Rewrite Under Armour Financial Capstone

SOURCE: Courtesy BEN & JERRY’S HOMEMADE, INC. www.benjerry.com

CHAPTER

A n O v e r v i e w o f F i na nc i a l Ma na ge me n t1

make money. For example, in a recent article in Fortune

magazine, Alex Taylor III commented that, “Operating a

business is tough enough. Once you add social goals to

the demands of serving customers, making a profit, and

returning value to shareholders, you tie yourself up in

knots.”

Ben & Jerry’s financial performance has had its ups

and downs. While the company’s stock grew by leaps

and bounds through the early 1990s, problems began to

arise in 1993. These problems included increased

competition in the premium ice cream market, along

with a leveling off of sales in that market, plus their

own inefficiencies and sloppy, haphazard product

development strategy.

The company lost money for the first time in 1994,

and as a result, Ben Cohen stepped down as CEO. Bob

Holland, a former consultant for McKinsey & Co. with a

reputation as a turnaround specialist, was tapped as

Cohen’s replacement. The company’s stock price

rebounded in 1995, as the market responded positively

to the steps made by Holland to right the company. The

stock price, however, floundered toward the end of

1996, following Holland’s resignation.

Over the last few years, Ben & Jerry’s has had a new

resurgence. Holland’s replacement, Perry Odak, has done

a number of things to improve the company’s financial

performance, and its reputation among Wall Street’s

or many companies, the decision would have been

an easy “yes.” However, Ben & Jerry’s Homemade

Inc. has always taken pride in doing things

differently. Its profits had been declining, but in 1995

the company was offered an opportunity to sell its

premium ice cream in the lucrative Japanese market.

However, Ben & Jerry’s turned down the business

because the Japanese firm that would have distributed

their product had failed to develop a reputation for

promoting social causes! Robert Holland Jr., Ben &

Jerry’s CEO at the time, commented that, “The only

reason to take the opportunity was to make money.”

Clearly, Holland, who resigned from the company in late

1996, thought there was more to running a business

than just making money.

The company’s cofounders, Ben Cohen and Jerry

Greenfield, opened the first Ben & Jerry’s ice cream shop

in 1978 in a vacant Vermont gas station with just

$12,000 of capital plus a commitment to run the business

in a manner consistent with their underlying values. Even

though it is more expensive, the company only buys milk

and cream from small local farms in Vermont. In addition,

7.5 percent of the company’s before-tax income is

donated to charity, and each of the company’s 750

employees receives three free pints of ice cream each day.

Many argue that Ben & Jerry’s philosophy and

commitment to social causes compromises its ability to

S T R I K I N G T H E R IG H T BA L A N C E

BEN & JERRY'S

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C H A P T E R 1 � A N O V E R V I E W O F F I N A N C I A L M A N AG E M E N T4

The purpose of this chapter is to give you an idea of what financial management

is all about. After you finish the chapter, you should have a reasonably good idea

of what finance majors might do after graduation. You should also have a better

understanding of (1) some of the forces that will affect financial management in

the future; (2) the place of finance in a firm’s organization; (3) the relationships

between financial managers and their counterparts in the accounting, marketing,

production, and personnel departments; (4) the goals of a firm; and (5) the way

financial managers can contribute to the attainment of these goals. �

C A R E E R O P P O R T U N I T I E S I N F I N A N C E

Finance consists of three interrelated areas: (1) money and capital markets, which deals with securities markets and financial institutions; (2) investments, which fo- cuses on the decisions made by both individual and institutional investors as

See http:// www.benjerry.com/ mission.html for Ben & Jerry’s interesting mission statement. It might be a

good idea to print it out and take it to class for discussion.

Information on finance careers, additional chapter links, and practice quizzes are available on the web site to accompany this

text: http://www.harcourtcollege. com/finance/concise3e.

analysts and institutional investors has benefited. Odak

quickly brought in a new management team to rework

the company’s production and sales operations, and he

aggressively opened new stores and franchises both in

the United States and abroad.

In April 2000, Ben & Jerry’s took a more dramatic

step to benefit its shareholders. It agreed to be acquired

by Unilever, a large Anglo-Dutch conglomerate that

owns a host of major brands including Dove Soap,

Lipton Tea, and Breyers Ice Cream. Unilever agreed to

pay $43.60 for each share of Ben & Jerry’s stock—a 66

percent increase over the price the stock traded at just

before takeover rumors first surfaced in December 1999.

The total price tag for Ben & Jerry’s was $326 million.

While the deal clearly benefited Ben & Jerry’s

shareholders, some observers believe that the company

“sold out” and abandoned its original mission. In

response to these concerns, Ben & Jerry’s will retain its

Vermont headquarters and its separate board, and its

social missions will remain intact. Others have

suggested that Ben & Jerry’s philosophy may even

induce Unilever to increase its own corporate

philanthropy. Despite these assurances, it still remains

to be seen whether Ben & Jerry’s vision can be

maintained within the confines of a large conglomerate.

As you will see throughout the book, many of today’s

companies face challenges similar to those of Ben &

Jerry’s. Every day, corporations struggle with decisions

such as these: Is it fair to our labor force to shift

production overseas? What is the appropriate level of

compensation for senior management? Should we

increase, or decrease, our charitable contributions? In

general, how do we balance social concerns against the

need to create shareholder value? �

5

they choose securities for their investment portfolios; and (3) financial manage- ment, or “business finance,” which involves decisions within firms. The career opportunities within each field are many and varied, but financial managers must have a knowledge of all three areas if they are to do their jobs well.

MONEY AND CAPITAL MARKETS

Many finance majors go to work for financial institutions, including banks, in- surance companies, mutual funds, and investment banking firms. For success here, one needs a knowledge of valuation techniques, the factors that cause in- terest rates to rise and fall, the regulations to which financial institutions are subject, and the various types of financial instruments (mortgages, auto loans, certificates of deposit, and so on). One also needs a general knowledge of all as- pects of business administration, because the management of a financial insti- tution involves accounting, marketing, personnel, and computer systems, as well as financial management. An ability to communicate, both orally and in writing, is important, and “people skills,” or the ability to get others to do their jobs well, are critical.

INVESTMENTS

Finance graduates who go into investments often work for a brokerage house such as Merrill Lynch, either in sales or as a security analyst. Others work for banks, mutual funds, or insurance companies in the management of their in- vestment portfolios; for financial consulting firms advising individual investors or pension funds on how to invest their capital; for investment banks whose pri- mary function is to help businesses raise new capital; or as financial planners whose job is to help individuals develop long-term financial goals and portfolios. The three main functions in the investments area are sales, analyzing individual securities, and determining the optimal mix of securities for a given investor.

FINANCIAL MANAGEMENT

Financial management is the broadest of the three areas, and the one with the most job opportunities. Financial management is important in all types of busi- nesses, including banks and other financial institutions, as well as industrial and retail firms. Financial management is also important in governmental opera- tions, from schools to hospitals to highway departments. The job opportunities in financial management range from making decisions regarding plant expan- sions to choosing what types of securities to issue when financing expansion. Financial managers also have the responsibility for deciding the credit terms under which customers may buy, how much inventory the firm should carry, how much cash to keep on hand, whether to acquire other firms (merger analy- sis), and how much of the firm’s earnings to plow back into the business versus pay out as dividends.

Regardless of which area a finance major enters, he or she will need a knowl- edge of all three areas. For example, a bank lending officer cannot do his or her

C A R E E R O P P O R T U N I T I E S I N F I N A N C E

Consult http:// www.careers-in- business.com for an excellent site containing information on a variety of

business career areas, listings of current jobs, and a variety of other reference materials.

C H A P T E R 1 � A N O V E R V I E W O F F I N A N C I A L M A N AG E M E N T6

SELF-TEST QUESTIONS

What are the three main areas of finance?

If you have definite plans to go into one area, why is it necessary that you know something about the other areas?

Why is it necessary for business students who do not plan to major in fi- nance to understand the basics of finance?

job well without a good understanding of financial management, because he or she must be able to judge how well a business is being operated. The same thing holds true for Merrill Lynch’s security analysts and stockbrokers, who must have an understanding of general financial principles if they are to give their cus- tomers intelligent advice. Similarly, corporate financial managers need to know what their bankers are thinking about, and they also need to know how investors judge a firm’s performance and thus determine its stock price. So, if you decide to make finance your career, you will need to know something about all three areas.

But suppose you do not plan to major in finance. Is the subject still important to you? Absolutely, for two reasons: (1) You need a knowledge of finance to make many personal decisions, ranging from investing for your retirement to decid- ing whether to lease versus buy a car. (2) Virtually all important business deci- sions have financial implications, so important decisions are generally made by teams from the accounting, finance, legal, marketing, personnel, and production departments. Therefore, if you want to succeed in the business arena, you must be highly competent in your own area, say, marketing, but you must also have a familiarity with the other business disciplines, including finance.

Thus, there are financial implications in virtually all business decisions, and nonfi- nancial executives simply must know enough finance to work these implications into their own specialized analyses.1 Because of this, every student of business, regard- less of his or her major, should be concerned with financial management.

1 It is an interesting fact that the course “Financial Management for Nonfinancial Executives” has the highest enrollment in most executive development programs.

F I N A N C I A L M A N AG E M E N T I N T H E N E W M I L L E N N I U M

When financial management emerged as a separate field of study in the early 1900s, the emphasis was on the legal aspects of mergers, the formation of new firms, and the various types of securities firms could issue to raise capital. Dur- ing the Depression of the 1930s, the emphasis shifted to bankruptcy and reor- ganization, corporate liquidity, and the regulation of security markets. During the 1940s and early 1950s, finance continued to be taught as a descriptive, in- stitutional subject, viewed more from the standpoint of an outsider rather than that of a manager. However, a movement toward theoretical analysis began during the late 1950s, and the focus shifted to managerial decisions designed to maximize the value of the firm.

7

The focus on value maximization continues as we begin the 21st century. However, two other trends are becoming increasingly important: (1) the glob- alization of business and (2) the increased use of information technology. Both of these trends provide companies with exciting new opportunities to increase profitability and reduce risks. However, these trends are also leading to in- creased competition and new risks. To emphasize these points throughout the book, we regularly profile how companies or industries have been affected by increased globalization and changing technology. These profiles are found in the boxes labeled “Global Perspectives” and “Technology Matters.”

GLOBALIZAT ION OF BUSINESS

Many companies today rely to a large and increasing extent on overseas opera- tions. Table 1-1 summarizes the percentage of overseas revenues and profits for 10 well-known corporations. Very clearly, these 10 “American” companies are really international concerns.

Four factors have led to the increased globalization of businesses: (1) Im- provements in transportation and communications lowered shipping costs and made international trade more feasible. (2) The increasing political clout of consumers, who desire low-cost, high-quality products. This has helped lower trade barriers designed to protect inefficient, high-cost domestic manufacturers and their workers. (3) As technology has become more advanced, the costs of developing new products have increased. These rising costs have led to joint ventures between such companies as General Motors and Toyota, and to global operations for many firms as they seek to expand markets and thus spread development costs over higher unit sales. (4) In a world populated with multi- national firms able to shift production to wherever costs are lowest, a firm whose manufacturing operations are restricted to one country cannot compete unless costs in its home country happen to be low, a condition that does not

F I N A N C I A L M A N AG E M E N T I N T H E N E W M I L L E N N I U M

T A B L E 1 - 1

PERCENTAGE OF REVENUE PERCENTAGE OF NET INCOME COMPANY ORIGINATED OVERSEAS GENERATED OVERSEAS

Chase Manhattan 23.9 21.9 Coca-Cola 61.2 65.1 Exxon Mobil 71.8 62.7 General Electric 31.7 22.8 General Motors 26.3 55.3 IBM 57.5 49.6 McDonald’s 61.6 60.9 Merck 21.6 43.4 Minn. Mining & Mfg. 52.1 27.2 Walt Disney 15.4 16.6

SOURCE: Forbes Magazine’s 1999 Ranking of the 100 Largest U.S. Multinationals; Forbes, July 24, 2000, 335–338.

Percentage of Revenue and Net Income from Overseas Operations for 10 Well-Known Corporations

Check out http:// www.nummi.com/ home.htm to find out more about New United Motor Manufacturing, Inc.

(NUMMI), the joint venture between Toyota and General Motors. Read about NUMMI’s history and organizational goals.

C H A P T E R 1 � A N O V E R V I E W O F F I N A N C I A L M A N AG E M E N T8

necessarily exist for many U.S. corporations. As a result of these four factors, survival requires that most manufacturers produce and sell globally.

Service companies, including banks, advertising agencies, and accounting firms, are also being forced to “go global,” because these firms can best serve their multinational clients if they have worldwide operations. There will, of course, al- ways be some purely domestic companies, but the most dynamic growth, and the best employment opportunities, are often with companies that operate worldwide.

Even businesses that operate exclusively in the United States are not immune to the effects of globalization. For example, the costs to a homebuilder in rural Nebraska are affected by interest rates and lumber prices — both of which are de- termined by worldwide supply and demand conditions. Furthermore, demand for the homebuilder’s houses is influenced by interest rates and also by conditions in the local farm economy, which depend to a large extent on foreign demand for wheat. To operate efficiently, the Nebraska builder must be able to forecast the de- mand for houses, and that demand depends on worldwide events. So, at least some knowledge of global economic conditions is important to virtually everyone, not just to those involved with businesses that operate internationally.

INFORMATION TECHNOLOGY

As we advance into the new millennium, we will see continued advances in com- puter and communications technology, and this will continue to revolutionize the way financial decisions are made. Companies are linking networks of personal

During the past 20 years, Coca-Cola has createdtremendous value for its shareholders. A $10,000 investment in Coke stock in January 1980 would have grown to nearly $600,000 by mid-1998. A large part of that im- pressive growth was due to Coke’s overseas expansion program. Today nearly 75 percent of Coke’s profit comes from overseas, and Coke sells roughly half of the world’s soft drinks.

More recently, Coke has discovered that there are also risks when investing overseas. Indeed, between mid-1998 and Janu- ary 2001, Coke’s stock fell by roughtly a third—which means that the $600,000 stock investment decreased in value to $400,000 in about 2.5 years. Coke’s poor performance during this period was due in large part to troubles overseas. Weak economic conditions in Brazil, Germany, Japan, Southeast Asia, Venezuela, Colombia, and Russia, plus a quality scare in Bel- gium and France, hurt the company’s bottom line.

Despite its recent difficulties, Coke remains committed to its global vision. Coke is also striving to learn from these difficul- ties. The company’s leaders have acknowledged that Coke may have become overly centralized. Centralized control enabled Coke to standardize quality and to capture operating efficiencies, both of which initially helped to establish its brand name throughout the world. More recently, however, Coke has become concerned

that too much centralized control has made it slow to respond to changing circumstances and insensitive to differences among the various local markets it serves.

