stockholder or creditor who potentially has a claim

on the cash flows of the firm. Such groups will also attempt to exert control over the firm,

perhaps to the detriment of the owners.

1.6

R E G U L AT I O N

Until now, we have talked mostly about the actions that shareholders and boards of directors can take to reduce the conflicts of interest between themselves and management. We

have not talked about regulation.4 Until recently the main thrust of federal regulation has

been to require that companies disclose all relevant information to investors and potential

investors. Disclosure of relevant information by corporations is intended to put all investors

on a level information playing field and, thereby to reduce conflicts of interest. Of course,

regulation imposes costs on corporations and any analysis of regulation must include both

benefits and costs. Our nearby The Real World box discusses some of the costs exchangelisted companies face arising from disclosure requirements.

4

At this stage in our book, we focus on the regulation of corporate governance. We do not talk about many other regulators in financial markets such as the Federal Reserve Board. In Chapter 8, we discuss the nationally recognized statistical rating organizations

(NRSROs) in the U.S. They are Fitch Ratings, Moody’s, and Standard & Poor’s. Their ratings are used by market participants to help

value securities such as corporate bonds. Many critics of the rating agencies blame the 2007–2009 subprime credit crisis on weak

regulatory oversight of these agencies.

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THE REAL WORLD

SARBANES-OXLEY

In response to corporate scandals at companies such as Enron, WorldCom, Tyco, and Adelphia, Congress enacted

the Sarbanes-Oxley Act in 2002. The act, better known as “Sarbox,” is intended to protect investors from corporate

abuses. For example, one section of Sarbox prohibits personal loans from a company to its officers, such as the

ones that were received by WorldCom CEO Bernie Ebbers.

One of the key sections of Sarbox took effect on November 15, 2004. Section 404 requires, among other things,

that each company’s annual report must have an assessment of the company’s internal control structure and financial reporting. The auditor must then evaluate and attest to management’s assessment of these issues.

Sarbox contains other key requirements. For example, the officers of the corporation must review and sign the

annual reports. They must explicitly declare that the annual report does not contain any false statements or material omissions; that the financial statements fairly represent the financial results; and that they are responsible for

all internal controls. Finally, the annual report must list any deficiencies in internal controls. In essence, Sarbox

makes company management responsible for the accuracy of the company’s financial statements.

Of course, as with any law, there are costs. Sarbox has increased the expense of corporate audits, sometimes

dramatically. In 2004, the average compliance cost was $ 4.51 million. By 2007, the average compliance cost had

fallen to $1.7 million, so the burden seems to be dropping, but it is still not trivial, particularly for a smaller firm. This

added expense has led to several unintended results. For example, in 2003, 198 firms delisted their shares from exchanges, or “went dark,” and about the same number delisted in 2004. Both numbers were up from 30 delistings in

1999. Many of the companies that delisted stated the reason was to avoid the cost of compliance with Sarbox. And

not only small companies delist because of Sarbox; in September 2009, German insurer Allianz applied to delist its

shares from the New York Stock Exchange. The company estimated that canceling its listings outside of its home

exchange of Frankfurt could save 5 million euros ($ 8.1 million) per year.

A company that goes dark does not have to file quarterly or annual reports. Annual audits by independent auditors are not required, and executives do not have to certify the accuracy of the financial statements, so the savings

can be huge. Of course, there are costs. Stock prices typically fall when a company announces it is going dark.

Further, such companies will typically have limited access to capital markets and usually will have a higher interest

cost on bank loans.

Sarbox has also probably affected the number of companies choosing to go public in the United States. For

example, when Peach Holdings, based in Boynton Beach, Florida, decided to go public in 2006, it shunned the

U.S. stock markets, instead choosing the London Stock Exchange’s Alternative Investment Market (AIM). To go

public in the United States, the firm would have paid a $100,000 fee, plus about $2 million to comply with Sarbox.

Instead, the company spent only $500,000 on its AIM stock offering. Overall, the European exchanges had a record

year in 2006, with 651 companies going public, while the U.S. exchanges had a lackluster year, with 224 companies

going public.

The Securities Act of 1933 and the Securities

Exchange Act of 1934

The Securities Act of 1933 (the 1933 Act) and the Securities Exchange Act of 1934 (the

1934 Act) provide the basic regulatory framework in the United States for the public trading of securities.

The 1933 Act focuses on the issuing of new securities. Basically, the 1933 Act requires

a corporation to file a registration statement with the Securities and Exchange Commission (SEC) that must be made available to every buyer of a new security. The intent

of the registration statement is to provide potential stockholders with all the necessary

information to make a reasonable decision. The 1934 Act extends the disclosure requirements of the 1933 Act to securities trading in markets after they have been issued. The

1934 Act establishes the SEC and covers a large number of issues including corporate

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reporting, tender offers, and insider trading. The 1934 Act requires corporations to file

reports to the SEC on an annual basis (Form 10K), on a quarterly basis (Form 10Q), and

on a monthly basis (Form 8K).

As mentioned, the 1934 Act deals with the important issue of insider trading. Illegal

insider trading occurs when any person who has acquired nonpublic, special information

(i.e., inside information) buys or sells securities based upon that information. One section

of the 1934 Act deals with insiders such as directors, officers, and large shareholders, while

another deals with any person who has acquired inside information. The intent of these sections of the 1934 Act is to prevent insiders or persons with inside information from taking

unfair advantage of this information when trading with outsiders.

To illustrate, suppose you learned that ABC firm was about to publicly announce that

it had agreed to be acquired by another firm at a price significantly greater than its current

price. This is an example of inside information. The 1934 Act prohibits you from buying

ABC stock from shareholders who do not have this information. This prohibition would

be especially strong if you were the CEO of the ABC firm. Other kinds of a firm’s inside

information could be knowledge of an initial dividend about to be paid, the discovery of a

drug to cure cancer, or the default of a debt obligation.

A recent example of insider trading involved Raj Rajaratnam, founder of the Galleon

Group, a hedge fund that managed more than $7 billion. Rajaratnam was arrested in October 2009 on insider trading charges involving several public companies. For example, he

was accused of receiving inside information regarding Intel Capital’s decision to invest in

Clearwire before the investment was made public. Conversations between Rajaratnam and

Rajiv Goel, managing director at Intel Capital, included a discussion of the future price of

Clearwire and whether Intel would provide additional capital to the company.

SUMMARY AND CONCLUSIONS

This chapter introduced you to some of the basic ideas in corporate finance:

1. Corporate finance has three main areas of concern:

a. Capital budgeting: What long-term investments should the firm take?

b. Capital structure: Where will the firm get the short-term and long-term financing to pay for its

investments? Also, what mixture of debt and equity should it use to fund operations?

c. Working capital management: How should the firm manage its everyday financial

activities?

2. The goal of financial management in a for-profit business is to make decisions that increase the

value of the stock, or, more generally, increase the value of the equity.

3. The corporate form of organization is superior to other forms when it comes to raising money

and transferring ownership interests, but it has the significant disadvantage of double taxation.

4. There is the possibility of conflicts between stockholders and management in a large

corporation. We called these conflicts agency problems and discussed how they might be

controlled and reduced.

5. The advantages of the corporate form are enhanced by the existence of financial markets.

Of the topics we’ve discussed thus far, the most important is the goal of financial management: maximizing the value of the stock. Throughout the text we will be analyzing many different financial decisions, but we will always ask the same question: How does the decision under consideration affect

the value of the stock?

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CONCEPT QUESTIONS

1. Forms of Business What are the three basic legal forms of organizing a business? What are

the advantages and disadvantages of each? What business form do most start-up companies

take? Why?

2. Goal of Financial Management What goal should always motivate the actions of the firm’s

financial manager?

3. Agency Problems Who owns a corporation? Describe the process whereby the owners

control the firm’s management. What is the main reason that an agency relationship

exists in the corporate form of organization? In this context, what kinds of problems can

arise?

4. Not-for-Profit Firm Goals Suppose you were the financial manager of a not-for-profit

business (a not-for-profit hospital, perhaps). What kinds of goals do you think would be

appropriate?

5. Goal of the Firm Evaluate the following statement: Managers should not focus on the current

stock value because doing so will lead to an overemphasis on short-term profits at the expense

of long-term profits.

6. Ethics and Firm Goals Can our goal of maximizing the value of the stock conflict with other

goals, such as avoiding unethical or illegal behavior? In particular, do you think subjects

like customer and employee safety, the environment, and the general good of society fit in this

framework, or are they essentially ignored? Try to think of some specific scenarios to illustrate

your answer.

7. International Firm Goal Would our goal of maximizing the value of the stock be different if we

were thinking about financial management in a foreign country? Why or why not?

8. Agency Problems Suppose you own stock in a company. The current price per share is $25.

Another company has just announced that it wants to buy your company and will pay $35 per

share to acquire all the outstanding stock. Your company’s management immediately begins

fighting off this hostile bid. Is management acting in the shareholders’ best interests? Why or

why not?

9. Agency Problems and Corporate Ownership Corporate ownership varies around the world.

Historically, individuals have owned the majority of shares in public corporations in the United

States. In Germany and Japan, however, banks, other large financial institutions, and other

companies own most of the stock in public corporations. Do you think agency problems are

likely to be more or less severe in Germany and Japan than in the United States? Why? In recent

years, large financial institutions such as mutual funds and pension funds have been becoming

the dominant owners of stock in the United States, and these institutions are becoming more

active in corporate affairs. What are the implications of this trend for agency problems and

corporate control?

10. Executive Compensation Critics have charged that compensation to top management in the

United States is simply too high and should be cut back. For example, focusing on large corporations, Ray Irani of Occidental Petroleum has been one of the best compensated CEOs in the United

States, earning about $223 million in 2008 alone and $744 million over the 2004–2008 period. Are

such amounts excessive? In answering, it might be helpful to recognize that superstar athletes

such as Tiger Woods, top people in entertainment such as Oprah Winfrey and Jerry Bruckheimer,

and many others at the peak of their respective fields can earn at least as much, if not a great

deal more.

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W H AT ’ S O N T H E W E B ?

1. Listing Requirements This chapter discussed some of the listing requirements for the NYSE

and NASDAQ. Find the complete listing requirements for the New York Stock Exchange at

www.nyse.com and NASDAQ at www.nasdaq.com. Which exchange has more stringent listing

requirements? Why don’t the exchanges have the same listing requirements?

2. Business Formation As you may (or may not) know, many companies incorporate in Delaware

for a variety of reasons. Visit Bizfilings at www.bizfilings.com to find out why. Which state

has the highest fee for incorporation? For an LLC? While at the site, look at the FAQ section

regarding corporations and LLCs.

In 1969, Tom Warren founded East Coast Yachts. The company’s operations are located near Hilton

Head Island, South Carolina, and the company is structured as a sole proprietorship. The company

has manufactured custom midsize, high-performance yachts for clients, and its products have received high reviews for safety and reliability. The company’s yachts have also recently received the

highest award for customer satisfaction. The yachts are primarily purchased by wealthy individuals

for pleasure use, Occasionally, a yacht is manufactured for purchase by a company for business

purposes.

The custom yacht industry is fragmented, with a number of manufacturers. As with any industry,

there are market leaders, but the diverse nature of the industry ensures that no manufacturer dominates the market. The competition in the market, as well as the product cost, ensures that attention

to detail is a necessity. For instance, East Coast Yachts will spend 80 to 100 hours on hand-buffing the

stainless steel stem-iron, which is the metal cap on the yacht’s bow that conceivably could collide

with a dock or another boat.

Several years ago, Tom retired from the day-to-day operations of the company and turned the

operations of the company over to his daughter, Larissa. Because of the dramatic changes in the

company, Larissa has approached you to help manage and direct the company’s growth. Specifically,

she has asked you to answer the following questions.

CLOSING CASE

E A S T C O A S T YA C H T S

1. What are the advantages and disadvantages of changing the company organization from a sole

proprietorship to an LLC?

2. What are the advantages and disadvantages of changing the company organization from a sole

proprietorship to a corporation?

3. Ultimately, what action would you recommend the company undertake? Why?

CHAPTER 1 Introduction to Corporate Finance

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CHAPTER

2

Financial Statements

and Cash Flow

OPENING CASE

I

n November 2009, mortgage giant Fannie Mae announced that it was reviewing a potential writeoff of $5.2 billion in low-income housing tax credits. A so-called write-off occurs when a company

decides that the reported value of one or more of its assets is too high and needs to be reduced

to more accurately represent the company’s finances. In Fannie Mae’s case, the write-off came

about because Fannie Mae owned potentially valuable tax credits, but the company was unlikely

to be profitable enough to use them, so their value was overstated. Fannie Mae’s case was unique

because the Treasury Department would not allow Fannie Mae to sell the tax credits, an option the

company had explored.

While Fannie Mae’s write-off is large, the record holder is media giant Time Warner, which took a

charge of $45.5 billion in the fourth quarter of 2002. This enormous write-off followed an earlier, even

larger, charge of $54 billion.

So, did the stockholders in these companies lose billions of dollars when these assets were written off? Fortunately for them, the answer is probably not. Understanding why ultimately leads us to

the main subject of this chapter, that all-important substance known as cash flow.

2.1

THE BALANCE SHEET

The balance sheet is an accountant’s snapshot of the firm’s accounting value on a particular

date, as though the firm stood momentarily still. The balance sheet has two sides: On the

left are the assets and on the right are the liabilities and stockholders’ equity. The balance

sheet states what the firm owns and how it is financed. The accounting definition that underlies the balance sheet and describes the balance is

Assets ⬅ Liabilities Stockholders’ equity

We have put a three-line equality in the balance equation to indicate that it must always

hold, by definition. In fact, the stockholders’ equity is defined to be the difference between

the assets and the liabilities of the firm. In principle, equity is what the stockholders would

have remaining after the firm discharged its obligations.

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TABLE 2.1

The Balance Sheet of the U.S. Composite Corporation

U . S . C O M P O S I T E C O R P O R AT I O N

Balance Sheet

2009 a n d 2010

( i n $ m i l l i o n s)

ASSE T S

Current assets:

Cash and equivalents

Accounts receivable

Inventories

Other

Total current assets

Fixed assets:

Property, plant, and equipment

Less accumulated depreciation

Net property, plant, and equipment

Intangible assets and others

Total fixed assets

2009

2010

$ 107

270

280

50

$ 707

$ 140

294

269

58

$ 761

$ 1,274

460

$ 814

221

$ 1,035

$1,423

550

$ 873

245

$1,118

LI A B I LI T I E S ( D E B T ) A N D

S T O C K H O LD E R S ’ E Q U I T Y

2009

2010

Current liabilities:

Accounts payable

Notes payable

Accrued expenses

Total current liabilities

$ 197

53

205

$ 455

$ 213

50

223

$ 486

Long-term liabilities:

Deferred taxes

Long-term debt*

Total long-term liabilities

$ 104

458

$ 562

$ 117

471

$ 588

$

39

32

327

347

20

$ 725

$

$1,742

$1,879

Stockholders’ equity:

Preferred stock

Common stock ($1 par value)

Capital surplus

Accumulated retained earnings

Less treasury stock†

Total equity

Total assets

$1,742

$1,879

Total liabilities and

stockholders’ equity‡

39

55

347

390

26

$ 805

*Long-term debt rose by $471 million 458 million $13 million. This is the difference between $86 million new debt and $73 million in retirement of old debt.

†

Treasury stock rose by $6 million. This reflects the repurchase of $6 million of U.S. Composite’s company stock.

‡

U.S. Composite reports $43 million in new equity. The company issued 23 million shares at a price of $1.87. The par value of common stock increased by $23 million,

and capital surplus increased by $20 million.

Table 2.1 gives the 2009 and 2010 balance sheets for the fictitious U.S. Composite

Corporation. The assets in the balance sheet are listed in order by the length of time it

normally would take an ongoing firm to convert them to cash. The asset side depends on

the nature of the business and how management chooses to conduct it. Management must

make decisions about cash versus marketable securities, credit versus cash sales, whether

to make or buy commodities, whether to lease or purchase items, the types of business in

which to engage, and so on. The liabilities and the stockholders’ equity are listed in the

order in which they would typically be paid over time.

The liabilities and stockholders’ equity side reflects the types and proportions of financing, which depend on management’s choice of capital structure, as between debt and equity

and between current debt and long-term debt.

When analyzing a balance sheet, the financial manager should be aware of three concerns: accounting liquidity, debt versus equity, and value versus cost.

Two excellent sources

for company financial

information are

finance.yahoo.com and

money.cnn.com.

Accounting Liquidity

Accounting liquidity refers to the ease and quickness with which assets can be converted

to cash. Current assets are the most liquid and include cash and those assets that will be

turned into cash within a year from the date of the balance sheet. Accounts receivable are

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Annual and quarterly

financial statements

for most public U.S.

corporations can be

found in the EDGAR

database at

www.sec.gov.

amounts not yet collected from customers for goods or services sold to them (after adjustment for potential bad debts). Inventory is composed of raw materials to be used in production, work in process, and finished goods. Fixed assets are the least liquid kind of assets.

Tangible fixed assets include property, plant, and equipment. These assets do not convert

to cash from normal business activity, and they are not usually used to pay expenses such

as payroll.

Some fixed assets are not tangible. Intangible assets have no physical existence but can

be very valuable. Examples of intangible assets are the value of a trademark or the value of

a patent. The more liquid a firm’s assets, the less likely the firm is to experience problems

meeting short-term obligations. Thus, the probability that a firm will avoid financial distress can be linked to the firm’s liquidity. Unfortunately, liquid assets frequently have lower

rates of return than fixed assets; for example, cash generates no investment income. To the

extent a firm invests in liquid assets, it sacrifices an opportunity to invest in more profitable

investment vehicles.

Debt versus Equity

Liabilities are obligations of the firm that require a payout of cash within a stipulated time

period. Many liabilities involve contractual obligations to repay a stated amount and interest over a period. Thus, liabilities are debts and are frequently associated with nominally

fixed cash burdens, called debt service, that put the firm in default of a contract if they are

not paid. Stockholders’ equity is a claim against the firm’s assets that is residual and not

fixed. In general terms, when the firm borrows, it gives the bondholders first claim on the

firm’s cash flow.1 Bondholders can sue the firm if the firm defaults on its bond contracts.

This may lead the firm to declare itself bankrupt. Stockholders’ equity is the residual difference between assets and liabilities:

Assets Liabilities ⬅ Stockholders’ equity

This is the stockholders’ share in the firm stated in accounting terms. The accounting value

of stockholders’ equity increases when retained earnings are added. This occurs when the

firm retains part of its earnings instead of paying them out as dividends.

The home page for the

Financial Accounting

Standards Board

(FASB) is

www.fasb.org.

Value versus Cost

The accounting value of a firm’s assets is frequently referred to as the carrying value or

the book value of the assets.2 Under generally accepted accounting principles (GAAP),

audited financial statements of firms in the United States carry the assets at cost.3 Thus the

terms carrying value and book value are unfortunate. They specifically say “value,” when

in fact the accounting numbers are based on cost. This misleads many readers of financial

statements to think that the firm’s assets are recorded at true market values. Market value

is the price at which willing buyers and sellers would trade the assets. It would be only a

coincidence if accounting value and market value were the same. In fact, management’s job

is to create value for the firm that exceeds its cost.

Many people use the balance sheet, but the information each may wish to extract is not

the same. A banker may look at a balance sheet for evidence of accounting liquidity and

working capital. A supplier may also note the size of accounts payable and therefore the

1

Bondholders are investors in the firm’s debt. They are creditors of the firm. In this discussion, the term bondholder means the

same thing as creditor.

2

Confusion often arises because many financial accounting terms have the same meaning. This presents a problem with jargon

for the reader of financial statements. For example, the following terms usually refer to the same thing: assets minus liabilities, net

worth, stockholders’ equity, owners’ equity, book equity, and equity capitalization.

3

Generally, GAAP require assets to be carried at the lower of cost or market value. In most instances, cost is lower than market

value. However, in some cases when a fair market value can be readily determined, the assets have their value adjusted to the

fair market value.

22

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EXAMPLE

2.1

general promptness of payments. Many users of financial statements, including managers

and investors, want to know the value of the firm, not its cost. This information is not found

on the balance sheet. In fact, many of the true resources of the firm do not appear on the

balance sheet: good management, proprietary assets, favorable economic conditions, and

so on. Henceforth, whenever we speak of the value of an asset or the value of the firm, we

will normally mean its market value. So, for example, when we say the goal of the financial

manager is to increase the value of the stock, we mean the market value of the stock.

Market Value versus Book Value

The Cooney Corporation has fixed assets with a book value of $700 and an appraised market value of

about $1,000. Net working capital is $400 on the books, but approximately $600 would be realized if all

the current accounts were liquidated. Cooney has $500 in long-term debt, both book value and market

value. What is the book value of the equity? What is the market value?

We can construct two simplified balance sheets, one in accounting (book value) terms and one in

economic (market value) terms:

COO N E Y C O R P O R AT I O N

Balance Sheets

M a r k e t Va l u e ve r su s B o o k Va l u e

As s e t s

Net working capital

Net fixed assets

BOOK

M ARK E T

$ 400

700

$1,100

$ 600

1,000

$1,600

Li a b i l i t i e s a n d S h a r e h o l d e r s’ E q u i t y

Long-term debt

Shareholders’ equity

BOOK

MARKET

$ 500

600

$1,100

$ 500

1,100

$1,600

In this example, shareholders’ equity is actually worth almost twice as much as what is shown on the

books. The distinction between book and market values is important precisely because book values

can be so different from true economic value.

2.2

T H E I N C O M E S TAT E M E N T

The income statement measures performance over a specific period of time, say, a year.

The accounting definition of income is:

Revenue Expenses ⬅ Income

If the balance sheet is like a snapshot, the income statement is like a video recording of

what the people did between two snapshots. Table 2.2 gives the income statement for the

U.S. Composite Corporation for 2010.

The income statement usually includes several sections. The operations section reports

the firm’s revenues and expenses from principal operations. One number of particular importance is earnings before interest and taxes (EBIT), which summarizes earnings before

taxes and financing costs. Among other things, the nonoperating section of the income

statement includes all financing costs, such as interest expense. Usually a second section

reports as a separate item the amount of taxes levied on income. The last item on the income statement is the bottom line, or net income. Net income is frequently expressed per

share of common stock, that is, earnings per share.

CHAPTER 2 Financial Statements and Cash Flow

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TABLE 2.2

U . S . C O M P O S I T E C O R P O R AT I O N

Income Statement

2010

( i n $ m i l l i o n s)

The Income Statement

of the U.S. Composite

Corporation

Total operating revenues

Cost of goods sold

Selling, general, and administrative expenses

Depreciation

Operating income

Other income

Earnings before interest and taxes (EBIT)

Interest expense

Pretax income

Taxes

Current: $71

Deferred: $13

Net income

Addition to retained earnings:

Dividends:

$2,262

1,655

327

90

$ 190

29

$ 219

49

$ 170

84

$

$

86

43

43

Note: There are 29 million shares outstanding. Earnings per share and dividends per share can be calculated as follows:

Net income

Earnings per share ____________________

Total shares outstanding

$86

___

29

$2.97 per share

Dividends

Dividends per share ____________________

Total shares outstanding

$43

___

29

$1.48 per share

When analyzing an income statement, the financial manager should keep in mind GAAP,

noncash items, time, and costs.

Generally Accepted Accounting Principles

Revenue is recognized on an income statement when the earnings process is virtually

completed and an exchange of goods or services has occurred. Therefore, the unrealized

appreciation from owning property will not be recognized as income. This provides a

device for smoothing income by selling appreciated property at convenient times. For

example, if the firm owns a tree farm that has doubled in value, then, in a year when its

earnings from other businesses are down, it can raise overall earnings by selling some

trees. The matching principle of GAAP dictates that revenues be matched with expenses.

Thus, income is reported when it is earned, or accrued, even though no cash flow has

necessarily occurred (for example, when goods are sold for credit, sales and profits are

reported).

Noncash Items

The economic value of assets is intimately connected to their future incremental cash flows.

However, cash flow does not appear on an income statement. There are several noncash

items that are expenses against revenues, but that do not affect cash flow. The most important of these is depreciation. Depreciation reflects the accountant’s estimate of the cost of

24

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equipment used up in the production process. For example, suppose an asset with a fiveyear life and no resale value is purchased for $1,000. According to accountants, the $1,000

cost must be expensed over the useful life of the asset. If straight-line depreciation is used,

there will be five equal installments and $200 of depreciation expense will be incurred each

year. From a finance perspective, the cost of the asset is the actual negative cash flow incurred when the asset is acquired (that is, $1,000, not the accountant’s smoothed $200-peryear depreciation expense).

Another noncash expense is deferred taxes. Deferred taxes result from differences between accounting income and true taxable income.4 Notice that the accounting tax shown

on the income statement for the U.S. Composite Corporation is $84 million. It can be broken down as current taxes and deferred taxes. The current tax portion is actually sent to the

tax authorities (for example, the Internal Revenue Service). The deferred tax portion is not.

However, the theory is that if taxable income is less than accounting income in the current

year, it will be more than accounting income later on. Consequently, the taxes that are not

paid today will have to be paid in the future, and they represent a liability of the firm. This

shows up on the balance sheet as deferred tax liability. From the cash flow perspective,

though, deferred tax is not a cash outflow.

In practice, the difference between cash flows and accounting income can be quite dramatic, so it is important to understand the difference. For example, Sirius XM Radio reported a net loss of about $413 million for the third quarter of 2009. That sounds bad, but

Sirius XM also reported a positive cash flow of $116 million from operating activities for

the same quarter!

Time and Costs

It is often useful to think of all of future time as having two distinct parts, the short run

and the long run. The short run is that period of time in which certain equipment, resources, and commitments of the firm are fixed; but the time is long enough for the firm

to vary its output by using more labor and raw materials. The short run is not a precise

period of time that will be the same for all industries. However, all firms making decisions in the short run have some fixed costs, that is, costs that will not change because of

fixed commitments. In real business activity, examples of fixed costs are bond interest,

overhead, and property taxes. Costs that are not fixed are variable. Variable costs change

as the output of the firm changes; some examples are raw materials and wages for laborers

on the production line.

In the long run, all costs are variable. Financial accountants do not distinguish between

variable costs and fixed costs. Instead, accounting costs usually fit into a classification that

distinguishes product costs from period costs. Product costs are the total production costs

incurred during a period—raw materials, direct labor, and manufacturing overhead—and

are reported on the income statement as cost of goods sold. Both variable and fixed costs

are included in product costs. Period costs are costs that are allocated to a time period;

they are called selling, general, and administrative expenses. One period cost would be the

company president’s salary.

2.3

TA X E S

Taxes can be one of the largest cash outflows that a firm experiences. For example,

for the fiscal year 2009, ExxonMobil’s earnings before taxes were about $34.8 billion.

Its tax bill, including all taxes paid worldwide, was a whopping $15.1 billion, or about

43.4 percent of its pretax earnings. The size of the tax bill is determined through the tax

4

One situation in which taxable income may be lower than accounting income is when the firm uses accelerated depreciation

expense procedures for the IRS but uses straight-line procedures allowed by GAAP for reporting purposes.

CHAPTER 2 Financial Statements and Cash Flow

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TABLE 2.3

TAXA B LE I N C O M E

TA X R AT E

Corporate Tax Rates

$

0–50,000

50,001–75,000

75,001–100,000

100,001–335,000

335,001–10,000,000

10,000,001–15,000,000

15,000,001–18,333,333

18,333,334

15%

25

34

39

34

35

38

35

code, an often amended set of rules. In this section, we examine corporate tax rates and

how taxes are calculated.

If the various rules of taxation seem a little bizarre or convoluted to you, keep in mind

that the tax code is the result of political, not economic, forces. As a result, there is no reason why it has to make economic sense.

Corporate Tax Rates

Corporate tax rates in effect for 2010 are shown in Table 2.3. A peculiar feature of

taxation instituted by the Tax Reform Act of 1986 and expanded in the 1993 Omnibus

Budget Reconciliation Act is that corporate tax rates are not strictly increasing. As

shown, corporate tax rates rise from 15 percent to 39 percent, but they drop back to

34 percent on income over $335,000. They then rise to 38 percent and subsequently fall

to 35 percent.

According to the originators of the current tax rules, there are only four corporate rates:

15 percent, 25 percent, 34 percent, and 35 percent. The 38 and 39 percent brackets arise

because of “surcharges” applied on top of the 34 and 35 percent rates. A tax is a tax is a tax,

however, so there are really six corporate tax brackets, as we have shown.

Average versus Marginal Tax Rates

In making financial decisions, it is frequently important to distinguish between average and marginal tax rates. Your average tax rate is your tax bill divided by your

taxable income, in other words, the percentage of your income that goes to pay taxes.

Your marginal tax rate is the tax you would pay (in percent) if you earned one

more dollar. The percentage tax rates shown in Table 2.3 are all marginal rates. Put

another way, the tax rates apply to the part of income in the indicated range only, not

all income.

The difference between average and marginal tax rates can best be illustrated with a

simple example. Suppose our corporation has a taxable income of $200,000. What is the

tax bill? Using Table 2.3, we can figure our tax bill as:

.15($ 50,000)

$ 7,500

.25($ 75,000 50,000)

6,250

.34($100,000 75,000)

8,500

.39($200,000 100,000) 39,000

$61,250

The IRS has a great

Web site!

(www.irs.gov)

26

Our total tax is thus $61,250.

In our example, what is the average tax rate? We had a taxable income of $200,000 and

a tax bill of $61,250, so the average tax rate is $61,250/200,000 30.625%. What is the

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EXAMPLE

2.2

marginal tax rate? If we made one more dollar, the tax on that dollar would be 39 cents, so

our marginal rate is 39 percent.

D e e p i n t h e H e a r t o f Ta x e s

Algernon, Inc., has a taxable income of $85,000. What is its tax bill? What is its average tax rate? Its

marginal tax rate?

From Table 2.3, we see that the tax rate applied to the first $50,000 is 15 percent; the rate applied to

the next $25,000 is 25 percent, and the rate applied after that up to $100,000 is 34 percent. So Algernon

must pay .15 $50,000 .25 25,000 .34 (85,000 75,000) $17,150. The average tax rate is

thus $17,150/85,000 20.18%. The marginal rate is 34 percent because Algernon’s taxes would rise by

34 cents if it had another dollar in taxable income.

Table 2.4 summarizes some different taxable incomes, marginal tax rates, and average

tax rates for corporations. Notice how the average and marginal tax rates come together at

35 percent.

With a flat-rate tax, there is only one tax rate, so the rate is the same for all income

levels. With such a tax, the marginal tax rate is always the same as the average tax rate. As

it stands now, corporate taxation in the United States is based on a modified flat-rate tax,

which becomes a true flat rate for the highest incomes.

In looking at Table 2.4, notice that the more a corporation makes, the greater is the

percentage of taxable income paid in taxes. Put another way, under current tax law, the average tax rate never goes down, even though the marginal tax rate does. As illustrated, for

corporations, average tax rates begin at 15 percent and rise to a maximum of 35 percent.

It will normally be the marginal tax rate that is relevant for financial decision making.

The reason is that any new cash flows will be taxed at that marginal rate. Because financial

decisions usually involve new cash flows or changes in existing ones, this rate will tell us

the marginal effect of a decision on our tax bill.

There is one last thing to notice about the tax code as it affects corporations. It’s easy

to verify that the corporate tax bill is just a flat 35 percent of taxable income if our taxable

income is more than $18.33 million. Also, for the many midsize corporations with taxable

incomes in the range of $335,000 to $10,000,000, the tax rate is a flat 34 percent. Because

we will normally be talking about large corporations, you can assume that the average and

marginal tax rates are 35 percent unless we explicitly say otherwise.

Before moving on, we should note that the tax rates we have discussed in this section

relate to federal taxes only. Overall tax rates can be higher once state, local, and any other

taxes are considered.

(1)

TAX ABL E I NCOM E

$

45,000

70,000

95,000

250,000

1,000,000

17,500,000

50,000,000

100,000,000

(2)

M ARGI NAL TA X R AT E

15%

25

34

39

34

38

35

35

( 3)

T O TA L TA X

$

6,750

12,500

20,550

80,750

340,000

6,100,000

17,500,000

35,000,000

( 3) / ( 1)

AV E R A G E TA X R AT E

TABLE 2.4

Corporate Taxes

and Tax Rates

15.00%

17.86

21.63

32.30

34.00

34.86

35.00

35.00

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2.4

N E T W O R K I N G C A P I TA L

Net working capital is current assets minus current liabilities. Net working capital is positive when current assets are greater than current liabilities. This means the cash that will

become available over the next 12 months will be greater than the cash that must be paid

out. The net working capital of the U.S. Composite Corporation is $275 million in 2010

and $252 million in 2009:

Current assets

($ millions)

Current liabilities

($ millions)

Net working capital

($ millions)

2010

$761

$486

$275

2009

707

455

252

In addition to investing in fixed assets (i.e., capital spending), a firm can invest in net working capital. This is called the change in net working capital. The change in net working

capital in 2010 is the difference between the net working capital in 2010 and 2009; that is,

$275 million 252 million $23 million. The change in net working capital is usually

positive in a growing firm.

2.5

FINANCIAL CASH FLOW

Perhaps the most important item that can be extracted from financial statements is the actual cash flow of the firm. There is an official accounting statement called the statement of

cash flows. This statement helps to explain the change in accounting cash and equivalents,

which for U.S. Composite is $33 million in 2010. (See Section 2.6.) Notice in Table 2.1 that

cash and equivalents increase from $107 million in 2009 to $140 million in 2010. However,

we will look at cash flow from a different perspective, the perspective of finance. In finance,

the value of the firm is its ability to generate financial cash flow. (We will talk more about

financial cash flow in Chapter 8.)

