Essentials of corporate finance

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McGRAW-HILL INTERNATIONAL EDITION

'ON

Corporate Finance

Asian Network sixth edition

for Higher Education

no.()02 5

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

Consu lting Editor, Stephen A. Ross

Franco Modigliani Professor of Finance and Economics

Sloan School of Management. Massachusetts Institute of Technology

FINANCIAL MANAGEMENT

A d a ir

Excel Applications fo r Corporate Finance

F irst Edition

Block a n d H irt

Foundations o f Financial M anagem ent

Twelfth Edition

B realey, M yers, a n d Allen

Principles o f Corporate Finance

N inth Edition

B realey, M yers, a n d Allen

Corporate Finance, B rie f Edition

First Edition

B realey, M yers, a n d M arcu s

Fundam entals o f Corporate Finance

Fifth Edition

B rooks

FinG am e Online 5.0

B ru n er

Case Studies in Finance: M anaging fo r

Corporate Value Creation

Fifth Edition

C hew

The N ew Corporate Finance: Where Theory

M eets Practice

Third Edition

D eM ello

Cases in Finance

Second Edition

G rin b la tt (editor)

Stephen A. Ross, M entor: Influence through

G enerations

G rin b la tt a n d T itm a n

Financial M arkets and Corporate Strategy

Second Edition

H elfert

Techniques o f Financial Analysis: A Guide

to Value Creation

Eleventh Edition

Higgins

Analysis fo r Financial M anagem ent

Eighth Edition

K ester, R u b ack , an d T\ifano

Case Problem s in Finance

Twelfth Edition

R oss, YVesterfield, a n d Jaffe

C orporate Finance

Eighth Edition

R oss, W esterfield, Ja ffe , a n d J o rd a n

C orporate Finance: Core Principles

and Applications

First Edition

Ross, W esterfield, a n d J o rd a n

Essentials o f Corporate Finance

Sixth Edition

Ross, W esterfield, a n d J o rd a n

Fundam entals o f Corporate Finance

Eighth Edition

S hefrin

Behavioral Corporate Finance: Decisions

That Create Value

First Edition

W hite

Financial Analysis with an Electronic

Calculator

Sixth Edition

INVESTMENTS

A d a ir

Excel Applications fo r Investm ents

First Edition

Bodie, K ane, an d M arcu s

Essentials o f Investm ents

Seventh Edition

Bodie, K ane, an d M arcu s

Investm ents

Eighth Edition

H irt an d Block

Fundam entals o f Investm ent M anagem ent

N inth Edition

H irschey a n d N ofsinger

Investm ents: Analysis and Behavior

First Edition

J o rd a n a n d M iller

Fundam entals o f Investm ents: Valuation

a nd M anagem ent

Fourth Edition

FINANCIAL INSTITUTIONS

AND MARKETS

Rose a n d H udgins

Bank M anagem ent and Financial S e n ’ices

Seventh Edition

Rose a n d M arq u is

M oney and C apital M arkets: Financial

Institutions and Instrum ents in a

G lobal M arketplace

Tenth Edition

S a u n d e rs a n d C o rn e tt

Financial Institutions M anagem ent: A Risk

M anagem ent Approach

Sixth Edition

Saunders and Cornett

Financial M arkets an d Institutions: An

Introduction to the Risk M anagem ent

Approach

Third Edition

INTERNATIONAL FINANCE

E u n and Resnick

International Financial M anagem ent

Fourth Edition

Kuemmerle

Case Studies in International

Entrepreneurship: M anaging and Financing

Ventures in the G lobal Econom y

First Edition

REAL ESTATE

B rueggem an a n d F ish e r

Real Estate Finance a nd Investm ents

Thirteenth Edition

C orgel, L ing, a n d S m ith

R eal Estate Perspectives: A n Introduction to

R eal Estate

Fourth Edition

L ing a n d A rch er

R eal Estate P rinciples: A Value Approach

Second Edition

FINANCIAL PLANNING

AND INSURANCE

A llen, M elone, R osenbloom , an d

M ahoney

Retirem ent Plans: 401(k)s, IRAs, a nd O ther

D eferred C om pensation Approaches

Tenth Edition

A ltfest

P ersonal Financial Planning

First Edition

H a rrin g to n a n d N iehaus

R isk M anagem ent and Insurance

Second Edition

K apoor, D labay, a n d H ughes

Focus on Personal Finance: A n A ctive

Approach to H elp You D evelop Successful

Financial Skills

Second Edition

K apoor, D labay, a n d H ughes

Personal F inance

Eighth Edition

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Essentials of

Corporate Finance

SIXTH EDITION

Stephen A. Ross

Massachusetts Institute of Technology

Randolph W. Westerfield

University of Southern California

Bradford D. Jordan

University of Kentucky

¡ a McGraw-Hill

rrm Irwin

Boston Burr Ridge. IL Dubuque, IA New York San Francisco St. Louis

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McGraw-Hill

Irwin

ESSEN TIALS O F CORPORATE FINAN CE

Published by M cG raw -H ill/Irw in, a business unit o f T he M cG raw-Hill Com panies. Inc.. 1221 Avenue o f the

A m ericas, New York. NY, 10020. C opyright © 2008 by The M cG raw-Hill Com panies. Inc. All rights reserved.

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United States.