Coke’s CEO, Douglas N. Daft, reflected these concerns in a re- cent editorial that was published in the March 27, 2000, edi- tion of Financial Times. Daft’s concluding comments appear below:

So overall, we will draw on a long-standing belief that Coca- Cola always flourishes when our people are allowed to use their insight to build the business in ways best suited to their local culture and business conditions.

We will, of course, maintain clear order. Our small corpo- rate team will communicate explicitly the clear strategy, pol- icy, values, and quality standards needed to keep us cohe- sive and efficient. But just as important, we will also make sure we stay out of the way of our local people and let them do their jobs. That will enhance significantly our ability to unlock growth opportunities, which will enable us to consis- tently meet our growth expectations.

In our recent past, we succeeded because we understood and appealed to global commonalties. In our future, we’ll succeed because we will also understand and appeal to local differences. The 21st century demands nothing less.

COKE RIDES THE GLOBAL ECONOMY WAVE

For more information about the Coca-Cola Company, go to http://www.thecoca- colacompany.com/world/

index.html, where you can find profiles of Coca-Cola’s presence in foreign countries. You may follow additional links to Coca-Cola web sites in foreign countries.

9F I N A N C I A L M A N AG E M E N T I N T H E N E W M I L L E N N I U M

eTOYS TAKES ON TOYS “ ” USR

The toy market illustrates how electronic commerce is chang-ing the way firms operate. Over the past decade, this market has been dominated by Toys “ ” Us, although Toys “ ” Us has faced increasing competition from retail chains such as Wal- Mart, Kmart, and Target. Then, in 1997, Internet startup eToys Inc. began selling and distributing toys through the Internet.

When eToys first emerged, many analysts believed that the Internet provided toy retailers with a sensational opportunity. This point was made amazingly clear in May 1999 when eToys issued stock to the public in an initial public offering (IPO). The stock immediately rose from its $20 offering price to $76 per share, and the company’s market capitalization (calculated by multiplying stock price by the number of shares outstanding) was a mind-blowing $7.8 billion.

To put this valuation in perspective, eToys’ market value at the time of the offering ($7.8 billion) was 35 percent greater than that of Toys “ ” Us ($5.7 billion). eToys’ valuation was particularly startling given that the company had yet to earn a profit. (It lost $73 million in the year ending March 1999.) Moreover, while Toys “ ” Us had nearly 1,500 stores and rev- enues in excess of $11 billion, eToys had no stores and rev- enues of less than $35 million.

Investors were clearly expecting that an increasing number of toys will be bought over the Internet. One analyst esti- mated at the time of the offering that eToys would be worth $10 billion within a decade. His analysis assumed that in 10 years the toy market would total $75 billion, with $20 billion

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coming from online sales. Indeed, online sales do appear to be here to stay. For many customers, online shopping is quicker and more convenient, particularly for working parents of young children, who purchase the lion’s share of toys. From the company’s perspective, Internet commerce has a number of other advantages. The costs of maintaining a web site and distributing toys online may be smaller than the costs of maintaining and managing 1,500 retail stores.

Not surprisingly, Toys “ ” Us did not sit idly by — it re- cently announced plans to invest $64 million in a separate on- line subsidiary, Toysrus.com. The company also announced an online partnership with Internet retailer Amazon.com. In addi- tion, Toys “ ” Us is redoubling its efforts to make traditional store shopping more enjoyable and less frustrating.

While the Internet provides toy companies with new and in- teresting opportunities, these companies also face tremendous risks as they try to respond to the changing technology. In- deed, in the months following eToys’ IPO, Toys “ ” Us’ stock fell sharply, and by January 2000, its market value was only slightly above $2 billion. Since then, Toys “ ” Us stock has rebounded, and its market capitalization was once again approaching $5 bil- lion. The shareholders of eToys were less fortunate. Concerns about inventory management during the 1999 holiday season and the collapse of many Internet stocks spurred a tremendous collapse in eToys’ stock — its stock fell from a post–IPO high of $76 a share to $0.31 a share in January 2001. Two months later, eToys declared bankruptcy.

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computers to one another, to the firms’ own mainframe computers, to the Inter- net and the World Wide Web, and to their customers’ and suppliers’ computers. Thus, financial managers are increasingly able to share information and to have “face-to-face” meetings with distant colleagues through video teleconferencing. The ability to access and analyze data on a real-time basis also means that quan- titative analysis is becoming more important, and “gut feel” less sufficient, in business decisions. As a result, the next generation of financial managers will need stronger computer and quantitative skills than were required in the past.

Changing technology provides both opportunities and threats. Improved technology enables businesses to reduce costs and expand markets. At the same time, however, changing technology can introduce additional competition, which may reduce profitability in existing markets.

The banking industry provides a good example of the double-edged technol- ogy sword. Improved technology has allowed banks to process information much more efficiently, which reduces the costs of processing checks, providing credit, and identifying bad credit risks. Technology has also allowed banks to serve customers better. For example, today bank customers use automatic teller machines (ATMs) everywhere, from the supermarket to the local mall. Today,

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many banks also offer products that allow their customers to use the Internet to manage their accounts and to pay bills. However, changing technology also threatens banks’ profitability. Many customers no longer feel compelled to use a local bank, and the Internet allows them to shop worldwide for the best deposit and loan rates. An even greater threat is the continued development of elec- tronic commerce. Electronic commerce allows customers and businesses to transact directly, thus reducing the need for intermediaries such as commercial banks. In the years ahead, financial managers will have to continue to keep abreast of technological developments, and they must be prepared to adapt their businesses to the changing environment.

SELF-TEST QUESTIONS

What two key trends are becoming increasingly important in financial man- agement today?

How has financial management changed from the early 1900s to the present?

How might a person become better prepared for a career in financial man- agement?

T H E F I N A N C I A L S TA F F ’ S R E S P O N S I B I L I T I E S

The financial staff’s task is to acquire and then help operate resources so as to maximize the value of the firm. Here are some specific activities:

1. Forecasting and planning. The financial staff must coordinate the plan- ning process. This means they must interact with people from other de- partments as they look ahead and lay the plans that will shape the firm’s future.

2. Major investment and financing decisions. A successful firm usually has rapid growth in sales, which requires investments in plant, equip- ment, and inventory. The financial staff must help determine the optimal sales growth rate, help decide what specific assets to acquire, and then choose the best way to finance those assets. For example, should the firm finance with debt, equity, or some combination of the two, and if debt is used, how much should be long term and how much short term?

3. Coordination and control. The financial staff must interact with other personnel to ensure that the firm is operated as efficiently as possible. All business decisions have financial implications, and all managers — finan- cial and otherwise — need to take this into account. For example, mar- keting decisions affect sales growth, which in turn influences investment requirements. Thus, marketing decision makers must take account of how their actions affect and are affected by such factors as the availability of funds, inventory policies, and plant capacity utilization.

4. Dealing with the financial markets. The financial staff must deal with the money and capital markets. As we shall see in Chapter 5, each firm af- fects and is affected by the general financial markets where funds are

11A LT E R N AT I V E F O R M S O F B U S I N E S S O R GA N I Z AT I O N

SELF-TEST QUESTION

What are some specific activities with which a firm’s finance staff is involved?

raised, where the firm’s securities are traded, and where investors either make or lose money.

5. Risk management. All businesses face risks, including natural disasters such as fires and floods, uncertainties in commodity and security mar- kets, volatile interest rates, and fluctuating foreign exchange rates. However, many of these risks can be reduced by purchasing insurance or by hedging in the derivatives markets. The financial staff is respon- sible for the firm’s overall risk management program, including identi- fying the risks that should be managed and then managing them in the most efficient manner.

In summary, people working in financial management make decisions regarding which assets their firms should acquire, how those assets should be financed, and how the firm should conduct its operations. If these responsibilities are per- formed optimally, financial managers will help to maximize the values of their firms, and this will also contribute to the welfare of consumers and employees.

Sole Proprietorship An unincorporated business owned by one individual.

A LT E R N AT I V E F O R M S O F B U S I N E S S O R GA N I Z AT I O N

There are three main forms of business organization: (1) sole proprietorships, (2) partnerships, and (3) corporations, plus several hybrid forms. In terms of numbers, about 80 percent of businesses are operated as sole proprietorships, while most of the remainder are divided equally between partnerships and cor- porations. Based on the dollar value of sales, however, about 80 percent of all business is conducted by corporations, about 13 percent by sole proprietor- ships, and about 7 percent by partnerships and hybrids. Because most business is conducted by corporations, we will concentrate on them in this book. How- ever, it is important to understand the differences among the various forms.

SOLE PROPRIETORSHIP

A sole proprietorship is an unincorporated business owned by one individual. Going into business as a sole proprietor is easy — one merely begins business operations. However, even the smallest businesses normally must be licensed by a governmental unit.

The proprietorship has three important advantages: (1) It is easily and inex- pensively formed, (2) it is subject to few government regulations, and (3) the business avoids corporate income taxes.

The proprietorship also has three important limitations: (1) It is difficult for a proprietorship to obtain large sums of capital; (2) the proprietor has unlim- ited personal liability for the business’s debts, which can result in losses that

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exceed the money he or she has invested in the company; and (3) the life of a business organized as a proprietorship is limited to the life of the individual who created it. For these three reasons, sole proprietorships are used primar- ily for small-business operations. However, businesses are frequently started as proprietorships and then converted to corporations when their growth causes the disadvantages of being a proprietorship to outweigh the advantages.

PARTNERSHIP

A partnership exists whenever two or more persons associate to conduct a noncorporate business. Partnerships may operate under different degrees of formality, ranging from informal, oral understandings to formal agreements filed with the secretary of the state in which the partnership was formed. The major advantage of a partnership is its low cost and ease of formation. The disadvantages are similar to those associated with proprietorships: (1) unlim- ited liability, (2) limited life of the organization, (3) difficulty of transferring ownership, and (4) difficulty of raising large amounts of capital. The tax treat- ment of a partnership is similar to that for proprietorships, which is often an advantage, as we demonstrate in Chapter 2.

Regarding liability, the partners can potentially lose all of their personal as- sets, even assets not invested in the business, because under partnership law, each partner is liable for the business’s debts. Therefore, if any partner is un- able to meet his or her pro rata liability in the event the partnership goes bank- rupt, the remaining partners must make good on the unsatisfied claims, draw- ing on their personal assets to the extent necessary. The partners of the national accounting firm Laventhol and Horwath, a huge partnership that went bank- rupt as a result of suits filed by investors who relied on faulty audit statements, learned all about the perils of doing business as a partnership. Thus, a Texas partner who audits a business that goes under can bring ruin to a millionaire New York partner who never went near the client company.

The first three disadvantages — unlimited liability, impermanence of the or- ganization, and difficulty of transferring ownership — lead to the fourth, the difficulty partnerships have in attracting substantial amounts of capital. This is generally not a problem for a slow-growing business, but if a business’s prod- ucts or services really catch on, and if it needs to raise large amounts of capital to capitalize on its opportunities, the difficulty in attracting capital becomes a real drawback. Thus, growth companies such as Hewlett-Packard and Mi- crosoft generally begin life as a proprietorship or partnership, but at some point their founders find it necessary to convert to a corporation.

CORPORAT ION

A corporation is a legal entity created by a state, and it is separate and distinct from its owners and managers. This separateness gives the corporation three major advantages: (1) Unlimited life. A corporation can continue after its origi- nal owners and managers are deceased. (2) Easy transferability of ownership inter- est. Ownership interests can be divided into shares of stock, which, in turn, can be transferred far more easily than can proprietorship or partnership interests. (3) Limited liability. Losses are limited to the actual funds invested. To illustrate limited liability, suppose you invested $10,000 in a partnership that then went

Corporation A legal entity created by a state, separate and distinct from its owners and managers, having unlimited life, easy transferability of ownership, and limited liability.

Partnership An unincorporated business owned by two or more persons.

13

bankrupt, owing $1 million. Because the owners are liable for the debts of a partnership, you could be assessed for a share of the company’s debt, and you could be held liable for the entire $1 million if your partners could not pay their shares. Thus, an investor in a partnership is exposed to unlimited liability. On the other hand, if you invested $10,000 in the stock of a corporation that then went bankrupt, your potential loss on the investment would be limited to your $10,000 investment.2 These three factors — unlimited life, easy transfer- ability of ownership interest, and limited liability — make it much easier for corporations than for proprietorships or partnerships to raise money in the capital markets.

The corporate form offers significant advantages over proprietorships and partnerships, but it also has two disadvantages: (1) Corporate earnings may be subject to double taxation — the earnings of the corporation are taxed at the corporate level, and then any earnings paid out as dividends are taxed again as income to the stockholders. (2) Setting up a corporation, and filing the many required state and federal reports, is more complex and time-consuming than for a proprietorship or a partnership.

A proprietorship or a partnership can commence operations without much paperwork, but setting up a corporation requires that the incorporators prepare a charter and a set of bylaws. Although personal computer software that creates charters and bylaws is now available, a lawyer is required if the fledgling cor- poration has any nonstandard features. The charter includes the following in- formation: (1) name of the proposed corporation, (2) types of activities it will pursue, (3) amount of capital stock, (4) number of directors, and (5) names and addresses of directors. The charter is filed with the secretary of the state in which the firm will be incorporated, and when it is approved, the corporation is officially in existence.3 Then, after the corporation is in operation, quarterly and annual employment, financial, and tax reports must be filed with state and federal authorities.

The bylaws are a set of rules drawn up by the founders of the corporation. In- cluded are such points as (1) how directors are to be elected (all elected each year, or perhaps one-third each year for three-year terms); (2) whether the existing stockholders will have the first right to buy any new shares the firm issues; and (3) procedures for changing the bylaws themselves, should conditions require it.

The value of any business other than a very small one will probably be max- imized if it is organized as a corporation for the following three reasons:

1. Limited liability reduces the risks borne by investors, and, other things held constant, the lower the firm’s risk, the higher its value.

2. A firm’s value is dependent on its growth opportunities, which in turn are dependent on the firm’s ability to attract capital. Since corporations can attract capital more easily than can unincorporated businesses, they are better able to take advantage of growth opportunities.

A LT E R N AT I V E F O R M S O F B U S I N E S S O R GA N I Z AT I O N

2 In the case of small corporations, the limited liability feature is often a fiction, because bankers and other lenders frequently require personal guarantees from the stockholders of small, weak busi- nesses. 3 Note that more than 60 percent of major U.S. corporations are chartered in Delaware, which has, over the years, provided a favorable legal environment for corporations. It is not necessary for a firm to be headquartered, or even to conduct operations, in its state of incorporation.

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3. The value of an asset also depends on its liquidity, which means the ease of selling the asset and converting it to cash at a “fair market value.” Since an investment in the stock of a corporation is much more liquid than a similar investment in a proprietorship or partnership, this too enhances the value of a corporation.

As we will see later in the chapter, most firms are managed with value maxi- mization in mind, and this, in turn, has caused most large businesses to be or- ganized as corporations.