The first point we should mention is that cash flow is not the same as net working capital. For example, increasing inventory requires using cash. Because both inventories and

cash are current assets, this does not affect net working capital. In this case, an increase in

a particular net working capital account, such as inventory, is associated with decreasing

cash flow.

Just as we established that the value of a firm’s assets is always equal to the value of the

liabilities and the value of the equity, the cash flows received from the firm’s assets (that

is, its operating activities), CF(A), must equal the cash flows to the firm’s creditors, CF(B),

and equity investors, CF(S):

CF(A) ⬅ CF(B) CF(S)

The first step in determining cash flows of the firm is to figure out the cash flow from

operations. As can be seen in Table 2.5, operating cash flow is the cash flow generated by

business activities, including sales of goods and services. Operating cash flow reflects tax

payments, but not financing, capital spending, or changes in net working capital.

I N $ M I LLI O N S

Earnings before interest and taxes

Depreciation

Current taxes

Operating cash flow

$219

90

71

$238

Another important component of cash flow involves changes in fixed assets. For example,

when U.S. Composite sold its power systems subsidiary in 2010, it generated $25 in

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TABLE 2.5

U.S. COM P O S I T E C O R P O R AT I O N

F i na n c i a l C a sh Fl o w

2010

( i n $ m i l l i o n s)

Financial Cash Flow

of the U.S. Composite

Corporation

Cash Flow of the Firm

Operating cash flow

(Earnings before interest and taxes plus depreciation minus taxes)

Capital spending

(Acquisitions of fixed assets minus sales of fixed assets)

Additions to net working capital

Total

$238

173

23

$ 42

Cash Flow to Investors in the Firm

Debt

(Interest plus retirement of debt minus long-term debt financing)

Equity

(Dividends plus repurchase of equity minus new equity financing)

Total

$ 36

6

$ 42

cash flow. The net change in fixed assets equals the acquisition of fixed assets minus sales

of fixed assets. The result is the cash flow used for capital spending:

Acquisition of fixed assets

Sales of fixed assets

Capital spending

$198

25

$173

($149 24 Increase in property,

plant, and equipment Increase

in intangible assets)

We can also calculate capital spending simply as:

Capital spending Ending net fixed assets Beginning net fixed assets

Depreciation

$1,118 1,035 90

$173

Cash flows are also used for making investments in net working capital. In U.S. Composite Corporation in 2010, additions to net working capital are:

Additions to net working capital

$23

Note that this $23 is the change in net working capital we previously calculated.

Total cash flows generated by the firm’s assets are the sum of:

Operating cash flow

Capital spending

Additions to net working capital

Total cash flow of the firm

$238

173

23

$ 42

The total outgoing cash flow of the firm can be separated into cash flow paid to creditors

and cash flow paid to stockholders. The cash flow paid to creditors represents a regrouping

of the data in Table 2.5 and an explicit recording of interest expense. Creditors are paid an

amount generally referred to as debt service. Debt service is interest payments plus repayments of principal (that is, retirement of debt).

An important source of cash flow is the sale of new debt. U.S. Composite’s longterm debt increased by $13 million (the difference between $86 million in new debt and

CHAPTER 2 Financial Statements and Cash Flow

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$73 million in retirement of old debt).5 Thus, an increase in long-term debt is the net effect

of new borrowing and repayment of maturing obligations plus interest expense.

C A S H FLO W PA I D T O C R E D I T O R S

( i n $ m i l l i o n s)

Interest

Retirement of debt

Debt service

Proceeds from long-term debt sales

Total

$ 49

73

122

86

$ 36

Cash flow paid to creditors can also be calculated as:

Cash flow paid to creditors Interest paid Net new borrowing

Interest paid (Ending long-term debt

Beginning long-term debt)

$49 (471 458)

$36

Cash flow of the firm also is paid to the stockholders. It is the net effect of paying dividends plus repurchasing outstanding shares of stock and issuing new shares of stock.

C A S H FLO W T O S T O C K H O LD E R S

( i n $ m i l l i o n s)

Dividends

Repurchase of stock

Cash to stockholders

Proceeds from new stock issue

Total

$43

6

49

43

$ 6

In general, cash flow to stockholders can be determined as:

Cash flow to stockholders Dividends paid Net new equity raised

Dividends paid (Stock sold

Stock repurchased)

To determine stock sold, notice that the common stock and capital surplus accounts went

up by a combined $23 20 $43, which implies that the company sold $43 million worth

of stock. Second, Treasury stock went up by $6, indicating that the company bought back

$6 million worth of stock. Net new equity is thus $43 6 $37. Dividends paid were $43,

so the cash flow to stockholders was:

Cash flow to stockholders $43 (43 6) $6,

which is what we previously calculated.

Some important observations can be drawn from our discussion of cash flow:

1. Several types of cash flow are relevant to understanding the financial situation

of the firm. Operating cash flow, defined as earnings before interest and depreciation minus taxes, measures the cash generated from operations not counting

capital spending or working capital requirements. It is usually positive; a firm is

in trouble if operating cash flow is negative for a long time because the firm is

5

30

New debt and the retirement of old debt are usually found in the “notes” to the balance sheet.

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not generating enough cash to pay operating costs. Total cash flow of the firm

includes adjustments for capital spending and additions to net working capital. It

will frequently be negative. When a firm is growing at a rapid rate, the spending

on inventory and fixed assets can be higher than cash flow from sales.

2. Net income is not cash flow. The net income of the U.S. Composite Corporation

in 2010 was $86 million, whereas cash flow was $42 million. The two numbers

are not usually the same. In determining the economic and financial condition of

a firm, cash flow is more revealing.

A firm’s total cash flow sometimes goes by a different name, free cash flow. Of course,

there is no such thing as “free” cash (we wish!). Instead, the name refers to cash that the

firm is free to distribute to creditors and stockholders because it is not needed for working capital or fixed asset investments. We will stick with “total cash flow of the firm” as

our label for this important concept because, in practice, there is some variation in exactly

how free cash flow is computed; different users calculate it in different ways. Nonetheless,

whenever you hear the phrase “free cash flow,” you should understand that what is being

discussed is cash flow from assets or something quite similar.

2 . 6 T H E A C C O U N T I N G S TAT E M E N T

OF CASH FLOWS

As previously mentioned, there is an official accounting statement called the statement

of cash flows. This statement helps explain the change in accounting cash, which for U.S.

Composite is $33 million in 2010. It is very useful in understanding financial cash flow.

The first step in determining the change in cash is to figure out cash flow from operating

activities. This is the cash flow that results from the firm’s normal activities producing and

selling goods and services. The second step is to make an adjustment for cash flow from

investing activities. The final step is to make an adjustment for cash flow from financing

activities. Financing activities are the net payments to creditors and owners (excluding

interest expense) made during the year.

The three components of the statement of cash flows are determined below.

Cash Flow from Operating Activities

To calculate cash flow from operating activities we start with net income. Net income can

be found on the income statement and is equal to $86 million. We now need to add back

noncash expenses and adjust for changes in current assets and liabilities (other than cash

and notes payable). The result is cash flow from operating activities.

U.S. COM P O S I T E C O R P O R AT I O N

Ca s h F l o w f r o m O p e r a t i n g A c t i vi t i e s

2010

( i n $ m i l l i o n s)

Net income

Depreciation

Deferred taxes

Change in assets and liabilities

Accounts receivable

Inventories

Accounts payable

Accrued expense

Other

Cash flow from operating activities

$ 86

90

13

24

11

16

18

8

$202

CHAPTER 2 Financial Statements and Cash Flow

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THE REAL WORLD

PUTTING A SPIN ON CASH FLOWS

One of the reasons why cash flow analysis is popular is the difficulty in manipulating, or spinning, cash flows. GAAP

accounting principles allow for significant subjective decisions to be made regarding many key areas. The use of cash

flow as a metric to evaluate a company comes from the idea that there is less subjectivity involved, and, therefore, it

is harder to spin the numbers. But several recent examples have shown that companies can still find ways to do it.

In November 2009, the SEC settled charges against SafeNet, Inc. and some of its former officers, employees,

and accountants, in connection with earnings management and options backdating schemes. This case represented the SEC’s first enforcement action brought under Regulation G of Sarbox. Of course other companies have

spun financial results without legal action. For example, in March 2007, rental car company Avis Budget Group was

forced to revise its first quarter 2007 operating cash flow by more than $45 million. The company had improperly

classified the cash flow as an operating cash flow rather than an investing cash flow. This maneuver had the effect

of increasing operating cash flows and decreasing investing cash flows by the same amount.

Tyco used several ploys to alter cash flows. For example, the company purchased more than $800 million of

customer security alarm accounts from dealers. The cash flows from these transactions were reported in the

financing activity section of the accounting statement of cash flows. When Tyco received payments from customers, the cash inflows were reported as operating cash flows. Another method used by Tyco was to have acquired

companies prepay operating expenses. In other words, the company acquired by Tyco would pay vendors for

items not yet received. In one case, the payments totaled more than $50 million. When the acquired company was

consolidated with Tyco, the prepayments reduced Tyco’s cash outflows, thus increasing the operating cash flows.

Dynegy, the energy giant, was accused of engaging in a number of complex “round trip trades.” The round trip

trades essentially involved the sale of natural resources to a counterparty, with the repurchase of the resources

from the same party at the same price. In essence, Dynegy would sell an asset for $100, and immediately repurchase it from the buyer for $100. The problem arose with the treatment of the cash flows from the sale. Dynegy

treated the cash from the sale of the asset as an operating cash flow, but classified the repurchase as an investing

cash outflow. The total cash flows of the contracts traded by Dynegy in these round trip trades totaled $300 million.

Adelphia Communications was another company that apparently manipulated cash flows. In Adelphia’s case,

the company capitalized the labor required to install cable. In other words, the company classified this labor expense as a fixed asset. While this practice is fairly common in the telecommunications industry, Adelphia capitalized a higher percentage of labor than is common. The effect of this classification was that the labor was treated

as an investment cash flow, which increased the operating cash flow.

In each of these examples, the companies were trying to boost operating cash flows by shifting cash flows to a

different heading. The important thing to notice is that these movements don’t affect the total cash flow of the firm,

which is why we recommend focusing on this number, not just operating cash flow.

We should also note that, for 2008, the total number of financial restatements fell nearly 30 percent from 2007,

which had itself experienced a 31 percent decline in restatements from 2006. While this is a positive trend, restatements due to cash flow misclassification increased in prevalence over the same period.

Cash Flow from Investing Activities

Cash flow from investing activities involves changes in capital assets: acquisition of fixed assets

and sales of fixed assets (i.e., net capital expenditures). The result for U.S. Composite is below.

U . S . C O M P O S I T E C O R P O R AT I O N

C a sh Fl o w f r o m I n ve st i n g A c t i vi t i e s

2010

( i n $ m i l l i o n s)

Acquisition of fixed assets

Sales of fixed assets

Cash flow from investing activities

32

$198

25

$173

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Cash Flow from Financing Activities

Cash flows to and from creditors and owners include changes in equity and debt.

U.S. COM P O S I T E C O R P O R AT I O N

Ca s h F l o w f r o m Fi n a n c i n g A c t i vi t i e s

2010

( i n $ m i l l i o n s)

Retirement of long-term debt

Proceeds from long-term debt sales

Change in notes payable

Dividends

Repurchase of stock

Proceeds from new stock issue

Cash flow from financing activities

$73

86

3

43

6

43

$ 4

The statement of cash flows is the addition of cash flows from operations, cash flows

from investing activities, and cash flows from financing activities, and is produced in

Table 2.6. When we add all the cash flows together, we get the change in cash on the balance sheet of $33 million.

TABLE 2.6

U.S. COM P O S I T E C O R P O R AT I O N

St a t em e n t o f C a sh Fl o w s

2010

( i n $ m i l l i o n s)

Statement of

Consolidated Cash Flows

of the U.S. Composite

Corporation

Operations

Net income

Depreciation

Deferred taxes

Changes in assets and liabilities

Accounts receivable

Inventories

Accounts payable

Accrued expenses

Other

Total cash flow from operations

24

11

16

18

8

$202

Investing activities

Acquisition of fixed assets

Sales of fixed assets

Total cash flow from investing activities

$198

25

$173

Financing activities

Retirement of long-term debt

Proceeds from long-term debt sales

Change in notes payable

Dividends

Repurchase of stock

Proceeds from new stock issue

Total cash flow from financing activities

Change in cash (on the balance sheet)

$ 73

86

3

43

6

43

$ 4

$ 33

$ 86

90

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There is a close relationship between the official accounting statement called the statement of cash flows and the total cash flow of the firm used in finance. Going back to the previous section, you should note a slight conceptual problem here. Interest paid should really

go under financing activities, but unfortunately that is not how the accounting is handled.

The reason is that interest is deducted as an expense when net income is computed. As a

consequence, a primary difference between the accounting cash flow and the financial cash

flow of the firm (see Table 2.5) is interest expense. The Real World box on page 32 discusses

some ways in which companies have attempted to “spin the numbers” in the accounting

statement of cash flows.

SUMMARY AND CONCLUSIONS

Besides introducing you to corporate accounting, the purpose of this chapter has been to teach you

how to determine cash flow from the accounting statements of a typical company.

1. Cash flow is generated by the firm and paid to creditors and shareholders. It can be classified as:

a. Cash flow from operations.

b. Cash flow from changes in fixed assets.

c. Cash flow from changes in working capital.

2. Calculations of cash flow are not difficult, but they require care and particular attention to detail

in properly accounting for noncash expenses such as depreciation and deferred taxes. It is

especially important that you do not confuse cash flow with changes in net working capital and

net income.

CONCEPT QUESTIONS

1. Liquidity What does liquidity measure? Explain the trade-off a firm faces between high liquidity and low liquidity levels.

2. Accounting and Cash Flows Why is it that the revenue and cost figures shown on a standard

income statement may not be representative of the actual cash inflows and outflows that occurred during the period?

3. Accounting Statement of Cash Flows Looking at the accounting statement of cash flows, what

does the bottom line number mean? How useful is this number for analyzing a company?

4. Cash Flows How do financial cash flows and the accounting statement of cash flows differ?

Which is more useful when analyzing a company?

5. Book Values versus Market Values Under standard accounting rules, it is possible for a company’s liabilities to exceed its assets. When this occurs, the owners’ equity is negative. Can this

happen with market values? Why or why not?

6. Cash Flow from Assets Suppose a company’s cash flow from assets was negative for a

particular period. Is this necessarily a good sign or a bad sign?

7. Operating Cash Flow Suppose a company’s operating cash flow was negative for several

years running. Is this necessarily a good sign or a bad sign?

8. Net Working Capital and Capital Spending Could a company’s change in net working capital

be negative in a given year? (Hint: Yes.) Explain how this might come about. What about net

capital spending?

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9. Cash Flow to Stockholders and Creditors Could a company’s cash flow to stockholders be

negative in a given year? (Hint: Yes.) Explain how this might come about. What about cash flow

to creditors?

10. Firm Values Referring back to the Fannie Mae example used at the beginning of the chapter,

note that we suggested that Fannie Mae’s stockholders probably didn’t suffer as a result of the

reported loss. What do you think was the basis for our conclusion?

QUESTIONS AND PROBLEMS

1. Building a Balance Sheet Brees, Inc., has current assets of $7,500, net fixed assets of $28,900,

current liabilities of $5,900, and long-term debt of $18,700. What is the value

of the shareholders’ equity account for this firm? How much is net working capital?

Basic

(Questions 1–10)

2. Building an Income Statement Tyler, Inc., has sales of $753,000, costs of $308,000, depreciation expense of $46,000, interest expense of $21,500, and a tax rate of 35 percent. What is the net

income for the firm? Suppose the company paid out $67,000 in cash dividends. What is the addition to retained earnings?

3. Market Values and Book Values Klingon Cruisers, Inc., purchased new cloaking machinery

three years ago for $7 million. The machinery can be sold to the Romulans today for $5.2 million. Klingon’s current balance sheet shows net fixed assets of $4.5 million, current liabilities of

$1.8 million, and net working capital of $750,000. If all the current assets were liquidated today,

the company would receive $2.7 million cash. What is the book value of Klingon’s assets today?

What is the market value?

4. Calculating Taxes The Conard Co. had $285,000 in taxable income. Using the rates from Table

2.3 in the chapter, calculate the company’s income taxes. What is the average tax rate? What is

the marginal tax rate?

5. Calculating OCF Williams, Inc., has sales of $25,300, costs of $9,100, depreciation expense

of $1,700, and interest expense of $950. If the tax rate is 40 percent, what is the operating cash

flow, or OCF?

6. Calculating Net Capital Spending Martin Driving School’s 2009 balance sheet showed net

fixed assets of $4.7 million, and the 2010 balance sheet showed net fixed assets of $5.3 million.

The company’s 2010 income statement showed a depreciation expense of $760,000. What was

the company’s net capital spending for 2010?

7. Building a Balance Sheet The following table presents the long-term liabilities and stockholders’ equity of Information Control Corp. one year ago:

Long-term debt

Preferred stock

Common stock ($1 par value)

Capital surplus

Accumulated retained earnings

$35,000,000

4,000,000

11,000,000

26,000,000

75,000,000

During the past year, Information Control issued 8 million shares of new stock at a total price of

$29 million, and issued $6 million in new long-term debt. The company generated $7 million in

net income and paid $2.5 million in dividends. Construct the current balance sheet reflecting the

changes that occurred at Information Control Corp. during the year.

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8. Cash Flow to Creditors The 2009 balance sheet of Maria’s Tennis Shop, Inc., showed longterm debt of $2.4 million, and the 2010 balance sheet showed long-term debt of $2.5 million. The

2010 income statement showed an interest expense of $195,000. What was the firm’s cash flow

to creditors during 2010?

9. Cash Flow to Stockholders The 2009 balance sheet of Maria’s Tennis Shop, Inc., showed

$730,000 in the common stock account and $6.2 million in the additional paid-in surplus account.

The 2010 balance sheet showed $775,000 and $6.9 million in the same two accounts, respectively. If the company paid out $400,000 in cash dividends during 2010, what was the cash flow to

stockholders for the year?

10. Calculating Total Cash Flows Given the information for Maria’s Tennis Shop, Inc., in the previous two problems, suppose you also know that the firm’s net capital spending for 2010 was

$810,000, and that the firm reduced its net working capital investment by $85,000. What was the

firm’s 2010 operating cash flow, or OCF?

Intermediate

(Questions 11–25)

11. Cash Flows Ritter Corporation’s accountants prepared the following financial statements for

year-end 2010.

R I T T E R C O R P O R AT I O N

Income Statement

2010

Revenue

Expenses

Depreciation

EBT

Tax

Net income

Dividends

$780

620

50

$110

39

$ 71

$ 22

R I T T E R C O R P O R AT I O N

Balance Sheets

D e c e m b e r 31

Assets

Cash

Other current assets

Net fixed assets

Total assets

Liabilities and Equity

Accounts payable

Long-term debt

Stockholders’ equity

Total liabilities and equity

2009

2010

$ 38

143

320

$501

$ 45

140

408

$593

$140

0

361

$501

$143

40

410

$593

a. Explain the change in cash during the year 2010.

b. Determine the change in net working capital in 2010.

c. Determine the cash flow generated by the firm’s assets during the year 2010.

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12. Cash Flow Identity Freeman, Inc., reported the following financial statements for the last two

years. Construct the cash flow identity for the company. Explain what each number means.

2010 INCOME STATEMENT

Sales

Cost of goods sold

Selling & administrative

Depreciation

EBIT

Interest

EBT

Taxes

$565,200

274,025

124,733

54.576

$111,866

19,296

$ 92,570

48,137

$ 44,433

$ 9,600

$ 34,833

Net income

Dividends

Addition to retained earnings

Fr e e m a n , I n c .

Ba l a n c e Sh ee t a s o f D e c e m b e r 31, 2009

Cash

Accounts receivable

Inventory

Current assets

Net fixed assets

Total assets

$ 13,320

18,994

13,794

$ 46,108

$344,426

$390,534

Accounts payable

Notes payable

Current liabilities

Long-term debt

Owners’ equity

Total liabilities and

owners’ equity

$ 9,504

14,508

$ 24,012

$136,800

$229,722

$390,534

Fr e e m a n , I n c .

Ba l a n c e Sh ee t a s o f D e c e m b e r 31, 2010

Cash

Accounts receivable

Inventory

Current assets

Net fixed assets

Total assets

$ 14,306

21,099

22,754

$ 58,159

$406,311

$464,470

Accounts payable

Notes payable

Current liabilities

Long-term debt

Owners’ equity

Total liabilities and

owners’ equity

$ 10,512

16,466

$ 26,978

$152,000

$285,492

$464,470

13. Financial Cash Flows The Stancil Corporation provided the following current information:

Proceeds from long-term borrowing

Proceeds from the sale of common stock

Purchases of fixed assets

Purchases of inventories

Payment of dividends

$12,000

3,000

15,000

2,100

6,000

Determine the cash flows from the firm and the cash flows to investors of the firm.

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14. Building an Income Statement During the year, the Senbet Discount Tire Company had gross

sales of $870,000. The firm’s cost of goods sold and selling expenses were $280,000 and $155,000,

respectively. Senbet also had notes payable of $650,000. These notes carried an interest rate of

6 percent. Depreciation was $86,000. Senbet’s tax rate was 35 percent.

a. What was Senbet’s net income?

b. What was Senbet’s operating cash flow?

15. Calculating Total Cash Flows Schwert Corp. shows the following information on its 2010

income statement: sales $193,000; costs $96,500; other expenses $5,100; depreciation

expense $13,800; interest expense $10,400; taxes $23,520; dividends $12,500. In addition, you’re told that the firm issued $6,000 in new equity during 2010, and redeemed $7,500 in

outstanding long-term debt.

a. What was the 2010 operating cash flow?

b. What was the 2010 cash flow to creditors?

c. What was the 2010 cash flow to stockholders?

d. If net fixed assets increased by $28,000 during the year, what was the addition to NWC?

16. Using Income Statements Given the following information for O’Hara Marine Co., calculate the

depreciation expense: sales $43,000; costs $26,000; addition to retained earnings $5,600;

dividends paid $1,300; interest expense $1,900; tax rate 35 percent.

17. Preparing a Balance Sheet Prepare a 2010 balance sheet for Jarrow Corp. based on the following information: cash $175,000; patents and copyrights $730,000; accounts payable

$435,000; accounts receivable $240,000; tangible net fixed assets $3,650,000; inventory

$405,000; notes payable $160,000; accumulated retained earnings $1,980,000; long-term

debt $2,140,000.

18. Residual Claims Huang, Inc., is obligated to pay its creditors $12,500 very soon.

a. What is the market value of the shareholders’ equity if assets have a market value of $15,100?

b. What if assets equal $10,200?

19. Marginal versus Average Tax Rates (Refer to Table 2.3.) Corporation Growth has $86,000 in

taxable income, and Corporation Income has $8,600,000 in taxable income.

a. What is the tax bill for each firm?

b. Suppose both firms have identified a new project that will increase taxable income by

$10,000. How much in additional taxes will each firm pay? Why is this amount the same?

20. Net Income and OCF During 2010, Raines Umbrella Corp. had sales of $835,000. Cost of goods

sold, administrative and selling expenses, and depreciation expenses were $620,000, $120,000,

and $85,000, respectively. In addition, the company had an interest expense of $68,000 and a tax

rate of 35 percent. (Ignore any tax loss carryback or carryforward provisions.)

a. What was Raines’s net income for 2010?

b. What was its operating cash flow?

c. Explain your results in (a) and (b).

21. Accounting Values versus Cash Flows In the previous problem, suppose Raines Umbrella

Corp. paid out $45,000 in cash dividends. Is this possible? If spending on net fixed assets and net

working capital was zero, and if no new stock was issued during the year, what was the change

in the firm’s long-term debt account?

22. Calculating Cash Flows Cusic Industries had the following operating results for 2010; sales

$25,700; cost of goods sold $18,400; depreciation expense $3,450; interest expense $790;

dividends paid $1,100. At the beginning of the year, net fixed assets were $19,280, current

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assets were $5,100, and current liabilities were $3,400. At the end of the year, net fixed assets

were $23,650, current assets were $5,830, and current liabilities were $3,580. The tax rate for

2010 was 40 percent.

a. What was net income for 2010?

b. What was the operating cash flow for 2010?

c. What was the cash flow from assets for 2010? Is this possible? Explain.

d. If no new debt was issued during the year, what was the cash flow to creditors? What was

the cash flow to stockholders? Explain and interpret the positive and negative signs of your

answers in (a) through (d).

23. Calculating Cash Flows Consider the following abbreviated financial statements for Weston

Enterprises:

W E ST ON E NT E RPR I S E S

2 0 0 9 a n d 2 0 1 0 Pa r t i a l Ba l a n c e S h e e t s

WE S T O N E N T E R P R I S E S

2010 I n c o m e S t a t e m e n t

Assets

Sales

Costs

Depreciation

Interest paid

Current assets

Net fixed assets

Liabilities and Owners’ Equity

2009

$ 740

3,600

2010

$ 795

3,800

Current liabilities

Long-term debt

2009

$ 330

2,000

2010

$ 360

2,150

$10,900

4,680

930

390

a. What was owners’ equity for 2009 and 2010?

b. What was the change in net working capital for 2010?

c. In 2010, Weston Enterprises purchased $1,900 in new fixed assets. How much in fixed assets

did Weston Enterprises sell? What was the cash flow from assets for the year? (The tax rate

is 35 percent.)

d. During 2010, Weston Enterprises raised $440 in new long-term debt. How much long-term

debt must Weston Enterprises have paid off during the year? What was the cash flow to

creditors?

Use the following information for Ingersoll, Inc., for Problems 24 and 25 (assume the tax rate

is 35 percent):

Sales

Depreciation

Cost of goods sold

Other expenses

Interest

Cash

Accounts receivable

Short-term notes payable

Long-term debt

Net fixed assets

Accounts payable

Inventory

Dividends

2009

2010

$ 26,115

3,750

8,985

2,130

1,345

13,695

18,130

2,645

45,865

114,850

14,885

32,235

3,184

$ 28,030

3,755

10,200

1,780

2,010

14,010

20,425

2,485

53,510

117,590

13,950

33,125

3,505

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24. Financial Statements Draw up an income statement and balance sheet for this company for

2009 and 2010.

25. Calculating Cash Flow For 2010, calculate the cash flow from assets, cash flow to creditors,

and cash flow to stockholders.

Challenge

(Questions 26–28)

26. Cash Flows You are researching Time Manufacturing and have found the following accounting statement of cash flows for the most recent year. You also know that the company paid

$231 million in current taxes and had an interest expense of $120 million. Use the accounting

statement of cash flows to construct the financial statement of cash flows.

T I M E M A N U FA C T U R I N G

S t a t e m e n t o f C a sh Fl o w s

( i n $ m i l l i o n s)

Operations

Net income

Depreciation

Deferred taxes

Changes in assets and liabilities

Accounts receivable

Inventories

Accounts payable

Accrued expenses

Other

Total cash flow from operations

Investing activities

Acquisition of fixed assets

Sale of fixed assets

Total cash flow from investing activities

Financing activities

Retirement of long-term debt

Proceeds from long-term debt sales

Change in notes payable

Dividends

Repurchase of stock

Proceeds from new stock issue

Total cash flow from financing activities

Change in cash (on balance sheet)

$401

221

43

65

51

41

21

5

$676

$415

53

$362

$240

131

12

198

32

62

$265

$ 49

27. Net Fixed Assets and Depreciation On the balance sheet, the net fixed assets (NFA) account

is equal to the gross fixed assets (FA) account, which records the acquisition cost of fixed

assets, minus the accumulated depreciation (AD) account, which records the total depreciation

taken by the firm against its fixed assets. Using the fact that NFA FA AD, show that the

expression given in the chapter for net capital spending, NFAend NFAbeg D (where D is

the depreciation expense during the year), is equivalent to FAend FAbeg.

28. Tax Rates Refer to the corporate marginal tax rate information in Table 2.3.

a. Why do you think the marginal tax rate jumps up from 34 percent to 39 percent at a taxable

income of $100,001, and then falls back to a 34 percent marginal rate at a taxable income

of $335,001?

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b. Compute the average tax rate for a corporation with exactly $335,001 in taxable income. Does

this confirm your explanation in part (a)? What is the average tax rate for a corporation with

exactly $18,333,334? Is the same thing happening here?

c. The 39 percent and 38 percent tax rates both represent what is called a tax “bubble.”

Suppose the government wanted to lower the upper threshold of the 39 percent marginal

tax bracket from $335,000 to $200,000. What would the new 39 percent bubble rate have

to be?

W H AT ’ S O N T H E W E B ?

1. Change in Net Working Capital Find the most recent abbreviated balance sheets for General

Dynamics at finance.yahoo.com. Enter the ticker symbol “GD” and follow the “Balance Sheet”

link. Using the two most recent balance sheets, calculate the change in net working capital.

What does this number mean?

2. Book Values versus Market Values The home page for Coca-Cola Company can be found at

www.coca-cola.com. Locate the most recent annual report, which contains a balance sheet for

the company. What is the book value of equity for Coca-Cola? The market value of a company

is the number of shares of stock outstanding times the price per share. This information can

be found at finance.yahoo.com using the ticker symbol for Coca-Cola (KO). What is the market

value of equity? Which number is more relevant for shareholders?

3. Cash Flows to Stockholders and Creditors Cooper Tire and Rubber Company provides financial information for investors on its Web site at www.coopertires.com. Follow the “Investors”

link and find the most recent annual report. Using the consolidated statements of cash flows,

calculate the cash flow to stockholders and the cash flow to creditors.

CHAPTER 2 Financial Statements and Cash Flow

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CLOSING CASE

C A S H F L O W S AT E A S T C O A S T YA C H T S

Because of the dramatic growth at East Coast Yachts, Larissa decided that the company should be

reorganized as a corporation (see our Chapter 1 Closing Case for more detail). Time has passed and,

today, the company is publicly traded under the ticker symbol “ECY”.

Dan Ervin was recently hired by East Coast

E A S T C O A S T YA C H T S

Yachts to assist the company with its short2008 I n c o m e S t a t e m e n t

term financial planning and also to evaluate the

company’s financial performance. Dan graduSales

$617,760,000

ated from college five years ago with a finance

Cost of goods sold

435,360,000

degree, and he has been employed in the treaSelling, general, and administrative

73,824,000

sury department of a Fortune 500 company

Depreciation

20,160,000

since then.

EBIT

$ 88,416,000

The company’s past growth has been someInterest expense

11,112,000

what hectic, in part due to poor planning. In anEBT

$ 77,304,000

ticipation of future growth, Larissa has asked

Taxes

30,921,600

Dan to analyze the company’s cash flows. The

Net

income

$

46,382,400

company’s financial statements are prepared

by an outside auditor. Below you will find the

Dividends

$ 17,550,960

most recent income statement and the balance

Retained earnings

$ 28,831,440

sheets for the past two years.

E A S T C O A S T YA C H T S

Balance Sheet

2009

2010

$ 10,752,000

19,116,000

17,263,200

1,108,800

$ 48,240,000

$ 11,232,000

20,208,000

22,656,000

1,184,000

$ 55,280,000

$408,816,000

(94,836,000)

$313,980,000

6,840,000

$320,820,000

$ 462,030,000

(114,996,000)

$ 347,034,000

6,840,000

$ 353,874,000

Current assets

Cash and equivalents

Accounts receivable

Inventories

Other

Total current assets

Less accumulated depreciation

Net property, plant, and equipment

Intangible assets and others

Total fixed assets

Accounts payable

Notes payable

Accrued expenses

Total current liabilities

Long-term debt

Total long-term liabilities

Preferred stock

Capital surplus

Accumulated retained earnings

Less treasury stock

Total equity

42

$ 23,701,440

20,220,000

5,472,000

$ 49,393,440

$ 24,546,000

18,725,000

6,185,000

$ 49,456,000

$ 129,360,000

$ 129,360,000

$146,560,000

$146,560,000

$

3,000,000

30,000,000

12,000,000

157,306,560

(12,000,000)

$ 190,306,560

$ 3,000,000

40,800,000

31,200,000

186,138,000

(48,000,000)

$213,138,000

$ 369,060,000

$409,154,000

Stockholders’ equity

Common stock

Total assets

2010

Current liabilities

Fixed assets

Property, plant, and equipment

2009

$369,060,000

$ 409,154,000

Total liabilities and shareholders’

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Larissa has also provided the following information. During the year, the company raised

$40 million in new long-term debt and retired $22.8 million in long-term debt. The company also

sold $30 million in new stock and repurchased $36 million. The company purchased $60 million in

fixed assets, and sold $6,786,000 in fixed assets.

Larissa has asked Dan to prepare the financial statement of cash flows and the accounting statement of cash flows. She has also asked you to answer the following questions:

1. How would you describe East Coast Yachts’ cash flows?

2. Which cash flows statement more accurately describes the cash flows at the company?

3. In light of your previous answers, comment on Larissa’s expansion plans.

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CHAPTER

3

Financial Statements

Analysis and Financial

Models

OPENING CASE

T

he price of a share of common stock in electronics retailer Best Buy closed at about $40

on January 4, 2010. At that price, Best Buy had a price-earnings (PE) ratio of 15.4. That is,

investors were willing to pay $15.4 for every dollar in income earned by Best Buy. At the

same time, investors were willing to pay $6.0, $24.9, and $40.4 for each dollar earned by

Jackson Hewitt Tax Service, American Eagle Outfitters, and Google, respectively. At the

other extreme was the greeting card company, American Greetings, which had negative earnings for

the previous year, yet the stock was priced at about $22 per share. Because it had negative earnings,

the PE ratio would have been negative, so it was not reported. At the same time, the typical stock

in the S&P 500 Index of large company stocks was trading at a PE of about 15.8, or about 15.8 times

earnings, as they say on Wall Street.