This book is printed on acid-free paper.

Printed in China

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ISBN 978-0-07-128340-3

M H ID 0-07-128340-4

Me

Graw

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About the Authors

S te p h e n A. R o ss

Sloan School of Management,

Franco Modigliani Professor

of Finance and Economics,

Massachusetts Institute

of Technology

Stephen A. Ross is the Franco

Modigliani Professor of Finance and

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 and

his 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 and

Freddie Mac.

R a n d o lp h W. W e ste rfie ld

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 of Finance.

He came to USC from the Wharton

School. University of Pennsylvania,

where he was the chairman of the

finance department and a member

of the finance faculty for 20 years.

He is a member of several public

company boards of directors including

Health Management Associates. Inc.,

and the Nicholas Applegate Growth

Fund. His areas of expertise include

corporate financial policy, investment

management, and stock market price

behavior.

B ra d fo rd D. J o rd a n

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 on

issues such as the cost of capital,

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, 4th edition, a leading

investments text, also published by

McGraw-Hill/Irwin.

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From the Authors

W

hen we first wrote Essentials o f Corporate Finance, we thought there might be a

small niche for a briefer book that really focused on w hat students with widely vary￾ing backgrounds and interests needed to carry away from an introductory finance course.

We were wrong. There was a huge niche! What we learned is that our text closely matches

the needs of instructors and faculty at hundreds of schools across the country. As a result,

the growth we have experienced through the first five editions of Essentials has far ex￾ceeded anything we thought possible.

With the sixth edition of Essentials o f Corporate Finance, we have continued to refine

our focus on our target audience, which is the undergraduate student taking a core course

in business or corporate finance. This can be a tough course to teach. One reason is that

the class is usually required of all business students, so it is not uncommon for a majority of the

students to be nonfinance majors. In fact, this may be the only finance course many of them

will ever have. With this in mind, our goal in Essentials is to convey the most important

concepts and principles at a level that is approachable for the widest possible audience.

To achieve our goal, we have worked to distill the subject down to its bare essentials

(hence, the name of this book), w hile retaining a decidedly modem approach to finance.

We have always maintained that the subject of corporate finance can be viewed as the

working of a few very powerful intuitions. We also think that understanding the “why" is

just as important, if not more so, than understanding the “how," especially in an introduc￾tory course. Based on the gratifying market feedback we have received from our previous

editions, as w ell as from our other text. Fundamentals o f Corporate Finance (now in its

8th edition), many of you agree.

By design, this book is not encyclopedic. As the table of contents indicates, we have

a total of 18 chapters. Chapter length is about 30 pages, so the text is aimed squarely at a

single-term course, and most of the book can be realistically covered in a typical semes￾ter or quarter. Writing a book for a one-term course necessarily means some picking and

choosing, with regard to both topics and depth of coverage. Throughout, we strike a bal￾ance by introducing and covering the essentials (there's that word again!) while leaving

some more specialized topics to follow -up courses.

The other things we have always stressed, and have continued to improve with this

edition, are readability and pedagogy. Essentials is written in a relaxed, conversational

style that invites the students to join in the learning process rather than being a passive

information absorber. We have found that this approach dramatically increases students*

willingness to read and learn on their own. Between larger and larger class sizes and the

ever-growing demands on faculty time, we think this is an essential (!) feature for a text in

an introductor}' course.

Throughout the development of this book, we have continued to take a hard look at

what is truly relevant and useful. In doing so, we have worked to downplay purely theoreti￾cal issues and minimize the use of extensive and elaborate calculations to illustrate points

that are either intuitively obvious or of limited practical use.