HYBRID FORMS OF ORGANIZAT ION

Although the three basic types of organization — proprietorships, partnerships, and corporations — dominate the business scene, several hybrid forms are gain- ing popularity. For example, there are some specialized types of partnerships that have somewhat different characteristics than the “plain vanilla” kind. First, it is possible to limit the liabilities of some of the partners by establishing a lim- ited partnership, wherein certain partners are designated general partners and others limited partners. In a limited partnership, the limited partners are liable only for the amount of their investment in the partnership, while the general partners have unlimited liability. However, the limited partners typically have no control, which rests solely with the general partners, and their returns are likewise limited. Limited partnerships are common in real estate, oil, and equipment leasing ventures. However, they are not widely used in general busi- ness situations because no one partner is usually willing to be the general part- ner and thus accept the majority of the business’s risk, while would-be limited partners are unwilling to give up all control.

The limited liability partnership (LLP), sometimes called a limited liabil- ity company (LLC), is a relatively new type of partnership that is now permit- ted in many states. In both regular and limited partnerships, at least one part- ner is liable for the debts of the partnership. However, in an LLP, all partners enjoy limited liability with regard to the business’s liabilities, and, in that regard, they are similar to shareholders in a corporation. In effect, the LLP form of or- ganization combines the limited liability advantage of a corporation with the tax advantages of a partnership. Of course, those who do business with an LLP as opposed to a regular partnership are aware of the situation, which increases the risk faced by lenders, customers, and others who deal with the LLP.

There are also several different types of corporations. One type that is com- mon among professionals such as doctors, lawyers, and accountants is the pro- fessional corporation (PC), or in some states, the professional association (PA). All 50 states have statutes that prescribe the requirements for such cor- porations, which provide most of the benefits of incorporation but do not re- lieve the participants of professional (malpractice) liability. Indeed, the primary motivation behind the professional corporation was to provide a way for groups of professionals to incorporate and thus avoid certain types of unlimited liabil- ity, yet still be held responsible for professional liability.

Finally, note that if certain requirements are met, particularly with regard to size and number of stockholders, one (or more) individual can establish a cor- poration but elect to be taxed as if the business were a proprietorship or part- nership. Such firms, which differ not in organizational form but only in how

Limited Partnership A hybrid form of organization consisting of general partners, who have unlimited liability for the partnership’s debts, and limited partners, whose liability is limited to the amount of their investment.

Limited Liability Partnership (Limited Liability Company) A hybrid form of organization in which all partners enjoy limited liability for the business’s debts. It combines the limited liability advantage of a corporation with the tax advantages of a partnership.

Professional Corporation (Professional Association) A type of corporation common among professionals that provides most of the benefits of incorporation but does not relieve the participants of malpractice liability.

15F I N A N C E I N T H E O R GA N I Z AT I O N A L S T R U C T U R E O F T H E F I R M

SELF-TEST QUESTIONS

What are the key differences between sole proprietorships, partnerships, and corporations?

Why will the value of any business other than a very small one probably be maximized if it is organized as a corporation?

F I G U R E 1 - 1 Role of Finance in a Typical Business Organization

2. Plans the Firm’s Capital Structure. 3. Manages the Firm's Pension Fund. 4. Manages Risk.

1. Manages Directly Cash and Marketable Securities.

Board of Directors

President

Vice-President: Finance

ControllerTreasurer

Vice-President: Sales Vice-President: Operations

Credit Manager

Inventory Manager

Director of Capital Budgeting

Cost Accounting

Financial Accounting

Tax Department

F I N A N C E I N T H E O R GA N I Z AT I O N A L S T R U C T U R E O F T H E F I R M

Organizational structures vary from firm to firm, but Figure 1-1 presents a fairly typical picture of the role of finance within a corporation. The chief fi- nancial officer (CFO) generally has the title of vice-president: finance, and he

their owners are taxed, are called S corporations. Although S corporations are similar in many ways to limited liability partnerships, LLPs frequently offer more flexibility and benefits to their owners — so many that large numbers of S corporation businesses are converting to this relatively new organizational form.

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SELF-TEST QUESTION

Identify the two primary subordinates who report to the firm’s chief finan- cial officer, and indicate the primary responsibilities of each.

T H E G OA L S O F T H E C O R P O R AT I O N

Shareholders are the owners of a corporation, and they purchase stocks because they are looking for a financial return. In most cases, shareholders elect direc- tors, who then hire managers to run the corporation on a day-to-day basis. Since managers are working on behalf of shareholders, it follows that they should pursue policies that enhance shareholder value. Consequently, through- out this book we operate on the assumption that management’s primary goal is stockholder wealth maximization, which translates into maximizing the price of the firm’s common stock. Firms do, of course, have other objectives — in par- ticular, the managers who make the actual decisions are interested in their own personal satisfaction, in their employees’ welfare, and in the good of the com- munity and of society at large. Still, for the reasons set forth in the following sections, stock price maximization is the most important goal for most corporations.

MANAGERIAL INCENT IVES TO MAXIMIZE SHAREHOLDER WEALTH

Stockholders own the firm and elect the board of directors, which then selects the management team. Management, in turn, is supposed to operate in the best interests of the stockholders. We know, however, that because the stock of most large firms is widely held, managers of large corporations have a great deal of autonomy. This being the case, might not managers pursue goals other than stock price maximization? For example, some have argued that the managers of large, well-entrenched corporations could work just hard enough to keep stock- holder returns at a “reasonable” level and then devote the remainder of their effort and resources to public service activities, to employee benefits, to higher executive salaries, or to golf.

It is almost impossible to determine whether a particular management team is trying to maximize shareholder wealth or is merely attempting to keep

Stockholder Wealth Maximization The primary goal for management decisions; considers the risk and timing associated with expected earnings per share in order to maximize the price of the firm’s common stock.

or she reports to the president. The financial vice-president’s key subordinates are the treasurer and the controller. In most firms the treasurer has direct responsibility for managing the firm’s cash and marketable securities, for plan- ning its capital structure, for selling stocks and bonds to raise capital, for over- seeing the corporate pension plan, and for managing risk. The treasurer also supervises the credit manager, the inventory manager, and the director of cap- ital budgeting (who analyzes decisions related to investments in fixed assets). The controller is typically responsible for the activities of the accounting and tax departments.

17

stockholders satisfied while managers pursue other goals. For example, how can we tell whether employee or community benefit programs are in the long-run best interests of the stockholders? Similarly, are huge executive salaries really necessary to attract and retain excellent managers, or are they just another ex- ample of managers taking advantage of stockholders?

It is impossible to give definitive answers to these questions. However, we do know that the managers of a firm operating in a competitive market will be forced to undertake actions that are reasonably consistent with shareholder wealth maximization. If they depart from that goal, they run the risk of being removed from their jobs, either by the firm’s board of directors or by outside forces. We will have more to say about this in a later section.

SOCIAL RESPONSIB IL I TY

Another issue that deserves consideration is social responsibility: Should businesses operate strictly in their stockholders’ best interests, or are firms also responsible for the welfare of their employees, customers, and the com- munities in which they operate? Certainly firms have an ethical responsibility to provide a safe working environment, to avoid polluting the air or water, and to produce safe products. However, socially responsible actions have costs, and not all businesses would voluntarily incur all such costs. If some firms act in a socially responsible manner while others do not, then the socially re- sponsible firms will be at a disadvantage in attracting capital. To illustrate, suppose all firms in a given industry have close to “normal” profits and rates of return on investment, that is, close to the average for all firms and just sufficient to attract capital. If one company attempts to exercise social respon- sibility, it will have to raise prices to cover the added costs. If other firms in its industry do not follow suit, their costs and prices will be lower. The so- cially responsible firm will not be able to compete, and it will be forced to abandon its efforts. Thus, any voluntary socially responsible acts that raise costs will be difficult, if not impossible, in industries that are subject to keen competition.

What about oligopolistic firms with profits above normal levels — cannot such firms devote resources to social projects? Undoubtedly they can, and many large, successful firms do engage in community projects, employee bene- fit programs, and the like to a greater degree than would appear to be called for by pure profit or wealth maximization goals.4 Furthermore, many such firms contribute large sums to charities. Still, publicly owned firms are constrained by capital market forces. To illustrate, suppose a saver who has funds to invest is considering two alternative firms. One devotes a substantial part of its re- sources to social actions, while the other concentrates on profits and stock prices. Many investors would shun the socially oriented firm, thus putting it at a disadvantage in the capital market. After all, why should the stockholders of one corporation subsidize society to a greater extent than those of other busi- nesses? For this reason, even highly profitable firms (unless they are closely

T H E G OA L S O F T H E C O R P O R AT I O N

Social Responsibility The concept that businesses should be actively concerned with the welfare of society at large.

Normal Profits and Rates of Return Those profits and rates of return that are close to the average for all firms and are just sufficient to attract capital.

4 Even firms like these often find it necessary to justify such projects at stockholder meetings by stating that these programs will contribute to long-run profit maximization.

held rather than publicly owned) are generally constrained against taking uni- lateral cost-increasing social actions.

Does all this mean that firms should not exercise social responsibility? Not at all. But it does mean that most significant cost-increasing actions will have to be put on a mandatory rather than a voluntary basis to ensure that the bur- den falls uniformly on all businesses. Thus, such social benefit programs as fair hiring practices, minority training, product safety, pollution abatement, and antitrust actions are most likely to be effective if realistic rules are established initially and then enforced by government agencies. Of course, it is critical that industry and government cooperate in establishing the rules of corporate be- havior, and that the costs as well as the benefits of such actions be estimated ac- curately and then taken into account.

In spite of the fact that many socially responsible actions must be man- dated by government, in recent years numerous firms have voluntarily taken such actions, especially in the area of environmental protection, because they helped sales. For example, many detergent manufacturers now use recycled paper for their containers, and food companies are packaging more and more products in materials that consumers can recycle or that are biodegrad- able. To illustrate, McDonald’s replaced its styrofoam boxes, which take years to break down in landfills, with paper wrappers that are less bulky and de- compose more rapidly. Some companies, such as The Body Shop and Ben & Jerry’s Ice Cream, go to great lengths to be socially responsible. According to the president of The Body Shop, the role of business is to promote the public good, not just the good of the firm’s shareholders. Furthermore, she argues that it is impossible to separate business from social responsibility. For some firms, socially responsible actions may not de facto be costly — the companies heavily advertise their actions, and many consumers prefer to buy from socially responsible companies rather than from those that shun social responsibility.

STOCK PRICE MAXIMIZAT ION AND SOCIAL WELFARE

If a firm attempts to maximize its stock price, is this good or bad for soci- ety? In general, it is good. Aside from such illegal actions as attempting to form monopolies, violating safety codes, and failing to meet pollution control requirements, the same actions that maximize stock prices also benefit society. First, note that stock price maximization requires efficient, low-cost busi- nesses that produce high-quality goods and services at the lowest possible cost. Second, stock price maximization requires the development of products and services that consumers want and need, so the profit motive leads to new technology, to new products, and to new jobs. Finally, stock price max- imization necessitates efficient and courteous service, adequate stocks of mer- chandise, and well-located business establishments — these are the factors that lead to sales, which in turn are necessary for profits. Therefore, most actions that help a firm increase the price of its stock also benefit society at large. This is why profit-motivated, free-enterprise economies have been so much more successful than socialistic and communistic economic systems. Since financial management plays a crucial role in the operations of success- ful firms, and since successful firms are absolutely necessary for a healthy,

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Go to http://www.the- body-shop.com/usa/ aboutus/values.html to see the corporate values The Body Shop embraces.

productive economy, it is easy to see why finance is important from a social welfare standpoint.5

LEVI STRAUSS TRIES TO BLEND PROFITS WITH SOCIAL ACTIVISM

19T H E G OA L S O F T H E C O R P O R AT I O N

Levi Strauss & Company has been around fornearly 150 years. Well known for its Dockers and 501 jeans, the firm has also been recognized for its commitment to social values. Indeed, when Levi

Strauss first issued stock to the public in 1971, it took the un- usual step of warning potential investors that the company’s dedication to social activism was so deep that it might com- promise corporate profits.

Levi Strauss’ words and actions continually reflect this strong devotion to social causes. In 1987, CEO Bob Haas de- veloped the company’s Mission and Aspiration Statement, which highlighted an emphasis on diversity, teamwork, and in- tegrity. A few years later, the company created a 10-day course for employees that focused on ethical decision making. As one of the course developers put it: “It was about asking, ‘How do I find meaning in the workplace?’ It was about see- ing that work is noble, that we’re more than getting pants out the door.”

Moreover, the company’s philosophy had a profound effect on its business decisions. For example, it withdrew its invest- ments in China to protest human rights violations. This action contrasted sharply with those of most other companies, which continued making investments in China in order to enhance shareholder value.

Levi Strauss has received considerable praise and numerous awards for its vision, and until recently, the company was able to practice social activism while maintaining strong profitabil- ity. However, the company’s profitability has fallen recently, causing many to argue that it must rethink its vision if it is to survive. In the face of huge losses, it is not surprising that ten- sion has arisen between the conflicting goals of social activism and profitability. Peter Jacobi, who recently retired as president of Levi Strauss, summarized this tension when he was quoted in a recent Fortune magazine article:

The problem is [that] some people thought the values were an end in themselves. You have some people who say, “Our objective is to be the most enlightened work environment in the world.” And then you have others that say, “Our objec- tive is to make a lot of money.” The value-based [socially oriented] people look at the commercial folks as heathens; the commercial people look at the values people as wusses getting in the way.

Despite these concerns, Levi Strauss’ recent problems may not be solely or even predominantly attributed to its social ac- tivism. The company has been slow to respond to fashion trends and to changing distribution system technology. Despite large investments, the company is still way behind its competitors in managing inventory and getting product to market.

To be sure, all is not completely bleak for Levi Strauss. The company still has a very strong brand name, and it still continues to generate a lot of cash. For example, in 1998, the company gen- erated cash flow of $1.1 billion, more than either Gap or Nike.

One factor that makes Levi Strauss unique is its ownership structure. The Haas family has long controlled the company. Moreover, after completing a leveraged buyout in 1996, the company is once again privately held. As part of the buyout agreement, investors who wanted to maintain their ownership stake had to grant complete power for 15 years to four family members led by Bob Haas. This ownership structure has enabled Levi Strauss to pursue its social objectives without facing the types of pressure that a more shareholder-oriented company would face. Arguably, however, the lack of external pressure helps explain why the company has been so slow to adapt to changing technology and market conditions.

SOURCE: “How Levi’s Trashed a Great American Brand,” Fortune, April 12, 1999, 82–90.

Go to http:// www.levistrauss.com/ index_about.html to take a look at Levi Strauss & Co.’s vision statement,

history, other general information about the company, and its ideals.