Price-to-earnings comparisons are examples of the use of financial ratios. As we will see in this

chapter, there are a wide variety of financial ratios, all designed to summarize specific aspects of a

firm’s financial position. In addition to discussing how to analyze financial statements and compute

financial ratios, we will have quite a bit to say about who uses this information and why.

3.1

F I N A N C I A L S TAT E M E N T S A N A LY S I S

In Chapter 2, we discussed some of the essential concepts of financial statements and cash

flows. This chapter continues where our earlier discussion left off. Our goal here is to

expand your understanding of the uses (and abuses) of financial statement information.

A good working knowledge of financial statements is desirable simply because such

statements, and numbers derived from those statements, are the primary means of communicating financial information both within the firm and outside the firm. In short, much of

the language of business finance is rooted in the ideas we discuss in this chapter.

Clearly, one important goal of the accountant is to report financial information to the

user in a form useful for decision making. Ironically, the information frequently does not

come to the user in such a form. In other words, financial statements don’t come with a

user’s guide. This chapter is a first step in filling this gap.

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Standardizing Statements

One obvious thing we might want to do with a company’s financial statements is to compare them to those of other, similar companies. We would immediately have a problem,

however. It’s almost impossible to directly compare the financial statements for two

companies because of differences in size.

For example, Ford and GM are obviously serious rivals in the auto market, but GM

is larger, so it is difficult to compare them directly. For that matter, it’s difficult even to

compare financial statements from different points in time for the same company if the

company’s size has changed. The size problem is compounded if we try to compare GM

and, say, Toyota. If Toyota’s financial statements are denominated in yen, then we have size

and currency differences.

To start making comparisons, one obvious thing we might try to do is to somehow standardize the financial statements. One common and useful way of doing this is to work with

percentages instead of total dollars. The resulting financial statements are called commonsize statements. We consider these next.

Common-Size Balance Sheets

For easy reference, Prufrock Corporation’s 2009 and 2010 balance sheets are provided in

Table 3.1. Using these, we construct common-size balance sheets by expressing each item

as a percentage of total assets. Prufrock’s 2009 and 2010 common-size balance sheets are

shown in Table 3.2.

Notice that some of the totals don’t check exactly because of rounding errors. Also

notice that the total change has to be zero because the beginning and ending numbers must

add up to 100 percent.

TABLE 3.1

PRUF R O C K C O R P O R AT I O N

Ba l a n c e Sh e e t s as o f D e c e m b e r 31, 2009 a n d 2010

( $ i n m i l l i o n s)

Assets

Current assets

Cash

Accounts receivable

Inventory

Total

Fixed assets

Net plant and equipment

Total assets

Liabilities and Owners’ Equity

Current liabilities

Accounts payable

Notes payable

Total

Long-term debt

Owners’ equity

Common stock and paid-in surplus

Retained earnings

Total

Total liabilities and owners’ equity

2009

2010

$

84

165

393

$ 642

$

98

188

422

$ 708

$ 2,731

$ 3,373

$ 2,880

$ 3,588

$ 312

231

$ 543

$ 531

$ 344

196

$ 540

$ 457

$ 500

1,799

$ 2,299

$ 3,373

$ 550

2,041

$ 2,591

$ 3,588

CHAPTER 3 Financial Statements Analysis and Financial Models

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TABLE 3.2

P R U FR O C K C O R P O R AT I O N

C o m m o n - S i ze B a l a n c e S h e e t s

D e c e m b e r 31, 2009 a n d 2010

As s e t s

Current assets

Cash

Accounts receivable

Inventory

Total

Fixed assets

Net plant and equipment

Total assets

Liabilities and Owners’ Equity

Current liabilities

Accounts payable

Notes payable

Total

Long-term debt

Owners’ equity

Common stock and paid-in surplus

Retained earnings

Total

Total liabilities and owners’ equity

2009

2010

C h a nge

2.5%

4.9

11.7

19.0

2.7%

5.2

11.8

19.7

.2%

.3

.1

.7

81.0

100.0%

80.3

100.0%

.7

.0%

9.2%

6.8

16.1

15.7

9.6%

5.5

15.1

12.7

.4%

1.3

1.0

3.0

14.8

53.3

68.2

100.0%

15.3

56.9

72.2

100.0%

.5

3.5

4.1

.0%

In this form, financial statements are relatively easy to read and compare. For example, just looking at the two balance sheets for Prufrock, we see that current assets

were 19.7 percent of total assets in 2010, up from 19.0 percent in 2009. Current liabilities declined from 16.1 percent to 15.1 percent of total liabilities and equity over that

same time. Similarly, total equity rose from 68.2 percent of total liabilities and equity to

72.2 percent.

Overall, Prufrock’s liquidity, as measured by current assets compared to current liabilities, increased over the year. Simultaneously, Prufrock’s indebtedness diminished as a percentage of total assets. We might be tempted to conclude that the balance sheet has grown

“stronger.”

Common-Size Income Statements

Table 3.3 describes some commonly used measures of earnings. A useful way of standardizing the income statement shown in Table 3.4 is to express each item as a percentage of

total sales, as illustrated for Prufrock in Table 3.5.

This income statement tells us what happens to each dollar in sales. For Prufrock,

interest expense eats up $.061 out of every sales dollar, and taxes take another $.081.

When all is said and done, $.157 of each dollar flows through to the bottom line (net

income), and that amount is split into $.105 retained in the business and $.052 paid out

in dividends.

These percentages are useful in comparisons. For example, a relevant figure is the cost

percentage. For Prufrock, $.582 of each $1.00 in sales goes to pay for goods sold. It would

be interesting to compute the same percentage for Prufrock’s main competitors to see how

Prufrock stacks up in terms of cost control.

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Investors and analysts look closely at the income statement for clues on how well a company has performed

during a particular year. Here are some commonly used measures of earnings (numbers in millions).

Net Income

The so-called bottom line, defined as total revenue minus total expenses. Net income

for Prufrock in the latest period is $363 million. Net income reflects differences in a

firm’s capital structure and taxes as well as operating income. Interest expense and

taxes are subtracted from operating income in computing net income. Shareholders

look closely at net income because dividend payout and retained earnings are closely

linked to net income.

EPS

Net income divided by the number of shares outstanding. It expresses net income

on a per-share basis. For Prufrock, the EPS (Net income)/(Shares outstanding)

$363/33 $11.

EBIT

Earnings before interest expense and taxes. EBIT is usually called “income from

operations” on the income statement and is income before unusual items, discontinued

operating or extraordinary items. To calculate EBIT, operating expenses are subtracted

from total operations revenues. Analysts like EBIT because it abstracts from

differences in earnings from a firm’s capital structure (interest expense) and taxes.

For Prufrock, EBIT is $691 million.

EBITDA

Earnings before interest expense, taxes, depreciation, and amortization. EBITDA

EBIT depreciation and amortization. Here amortization refers to a noncash expense

similar to depreciation except it applies to an intangible asset (such as a patent), rather

than a tangible asset (such as a machine). The word amortization here does not refer

to the payment of debt. There is no amortization in Prufrock’s income statement. For

Prufrock, EBITDA $691 $276 $967 million. Analysts like to use EBITDA because

it adds back two noncash items (depreciation and amortization) to EBIT and thus is a

better measure of before-tax operating cash flow.

TABLE 3.3

Measures of Earnings

Sometimes these measures of earnings are preceded by the letters LTM, meaning the last twelve months. For

example, LTM EPS is the last twelve months of EPS and LTM EBITDA is the last twelve months of EBITDA. At

other times, the letters TTM are used, meaning trailing twelve months. Needless to say, LTM is the same as TTM.

TABLE 3.4

PRUF R O C K C O R P O R AT I O N

2010 Income Statement

( $ i n m i l l i o n s)

Sales

Cost of goods sold

Depreciation

Earnings before interest and taxes

Interest paid

Taxable income

Taxes (34%)

Net income

Dividends

Addition to retained earnings

$2,311

1,344

276

$ 691

141

$ 550

187

$ 363

$121

242

TABLE 3.5

PRUF R O C K C O R P O R AT I O N

Co mmo n - S i ze I n c o m e S t a t e m e n t 2010

Sales

Cost of goods sold

Depreciation

Earnings before interest and taxes

Interest paid

Taxable income

Taxes (34%)

Net income

Dividends

Addition to retained earnings

100.0%

58.2

11.9

29.9

6.1

23.8

8.1

15.7%

5.2%

10.5

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3.2

R AT I O A N A LY S I S

Another way of avoiding the problems involved in comparing companies of different sizes

is to calculate and compare financial ratios. Such ratios are ways of comparing and investigating the relationships between different pieces of financial information. We cover some

of the more common ratios next (there are many others we don’t discuss here).

One problem with ratios is that different people and different sources frequently don’t

compute them in exactly the same way, and this leads to much confusion. The specific

definitions we use here may or may not be the same as ones you have seen or will see elsewhere. If you are using ratios as tools for analysis, you should be careful to document how

you calculate each one; and, if you are comparing your numbers to those of another source,

be sure you know how their numbers are computed.

We will defer much of our discussion of how ratios are used and some problems that

come up with using them until later in the chapter. For now, for each ratio we discuss,

several questions come to mind:

Go to

www.reuters.com/

finance/stocks

and find the ratios link

to examine comparative

ratios for a huge number

of companies.

1.

2.

3.

4.

How is it computed?

What is it intended to measure, and why might we be interested?

What is the unit of measurement?

What might a high or low value be telling us? How might such values be

misleading?

5. How could this measure be improved?

Financial ratios are traditionally grouped into the following categories:

1.

2.

3.

4.

5.

Short-term solvency, or liquidity, ratios.

Long-term solvency, or financial leverage, ratios.

Asset management, or turnover, ratios.

Profitability ratios.

Market value ratios.

We will consider each of these in turn. In calculating these numbers for Prufrock, we will

use the ending balance sheet (2010) figures unless we explicitly say otherwise.

Short-Term Solvency or Liquidity Measures

As the name suggests, short-term solvency ratios as a group are intended to provide information about a firm’s liquidity, and these ratios are sometimes called liquidity measures.

The primary concern is the firm’s ability to pay its bills over the short run without undue

stress. Consequently, these ratios focus on current assets and current liabilities.

For obvious reasons, liquidity ratios are particularly interesting to short-term creditors. Because financial managers are constantly working with banks and other short-term

lenders, an understanding of these ratios is essential.

One advantage of looking at current assets and liabilities is that their book values and

market values are likely to be similar. Often (though not always), these assets and liabilities

just don’t live long enough for the two to get seriously out of step. On the other hand, like

any type of near-cash, current assets and liabilities can and do change fairly rapidly, so

today’s amounts may not be a reliable guide to the future.

One of the best-known and most widely used ratios is the current ratio. As

you might guess, the current ratio is defined as:

Current Ratio

Current assets

Current ratio ___________________

Current liabilities

48

[3.1]

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For Prufrock, the 2010 current ratio is:

$708

Current ratio ______ 1.31 times

$540

EXAMPLE

3.1

Because current assets and liabilities are, in principle, converted to cash over the following

12 months, the current ratio is a measure of short-term liquidity. The unit of measurement is

either dollars or times. So, we could say Prufrock has $1.31 in current assets for every $1 in

current liabilities, or we could say Prufrock has its current liabilities covered 1.31 times over.

To a creditor, particularly a short-term creditor such as a supplier, the higher the current

ratio, the better. To the firm, a high current ratio indicates liquidity, but it also may indicate

an inefficient use of cash and other short-term assets. Absent some extraordinary circumstances, we would expect to see a current ratio of at least 1; a current ratio of less than 1

would mean that net working capital (current assets less current liabilities) is negative. This

would be unusual in a healthy firm, at least for most types of businesses.

The current ratio, like any ratio, is affected by various types of transactions. For example, suppose the firm borrows over the long term to raise money. The short-run effect

would be an increase in cash from the issue proceeds and an increase in long-term debt.

Current liabilities would not be affected, so the current ratio would rise.

Current Events

Suppose a firm were to pay off some of its suppliers and short-term creditors. What would happen to

the current ratio? Suppose a firm buys some inventory. What happens in this case? What happens if

a firm sells some merchandise?

The first case is a trick question. What happens is that the current ratio moves away from 1. If it is

greater than 1 (the usual case), it will get bigger, but if it is less than 1, it will get smaller. To see this,

suppose the firm has $4 in current assets and $2 in current liabilities for a current ratio of 2. If we use

$1 in cash to reduce current liabilities, the new current ratio is ($4 1)/($2 1) 3. If we reverse the

original situation to $2 in current assets and $4 in current liabilities, the change will cause the current

ratio to fall to 1/3 from 1/2.

The second case is not quite as tricky. Nothing happens to the current ratio because cash goes

down while inventory goes up—total current assets are unaffected.

In the third case, the current ratio would usually rise because inventory is normally shown at

cost and the sale would normally be at something greater than cost (the difference is the markup).

The increase in either cash or receivables is therefore greater than the decrease in inventory. This

increases current assets, and the current ratio rises.

Finally, note that an apparently low current ratio may not be a bad sign for a company

with a large reserve of untapped borrowing power.

Quick (or Acid-Test) Ratio Inventory is often the least liquid current asset. It’s also the one

for which the book values are least reliable as measures of market value because the quality

of the inventory isn’t considered. Some of the inventory may later turn out to be damaged,

obsolete, or lost.

More to the point, relatively large inventories are often a sign of short-term trouble. The

firm may have overestimated sales and overbought or overproduced as a result. In this case,

the firm may have a substantial portion of its liquidity tied up in slow-moving inventory.

To further evaluate liquidity, the quick, or acid-test, ratio is computed just like the current ratio, except inventory is omitted:

Current assets Inventory

Quick ratio _____________________________

Current liabilities

[3.2]

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Notice that using cash to buy inventory does not affect the current ratio, but it reduces the

quick ratio. Again, the idea is that inventory is relatively illiquid compared to cash.

For Prufrock, this ratio in 2010 was:

$708 422

Quick ratio _____________ .53 times

$540

The quick ratio here tells a somewhat different story than the current ratio because inventory accounts for more than half of Prufrock’s current assets. To exaggerate the point, if

this inventory consisted of, say, unsold nuclear power plants, then this would be a cause

for concern.

To give an example of current versus quick ratios, based on recent financial statements,

Walmart and Manpower, Inc., had current ratios of .88 and 1.61, respectively. However,

Manpower carries no inventory to speak of, whereas Walmart’s current assets are virtually

all inventory. As a result, Walmart’s quick ratio was only .22, and Manpower’s was 1.61, the

same as its current ratio.

Cash Ratio

A very short-term creditor might be interested in the cash ratio:

Cash

Cash ratio ___________________

Current liabilities

[3.3]

You can verify that this works out to be .18 times for Prufrock.

Long-Term Solvency Measures

Long-term solvency ratios are intended to address the firm’s long-run ability to meet its

obligations or, more generally, its financial leverage. These ratios are sometimes called

financial leverage ratios or just leverage ratios. We consider three commonly used measures and some variations.

The total debt ratio takes into account all debts of all maturities to all

creditors. It can be defined in several ways, the easiest of which is this:

Total Debt Ratio

Total assets Total equity

Total debt ratio ____________________________

Total assets

$3,588 2,591

_________________ .28 times

$3,588

[3.4]

In this case, an analyst might say that Prufrock uses 28 percent debt.1 Whether this is high

or low or whether it even makes any difference depends on whether capital structure matters, a subject we discuss in a later chapter.

Prufrock has $.28 in debt for every $1 in assets. Therefore, there is $.72 in equity

($1 – .28) for every $.28 in debt. With this in mind, we can define two useful variations

on the total debt ratio, the debt-equity ratio and the equity multiplier:

The online Women’s

Business Center has

more information about

financial statements,

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business topics at

www.sba.gov.

Debt- equity ratio Total debt / Total equity

$.28/$.72 .39 times

[3.5]

Equity multiplier Total assets/ Total equity

$1/$.72 1.39 times

[3.6]

The fact that the equity multiplier is 1 plus the debt-equity ratio is not a coincidence:

Equity multiplier Total assets / Total equity $1/$.72 1.39 times

(Total equity Total debt)/ Total equity

1 Debt- equity ratio 1.39 times

1

Total equity here includes preferred stock, if there is any. An equivalent numerator in this ratio would be (Current liabilities

Long-term debt).

50

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The thing to notice here is that given any one of these three ratios, you can immediately

calculate the other two, so they all say exactly the same thing.

Times Interest Earned Another common measure of long-term solvency is the times interest earned (TIE) ratio. Once again, there are several possible (and common) definitions,

but we’ll stick with the most traditional:

EBIT

Times interest earned ratio _________

Interest

[3.7]

$691

______ 4.9 times

$141

As the name suggests, this ratio measures how well a company has its interest obligations

covered, and it is often called the interest coverage ratio. For Prufrock, the interest bill is

covered 4.9 times over.

A problem with the TIE ratio is that it is based on EBIT, which is not really

a measure of cash available to pay interest. The reason is that depreciation and amortization, noncash expenses, have been deducted out. Because interest is most definitely a cash

outflow (to creditors), one way to define the cash coverage ratio is:

Cash Coverage

EBIT (Depreciation and amortization)

Cash coverage ratio __________________________________________

Interest

[3.8]

$691 276

$967

_____________ ______ 6.9 times

$141

$141

The numerator here, EBIT plus depreciation and amortization, is often abbreviated

EBITDA (earnings before interest, taxes, depreciation, and amortization). It is a basic measure of the firm’s ability to generate cash from operations, and it is frequently used as a

measure of cash flow available to meet financial obligations.

More recently another long-term solvency measure is increasingly seen in financial

statement analysis and in debt covenants. It uses EBITDA and interest bearing debt. Specifically, for Prufrock:

Interest bearing debt

$196 million 457 million

_______________________

_____________________________ .68 times

EBITDA

$967 million

Here we include notes payable (most likely notes payable is bank debt) and long-term debt

in the numerator and EBITDA in the denominator. Values below 1 on this ratio are considered very strong and values below 5 are considered weak. However a careful comparison

with other comparable firms is necessary to properly interpret the ratio.

Asset Management or Turnover Measures

We next turn our attention to the efficiency with which Prufrock uses its assets. The

measures in this section are sometimes called asset management or utilization ratios.

The specific ratios we discuss can all be interpreted as measures of turnover. What

they are intended to describe is how efficiently, or intensively, a firm uses its assets to generate sales. We first look at two important current assets: inventory and

receivables.

During the year, Prufrock had a cost of

goods sold of $1,344. Inventory at the end of the year was $422. With these numbers,

inventory turnover can be calculated as:

Inventory Turnover and Days’ Sales in Inventory

Cost of goods sold

Inventory turnover _____________________

Inventory

[3.9]

$1,344

________ 3.2 times

$422

CHAPTER 3 Financial Statements Analysis and Financial Models

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In a sense, we sold off, or turned over, the entire inventory 3.2 times during the year. As

long as we are not running out of stock and thereby forgoing sales, the higher this ratio is,

the more efficiently we are managing inventory.

If we know that we turned our inventory over 3.2 times during the year, we can immediately figure out how long it took us to turn it over on average. The result is the average

days’ sales in inventory:

365 days

Days’ sales in inventory ____________________

Inventory turnover

365 114 days

_____

3.2

[3.10]

This tells us that, roughly speaking, inventory sits 114 days on average before it is sold.

Alternatively, assuming we used the most recent inventory and cost figures, it will take

about 114 days to work off our current inventory.

For example, in September 2007, sales of General Motors (GM) pickup trucks could have

used a pickup. At that time, the company had a 120-day supply of the GMC Sierra and a

114-day supply of the Chevrolet Silverado. These numbers mean that at the then-current

rate of sales, it would take GM 120 days to deplete the available supply of Sierras whereas

a 60-day supply is considered normal in the industry. Of course, the days in inventory are

lower for better-selling models, and, fortunately for GM, its crossover vehicles were a hit. The

company had only a 22-day supply of Buick Enclaves and a 32-day supply of GMC Acadias.

Receivables Turnover and Days’ Sales in Receivables Our inventory measures give some

indication of how fast we can sell products. We now look at how fast we collect on those

sales. The receivables turnover is defined in the same way as inventory turnover:

Sales

Receivables turnover ______________________

Accounts receivable

$2,311

________ 12.3 times

$188

[3.11]

Loosely speaking, we collected our outstanding credit accounts and lent the money again

12.3 times during the year.2

This ratio makes more sense if we convert it to days, so the days’ sales in receivables is:

365 days

Days’ sales in receivables _______________________

Receivables turnover

365 30 days

_____

12.3

[3.12]

EXAMPLE

3.2

Therefore, on average, we collect on our credit sales in 30 days. For obvious reasons, this ratio

is frequently called the average collection period (ACP). Also note that if we are using the most

recent figures, we can also say that we have 30 days’ worth of sales currently uncollected.

P a y a b l e s Tu r n o v e r

Here is a variation on the receivables collection period. How long, on average, does it take for

Prufrock Corporation to pay its bills? To answer, we need to calculate the accounts payable turnover

rate using cost of goods sold. We will assume that Prufrock purchases everything on credit.

The cost of goods sold is $1,344, and accounts payable are $344. The turnover is therefore

$1,344/$344 3.9 times. So, payables turned over about every 365/3.9 94 days. On average, then,

Prufrock takes 94 days to pay. As a potential creditor, we might take note of this fact.

2

Here we have implicitly assumed that all sales are credit sales. If they were not, we would simply use total credit sales in these

calculations, not total sales.

52

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Total Asset Turnover Moving away from specific accounts like inventory or receivables, we

can consider an important “big picture” ratio, the total asset turnover ratio. As the name

suggests, total asset turnover is:

Sales

Total asset turnover _____________

Total assets

[3.13]

$2,311

________ .64 times

$3,588

PricewaterhouseCoopers has a useful

utility for extracting

EDGAR data. Try it at

www.edgarscan.

pwcglobal.com.

In other words, for every dollar in assets, we generated $.64 in sales.

3.3

M o r e Tu r n o v e r

EXAMPLE

Suppose you find that a particular company generates $.40 in annual sales for every dollar in total

assets. How often does this company turn over its total assets?

The total asset turnover here is .40 times per year. It takes 1/.40 2.5 years to turn assets over

completely.

Profitability Measures

The three types of measures we discuss in this section are probably the best-known and most

widely used of all financial ratios. In one form or another, they are intended to measure

how efficiently the firm uses its assets and how efficiently the firm manages its operations.

Profit Margin

Companies pay a great deal of attention to their profit margin:

Net income

Profit margin _____________

Sales

$363

________ 15.7%

$2,311

[3.14]

This tells us that Prufrock, in an accounting sense, generates a little less than 16 cents in

net income for every dollar in sales.

EBITDA Margin Another commonly used measure of profitability is the EBITDA margin.

As mentioned, EBITDA is a measure of before-tax operating cash flow. It adds back noncash expenses and does not include taxes or interest expense. As a consequence, EBITDA

margin looks more directly at operating cash flows than does net income and does not

include the effect of capital structure or taxes. For Prufrock, EBITDA margin is:

$967 million

EBITDA ________________

_________

41.8%

Sales

$2,311 million

All other things being equal, a relatively high margin is obviously desirable. This situation

corresponds to low expense ratios relative to sales. However, we hasten to add that other

things are often not equal.

For example, lowering our sales price will usually increase unit volume but will normally cause margins to shrink. Total profit (or, more importantly, operating cash flow) may

go up or down, so the fact that margins are smaller isn’t necessarily bad. After all, isn’t it

possible that, as the saying goes, “Our prices are so low that we lose money on everything

we sell, but we make it up in volume”?3

3

No, it’s not.

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Margins are very different for different industries. Grocery stores have a notoriously

low profit margin, generally around 2 percent. In contrast, the profit margin for the

pharmaceutical industry is about 18 percent. So, for example, it is not surprising that

recent profit margins for Kroger and Pfizer were about 0.2 percent and 17.7 percent,

respectively.

Return on Assets Return on assets (ROA) is a measure of profit per dollar of assets. It can

be defined several ways,4 but the most common is:

Net income

Return on assets _____________

Total assets

$363

________ 10.12%

$3,588

[3.15]

Return on equity (ROE) is a measure of how the stockholders fared during the year. Because benefiting shareholders is our goal, ROE is, in an accounting sense,

the true bottom-line measure of performance. ROE is usually measured as:

Return on Equity

Net income

Return on equity _____________

Total equity

$363

________ 14.01%

$2,591

[3.16]

Therefore, for every dollar in equity, Prufrock generated 14 cents in profit; but, again, this

is correct only in accounting terms.

Because ROA and ROE are such commonly cited numbers, we stress that it is important to remember they are accounting rates of return. For this reason, these measures

should properly be called return on book assets and return on book equity. In addition,

ROE is sometimes called return on net worth. Whatever it’s called, it would be inappropriate to compare the result to, for example, an interest rate observed in the financial

markets.

The fact that ROE exceeds ROA reflects Prufrock’s use of financial leverage. We will

examine the relationship between these two measures in the next section.

Market Value Measures

Our final group of measures is based, in part, on information not necessarily contained in

financial statements—the market price per share of the stock. Obviously, these measures

can be calculated directly only for publicly traded companies.

We assume that Prufrock has 33 million shares outstanding and the stock sold for

$88 per share at the end of the year. If we recall that Prufrock’s net income was $363 million, then we can calculate that its earnings per share were:

$363

Net income

______ $11

EPS _____________________

33

Shares outstanding

[3.17]

4

For example, we might want a return on assets measure that is neutral with respect to capital structure (interest expense) and

taxes. Such a measure for Prufrock would be:

$691

EBIT

_____________

________ 19.3%

Total assets

$3,588

This measure has a very natural interpretation. If 19.3 percent exceeds Prufrock’s borrowing rate, Prufrock will earn more money

on its investments than it will pay out to its creditors. The surplus will be available to Prufrock’s shareholders after adjusting for

taxes.

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Price-Earnings Ratio The first of our market value measures, the price-earnings or

PE ratio (or multiple), is defined as:

Price per share

PE ratio ____________________

Earnings per share

[3.18]

$88

_____ 8 times

$11

In the vernacular, we would say that Prufrock shares sell for eight times earnings, or we

might say that Prufrock shares have, or “carry,” a PE multiple of 8.

Because the PE ratio measures how much investors are willing to pay per dollar of current earnings, higher PEs are often taken to mean that the firm has significant prospects for

future growth. Of course, if a firm had no or almost no earnings, its PE would probably be

quite large; so, as always, care is needed in interpreting this ratio.

Market-to-Book Ratio

A second commonly quoted measure is the market-to-book ratio:

Market value per share

Market-to-book ratio _________________________

Book value per share

$88

$88

___________ _______ 1.12 times

$2,591/33

$78.5

[3.19]

Notice that book value per share is total equity (not just common stock) divided by the

number of shares outstanding.

Book value per share is an accounting number that reflects historical costs. In a loose

sense, the market-to-book ratio therefore compares the market value of the firm’s investments to their cost. A value less than 1 could mean that the firm has not been successful

overall in creating value for its stockholders.

Market Capitalization The market capitalization of a public firm is equal to the firm’s

stock market price per share multiplied by the number of shares outstanding. For Prufrock,

this is:

Price per share Shares outstanding $88 33 million $2,904 million

This is a useful number for potential buyers of Prufrock. A prospective buyer of all of the

outstanding shares of Prufrock (in a merger or acquisition) would need to come up with at

least $2,904 million plus a premium.

Enterprise Value Enterprise value is a measure of firm value that is very closely related to

market capitalization. Instead of focusing on only the market value of outstanding shares of

stock, it measures the market value of outstanding shares of stock plus the market value of

outstanding interest bearing debt less cash on hand. We know the market capitalization

of Prufrock but we do not know the market value of its outstanding interest bearing debt.

In this situation, the common practice is to use the book value of outstanding interest

bearing debt less cash on hand as an approximation. For Prufrock, enterprise value is (in

millions):

EV Market capitalization Market value of interest bearing debt cash

[3.20]

$2,904 ($196 457) $98 $3,459 million

The purpose of the EV measure is to better estimate how much it would take to buy all of

the outstanding stock of a firm and also to pay off the debt. The adjustment for cash is to

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recognize that if we were a buyer the cash could be used immediately to buy back debt or

pay a dividend.

Financial analysts use valuation multiples based upon a firm’s

enterprise value when the goal is to estimate the value of the firm’s total business rather

than just focusing on the value of its equity. To form an appropriate multiple, enterprise

value is divided by EBITDA. For Prufrock, the enterprise value multiple is:

Enterprise Value Multiples

$3,459 million

EV

_________

________________ 3.6 times

EBITDA

$967 million

The multiple is especially useful because it allows comparison of one firm with another

when there are differences in capital structure (interest expense), taxes, or capital spending.

The multiple is not directly affected by these differences.

Similar to PE ratios, we would expect a firm with high growth opportunities to have high

EV multiples.

This completes our definition of some common ratios. We could tell you about more of

them, but these are enough for now. We’ll leave it here and go on to discuss some ways of

using these ratios instead of just how to calculate them. Table 3.6 summarizes some of the

ratios we’ve discussed.

TABLE 3.6

Common Financial Ratios

I.

Short-Term Solvency, or Liquidity, Ratios

Current assets

Current ratio ______________

Current liabilities

365 days

Days’ sales in receivables __________________

Receivables turnover

Current assets Inventory

Quick ratio ______________________

Current liabilities

Sales

Total asset turnover __________

Total assets

Cash

Cash ratio ______________

Current liabilities

Total assets

Capital intensity __________

Sales

II. Long-Term Solvency, or Financial Leverage, Ratios

IV. Profitability Ratios

Total assets Total equity

Total debt ratio ______________________

Total assets

Net income

Profit margin __________

Sales

Debt-equity ratio Total debt/Total equity

Net income

Return on assets (ROA) __________

Total assets

Equity multiplier Total assets/Total equity

Net income

Return on equity (ROE) __________

Total equity

EBIT

Times interest earned ratio _______

Interest

Sales ______

Net income ______

Assets

ROE __________

Assets

Equity

Sales

EBITDA

Cash coverage ratio _______

Interest

III. Asset Utilization, or Turnover, Ratios

56

V.

Market Value Ratios

Cost of goods sold

Inventory turnover _______________

Inventory

Price per share

Price -earnings ratio ________________

Earnings per share

365 days

Days’ sales in inventory _______________

Inventory turnover

Market value per share

Market-to-book ratio ___________________

Book value per share

Sales

Receivables turnover _________________

Accounts receivable

Enterprise value

EV multiple ______________

EBITDA

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3.4

EXAMPLE

Atlantic and Pacific

Consider the following 2009 data for Atlantic’s Companies and Pacific Depot (billions except for price

per share):

AT L ANT I C ’ S C O M PA N I E S , I N C .

T H E PA C I FI C D E P O T, I N C .

$48.3

$ 4.8

$ 2.8

$ .5

$ 1.5

$ 6.7

$30.9

$24

1.5

$16.1

$77.3

$ 7.3

$ 4.4

$ .5

$ 1.9

$13.4

$44.3

$27

1.7

$17.7

Sales

EBIT

Net income

Cash

Depreciation

Interest bearing debt

Total assets

Price per share

Shares outstanding

Shareholder equity

1. Determine the profit margin, ROE, market capitalization, enterprise value, PE multiple, and EV

multiple for both Atlantic’s and Pacific Depot.

Equity multiplier

Asset turnover

Profit margin

ROE

Market capitalization

Enterprise value

PE multiple

EBITDA

EV multiple

AT L ANT I C’S C O M PA N I E S , I N C .

T H E PA C I FI C D E P O T, I N C .

30.9/16.1 1.9

48.3/30.9 1.6

2.8/48.3 5.8%

2.8/16.1 17.4%

1.5 24 $36 billion

(1.5 24) 6.7 .5 $42.2 billion

24/1.87 12.8

4.8 1.5 $6.3

42.2/6.3 6.7

44.3/17.7 2.5

77.3/44.3 1.7

4.4/77.3 5.7%

4.4/17.7 24.9%

1.7 27 $45.9 billion

(1.7 27) 13.4 .5 $58.8 billion

27/2.6 10.4

7.3 1.9 $9.2

58.8/9.2 6.4

2. How would you describe these two companies from a financial point of view? These are similarly

situated companies. In 2009, Pacific Depot had a higher ROE (partially because of using more debt

and higher turnover), but Atlantic’s had slightly higher PE and EV multiples. Both companies’ multiples were somewhat below the general market, raising questions about future growth prospects.

3.3

THE DU PONT IDENTITY

As we mentioned in discussing ROA and ROE, the difference between these two profitability measures reflects the use of debt financing or financial leverage. We illustrate the

relationship between these measures in this section by investigating a famous way of

decomposing ROE into its component parts.

A Closer Look at ROE

To begin, let’s recall the definition of ROE:

Net income

Return on equity _____________

Total equity

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If we were so inclined, we could multiply this ratio by Assets/Assets without changing

anything:

Assets

Net income _____________

Net income ________

Return on equity _____________

Total equity

Total equity

Assets

Assets

Net income _____________

_____________

Assets

Total equity

Notice that we have expressed the ROE as the product of two other ratios—ROA and the

equity multiplier:

ROE ROA Equity multiplier ROA (1 Debt-equity ratio)

Looking back at Prufrock, for example, we see that the debt-equity ratio was .39 and ROA

was 10.12 percent. Our work here implies that Prufrock’s ROE, as we previously calculated, is:

ROE 10.12% 1.39 14.01%

The difference between ROE and ROA can be substantial, particularly for certain businesses. For example, based on recent financial statements, Wells Fargo has an ROA of only

0.75 percent, which is actually fairly typical for a bank. However, banks tend to borrow a

lot of money, and, as a result, have relatively large equity multipliers. For Wells Fargo, ROE

is about 6.69 percent, implying an equity multiplier of 8.9.