As a result of this process, three basic themes emerge as our central focus in writing

Essentials o f Corporate Finance:

An Emphasis on Intuition We always try to separate and explain the principles

at work on a commonsense, intuitive level before launching into any specifics. The

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underlying ideas are discussed first in very general terms and then by way of examples

that illustrate in more concrete terms how a financial manager might proceed in a given

situation.

A Unified Valuation Approach We treat net present value (NPV) as the basic con￾cept underlying corporate finance. Many texts stop well short of consistently integrating

this important principle. The most basic and important notion, that NPV represents the

excess of market value over cost, often is lost in an overly mechanical approach that em￾phasizes 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 deci￾sions have valuation effects.

A M anagerial Focus Students shouldn't lose sight of the fact that financial manage￾ment concerns 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 finance, and, where appropriate, the approximate, pragmatic

nature of financial analysis is made explicit, possible pitfalls are described, and limitations

are discussed.

Today, as we prepare to once again enter the market, our goal is to stick with and

build on the principles that have brought us this far. However, based on an enormous

amount of feedback we have received from you and your colleagues, we have made this

edition and its package even more flexible than previous editions. We offer flexibility

in coverage and pedagogy by providing a wide variety of features in the book to help

students to learn about corporate finance. We also provide flexibility in package options

by offering the most extensive collection of teaching, learning, and technology aids of any

corporate finance text. Whether you use just the textbook, or the book in conjunction with

other products, we believe you will find a combination with this edition that will meet

your current as well as your changing needs.

Stephen A. Ross

Randolph W. Westerfield

Bradford D. Jordan

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Organization of the Text

W

e designed Essentials o f Corporate Finance to be as flexible and modular as pos￾sible. There are a total of nine parts, and, in broad terms, the instructor is free to

decide the particular sequence. Further, within each part, the first chapter generally con￾tains an overview and survey. Thus, when time is limited, subsequent chapters can be

omitted. Finally, the sections placed early in each chapter are generally the most important,

and later sections frequently can be omitted without loss of continuity. For these reasons,

the instructor has great control over the topics covered, the sequence in which they are

covered, and the depth of coverage.

Just to get an idea of the breadth of coverage in the sixth edition of Essentials, the

following grid presents for each chapter some of the most significant new features, as

well as a few selected chapter highlights. Of course, in every chapter, opening vignettes,

boxed features, and in-chapter illustrations and examples using real companies have been

thoroughly updated as well. Also, end-of-chapter material has been revised, and we have

included new “challenge” problems in many places in this edition.

Chapter 2 Cash flow vs. earnings.

Market values vs. book values.

Chapter 3 New material: Additional explanation of

alternative formulas for sustainable and

internal growth rates.

New material: Price-sales ratios.

New material: EBITDA.

Clearly defines cash flow and spells out the differences

between cash flow and earnings.

Emphasizes the relevance of market values over book

values.

Expanded explanation of growth rate formulas clears

up a common misunderstanding about these formulas

and the circumstances under which alternative formulas

are correct.

Explains price-sales ratios, emphasizing their usefulness

in cases where companies have negative earnings.

Explains the commonly used quantity earnings before

interest, taxes, depreciation, and amortization.

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PART THREE Valuation of Future Cash Flows

Chapter 4

Chapter 5

First of two chapters on time value

of money.

Second of two chapters on time value of

money.

Relatively short chapter introduces just the basic ideas

on time value of money to get students started on this

traditionally difficult topic.

Covers more advanced time value topics with numerous

examples, calculator tips, and Excel spreadsheet

exhibits. Contains many real-world examples.

I PART FOUR Valuing Stocks and Bonds

Chapter 6 Bond valuation. Thorough coverage of bond price/yield concepts.

Interest rates and inflation. Highly intuitive discussion of inflation, the Fisher effect,

and the term structure of interest rates.

“Clean” vs. “dirty" bond prices and Clears up the pricing of bonds between coupon payment

accrued interest. dates and also bond market quoting conventions.

NASD's TRACE system and Up-to-date discussion of new developments in fixed

transparency in the corporate bond income with regard to price, volume, and transactions

market. reporting.

“Make-whole" call provisions. Up-to-date discussion of relatively new type of call

provision that has become very common.

Chapter 7 Stock valuation. Thorough coverage of constant and nonconstant growth

models.