5 People sometimes argue that firms, in their efforts to raise profits and stock prices, increase prod- uct prices and gouge the public. In a reasonably competitive economy, which we have, prices are constrained by competition and consumer resistance. If a firm raises its prices beyond reasonable levels, it will simply lose its market share. Even giant firms such as General Motors lose business to the Japanese and German automakers, as well as to Ford, if they set prices above levels necessary to cover production costs plus a “normal” profit. Of course, firms want to earn more, and they con- stantly try to cut costs, to develop new products, and so on, and thereby to earn above-normal prof- its. Note, though, that if they are indeed successful and do earn above-normal profits, those very profits will attract competition, which will eventually drive prices down, so again the main long- term beneficiary is the consumer.

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B U S I N E S S E T H I C S

The word ethics is defined in Webster’s dictionary as “standards of conduct or moral behavior.” Business ethics can be thought of as a company’s attitude and conduct toward its employees, customers, community, and stockholders. High standards of ethical behavior demand that a firm treat each party that it deals with in a fair and honest manner. A firm’s commitment to business ethics can be measured by the tendency of the firm and its employees to adhere to laws and regulations relating to such factors as product safety and quality, fair em- ployment practices, fair marketing and selling practices, the use of confidential information for personal gain, community involvement, bribery, and illegal payments to obtain business.

Most firms today have in place strong codes of ethical behavior, and they also conduct training programs designed to ensure that employees understand the correct behavior in different business situations. However, it is imperative that top management — the chairman, president, and vice-presidents — be openly committed to ethical behavior, and that they communicate this com- mitment through their own personal actions as well as through company poli- cies, directives, and punishment/reward systems.

When conflicts arise between profits and ethics, sometimes the ethical considerations are so strong that they clearly dominate. However, in many cases the choice between ethics and profits is not clear cut. For example, sup- pose Norfolk Southern’s managers know that its coal trains are polluting the air along its routes, but the amount of pollution is within legal limits and pre- ventive actions would be costly. Are the managers ethically bound to reduce pollution? Similarly, suppose a medical products company’s own research in- dicates that one of its new products may cause problems. However, the evi- dence is relatively weak, other evidence regarding benefits to patients is strong, and independent government tests show no adverse effects. Should the company make the potential problem known to the public? If it does re- lease the negative (but questionable) information, this will hurt sales and profits, and possibly keep some patients who would benefit from the new product from using it. There are no obvious answers to questions such as these, but companies must deal with them on a regular basis, and a failure to handle the situation properly can lead to huge product liability suits, which could push a firm into bankruptcy.

Business Ethics A company’s attitude and conduct toward its employees, customers, community, and stockholders.

SELF-TEST QUESTIONS

What is management’s primary goal?

What actions could be taken to remove a management team if it departs from the goal of maximizing shareholder wealth?

What would happen if one firm attempted to exercise costly socially respon- sible programs but its competitors did not follow suit?

How does the goal of stock price maximization benefit society at large?

21

AG E N C Y R E L AT I O N S H I P S

It has long been recognized that managers may have personal goals that com- pete with shareholder wealth maximization. Managers are empowered by the owners of the firm — the shareholders — to make decisions, and that creates a potential conflict of interest known as agency theory.

An agency relationship arises whenever one or more individuals, called princi- pals, hire another individual or organization, called an agent, to perform some service and delegate decision-making authority to that agent. In financial man- agement, the primary agency relationships are those between (1) stockholders and managers and (2) managers and debtholders.6

STOCKHOLDERS VERSUS MANAGERS

A potential agency problem arises whenever the manager of a firm owns less than 100 percent of the firm’s common stock. If the firm is a proprietorship managed by its owner, the owner-manager will presumably operate so as to maximize his or her own welfare, with welfare measured in the form of in- creased personal wealth, more leisure, or perquisites.7 However, if the owner- manager incorporates and then sells some of the stock to outsiders, a potential conflict of interests immediately arises. Now the owner-manager may decide to lead a more relaxed lifestyle and not work as strenuously to maximize share- holder wealth, because less of this wealth will accrue to him or her. Also, the owner-manager may decide to consume more perquisites, because some of those costs will be borne by the outside shareholders. In essence, the fact that the owner-manager will neither gain all the benefits of the wealth created by his or her efforts nor bear all of the costs of perquisites will increase the incentive to take actions that are not in the best interests of other shareholders.

In most large corporations, potential agency conflicts are important, be- cause large firms’ managers generally own only a small percentage of the stock. In this situation, shareholder wealth maximization could take a back seat to any number of conflicting managerial goals. For example, people have argued that some managers’ primary goal seems to be to maximize the size of their firms. By creating a large, rapidly growing firm, managers (1) increase their job security, because a hostile takeover is less likely; (2) increase their

AG E N C Y R E L AT I O N S H I P S

SELF-TEST QUESTIONS

How would you define “business ethics”?

Is “being ethical” good for profits in the long run? In the short run?

6 The classic work on the application of agency theory to financial management was by Michael C. Jensen and William H. Meckling, “Theory of the Firm, Managerial Behavior, Agency Costs, and Ownership Structure,” Journal of Financial Economics, October 1976, 305–360. 7 Perquisites are fringe benefits such as luxurious offices, executive assistants, expense accounts, lim- ousines, corporate jets, generous retirement plans, and the like.

Agency Problem A potential conflict of interests between the agent (manager) and (1) the outside stockholders or (2) the creditors (debtholders).

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own power, status, and salaries; and (3) create more opportunities for their lower- and middle-level managers. Furthermore, since the managers of most large firms own only a small percentage of the stock, it has been argued that they have a voracious appetite for salaries and perquisites, and that they gen- erously contribute corporate dollars to their favorite charities because they get the glory but outside stockholders bear the cost.8

Managers can be encouraged to act in stockholders’ best interests through incentives that reward them for good performance but punish them for poor performance. Some specific mechanisms used to motivate managers to act in shareholders’ best interests include (1) managerial compensation, (2) direct intervention by shareholders, (3) the threat of firing, and (4) the threat of takeover.

1. Managerial compensation. Managers obviously must be compensated, and the structure of the compensation package can and should be de- signed to meet two primary objectives: (a) to attract and retain able man- agers and (b) to align managers’ actions as closely as possible with the

8 An excellent article that reviews the effectiveness of various mechanisms for aligning managerial and shareholder interests is Andrei Shleifer and Robert Vishny, “A Survey of Corporate Gover- nance,” Journal of Finance, June 1997, 737–783. Another paper that looks at managerial stockhold- ing worldwide is Rafael La Porta, Florencio Lopez-De-Silanes, and Andrei Shleifer, “Corporate Ownership Around the World,” Journal of Finance, April 1999, 471–517.

ARE CEOs OVERPAID?

Business Week’s annual survey of executive compensation re-cently reported that the average large-company CEO made $12.4 million in 1999, up from $2 million in 1990. This dra- matic increase can be attributed to the fact that CEOs increas- ingly receive most of their compensation in the form of stock and stock options, which skyrocketed in value because of a strong stock market in the 1990s.

Heading the pack on the Business Week list was Computer Associates International Inc.’s Charles Wang, who in 1999 made $655.4 million, mostly from stock options. Rounding out the top five were L. Dennis Kozlowski of Tyco International ($170.0 million), David Pottruck of Charles Schwab ($127.9 million), John Chambers of Cisco Systems ($121.7 million), and Stephen Case of America Online ($117.0 million). It is worth noting that these payouts occurred in large part because the executives ex- ercised stock options granted in earlier years. Thus, their 1999 reported compensation overstated their average compensation over time. More importantly, note that their stock options pro- vided these CEOs with an incentive to raise their companies’ stock prices. Indeed, most observers believe there is a strong

causal relationship between CEO compensation procedures and stock price performance.

However, some critics argue that although performance in- centives are entirely appropriate as a method of compensation, the overall level of CEO compensation is just too high. The crit- ics ask such questions as these: Would these CEOs have been unwilling to take their jobs if they had been offered only half as many stock options? Would they have put forth less effort, and would their firms’ stock prices have not gone up as much? It is hard to say. Other critics lament that the exercise of stock options has dramatically increased the compensation of not only truly excellent CEOs, but it has also dramatically increased the compensation of some pretty average CEOs, who were lucky enough to have had the job during a stock market boom that raised the stock prices of even companies with rather poor performance. Another problem is that the huge CEO salaries are widening the gap between top executives and middle manager salaries. This is leading to employee discontent and a decrease in employee morale and loyalty.

23

interests of stockholders, who are primarily interested in stock price max- imization. Different companies follow different compensation practices, but a typical senior executive’s compensation is structured in three parts: (a) a specified annual salary, which is necessary to meet living expenses; (b) a bonus paid at the end of the year, which depends on the company’s profitability during the year; and (c) options to buy stock, or actual shares of stock, which reward the executive for long-term performance.

Managers are more likely to focus on maximizing stock prices if they are themselves large shareholders. Often, companies grant senior managers performance shares, where the executive receives a number of shares dependent upon the company’s actual performance and the executive’s continued service. For example, in 1991 Coca-Cola granted one million shares of stock worth $81 million to its CEO at the time, the late Roberto Goizueta. The award was based on Coke’s performance under Goizueta’s leadership, but it also stipulated that Goizueta would receive the shares only if he stayed with the company for the remainder of his career.

Most large corporations also provide executive stock options, which allow managers to purchase stock at some future time at a given price. Obviously, a manager who has an option to buy, say, 10,000 shares of stock at a price of $10 during the next 5 years will have an incentive to help raise the stock’s value to an amount greater than $10.

The number of performance shares or options awarded is generally based on objective criteria. Years ago, the primary criteria were account- ing measures such as earnings per share (EPS) and return on equity (ROE). Today, though, the focus is more on the market value of the firm’s shares or, better yet, on the performance of its shares relative to other stocks in its industry. Various procedures are used to structure compensa- tion programs, and good programs are relatively complicated. Still, it has been thoroughly established that a well-designed compensation program can do wonders to improve a company’s financial performance.

2. Direct intervention by shareholders. Years ago most stock was owned by individuals, but today the majority is owned by institutional investors such as insurance companies, pension funds, and mutual funds. There- fore, the institutional money managers have the clout, if they choose to use it, to exercise considerable influence over most firms’ operations. First, they can talk with a firm’s management and make suggestions re- garding how the business should be run. In effect, institutional investors act as lobbyists for the body of stockholders. Second, any shareholder who has owned at least $2,000 of a company’s stock for one year can sponsor a proposal that must be voted on at the annual stockholders’ meeting, even if the proposal is opposed by management. Although shareholder-sponsored proposals are nonbinding and are limited to issues outside of day-to-day operations, the results of such votes are clearly heard by top management.9

3. The threat of firing. Until recently, the probability of a large firm’s management being ousted by its stockholders was so remote that it posed

AG E N C Y R E L AT I O N S H I P S

Performance Shares Stock that is awarded to executives on the basis of the company’s performance.

Executive Stock Option An option to buy stock at a stated price within a specified time period that is granted to an executive as part of his or her compensation package.

9 A recent article that provides a detailed investigation of shareholder proposals during 1997 is Cynthia J. Campbell, Stuart L. Gillan, and Cathy M. Niden, “Current Perspectives on Shareholder Proposals: Lessons from the 1997 Proxy Season,” Financial Management, Spring 1999, 89–98.

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little threat. This situation existed because the shares of most firms were so widely distributed, and management’s control over the voting mecha- nism was so strong, that it was almost impossible for dissident stockhold- ers to get the votes needed to overthrow a management team. However, as noted above, that situation is changing.

Consider the case of Eckhard Pfeiffer, who recently lost his job as CEO of Compaq Computer Corporation. Under Pfeiffer’s leadership, Compaq became the world’s largest computer manufacturer. However, the company has struggled in recent years to maintain profitability in a time of rapidly falling computer prices. Soon after Compaq announced another sub-par quarterly earnings report for the first quarter of 1999, the board of directors told Pfeiffer that they wanted new leadership. Pfeiffer resigned the following day.

Indeed, in recent years the top executives at Mattel, Coca-Cola, Lu- cent, Gillette, Procter & Gamble, Maytag, and Xerox have resigned or been fired after serving as CEO only a short period of time. Most of these departures were no doubt due to their companies’ poor perfor- mance.

4. The threat of takeovers. Hostile takeovers (when management does not want the firm to be taken over) are most likely to occur when a firm’s stock is undervalued relative to its potential because of poor management. In a hostile takeover, the managers of the acquired firm are generally fired, and any who manage to stay on lose status and authority. Thus, managers have a strong incentive to take actions designed to maximize stock prices. In the words of one company president, “If you want to keep your job, don’t let your stock sell at a bargain price.”

STOCKHOLDERS (THROUGH MANAGERS) VERSUS CREDITORS

In addition to conflicts between stockholders and managers, there can also be conflicts between creditors and stockholders. Creditors have a claim on part of the firm’s earnings stream for payment of interest and principal on the debt, and they have a claim on the firm’s assets in the event of bankruptcy. However, stockholders have control (through the managers) of decisions that affect the profitability and risk of the firm. Creditors lend funds at rates that are based on (1) the riskiness of the firm’s existing assets, (2) expectations concerning the riskiness of future asset additions, (3) the firm’s existing capital structure (that is, the amount of debt financing used), and (4) expectations concerning future capital structure decisions. These are the primary determinants of the riskiness of a firm’s cash flows, hence the safety of its debt issues.

Now suppose stockholders, acting through management, cause a firm to take on a large new project that is far riskier than was anticipated by the cred- itors. This increased risk will cause the required rate of return on the firm’s debt to increase, and that will cause the value of the outstanding debt to fall. If the risky project is successful, all the benefits go to the stockholders, because creditors’ returns are fixed at the old, low-risk rate. However, if the project is unsuccessful, the bondholders may have to share in the losses. From the stock-

Hostile Takeover The acquisition of a company over the opposition of its management.

25

holders’ point of view, this amounts to a game of “heads I win, tails you lose,” which is obviously not good for the creditors. Similarly, suppose its managers borrow additional funds and use the proceeds to repurchase some of the firm’s outstanding stock in an effort to “leverage up” stockholders’ return on equity. The value of the debt will probably decrease, because more debt will have a claim against the firm’s cash flows and assets. In both the riskier asset and the increased leverage situations, stockholders tend to gain at the expense of creditors.

Can and should stockholders, through their managers/agents, try to expro- priate wealth from creditors? In general, the answer is no, for unethical behav- ior is penalized in the business world. First, creditors attempt to protect them- selves against stockholders by placing restrictive covenants in debt agreements. Moreover, if creditors perceive that a firm’s managers are trying to take advan- tage of them, they will either refuse to deal further with the firm or else will charge a higher-than-normal interest rate to compensate for the risk of possi- ble exploitation. Thus, firms that deal unfairly with creditors either lose access to the debt markets or are saddled with high interest rates and restrictive covenants, all of which are detrimental to shareholders.