We can further decompose ROE by multiplying the top and bottom by total sales:

Sales _____________

Assets

Net income _____________

ROE ______

Assets

Total equity

Sales

If we rearrange things a bit, ROE is:

Sales _____________

Assets

Net income ________

ROE _____________

Assets

Total equity

Sales

Return on assets

Profit margin Total asset turnover Equity multiplier

[3.21]

What we have now done is to partition ROA into its two component parts, profit margin

and total asset turnover. The last expression of the preceding equation is called the Du Pont

identity after the Du Pont Corporation, which popularized its use.

We can check this relationship for Prufrock by noting that the profit margin was 15.7 percent and the total asset turnover was .64. ROE should thus be:

ROE Profit margin Total asset turnover Equity multiplier

15.7%

.64

1.39

14%

This 14 percent ROE is exactly what we had before.

The Du Pont identity tells us that ROE is affected by three things:

1. Operating efficiency (as measured by profit margin).

2. Asset use efficiency (as measured by total asset turnover).

3. Financial leverage (as measured by the equity multiplier).

Weakness in either operating or asset use efficiency (or both) will show up in a diminished

return on assets, which will translate into a lower ROE.

Considering the Du Pont identity, it appears that the ROE could be leveraged up by increasing the amount of debt in the firm. However, notice that increasing debt also increases

interest expense, which reduces profit margins, which acts to reduce ROE. So, ROE could

go up or down, depending. More important, the use of debt financing has a number of other

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TABLE 3.7

The Du Pont Breakdown for Yahoo! and Google

Yahoo!

TW E LVE M ONT HS E NDI NG

ROE

P R O FI T M A R G I N

T O TA L A S S E T T U R N O V E R

E Q U I T Y M ULTIP LIER

12/09

12/08

12/07

4.8%

3.8%

6.9%

9.3%

5.9%

9.5%

0.433

0.527

0.570

1.20

1.22

1.28

Google

TW ELVE M ONT HS E NDI NG

ROE

P R O FI T M A R G I N

T O TA L A S S E T T U R N O V E R

E Q U I T Y M ULTIP LIER

12/09

12/08

12/07

18.1%

14.9%

18.6%

27.6%

19.4%

25.3%

0.584

0.686

0.655

1.12

1.12

1.12

effects, and, as we discuss at some length in later chapters, the amount of leverage a firm

uses is governed by its capital structure policy.

The decomposition of ROE we’ve discussed in this section is a convenient way of systematically approaching financial statement analysis. If ROE is unsatisfactory by some

measure, then the Du Pont identity tells you where to start looking for the reasons.

Yahoo! and Google are among the most important Internet companies in the world.

Yahoo! and Google may be good examples of how Du Pont analysis can be useful in helping to ask the right questions about a firm’s financial performance. The Du Pont breakdowns for Yahoo! and Google are summarized in Table 3.7.

As can be seen, in 2009, Yahoo! had an ROE of 4.8 percent, up from its ROE in 2008 of

3.8 percent. In contrast, in 2009, Google had an ROE of 18.1 percent, up from its ROE in

2008 of 14.9 percent. Given this information, how is it possible that Google’s ROE could

be so much higher than the ROE of Yahoo! during this period of time, and what accounts

for the decline in Yahoo!’s ROE?

On close inspection of the Du Pont breakdown, we see that Yahoo!’s profit margin in

2009 was only 4.8 percent. Meanwhile Google’s profit margin was 18.1 percent in 2009.

Yet Yahoo! and Google have very comparable asset turnover and financial leverage. What

can account for Google’s advantage over Yahoo! in profit margin? Operating efficiencies can come from higher volumes, higher prices, and/or lower costs. It is clear that the

big difference in ROE between the two firms can be attributed to the difference in profit

margins.

Problems with Financial Statement Analysis

We continue our chapter by discussing some additional problems that can arise in using

financial statements. In one way or another, the basic problem with financial statement

analysis is that there is no underlying theory to help us identify which quantities to look at

and to guide us in establishing benchmarks.

As we discuss in other chapters, there are many cases in which financial theory and economic logic provide guidance in making judgments about value and risk. Little such help

exists with financial statements. This is why we can’t say which ratios matter the most and

what a high or low value might be.

One particularly severe problem is that many firms are conglomerates, owning more or

less unrelated lines of business. GE is a well-known example. The consolidated financial

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THE REAL WORLD

W H AT ’ S I N A R AT I O ?

Abraham Briloff, a well-known financial commentator, famously remarked that “financial statements are like fine

perfume; to be sniffed but not swallowed.” As you have probably figured out by now, his point is that information

gleaned from financial statements—and ratios and growth rates computed from that information—should be taken

with a grain of salt.

For example, in early 2010, shares in Green Mountain Coffee Roasters had a PE ratio of about 58 times earnings.

You would expect that this stock would have a high growth rate, and indeed analysts thought so. The estimated

earnings growth rate for Green Mountain for the next year was 68 percent. At the same time, greeting card company American Greetings also had a PE ratio of about 68, but analysts estimated an earnings growth rate of only

9 percent for the next year. Why is the PE so high? The answer is that American Greetings simply had low earnings

the previous year. The “forward” PE ratio, which uses next year’s estimated earnings instead of past earnings was

only 9. So, caution is warranted when looking at PE ratios.

U.S. Airways illustrates another issue. If you calculated its ROE in 2009, you would get about 57.7 percent, which

is quite good. What’s strange is the company reported a loss of about $205 million dollars during 2009! What’s going

on is that U.S. Airways had a book value of equity balance of negative $355 million. In this situation, the more U.S.

Airways loses, the higher the ROE becomes. Of course, U.S. Airways’ market-to-book and PE ratios are also both

negative. How do you interpret a negative PE? We’re not really sure, either. Whenever a company has a negative

book value of equity, it means that losses have been so large that book equity has been wiped out. In such cases,

the ROE, PE ratio, and market-to-book ratio are often not reported because they are meaningless.

Even if a company’s book equity is positive, you still have to be careful. For example, consider venerable consumer products company Clorox, which had a market-to-book ratio of about 53 in late 2007. Since the market-tobook ratio measures the value created by the company for shareholders, this would seem to be a good sign. But

a closer look shows that Clorox’s book value of equity per share dropped from $7.23 in 2004 to $1.03 in 2006. This

decline had to do with accounting for stock repurchases made by the company, not gains or losses, but it nonetheless dramatically increased the market-to-book ratio in that year and subsequent years as well.

Financial ratios are important tools used in evaluating companies of all types, but you cannot simply take a number

as given. Instead, before doing any analysis, the first step is to ask whether the number actually makes sense.

statements for such firms don’t really fit any neat industry category. More generally, the

kind of peer group analysis we have been describing is going to work best when the firms

are strictly in the same line of business, the industry is competitive, and there is only one

way of operating.

Another problem that is becoming increasingly common is that major competitors and

natural peer group members in an industry may be scattered around the globe. The automobile industry is an obvious example. The problem here is that financial statements from

outside the United States do not necessarily conform to GAAP. The existence of different

standards and procedures makes it difficult to compare financial statements across national

borders.

Even companies that are clearly in the same line of business may not be comparable.

For example, electric utilities engaged primarily in power generation are all classified in

the same group. This group is often thought to be relatively homogeneous. However, most

utilities operate as regulated monopolies, so they don’t compete much with each other, at

least not historically. Many have stockholders, and many are organized as cooperatives

with no stockholders. There are several different ways of generating power, ranging from

hydroelectric to nuclear, so the operating activities of these utilities can differ quite a bit.

Finally, profitability is strongly affected by the regulatory environment, so utilities in different locations can be similar but show different profits.

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Several other general problems frequently crop up. First, different firms use different

accounting procedures—for inventory, for example. This makes it difficult to compare

statements. Second, different firms end their fiscal years at different times. For firms in

seasonal businesses (such as a retailer with a large Christmas season), this can lead to

difficulties in comparing balance sheets because of fluctuations in accounts during the

year. Finally, for any particular firm, unusual or transient events, such as a one-time profit

from an asset sale, may affect financial performance. Such events can give misleading

signals as we compare firms. The nearby The Real World box discusses some issues along

these lines.

3.4

FINANCIAL MODELS

Financial planning is another important use of financial statements. Most financial planning models output pro forma financial statements, where pro forma means “as a matter of

form.” In our case, this means that financial statements are the form we use to summarize

the projected future financial status of a company.

A Simple Financial Planning Model

We can begin our discussion of financial planning models with a relatively simple example. The

Computerfield Corporation’s financial statements from the most recent year are shown below.

Unless otherwise stated, the financial planners at Computerfield assume that all variables are tied directly to sales and current relationships are optimal. This means that all

items will grow at exactly the same rate as sales. This is obviously oversimplified; we use

this assumption only to make a point.

COM PUT E R FI E LD C O R P O R AT I O N

F i na n c i a l S t a t e m e n t s

I NCOM E STAT E M E NT

Sales

Costs

Net income

$1,000

800

$ 200

B A LA N C E S H E E T

Assets

$500

Total

$500

Debt

Equity

Total

$250

250

$500

Suppose sales increase by 20 percent, rising from $1,000 to $1,200. Planners would

then also forecast a 20 percent increase in costs, from $800 to $800 1.2 $960. The

pro forma income statement would thus look like this:

Pr o F or m a I n c o m e S t a t e m e n t

Sales

Costs

Net income

$1,200

960

$ 240

The assumption that all variables will grow by 20 percent lets us easily construct the

pro forma balance sheet as well:

Pr o Fo r m a B a l a n c e S h e e t

Assets

$600 (100)

Total

$600 (100)

Debt

Equity

Total

$300 (50)

300 (50)

$600 (100)

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Planware provides

insight into cash flow

forecasting at

www.planware.org.

Notice we have simply increased every item by 20 percent. The numbers in parentheses are

the dollar changes for the different items.

Now we have to reconcile these two pro forma statements. How, for example, can net

income be equal to $240 and equity increase by only $50? The answer is that Computerfield

must have paid out the difference of $240 50 $190, possibly as a cash dividend. In this

case dividends are the “plug” variable.

Suppose Computerfield does not pay out the $190. In this case, the addition to retained

earnings is the full $240. Computerfield’s equity will thus grow to $250 (the starting

amount) plus $240 (net income), or $490, and debt must be retired to keep total assets

equal to $600.

With $600 in total assets and $490 in equity, debt will have to be $600 490 $110.

Because we started with $250 in debt, Computerfield will have to retire $250 110 $140

in debt. The resulting pro forma balance sheet would look like this:

P r o Fo r m a B a l a n c e S h e e t

Assets

$600 (100)

Total

$600 (100)

Debt

Equity

Total

$110 (140)

490 (240)

$600 (100)

In this case, debt is the plug variable used to balance projected total assets and liabilities.

This example shows the interaction between sales growth and financial policy. As sales

increase, so do total assets. This occurs because the firm must invest in net working capital

and fixed assets to support higher sales levels. Because assets are growing, total liabilities

and equity, the right side of the balance sheet, will grow as well.

The thing to notice from our simple example is that the way the liabilities and owners’

equity change depends on the firm’s financing policy and its dividend policy. The growth in

assets requires that the firm decide on how to finance that growth. This is strictly a managerial decision. Note that in our example the firm needed no outside funds. This won’t usually

be the case, so we explore a more detailed situation in the next section.

The Percentage of Sales Approach

In the previous section, we described a simple planning model in which every item increased at the same rate as sales. This may be a reasonable assumption for some elements.

For others, such as long-term borrowing, it probably is not: The amount of long-term borrowing is set by management, and it does not necessarily relate directly to the level of sales.

In this section, we describe an extended version of our simple model. The basic idea is

to separate the income statement and balance sheet accounts into two groups, those that

vary directly with sales and those that do not. Given a sales forecast, we will then be able

to calculate how much financing the firm will need to support the predicted sales level.

The financial planning model we describe next is based on the percentage of sales

approach. Our goal here is to develop a quick and practical way of generating pro forma

statements. We defer discussion of some “bells and whistles” to a later section.

The Income Statement We start out with the most recent income statement for the Rosengarten Corporation, as shown in Table 3.8. Notice that we have still simplified things by

including costs, depreciation, and interest in a single cost figure.

Rosengarten has projected a 25 percent increase in sales for the coming year, so we are

anticipating sales of $1,000 1.25 $1,250. To generate a pro forma income statement,

we assume that total costs will continue to run at $800/1,000 80 percent of sales. With

this assumption, Rosengarten’s pro forma income statement is as shown in Table 3.9. The

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TABLE 3.8

ROSE NG A R T E N C O R P O R AT I O N

Income Statement

Sales

Costs

Taxable income

Taxes (34%)

Net income

Dividends

$1,000

800

$ 200

68

$ 132

Addition to retained earnings

$44

88

TABLE 3.9

ROSE NG A R T E N C O R P O R AT I O N

Pr o F o r m a I n c o m e S t a t e m e n t

Sales (projected)

Costs (80% of sales)

Taxable income

Taxes (34%)

$1,250

1,000

$ 250

85

$ 165

Net income

effect here of assuming that costs are a constant percentage of sales is to assume that the

profit margin is constant. To check this, notice that the profit margin was $132/1,000

13.2 percent. In our pro forma statement, the profit margin is $165/1,250 13.2 percent;

so it is unchanged.

Next, we need to project the dividend payment. This amount is up to Rosengarten’s

management. We will assume Rosengarten has a policy of paying out a constant fraction of

net income in the form of a cash dividend. For the most recent year, the dividend payout

ratio was:

Dividend payout ratio Cash dividends/Net income

$44/132 33 1/3%

[3.22]

We can also calculate the ratio of the addition to retained earnings to net income:

Addition to retained earnings/Net income $88/132 66 2/3%

This ratio is called the retention ratio or plowback ratio, and it is equal to 1 minus the

dividend payout ratio because everything not paid out is retained. Assuming that the payout

ratio is constant, the projected dividends and addition to retained earnings will be:

Projected dividends paid to shareholders $165 1/3 $ 55

Projected addition to retained earnings $165 2/3 110

$165

To generate a pro forma balance sheet, we start with the most recent

statement, as shown in Table 3.10.

On our balance sheet, we assume that some items vary directly with sales and others

do not. For those items that vary with sales, we express each as a percentage of sales for

the year just completed. When an item does not vary directly with sales, we write “n/a” for

“not applicable.”

The Balance Sheet

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TABLE 3.10

R O S E N G A R T E N C O R P O R AT I O N

Balance Sheet

As s e t s

Current assets

Cash

Accounts receivable

Inventory

Total

Fixed assets

Net plant and equipment

Total assets

Li a b i l i t i e s a n d O w n e r s’ E q u i t y

$

PE RCE N TA G E

OF SA LE S

$ 160

440

600

$1,200

16%

44

60

120

$1,800

180

$3,000

300%

Current liabilities

Accounts payable

Notes payable

Total

Long-term debt

Owners’ equity

Common stock and paid-in

surplus

Retained earnings

Total

Total liabilities and owners’ equity

$

P E R C E N TAGE

O F S ALES

$ 300

100

$ 400

$ 800

30%

n/a

n/a

n/a

$ 800

n/a

1,000

$1,800

$3,000

n/a

n/a

n/a

For example, on the asset side, inventory is equal to 60 percent of sales ($600/1,000)

for the year just ended. We assume this percentage applies to the coming year, so for each

$1 increase in sales, inventory will rise by $.60. More generally, the ratio of total assets to

sales for the year just ended is $3,000/1,000 3, or 300 percent.

This ratio of total assets to sales is sometimes called the capital intensity ratio. It tells

us the amount of assets needed to generate $1 in sales; the higher the ratio is, the more

capital intensive is the firm. Notice also that this ratio is just the reciprocal of the total asset

turnover ratio we defined previously.

For Rosengarten, assuming that this ratio is constant, it takes $3 in total assets to generate $1 in sales (apparently Rosengarten is in a relatively capital-intensive business). Therefore, if sales are to increase by $100, Rosengarten will have to increase total assets by three

times this amount, or $300.

On the liability side of the balance sheet, we show accounts payable varying with sales.

The reason is that we expect to place more orders with our suppliers as sales volume increases, so payables will change “spontaneously” with sales. Notes payable, on the other

hand, represents short-term debt such as bank borrowing. This will not vary unless we take

specific actions to change the amount, so we mark this item as “n/a.”

Similarly, we use “n/a” for long-term debt because it won’t automatically change with

sales. The same is true for common stock and paid-in surplus. The last item on the right

side, retained earnings, will vary with sales, but it won’t be a simple percentage of sales.

Instead, we will explicitly calculate the change in retained earnings based on our projected

net income and dividends.

We can now construct a partial pro forma balance sheet for Rosengarten. We do this by

using the percentages we have just calculated wherever possible to calculate the projected

amounts. For example, net fixed assets are 180 percent of sales; so, with a new sales level

of $1,250, the net fixed asset amount will be 1.80 $1,250 $2,250, representing an

increase of $2,250 1,800 $450 in plant and equipment. It is important to note that for

items that don’t vary directly with sales, we initially assume no change and simply write in

the original amounts. The result is shown in Table 3.11. Notice that the change in retained

earnings is equal to the $110 addition to retained earnings we calculated earlier.

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TABLE 3.11

R O S E N G A R T E N C O R P O R AT I O N

P a r t i a l P r o Fo r m a B a l a n c e S h e e t

As s e t s

Current assets

Cash

Accounts receivable

Inventory

Total

Fixed assets

Net plant and equipment

Total assets

Li a b i l i t i e s a n d O w n e r s’ E q u i ty

NE XT

YE AR

CHANGE

FR O M

CURRENT

YEAR

$ 200

550

750

$1,500

$ 40

110

150

$300

$2,250

$450

$3,750

$750

Current liabilities

Accounts payable

Notes payable

Total

Long-term debt

Owners’ equity

Common stock and paid-in

surplus

Retained earnings

Total

Total liabilities and owners’ equity

External financing needed

NEXT

YEAR

C HANGE

FR OM

C UR R ENT

Y EAR

$ 375

100

$ 475

$ 800

$ 75

0

$ 75

$ 0

$ 800

$ 0

1,110

$1,910

$3,185

$ 565

110

$110

$185

$565

Inspecting our pro forma balance sheet, we notice that assets are projected to increase

by $750. However, without additional financing, liabilities and equity will increase by only

$185, leaving a shortfall of $750 185 $565. We label this amount external financing

needed (EFN).

Rather than create pro forma statements, if we were so inclined, we could calculate EFN

directly as follows:

Spontaneous liabilities

Assets Sales _________________________

EFN ________

Sales PM

Sales

Sales

Projected sales (1 d )

[3.23]

In this expression, “Sales” is the projected change in sales (in dollars). In our example

projected sales for next year are $1,250, an increase of $250 over the previous year, so

Sales $250. By “Spontaneous liabilities,” we mean liabilities that naturally move up

and down with sales. For Rosengarten, the spontaneous liabilities are the $300 in accounts

payable. Finally, PM and d are the profit margin and dividend payout ratios, which we previously calculated as 13.2 percent and 33 1/3 percent, respectively. Total assets and sales

are $3,000 and $1,000, respectively, so we have:

$3,000

$300

1 $565

EFN ________ $250 _______ $250 .132 $1,250 1 __

1,000

1,000

3

(

)

In this calculation, notice that there are three parts. The first part is the projected

increase in assets, which is calculated using the capital intensity ratio. The second is

the spontaneous increase in liabilities. The third part is the product of profit margin and

projected sales, which is projected net income, multiplied by the retention ratio. Thus, the

third part is the projected addition to retained earnings.

A Particular Scenario Our financial planning model now reminds us of one of those good

news–bad news jokes. The good news is we’re projecting a 25 percent increase in sales. The bad

news is this isn’t going to happen unless Rosengarten can somehow raise $565 in new financing.

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TABLE 3.12

R O S E N G A R T E N C O R P O R AT I O N

P r o Fo r m a B a l a n c e S h e e t

As s e t s

Current assets

Cash

Accounts receivable

Inventory

Total

Fixed assets

Net plant and equipment

Total assets

Li a b i l i t i e s a n d O w n e r s’ E q u i t y

NE XT

YE AR

CHANG E

F ROM

CURRE N T

YE AR

$ 200

550

750

$1,500

$ 40

110

150

$300

$2,250

$450

$3,750

$750

Current liabilities

Accounts payable

Notes payable

Total

Long-term debt

Owners’ equity

Common stock and paid-in surplus

Retained earnings

Total

Total liabilities and owners’ equity

NEXT

YEAR

C H ANGE

FR OM

C U RR ENT

Y EAR

$ 375

325

$ 700

$1,140

$ 75

225

$300

$340

$ 800

1,110

$1,910

$3,750

$ 0

110

$110

$750

This is a good example of how the planning process can point out problems and potential conflicts. If, for example, Rosengarten has a goal of not borrowing any additional funds

and not selling any new equity, then a 25 percent increase in sales is probably not feasible.

If we take the need for $565 in new financing as given, we know that Rosengarten has

three possible sources: short-term borrowing, long-term borrowing, and new equity. The

choice of some combination among these three is up to management; we will illustrate only

one of the many possibilities.

Suppose Rosengarten decides to borrow the needed funds. In this case, the firm might

choose to borrow some over the short term and some over the long term. For example, current assets increased by $300 whereas current liabilities rose by only $75. Rosengarten could

borrow $300 75 $225 in short-term notes payable and leave total net working capital

unchanged. With $565 needed, the remaining $565 225 $340 would have to come from

long-term debt. Table 3.12 shows the completed pro forma balance sheet for Rosengarten.

We have used a combination of short- and long-term debt as the plug here, but we

emphasize that this is just one possible strategy; it is not necessarily the best one by any

means. We could (and should) investigate many other scenarios. The various ratios we discussed earlier come in handy here. For example, with the scenario we have just examined,

we would surely want to examine the current ratio and the total debt ratio to see if we were

comfortable with the new projected debt levels.

3.5

EXTERNAL FINANCING AND GROWTH

External financing needed and growth are obviously related. All other things staying the

same, the higher the rate of growth in sales or assets, the greater will be the need for external financing. In the previous section, we took a growth rate as given, and then we determined the amount of external financing needed to support that growth. In this section, we

turn things around a bit. We will take the firm’s financial policy as given and then examine

the relationship between that financial policy and the firm’s ability to finance new investments and thereby grow.

We emphasize that we are focusing on growth not because growth is an appropriate goal; instead, for our purposes, growth is simply a convenient means of examining

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the interactions between investment and financing decisions. In effect, we assume that the

use of growth as a basis for planning is just a reflection of the very high level of aggregation

used in the planning process.

EFN and Growth

The first thing we need to do is establish the relationship between EFN and growth. To

do this, we introduce the simplified income statement and balance sheet for the Hoffman

Company in Table 3.13. Notice that we have simplified the balance sheet by combining

short-term and long-term debt into a single total debt figure. Effectively, we are assuming

that none of the current liabilities vary spontaneously with sales. This assumption isn’t as

restrictive as it sounds. If any current liabilities (such as accounts payable) vary with sales,

we can assume that any such accounts have been netted out in current assets. Also, we continue to combine depreciation, interest, and costs on the income statement.

Suppose the Hoffman Company is forecasting next year’s sales level at $600, a $100

increase. Notice that the percentage increase in sales is $100/500 20 percent. Using the

percentage of sales approach and the figures in Table 3.13, we can prepare a pro forma income statement and balance sheet as in Table 3.14. As Table 3.14 illustrates, at a 20 percent

growth rate, Hoffman needs $100 in new assets. The projected addition to retained earnings

is $52.8, so the external financing needed, EFN, is $100 52.8 $47.2.

Notice that the debt-equity ratio for Hoffman was originally (from Table 3.13) equal to

$250/250 1.0. We will assume that the Hoffman Company does not wish to sell new equity. In this case, the $47.2 in EFN will have to be borrowed. What will the new debt-equity

ratio be? From Table 3.14, we know that total owners’ equity is projected at $302.8. The

new total debt will be the original $250 plus $47.2 in new borrowing, or $297.2 total. The

debt-equity ratio thus falls slightly from 1.0 to $297.2/302.8 .98.

Table 3.15 shows EFN for several different growth rates. The projected addition to retained earnings and the projected debt-equity ratio for each scenario are also given (you

should probably calculate a few of these for practice). In determining the debt-equity ratios,

TABLE 3.13

H O FFM A N C O M PA N Y

Income Statement and Balance Sheet

I N C O M E S TAT E M E N T

Sales

Costs

Taxable income

Taxes (34%)

Net income

Dividends

Addition to retained earnings

$500

400

$100

34

$ 66

$22

44

B A LA N C E S H E E T

As s e t s

Current assets

Net fixed assets

Total assets

Li a b i l i t i e s a n d O w n e r s’ E q u i t y

$

P E R C E N TA G E

O F S A LE S

$200

300

$500

40%

60

100%

Total debt

Owners’ equity

Total liabilities and owners’ equity

$

P ER C ENTAGE

OF S ALES

$250

250

$500

n/a

n/a

n/a

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TABLE 3.14

H O FFM A N C O M PA N Y

Pr o F o r ma I n c o m e S t a t e m e n t a n d B a l a n c e S h e e t

I N C O M E S TAT E M E N T

Sales (projected)

Costs (80% of sales)

Taxable income

Taxes (34%)

Net income

Dividends

Addition to retained earnings

$600.0

480.0

$120.0

40.8

$ 79.2

$26.4

52.8

B A LA N C E S H E E T

As s e t s

Current assets

Net fixed assets

Total assets

Li a b i l i t i e s a n d O w n e r s’ E q u i t y

$

PE RCE N TA G E

OF SA LE S

$240.0

360.0

$600.0

40%

60

100%

Total debt

Owners’ equity

Total liabilities and owners’ equity

External financing needed

$

P E R C E N TAGE

O F S A LES

$250.0

302.8

$552.8

$ 47.2

n/a

n/a

n/a

n/a

we assumed that any needed funds were borrowed, and we also assumed any surplus funds

were used to pay off debt. Thus, for the zero growth case the debt falls by $44, from $250 to

$206. In Table 3.15, notice that the increase in assets required is simply equal to the original

assets of $500 multiplied by the growth rate. Similarly, the addition to retained earnings is

equal to the original $44 plus $44 times the growth rate.

Table 3.15 shows that for relatively low growth rates, Hoffman will run a surplus, and

its debt-equity ratio will decline. Once the growth rate increases to about 10 percent, however, the surplus becomes a deficit. Furthermore, as the growth rate exceeds approximately

20 percent, the debt-equity ratio passes its original value of 1.0.

Figure 3.1 illustrates the connection between growth in sales and external financing

needed in more detail by plotting asset needs and additions to retained earnings from

Table 3.15 against the growth rates. As shown, the need for new assets grows at a much

faster rate than the addition to retained earnings, so the internal financing provided by the

addition to retained earnings rapidly disappears.

As this discussion shows, whether a firm runs a cash surplus or deficit depends on growth.

Microsoft is a good example. Its revenue growth in the 1990s was amazing, averaging well

TABLE 3.15

Growth and Projected

EFN for the Hoffman

Company

PROJ E CT E D

SAL E S

GROW T H

INCREASE

IN ASSETS

REQUIRED

ADDITION TO

R E TA I N E D

EARNINGS

EXTERNAL

FI N A N C I N G

N E E D E D , E FN

P R O J E C TED

D E B T- E Q UITY

R AT I O

0%

5

10

15

$ 0

25

50

75

100

125

$44.0

46.2

48.4

50.6

52.8

55.0

$44.0

21.2

1.6

24.4

47.2

70.0

.70

.77

.84

.91

.98

1.05

20

25

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Asset needs and retained earnings ($)

FIGURE 3.1

Increase

in assets

required

125

Growth and Related

Financing Needed for the

Hoffman Company

100

EFN ⬎ 0

(deficit)

75

50

44

25

Projected

addition

to retained

earnings

EFN ⬍ 0

(surplus)

5

15

20

10

Projected growth in sales (%)

25

over 30 percent per year for the decade. Growth slowed down noticeably over the 2000–2009

period, but, nonetheless, Microsoft’s combination of growth and substantial profit margins

led to enormous cash surpluses. In part because Microsoft paid few dividends, the cash really

piled up; in 2010, Microsoft’s cash and short-term investment horde exceeded $36 billion.

Financial Policy and Growth

Based on our discussion just preceding, we see that there is a direct link between growth

and external financing. In this section, we discuss two growth rates that are particularly

useful in long-range planning.

The first growth rate of interest is the maximum growth rate

that can be achieved with no external financing of any kind. We will call this the internal

growth rate because this is the rate the firm can maintain with internal financing only. In

Figure 3.1, this internal growth rate is represented by the point where the two lines cross.

At this point, the required increase in assets is exactly equal to the addition to retained earnings, and EFN is therefore zero. We have seen that this happens when the growth rate is

slightly less than 10 percent. With a little algebra (see Problem 28 at the end of the chapter),

we can define this growth rate more precisely as:

The Internal Growth Rate

ROA b

Internal growth rate ______________

1 ROA b

[3.24]

where ROA is the return on assets we discussed earlier, and b is the plowback, or retention,

ratio also defined earlier in this chapter.

For the Hoffman Company, net income was $66 and total assets were $500. ROA is thus

$66/500 13.2 percent. Of the $66 net income, $44 was retained, so the plowback ratio, b,

is $44/66 2/3. With these numbers, we can calculate the internal growth rate as:

ROA b

Internal growth rate ______________

1 ROA b

.132 (2/3)

_________________

1 .132 (2/3)

9.65%

Thus, the Hoffman Company can expand at a maximum rate of 9.65 percent per year without external financing.

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The Sustainable Growth Rate We have seen that if the Hoffman Company wishes to grow

more rapidly than at a rate of 9.65 percent per year, external financing must be arranged.

The second growth rate of interest is the maximum growth rate a firm can achieve with no

external equity financing while it maintains a constant debt-equity ratio. This rate is commonly called the sustainable growth rate because it is the maximum rate of growth a firm

can maintain without increasing its financial leverage.

There are various reasons why a firm might wish to avoid equity sales. For example, new

equity sales can be expensive because of the substantial fees that may be involved. Alternatively, the current owners may not wish to bring in new owners or contribute additional

equity. Why a firm might view a particular debt-equity ratio as optimal is discussed in later

chapters; for now, we will take it as given.

Based on Table 3.15, the sustainable growth rate for Hoffman is approximately 20 percent because the debt-equity ratio is near 1.0 at that growth rate. The precise value can be

calculated as follows (see Problem 28 at the end of the chapter):

ROE b

Sustainable growth rate ______________

1 ROE b

[3.25]

This is identical to the internal growth rate except that ROE, return on equity, is used instead of ROA.

For the Hoffman Company, net income was $66 and total equity was $250; ROE is thus

$66/250 26.4 percent. The plowback ratio, b, is still 2/3, so we can calculate the sustainable growth rate as:

ROE b

Sustainable growth rate ______________

1 ROE b

.264 (2/3)

_________________

1 .264 (2/3)

21.36%

EXAMPLE

3.5

Thus, the Hoffman Company can expand at a maximum rate of 21.36 percent per year

without external equity financing.

Sustainable Growth

Suppose Hoffman grows at exactly the sustainable growth rate of 21.36 percent. What will the pro

forma statements look like?

At a 21.36 percent growth rate, sales will rise from $500 to $606.8. The pro forma income statement

will look like this:

H O FFM A N C O M PA N Y

P r o Fo r m a I n c o m e S t a t e m e n t

Sales (projected)

Costs (80% of sales)

Taxable income

Taxes (34%)

Net income

Dividends

Addition to retained earnings

$606.8

485.4

$121.4

41.3

$ 80.1

$26.7

53.4

(continued )

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We construct the balance sheet just as we did before. Notice, in this case, that owners’ equity will rise

from $250 to $303.4 because the addition to retained earnings is $53.4.

HO FFM A N C O M PA N Y

Pr o F o r m a B a l a n c e S h e e t

As s e t s

Current assets

Net fixed assets

Total assets

Li a b i l i t i e s a n d O w n e r s’ E q u i t y

$

PE RCE NTA G E

OF SALE S

$242.7

364.1

$606.8

40%

60

100%

Total debt

Owners’ equity

Total liabilities and

owners’ equity

External financing

needed

$

P E R C E N TA G E

O F S A LE S

$250.0

303.4

$553.4

n/a

n/a

n/a

$ 53.4

n/a

As illustrated, EFN is $53.4. If Hoffman borrows this amount, then total debt will rise to $303.4, and the

debt-equity ratio will be exactly 1.0, which verifies our earlier calculation. At any other growth rate,

something would have to change.

Determinants of Growth Earlier in this chapter, we saw that the return on equity, ROE,

could be decomposed into its various components using the Du Pont identity. Because

ROE appears so prominently in the determination of the sustainable growth rate, it is obvious that the factors important in determining ROE are also important determinants of

growth.

From our previous discussions, we know that ROE can be written as the product of three

factors:

ROE Profit margin Total asset turnover Equity multiplier

If we examine our expression for the sustainable growth rate, we see that anything that

increases ROE will increase the sustainable growth rate by making the top bigger and the

bottom smaller. Increasing the plowback ratio will have the same effect.

Putting it all together, what we have is that a firm’s ability to sustain growth depends

explicitly on the following four factors:

1. Profit margin: An increase in profit margin will increase the firm’s ability to

generate funds internally and thereby increase its sustainable growth.

2. Dividend policy: A decrease in the percentage of net income paid out as

dividends will increase the retention ratio. This increases internally generated

equity and thus increases sustainable growth.