NYSE and Nasdaq Market operations. Up-to-date description of major stock market operations.

New chapter case: Stock Valuation at New case for this edition examines small company

Ragan, Inc. valuation.

PART FIVE Capital Budgeting

Chapter 8 First of two chapters on capital budgeting. Relatively short chapter introduces key ideas on an

intuitive level to help students with this traditionally

difficult topic.

NPV, IRR. payback, discounted payback, Consistent, balanced examination of advantages and

accounting rate of return. disadvantages of various criteria.

New material: MIRR. Thorough, but straightforward, coverage of modified

internal rate of return (MIRR) concepts and calculations.

New chapter case: Bullock Gold Mining. New case for this edition examines basic capital

budgeting using a spreadsheet.

Chapter 9 Project cash flow. Thorough coverage of project cash flows and the

relevant numbers for a project analysis.

Scenario and sensitivity “what-if" Illustrates how to actually apply and interpret these tools

analyses. in a project analysis.

PART SIX Risk and Return

Chapter 10 Capital market history. Extensive coverage of historical returns, volatilities, and

risk premiums.

Market efficiency. Efficient markets hypothesis discussed along with

common misconceptions.

Geometric vs. arithmetic returns. Discusses calculation and interpretation of geometric

returns. Clarifies common misconceptions regarding

appropriate use of arithmetic vs. geometric average

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C h a p te rs S e lected T o p ics B e n e fits to U se rs

Chapter 11 Diversification, systematic, and Illustrates basics of risk and return in a straightforward

unsystematic risk. fashion.

Beta and the security market line. Develops the security market line with an intuitive

approach that bypasses much of the usual portfolio

theory and statistics.

New chapter case: The Beta for American New case for this edition explores beta estimation and

Standard. issues that arise in that context.

I PART SEVEN Long-Term Financing

Chapter 12 Cost of capital estimation. Intuitive development of the WACC and a complete,

Web-based illustration of cost of capital for a real

company.

Geometric vs. arithmetic growth rates. Both approaches are used in practice. Clears up issues

surrounding growth rate estimates.

Chapter 13 New material: BAPCPA. Brief discussion of the 2005 Bankruptcy Abuse

Prevention and Consumer Protection Act.

Basics of financial leverage. Illustrates effect of leverage on risk and return.

Optimal capital structure. Describes the basic trade-offs leading to an optimal

capital structure.

Financial distress and bankruptcy. Briefly surveys the bankruptcy process.

New chapter case: Stephenson Real New case for this edition explores debt/equity trade-offs

Estate Recapitalization. in a project finance context.

Chapter 14 Dividends and dividend policy. Describes dividend payments and the factors favoring

higher and lower payout policies. Includes recent survey

results on setting dividend policy.

New chapter case: Electronic Timing, Inc. New case for this edition examines dividends and share

repurchases in a small company context.

Chapter 15 IPO valuation. Extensive, up-to-date discussion of IPOs, including the

1999-2000 period.

Dutch auctions. Explains uniform price (“Dutch”) auctions using Google

IPO as an example.

New chapter case: S&S Air Goes Public. New case for this edition examines the cost of going

public and other issues.

PART EIGHT Short-Term Financial Management

Chapter 16 Operating and cash cycles. Stresses the importance of cash flow timing.

Short-term financial planning. Illustrates creation of cash budgets and potential need

for financing.

Chapter 17 Cash collection and disbursement. Examination of systems used by firms to handle cash

inflows and outflows.

Credit management. Analysis of credit policy and implementation.

Inventory management. Brief overview of important inventory concepts.

New chapter case: Piepkorn New case written for this edition evaluates working

Manufacturing Working Capital

Management, Part 2.

capital issues for a small firm.

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PART NINE Topics in Business Finance

Chapter 18 Foreign exchange.

International capital budgeting.

Exchange rate and political risk.

Covers essentials of exchange rates and their

determination.

Shows how to adapt basic DCF approach to handle

exchange rates.

Discusses hedging and issues surrounding sovereign risk.

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Learning Solutions

I

n addition to illustrating relevant concepts and presenting up-to-date coverage. Essen￾tials o f Corporate Finance strives to present the material in a way that makes it coher￾ent and easy to understand. To meet the varied needs of the intended audience. Essentials

o f Corporate Finance is rich in valuable learning tools and support.