In view of these constraints, it follows that to best serve their shareholders in the long run, managers must play fairly with creditors. As agents of both shareholders and creditors, managers must act in a manner that is fairly bal- anced between the interests of the two classes of security holders. Similarly, because of other constraints and sanctions, management actions that would expropriate wealth from any of the firm’s other stakeholders, including its em- ployees, customers, suppliers, and community, will ultimately be to the detri- ment of its shareholders. In our society, stock price maximization requires fair treatment for all parties whose economic positions are affected by managerial decisions.

M A N AG E R I A L AC T I O N S TO M A X I M I Z E S H A R E H O L D E R W E A LT H

SELF-TEST QUESTIONS

What are agency costs, and who bears them?

What are some mechanisms that encourage managers to act in the best in- terests of stockholders? To not take advantage of bondholders?

Why should managers not take actions that are unfair to any of the firm’s stakeholders?

M A N AG E R I A L AC T I O N S TO M A X I M I Z E S H A R E H O L D E R W E A LT H

What types of actions can managers take to maximize the price of a firm’s stock? To answer this question, we first need to ask, “What factors determine the price of a company’s stock?” While we will address this issue in detail in

C H A P T E R 1 � A N O V E R V I E W O F F I N A N C I A L M A N AG E M E N T26

Chapter 9, we can lay out three basic facts here. (1) Any financial asset, includ- ing a company’s stock, is valuable only to the extent that the asset generates cash flows. (2) The timing of the cash flows matters — cash received sooner is better, because it can be reinvested to produce additional income. (3) Investors are generally averse to risk, so all else equal, they will pay more for a stock whose cash flows are relatively certain than for one with relatively risky cash flows. Because of these three factors, managers can enhance their firms’ value (and the stock price) by increasing expected cash flows, speeding them up, and reducing their riskiness.

Within the firm, managers make investment decisions regarding the types of products or services produced, as well as the way goods and services are pro- duced and delivered. Also, managers must decide how to finance the firm — what mix of debt and equity should be used, and what specific types of debt and eq- uity securities should be issued? In addition, the financial manager must decide what percentage of current earnings to pay out as dividends rather than retain and reinvest; this is called the dividend policy decision. Each of these invest- ment and financing decisions is likely to affect the level, timing, and riskiness of the firm’s cash flows, and therefore the price of its stock. Naturally, managers should make investment and financing decisions designed to maximize the firm’s stock price.

Although managerial actions affect the value of a firm’s stock, stock prices are also affected by such external factors as legal constraints, the general level of economic activity, tax laws, interest rates, and conditions in the stock market. Figure 1-2 diagrams these general relationships. Working within the set of ex- ternal constraints shown in the box at the extreme left, management makes a set of long-run strategic policy decisions that chart a future course for the firm. These policy decisions, along with the general level of economic activity and the level of corporate income taxes, influence the firm’s expected cash flows, their timing, their eventual payment to stockholders as dividends, and their

Dividend Policy Decision The decision as to how much of current earnings to pay out as dividends rather than retain for reinvestment in the firm.

F I G U R E 1 - 2 Summary of Major Factors Affecting Stock Prices

External Constraints: Strategic Policy Decisions Controlled by Management:

1. Antitrust Laws 1. Types of Products or Services Produced 2. Production Methods Used 3. Research and Development Efforts 4. Relative Use of Debt Financing 5. Dividend Policy 6. And So Forth

3. Product and Workplace Safety Regulations 4. Employment Practices Rules 5. Federal Reserve Policy

Level of Economic Activity and Corporate Taxes

Expected Cash Flows

Timing of Cash Flows

Perceived Riskiness of Cash Flows

Stock Market Conditions

Stock Price

2. Environmental Regulations

6. International Rules 7. And So Forth

27

D O E S I T M A K E S E N S E TO T R Y TO M A X I M I Z E E A R N I N G S P E R S H A R E ?

In arguing that managers should take steps to maximize the firm’s stock price, we have said nothing about the traditional objective, profit maximization, or the maximization of earnings per share (EPS). However, while a growing number of analysts rely on cash flow projections to assess performance, at least as much attention is still paid to accounting measures, especially EPS. The tra- ditional accounting performance measures are appealing because (1) they are easy to use and understand; (2) they are calculated on the basis of more or less standardized accounting practices, which reflect the accounting profession’s best efforts to measure financial performance on a consistent basis both across firms and over time; and (3) net income is supposed to be reflective of the firm’s potential to produce cash flows over time.

Generally, there is a high correlation between EPS, cash flow, and stock price, and all of them generally rise if a firm’s sales rise. Nevertheless, as we will see in subsequent chapters, stock prices depend not just on today’s earnings and cash flows—future cash flows and the riskiness of the future earnings stream also affect stock prices. Some actions may increase earnings and yet reduce stock price, while other actions may boost stock price but reduce earnings. For example, consider a company that undertakes large expenditures today that are designed to improve future performance. These expenditures will likely reduce earnings per share, yet the stock market may respond positively if it believes that these expenditures will significantly enhance future earnings. By contrast, a company that undertakes actions today to enhance its earnings may see a drop in its stock price, if the market believes that these actions compromise future earnings and/or dramatically increase the firm’s risk.

Even though the level and riskiness of current and future cash flows ulti- mately determine stockholder value, financial managers cannot ignore the ef- fects of their decisions on reported EPS, because earnings announcements send messages to investors. Say, for example, a manager makes a decision that will ultimately enhance cash flows and stock price, yet the short-run ef- fect is to lower this year’s profitability and EPS. Such a decision might be a change in inventory accounting policy that increases reported expenses but also increases cash flow because it reduces current taxes. In this case, it makes sense for the manager to adopt the policy because it generates additional cash, even though it reduces reported profits. Note, though, that manage- ment must communicate the reason for the earnings decline, for otherwise the company’s stock price will probably decline after the lower earnings are reported.

D O E S I T M A K E S E N S E TO T R Y TO M A X I M I Z E E A R N I N G S P E R S H A R E ?

Profit Maximization The maximization of the firm’s net income.

Earnings Per Share (EPS) Net income divided by the number of shares of common stock outstanding.

SELF-TEST QUESTION

Identify some factors beyond a firm’s control that influence its stock price.

riskiness. These factors all affect the price of the stock, but so does another fac- tor, conditions in the stock market as a whole.

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O R GA N I Z AT I O N O F T H E B O O K

The primary goal of all managers is to maximize the value of the firm. To achieve this goal, all managers must have a general understanding of how busi- nesses are organized, how financial markets operate, how interest rates are de- termined, how the tax system operates, and how accounting data are used to evaluate a business’s performance. In addition, managers must have a good un- derstanding of such fundamental concepts as the time value of money, risk mea- surement, asset valuation, and evaluation of specific investment opportunities. This background information is essential for anyone involved with the kinds of decisions that affect the value of a firm’s securities.

The organization of this book reflects these considerations, so the five chap- ters of Part I present some important background material. Chapter 1 discusses the goals of the firm and the “philosophy” of financial management. Chapter 2 describes the key financial statements, discusses what they are designed to do, and then explains how our tax system affects earnings, cash flows, stock prices, and managerial decisions. Chapter 3 shows how financial statements are ana- lyzed, while Chapter 4 develops techniques for forecasting financial statements. Chapter 5 discusses how financial markets operate and how interest rates are determined.

Part II considers two of the most fundamental concepts in financial manage- ment. First, Chapter 6 explains how risk is measured and how it affects security prices and rates of return. Next, Chapter 7 discusses the time value of money and its effects on asset values and rates of return.

Part III covers the valuation of stocks and bonds. Chapter 8 focuses on bonds, and Chapter 9 considers stocks. Both chapters describe the relevant in- stitutional details, then explain how risk and time value jointly determine stock and bond prices.

Part IV, “Investing in Long-Term Assets: Capital Budgeting,” applies the concepts covered in earlier chapters to decisions related to fixed asset invest- ments. First, Chapter 10 explains how to measure the cost of the funds used to acquire assets, or the cost of capital. Next, Chapter 11 shows how this infor- mation is used to evaluate potential capital investments by answering this ques- tion: Can we expect a project to provide a higher rate of return than the cost of the funds used to finance it? Only if the expected return exceeds the cost of capital will accepting a project increase stockholders’ wealth. Chapter 12 goes into more detail on capital budgeting decisions, looking at relevant cash flows, new (expansion) projects, and project risk analysis.

Part V discusses how firms should finance their long-term assets. First, Chapter 13 examines capital structure theory, or the issue of how much debt

SELF-TEST QUESTIONS

Is profit maximization an appropriate goal for financial managers?

Should financial managers concentrate strictly on cash flow and ignore the impact of their decisions on EPS?

29

versus equity the firm should use. Then, Chapter 14 considers dividend policy, or the decision to retain earnings versus paying them out as dividends.

In Part VI, our focus shifts from long-term, strategic decisions to short- term, day-to-day operating decisions and multinational financial management. In Chapter 15, we see how cash, inventories, and accounts receivable are man- aged and the best way of financing these current assets. Chapter 16 discusses multinational financial management issues such as exchange rates, exchange rate risk, and political risk.

It is worth noting that some instructors may choose to cover the chapters in a different sequence from their order in the book. The chapters are written to a large extent in a modular, self-contained manner, so such reordering should present no major difficulties.

T Y I N G I T A L L TO G E T H E R

This chapter has provided an overview of financial management. The key con- cepts covered are listed below.

� Finance consists of three interrelated areas: (1) money and capital mar- kets, (2) investments, and (3) financial management.

� In recent years the two most important trends in finance have been the increased globalization of business and the growing use of computers and information technology. These trends are likely to continue in the future.

� The financial staff’s task is to obtain and use funds so as to maximize the value of the firm.

� The three main forms of business organization are the sole proprietor- ship, the partnership, and the corporation.

� Although each form of organization offers advantages and disadvantages, most business is conducted by corporations because this organiza- tional form maximizes larger firms’ values.

� The primary goal of management should be to maximize stockholders’ wealth, and this means maximizing the firm’s stock price. Note, though, that actions that maximize stock prices also increase social welfare.

� An agency problem is a potential conflict of interests that can arise between a principal and an agent. Two important agency relationships are (1) those between the owners of the firm and its management and (2) those between the managers, acting for stockholders, and the debtholders.

� There are a number of ways to motivate managers to act in the best in- terests of stockholders, including (1) properly structured managerial compensation, (2) direct intervention by stockholders, (3) the threat of firing, and (4) the threat of takeovers.

� The price of a firm’s stock depends on the cash flows paid to share- holders, the timing of the cash flows, and their riskiness. The level and

C H A P T E R 1 � A N O V E R V I E W O F F I N A N C I A L M A N AG E M E N T30

riskiness of cash flows are affected by the financial environment as well as by investment, financing, and dividend policy decisions made by fi- nancial managers.

Q U E S T I O N S

1-1 What are the three principal forms of business organization? What are the advantages and disadvantages of each?

1-2 Would the “normal” rate of return on investment be the same in all industries? Would “normal” rates of return change over time? Explain.

1-3 Would the role of a financial manager be likely to increase or decrease in importance relative to other executives if the rate of inflation increased? Explain.

1-4 Should stockholder wealth maximization be thought of as a long-term or a short-term goal — for example, if one action would probably increase the firm’s stock price from a current level of $20 to $25 in 6 months and then to $30 in 5 years but another action would probably keep the stock at $20 for several years but then increase it to $40 in 5 years, which action would be better? Can you think of some specific corporate actions that might have these general tendencies?

1-5 Drawing on your background in accounting, can you think of any accounting differences that might make it difficult to compare the relative performance of different firms?

1-6 Would the management of a firm in an oligopolistic or in a competitive industry be more likely to engage in what might be called “socially conscious” practices? Explain your reasoning.

1-7 What’s the difference between stock price maximization and profit maximization? Under what conditions might profit maximization not lead to stock price maximization?

1-8 If you were the president of a large, publicly owned corporation, would you make deci- sions to maximize stockholders’ welfare or your own personal interests? What are some actions stockholders could take to ensure that management’s interests and those of stockholders coincided? What are some other factors that might influence manage- ment’s actions?

1-9 The president of Southern Semiconductor Corporation (SSC) made this statement in the company’s annual report: “SSC’s primary goal is to increase the value of the com- mon stockholders’ equity over time.” Later on in the report, the following announce- ments were made: a. The company contributed $1.5 million to the symphony orchestra in Birmingham,

Alabama, its headquarters city. b. The company is spending $500 million to open a new plant in Mexico. No revenues

will be produced by the plant for 4 years, so earnings will be depressed during this period versus what they would have been had the decision not been made to open the new plant.

c. The company is increasing its relative use of debt. Whereas assets were formerly fi- nanced with 35 percent debt and 65 percent equity, henceforth the financing mix will be 50-50.

d. The company uses a great deal of electricity in its manufacturing operations, and it generates most of this power itself. Plans are to utilize nuclear fuel rather than coal to produce electricity in the future.

e. The company has been paying out half of its earnings as dividends and retaining the other half. Henceforth, it will pay out only 30 percent as dividends.

Discuss how each of these actions would be reacted to by SSC’s stockholders and cus- tomers, and then how each action might affect SSC’s stock price.

1-10 Assume that you are serving on the board of directors of a medium-sized corporation and that you are responsible for establishing the compensation policies of senior man- agement. You believe that the company’s CEO is very talented, but your concern is that

31

she is always looking for a better job and may want to boost the company’s short-run performance (perhaps at the expense of long-run profitability) to make herself more marketable to other corporations. What effect would these concerns have on the com- pensation policy you put in place?

1-11 If the overall stock market is extremely volatile, and if many analysts foresee the possi- bility of a stock market crash, how might these factors influence the way corporations choose to compensate their senior executives?

1-12 Teacher’s Insurance and Annuity Association–College Retirement Equity Fund (TIAA– CREF) is the largest institutional shareholder in the United States. Traditionally, TIAA–CREF has acted as a passive investor. However, TIAA–CREF announced a tough new corporate governance policy begninning October 5, 1993.

In a statement mailed to all 1,500 companies in which it invests, TIAA–CREF out- lined a policy designed to improve corporate performance, including a goal of higher stock prices for the $52 billion in stock assets it holds, and to encourage corporate boards to have a majority of independent (outside) directors. TIAA–CREF wants to see management more accountable to shareholder interests, as evidenced by its statement that the fund will vote against any director “where companies don’t have an effective, independent board which can challenge the CEO.”

Historically, TIAA–CREF did not quickly sell poor-performing stocks. In addition, the fund invested a large part of its assets to match performance of the major market in- dexes locking TIAA–CREF into ownership of certain companies. Further complicating the problem, TIAA–CREF owns stakes of from 1 percent to 10 percent in several com- panies, and selling such large blocks of stock would depress their prices.

Common stock ownership confers a right to sponsor initiatives to shareholders re- garding the corporation. A corresponding voting right exists for shareholders. a. Is TIAA–CREF an ordinary shareholder? b. Due to its asset size, TIAA–CREF assumes large positions with which it plans to ac-

tively vote. However, who owns TIAA–CREF? c. Should the investment managers of a fund like TIAA–CREF determine the voting

practices of the fund’s shares, or should the voting rights be passed on to TIAA–CREF’s stakeholders?