3. Financial policy: An increase in the debt-equity ratio increases the firm’s

financial leverage. Because this makes additional debt financing available, it

increases the sustainable growth rate.

4. Total asset turnover: An increase in the firm’s total asset turnover increases the

sales generated for each dollar in assets. This decreases the firm’s need for new

assets as sales grow and thereby increases the sustainable growth rate. Notice that

increasing total asset turnover is the same thing as decreasing capital intensity.

The sustainable growth rate is a very useful planning number. What it illustrates is the

explicit relationship between the firm’s four major areas of concern: its operating efficiency

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EXAMPLE

3.6

as measured by profit margin, its asset use efficiency as measured by total asset turnover,

its dividend policy as measured by the retention ratio, and its financial policy as measured

by the debt-equity ratio.

Profit Margins and Sustainable Growth

The Sandar Co. has a debt-equity ratio of .5, a profit margin of 3 percent, a dividend payout ratio of

40 percent, and a capital intensity ratio of 1. What is its sustainable growth rate? If Sandar desired a

10 percent sustainable growth rate and planned to achieve this goal by improving profit margins, what

would you think?

ROE is .03 1 1.5 4.5 percent. The retention ratio is 1 .40 .60. Sustainable growth is

thus .045(.60)/[1 .045(.60)] 2.77 percent.

For the company to achieve a 10 percent growth rate, the profit margin will have to rise. To see

this, assume that sustainable growth is equal to 10 percent and then solve for profit margin, PM:

.10 PM(1.5)(.6)/[1 PM(1.5)(.6)]

PM .1/.99 10.1%

For the plan to succeed, the necessary increase in profit margin is substantial, from 3 percent to

about 10 percent. This may not be feasible.

Given values for all four of these, there is only one growth rate that can be achieved.

This is an important point, so it bears restating:

If a firm does not wish to sell new equity and its profit margin, dividend policy,

financial policy, and total asset turnover (or capital intensity) are all fixed, then there

is only one possible growth rate.

One of the primary benefits of financial planning is that it ensures internal consistency

among the firm’s various goals. The concept of the sustainable growth rate captures this

element nicely. Also, we now see how a financial planning model can be used to test the

feasibility of a planned growth rate. If sales are to grow at a rate higher than the sustainable

growth rate, the firm must increase profit margins, increase total asset turnover, increase

financial leverage, increase earnings retention, or sell new shares.

The two growth rates, internal and sustainable, are summarized in Table 3.16.

A Note about Sustainable Growth Rate Calculations

Very commonly, the sustainable growth rate is calculated using just the numerator in

our expression, ROE b. This causes some confusion, which we can clear up here. The

issue has to do with how ROE is computed. Recall that ROE is calculated as net income

divided by total equity. If total equity is taken from an ending balance sheet (as we have

done consistently, and is commonly done in practice), then our formula is the right one.

However, if total equity is from the beginning of the period, then the simpler formula is

the correct one.

In principle, you’ll get exactly the same sustainable growth rate regardless of which

way you calculate it (as long as you match up the ROE calculation with the right formula).

In reality, you may see some differences because of accounting-related complications. By

the way, if you use the average of beginning and ending equity (as some advocate), yet

another formula is needed. Also, all of our comments here apply to the internal growth

rate as well.

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TABLE 3.16

I. Internal Growth Rate

Summary of Internal

and Sustainable

Growth Rates

ROA b

Internal growth rate __________

1 ROA b

where

ROA Return on assets Net income/Total assets

b Plowback (retention) ratio

Addition to retained earnings/Net income

The internal growth rate is the maximum growth rate that can be achieved with no external financing

of any kind.

II. Sustainable Growth Rate

ROE b

Sustainable growth rate _________

1 ROE b

where

ROE Return on equity Net income/Total equity

b Plowback (retention) ratio

Addition to retained earnings/Net income

The sustainable growth rate is the maximum growth rate that can be achieved with no external equity

financing while maintaining a constant debt-equity ratio.

3 . 6 S O M E C A V E AT S R E G A R D I N G F I N A N C I A L

PLANNING MODELS

Financial planning models do not always ask the right questions. A primary reason is that they

tend to rely on accounting relationships and not financial relationships. In particular, the three

basic elements of firm value tend to get left out—namely, cash flow size, risk, and timing.

Because of this, financial planning models sometimes do not produce output that gives

the user many meaningful clues about what strategies will lead to increases in value. Instead, they divert the user’s attention to questions concerning the association of, say, the

debt-equity ratio and firm growth.

The financial model we used for the Hoffman Company was simple—in fact, too simple.

Our model, like many in use today, is really an accounting statement generator at heart.

Such models are useful for pointing out inconsistencies and reminding us of financial

needs, but they offer little guidance concerning what to do about these problems.

In closing our discussion, we should add that financial planning is an iterative process.

Plans are created, examined, and modified over and over. The final plan will be a result

negotiated between all the different parties to the process. In fact, long-term financial planning in most corporations relies on what might be called the Procrustes approach.5 Upperlevel management has a goal in mind, and it is up to the planning staff to rework and to

ultimately deliver a feasible plan that meets that goal.

The final plan will therefore implicitly contain different goals in different areas and also

satisfy many constraints. For this reason, such a plan need not be a dispassionate assessment of what we think the future will bring; it may instead be a means of reconciling the

planned activities of different groups and a way of setting common goals for the future.

However it is done, the important thing to remember is that financial planning should

not become a purely mechanical exercise. If it does, it will probably focus on the wrong

things. Nevertheless, the alternative to planning is stumbling into the future. Perhaps the

immortal Yogi Berra (the baseball catcher, not the cartoon character), said it best: “Ya

gotta watch out if you don’t know where you’re goin’. You just might not get there.”6

5

In Greek mythology, Procrustes is a giant who seizes travelers and ties them to an iron bed. He stretches them or cuts off their

legs as needed to make them fit the bed.

6

We’re not exactly sure what this means, either, but we like the sound of it.

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SUMMARY AND CONCLUSIONS

This chapter focuses on working with information contained in financial statements. Specifically, we

studied standardized financial statements, ratio analysis, and long-term financial planning.

1. We explained that differences in firm size make it difficult to compare financial statements, and

we discussed how to form common-size statements to make comparisons easier and more

meaningful.

2. Evaluating ratios of accounting numbers is another way of comparing financial statement information. We defined a number of the most commonly used ratios, and we discussed the famous

Du Pont identity.

3. We showed how pro forma financial statements can be generated and used to plan for future

financing needs.

After you have studied this chapter, we hope that you have some perspective on the uses and abuses

of financial statement information. You should also find that your vocabulary of business and financial

terms has grown substantially.

CONCEPT QUESTIONS

1. Financial Ratio Analysis A financial ratio by itself tells us little about a company since financial

ratios vary a great deal across industries. There are two basic methods for analyzing financial

ratios for a company: time trend analysis and peer group analysis. Why might each of these

analysis methods be useful? What does each tell you about the company’s financial health?

2. Industry-Specific Ratios So-called “same-store sales” are a very important measure for

companies as diverse as McDonald’s and Sears. As the name suggests, examining same-store

sales means comparing revenues from the same stores or restaurants at two different points in

time. Why might companies focus on same-store sales rather than total sales?

3. Sales Forecast Why do you think most long-term financial planning begins with sales forecasts? Put differently, why are future sales the key input?

4. Sustainable Growth In the chapter, we used Rosengarten Corporation to demonstrate how

to calculate EFN. The ROE for Rosengarten is about 7.3 percent, and the plowback ratio is about

67 percent. If you calculate the sustainable growth rate for Rosengarten, you will find it is only

5.14 percent. In our calculation for EFN, we used a growth rate of 25 percent. Is this possible?

(Hint: Yes. How?)

5. EFN and Growth Rate Broslofski Co. maintains a positive retention ratio and keeps its debtequity ratio constant every year. When sales grow by 20 percent, the firm has a negative

projected EFN. What does this tell you about the firm’s sustainable growth rate? Do you know,

with certainty, if the internal growth rate is greater than or less than 20 percent? Why? What

happens to the projected EFN if the retention ratio is increased? What if the retention ratio is

decreased? What if the retention ratio is zero?

6. Common-Size Financials One tool of financial analysis is common-size financial statements.

Why do you think common-size income statements and balance sheets are used? Note that the

accounting statement of cash flows is not converted into a common-size statement. Why do you

think this is?

7. Asset Utilization and EFN One of the implicit assumptions we made in calculating the external

funds needed was that the company was operating at full capacity. If the company is operating

at less than full capacity, how will this affect the external funds needed?

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Use the following information to answer the next five questions: A small business called The

Grandmother Calendar Company began selling personalized photo calendar kits. The kits were a hit,

and sales soon sharply exceeded forecasts. The rush of orders created a huge backlog, so the company leased more space and expanded capacity, but it still could not keep up with demand. Equipment failed from overuse and quality suffered. Working capital was drained to expand production,

and, at the same time, payments from customers were often delayed until the product was shipped.

Unable to deliver on orders, the company became so strapped tor cash that employee paychecks

began to bounce Finally, out of cash, the company ceased operations entirely three years later.

8. Product Sales Do you think the company would have suffered the same fate if its product had

been less popular? Why or why not?

9. Cash Flow The Grandmother Calendar Company clearly had a cash flow problem. In the context of the cash flow analysis we developed in Chapter 2, what was the impact of customers’ not

paying until orders were shipped?

10. Corporate Borrowing If the firm was so successful at selling, why wouldn’t a bank or some

other lender step in and provide it with the cash it needed to continue?

11. Cash Flow Which is the biggest culprit here: too many orders, too little cash, or too little

production capacity?

12. Cash Flow What are some of the actions that a small company like The Grandmother Calendar

Company can take (besides expansion of capacity) if it finds itself in a situation in which growth

in sales outstrips production?

13. Comparing ROE and ROA Both ROA and ROE measure profitability. Which one is more useful

for comparing two companies? Why?

14. Ratio Analysis Consider the ratio EBITDA/Assets. What does this ratio tell us? Why might it be

more useful than ROA in comparing two companies?

QUESTIONS AND PROBLEMS

1. Du Pont Identity If Alexander, Inc., has an equity multiplier of 2.50, total asset turnover of 1.15,

and a profit margin of 6.4 percent, what is its ROE?

2. Equity Multiplier and Return on Equity Draiman Company has a debt-equity ratio of 0.75.

Return on assets is 10.4 percent, and total equity is $900,000. What is the equity multiplier?

Return on equity? Net income?

Basic

(Questions 1–10)

3. Using the Du Pont Identity Y3K, Inc., has sales of $4,350, total assets of $3,218, and a debtequity ratio of 0.65. If its return on equity is 15 percent, what is its net income?

4. EFN

The most recent financial statements for Cornell, Inc., are shown here:

I NCOM E STAT E M E NT

Sales

Costs

Taxable income

Taxes (34%)

Net income

$34,000

25,800

$ 8,200

2,788

$ 5,412

B A LA N C E S H E E T

Assets

$100,300

Total

$100,300

Debt

Equity

Total

$ 26,500

73,800

$100,300

Assets and costs are proportional to sales. Debt and equity are not. A dividend of $1,623.60

was paid, and the company wishes to maintain a constant payout ratio. Next year’s sales are

projected to be $38,420. What is the external financing needed?

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5. Sales and Growth The most recent financial statements for Weyland Co. are shown here:

I NCOM E STAT E M E N T

Sales

Costs

Taxable income

Taxes (34%)

Net income

$59,000

36,400

$22,600

7,684

$14,916

B A LA N C E S H E E T

Current assets

Fixed assets

Total

$ 17,000

139,000

$156,000

Long-term debt

Equity

Total

$ 51,000

105,000

$156,000

Assets and costs are proportional to sales. The company maintains a constant 30 percent

dividend payout ratio and a constant debt-equity ratio. What is the maximum increase in sales

that can be sustained assuming no new equity is issued?

6. Sustainable Growth If the SGS Corp. has a 13 percent ROE and a 25 percent payout ratio, what

is its sustainable growth rate?

7. Sustainable Growth Assuming the following ratios are constant, what is the sustainable

growth rate?

2.50

6.5%

1.10

60%

Total asset turnover

Profit margin

Equity multiplier

Payout ratio

8. Calculating EFN The most recent financial statements for Incredible Edibles, Inc., are shown

here (assuming no income taxes):

I NCOM E STAT E M E N T

Sales

Costs

Net income

$8,400

6,190

$2,210

B A LA N C E S H E E T

Assets

$21,500

Total

$21,500

Debt

Equity

Total

$ 4,200

17,300

$21,500

Assets and costs are proportional to sales. Debt and equity are not. No dividends are paid. Next

year’s sales are projected to be $9,660. What is the external financing needed?

9. External Funds Needed Cheryl Colby, CFO of Charming Florist Ltd., has created the firm’s

pro forma balance sheet for the next fiscal year. Sales are projected to grow by 15 percent to

$317.4 million. Current assets, fixed assets, and short-term debt are 20 percent, 90 percent,

and 15 percent of sales, respectively. Charming Florist pays out 40 percent of its net income in

dividends. The company currently has $40 million of long-term debt, and $20 million in common

stock par value. The profit margin is 10 percent.

a. Construct the current balance sheet for the firm using the projected sales figure.

b. Based on Ms. Colby’s sales growth forecast, how much does Charming Florist need in external funds for the upcoming fiscal year?

c. Construct the firm’s pro forma balance sheet for the next fiscal year and confirm the external

funds needed that you calculated in part (b).

10. Sustainable Growth Rate The Steiben Company has an ROE of 8.45 percent and a payout ratio

of 30 percent.

a. What is the company’s sustainable growth rate?

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b. Can the company’s actual growth rate be different from its sustainable growth rate? Why or

why not?

c. How can the company increase its sustainable growth rate?

11. Return on Equity Firm A and Firm B have debt / total asset ratios of 35 percent and 30 percent

and returns on total assets of 10 percent and 12 percent, respectively. Which firm has a greater

return on equity?

Intermediate

(Questions 11–23)

12. Ratios and Foreign Companies Prince Albert Canning PLC had a net loss of £18,351 on sales

of £163,184. What was the company’s profit margin? Does the fact that these figures are quoted

in a foreign currency make any difference? Why? In dollars, sales were $261,070. What was the

net loss in dollars?

13. External Funds Needed The Optical Scam Company has forecast an 18 percent sales growth

rate for next year. The current financial statements are shown below. Current assets, fixed

assets, and short-term debt are proportional to sales.

I N C O M E S TAT E M E N T

Sales

Costs

Taxable income

Taxes

Net income

Dividends

Additions to retained earnings

$37,000,000

28,900,000

$ 8,100,000

2,835,000

$ 5,265,000

$1,579,500

$3,685,500

B A LA N C E S H E E T

As s e t s

Current assets

Fixed assets

Total assets

Li a b i l i t i e s a n d E q u i t y

$10,500,000

Short-term debt

Long-term debt

$ 6,500,000

7,000,000

Common stock

Accumulated retained earnings

Total equity

Total liabilities and equity

$ 3,000,000

24,000,000

$27,000,000

$40,500,000

30,000,000

$40,500,000

a. Using the equation from the chapter, calculate the external funds needed for next year.

b. Construct the firm’s pro forma balance sheet for next year and confirm the external funds

needed you calculated in part (a).

c. Calculate the sustainable growth rate for the company.

d. Can Optical Scam eliminate the need for external funds by changing its dividend policy?

What other options are available to the company to meet its growth objectives?

14. Days’ Sales in Receivables A company has net income of $187,000, a profit margin of

6.5 percent, and an accounts receivable balance of $145,900. Assuming 80 percent of sales are

on credit, what is the company’s days’ sales in receivables?

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15. Ratios and Fixed Assets The Burk Company has a ratio of long-term debt to long-term debt

plus equity of 0.40 and a current ratio of 1.25. Current liabilities are $1,075, sales are $6,180,

profit margin is 8.5 percent, and ROE is 16.25 percent. What is the amount of the firm’s net

fixed assets?

16. Calculating the Cash Coverage Ratio FVA Inc.’s net income for the most recent year was

$17,590. The tax rate was 34 percent. The firm paid $4,150 in total interest expense and deducted

$5,820 in depreciation expense. What was FVA’s cash coverage ratio for the year?

17. Cost of Goods Sold Sexton Corp. has current liabilities of $325,000, a quick ratio of 0.85,

inventory turnover of 9.5, and a current ratio of 1.25. What is the cost of goods sold for the

company?

18. Common-Size and Common-Base Year Financial Statements In addition to common-size

financial statements, common-base year financial statements are often used. Common-base

year financial statements are constructed by dividing the current year account value by the

base year account value. Thus, the result shows the growth rate in the account. Using the

financial statements below, construct the common-size balance sheet and common-base year

balance sheet for the company. Use 2009 as the base year.

J A R R O W C O R P O R AT I O N

2009 a n d 2010 B a l a n c e S h e e t s

ASSETS

Current assets

Cash

Accounts receivable

Inventory

Total

Fixed assets

Net plant and

equipment

LI A B I LI T I E S A N D O WN E R S ’ E Q U I TY

2009

2010

$ 13,582

21,640

36,823

$ 72,045

$ 15,675

22,340

39,703

$ 77,718

$274,583

$290,586

Current liabilities

Accounts payable

Notes payable

Total

Long-term debt

Owners’ equity

Common stock and

paid-in surplus

Accumulated retained

earnings

Total

Total assets

$346,628

$368,304

Total liabilities and

owners’ equity

2009

2010

$ 19,085

24,530

$ 43,615

$ 35,000

$ 20,640

25,305

$ 45,945

$ 50,000

$ 45,000

$ 45,000

223,013

227,359

$268,013

$272,359

$346,628

$368,304

19. Full-Capacity Sales Pumpkin Mfg., Inc., is currently operating at only 92 percent of fixed asset

capacity. Current sales are $725,000. How fast can sales grow before any new fixed assets are

needed?

20. Fixed Assets and Capacity Usage For the company in the previous problem, suppose fixed assets are $645,000 and sales are projected to grow to $850,000. How much in new fixed assets is

required to support this growth in sales? Assume the company operates at full capacity.

21. Calculating EFN The most recent financial statements for Retro Machine, Inc., follow. Sales

for 2010 are projected to grow by 20 percent. Interest expense will remain constant; the tax rate

and the dividend payout rate will also remain constant. Costs, other expenses, current assets,

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fixed assets, and accounts payable increase spontaneously with sales. If the firm is operating

at full capacity and no new debt or equity are issued, what is the external financing needed to

support the 20 percent growth rate in sales?

RETRO MACHINE INC

2 0 09 I n c o m e S t a t e m e n t

Sales

Costs

Other expenses

Earnings before interest and taxes

Interest paid

Taxable income

Taxes (35%)

Net income

Dividends

Addition to retained earnings

$929,000

723,000

19,000

$187,000

14,000

$173,000

60,550

$112,450

$ 33,735

78,715

RETRO MACHINE, INC

Ba l a n c e S h e e t a s o f D e c e m b e r 31, 2009

ASSE T S

Current assets

Cash

Accounts receivable

Inventory

Total

Fixed assets

Net plant and

equipment

Total assets

LI A B I LI T I E S A N D O WN E R S ’ E Q U I T Y

$ 25,300

40,700

86,900

$152,900

$413,000

$565,900

Current liabilities

Accounts payable

Notes payable

Total

Long-term debt

Owners’ equity

Common stock and paid-in surplus

Accumulated retained earnings

Total

Total liabilities and owners’ equity

$ 68,000

17,000

$ 85,000

$158,000

$140,000

182,900

$322,900

$565,900

22. Capacity Usage and Growth In the previous problem, suppose the firm was operating at only

80 percent capacity in 2009. What is EFN now?

23. Calculating EFN In Problem 21, suppose the firm wishes to keep its debt-equity ratio constant.

What is EFN now?

24. EFN and Internal Growth Redo Problem 21 using sales growth rates of 15 and 25 percent in

addition to 20 percent. Illustrate graphically the relationship between EFN and the growth rate,

and use this graph to determine the relationship between them.

Challenge

(Questions 24–30)

25. EFN and Sustainable Growth Redo Problem 23 using sales growth rates of 30 and 35 percent

in addition to 20 percent. Illustrate graphically the relationship between EFN and the growth

rate, and use this graph to determine the relationship between them.

26. Constraints on Growth Dahlia, Inc., wishes to maintain a growth rate of 9 percent per year

and a debt-equity ratio of 0.55. Profit margin is 6.2 percent, and the ratio of total assets to sales

is constant at 1.90. Is this growth rate possible? To answer, determine what the dividend payout

ratio must be. How do you interpret the result?

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27. EFN Define the following:

S Previous year’s sales

A Total assets

D Total debt

E Total equity

g Projected growth in sales

PM Profit margin

b Retention (plowback) ratio

Show that EFN can be written as:

EFN PM(S)b [A PM(S)b] g

Hint: Asset needs will equal A g. The addition to retained earnings will equal PM(S)b (1 g).

28. Sustainable Growth Rate Based on the results in Problem 27, show that the internal and sustainable growth rates can be calculated as shown in equations 3.24 and 3.25. Hint: For the internal growth rate, set EFN equal to zero and solve for g.

29. Sustainable Growth Rate In the chapter, we discussed one calculation of the sustainable

growth rate as:

ROE b

Sustainable growth rate ___________

1 ROE b

In practice, probably the most commonly used calculation of the sustainable growth rate is

ROE b. This equation is identical to the two sustainable growth rate equations presented in

the chapter if the ROE is calculated using the beginning of period equity. Derive this equation

from the equation presented in the chapter.

30. Sustainable Growth Rate Use the sustainable growth rate equations from the previous problem to answer the following questions. No Return, Inc., had total assets of $380,000 and equity

of $230,000 at the beginning of the year. At the end of the year, the company had total assets

of $430,000. During the year the company sold no new equity. Net income for the year was

$95,000 and dividends were $43,000. What is the approximate sustainable growth rate for the

company? What is the exact sustainable growth rate? What is the approximate sustainable

growth rate if you calculate ROE based on the beginning of period equity? Is this number too

high or too low? Why?

W H AT ’ S O N T H E W E B ?

1. Du Pont Identity You can find financial statements for Walt Disney Company at Disney’s home

page, disney.go.com. For the three most recent years, calculate the Du Pont identity for Disney.

How has ROE changed over this period? How have changes in each component of the Du Pont

identity affected ROE over this period?

2. Ratio Analysis You want to examine the financial ratios for Dell Computer Corporation. Go to

www.reuters.com and type in the ticker symbol for the company (DELL). Now find financial ratios for Dell and the industry, sector, and S&P 500 averages for each ratio.

a. What do TTM and MRQ mean?

b. How do Dell’s recent profitability ratios compare to their values over the past five years? To

the industry averages? To the sector averages? To the S&P 500 averages? Which is the better comparison group for Dell: the industry, sector, or S&P 500 averages? Why?

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c. In what areas does Dell seem to outperform its competitors based on the financial ratios?

Where does Dell seem to lag behind its competitors?

d. Dell’s inventory turnover ratio is much larger than that for all comparison groups. Why do

you think this is?

3. Applying Percentage of Sales Locate the most recent annual financial statements for Du

Pont at www.dupont.com under the “Investor Center” link. Locate the annual report. Using the

growth in sales for the most recent year as the projected sales growth for next year, construct

a pro forma income statement and balance sheet. Based on these projections, what are the

external funds needed?

4. Growth Rates You can find the home page for Caterpillar, Inc., at www.cat.com. Go to the

Web page and find the most recent annual report. Using the information from the financial

statements, what is the sustainable growth rate?

After Dan’s analysis of East Coast Yachts’ cash flow (at the end of our previous chapter), Larissa

approached Dan about the company’s performance and future growth plans. First, Larissa wants

to find out how East Coast Yachts is performing relative to its peers. Additionally, she wants to find

out the future financing necessary to fund the company’s growth. In the past, East Coast Yachts

experienced difficulty in financing its growth plan, in large part because of poor planning. In fact,

the company had to turn down several large jobs because its facilities were unable to handle the

additional demand. Larissa hoped that Dan would be able to estimate the amount of capital the

company would have to raise next year so that East Coast Yachts would be better prepared to fund

its expansion plans.

To get Dan started with his analyses, Larissa provided the following financial statements. Dan then

gathered the industry ratios for the yacht manufacturing industry.

CLOSING CASE

R AT I O S A N D F I N A N C I A L P L A N N I N G

AT E A S T C O A S T YA C H T S

E A S T C O A S T YA C H T S

2010 Income Statement

Sales

Cost of goods sold

Selling, general, and administrative

Depreciation

EBIT

Interest expense

EBT

Taxes

Net income

Dividends

Retained earnings

$617,760,000

435,360,000

73,824,000

20,160,000

$ 88,416,000

11,112,000

$ 77,304,000

30,921,600

$ 46,382,400

$ 17,550,960

$ 28,831,440

(continued )

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E A S T C O A S T YA C H T S

2010 B a l a n c e S h e e t

Current assets

Cash and equivalents

Accounts receivable

Inventories

Other

Total current assets

Fixed assets

Property, plant, and equipment

Less accumulated depreciation

Net property, plant, and equipment

Intangible assets and others

Total fixed assets

Total assets

$ 11,232,000

20,208,000

22,656,000

1,184,000

$ 55,280,000

Current liabilities

Accounts payable

Notes payable

Accrued expenses

Total current liabilities

$ 24,546,000

18,725,000

6,185,000

$ 49,456,000

Long-term debt

$462,030,000

Total long-term liabilities

(114,996,000)

$347,034,000

6,840,000 Stockholders’ equity

$353,874,000

Preferred stock

Common stock

Capital surplus

Accumulated retained earnings

Less treasury stock

Total equity

$409,154,000 Total liabilities and shareholders’ equity

$146,560,000

$146,560,000

$ 3,000,000

40,800,000

31,200,000

186,138,000

(48,000,000)

$213,138,000

$409,154,000

Ya c h t I n d u st r y R a t i o s

Current ratio

Quick ratio

Total asset turnover

Inventory turnover

Receivables turnover

Debt ratio

Debt-equity ratio

Equity multiplier

Interest coverage

Profit margin

Return on assets

Return on equity

LOWER QUARTILE

MEDIAN

U P P E R Q U A R T I LE

0.86

0.43

1.10

12.18

10.25

0.32

0.51

1.51

5.72

5.02%

7.05%

9.06%

1.51

0.75

1.27

14.38

17.65

0.49

0.83

1.83

8.21

7.48%

10.67%

14.32%

1.97

1.01

1.46

16.43

22.43

0.61

1.03

2.03

10.83

9.05%

14.16%

22.41%

1. East Coast Yachts uses a small percentage of preferred stock as a source of financing. In calculating the ratios for the company, should preferred stock be included as part of the company’s

total equity?

2. Calculate all of the ratios listed in the industry table for East Coast Yachts.

3. Compare the performance of East Coast Yachts to the industry as a whole. For each ratio, comment on why it might be viewed as positive or negative relative to the industry. Suppose you

create an inventory ratio calculated as inventory divided by current liabilities. How would you

interpret this ratio? How does East Coast Yachts compare to the industry average for this ratio?

4. Calculate the sustainable growth rate for East Coast Yachts. Calculate external funds needed

(EFN) and prepare pro forma income statements and balance sheets assuming growth at

precisely this rate. Recalculate the ratios in the previous question. What do you observe?

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5. As a practical matter, East Coast Yachts is unlikely to be willing to raise external equity capital,

in part because the shareholders don’t want to dilute their existing ownership and control positions. However, East Coast Yachts is planning for a growth rate of 20 percent next year. What are

your conclusions and recommendations about the feasibility of East Coast’s expansion plans?

6. Most assets can be increased as a percentage of sales. For instance, cash can be increased

by any amount. However, fixed assets often must be increased in specific amounts since it is

impossible, as a practical matter, to buy part of a new plant or machine. In this case, a company

has a “staircase” or “lumpy” fixed cost structure. Assume that East Coast Yachts is currently

producing at 100 percent of capacity and sales are expected to grow at 20 percent. As a result,

to expand production, the company must set up an entirely new line at a cost of $95,000,000.

Prepare the pro forma income statement and balance sheet. What is the new EFN with these

assumptions? What does this imply about capacity utilization for East Coast Yachts next year?

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CHAPTER

4

Discounted Cash Flow

Valuation

PART TWO Valuation and Capital Budgeting

OPENING CASE

W

hat do Chris Iannetta, John Lackey, and Matt Holliday have in common? All

three are star athletes who signed big-money contracts during late 2009 or

early 2010. Their contract values were reported as $8.35 million, $82.5 million, and $120 million, respectively. But reported numbers can be misleading.

For example, catcher Chris Ianetta re-signed with the Colorado Rockies. His

deal called for salaries of $1.75 million, $2.55 million, and $3.55 million over the next three years,

respectively, with a contract buyout of $500,000 or a salary of $5,000,000 in four years. Not bad,

especially for someone who makes a living using the “tools of ignorance” (jock jargon for a catcher’s

equipment).

A closer look at the numbers shows that Chris, John, and Matt did pretty well, but nothing like the

quoted figures. Using Matt’s contract as an example, the value was reported to be $120 million, but it

was actually payable over several years. The terms called for a salary of $17 million per year for seven

years, then a club option for $17 million in 2017 or a club buyout of $1 million. However, of the $17 million annual salary, $2 million each year was to be deferred and paid annually from 2020 to 2029. Since

the payments are spread out over time, we must consider the time value of money, which means his

contract was worth less than reported. How much did he really get? This chapter gives you the “tools

of knowledge” to answer this question.

4.1

V A L U AT I O N : T H E O N E - P E R I O D C A S E

Keith Vaughan is trying to sell a piece of raw land in Alaska. Yesterday, he was offered

$10,000 for the property. He was about ready to accept the offer when another individual

offered him $11,424. However, the second offer was to be paid a year from now. Keith

has satisfied himself that both buyers are honest and financially solvent, so he has no fear

that the offer he selects will fall through. These two offers are pictured as cash flows in

Figure 4.1. Which offer should Mr. Vaughan choose?

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Alternative

sale prices

Year

$10,000

$11,424

0

1

FIGURE 4.1

Cash Flow for

Mr. Vaughan’s Sale

Mike Tuttle, Keith’s financial adviser, points out that if Keith takes the first offer, he

could invest the $10,000 in the bank at an insured rate of 12 percent. At the end of one year,

he would have

$10,000 (0.12 $10,000) $10,000 1.12 $11,200

Return of

Interest

principal

Because this is less than the $11,424 Keith could receive from the second offer, Mr. Tuttle

recommends that he take the latter. This analysis uses the concept of future value or

compound value, which is the value of a sum after investing over one or more periods. The

compound or future value of $10,000 at 12 percent is $11,200.

An alternative method employs the concept of present value. One can determine

present value by asking the following question: How much money must Keith put in

the bank today at 12 percent so that he will have $11,424 next year? We can write this

algebraically as

PV 1.12 $11,424

We want to solve for present value (PV), the amount of money that yields $11,424 if

invested at 12 percent today. Solving for PV, we have

$11,424

PV _________ $10,200

1.12

The formula for PV can be written as

Present Value of Investment:

C1

PV ______

1r

[4.1]

where C1 is cash flow at date 1 and r is the rate of return that Keith Vaughan requires on his

land sale. It is sometimes referred to as the discount rate.

Present value analysis tells us that a payment of $11,424 to be received next year has a

present value of $10,200 today. In other words, at a 12-percent interest rate, Mr. Vaughan

is indifferent between $10,200 today or $11,424 next year. If you gave him $10,200 today,

he could put it in the bank and receive $11,424 next year.

Because the second offer has a present value of $10,200, whereas the first offer is for

only $10,000, present value analysis also indicates that Mr. Vaughan should take the second

offer. In other words, both future value analysis and present value analysis lead to the same

decision. As it turns out, present value analysis and future value analysis must always lead

to the same decision.

As simple as this example is, it contains the basic principles that we will be working

with over the next few chapters. We now use another example to develop the concept of net

present value.

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4.1

EXAMPLE

Present Value

Lida Jennings, a financial analyst at Kaufman & Broad, a leading real estate firm, is thinking about

recommending that Kaufman & Broad invest in a piece of land that costs $85,000. She is certain that

next year the land will be worth $91,000, a sure $6,000 gain. Given that the guaranteed interest rate

in the bank is 10 percent, should Kaufman & Broad undertake the investment in land? Ms. Jennings’s

choice is described in Figure 4.2 with the cash flow time chart.

FIGURE 4.2

Cash Flows for Land Investment

Cash inflow

$91,000

Time

0

1

$85,000

Cash outflow

A moment’s thought should be all it takes to convince her that this is not an attractive business

deal. By investing $85,000 in the land, she will have $91,000 available next year. Suppose, instead, that

Kaufman & Broad puts the same $85,000 into the bank. At the interest rate of 10 percent, this $85,000

would grow to

(1 .10) $85,000 $93,500

next year.

It would be foolish to buy the land when investing the same $85,000 in the financial market would

produce an extra $2,500 (that is, $93,500 from the bank minus $91,000 from the land investment). This is

a future value calculation.

Alternatively, she could calculate the present value of the sale price next year as

$91,000

Present value ______ $82,727.27

1.10

Because the present value of next year’s sales price is less than this year’s purchase price of $85,000,

present value analysis also indicates that she should not recommend purchasing the property.

Frequently, businesspeople want to determine the exact cost or benefit of a decision.

The decision to buy this year and sell next year can be evaluated as

Net Present Value of Investment:

$2,273

$85,000

Cost of land

today

$91,000

_________

1.10

Present value of

next year’s sales price

The formula for NPV can be written as

NPV

Cost

PV

[4.2]

Equation 4.2 says that the value of the investment is $2,273, after stating all the benefits

and all the costs as of date 0. We say that $2,273 is the net present value (NPV) of the

investment. That is, NPV is the present value of future cash flows minus the present value

of the cost of the investment. Because the net present value is negative, Lida Jennings

should not recommend purchasing the land.