Each feature can be categorized by the benefit to the student:

Real financial decisions

Application tools

Study aids

REAL FINANCIAL DECISIONS

We have included two key features that help students connect chapter concepts to how

decision makers use this material in the real world.

C h apter-O pening V ig n ettes w ith

Fu n ctio n al In te g ra tio n Links

Each chapter begins with a recent real-world

event to introduce students to chapter concepts.

Since many nonfinance majors will use this

text, a brief paragraph linking the vignette

and chapter concepts to majors in marketing,

management, and accounting is included.

position. In addition to discussing financial ratios and what they mean, we will have quite

a bit to say about who uses this information and why.

Everybody needs to understand ratios Managers will find that almost every business

characteristic, from profitability to employee productivity, is summarized in some kind of

ratio Marketers examine ratios dealing with costs, markups, and margins. Production per￾sonnel focus on ratios dealing with issues such as operating efficiency. Accountants need

to understand ratios because, among other things, ratios are one of the most common and

important forms of financial statement information

In fact, regardless of your field, you may very well find that your compensation is tied

to some ratio or group of ratios. Perhaps that is the best reason to study up'

How Fast Is Too Fast?

vaUng a company’s suck When Bwtaig about (and calculai￾mg) growm ratas, a «Be common sense goes a long way. For

eiamoie. »1 2007 relating giant Wal-Mart had about 1 b*on

square lee« ol sfcres. dsJrOutton centers, ana so toflh The

company enacted 10 increase « square looiage try about

7 5 percent over iw next year The doesn’t kuM loo outra￾geous. tut can Wal-Mart grow its square lootage at 7 5 percent

Wei get mi

assume that Wal-Mart grows at 7 5 percent per year over 9ie next

1S9 years, the company w« haw about 96 tn*on square leet ol

States' In other wonls. it Wal-Mart keeps growing at 7 5 percent,

the enOre coixitry *-i eventually be one dig Wal-Mart Scary

XM Satehte Rad» a another example The company

had total revenues 01 about S500 000 n 2001 and S333 m*on

in 2006 Thu represents an annual increase 01 250 percent'

How Hte*y do you tfunk it e that the company can continue this

growth rate? II this growth continued, the company would have

revenues ol about S21 trfllon In |ust 8 years, which exceeds the

gross domestic product (GOP) ot the Unfed States Obviously.

XM Radio's growth rate ml slow substantial1» m the neu sev￾What about growth m cash Dow? As a! the begmnng 0I

2007. cash now lor Internet auction Web site eBay had grown at

an annual rateol about 80 5 percent lor the past five years The

company generated about $1 9 b*on n cash Dow tor 2006 If

eBay's cash now grew at the same rate tor the next 11 years,

the company would generate about Si 25 tnBion dollars per

yoar, or more than the $972 Billion of U.S. currency circulating

In the world

As these examples show, growth rates can be Oecervmg

It is fairly easy lor a small company to grow very fast It a com￾pany has $100 dollars m sales. II only has to increase sales

by another $100 to have a 100 percent increase m sales. II

the company's sale!

by another $10 Mb

crease So. long-term grow

very carefully As a rule ot

estimates, you should probably

not grow much laster than the economy

about 1 to 3 percenl (mftation-adiusted)

R e a lity B y tes B oxes

Most chapters include at least one

Reality Bytes box, which takes a

chapter issue and shows how it is

being used right now in everyday

financial decision making.

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C h a p te r C ases

Located at the end of each chapter, these chapter cases focus on

hypothetical company situations that embody 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 from the chapters in that

part. Great for homework or in-class exercises and discussions!

C H A P T E R C A S E

RATIOS A N D F IN A N C IA L PLANNING AT S&S AIR, INC. 1

s complete In contrast a commercial airplane may I

ake one and one-hall to two years to manufacture I

jnce the order is placed

Mark and Todd have provided the following tinan- I

il statements Chris has gathered the industry ratios I

C

hns Guthne was recently hired by S&S Air, Inc ,

to assist the company with its financial planning,

and to evaluate the company’s performance Ghns

graduated from college five years ago with a finance

degree He has been employed in the finance depart￾ment ol a Fortune 500 company 9ince then

S4S Air was founded 10 years ago by friends Mark

Sexton and Todd Story The company has manufac￾tured and sold light airplanes over this period, and the

company's products have received high reviews for

safety and reliability The company has a niche market

in that it sells pnmanly to individuals who own and fly

their own airplanes The company has two models, the

Birdie which sells lor SS3.000. and the Eagle, which

sells tor $78,000

While the company manufactures aircraft. Its

operations are different from commercial aircraft

companies SAS Air builds aircraft to order By using

prefabricated parts, the company is able to complete

the manufacture of an airplane in only five weeks

The company also receives a deposit on each order,

as well as another partial payment before the order

for the light airplane manufacturing industry.