1-13 The senior managers of Hancock Oil are evaluating a new oil exploration project. The project requires a large amount of capital and is quite risky, but it has the possi- bility of being extremely profitable. In a separate action, the company’s managers are also considering increasing Hancock’s dividend payout ratio. The proposed project and proposed dividend increase are both expected to increase the company’s stock price. a. How would the proposed exploration project affect Hancock’s outstanding bond-

holders? b. How would the proposed dividend increase affect Hancock’s outstanding bondholders? c. Should Hancock’s managers go ahead with the proposed project and dividend

increase? d. What steps can bondholders take to protect themselves against managerial decisions

that reduce the value of their bonds? 1-14 Stewart Web Design currently operates an unincorporated partnership with 75 employ-

ees. The partners are contemplating organizing as a corporation. How might each of the following actions affect the firm’s decision to incorporate? a. Congress is considering a tax bill that would reduce individual tax rates but increase

corporate tax rates. b. Congress is considering a bill that would extend the coverage of a large number of

environmental and labor regulations to now include companies that have more than 50 employees. Presently, companies with fewer than 200 employees are excluded from these regulations.

1-15 Edmund Enterprises recently made a large investment in upgrading its technology. While the technology improvements will not have much of an impact on performance in the short run, they are expected to produce significant cost savings over the next several years. What impact will this investment have on Edmund Enterprises’ earnings per share this year? What impact might this investment have on the company’s stock price?

Q U E S T I O N S

C H A P T E R 1 � A N O V E R V I E W O F F I N A N C I A L M A N AG E M E N T32

The information related to the cyberproblems is likely to change over time, due to the release of new information and the ever-changing nature of the World Wide Web. With these changes in mind, we will periodically update these problems on the textbook’s web site. To avoid problems, please check for these updates before proceeding with the cyberproblems.

Management’s primary goal is to maximize stockholder wealth. Firms often award stock options and bonuses on the basis of management performance, thus linking management’s personal wealth with the firm’s financial performance. The better the job managers do in maximizing share price, the greater their compensation.

Walt Disney’s CEO, Michael Eisner, draws a compensation package in part based on the net income and return on shareholder equity of The Walt Disney Company. In 1994, he attracted a lot of attention when he exercised stock options on 5.4 million Disney shares for a net profit (after taxes and brokerage expenses) of around $127

1-1 Overview of financial

management

S E L F - T E S T P R O B L E M ( S O L U T I O N A P P E A R S I N A P P E N D I X B )

Define each of the following terms: a. Sole proprietorship; partnership; corporation b. Limited partnership; limited liability partnership; professional corporation c. Stockholder wealth maximization d. Social responsibility; business ethics e. Normal profits; normal rate of return f. Agency problem g. Performance shares; executive stock options h. Hostile takeover i. Profit maximization j. Earnings per share k. Dividend policy decision

ST-1 Key terms

TAKE A DIVE

1-2 Financial Management Overview Kato Summers opened Take A Dive 17 years ago; the store is located in Malibu, California, and sells surfing-related equipment. Today, Take a Dive has 50 employees including Kato and his daughter Amber, who works part time in the store to help pay for her college education.

Kato’s business has boomed in recent years, and he is looking for new ways to take advantage of his increasing business opportunities. Although Kato’s formal business training is limited, Amber will soon graduate with a de- gree in finance. Kato has offered her the opportunity to join the business as a full-fledged partner. Amber is inter- ested, but she is also considering other career opportuni- ties in finance.

Right now, Amber is leaning toward staying with the family business, partly because she thinks it faces a number of interesting challenges and opportunities. Amber is partic- ularly interested in further expanding the business and then incorporating it. Kato is intrigued by her ideas, but he is also concerned that her plans might change the way in which he does business. In particular, Kato has a strong commitment to social activism, and he has always tried to strike a balance between work and pleasure. He is worried that these goals will be compromised if the company incorporates and brings in outside shareholders.

Amber and Kato plan to take a long weekend off to sit down and think about all of these issues. Amber, who is highly organized, has outlined a series of questions for them to address: a. What kinds of career opportunities are open to finance

majors? b. What are the primary responsibilities of a corporate fi-

nancial staff? c. What are the most important financial management is-

sues today? d. (1) What are the alternative forms of business organiza-

tion? (2) What are their advantages and disadvantages?

e. What is the primary goal of the corporation? (1) Do firms have any responsibilities to society at large? (2) Is stock price maximization good or bad for society? (3) Should firms behave ethically?

f. What is an agency relationship? (1) What agency relationships exist within a corporation? (2) What mechanisms exist to influence managers to act

in shareholders’ best interests? (3) Should shareholders (through managers) take actions

that are detrimental to bondholders? g. Is maximizing stock price the same thing as maximizing

profit? h. What factors affect stock prices? i. What factors affect the level and riskiness of cash flows?

33I N T E G R AT E D C A S E

million. At the time, he had also earned another 8 million stock options, then valued at about $161 million. Year after year, Eisner ranks among the most highly compen- sated CEOs in America. In 1999, Michael Eisner’s total compensation from Walt Disney Co. totaled $50.7 million in salary and exercised stock options.

Let’s see if Mr. Eisner deserves such generous bonuses and stock options. Look at Disney’s 1999 Annual Report on the web at http://disney.go.com/investors/ annual99/index.html to answer the following questions: a. Click on the page and then click on Financial Review. Describe how Disney’s

three main business segments have been divided into five distinct operating seg- ments. What percentage of operating income did each contribute to the firm?

b. If on November 30, 1984, you invested $1,000 in Disney stock and reinvested all your dividends, how much would you have had on November 30, 1999?

c. How does the compound annual return on your Disney stock during this 15-year period compare to the return earned on the S&P 500 during this same period?

d. If you had purchased 100 shares of Disney stock for $2,500 in the company’s ini- tial public offering 59 years ago and had purchased no additional Disney shares, how many shares would you have, and how much would they be worth, as of No- vember 30, 1999?

e. What is the compound annual growth rate of the stock’s value over this 59-year period?

f. On the basis of the company’s performance through 1999, do you think that Mr. Eisner and his management team have done a good job? Has this impression changed based on the company’s recent performance?

F i na nc i a l S t a t e me n t s , C a s h F l o w, a nd Ta xe s

SOURCE: © Bill O’Connell/Black Star

CHAPTER 2

4

The trick is to find a product that will boom, yet

whose manufacturer’s stock is undervalued. If this

sounds too easy, you are right. Lynch argues that once

you have discovered a good product, there is still much

homework to be done. This involves combing through

the vast amount of financial information that is

regularly provided by companies. It also requires taking

a closer and more critical look at how the company

conducts its business — Lynch refers to this as “kicking

the tires.”

To illustrate his point, Lynch relates his experience

with Dunkin’ Donuts. As a consumer, Lynch was

impressed with the quality of the product. This

impression led him to take a closer look at the

company’s financial statements and operations. He liked

what he saw, and Dunkin’ Donuts became one of the

best investments in his portfolio.

The next two chapters discuss what financial

statements are and how they are analyzed. Once you

have identified a good product as a possible investment,

the principles discussed in these chapters will help you

“kick the tires.” �

uppose you are a small investor who knows a

little about finance and accounting. Could you

compete successfully against large institutional

investors with armies of analysts, high-powered

computers, and state-of-the-art trading strategies?

The answer, according to one Wall Street legend, is a

resounding yes! Peter Lynch, who had an outstanding

track record as manager of the $10 billion Fidelity

Magellan fund and then went on to become the best-

selling author of One Up on Wall Street and Beating the

Street, has long argued that small investors can beat

the market by using common sense and information

available to all of us as we go about our day-to-day

lives.

For example, a college student may be more adept at

scouting out the new and interesting products that will

become tomorrow’s success stories than is an

investment banker who works 75 hours a week in a New

York office. Parents of young children are likely to know

which baby foods will succeed, or which diapers are

best. Couch potatoes may have the best feel for which

tortilla chips have the brightest future, or whether a

new remote control is worth its price.

D O I N G YO U R HO M E W O R K W I T H F I N A N C I A L S TAT E M E N TS $

S

35

C H A P T E R 2 � F I N A N C I A L S TAT E M E N TS , C A S H F L O W, A N D TA X E S36

A manager’s primary goal is to maximize the value of his or her firm’s stock. Value

is based on the stream of cash flows the firm will generate in the future. But how

does an investor go about estimating future cash flows, and how does a manager

decide which actions are most likely to increase cash flows? The answers to both

questions lie in a study of the financial statements that publicly traded firms must

provide to investors. Here “investors” include both institutions (banks, insurance

companies, pension funds, and the like) and individuals. Thus, this chapter begins

with a discussion of what the basic financial statements are, how they are used,

and what kinds of financial information users need.

The value of any business asset — whether it is a financial asset such as a stock

or a bond, or a real (physical) asset such as land, buildings, and equipment —

depends on the usable, after-tax cash flows the asset is expected to produce.

Therefore, the chapter also explains the difference between accounting income

and cash flow. Finally, since it is after-tax cash flow that is important, the chap-

ter provides an overview of the federal income tax system.

Much of the material in this chapter reviews concepts covered in basic ac-

counting courses. However, the information is important enough to go over again.

Accounting is used to “keep score,” and if a firm’s managers do not know the

score, they won’t know if their actions are appropriate. If you took midterm exams

but were not told how you were doing, you would have a difficult time improving

your grades. The same thing holds in business. If a firm’s managers — whether

they are in marketing, personnel, production, or finance — do not understand fi-

nancial statements, they will not be able to judge the effects of their actions, and

the firm will not be successful. Although only accountants need to know how to

make financial statements, everyone involved with business needs to know how to

interpret them. �

37

A B R I E F H I S TO R Y O F AC C O U N T I N G A N D F I N A N C I A L S TAT E M E N T S

Financial statements are pieces of paper with numbers written on them, but it is important to also think about the real assets that underlie the numbers. If you understand how and why accounting began, and how financial statements are used, you can better visualize what is going on, and why accounting informa- tion is so important.

Thousands of years ago, individuals (or families) were self-contained in the sense that they gathered their own food, made their own clothes, and built their own shelters. Then specialization began — some people became good at mak- ing pots, others at making arrowheads, others at making clothing, and so on.

As specialization began, so did trading, initially in the form of barter. At first, each artisan worked alone, and trade was strictly local. Eventually, though, mas- ter craftsmen set up small factories and employed workers, money (in the form of clamshells) began to be used, and trade expanded beyond the local area. As these developments occurred, a primitive form of banking began, with wealthy merchants lending profits from past dealings to enterprising factory owners who needed capital to expand or to young traders who needed money to buy wagons, ships, and merchandise.

When the first loans were made, lenders could physically inspect borrowers’ assets and judge the likelihood of the loan’s being repaid. Eventually, though, lending became more complex — borrowers were developing larger factories, traders were acquiring fleets of ships and wagons, and loans were being made to develop distant mines and trading posts. At that point, lenders could no longer personally inspect the assets that backed their loans, and they needed some way of summarizing borrowers’ assets. Also, some investments were made on a share-of-the-profits basis, and this meant that profits (or income) had to be determined. At the same time, factory owners and large merchants needed reports to see how effectively their own enterprises were being run, and gov- ernments needed information for use in assessing taxes. For all these reasons, a need arose for financial statements, for accountants to prepare those state- ments, and for auditors to verify the accuracy of the accountants’ work.

The economic system has grown enormously since its beginning, and ac- counting has become more complex. However, the original reasons for finan- cial statements still apply: Bankers and other investors need accounting infor- mation to make intelligent decisions, managers need it to operate their businesses efficiently, and taxing authorities need it to assess taxes in a reason- able way.

It should be intuitively clear that it is not easy to translate physical assets into numbers, which is what accountants do when they construct financial state- ments. The numbers shown on balance sheets generally represent the histori- cal costs of assets. However, inventories may be spoiled, obsolete, or even miss- ing; fixed assets such as machinery and buildings may have higher or lower values than their historical costs; and accounts receivable may be uncollectable. Also, some liabilities such as obligations to pay retirees’ medical costs may not even show up on the balance sheet. Similarly, some costs reported on the in- come statement may be understated, as would be true if a plant with a useful life of 10 years were being depreciated over 40 years. When you examine a set

A B R I E F H I S TO R Y O F AC C O U N T I N G A N D F I N A N C I A L S TAT E M E N T S

Are you interested in learning more about the history of accounting? If so, take a tour through the “Virtual History of

Accounting” organized by the Association of Chartered Accountants in the United States and located at http://www.acaus.org/history/ index.html.

C H A P T E R 2 � F I N A N C I A L S TAT E M E N TS , C A S H F L O W, A N D TA X E S38

of financial statements, you should keep in mind that a physical reality lies be- hind the numbers, and you should also realize that the translation from physi- cal assets to “correct” numbers is far from precise.

As mentioned previously, it is important for accountants to be able to gen- erate financial statements, while others involved in the business need to know how to interpret them. Particularly, financial managers must have a working knowledge of financial statements and what they reveal to be effective. Spread- sheets provide financial managers with a powerful and reliable tool to conduct financial analysis, and several different types of spreadsheet models are pro- vided with the text. These models demonstrate how financial principles taught in this book are applied in practice. Readers are encouraged to use these mod- els to gain further insights into various concepts and procedures.

F I N A N C I A L S TAT E M E N T S A N D R E P O R T S

Of the various reports corporations issue to their stockholders, the annual re- port is probably the most important. Two types of information are given in this report. First, there is a verbal section, often presented as a letter from the chair- man, that describes the firm’s operating results during the past year and dis- cusses new developments that will affect future operations. Second, the annual report presents four basic financial statements — the balance sheet, the income statement, the statement of retained earnings, and the statement of cash flows. Taken together, these statements give an accounting picture of the firm’s operations and financial position. Detailed data are provided for the two or three most re- cent years, along with historical summaries of key operating statistics for the past 5 or 10 years.1

The quantitative and verbal materials are equally important. The financial statements report what has actually happened to assets, earnings, and dividends over the past few years, whereas the verbal statements attempt to explain why things turned out the way they did.

For illustrative purposes, we shall use data taken from Allied Food Products, a processor and distributor of a wide variety of staple foods, to discuss the basic financial statements. Formed in 1978 when several regional firms merged, Al- lied has grown steadily, and it has earned a reputation for being one of the best firms in its industry. Allied’s earnings dropped a bit in 2001, to $113.5 million versus $117.8 million in 2000. Management reported that the drop resulted from losses associated with a drought and from increased costs due to a three- month strike. However, management then went on to paint a more optimistic picture for the future, stating that full operations had been resumed, that sev- eral unprofitable businesses had been eliminated, and that 2002 profits were ex- pected to rise sharply. Of course, an increase in profitability may not occur, and

Annual Report A report issued annually by a corporation to its stockholders. It contains basic financial statements, as well as management’s analysis of the past year’s operations and opinions about the firm’s future prospects.