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EXAMPLE

4.2

Both the Vaughan and the Jennings examples deal with perfect certainty. That is, Keith

Vaughan knows with perfect certainty that he could sell his land for $11,424 next year.

Similarly, Lida Jennings knows with perfect certainty that Kaufman & Broad could receive

$91,000 for selling its land. Unfortunately, businesspeople frequently do not know future

cash flows. This uncertainty is treated in the next example.

Uncertainty and Valuation

Professional Artworks, Inc., is a firm that speculates in modern paintings. The manager is thinking

of buying an original Picasso for $400,000 with the intention of selling it at the end of one year. The

manager expects that the painting will be worth $480,000 in one year. The relevant cash flows are

depicted in Figure 4.3.

FIGURE 4.3

Cash Flows for Investment in Painting

Expected cash inflow

$480,000

Time

Cash outflow

0

1

$400,000

Of course, this is only an expectation—the painting could be worth more or less than $480,000.

Suppose the guaranteed interest rate granted by banks is 10 percent. Should the firm purchase the

piece of art?

Our first thought might be to discount at the interest rate, yielding

$480,000

_______

$436,364

1.10

Because $436,364 is greater than $400,000, it looks at first glance as if the painting should be purchased. However, 10 percent is the return one can earn on a riskless investment. Because the

painting is quite risky, a higher discount rate is called for. The manager chooses a rate of 25 percent

to reflect this risk. In other words, he argues that a 25 percent expected return is fair compensation

for an investment as risky as this painting.

The present value of the painting becomes

$480,000

_______

$384,000

1.25

Thus, the manager believes that the painting is currently overpriced at $400,000 and does not make

the purchase.

The preceding analysis is typical of decision making in today’s corporations, though

real-world examples are, of course, much more complex. Unfortunately, any example with

risk poses a problem not faced by a riskless example. In an example with riskless cash

flows, the appropriate interest rate can be determined by simply checking with a few banks.

The selection of the discount rate for a risky investment is quite a difficult task. We simply

don’t know at this point whether the discount rate on the painting should be 11 percent,

25 percent, 52 percent, or some other percentage.

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Because the choice of a discount rate is so difficult, we merely wanted to broach the

subject here. We must wait until the specific material on risk and return is covered in later

chapters before a risk-adjusted analysis can be presented.

4.2

T H E M U LT I P E R I O D C A S E

The previous section presented the calculation of future value and present value for one

period only. We will now perform the calculations for the multiperiod case.

Future Value and Compounding

Suppose an individual were to make a loan of $1. At the end of the first year, the borrower

would owe the lender the principal amount of $1 plus the interest on the loan at the interest

rate of r. For the specific case where the interest rate is, say, 9 percent, the borrower owes

the lender

$1 (1 r ) $1 1.09 $1.09

At the end of the year, though, the lender has two choices. She can either take the $1.09—

or, more generally, (1 r)—out of the financial market, or she can leave it in and lend

it again for a second year. The process of leaving the money in the financial market and

lending it for another year is called compounding.

Suppose that the lender decides to compound her loan for another year. She does this

by taking the proceeds from her first one-year loan, $1.09, and lending this amount for the

next year. At the end of next year, then, the borrower will owe her

$1 (1 r ) (1 r ) $1 (1 r )2 1 2r r 2

$1 (1.09) (1.09) $1 (1.09)2 $1 $0.18 $0.0081 $1.1881

This is the total she will receive two years from now by compounding the loan.

In other words, the capital market enables the investor, by providing a ready opportunity

for lending, to transform $1 today into $1.1881 at the end of two years. At the end of three

years, the cash will be $1 (1.09)3 $1.2950.

The most important point to notice is that the total amount that the lender receives is not

just the $1 that she lent out plus two years’ worth of interest on $1:

2 r 2 $0.09 $0.18

The lender also gets back an amount r 2, which is the interest in the second year on the

interest that was earned in the first year. The term, 2 r, represents simple interest over

the two years, and the term, r 2, is referred to as the interest on interest. In our example this

latter amount is exactly

r 2 ($0.09)2 $0.0081

When cash is invested at compound interest, each interest payment is reinvested. With

simple interest, the interest is not reinvested. Benjamin Franklin’s statement, “Money makes

money and the money that money makes makes more money,” is a colorful way of explaining compound interest. The difference between compound interest and simple interest is

illustrated in Figure 4.4. In this example, the difference does not amount to much because

the loan is for $1. If the loan were for $1 million, the lender would receive $1,188,100 in

two years’ time. Of this amount, $8,100 is interest on interest. The lesson is that those small

numbers beyond the decimal point can add up to big dollar amounts when the transactions

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FIGURE 4.4

$1.295

$1.270

Simple and Compound

Interest

$1.188

$1.180

$1.09

$1

1 year

2 years

3 years

The red-shaded area represents the initial investment. The

green-shaded area represents the simple interest. The blueshaded area represents interest on interest.

are for big amounts. In addition, the longer-lasting the loan, the more important interest on

interest becomes.

The general formula for an investment over many periods can be written as

Future Value of an Investment:

FV C0 (1 r)T

[4.3]

EXAMPLE

4.3

where C0 is the cash to be invested at date 0 (i.e., today), r is the interest rate per period, and

T is the number of periods over which the cash is invested.

Interest on Interest

Suh-Pyng Ku has put $500 in a savings account at the First National Bank of Kent. The account earns

7 percent, compounded annually. How much will Ms. Ku have at the end of three years?

$500 1.07 1.07 1.07 $500 (1.07)3 $612.52

Figure 4.5 illustrates the growth of Ms. Ku’s account.

FIGURE 4.5

Suh-Pyng Ku’s Savings Account

Dollars

$612.52

$500

$612.52

0

1

2

Time

3

0

$500

1

2

3

Time

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4.4

EXAMPLE

Compound Growth

Jay Ritter invested $1,000 in the stock of the SDH Company. The company pays a current dividend of

$2, which is expected to grow by 20 percent per year for the next two years. What will the dividend of

the SDH Company be after two years?

$2 (1.20)2 $2.88

Figure 4.6 illustrates the increasing value of SDH’s dividends.

FIGURE 4.6

The Growth of the SDH Dividends

$2.88

Dollars

$2.88

Cash inflows

$2.00

$2.40

$2.00

0

1

Time

2

0

$2.40

1

Time

2

The two previous examples can be calculated in any one of four ways. The computations could be done by hand, by calculator, by spreadsheet, or with the help of a table.

The appropriate table is Table A.3, which appears in the back of the text. This table

presents future value of $1 at the end of T periods. The table is used by locating the

appropriate interest rate on the horizontal axis and the appropriate number of periods

on the vertical axis.

For example, Suh-Pyng Ku would look at the following portion of Table A.3:

I N T E R E S T R AT E

PERIOD

1

2

3

4

6%

7%

8%

1.0600

1.1236

1.1910

1.2625

1.0700

1.1449

1.2250

1.3108

1.0800

1.1664

1.2597

1.3605

She could calculate the future value of her $500 as

$612.50

$500

1.2250

Initial investment

Future value of $1

In the example concerning Suh-Pyng Ku, we gave you both the initial investment and the

interest rate and then asked you to calculate the future value. Alternatively, the interest rate

could have been unknown, as shown in the following example.

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4.5

Finding the Rate

EXAMPLE

Carl Voigt, who recently won $10,000 in the lottery, wants to buy a car in five years. Carl estimates that

the car will cost $16,105 at that time. His cash flows are displayed in Figure 4.7.

What interest rate must he earn to be able to afford the car?

FIGURE 4.7

Cash Flows for Purchase of Carl Voigt’s Car

Cash inflow

$10,000

5

0

Cash outflow

Time

$16,105

The ratio of purchase price to initial cash is

$16,105

______

1.6105

$10,000

Thus, he must earn an interest rate that allows $1 to become $1.6105 in five years. Table A.3 tells us

that an interest rate of 10 percent will allow him to purchase the car.

One can express the problem algebraically as

$10,000 (1 r)5 $16,105

where r is the interest rate needed to purchase the car. Because $16,105/$10,000 1.6105, we have

(1 r)5 1.6105

Either the table or a hand calculator solves for r.

The Power of Compounding: A Digression

Most people who have had any experience with compounding are impressed with its power

over long periods of time. In fact, compound interest has been described as the “eighth wonder of the world” and “the most powerful force in the universe.”1 Take the stock market, for

example. Ibbotson and Sinquefield have calculated what the stock market returned as a whole

from 1926 through 2009.2 They find that one dollar placed in these stocks at the beginning of

1926 would have been worth $2,591.82 at the end of 2009. This is 9.81 percent compounded

annually for 84 years, i.e., ($1.0981)84 $2,591.82, ignoring a small rounding error.

The example illustrates the great difference between compound and simple interest. At

9.81 percent, simple interest on $1 is 9.81 cents a year (i.e., $.0981). Simple interest over

84 years is $8.24 (84 $.0981). That is, an individual withdrawing .0981 cents every year

would have withdrawn $8.24 (84 $.0981) over 84 years. This is quite a bit below the

$2,591.82 that was obtained by reinvestment of all principal and interest.

The results are more impressive over even longer periods of time. A person with no

experience in compounding might think that the value of $1 at the end of 168 years would

be twice the value of $1 at the end of 84 years, if the yearly rate of return stayed the same.

1

These quotes are often attributed to Albert Einstein (particularly the second one), but whether he really said either is not known.

The first quote is also often attributed to Baron Rothschild, John Maynard Keynes, Benjamin Franklin, and others.

2

Stocks, Bonds, Bills and Inflation [SBBI]. 2010 Yearbook, Ibbotson Associates, Chicago, 2010.

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EXAMPLE

4.6

Actually the value of $1 at the end of 168 years would be the square of the value of $1 at

the end of 84 years. That is, if the annual rate of return remained the same, a $1 investment

in common stocks should be worth $6,717,530.91 [$1 (2,591.82 2,591.82)].

A few years ago, an archaeologist unearthed a relic stating that Julius Caesar lent the

Roman equivalent of one penny to someone. Since there was no record of the penny ever

being repaid, the archaeologist wondered what the interest and principal would be if a descendant of Caesar tried to collect from a descendant of the borrower in the 20th century. The

archaeologist felt that a rate of 6 percent might be appropriate. To his surprise, the principal

and interest due after more than 2,000 years was vastly greater than the entire wealth on earth.

The power of compounding can explain why the parents of well-to-do families frequently bequeath wealth to their grandchildren rather than to their children. That is, they

skip a generation. The parents would rather make the grandchildren very rich than make

the children moderately rich. We have found that in these families the grandchildren have a

more positive view of the power of compounding than do the children.

How Much for That Island?

Some people have said that it was the best real estate deal in history. Peter Minuit, director-general of

New Netherlands, the Dutch West India Company’s Colony in North America, in 1626 allegedly bought

Manhattan Island from native Americans for 60 guilders’ worth of trinkets. By 1667, the Dutch were

forced to exchange it for Suriname with the British (perhaps the worst real estate deal ever). This

sounds cheap, but did the Dutch really get the better end of the deal? It is reported that 60 guilders

was worth about $24 at the prevailing exchange rate. If the native Americans had sold the trinkets at

a fair market value and invested the $24 at 5 percent (tax free), it would now, about 384 years later,

be worth about $3.3 billion. Today, Manhattan is undoubtedly worth more than $2.5 billion, and so,

at a 5 percent rate of return, the native Americans got the worst of the deal. However, if invested at

10 percent, the amount of money they received would be worth about

$24(1 r)T 24 1.1384 $188 quadrillion

This is a lot of money. In fact, $188 quadrillion is more than all the real estate in the world is worth

today. Note that no one in the history of the world has ever been able to find an investment yielding

10 percent every year for 384 years.

Present Value and Discounting

We now know that an annual interest rate of 9 percent enables the investor to transform $1

today into $1.1881 two years from now. In addition, we would like to know:

How much would an investor need to lend today so that she could receive $1 two years from

today?

Algebraically, we can write this as

PV (1.09)2 $1

In the preceding equation, PV stands for present value, the amount of money we must lend

today in order to receive $1 in two years’ time.

Solving for PV in this equation, we have

$1

PV ________ $.84

1.1881

This process of calculating the present value of a future cash flow is called discounting. It

is the opposite of compounding. The difference between compounding and discounting is

illustrated in Figure 4.8.

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FIGURE 4.8

$2,500.00

Compounding and

Discounting

Dollars

$2,000.00

$1,500.00

Compound

Simple

PV

$1,000.00

$500.00

$0.00

0

1

2

3

4 5 6 7

Future years

8

9 10

The top line shows the growth of $1,000 at compound interest with the funds

invested at 9%: $1,000 (1.09)10 $2,367.36. Simple interest is shown on the

next line. It is $1,000 [10 ($1,000 .09)] $1,900. The bottom line shows the

discounted value of $1,000 if the interest rate is 9%.

To be certain that $.84 is in fact the present value of $1 to be received in two years, we

must check whether or not, if we loaned out $.84 and rolled over the loan for two years,

we would get exactly $1 back. If this were the case, the capital markets would be saying

that $1 received in two years’ time is equivalent to having $.84 today. Checking the exact

numbers, we get

$.84168 1.09 1.09 $1

In other words, when we have capital markets with a sure interest rate of 9 percent, we

are indifferent between receiving $.84 today or $1 in two years. We have no reason to treat

these two choices differently from each other, because if we had $.84 today and loaned

it out for two years, it would return $1 to us at the end of that time. The value [1/(1.09)2]

is called the present value factor. It is the factor used to calculate the present value of a

future cash flow.

In the multiperiod case, the formula for PV can be written as

Present Value of Investment:

CT

PV ________

(1 r )T

[4.4]

EXAMPLE

4.7

where CT is cash flow at date T and r is the appropriate discount rate.

Multiperiod Discounting

Bernard Dumas will receive $10,000 three years from now. Bernard can earn 8 percent on his investments, and so the appropriate discount rate is 8 percent. What is the present value of his future cash

flow?

1 3

PV $10,000 ____

1.08

$10,000 .7938

$7,938

( )

(continued )

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Figure 4.9 illustrates the application of the present value factor to Bernard’s investment.

FIGURE 4.9

Discounting Bernard Dumas’ Opportunity

Dollars

$10,000

Cash inflows

$7,938

0

0

1

2

3

$10,000

1

2

Time

3

Time

When his investments grow at an 8 percent rate of interest, Bernard Dumas is equally inclined

toward receiving $7,938 now and receiving $10,000 in three years’ time. After all, he could convert the

$7,938 he receives today into $10,000 in three years by lending it at an interest rate of 8 percent.

Bernard Dumas could have reached his present value calculation in one of three ways. The computation could have been done by hand, by calculator, or with the help of Table A.1, which appears in

the back of the text. This table presents present value of $1 to be received after T periods. The table is

used by locating the appropriate interest rate on the horizontal and the appropriate number of periods

on the vertical. For example, Bernard Dumas would look at the following portion of Table A.1:

I N T E R E S T R AT E

PE R I O D

7%

8%

9%

1

2

3

4

.9346

.8734

.8163

.7629

.9259

.8573

.7938

.7350

.9174

.8417

.7722

.7084

The appropriate present value factor is .7938.

EXAMPLE

4.8

In the preceding example, we gave both the interest rate and the future cash flow. Alternatively, the interest rate could have been unknown.

94

Finding the Rate

A customer of the Chaffkin Corp. wants to buy a tugboat today. Rather than paying immediately, he

will pay $50,000 in three years. It will cost the Chaffkin Corp. $38,610 to build the tugboat immediately.

The relevant cash flows to Chaffkin Corp. are displayed in Figure 4.10. By charging what interest rate

would the Chaffkin Corp. neither gain nor lose on the sale?

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FIGURE 4.10

Cash Flows for Tugboat

Cash inflows

$50,000

Time 0

3

$38,610

Cash outflows

The ratio of construction cost to sale price is

$38,610

______

0.7722

$50,000

We must determine the interest rate that allows $1 to be received in three years to have a present

value of $.7722. Table A.1 tells us that 9 percent is that interest rate.

EXAMPLE

4.9

Frequently, an investor or a business will receive more than one cash flow. The present

value of the set of cash flows is simply the sum of the present values of the individual cash

flows. This is illustrated in the following examples.

Cash Flow Valuation

Dennis Draper has won the Kentucky state lottery and will receive the following set of cash flows over

the next two years:

YE A R

C A S H FLO W

1

2

$2,000

$5,000

Mr. Draper can currently earn 6 percent in his money market account, and so, the appropriate discount rate is 6 percent. The present value of the cash flows is

YE AR

1

2

CASH F L OW PR E S E N T VA LU E FA C T O R P R E S E N T VA LU E

1

$2,000 _

$2,000 .943

1.06

1 2 $5,000 .890

$5,000 _

1.06

Total

( )

$1,887

$4,450

$6,337

In other words, Mr. Draper is equally inclined toward receiving $6,337 today and receiving $2,000 and

$5,000 over the next two years.

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4.10

EXAMPLE

NPV

Finance.com has an opportunity to invest in a new high-speed computer that costs $50,000. The computer will generate cash flows (from cost savings) of $25,000 one year from now, $20,000 two years

from now, and $15,000 three years from now. The computer will be worthless after three years, and

no additional cash flows will occur. Finance.com has determined that the appropriate discount rate is

7 percent for this investment. Should Finance.com make this investment in a new high-speed computer? What is the present value of the investment?

The cash flows and present value factors of the proposed computer are as follows.

C A S H FLO WS

Year 0

$50,000

1

$25,000

2

3

P R E S E N T VA LU E FA C T O R

$20,000

$15,000

1

1

_

1.07

1

_

1.07

1

_

1.07

1

.9346

2

.8734

3

.8163

( )

( )

The present values of the cash flows are:

Cash flows Present value factor Present value

Year 0

1

2

3

$50,000 1

$25,000 .9346

$20,000 .8734

$15,000 .8163

Total

$50,000

$23,364.5

$17,468.8

$12,244.5

$ 3,077.8

Finance.com should invest in a new high-speed computer because the present value of its future cash

flows is greater than its cost. The NPV is $3,077.8.

The Algebraic Formula

To derive an algebraic formula for the net present value of a cash flow, recall that the PV of

receiving a cash flow one year from now is

PV C1/(1 r)

and the PV of receiving a cash flow two years from now is

PV C2/(1 r )2

We can write the NPV of a T-period project as

T

C1

C2

CT

Ci

NPV C0 __

__

__

C0 __

i

1r

(1 r )2

(1 r )T

i1 (1 r )

[4.5]

The initial flow, C0, is assumed to be negative because it represents an investment. The

is shorthand for the sum of the series.

We will close out this section by answering the question we posed at the beginning of

the chapter concerning baseball player Matt Holliday’s contract. Recall that the contract

called for a salary of $17 million in each year over the next seven years, with $2 million in

deferred salary. We will also assume that the option for 2017 is not picked up so he only

receives $1 million in that year. The deferred salary payments from 2020 to 2029 could

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actually be either $2 million or $3.2 million, depending on certain factors. In this case, we

will assume that the deferred payments are $3.2 million per year. If 12 percent is the appropriate discount rate, what kind of deal did the Cardinal’s outfielder catch?

To answer, we can calculate the present value by discounting each year’s salary back

to the present as follows (notice we assumed the future salaries will be paid at the end of

the year):

Year

Year

Year

Year

1:

2:

3:

4:

$15,000,000

$15,000,000

$15,000,000

$15,000,000

.

1/1.121

1/1.122

1/1.123

1/1.124

.

.

.

.

.

$ 3,200,000 1/1.12

Year 20:

$ 13,392,857.14

$ 11,957,908.16

$10,676,703.72

$ 9,532,771.18

.

.

.

20

$

331,733.65

If you fill in the missing rows and then add (do it for practice), you will see that Matt’s

contract had a present value of about $74.68 million, which is only about 60 percent of the

$120 million value reported, but still pretty good.

As you have probably noticed, doing extensive present value calculations can get to

be pretty tedious, so a nearby Spreadsheet Techniques box shows how we recommend

doing them. As an application, we take a look at lottery payouts in a The Real World box

on page 100.

4.3

COMPOUNDING PERIODS

So far we have assumed that compounding and discounting occur yearly. Sometimes

compounding may occur more frequently than just once a year. For example, imagine

that a bank pays a 10-percent interest rate “compounded semiannually.” This means that a

$1,000 deposit in the bank would be worth $1,000 1.05 $1,050 after six months, and

$1,050 1.05 $1,102.50 at the end of the year.

The end-of-the-year wealth can be written as

(

.10

$1,000 1 ____

2

)

2

$1,000 (1.05)2 $1,102.50

Of course, a $1,000 deposit would be worth $1,100 ($1,000 1.10) with yearly compounding.

Note that the future value at the end of one year is greater with semiannual compounding

than with yearly compounding. With yearly compounding, the original $1,000 remains the

investment base for the full year. The original $1,000 is the investment base only for the first

six months with semiannual compounding. The base over the second six months is $1,050.

Hence, one gets interest on interest with semiannual compounding.

Because $1,000 1.1025 $1,102.50, 10 percent compounded semiannually is the

same as 10.25 percent compounded annually. In other words, a rational investor could not

care less whether she is quoted a rate of 10 percent compounded semiannually, or a rate of

10.25 percent compounded annually.

Quarterly compounding at 10 percent yields wealth at the end of one year of

(

.10

$1,000 1 ____

4

)

4

$1,103.81

More generally, compounding an investment m times a year provides end-of-year

wealth of

r

C0 1 ___

m

(

m

)

[4.6]

where C0 is one’s initial investment and r is the stated annual interest rate. The stated

annual interest rate is the annual interest rate without consideration of compounding.

CHAPTER 4 Discounted Cash Flow Valuation

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How to Calculate Present Values with

Multiple Future Cash Flows Using a

Spreadsheet

SPREADSHEET TECHNIQUES

We can set up a basic spreadsheet to calculate the present values of the individual cash flows as follows.

Notice that we have simply calculated the present values one at a time and added them up:

A

B

C

D

E

1

Using a spreadsheet to value multiple future cash flows

2

3

4

5

6

7

8

9

What is the present value of $200 in one year, $400 the next year, $600 the next year, and

$800 the last year if the discount rate is 12 percent?

Rate:

0.12

Year

Cash flows

1

2

3

4

10

11

12

13

14

15

16

17

18

19

20

21

22

$200

$400

$600

$800

Total PV:

Present values

$178.57

$318.88

$427.07

$508.41

$1,432.93

Formula used

=PV($B$7,A10,0,⫺B10)

=PV($B$7,A11,0,⫺B11)

=PV($B$7,A12,0,⫺B12)

=PV($B$7,A13,0,⫺B13)

=SUM(C10:C13)

Notice the negative signs inserted in the PV formulas. These just make the present values have

positive signs. Also, the discount rate in cell B7 is entered as $B$7 (an "absolute" reference)

because it is used over and over. We could have just entered ".12" instead, but our approach is more

flexible.

EXAMPLE

4.11

Banks and other financial institutions may use other names for the stated annual interest

rate. Annual percentage rate (APR) is perhaps the most common synonym.3

EARs

What is the end-of-year wealth if Jane Christine receives a stated annual interest rate of 24 percent

compounded monthly on a $1 investment?

Using (4.6), her wealth is

.24

$1 1 ___

12

(

12

)

$1 (1.02)12

$1.2682

The annual rate of return is 26.82 percent. This annual rate of return is either called the effective

annual rate (EAR) or the effective annual yield (EAY). Due to compounding, the effective annual

(continued)

3

By law, lenders are required to report the APR on all loans. In this text, we compute the APR as the interest rate per period multiplied by the number of periods in a year. According to federal law, the APR is a measure of the cost of consumer credit expressed

as a yearly rate and it includes interest and certain noninterest charges and fees. In practice, the APR can be much higher than

the interest rate on the loan if the lender charges substantial fees that must be included in the federally mandated APR calculation.

98

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interest rate is greater than the stated annual interest rate of 24 percent. Algebraically, we can rewrite

the effective annual interest rate as

Effective Annual Rate:

( 1 __mr )

m

1

[4.7]

EXAMPLE

4.12

Students are often bothered by the subtraction of 1 in (4.7). Note that end-of-year wealth is composed

of both the interest earned over the year and the original principal. We remove the original principal

by subtracting 1 in (4.7).

Compounding Frequencies

If the stated annual rate of interest, 8 percent, is compounded quarterly, what is the effective annual

rate?

Using (4.7), we have

( 1 __mr )

m

4

.08 1 .0824 8.24%

1 1 ___

4

(

)

Referring back to our earlier example where C0 $1,000 and r 10%, we can generate the following table:

C0

COM POUNDI N G

F RE QUE NCY ( m )

C1

$1,000

1,000

1,000

1,000

Yearly (m 1)

Semiannually (m 2)

Quarterly (m 4)

Daily (m 365)

$1,100.00

1,102.50

1,103.81

1,105.16

E FFE C T I V E A N N U A L

R AT E

r m

1 _

m 1

(

)

.10

.1025

.10381

.10516

Distinction between Stated Annual Interest Rate

and Effective Annual Rate

The distinction between the stated annual interest rate (SAIR), or APR, and the effective

annual rate (EAR) is frequently quite troubling to students. One can reduce the confusion

by noting that the SAIR becomes meaningful only if the compounding interval is given. For

example, for an SAIR of 10 percent, the future value at the end of one year with semiannual

compounding is [1 (.10兾2)]2 1.1025. The future value with quarterly compounding is

[1 (.10兾4)]4 1.1038. If the SAIR is 10 percent but no compounding interval is given,

one cannot calculate future value. In other words, one does not know whether to compound

semiannually, quarterly, or over some other interval.

By contrast, the EAR is meaningful without a compounding interval. For example, an

EAR of 10.25 percent means that a $1 investment will be worth $1.1025 in one year. One

can think of this as an SAIR of 10 percent with semiannual compounding or an SAIR of

10.25 percent with annual compounding, or some other possibility.

There can be a big difference between an SAIR and an EAR when interest rates are

large. For example, consider “payday loans.” Payday loans are short-term term loans made

to consumers, often for less than two weeks, and are offered by companies such as AmeriCash Advance and National Payday. The loans work like this: you write a check today that

is postdated. When the check date arrives, you go to the store and pay the cash for the

check, or the company cashes the check. For example, AmeriCash Advance allows you to

write a postdated check for $120 for 15 days later. In this case, they would give you $100

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THE REAL WORLD

JACKPOT!

If you or someone you know is a regular lottery player, you probably already understand that you are 20 times more

likely to get struck by lightning than you are to win a big lottery jackpot. What are your odds of winning? Below you

will find a table with your chances of winning the Mega Millions Lottery compared to other events.

Odds of winning a Mega Millions jackpot

Odds of being killed by a venomous spider

Odds of being killed by a dog bite

Odds of being killed by lightning

Odds of being killed by drowning

Odds of being killed falling from a bed or other furniture

Odds of being killed in a car crash

1:135,145,920*

1:57,018,763

1:11,403,753

1:6,479,405

1:690,300

1:388,411

1:6,029

*Source: Virginia Lottery Web site. All other odds from the National Safety Council.

Sweepstakes may have different odds than lotteries, but these odds may not be much better. Probably the

largest advertised potential grand prize ever was Pepsi’s “Play for a Billion,” which, you guessed it, had a $1 billion

(billion!) prize. Not bad for a day’s work, but you still have to read the fine print. It turns out that the winner would

be paid $5 million per year for the next 20 years, $10 million per year for years 21 through 39, and a lump sum

$710 million in 40 years. From what you have learned, you know the value of the sweepstakes wasn’t even close to

$1 billion. In fact, at an interest rate of 10 percent, the present value is about $70.7 million.

In January 2010, a 59-year-old man and his 57-year-old wife in New York won the $162 million Mega Millions

jackpot. They were given the option of receiving the jackpot as $6.231 million immediately and $6.231 million per

year for the next 25 years, or $102 million immediately. So, what discount rate does this imply? After some computational effort, we find the interest rate is about 4.15 percent. Unfortunately for the winners, nearly $1 million was

placed in an escrow account over a dispute about the mismanagement of funds at a homeless shelter the couple

had previously operated.

Some lotteries make your decision a little tougher. The Ontario Lottery will pay you either $2,000 a week for the

rest of your life or $1.3 million now. (That’s in Canadian dollars or “loonies,” by the way.) Of course, there is the

chance you might die in the near future, so the lottery guarantees that your heirs will collect the $2,000 weekly

payments until the twentieth anniversary of the first payment, or until you would have turned 91, whichever comes

first. This payout scheme complicates your decision quite a bit. If you live for only the 20-year minimum, the breakeven interest rate between the two options is about 5.13 percent per year, compounded weekly. If you expect to

live longer than the 20-year minimum, you might be better off accepting $2,000 per week for life. Of course, if you

manage to invest the $1.3 million lump sum at a rate of return of about 8 percent per year (compounded weekly),

you can have your cake and eat it too because the investment will return $2,000 at the end of each week forever!

Taxes complicate the decision in this case because the lottery payments are all on an aftertax basis. Thus, the rates

of return in this example would have to be aftertax as well.

today. So what is the APR and EAR of this arrangement? First we need to find the interest

rate, which we can find by the FV equation as:

FV

$120

1.2

r

PV (1 r)t

$100 (1 r)1

(1 r)

.20 or 20%

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That doesn’t seem too bad until you remember this is the interest rate for 15 days! The

APR of the loan is:

APR .20 36515

APR 4.8667 or 486.67%

And the EAR for this loan is:

EAR (1 Quoted ratem)m 1

EAR (1 .20)36515 1

EAR 83.4780 or 8,347.80%

Now that’s an interest rate! Just to see what a difference a day makes, let’s look at another

loan by the same company. AmeriCash Advance also offers a 14-day (instead of 15-day)

option. The other terms are the same. Check for yourself that the APR of this arrangement

is 521.43 percent and the EAR is 11,497.60 percent—definitely not a loan we recommend

you take out!

Compounding over Many Years

Formula 4.6 applies for an investment over one year. For an investment over one or more

(T ) years, the formula becomes

Future Value with Compounding:

r

FV C0 1 _

m

EXAMPLE

4.13

(

)

mT

[4.8]

Multiyear Compounding

Harry DeAngelo is investing $5,000 at a stated annual interest rate of 12 percent per year, compounded

quarterly, for five years. What is his wealth at the end of five years?

Using formula (4.8), his wealth is

.12

$5,000 1 ___

4

(

45

)

$5,000 (1.03)20 $5,000 1.8061 $9,030.50

Continuous Compounding

The previous discussion shows that one can compound much more frequently than once

a year. One could compound semiannually, quarterly, monthly, daily, hourly, each minute,

or even more often. The limiting case would be to compound every infinitesimal instant,

which is commonly called continuous compounding. Surprisingly, banks and other

financial institutions sometimes quote continuously compounded rates, which is why we

study them.

Though the idea of compounding this rapidly may boggle the mind, a simple formula

is involved. With continuous compounding, the value at the end of T years is expressed as

C0 erT

[4.9]

where C0 is the initial investment, r is the stated annual interest rate, and T is the number

of years over which the investment runs. The number e is a constant and is approximately

equal to 2.718. It is not an unknown like C0, r, and T.

CHAPTER 4 Discounted Cash Flow Valuation

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EXAMPLE 4.14

Continuous Compounding

Linda DeFond invested $1,000 at a continuously compounded rate of 10 percent for one year. What is

the value of her wealth at the end of one year?

From formula (4.9) we have

$1,000 e .10 $1,000 1.1052 $1,105.20

This number can easily be read from our Table A.5. One merely sets r, the value on the horizontal

dimension, to 10 percent and T, the value on the vertical dimension, to 1. For this problem, the relevant

portion of the table is

C O N T I N U O U S LY C O M P O U N D E D R AT E ( r )

PE RI OD

(T )

9%

10%

11%

1

2

3

1.0942

1.1972

1.3100

1.1052

1.2214

1.3499

1.1163

1.2461

1.3910

EXAMPLE 4.15

Note that a continuously compounded rate of 10 percent is equivalent to an annually compounded

rate of 10.52 percent. In other words, Linda DeFond would not care whether her bank quoted a

continuously compounded rate of 10 percent or a 10.52-percent rate, compounded annually.

Continuous Compounding, Continued

Linda DeFond’s brother, Mark, invested $1,000 at a continuously compounded rate of 10 percent for

two years.

The appropriate formula here is

$1,000 e .102 $1,000 e .20 $1,221.40

Using the portion of the table of continuously compounded rates reproduced above, we find the value

to be 1.2214.

Figure 4.11 illustrates the relationship among annual, semiannual, and continuous compounding. Semiannual compounding gives rise to both a smoother curve and a higher ending value than does annual compounding. Continuous compounding has both the smoothest

curve and the highest ending value of all.

FIGURE 4.11

4

Interest

earned

3

2

4

Interest

earned

3

Dollars

Dollars

4

Dollars

Annual, Semiannual, and

Continuous Compounding

2

0

1

2

3

Years

4

Annual compounding

5

Interest

earned

2

1

1

1

3

0

1

2

3

Years

4

5

Semiannual compounding

0

1

2

3

Years

4

5

Continuous compounding

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EXAMPLE 4.16

Present Value with Continuous Compounding

The Michigan state lottery is going to pay you $1,000 at the end of four years. If the annual continuously compounded rate of interest is 8 percent, what is the present value of this payment?

1 $726.16

1 $1,000 ______

$1,000 ____

1.3771

e .084

4.4

S I M P L I F I C AT I O N S

The first part of this chapter has examined the concepts of future value and present value.