SAS Air Inc.

APPLICATION TOOLS

Realizing that there is more than one

way to solve problems in corporate

finance, we include many sections

that encourage students to learn

different problem-solving methods

and also help them learn or brush up

on their financial calculator and Excel

spreadsheet skills.

W ork th e W eb

These in-chapter boxes show students how to

research financial issues using the Web and how

to use the information they find to make business

decisions.

E x p lan ato ry W eb Links

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.

Learn more about

NAICS at

www.naics.com

bers of the Federal Reserve system. Table 3.8 is a list of selected two-digit codes (the first

two digits of the four-digit SIC codes) and the industries they represent.

Beginning in 1997. a new industry classification system was instituted. Specifically,

the North American Industry Classification System (NAICS, pronounced "nakes") is in￾tended to replace the older SIC codes, and it probably will eventually. Currently, however.

SIC codes are widely used.

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W hat’s On th e Web?

These end-of-chapter activities

show students how to use and

learn from the vast amount of

financial resources available

on the Internet.

WHAT’S ON

THE WEB?

Du Pont Identity. You can find financial statements for Wall Disney Company

on the "Investor Relations" link at Disney's home page, www.disney.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 Pom

identity affected ROE over this period?

Ratio Analysis. You wanl to examine the financial ratios for Dell Computer

Corporation. Go to www.marketguide.com and type in the ticker symbol for the

company (DELL). Next, go to the ratio link. You should find financial ratios for

Dell and the industry, sector, and S&P 500 averages for each ratio,

a. What do TTM and MRQ mean'*

We can illustrate how lo calculate unknown rates using a financial calculator using these numbers For

Pennsylvania, you would do Ihe following

-1 , 0 0 0 2 ,0 0 0 , 0 0 0

As in our previous examples, notice the minus sign on the presen! value, representing Franklin's outlay

made many years ago Whal do you change to work the problem for Massachusetts7

C a lc u la to r H ints

Calculator Hints is a self￾contained section occurring

in various chapters that first

introduces students to calculator

basics and then illustrates how

to solve problems with the

calculator. Appendix D goes

into more detailed instructions

by solving problems with two

specific calculators.

S p readsheet S trateg ies

The unique Spreadsheet Strategies feature

is also in a self-contained section, showing

students how to set up spreadsheets

to solve problems—a vital part of every

business student’s education.

To illustrate how you might use these formulas, we will go back to an example in the chapter

If you invest $25,000 at 12 percent per year, how long until you have $50,000? You might set up a

spreadsheet like this;

>

CD

o

D E I F I G H

1

I I

2 Using a spreadsheet for time value of money calculations

3 I I I I I I I

4 If we invest $25,000 at 12 percent, how long until we have S50.000'’ We need to solve for the

5 unknown number of periods, so we use the formula NPER (rate, pmt, pv. fv).

6

7 Present value (pv): S25.000

8 Future value (fv): S50.000

9 Rate (rate): 12

10

11 Periods: 6.116255

12

13 The formula entered in cell B11 is =NPER(B9.0,-B7,B8), nolice that pmt is zero and that pv has a

14 negative sign on it. Also notice that the rate is entered as a decimal, not a percentage.

7Z

14. Calculating Rates of Return. In 2006. a gold $3 coin minted in 1879 was

auciioned for $9,000. For this to have been true, what was the annual increase in the

value of the coin?

15. Calculating Rates of Return. Although appealing to more refined tastes, art as

a collectible has not always performed so profitably. During 2003. Sotheby's sold the

Edgar Degas bronze sculpture Petite danseuse de quariorze ans at auction for a price

of SI0.311.500. Unfortunately for the previous owner, he had purchased it in 1999 at

a price of SI2.377,500. What was his annual rate of return on this sculpture?

S p re ad sh ee t Tem plates

Indicated by an Excel icon next to

applicable end-of-chapter questions

and problems, spreadsheet templates

are available for selected problems on

the Student Edition of the book's Web

site, www.mhhe.com/rwj. These Excel

templates are a valuable extension of

the Spreadsheet Strategies feature.

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