1 Firms also provide quarterly reports, but these are much less comprehensive. In addition, larger firms file even more detailed statements, giving breakdowns for each major division or subsidiary, with the Securities and Exchange Commission (SEC). These reports, called 10-K reports, are made available to stockholders upon request to a company’s corporate secretary. Finally, many larger firms also publish statistical supplements, which give financial statement data and key ratios going back 10 to 20 years, and their reports are available on the World Wide Web.

For an excellent example of a corporate annual report, take a look at 3M’s annual report found at http://www.mmm.com/

about3M/index.jhtml. Then, click on investor relations and annual reports on the left-hand side of your screen. Here you can find several recent annual reports in Adobe Acrobat format.

39

analysts should compare management’s past statements with subsequent results. In any event, the information contained in an annual report is used by investors to help form expectations about future earnings and dividends. Therefore, the annual report is obviously of great interest to investors.

T H E BA L A N C E S H E E T

SELF-TEST QUESTIONS

What is the annual report, and what two types of information are given in it?

What four types of financial statements are typically included in the annual report?

Why is the annual report of great interest to investors?

T H E BA L A N C E S H E E T

The left-hand side of Allied’s year-end 2001 and 2000 balance sheets, which are given in Table 2-1, shows the firm’s assets, while the right-hand side shows the liabilities and equity, or the claims against these assets. The assets are listed in order of their “liquidity,” or the length of time it typically takes to convert them to cash. The claims are listed in the order in which they must be paid: Ac- counts payable must generally be paid within 30 days, notes payable within 90

T A B L E 2 - 1

ASSETS 2001 2000 LIABILITIES AND EQUITY 2001 2000

Cash and marketable securities $ 10 $ 80 Accounts payable $ 60 $ 30 Accounts receivable 375 315 Notes payable 110 60 Inventories 615 415 Accruals 140 130

Total current assets $1,000 $ 810 Total current liabilities $ 310 $ 220 Net plant and equipment 1,000 870 Long-term bonds 754 580

Total debt $1,064 $ 800 Preferred stock (400,000 shares) 40 40 Common stock (50,000,000 shares) 130 130 Retained earnings 766 710

Total common equity $ 896 $ 840 Total assets $2,000 $1,680 Total liabilities and equity $2,000 $1,680

NOTE: The bonds have a sinking fund requirement of $20 million a year. Sinking funds are discussed in Chapter 8, but in brief, a sinking fund simply involves the repayment of long-term debt. Thus, Allied was required to pay off $20 million of its mortgage bonds during 2001. The current portion of the long-term debt is included in notes payable here, although in a more detailed balance sheet it would be shown as a separate item under current liabilities.

Allied Food Products: December 31 Balance Sheets (Millions of Dollars)

Balance Sheet A statement of the firm’s financial position at a specific point in time.

C H A P T E R 2 � F I N A N C I A L S TAT E M E N TS , C A S H F L O W, A N D TA X E S40

days, and so on, down to the stockholders’ equity accounts, which represent ownership and need never be “paid off.”

Some additional points about the balance sheet are worth noting:

1. Cash versus other assets. Although the assets are all stated in terms of dollars, only cash represents actual money. (Marketable securities can be converted to cash within a day or two, so they are almost like cash and are reported with cash on the balance sheet.) Receivables are bills others owe Allied. Inventories show the dollars the company has invested in raw ma- terials, work-in-process, and finished goods available for sale. And net plant and equipment reflect the amount of money Allied paid for its fixed assets when it acquired those assets in the past, less accumulated depreci- ation. Allied can write checks for a total of $10 million (versus current li- abilities of $310 million due within a year). The noncash assets should produce cash over time, but they do not represent cash in hand, and the amount of cash they would bring if they were sold today could be higher or lower than the values at which they are carried on the books.

2. Liabilities versus stockholders’ equity. The claims against assets are of two types — liabilities (or money the company owes) and the stockhold- ers’ ownership position.2 The common stockholders’ equity, or net worth, is a residual. For example, at the end of 2001,

Suppose assets decline in value; for example, suppose some of the ac- counts receivable are written off as bad debts. Liabilities and preferred stock remain constant, so the value of the common stockholders’ equity must decline. Therefore, the risk of asset value fluctuations is borne by the common stockholders. Note, however, that if asset values rise (per- haps because of inflation), these benefits will accrue exclusively to the common stockholders.

3. Preferred versus common stock. Preferred stock is a hybrid, or a cross between common stock and debt. In the event of bankruptcy, preferred stock ranks below debt but above common stock. Also, the preferred div- idend is fixed, so preferred stockholders do not benefit if the company’s earnings grow. Finally, many firms do not use any preferred stock, and those that do generally do not use much of it. Therefore, when the term “equity” is used in finance, we generally mean “common equity” unless the word “total” is included.

4. Breakdown of the common equity accounts. The common equity sec- tion is divided into two accounts — “common stock” and “retained earn-

2 One could divide liabilities into (1) debts owed to someone and (2) other items, such as deferred taxes, reserves, and so on. Because we do not make this distinction, the terms debt and liabilities are used synonymously. It should be noted that firms occasionally set up reserves for certain contin- gencies, such as the potential costs involved in a lawsuit currently in the courts. These reserves rep- resent an accounting transfer from retained earnings to the reserve account. If the company wins the suit, retained earnings will be credited, and the reserve will be eliminated. If it loses, a loss will be recorded, cash will be reduced, and the reserve will be eliminated.

Common Stockholders’ Equity (Net Worth) The capital supplied by common stockholders — common stock, paid-in capital, retained earnings, and, occasionally, certain reserves. Total equity is common equity plus preferred stock.

Assets � Liabilities � Preferred stock � Commonstockholder’s equity $2,000,000,000 � $1,064,000,000 � $40,000,000 � $896,000,000

41

ings.” The retained earnings account is built up over time as the firm “saves” a part of its earnings rather than paying all earnings out as divi- dends. The common stock account arises from the issuance of stock to raise capital, as discussed in Chapter 9.

The breakdown of the common equity accounts is important for some purposes but not for others. For example, a potential stockholder would want to know whether the company actually earned the funds reported in its equity accounts or whether the funds came mainly from selling stock. A potential creditor, on the other hand, would be more interested in the total equity the owners have in the firm and would be less concerned with the source of the equity. In the remainder of this chapter, we generally aggregate the two common equity accounts and call this sum common eq- uity or net worth.

5. Inventory accounting. Allied uses the FIFO (first-in, first-out) method to determine the inventory value shown on its balance sheet ($615 mil- lion). It could have used the LIFO (last-in, first-out) method. During a period of rising prices, by taking out old, low-cost inventory and leaving in new, high-cost items, FIFO will produce a higher balance sheet inven- tory value but a lower cost of goods sold on the income statement. (This is strictly accounting; companies actually use older items first.) Since Al- lied uses FIFO, and since inflation has been occurring, (a) its balance sheet inventories are higher than they would have been had it used LIFO, (b) its cost of goods sold is lower than it would have been under LIFO, and (c) its reported profits are therefore higher. In Allied’s case, if the company had elected to switch to LIFO in 2001, its balance sheet figure for inventories would have been $585,000,000 rather than $615,000,000, and its earnings (which will be discussed in the next section) would have been reduced by $18,000,000. Thus, the inventory valuation method can have a significant effect on financial statements. This is important when an analyst is comparing different companies.

6. Depreciation methods. Most companies prepare two sets of financial statements — one for tax purposes and one for reporting to stockholders. Generally, they use the most accelerated method permitted under the law to calculate depreciation for tax purposes, but they use straight line, which results in a lower depreciation charge, for stockholder reporting. However, Allied has elected to use rapid depreciation for both stock- holder reporting and tax purposes. Had Allied elected to use straight line depreciation for stockholder reporting, its 2001 depreciation expense would have been $25,000,000 less, so the $1 billion shown for “net plant” on its balance sheet would have been $25,000,000 higher. Its net income and its retained earnings would also have been higher.

7. The time dimension. The balance sheet may be thought of as a snap- shot of the firm’s financial position at a point in time — for example, on December 31, 2000. Thus, on December 31, 2000, Allied had $80 mil- lion of cash and marketable securities, but this account had been reduced to $10 million by the end of 2001. The balance sheet changes every day as inventories are increased or decreased, as fixed assets are added or re- tired, as bank loans are increased or decreased, and so on. Companies whose businesses are seasonal have especially large changes in their bal- ance sheets. Allied’s inventories are low just before the harvest season, but

T H E BA L A N C E S H E E T

Retained Earnings That portion of the firm’s earnings that has been saved rather than paid out as dividends.

C H A P T E R 2 � F I N A N C I A L S TAT E M E N TS , C A S H F L O W, A N D TA X E S42

they are high just after the fall crops have been brought in and processed. Similarly, most retailers have large inventories just before Christmas but low inventories and high accounts receivable just after Christmas. There- fore, firms’ balance sheets change over the year, depending on when the statement is constructed.

SELF-TEST QUESTIONS

What is the balance sheet, and what information does it provide?

How is the order of the information shown on the balance sheet determined?

Why might a company’s December 31 balance sheet differ from its June 30 balance sheet?

T H E I N C O M E S TAT E M E N T

Table 2-2 gives the 2001 and 2000 income statements for Allied Food Prod- ucts. Net sales are shown at the top of each statement, after which various costs are subtracted to obtain the net income available to common shareholders, which is generally referred to as net income. These costs include operating costs, interest costs, and taxes. A report on earnings and dividends per share is given at the bottom of the income statement. Earnings per share (EPS) is called “the bottom line,” denoting that of all the items on the income statement, EPS is the most important. Allied earned $2.27 per share in 2001, down from $2.36 in 2000, but it still raised the dividend from $1.06 to $1.15.3

Taking a closer look at the income statement, we see that depreciation and amortization are important components of total operating costs. Depreciation and amortization are similar in that both represent allocations of the costs of assets over their useful lives; however, there are some important distinctions. Recall from accounting that depreciation is an annual charge against income that reflects the estimated dollar cost of the capital equipment used up in the production process. Depreciation applies to tangible assets, such as plant and equipment, whereas amortization applies to intangible assets such as patents, copyrights, trademarks, and goodwill. Some companies use amortization to write off research and development costs, or the accounting goodwill that is recorded when one firm purchases another for more than its book value. Since they are similar, depreciation and amortization are often lumped together on the income statement.

Managers, security analysts, and bank loan officers often calculate EBITDA, which is defined as earnings before interest, taxes, depreciation, and amorti-

3 Effective after December 15, 1997, companies must report “comprehensive income” as well as net income. Comprehensive income is equal to net income plus several comprehensive income items. One example of comprehensive income is the unrealized gain or loss that occurs when a marketable security, classified as available for sale, is marked-to-market. For our purposes, in this introductory finance text, we will assume that there are no comprehensive income items, so we will present only basic income statements throughout the text.

Income Statement A statement summarizing the firm’s revenues and expenses over an accounting period, generally a quarter or a year.

Depreciation The charge to reflect the cost of assets used up in the production process. Depreciation is not a cash outlay.

Tangible Assets Physical assets such as plant and equipment.

Amortization A noncash charge similar to depreciation except that it is used to write off the costs of intangible assets.

Intangible Assets Assets such as patents, copyrights, trademarks, and goodwill.

EBITDA Earnings before interest, taxes, depreciation, and amortization.

43

zation. Allied currently has no amortization charges, so the depreciation and amortization on its income statement comes solely from depreciation. In 2001, Allied’s EBITDA was $383.8 million. Subtracting the $100 million of de- preciation expense from its EBITDA leaves the company with $283.8 million in operating income (EBIT). After subtracting $88 million in interest expense

T H E I N C O M E S TAT E M E N T

T A B L E 2 - 2

2001 2000

Net sales $3,000.0 $2,850.0 Operating costs excluding depreciation and amortization 2,616.2 2,497.0 Earnings before interest, taxes, depreciation, and amortization (EBITDA) $ 383.8 $ 353.0 Depreciation 100.0 90.0 Amortization 0.0 0.0 Depreciation and amortization $ 100.0 $ 90.0 Earnings before interest and taxes (EBIT, or operating income) $ 283.8 $ 263.0

Less interest 88.0 60.0 Earnings before taxes (EBT) $ 195.8 $ 203.0

Taxes (40%) 78.3 81.2 Net income before preferred dividendsb $ 117.5 $ 121.8

Preferred dividends 4.0 4.0 Net income $ 113.5 $ 117.8 Common dividends $ 57.5 $ 53.0 Addition to retained earnings $ 56.0 $ 64.8 Per-share data:

Common stock price $23.00 $26.00 Earnings per share (EPS)a $ 2.27 $ 2.36 Dividends per share (DPS)a $ 1.15 $ 1.06 Book value per share (BVPS)a $17.92 $16.80 Cash flow per share (CFPS)a $ 4.27 $ 4.16

a There are 50,000,000 shares of common stock outstanding. Note that EPS is based on earnings after preferred dividends — that is, on net income available to common stockholders. Calculations of EPS, DPS, BVPS, and CFPS for 2001 are as follows:

b On a typical firm’s income statement, this line would be labeled “net income” rather than “net income before preferred dividends.” However, when we use the term net income in this text, we mean net income available to common shareholders. To simplify the terminology, we refer to net income available to common shareholders as simply net income. Students should understand that when they review annual reports, firms use the term net income to mean income after taxes but before preferred and common dividends.

Cash flow per share � CFPS � Net income � Depreciation � Amortization

Common shares outstanding �

$213,500,000 50,000,000

� $4.27.

Book value per share � BVPS � Total common equity

Common shares outstanding �

$896,000,000 50,000,000

� $17.92.

Dividends per share � DPS � Dividends paid to common stockholders

Common shares outstanding �

$57,500,000 50,000,000

� $1.15.

Earnings per share � EPS � Net income

Common shares outstanding �

$113,500,000 50,000,000

� $2.27.

Allied Food Products: Income Statements for Years Ending December 31 (Millions of Dollars, Except for Per-Share Data)

C H A P T E R 2 � F I N A N C I A L S TAT E M E N TS , C A S H F L O W, A N D TA X E S44

and $78.3 million in taxes, we obtain net income before preferred dividends of $117.5 million. Finally, we subtract out $4 million in preferred dividends, which leaves Allied with $113.5 million in net income available to common stockholders. When analysts refer to a company’s net income, they generally mean net income available to common shareholders. Likewise, throughout this book unless otherwise indicated, net income means net income available to common stockholders.

While the balance sheet can be thought of as a snapshot in time, the in- come statement reports on operations over a period of time, for example, dur- ing the calendar year 2001. During 2001 Allied had sales of $3 billion, and its net income available to common stockholders was $113.5 million. Income statements can cover any period of time, but they are usually prepared monthly, quarterly, or annually. Of course, sales, costs, and profits will be larger the longer the reporting period, and the sum of the last 12 monthly (or 4 quarterly) income statements should equal the values shown on the annual income statement.