Although these concepts allow one to answer a host of problems concerning the time value

of money, the human effort involved can frequently be excessive. For example, consider a

bank calculating the present value on a 20-year monthly mortgage. Because this mortgage

has 240 (20 12) payments, a lot of time is needed to perform a conceptually simple task.

Because many basic finance problems are potentially so time-consuming, we search out

simplifications in this section. We provide simplifying formulas for four classes of cash

flow streams:

■

■

■

■

Perpetuity

Growing perpetuity

Annuity

Growing annuity

Perpetuity

A perpetuity is a constant stream of cash flows without end. If you are thinking that perpetuities have no relevance to reality, it will surprise you that there is a well-known case of

an unending cash flow stream: the British bonds called consols. An investor purchasing a

consol is entitled to receive yearly interest from the British government forever.

How can the price of a consol be determined? Consider a consol that pays a coupon of

C dollars each year and will do so forever. Simply applying the PV formula gives us

C ________

C

C

PV ______

________

. . .

1r

(1 r )2

(1 r )3

where the dots at the end of the formula stand for the infinite string of terms that continues

the formula. Series like the preceding one are called geometric series. It is well known

that even though they have an infinite number of terms, the whole series has a finite sum

because each term is only a fraction of the preceding term. Before turning to our calculus

books, though, it is worth going back to our original principles to see if a bit of financial

intuition can help us find the PV.

The present value of the consol is the present value of all of its future coupons. In other

words, it is an amount of money that, if an investor had it today, would enable him to

achieve the same pattern of expenditures that the consol and its coupons would. Suppose

that an investor wanted to spend exactly C dollars each year. If he had the consol, he could

do this. How much money must he have today to spend the same amount? Clearly he would

need exactly enough so that the interest on the money would be C dollars per year. If he

had any more, he could spend more than C dollars each year. If he had any less, he would

eventually run out of money spending C dollars per year.

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The amount that will give the investor C dollars each year, and therefore the present

value of the consol, is simply

C

PV __

r

[4.10]

To confirm that this is the right answer, notice that if we lend the amount C/r, the interest

it earns each year will be

CrC

Interest __

r

which is exactly the consol payment. To sum up, we have shown that for a consol

Formula for Present Value of Perpetuity:

C __

C

C

PV __

__

1r

(1 r )2

(1 r )3

[4.11]

C

_

r

EXAMPLE

4.17

It is comforting to know how easily we can use a bit of financial intuition to solve this

mathematical problem.

Perpetuities

Consider a perpetuity paying $100 a year. If the relevant interest rate is 8 percent, what is the value

of the consol?

Using formula (4.10), we have

$100 $1,250

PV ____

.08

Now suppose that interest rates fall to 6 percent. Using (4.10), the value of the perpetuity is

$100 $1,666.67

PV ____

.06

Note that the value of the perpetuity rises with a drop in the interest rate. Conversely, the value of the

perpetuity falls with a rise in the interest rate.

Growing Perpetuity

Imagine an apartment building where cash flows to the landlord after expenses will be

$100,000 next year. These cash flows are expected to rise at 5 percent per year. If one assumes that this rise will continue indefinitely, the cash flow stream is termed a growing

perpetuity. The relevant interest rate is 11 percent. Therefore, the appropriate discount rate

is 11 percent and the present value of the cash flows can be represented as

$100,000(1.05)

$100,000(1.05)2

$100,000

PV ___ ____

____

1.11

(1.11)2

(1.11)3

$100,000(1.05)N1

____

(1.11)N

Algebraically, we can write the formula as

C (1 g )

C (1 g )2

C (1 g )N1

C ___

PV __

___

___

1r

(1 r )2

(1 r )3

(1 r )N

where C is the cash flow to be received one period hence, g is the rate of growth per period,

expressed as a percentage, and r is the appropriate discount rate.

Fortunately, this formula reduces to the following simplification:

Formula for Present Value of Growing Perpetuity:

C

PV ______

rg

[4.12]

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From Formula 4.12, the present value of the cash flows from the apartment building is

$100,000

___________

$1,666,667

.11 .05

There are three important points concerning the growing perpetuity formula:

EXAMPLE

4.18

1. The Numerator. The numerator in Formula 4.12 is the cash flow one period

hence, not at date 0. Consider the following example:

Paying Dividends

Rothstein Corporation is just about to pay a dividend of $3.00 per share. Investors anticipate that the

annual dividend will rise by 6 percent a year forever. The applicable discount rate is 11 percent. What

is the price of the stock today?

The numerator in Formula 4.12 is the cash flow to be received next period. Since the growth rate is

6 percent, the dividend next year is $3.18 ($3.00 1.06). The price of the stock today is

$66.60

$3.00

Imminent

dividend

$3.18

__

.11 .06

Present value of all

dividends beginning

a year from now

The price of $66.60 includes both the dividend to be received immediately and the present value of

all dividends beginning a year from now. Formula 4.12 only makes it possible to calculate the present

value of all dividends beginning a year from now. Be sure you understand this example; test questions

on this subject always seem to trip up a few of our students.

2. The Discount Rate and the Growth Rate. The discount rate r must be greater

than the growth rate g for the growing perpetuity formula to work. Consider the

case in which the growth rate approaches the discount rate in magnitude. Then

the denominator in the growing perpetuity formula gets infinitesimally small and

the present value grows infinitely large. The present value is in fact undefined

when r is less than g.

3. The Timing Assumption. Cash generally flows into and out of real-world firms

both randomly and nearly continuously. However, Formula 4.12 assumes that

cash flows are received and disbursed at regular and discrete points in time. In

the example of the apartment, we assumed that the net cash flows of $100,000

only occurred once a year. In reality, rent checks are commonly received every

month. Payments for maintenance and other expenses may occur anytime within

the year.

The growing perpetuity formula (4.12) can be applied only by assuming a

regular and discrete pattern of cash flow. Although this assumption is sensible

because the formula saves so much time, the user should never forget that it is an

assumption. This point will be mentioned again in the chapters ahead.

A few words should be said about terminology. Authors of financial textbooks generally use one of two conventions to refer to time. A minority of financial writers treat cash

flows as being received on exact dates, for example date 0, date 1, and so forth. Under this

convention, date 0 represents the present time. However, because a year is an interval, not a

specific moment in time, the great majority of authors refer to cash flows that occur at the

end of a year (or alternatively, the end of a period). Under this end-of-the-year convention,

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the end of year 0 is the present, the end of year 1 occurs one period hence, and so on. (The

beginning of year 0 has already passed and is not generally referred to.)4

The interchangeability of the two conventions can be seen from the following chart:

Date 0

Now

End of year 0

Now

Date 1

Date 2

Date 3

End of year 1

End of year 2

End of year 3

We strongly believe that the dates convention reduces ambiguity. However, we use both

conventions because you are likely to see the end-of-year convention in later courses. In

fact, both conventions may appear in the same example for the sake of practice.

Annuity

An annuity is a level stream of regular payments that lasts for a fixed number of periods.

Not surprisingly, annuities are among the most common kinds of financial instruments. The

pensions that people receive when they retire are often in the form of an annuity. Leases

and mortgages are also often annuities.

To figure out the present value of an annuity we need to evaluate the following equation:

C __

C

C

C

__

__

__

1r

(1 r)2

(1 r)3

(1 + r)T

The present value of only receiving the coupons for T periods must be less than the present

value of a consol, but how much less? To answer this we have to look at consols a bit more

closely.

Consider the following time chart:

Now

Date (or end of year)

Consol 1

Consol 2

Annuity

0

1

C

2

C

3

C...

T

C

C

C

C...

C

(T 1)

C

C

(T 2)

C...

C...

Consol 1 is a normal consol with its first payment at date 1. The first payment of consol 2

occurs at date T 1.

The present value of having a cash flow of C at each of T dates is equal to the present

value of consol 1 minus the present value of consol 2. The present value of consol 1 is

given by

C

PV __

r

[4.13]

Consol 2 is just a consol with its first payment at date T 1. From the perpetuity formula,

this consol will be worth C/r at date T.5 However, we do not want the value at date T. We

4

Sometimes financial writers merely speak of a cash flow in year x. Although this terminology is ambiguous, such writers generally

mean the end of year x.

5

Students frequently think that C /r is the present value at date T 1 because the consol’s first payment is at date T 1. However,

the formula values the annuity as of one period prior to the first payment.

106 PART 2 Valuation and Capital Budgeting

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want the value now; in other words, the present value at date 0. We must discount C/r back

by T periods. Therefore, the present value of consol 2 is

C __

1

PV _

r (1 + r)T

[

]

[4.14]

The present value of having cash flows for T years is the present value of a consol with its

first payment at date 1 minus the present value of a consol with its first payment at date

T 1. Thus, the present value of an annuity is Formula 4.13 minus Formula 4.14. This can

be written as

C_

C __

1

_

r

r (1 + r)T

[

]

This simplifies to

Formula for Present Value of Annuity:

1 __

1

PV C _

r

r (1 r)T

[

]

[4.15]

This can also be written as

1

1 __

(1 r)T

___

PV C

r

EXAMPLE

4.19

[

]

Lottery Valuation

Mark Young has just won the state lottery, paying $50,000 a year for 20 years. He is to receive his first

payment a year from now. The state advertises this as the Million Dollar Lottery because $1,000,000

$50,000 20. If the interest rate is 8 percent, what is the true value of the lottery?

Formula 4.15 yields

1

Present value of

1 __

(1.08)20

Million Dollar Lottery $50,000 __

.08

Periodic payment

Annuity factor

$50,000

9.8181

$490,905

[

]

Rather than being overjoyed at winning, Mr. Young sues the state for misrepresentation and fraud. His

legal brief states that he was promised $1 million but received only $490,905.

The term we use to compute the present value of the stream of level payments, C, for

T years is called an annuity factor. The annuity factor in the current example is 9.8181.

Because the annuity factor is used so often in PV calculations, we have included it in

Table A.2 in the back of this book. The table gives the values of these factors for a range of

interest rates, r, and maturity dates, T.

The annuity factor as expressed in the brackets of Formula 4.15 is a complex formula.

For simplification, we may from time to time refer to the present value annuity factor as

PVIFAr,T

That is, the above expression stands for the present value of $1 a year for T years at an

interest rate of r.

We can also provide a formula for the future value of an annuity:

(1 r )T

(1 r)T 1

1 C ___

FV C __

_

r

r

r

[

]

[

]

[4.16]

CHAPTER 4 Discounted Cash Flow Valuation

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As with present value factors for annuities, we have compiled future value factors in

Table A.3 in the back of this book. Of course, you can also use a spreadsheet as we illustrate below.

SPREADSHEET TECHNIQUES

Annuity Present Values

Using a spreadsheet to find annuity present values goes like this:

A

B

C

D

E

F

G

1

Using a spreadsheet to find annuity present values

2

EXAMPLE

4.20

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

What is the present value of $500 per year for 3 years if the discount rate is 10 percent?

We need to solve for the unknown present value, so we use the formula PV(rate, nper, pmt, fv).

Payment amount per period:

Number of payments:

Discount rate:

$500

3

0.1

Annuity present value:

$1,243.43

The formula entered in cell B11 is =PV(B9,B8,-B7,0); notice that fv is zero and that

pmt has a negative sign on it. Also notice that rate is entered as a decimal, not a percentage.

Retirement Investing

Suppose you put $3,000 per year into a Roth IRA. The account pays 6 percent per year. How much will

you have when you retire in 30 years?

This question asks for the future value of an annuity of $3,000 per year for 30 years at 6 percent,

which we can calculate as follows:

(1 r)T 1

1.0630 1

$3,000 __

FV C __

r

.06

[

]

[

]

$3,000 79.0582

$237,174.56

So, you’ll have close to a quarter million dollars in the account.

Our experience is that annuity formulas are not hard, but tricky, for the beginning

student. We present four tricks below.

TRICK 1: A DELAYED ANNUITY One of the tricks in working with annuities or perpetuities

is getting the timing exactly right. This is particularly true when an annuity or perpetuity

begins at a date many periods in the future. We have found that even the brightest beginning

student can make errors here. Consider the following example.

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4.21

EXAMPLE

Delayed Annuities

Danielle Caravello will receive a four-year annuity of $500 per year, beginning at date 6. If the interest

rate is 10 percent, what is the present value of her annuity? This situation can be graphed as:

0

1

2

3

4

5

6

$500

7

$500

8

$500

9

$500

10

The analysis involves two steps:

1. Calculate the present value of the annuity using Formula 4.15. This is

Present Value of Annuity at Date 5:

1

1_

(1.10)4 $500 PVIFA

$500 __

10%,4

.10

$500 3.1699

[

]

$1,584.95

Note that $1,584.95 represents the present value at date 5.

Students frequently think that $1,584.95 is the present value at date 6, because the annuity begins at date 6. However, our formula values the annuity as of one period prior to the first payment.

This can be seen in the most typical case where the first payment occurs at date 1. The formula

values the annuity as of date 0 in that case.

2. Discount the present value of the annuity back to date 0. That is

Present Value at Date 0:

$1,584.95

__

$984.13

(1.10)5

Again, it is worthwhile mentioning that, because the annuity formula brings Danielle’s annuity back

to date 5, the second calculation must discount over the remaining 5 periods. The two-step procedure is graphed in Figure 4.12.

FIGURE 4.12

Discounting Danielle Caravello’s Annuity

Date

0

Cash flow

$984.13

1

2

3

4

5

6

$500

7

$500

8

$500

9

$500

10

$1,584.95

Step one: Discount the four payments back to date 5 by using the annuity formula.

Step two: Discount the present value at date 5 ($1,584.95) back to present value at date 0.

TRICK 2: ANNUITY DUE The annuity formula of Formula 4.15 assumes that the first

annuity payment begins a full period hence. This type of annuity is sometimes called an

annuity in arrears or an ordinary annuity. What happens if the annuity begins today, in

other words, at date 0?

CHAPTER 4 Discounted Cash Flow Valuation

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4.22

EXAMPLE

Annuity Due

In a previous example, Mark Young received $50,000 a year for 20 years from the state lottery. In that

example, he was to receive the first payment a year from the winning date. Let us now assume that the

first payment occurs immediately. The total number of payments remains 20.

Under this new assumption, we have a 19-date annuity with the first payment occurring at

date 1-plus an extra payment at date 0. The present value is

$50,000

$50,000 PVIFA8%,19

Payment at date 0

19-year annuity

$50,000 ($50,000 9.6036)

$530,180

$530,180, the present value in this example, is greater than $490,905, the present value in the earlier

lottery example. This is to be expected because the annuity of the current example begins earlier.

An annuity with an immediate initial payment is called an annuity in advance or, more commonly,

an annuity due. Always remember that Formula 4.15, as well as Table A.2, in this book refers to an

ordinary annuity.

EXAMPLE

4.23

TRICK 3: THE INFREQUENT ANNUITY The following example treats an annuity with payments occurring less frequently than once a year.

Infrequent Annuities

Ms. Ann Chen receives an annuity of $450, payable once every two years. The annuity stretches out

over 20 years. The first payment occurs at date 2, that is, two years from today. The annual interest

rate is 6 percent.

The trick is to determine the interest rate over a two-year period. The interest rate over two

years is

(1.06 1.06) 1 12.36%

That is, $100 invested over two years will yield $112.36.

What we want is the present value of a $450 annuity over 10 periods, with an interest rate of

12.36 percent per period. This is

1

1 __________

(1 .1236)10

$450 ______________ $450 PVIFA12.36%,10 $2,505.57

.1236

[

]

EXAMPLE

4.24

TRICK 4: EQUATING PRESENT VALUE OF TWO ANNUITIES The following example

equates the present value of inflows with the present value of outflows.

Working with Annuities

Harold and Helen Nash are saving for the college education of their newborn daughter, Susan. The

Nashes estimate that college expenses will run $30,000 per year when their daughter reaches college

in 18 years. The annual interest rate over the next few decades will be 14 percent. How much money

must they deposit in the bank each year so that their daughter will be completely supported through

four years of college?

(continued)

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PART 2 Valuation and Capital Budgeting

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To simplify the calculations, we assume that Susan is born today. Her parents will make the first of

her four annual tuition payments on her 18th birthday. They will make equal bank deposits on each of

her first 17 birthdays, but no deposit at date 0. This is illustrated as

Date 0

Susan’s

birth

1

2

...

17

18

19

20

21

Parents’

1st

deposit

Parents’

2nd

deposit

...

Parents’

17th and

last

deposit

Tuition

payment

1

Tuition

payment

2

Tuition

payment

3

Tuition

payment

4

Mr. and Ms. Nash will be making deposits to the bank over the next 17 years. They will be withdrawing $30,000 per year over the following four years. We can be sure they will be able to withdraw

fully $30,000 per year if the present value of the deposits is equal to the present value of the four

$30,000 withdrawals.

This calculation requires three steps. The first two determine the present value of the withdrawals. The final step determines yearly deposits that will have a present value equal to that of the

withdrawals.

1. We calculate the present value of the four years at college using the annuity formula.

1

1 _____

(1.14)4

_________

$30,000 PVIFA14%,4

$30,000

[

.14

]

$30,000 2.9137 $87,411

We assume that Susan enters college on her 18th birthday. Given our discussion in Trick 1,

$87,411 represents the present value at date 17.

2. We calculate the present value of the college education at date 0 as

$87,411

______

$9,422.91

(1.14)17

3. Assuming that Helen and Harold Nash make deposits to the bank at the end of each of the

17 years, we calculate the annual deposit that will yield a present value of all deposits of

$9,422.91. This is calculated as

C PVIFA14%,17 $9,422.91

Because PVIFA14%,17 6.3729,

$9,422.91

C ________ $1,478.59

6.3729

Thus, deposits of $1,478.59 made at the end of each of the first 17 years and invested at 14 percent will

provide enough money to make tuition payments of $30,000 over the following four years.

An alternative method would be to (1) calculate the present value of the tuition payments at Susan’s 18th birthday and (2) calculate annual deposits such that the future value

of the deposits at her 18th birthday equals the present value of the tuition payments at that

date. Although this technique can also provide the right answer, we have found that it is

more likely to lead to errors. Therefore, we only equate present values in our presentation.

Growing Annuity

Cash flows in business are very likely to grow over time, due either to real growth or to inflation. The growing perpetuity, which assumes an infinite number of cash flows, provides

CHAPTER 4 Discounted Cash Flow Valuation

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one formula to handle this growth. We now consider a growing annuity, which is a finite

number of growing cash flows. Because perpetuities of any kind are rare, a formula for a

growing annuity would be useful indeed. The formula is

Formula for Present Value of Growing Annuity:

1g

1

1

______

______

PV C ______

rgrg 1r

[

(

T

)]

1g T

1 _______

1

r

C _____________

rg

[

(

)]

[4.17]

EXAMPLE

4.25

where, as before, C is the payment to occur at the end of the first period, r is the interest

rate, g is the rate of growth per period, expressed as a percentage, and T is the number of

periods for the annuity.

Growing Annuities

Stuart Gabriel, a second-year MBA student, has just been offered a job at $80,000 a year. He anticipates his salary increasing by 9 percent a year until his retirement in 40 years. Given an interest rate

of 20 percent, what is the present value of his lifetime salary?

We simplify by assuming he will be paid his $80,000 salary exactly one year from now, and that

his salary will continue to be paid in annual installments. The appropriate discount rate is 20 percent.

From (4.17), the calculation is

1.09 40

Present value

1 ____

1.20

$711,731

of Stuart’s $80,000 __________

.20 .09

lifetime salary

[

( )

]

EXAMPLE

4.26

Though the growing annuity is quite useful, it is more tedious than the other simplifying formulas.

Whereas most sophisticated calculators have special programs for perpetuity, growing perpetuity,

and annuity, there is no special program for growing annuity. Hence, one must calculate all the terms

in Formula 4.17 directly.

More Growing Annuities

In a previous example, Harold and Helen Nash planned to make 17 identical payments in order to fund

the college education of their daughter, Susan. Alternatively, imagine that they planned to increase

their payments at 4 percent per year. What would their first payment be?

The first two steps of the previous Nash family example showed that the present value of the college costs was $9,422.91. These two steps would be the same here. However, the third step must be

altered. Now we must ask, How much should their first payment be so that, if payments increase by

4 percent per year, the present value of all payments will be $9,422.91?

We set the growing-annuity formula equal to $9,422.91 and solve for C.

1g

1.04

1 _____

1 ____

1 r C __________

1.14

___________

C

rg

[

(

T

)]

[

17

( )

.14 .04

$9,422.91

]

Here, C $1,192.78. Thus, the deposit on their daughter’s first birthday is $1,192.78, the deposit on the

second birthday is $1,240.49 (1.04 $1,192.78), and so on.

112 PART 2 Valuation and Capital Budgeting

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4.5

L O A N T Y P E S A N D L O A N A M O R T I Z AT I O N

Whenever a lender extends a loan, some provision will be made for repayment of the

principal (the original loan amount). A loan might be repaid in equal installments, for

example, or it might be repaid in a single lump sum. Because the way that the principal

and interest are paid is up to the parties involved, there are actually an unlimited number

of possibilities.

In this section, we describe a few forms of repayment that come up quite often, and

more complicated forms can usually be built up from these. The three basic types of loans

are pure discount loans, interest-only loans, and amortized loans. Working with these loans

is a very straightforward application of the present value principles that we have already

developed.

Pure Discount Loans

The pure discount loan is the simplest form of loan. With such a loan, the borrower receives

money today and repays a single lump sum at some time in the future. A one-year, 10 percent pure discount loan, for example, would require the borrower to repay $1.10 in one year

for every dollar borrowed today.

Because a pure discount loan is so simple, we already know how to value one. Suppose

a borrower was able to repay $25,000 in five years. If we, acting as the lender, wanted a

12 percent interest rate on the loan, how much would we be willing to lend? Put another

way, what value would we assign today to that $25,000 to be repaid in five years? Based on

our previous work we know the answer is just the present value of $25,000 at 12 percent

for five years:

Present value $25,000/1.125

$25,000/1.7623

$14,186

EXAMPLE

4.27

Pure discount loans are common when the loan term is short, say a year or less. In recent

years, they have become increasingly common for much longer periods.

Tr e a s u r y B i l l s

When the U.S. government borrows money on a short-term basis (a year or less), it does so by selling

what are called Treasury bills, or T-bills for short. A T-bill is a promise by the government to repay a

fixed amount at some time in the future—for example, 3 months or 12 months.

Treasury bills are pure discount loans. If a T-bill promises to repay $10,000 in 12 months, and the

market interest rate is 7 percent, how much will the bill sell for in the market?

Because the going rate is 7 percent, the T-bill will sell for the present value of $10,000 to be repaid

in one year at 7 percent:

Present value $10,000/1.07 $9,345.79

Interest-Only Loans

A second type of loan repayment plan calls for the borrower to pay interest each period and

to repay the entire principal (the original loan amount) at some point in the future. Loans

with such a repayment plan are called interest-only loans. Notice that if there is just one

period, a pure discount loan and an interest-only loan are the same thing.

For example, with a three-year, 10 percent, interest-only loan of $1,000, the borrower

would pay $1,000 .10 $100 in interest at the end of the first and second years. At the

CHAPTER 4 Discounted Cash Flow Valuation

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end of the third year, the borrower would return the $1,000 along with another $100 in

interest for that year. Similarly, a 50-year interest-only loan would call for the borrower to

pay interest every year for the next 50 years and then repay the principal. In the extreme,

the borrower pays the interest every period forever and never repays any principal. As we

discussed earlier in the chapter, the result is a perpetuity.

Most corporate bonds have the general form of an interest-only loan. Because we will

be considering bonds in some detail in the next chapter, we will defer further discussion of

them for now.

Amortized Loans

With a pure discount or interest-only loan, the principal is repaid all at once. An alternative

is an amortized loan, with which the lender may require the borrower to repay parts of the

loan amount over time. The process of providing for a loan to be paid off by making regular

principal reductions is called amortizing the loan.

A simple way of amortizing a loan is to have the borrower pay the interest each period

plus some fixed amount. This approach is common with medium-term business loans. For

example, suppose a business takes out a $5,000, five-year loan at 9 percent. The loan agreement calls for the borrower to pay the interest on the loan balance each year and to reduce

the loan balance each year by $1,000. Because the loan amount declines by $1,000 each

year, it is fully paid in five years.

In the case we are considering, notice that the total payment will decline each year. The

reason is that the loan balance goes down, resulting in a lower interest charge each year,

whereas the $1,000 principal reduction is constant. For example, the interest in the first

year will be $5,000 .09 $450. The total payment will be $1,000 450 $1,450. In

the second year, the loan balance is $4,000, so the interest is $4,000 .09 $360, and the

total payment is $1,360. We can calculate the total payment in each of the remaining years

by preparing a simple amortization schedule as follows:

YE AR

1

2

3

4

5

Totals

BE GI N N I N G

BAL A N C E

T O TA L

PAY M E N T

INTEREST

PA I D

P R I N C I PA L

PA I D

E N D ING

B A LA NC E

$5,000

4,000

$1,450

1,360

1,270

1,180

1,090

$6,350

$ 450

360

270

180

90

$1,350

$1,000

1,000

1,000

1,000

1,000

$5,000

$4,000

3,000

2,000

1,000

0

3,000

2,000

1,000

Notice that in each year, the interest paid is given by the beginning balance multiplied by

the interest rate. Also notice that the beginning balance is given by the ending balance from

the previous year.

Probably the most common way of amortizing a loan is to have the borrower make a

single, fixed payment every period. Almost all consumer loans (such as car loans) and

mortgages work this way. For example, suppose our five-year, 9 percent, $5,000 loan was

amortized this way. How would the amortization schedule look?

We first need to determine the payment. From our discussion earlier in the chapter, we

know that this loan’s cash flows are in the form of an ordinary annuity. In this case, we can

solve for the payment as follows:

$5,000 C {[1 (1/1.095)]/.09}

C [(1 .6499)/.09]

114 PART 2 Valuation and Capital Budgeting

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This gives us:

C $5,000/3.8897

$1,285.46

The borrower will therefore make five equal payments of $1,285.46. Will this pay off the

loan? We will check by filling in an amortization schedule.

In our previous example, we knew the principal reduction each year. We then calculated

the interest owed to get the total payment. In this example, we know the total payment. We

will thus calculate the interest and then subtract it from the total payment to calculate the

principal portion in each payment.

In the first year, the interest is $450, as we calculated before. Because the total payment

is $1,285.46, the principal paid in the first year must be:

Principal paid $1,285.46 450 $835.46

The ending loan balance is thus:

Ending balance $5,000 835.46 $4,164.54

The interest in the second year is $4,164.54 .09 $374.81, and the loan balance declines

by $1,285.46 374.81 $910.65. We can summarize all of the relevant calculations in

the following schedule:

YEAR

1

2

3

4

5

Totals

BE GI NNI NG

BAL ANCE

T OTA L

PAYM E N T

INTEREST

PA I D

P R I N C I PA L

PA I D

ENDING

B A LA N C E

$5,000.00

4,164.54

$1,285.46

1,285.46

1,285.46

1,285.46

1,285.46

$6,427.30

$ 450.00

374.81

292.85

203.51

106.14

$1,427.31

$ 835.46

910.65

992.61

1,081.95

1,179.32

$5,000.00

$4,164.54

3,253.88

2,261.27

1,179.32

0.00

3,253.88

2,261.27

1,179.32

EXAMPLE

4.28

Because the loan balance declines to zero, the five equal payments do pay off the loan. Notice

that the interest paid declines each period. This isn’t surprising because the loan balance is

going down. Given that the total payment is fixed, the principal paid must be rising each period. To see how to calculate this loan in Excel, see the upcoming Spreadsheet Strategies box.

If you compare the two loan amortizations in this section, you will see that the total

interest is greater for the equal total payment case: $1,427.31 versus $1,350. The reason

for this is that the loan is repaid more slowly early on, so the interest is somewhat higher.

This doesn’t mean that one loan is better than the other; it simply means that one is effectively paid off faster than the other. For example, the principal reduction in the first year is

$835.46 in the equal total payment case as compared to $1,000 in the first case.

Partial Amortization, or “Bite the Bullet”

A common arrangement in real estate lending might call for a 5-year loan with, say, a 15-year

amortization. What this means is that the borrower makes a payment every month of a fixed amount

based on a 15-year amortization. However, after 60 months, the borrower makes a single, much larger

payment called a “balloon” or “bullet” to pay off the loan. Because the monthly payments don’t fully

pay off the loan, the loan is said to be partially amortized.

(continued)

CHAPTER 4 Discounted Cash Flow Valuation

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Suppose we have a $100,000 commercial mortgage with a 12 percent APR and a 20-year

(240-month) amortization. Further suppose the mortgage has a five-year balloon. What will the monthly

payment be? How big will the balloon payment be?

The monthly payment can be calculated based on an ordinary annuity with a present value of

$100,000. There are 240 payments, and the interest rate is 1 percent per month. The payment is:

$100,000 C [(1 1/1.01240)/.01]

C 90.8194

C $1,101.09

Now, there is an easy way and a hard way to determine the balloon payment. The hard way is to

actually amortize the loan for 60 months to see what the balance is at that time. The easy way is to

recognize that after 60 months, we have a 240 60 180-month loan. The payment is still $1,101.09

per month, and the interest rate is still 1 percent per month. The loan balance is thus the present value

of the remaining payments:

Loan balance $1,101.09 [(1 1/1.01180)/.01]

$1,101.09 83.3217

$91,744.69

The balloon payment is a substantial $91,744. Why is it so large? To get an idea, consider the first

payment on the mortgage. The interest in the first month is $100,000 .01 $1,000. Your payment is

$1,101.09, so the loan balance declines by only $101.09. Because the loan balance declines so slowly,

the cumulative “pay down” over five years is not great.

We will close this section with an example that may be of particular relevance. Federal

Stafford loans are an important source of financing for many college students, helping to

cover the cost of tuition, books, new cars, condominiums, and many other things. Sometimes students do not seem to fully realize that Stafford loans have a serious drawback:

they must be repaid in monthly installments, usually beginning six months after the student

leaves school.

Some Stafford loans are subsidized, meaning that the interest does not begin to accrue

until repayment begins (this is a good thing). If you are a dependent undergraduate student under this particular option, the total debt you can run up is, at most, $23,000. The

maximum interest rate is 8.25 percent, or 8.25/12 0.6875 percent per month. Under the

“standard repayment plan,” the loans are amortized over 10 years (subject to a minimum

payment of $50).

Suppose you max out borrowing under this program and also get stuck paying the maximum interest rate. Beginning six months after you graduate (or otherwise depart the ivory

tower), what will your monthly payment be? How much will you owe after making payments for four years?

Given our earlier discussions, see if you don’t agree that your monthly payment assuming a $23,000 total loan is $282.10 per month. Also, as explained in Example 4.28, after

making payments for four years, you still owe the present value of the remaining payments.

There are 120 payments in all. After you make 48 of them (the first four years), you have

72 to go. By now, it should be easy for you to verify that the present value of $282.10 per

month for 72 months at 0.6875 percent per month is just under $16,000, so you still have

a long way to go.

Of course, it is possible to rack up much larger debts. According to the Association of

American Medical Colleges, medical students who borrowed to attend medical school and

graduated in 2008 had an average student loan balance of $154,607. Ouch! How long will

it take the average student to pay off her medical school loans?

116 PART 2 Valuation and Capital Budgeting

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Loan Amortization Using a Spreadsheet

SPREADSHEET TECHNIQUES

Loan amortization is a common spreadsheet application. To illustrate, we will set up the problem that we

examined earlier: a five-year, $5,000, 9 percent loan with constant payments. Our spreadsheet looks like this:

A

B

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

C

D

E

F

G

H

Using a spreadsheet to amortize a loan

Loan amount:

Interest rate:

Loan term:

Loan payment:

$5,000

0.09

5

$1,285.46

Note: Payment is calculated using PMT(rate, nper, -pv, fv).

Amortization table:

Year

1

2

3

4

5

Totals

Beginning

Balance

$5,000.00

4,164.54

3,253.88

2,261.27

1,179.32

Total

Payment

$1,285.46

1,285.46

1,285.46

1,285.46

1,285.46

6,427.31

Interest

Paid

$450.00

374.81

292.85

203.51

106.14

1,427.31

Principal

Paid

$835.46

910.65

992.61

1,081.95

1,179.32

5,000.00

Ending

Balance

$4,164.54

3,253.88

2,261.27

1,179.32

0.00

Formulas in the amortization table:

Year

1

2

3

4

5

Beginning

Balance

=+D4

=+G13

=+G14

=+G15

=+G16

Total

Payment

=$D$7

=$D$7

=$D$7

=$D$7

=$D$7

Interest

Paid

=+$D$5*C13

=+$D$5*C14

=+$D$5*C15

=+$D$5*C16

=+$D$5*C17

Principal

Paid

=+D13-E13

=+D14-E14

=+D15-E15

=+D16-E16

=+D17-E17

Ending

Balance

=+C13-F13

=+C14-F14

=+C15-F15

=+C16-F16

=+C17-F17

Note: Totals in the amortization table are calculated using the SUM formula.

Let’s say she makes a monthly payment of $1,000, and the loan has an interest rate

of 7 percent per year, or .5833 percent per month. See if you agree that it will take

399 months, or just over 33 years, to pay off the loan. Maybe MD really stands for

“mucho debt!”

4.6

W H AT I S A F I R M W O R T H ?

Suppose you are in the business of trying to determine the value of small companies. (You

are a business appraiser.) How can you determine what a firm is worth? One way to think

about the question of how much a firm is worth is to calculate the present value of its future

cash flows.

Let us consider the example of a firm that is expected to generate net cash flows (cash

inflows minus cash outflows) of $5,000 in the first year and $2,000 for each of the next

five years. The firm can be sold for $10,000 seven years from now. The owners of the firm

would like to be able to make 10 percent on their investment in the firm.

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The value of the firm is found by multiplying the net cash flows by the appropriate

present value factor. The value of the firm is simply the sum of the present values of the

individual net cash flows.

The present value of the net cash flows is given next.

T H E P R E S E N T VA LU E O F T H E FI R M

E ND OF YE AR

N E T C A S H FLO W O F

T H E FI R M

P R E S E N T VA LU E

FA C T O R ( 10% )

P R E S E N T VA LU E OF

N E T C A S H FLOW S

1

2

3

4

5

6

7

$ 5,000

2,000

2,000

2,000

2,000

2,000

10,000

.90909

.82645

.75131

.68301

.62092

.56447

.51316

Present value of firm

$ 4,545.45

1,652.90

1,502.62

1,366.02

1,241.84

1,128.94

5,131.58

$16,569.35

We can also use the simplifying formula for an annuity to give us

(2,000 PVIFA

1.1

)

$5,000

10,000

10%,5

________

$16,569.35

_____________________ ________

7

1.1

(1.1)

Suppose you have the opportunity to acquire the firm for $12,000. Should you acquire the

firm? The answer is yes because the NPV is positive.

NPV PV Cost

$4,569.35 $16,569.35 $12,000

EXAMPLE

4.29

The incremental value (NPV) of acquiring the firm is $4,569.35.

Firm Valuation

The Trojan Pizza Company is contemplating investing $1 million in four new outlets in Los Angeles.

Andrew Lo, the firm’s chief financial officer (CFO), has estimated that the investments will pay out

cash flows of $200,000 per year for nine years and nothing thereafter. (The cash flows will occur

at the end of each year and there will be no cash flow after year 9.) Mr. Lo has determined that

the relevant discount rate for this investment is 15 percent. This is the rate of return that the firm

can earn at comparable projects. Should the Trojan Pizza Company make the investments in the

new outlets?

The decision can be evaluated as:

$200,000

$200,000 $200,000 . . . _______

NPV $1,000,000 _______ _______

1.15

(1.15)2

(1.15)9

$1,000,000 $200,000 PVIFA15%,9

$1,000,000 $954,316.78

$45,683.22

The present value of the four new outlets is only $954,316.78. The outlets are worth less

than they cost. The Trojan Pizza Company should not make the investment because the NPV is

$45,683.22. If the Trojan Pizza Company requires a 15 percent rate of return, the new outlets are not

a good investment.

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SUMMARY AND CONCLUSIONS

1. Two basic concepts, future value and present value, were introduced in the beginning of this

chapter. With a 10 percent interest rate, an investor with $1 today can generate a future value

of $1.10 in a year, $1.21 [$1 (1.10)2] in two years, and so on. Conversely, present value analysis

places a current value on a later cash flow. With the same 10 percent interest rate, a dollar to be

received in one year has a present value of $0.909 ($1/1.10) in year 0. A dollar to be received in

two years has a present value of $0.826 [$1/(1.10)2].

2. One commonly expresses the interest rate as, say, 12 percent per year. However, one can speak

of the interest rate as 3 percent per quarter. Although the stated annual interest rate remains

12 percent (3 percent 4), the effective annual interest rate is 12.55 percent [(1.03)4 1]. In

other words, the compounding process increases the future value of an investment. The limiting

case is continuous compounding, where funds are assumed to be reinvested every infinitesimal

instant.

3. A basic quantitative technique for financial decision making is net present value analysis.

The net present value formula for an investment that generates cash flows (Ci) in future

periods is

C2

C1

CT

______

C0

. . . ______

NPV C0 ______

(1 r) (1 r)2

(1 r)T

T

Ci

______

(1 r)

i1

i

The formula assumes that the cash flow at date 0 is the initial investment (a cash outflow).

4. Frequently, the actual calculation of present value is long and tedious. The computation of the

present value of a long-term mortgage with monthly payments is a good example of this. We

presented four simplifying formulas:

C

Perpetuity: PV __

r

C

Growing perpetuity: PV _____

rg

1

1 ______

(1 r)T

__________

Annuity: PV C

r

[

]

1g T

1 _____

1r

Growing annuity: PV C ___

rg

[

(

)]

5. We stressed a few practical considerations in the application of these formulas:

a. The numerator in each of the formulas, C, is the cash flow to be received one full period hence.

b. Cash flows are generally irregular in practice. To avoid unwieldy problems, assumptions to

create more regular cash flows are made both in this textbook and in the real world.

c. A number of present value problems involve annuities (or perpetuities) beginning a few

periods hence. Students should practice combining the annuity (or perpetuity) formula with

the discounting formula to solve these problems.

d. Annuities and perpetuities may have periods of every two or every n years, rather than once

a year. The annuity and perpetuity formulas can easily handle such circumstances.

e. One frequently encounters problems where the present value of one annuity must be

equated with the present value of another annuity.

6. Many loans are annuities. The process of providing for a loan to be paid off gradually is

called amortizing the loan, and we discussed how amortization schedules are prepared and

interpreted.

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CONCEPT QUESTIONS

1. Compounding and Period As you increase the length of time involved, what happens to future

values? What happens to present values?

2. Interest Rates What happens to the future value of an annuity if you increase the rate r ? What

happens to the present value?

3. Present Value Suppose two athletes sign 10-year contracts for $80 million. In one case, we’re

told that the $80 million will be paid in 10 equal installments. In the other case, we’re told that

the $80 million will be paid in 10 installments, but the installments will increase by 5 percent per

year. Who got the better deal?

4. APR and EAR Should lending laws be changed to require lenders to report EARs instead of

APRs? Why or why not?

5. Time Value On subsidized Stafford loans, a common source of financial aid for college

students, interest does not begin to accrue until repayment begins. Who receives a bigger

subsidy, a freshman or a senior? Explain.

Use the following information for Questions 6–10.

Toyota Motor Credit Corporation (TMCC), a subsidiary of Toyota Motor Corporation, offered some

securities for sale to the public on March 28, 2008. Under the terms of the deal, TMCC promised to

repay the owner of one of these securities $100,000 on March 28, 2038, but investors would receive

nothing until then. Investors paid TMCC $24,099 for each of these securities, so they gave up $24,099

on March 28, 2008, for the promise of a $100,000 payment 30 years later.

6. Time Value of Money Why would TMCC be willing to accept such a small amount today

($24,099) in exchange for a promise to repay about four times that amount ($100,000) in the future?

7. Call Provisions TMCC has the right to buy back the securities on the anniversary date at a

price established when the securities were issued (this feature is a term of this particular deal).

What impact does this feature have on the desirability of this security as an investment?

8. Time Value of Money Would you be willing to pay $24,099 today in exchange for $100,000 in

30 years? What would be the key considerations in answering yes or no? Would your answer

depend on who is making the promise to repay?

9. Investment Comparison Suppose that when TMCC offered the security for $24,099 the U.S.

Treasury had offered an essentially identical security. Do you think it would have had a higher or

lower price? Why?

10. Length of Investment The TMCC security is bought and sold on the New York Stock Exchange.

If you looked at the price today, do you think the price would exceed the $24,099 original price?

Why? If you looked in the year 2019, do you think the price would be higher or lower than today’s

price? Why?

QUESTIONS AND PROBLEMS

Basic

(Questions 1–20)

1. Simple Interest versus Compound Interest First City Bank pays 7 percent simple interest on

its savings account balances, whereas Second City Bank pays 7 percent interest compounded

annually. If you made a $6,000 deposit in each bank, how much more money would you earn

from your Second City Bank account at the end of 10 years?

2. Calculating Future Values

Compute the future value of $2,500 compounded annually for

a. 10 years at 6 percent

b. 10 years at 8 percent

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c. 20 years at 6 percent

d. Why is the interest earned in part (c) not twice the amount earned in part (a)?

3. Calculating Present Values For each of the following, compute the present value:

PRE SE NT VAL UE

YE A R S

I N T E R E S T R AT E

FU T U R E VA LU E

9

7%

6

9

$ 15,451

51,557

21

14

886,073

27

16

550,164

4. Calculating Interest Rates Solve for the unknown interest rate in each of the following:

PRE SE NT VAL UE

$

YE A R S

I N T E R E S T R AT E

FU T U R E VA LU E

243

3

405

10

$

896

307

34,500

13

162,181

51,285

26

483,500

5. Calculating the Number of Periods Solve for the unknown number of years in each of the

following:

PRE SE NT VAL UE

$

YE A R S

I N T E R E S T R AT E

FU T U R E VA LU E

625

7%

810

8

$ 1,284

4,341

18,400

13

402,662

21,500

16

173,439

6. Calculating the Number of Periods At 8 percent interest, how long does it take to double your

money? To quadruple it?

7. Calculating Present Values Imprudential, Inc., has an unfunded pension liability of $750 million

that must be paid in 20 years. To assess the value of the firm’s stock, financial analysts want to

discount this liability back to the present. If the relevant discount rate is 6.25 percent, what is the

present value of this liability?

8. Calculating Rates of Return Although appealing to more refined tastes, art as a collectible

has not always performed so profitably. During 2003, Sothebys sold the Edgar Degas bronze

sculpture Petite Danseuse de Quatorze Ans at auction for a price of $10,311,500. Unfortunately

for the previous owner, he had purchased it in 1999 at a price of $12,377,500. What was his

annual rate of return on this sculpture?

9. Perpetuities An investor purchasing a British consol is entitled to receive annual payments

from the British government forever. What is the price of a consol that pays $160 annually if the

next payment occurs one year from today? The market interest rate is 4.5 percent.

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10. Continuous Compounding

Compute the future value of $1,800 continuously compounded for

a. Five years at a stated annual interest rate of 14 percent.

b. Three years at a stated annual interest rate of 6 percent.

c. Ten years at a stated annual interest rate of 7 percent.

d. Eight years at a stated annual interest rate of 9 percent.

11. Present Value and Multiple Cash Flows Conoly Co. has identified an investment project with

the following cash flows. If the discount rate is 5 percent, what is the present value of these

cash flows? What is the present value at 13 percent? At 18 percent?

YEAR

C A S H FLO W

1

$ 850

2

740

3

1,090

4

1,310

12. Present Value and Multiple Cash Flows Investment X offers to pay you $6,000 per year for

nine years, whereas Investment Y offers to pay you $8,500 per year for five years. Which of

these cash flow streams has the higher present value if the discount rate is 9 percent? If the

discount rate is 21 percent?

13. Calculating Annuity Present Value An investment offers $7,000 per year for 15 years, with

the first payment occurring one year from now. If the required return is 8 percent, what is the

value of the investment? What would the value be if the payments occurred for 40 years? For

75 years? Forever?

14. Calculating Perpetuity Values The Perpetual Life Insurance Co. is trying to sell you an

investment policy that will pay you and your heirs $25,000 per year forever. If the required return

on this investment is 6 percent, how much will you pay for the policy? Suppose the Perpetual

Life Insurance Co. told you the policy costs $435,000. At what interest rate would this be a fair

deal?

15. Calculating EAR

Find the EAR in each of the following cases:

STAT E D RAT E ( A P R )

NUMBER OF TIMES COMPOUNDED

15%

Quarterly

12

Monthly

9

Daily

13

16. Calculating APR

E FFE C T I V E R AT E ( EAR )

Infinite

Find the APR, or stated rate, in each of the following cases:

STAT E D RAT E ( A P R )

NUMBER OF TIMES COMPOUNDED

E FFE C T I V E R AT E ( EAR )

Semiannually

10.2%

Monthly

8.4

Weekly

15.9

Infinite

18.7

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17. Calculating EAR First National Bank charges 15.1 percent compounded monthly on its business loans. First United Bank charges 15.5 percent compounded semiannually. As a potential

borrower, which bank would you go to for a new loan?

18. Interest Rates Well-known financial writer Andrew Tobias argues that he can earn 177 percent

per year buying wine by the case. Specifically, he assumes that he will consume one $10 bottle

of fine Bordeaux per week for the next twelve weeks. He can either pay $10 per week or buy a

case of 12 bottles today. If he buys the case, he receives a 10 percent discount, and, by doing

so, earns the 177 percent. Assume he buys the wine and consumes the first bottle today. Do you

agree with his analysis? Do you see a problem with his numbers?

19. Calculating Number of Periods One of your customers is delinquent on his accounts payable

balance. You’ve mutually agreed to a repayment schedule of $375 per month. You will charge

0.9 percent per month interest on the overdue balance. If the current balance is $13,200, how

long will it take for the account to be paid off?

20. Calculating EAR Friendly’s Quick Loans, Inc., offers you “three for four or I knock on your

door.” This means you get $3 today and repay $4 when you get your paycheck in one week (or

else). What’s the effective annual return Friendly’s earns on this lending business? If you were

brave enough to ask, what APR would Friendly’s say you were paying?

21. Future Value What is the future value in three years of $1,800 invested in an account with a

stated annual interest rate of 10 percent,

Intermediate

(Questions 21–52)

a. Compounded annually?

b. Compounded semiannually?

c. Compounded monthly?

d. Compounded continuously?

e. Why does the future value increase as the compounding period shortens?

22. Simple Interest versus Compound Interest First Simple Bank pays 7 percent simple interest

on its investment accounts. If First Complex Bank pays interest on its accounts compounded

annually, what rate should the bank set if it wants to match First Simple Bank over an investment

horizon of 10 years?

23. Calculating Annuities You are planning to save for retirement over the next 30 years. To do

this, you will invest $700 a month in a stock account and $300 a month in a bond account. The return of the stock account is expected to be 11 percent, and the bond account will pay 6 percent.

When you retire, you will combine your money into an account with an 8 percent return. How

much can you withdraw each month from your account assuming a 25-year withdrawal period?

24. Calculating Rates of Return Suppose an investment offers to quintuple your money in

12 months (don’t believe it). What rate of return per quarter are you being offered?

25. Calculating Rates of Return You’re trying to choose between two different investments, both

of which have up-front costs of $75,000. Investment G returns $125,000 in five years. Investment

H returns $245,000 in 11 years. Which of these investments has the higher return?

26. Growing Perpetuities Mark Weinstein has been working on an advanced technology in laser

eye surgery. His technology will be available in the near term. He anticipates his first annual

cash flow from the technology to be $210,000, received three years from today. Subsequent annual cash flows will grow at 3 percent, in perpetuity. What is the present value of the technology

if the discount rate is 12 percent?

27. Perpetuities A prestigious investment bank designed a new security that pays a quarterly

dividend of $3 in perpetuity. The first dividend occurs one quarter from today. What is the price

of the security if the stated annual interest rate is 9 percent, compounded quarterly?

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28. Annuity Present Values What is the present value of an annuity of $6,000 per year, with the

first cash flow received four years from today and the last one received 18 years from today?

Use a discount rate of 8 percent.

29. Annuity Present Values What is the value today of a 15-year annuity that pays $750 a year?

The annuity’s first payment occurs six years from today. The annual interest rate is 9 percent for

years 1 through 5, and 12 percent thereafter.

30. Balloon Payments Mike Bayles has just arranged to purchase a $750,000 vacation home in

the Bahamas with a 25 percent down payment. The mortgage has a 6.5 percent stated annual

interest rate, compounded monthly, and calls for equal monthly payments over the next 30 years.

His first payment will be due one month from now. However, the mortgage has an eight-year balloon

payment, meaning that the balance of the loan must be paid off at the end of year 8. There were

no other transaction costs or finance charges. How much will Mike’s balloon payment be in eight

years?

31. Calculating Interest Expense You receive a credit card application from Shady Banks Savings

and Loan offering an introductory rate of 1.80 percent per year, compounded monthly for the first

six months, increasing thereafter to 18 percent compounded monthly. Assuming you transfer

the $6,000 balance from your existing credit card and make no subsequent payments, how much

interest will you owe at the end of the first year?

32. Perpetuities Barrett Pharmaceuticals is considering a drug project that costs $875,000 today

and is expected to generate end-of-year annual cash flows of $61,000, forever. At what discount

rate would Barrett be indifferent between accepting or rejecting the project?

33. Growing Annuity Southern California Publishing Company is trying to decide whether or not

to revise its popular textbook, Financial Psychoanalysis Made Simple. It has estimated that the

revision will cost $95,000. Cash flows from increased sales will be $26,000 the first year. These

cash flows will increase by 6 percent per year. The book will go out of print five years from now.

Assume that the initial cost is paid now and revenues are received at the end of each year.

If the company requires an 11 percent return for such an investment, should it undertake the

revision?

34. Growing Annuity Your job pays you only once a year, for all the work you did over the

previous 12 months. Today, December 31, you just received your salary of $75,000 and you plan

to spend all of it. However, you want to start saving for retirement beginning next year. You have

decided that one year from today you will begin depositing 10 percent of your annual salary

in an account that will earn 9 percent per year. Your salary will increase at 4 percent per year

throughout your career. How much money will you have on the date of your retirement 35 years

from today?

35. Present Value and Interest Rates What is the relationship between the value of an annuity

and the level of interest rates? Suppose you just bought a 12-year annuity of $7,000 per

year at the current interest rate of 10 percent per year. What happens to the value of your

investment if interest rates suddenly drop to 5 percent? What if interest rates suddenly rise

to 15 percent?

36. Calculating the Number of Payments You’re prepared to make monthly payments of $125,

beginning at the end of this month, into an account that pays 10 percent interest compounded

monthly. How many payments will you have made when your account balance reaches

$25,000?

37. Calculating Annuity Present Values You want to borrow $75,000 from your local bank to

buy a new sailboat. You can afford to make monthly payments of $1,475, but no more.

Assuming monthly compounding, what is the highest rate you can afford on a 60-month

APR loan?

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38. Calculating Loan Payments You need a 30-year, fixed-rate mortgage to buy a new

home for $260,000. Your mortgage bank will lend you the money at a 6.1 percent APR for

this loan. However, you can only afford monthly payments of $1,150, so you offer to pay off

any remaining loan balance at the end of the loan in the form of a single balloon payment.

How large will this balloon payment have to be for you to keep your monthly payments at

$1,150?

39. Present and Future Values The present value of the following cash flow stream is $5,985 when

discounted at 10 percent annually. What is the value of the missing cash flow?

YE A R

C A S H FLO W

1

$1,750

2

?

3

1,380

4

2,230

40. Calculating Present Values You just won the TVM Lottery. You will receive $1 million today

plus another 10 annual payments that increase by $350,000 per year. Thus, in one year you

receive $1.35 million. In two years, you get $1.7 million, and so on. If the appropriate interest rate

is 8 percent, what is the present value of your winnings?

41. EAR versus APR You have just purchased a new warehouse. To finance the purchase,

you’ve arranged for a 30-year mortgage loan for 80 percent of the $2,400,000 purchase

price. The monthly payment on this loan will be $13,500. What is the APR on this loan?

The EAR?

42. Present Value and Break-Even Interest Consider a firm with a contract to sell an asset for

$140,000 three years from now. The asset costs $91,000 to produce today. Given a relevant discount rate on this asset of 13 percent per year, will the firm make a profit on this asset? At what

rate does the firm just break even?

43. Present Value and Multiple Cash Flows What is the present value of $2,500 per year, at a discount rate of 8 percent, if the first payment is received 7 years from now and the last payment is

received 30 years from now?

44. Variable Interest Rates A 15-year annuity pays $1,700 per month, and payments are made

at the end of each month. If the interest rate is 12 percent compounded monthly for the first

seven years, and 9 percent compounded monthly thereafter, what is the present value of the

annuity?

45. Comparing Cash Flow Streams You have your choice of two investment accounts. Investment

A is a 15-year annuity that features end-of-month $1,300 payments and has an interest rate of

8.75 percent compounded monthly. Investment B is an 8 percent continuously compounded

lump-sum investment, also good for 15 years. How much money would you need to invest in B

today for it to be worth as much as Investment A 15 years from now?

46. Calculating Present Value of a Perpetuity Given an interest rate of 8.2 percent per year,

what is the value at date t 7 of a perpetual stream of $2,100 payments that begin at date

t 15?

47. Calculating EAR A local finance company quotes a 17 percent interest rate on one-year loans.

So, if you borrow $15,000, the interest for the year will be $2,550. Because you must repay a total

of $17,550 in one year, the finance company requires you to pay $17,550/12, or $1,462.50, per month

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over the next 12 months. Is this a 17 percent loan? What rate would legally have to be quoted?

What is the effective annual rate?

48. Calculating Present Values A 5-year annuity of ten $10,000 semiannual payments will begin

9 years from now, with the first payment coming 9.5 years from now. If the discount rate is

10 percent compounded monthly, what is the value of this annuity five years from now? What is

the value three years from now? What is the current value of the annuity?

49. Calculating Annuities Due Suppose you are going to receive $8,000 per year for 10 years. The

appropriate interest rate is 9 percent.

a. What is the present value of the payments if they are in the form of an ordinary annuity?

What is the present value if the payments are an annuity due?

b. Suppose you plan to invest the payments for 10 years. What is the future value if the

payments are an ordinary annuity? What if the payments are an annuity due?

c. Which has the highest present value, the ordinary annuity or the annuity due? Which has the

highest future value? Will this always be true?

50. Calculating Annuities Due You want to buy a new sports car from Muscle Motors for $85,000.

The contract is in the form of a 60-month annuity due at a 6.8 percent APR. What will your

monthly payment be?

51. Amortization with Equal Payments Prepare an amortization schedule for a three-year loan

of $69,000. The interest rate is 9 percent per year, and the loan calls for equal annual payments.

How much interest is paid in the third year? How much total interest is paid over the life of the

loan?

52. Amortization with Equal Principal Payments Rework Problem 51 assuming that the loan agreement calls for a principal reduction of $23,000 every year instead of equal annual payments.

Challenge

(Questions 53–80)

53. Calculating Annuities Due You want to lease a set of golf clubs from Pings Ltd. The lease

contract is in the form of 24 equal monthly payments at an 11.50 percent stated annual interest

rate, compounded monthly. Since the clubs cost $3,500 retail, Pings wants the PV of the lease

payments to equal $3,500. Suppose that your first payment is due immediately. What will your

monthly lease payments be?

54. Annuities You are saving for the college education of your two children. They are two years

apart in age; one will begin college 15 years from today and the other will begin 17 years from today.

You estimate your children’s college expenses to be $55,000 per year per child, payable at the beginning of each school year. The annual interest rate is 7.25 percent. How much money must you

deposit in an account each year to fund your children’s education? Your deposits begin one year

from today. You will make your last deposit when your oldest child enters college. Assume

four years of college.

55. Growing Annuities Tom Adams has received a job offer from a large investment bank as a

clerk to an associate banker. His base salary will be $52,000. He will receive his first annual

salary payment one year from the day he begins to work. In addition, he will get an immediate

$10,000 bonus for joining the company. His salary will grow at 3.5 percent each year. Each year

he will receive a bonus equal to 10 percent of his salary. Mr. Adams is expected to work for

35 years. What is the present value of the offer if the discount rate is 9 percent?

56. Calculating Annuities You have recently won the super jackpot in the Set for Life lottery. On

reading the fine print, you discover that you have the following two options:

a. You will receive 31 annual payments of $400,000, with the first payment being delivered today.

The income will be taxed at a rate of 35 percent. Taxes will be withheld when the checks are

issued.

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b. You will receive $900,000 now, and you will not have to pay taxes on this amount. In addition,

beginning one year from today, you will receive $290,000 each year for 30 years. The cash

flows from this annuity will be taxed at 35 percent.

Using a discount rate of 10 percent, which option should you select?

57. Calculating Growing Annuities You have 30 years left until retirement and want to retire with

$2.2 million. Your salary is paid annually and you will receive $80,000 at the end of the current

year. Your salary will increase at 3 percent per year, and you can earn a 10 percent return on the

money you invest. If you save a constant percentage of your salary, what percentage of your

salary must you save each year?

58. Balloon Payments On September 1, 2008, Susan Chao bought a motorcycle for $30,000. She

paid $1,000 down and financed the balance with a five-year loan at a stated annual interest rate

of 7.8 percent, compounded monthly. She started the monthly payments exactly one month after

the purchase (i.e., October 1, 2008). Two years later, at the end of October 2010, Susan got a new

job and decided to pay off the loan. If the bank charges her a 1 percent prepayment penalty

based on the loan balance, how much must she pay the bank on November 1, 2010?

59. Calculating Annuity Values Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with a retirement income of

$15,000 per month for 20 years, with the first payment received 30 years and 1 month from

now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated

cost of $300,000. Third, after he passes on at the end of the 20 years of withdrawals, he

would like to leave an inheritance of $1,000,000 to his nephew Frodo. He can afford to save

$2,000 per month for the next 10 years. If he can earn a 10 percent EAR before he retires

and an 8 percent EAR after he retires, how much will he have to save each month in years

11 through 30?

60. Calculating Annuity Values After deciding to buy a new car, you can either lease the car or

purchase it with a 3-year loan. The car you wish to buy costs $30,000. The dealer has a special

leasing arrangement where you pay $1,500 today and $450 per month for the next three years.

If you purchase the car, you will pay it off in monthly payments over the next three years at an

8 percent APR. You believe that you will be able to sell the car for $19,000 in three years. Should

you buy or lease the car? What break-even resale price in three years would make you indifferent between buying and leasing?

61. Calculating Annuity Values An All-Pro defensive lineman is in contract negotiations. The team

has offered the following salary structure:

TIME

S A LA RY

0

$5,000,000

1

$4,000,000

2

$4,800,000

3

$5,600,000

4

$6,200,000

5

$6,800,000

6

$7,300,000

All salaries are to be paid in a lump sum. The player has asked you as his agent to renegotiate

the terms. He wants an $8 million signing bonus payable today and a contract value increase of

$1,500,000. He also wants an equal salary paid every three months, with the first paycheck three

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months from now. If the interest rate is 5 percent compounded daily, what is the amount of his

quarterly check? Assume 365 days in a year.

62. Discount Interest Loans This question illustrates what is known as discount interest. Imagine you are discussing a loan with a somewhat unscrupulous lender. You want to borrow

$20,000 for one year. The interest rate is 14 percent. You and the lender agree that the interest

on the loan will be .14 $20,000 $2,800. So the lender deducts this interest amount from

the loan up front and gives you $17,200. In this case, we say that the discount is $2,800. What’s

wrong here?

63. Calculating Annuity Values You are serving on a jury. A plaintiff is suing the city for injuries

sustained after a freak street sweeper accident. In the trial, doctors testified that it will be five

years before the plaintiff is able to return to work. The jury has already decided in favor of the

plaintiff. You are the foreperson of the jury and propose that the jury give the plaintiff an award

to cover the following: 1) The present value of two years’ back pay. The plaintiff’s annual salary for the last two years would have been $38,000 and $40,000, respectively. 2) The present

value of five years’ future salary. You assume the salary will be $45,000 per year. 3) $200,000

for pain and suffering. 4) $30,000 for court costs. Assume that the salary payments are equal

amounts paid at the end of each month. If the interest rate you choose is a 7 percent EAR,

what is the size of the settlement? If you were the plaintiff, would you like to see a higher or

lower interest rate?

64. Calculating EAR with Points You are looking at a one-year loan of $10,000. The interest rate

is quoted as 9 percent plus two points. A point on a loan is simply 1 percent (one percentage

point) of the loan amount. Quotes similar to this one are very common with home mortgages.

The interest rate quotation in this example requires the borrower to pay two points to the lender

up front and repay the loan later with 9 percent interest. What rate would you actually be paying here?

65. Calculating EAR with Points The interest rate on a one-year loan is quoted as 13 percent plus

three points (see the previous problem). What is the EAR? Is your answer affected by the loan

amount?

66. EAR versus APR There are two banks in the area that offer 30-year, $225,000 mortgages at

7.5 percent and charge a $2,500 loan application fee. However, the application fee charged by

Insecurity Bank and Trust is refundable if the loan application is denied, whereas that charged

by I. M. Greedy and Sons Mortgage Bank is not. The current disclosure law requires that any

fees that will be refunded if the applicant is rejected be included in calculating the APR, but this

is not required with nonrefundable fees (presumably because refundable fees are part of the

loan rather than a fee). What are the EARs on these two loans? What are the APRs?

67. Calculating EAR with Add-On Interest This problem illustrates a deceptive way of quoting interest

rates called add-on interest. Imagine that you see an advertisement for Crazy Judy’s Stereo City that

reads something like this: “$2,000 Instant Credit! 17% Simple Interest! Three Years to Pay! Low, Low

Monthly Payments!” You’re not exactly sure what all this means and somebody has spilled ink over

the APR on the loan contract, so you ask the manager for clarification.

Judy explains that if you borrow $2,000 for three years at 17 percent interest, in three years

you will owe:

$2,000 1.173 $2,000 1.601613 $3,203.23

Now, Judy recognizes that coming up with $3,203.23 all at once might be a strain, so she lets you

make “low, low monthly payments” of $3,203.23/36 $88.98 per month, even though this is extra

bookkeeping work for her.

Is this a 17 percent loan? Why or why not? What is the APR on this loan? What is the EAR?

Why do you think this is called add-on interest?

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68. Calculating Annuity Payments This is a classic retirement problem. A time line will help

in solving it. Your friend is celebrating her 35th birthday today and wants to start saving

for her anticipated retirement at age 65. She wants to be able to withdraw $140,000 from

her savings account on each birthday for 20 years following her retirement; the first

withdrawal will be on her 66th birthday. Your friend intends to invest her money in the

local credit union, which offers 7 percent interest per year. She wants to make equal

annual payments on each birthday into the account established at the credit union for her

retirement fund.

a. If she starts making these deposits on her 36th birthday and continues to make deposits until

she is 65 (the last deposit will be on her 65th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement?

b. Suppose your friend has just inherited a large sum of money. Rather than making equal

annual payments, she has decided to make one lump-sum payment on her 35th birthday

to cover her retirement needs. What amount does she have to deposit?

c. Suppose your friend’s employer will contribute $2,000 to the account every year as part of

the company’s profit-sharing plan. In addition, your friend expects a $50,000 distribution from

a family trust fund on her 55th birthday, which she will also put into the retirement account.

What amount must she deposit annually now to be able to make the desired withdrawals at

retirement?

69. Calculating the Number of Periods Your Christmas ski vacation was great, but it unfortunately

ran a bit over budget. All is not lost, because you just received an offer in the mail to transfer

your $10,000 balance from your current credit card, which charges an annual rate of 19.2 percent, to a new credit card charging a rate of 9.2 percent. How much faster could you pay the

loan off by making your planned monthly payments of $170 with the new card? What if there was

a 3 percent fee charged on any balances transferred?

70. Future Value and Multiple Cash Flows An insurance company is offering a new policy to its

customers. Typically, the policy is bought by a parent or grandparent for a child at the child’s

birth. The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company:

First birthday:

$ 700

Second birthday:

$ 700

Third birthday:

$ 800

Fourth birthday:

$ 800

Fifth birthday:

$ 900

Sixth birthday:

$ 900

After the child’s sixth birthday, no more payments are made. When the child reaches age 65,

he or she receives $500,000. If the relevant interest rate is 10 percent for the first six years and

8 percent for all subsequent years, is the policy worth buying?

71. Annuity Present Values and Effective Rates You have just won the lottery. You will receive

$4,000,000 today, and then receive 40 payments of $1,000,000. These payments will start one

year from now and will be paid every six months. A representative from Greenleaf Investments

has offered to purchase all the payments from you for $20.4 million. If the appropriate interest rate is an 8 percent APR compounded daily, should you take the offer? Assume there are

365 days per year.

72. Calculating Interest Rates A financial planning service offers a college savings program. The

plan calls for you to make six annual payments of $14,000 each, with the first payment occurring

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today, your child’s 12th birthday. Beginning on your child’s 18th birthday, the plan will provide

$30,000 per year for four years. What return is this investment offering?

73. Break-Even Investment Returns Your financial planner offers you two different investment

plans. Plan X is a $10,000 annual perpetuity. Plan Y is a 10-year, $21,000 annual annuity. Both

plans will make their first payment one year from today. At what discount rate would you be

indifferent between these two plans?

74. Perpetual Cash Flows What is the value of an investment that pays $17,000 every

other year forever, if the first payment occurs one year from today and the discount rate is

12 percent compounded daily? What is the value today if the first payment occurs four years

from today?

75. Ordinary Annuities and Annuities Due As discussed in the text, an annuity due is identical to

an ordinary annuity except that the periodic payments occur at the beginning of each period

and not at the end of the period. Show that the relationship between the value of an ordinary

annuity and the value of an otherwise equivalent annuity due is:

Annuity due value Ordinary annuity value (1 r )

Show this for both present and future values.

76. Calculating Annuities Due A 10-year annual annuity due with the first payment occurring at

date t 7 has a current value of $85,000. If the discount rate is 9 percent per year, what is the

annuity payment amount?

77. Calculating EAR A check-cashing store is in the business of making personal loans to walk-up

customers. The store makes only one-week loans at 7 percent interest per week.

a. What APR must the store report to its customers? What is the EAR that the customers are

actually paying?

b. Now suppose the store makes one-week loans at 7 percent discount interest per week (see

Question 62). What’s the APR now? The EAR?

c. The check-cashing store also makes one-month add-on interest loans at 7 percent discount

interest per week. Thus, if you borrow $100 for one month (four weeks), the interest will be

($100 1.074) 100 $31.08. Because this is discount interest, your net loan proceeds

today will be $68.92. You must then repay the store $100 at the end of the month. To help you

out, though, the store lets you pay off this $100 in installments of $25 per week. What is the

APR of this loan? What is the EAR?

78. Present Value of a Growing Perpetuity What is the equation for the present value of a

growing perpetuity with a payment of C one period from today if the payments grow by C each

period?

79. Rule of 72 A useful rule of thumb for the time it takes an investme...