For planning and control purposes, management generally forecasts monthly (or perhaps quarterly) income statements, and it then compares actual results to the budgeted statements. If revenues are below and costs above the forecasted levels, then management should take corrective steps before the problem becomes too serious.

SELF-TEST QUESTIONS

What is an income statement, and what information does it provide?

Why is earnings per share called “the bottom line”?

Differentiate between amortization and depreciation.

What is EBITDA?

Regarding the time period reported, how does the income statement differ from the balance sheet?

S TAT E M E N T O F R E TA I N E D E A R N I N G S

Changes in retained earnings between balance sheet dates are reported in the statement of retained earnings. Table 2-3 shows that Allied earned $113.5 million during 2001, paid out $57.5 million in common dividends, and plowed $56 million back into the business. Thus, the balance sheet item “Retained earnings” increased from $710 million at the end of 2000 to $766 million at the end of 2001.

Note that “Retained earnings” represents a claim against assets, not assets per se. Moreover, firms retain earnings primarily to expand the business, and this means investing in plant and equipment, in inventories, and so on, not pil- ing up cash in a bank account. Changes in retained earnings occur because

Statement of Retained Earnings A statement reporting how much of the firm’s earnings were retained in the business rather than paid out in dividends. The figure for retained earnings that appears here is the sum of the annual retained earnings for each year of the firm’s history.

45S TAT E M E N T O F R E TA I N E D E A R N I N G S

T A B L E 2 - 3

Balance of retained earnings, December 31, 2000 $710.0 Add: Net income, 2001 113.5 Less: Dividends to common stockholders (57.5)a

Balance of retained earnings, December 31, 2001 $766.0

aHere, and throughout the book, parentheses are used to denote negative numbers.

Allied Food Products: Statement of Retained Earnings for Year Ending December 31, 2001 (Millions of Dollars)

FINANCIAL ANALYSIS ON THE INTERNET

Awide range of valuable financial information is available onthe Internet. With just a couple of clicks, an investor can easily find the key financial statements for most publicly traded companies.

Say, for example, you are thinking about buying Disney stock, and you are looking for financial information regarding the company’s recent performance. Here’s a partial (but by no means a complete) list of places you can go to get started:

� One source is Yahoo’s finance web site, finance.yahoo. com.a Here you will find updated market information along with links to a variety of interesting research sites. Enter a stock’s ticker symbol, click on Get Quotes, and you will see the stock’s current price, along with recent news about the company. Click on Profile (under More Info) and you will find a report on the company’s key fi- nancial ratios. Links to the company’s income statement, balance sheet, and statement of cash flows can also be found. The Yahoo site also has a list of insider transac- tions, so you can tell if a company’s CEO and other key insiders are buying or selling their company’s stock. In addition, there is a message board where investors share opinions about the company, and there is a link to the company’s filings with the Securities and Exchange Com- mission (SEC). Note that, in most cases, a more complete list of the SEC filings can be found at www.sec.gov or at www.edgar-online.com.

� Other sources for up-to-date market information are cnnfn.com and cbs.marketwatch.com. Each also has an area where you can obtain stock quotes along with com- pany financials, links to Wall Street research, and links to SEC filings.

� Another good source is www.quicken.com. Enter the ticker symbol in the area labeled quotes and research. The site will take you to an area where you can find a link to the company’s financial statements, along with analysts’ earnings estimates and SEC filings. This site also has a section where you can estimate the stock’s intrinsic value. (In Chapter 9 we will discuss various methods for calculating intrinsic value.)

� If you are looking for charts of key accounting variables (for example, sales, inventory, depreciation and amortiza- tion, and reported earnings), along with the financial statements, take a look at www.smartmoney.com.

� Another good place to look is www.marketguide.com. Here you find links to analysts’ research reports along with the key financial statements.

� Two other places to consider: www.hoovers.com and my.zacks.com. Each has free research available along with more detailed information provided to subscribers.

Once you have accumulated all of this information, you may be looking for sites that provide opinions regarding the direc- tion of the overall market and views regarding individual stocks. Two popular sites in this category are The Motley Fool’s web site, www.fool.com, and the web site for The Street.com, www.thestreet.com.

Keep in mind that this list is just a small subset of the in- formation available online. You should also realize that a lot of these sites change their content over time, and new and inter- esting sites are always being added to the Internet.

aTo avoid redundancy, we have intentionally left off http:// in all web addresses given here. A quick way to change an address is to highlight the portion of the address that is different and type in the appropriate letters of the new address. Once you’re finished just press Enter.

ANALYSTS ARE INCREASINGLY RELYING ON CASH FLOW TO VALUE STOCKS

C H A P T E R 2 � F I N A N C I A L S TAT E M E N TS , C A S H F L O W, A N D TA X E S46

common stockholders allow the firm to reinvest funds that otherwise could be distributed as dividends. Thus, retained earnings as reported on the balance sheet do not represent cash and are not “available” for the payment of dividends or any- thing else.4

4 The amount reported in the retained earnings account is not an indication of the amount of cash the firm has. Cash (as of the balance sheet date) is found in the cash account, an asset account. A positive number in the retained earnings account indicates only that in the past the firm has earned some income, but its dividends have been less than its earnings. Even though a company reports record earnings and shows an increase in the retained earnings account, it still may be short of cash.

The same situation holds for individuals. You might own a new BMW (no loan), lots of clothes, and an expensive stereo, hence have a high net worth, but if you had only 23 cents in your pocket plus $5 in your checking account, you would still be short of cash.

Tokyo-based Softbank recently acquired several Internet-related businesses, including Ziff-Davis Inc., which publishes more than 80 magazines including PC Week and PC Magazine. Ziff-Davis also provides training courses in computer technol- ogy, and it distributes information through the Internet and computer trade shows.

In an article on Softbank, Barron’s indicated that Ziff-Davis has been “losing money,” and a quick look at the company’s re- cent income statements confirms that it had losses in 1998 and the first quarter of 1999. Despite the company’s negative re- ported earnings, the company’s chief financial officer, Timothy O’Brien, took exception with the notion that Ziff-Davis was “losing money.” So, he sent Barron’s the following response:

To the Editor:

In his discussion of Softbank, Neil Martin (International Trader, June 14) referred to Ziff-Davis as “losing money.” In fact, Ziff-Davis continues to generate significant positive cash flow.

We are a diversified media company. Analysts measure our strength and stability relative to our ability to generate EBITDA (earnings before interest, taxes, depreciation, and amortization). Analysts project that we will generate EBITDA of approximately $220 million in 1999, and that takes into account our substantial investment in ZDTV, the company’s 24-hour cable network devoted to computing and the Internet.

Ziff-Davis did report a net loss for 1998 and for the first quarter of 1999. However, this loss was due to noncash ex-

penses, primarily the amortization of approximately $120 million in goodwill per year. Even with continuing invest- ments in our key businesses, Ziff-Davis has the financial flexibility to continue to repay indebtedness with free cash flow.

Timothy C. O’Brien, Chief Financial Officer, Ziff-Davis

Cash-flow measures such as EBITDA have long been popular with bankers and other short-term lenders, who focus more on borrowers’ ability to generate cash to pay off loans than on ac- counting earnings. In the past, these measures were less popu- lar with stock analysts, who focused on reported earnings and price earnings ratios. However, today more and more Wall Street analysts are siding with Tim O’Brien, arguing that cash flow measures such as EBITDA often provide a better indication of true value than do earnings per share.

These analysts note that the DA part of EBITDA reduces re- ported profits but not cash, so EBITDA reflects the cash avail- able to a firm better than accounting profits. It is logical that credit analysts interested in a company’s ability to repay its loans focus heavily on EBITDA, but what about equity analysts, who are seeking to find a firm’s value to its stockholders? First, most analysts agree that a firm’s value depends on its ability to generate cash flows over the long run. If depreciation and amortization (DA) charges truly reflect a decline in the assets used to produce cash flows, then the DA will have to be rein- vested in the business if cash flows are to continue. The DA may reflect “available cash” in the short run, but it is not truly

47S TAT E M E N T O F R E TA I N E D E A R N I N G S

available to investors because it will have to be reinvested if the business is to continue to operate.

So, analysts must consider the nature of the D and A charges. If depreciation is related to essential assets, as it usu- ally is, then it is a cost that should be deducted to get an idea of the firm’s long-run cash generating potential. Amortization is analyzed similarly, but here there is more ambiguity, because amortization is related to two primary types of write-offs: (1) amortization of research and development costs associated with products such as airplanes, computers, software, and pharma- ceutical drugs, and (2) amortization of merger-related goodwill, which reflects the difference between the price a company pays when it acquires another company and the book value of the acquired company. Both types of amortization can be huge, so there can be huge differences between EBIT and EBITDA.

The key question then becomes, “Will the company be re- quired to reinvest the cash flow reflected in the DA part of EBITDA if it is to continue to generate cash flow on into the fu- ture?” If the answer is yes, then the DA component is not “free cash flow” that is available to investors, and it should be de- ducted when determining the firm’s long-run earning power. If the answer is no, then DA does represent free cash flow and is available to investors.

The situation where all this is most important is when merg- ers occur and large amounts of goodwill are created. Consider two examples. First, suppose Microsoft acquires a small software company whose owner developed and patented a new type of mouse. Microsoft paid $3.1 million for the company, whose book value was $100,000, so $3 million of goodwill was cre-

ated. The mouse will help Microsoft for three years, after which it will be obsolete. Here it would be appropriate for Microsoft to amortize the goodwill at the rate of $1 million per year; this $1 million would need to be reinvested to maintain Microsoft’s cash flow, and this $1 million of its EBITDA would not represent long-run earning potential.

Now consider the case of Softbank’s acquisition of Ziff- Davis. Softbank paid far more for Ziff-Davis than Ziff-Davis’ ac- counting value as reflected on its balance sheet, and that dif- ference was recorded as goodwill. Softbank paid the high price because Ziff-Davis was earning an abnormally high rate of re- turn on its book assets, and it was expected to earn high re- turns on into the future because it had created a niche in the publishing industry that would be hard for a new competitor to overcome. Here, because the above-normal earning power is likely to be sustained over time, EBITDA is more reflective of long-run cash flow potential than is accounting profit.

Amortization will be high in an industry if patents are im- portant, as is the case in the pharmaceutical industry, or if mergers are producing a lot of goodwill, as has been the case with high-tech and financial services firms. This was spelled out in a recent “Heard on the Street” column in The Wall Street Journal, which noted that cash flow valuations are now in vogue in the cable, high-tech, Internet, pharmaceutical, and fi- nancial services sectors.

SOURCES: Barron’s, July 19, 1999, 54; and “Analysts Increasingly Favor Using Cash Flow Over Reported Earnings in Stock Valuations,” Heard on The Street, The Wall Street Journal, April 1, 1999, C2.

SELF-TEST QUESTIONS

What is the statement of retained earnings, and what information does it provide?

Why do changes in retained earnings occur?

Explain why the following statement is true: “Retained earnings as reported on the balance sheet do not represent cash and are not ‘available’ for the payment of dividends or anything else.”

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N E T C A S H F L OW

When you studied income statements in accounting, the emphasis was proba- bly on the firm’s net income. In finance, however, we focus on net cash flow. The value of an asset (or a whole firm) is determined by the cash flow it gen- erates. The firm’s net income is important, but cash flow is even more impor- tant because dividends must be paid in cash and because cash is necessary to purchase the assets required to continue operations.

As we discussed in Chapter 1, the firm’s goal should be to maximize its stock price. Since the value of any asset, including a share of stock, depends on the cash flow produced by the asset, managers should strive to maximize the cash flow available to investors over the long run. A business’s net cash flow generally differs from its accounting profit because some of the revenues and expenses listed on the income statement were not paid in cash during the year. The re- lationship between net cash flow and net income can be expressed as follows:

Net cash flow � Net income � Noncash revenues � Noncash charges. (2-1)

The primary examples of noncash charges are depreciation and amortization. These items reduce net income but are not paid out in cash, so we add them back to net income when calculating net cash flow. Another example of a non- cash charge is deferred taxes. In some instances, companies are allowed to defer tax payments to a later date even though the tax payment is reported as an ex- pense on the income statement. Therefore, deferred tax payments would be added to net income when calculating net cash flow.5 At the same time, some revenues may not be collected in cash during the year, and these items must be subtracted from net income when calculating net cash flow.

Typically, depreciation and amortization are by far the largest noncash items, and in many cases the other noncash items roughly net out to zero. For this reason, many analysts assume that net cash flow equals net income plus depre- ciation and amortization:

Net cash flow � Net income � Depreciation and amortization. (2-2)

To keep things simple, we will generally assume Equation 2-2 holds. However, you should remember that Equation 2-2 will not accurately reflect net cash flow in those instances where there are significant noncash items beyond de- preciation and amortization.

We can illustrate Equation 2-2 with 2001 data for Allied taken from Table 2-2:

Net cash flow � $113.5 � $100.0 � $213.5 million.

To illustrate depreciation itself, suppose a machine with a life of five years and a zero expected salvage value was purchased in 2000 for $100,000 and placed into service in 2001. This $100,000 cost is not expensed in the purchase year; rather, it is charged against production over the machine’s five-year de- preciable life. If the depreciation expense were not taken, profits would be overstated, and taxes would be too high. So, the annual depreciation charge is deducted from sales revenues, along with such other costs as labor and raw ma-

Net Cash Flow The actual net cash, as opposed to accounting net income, that a firm generates during some specified period.

Accounting Profit A firm’s net income as reported on its income statement.

5 Deferred taxes may arise, for example, if a company uses accelerated depreciation for tax purposes but straight-line depreciation for reporting its financial statements to investors.

IN VALUING STOCKS, IS IT EARNINGS OR CASH FLOW THAT MATTERS?

49

terials, to determine income. However, because the $100,000 was actually ex- pended back in 2000, the depreciation charged against income in 2001 and subsequent years is not a cash outlay, as are labor or raw materials charges. De- preciation is a noncash charge, so it must be added back to net income to obtain the net cash flow. If we assume that all other noncash items (including amortization) sum to zero, then net cash flow is simply equal to net income plus depreciation.

S TAT E M E N T O F C A S H F L OW S

When it comes to valuing a company’s stock, what’s moreimportant: cash flow or earnings? Analysts often disagree, and the measure used often depends on the industry. For ex- ample, analysts have traditionally emphasized cash flow rather than earnings when valuing cable stocks. This distinction has been important because, traditionally, cable companies have had to make large capital expenditures. These expenditures generate large depreciation expenses, which depress reported earnings. However, since depreciation is a noncash expense, cable companies often continue to show strong cash flows, even when earnings are declining or even negative.

For example, in recent years leading cable companies such as Tele-Communications Inc., Cox Communications, and Comcast Corporation have all reported low or negative earnings. Never- theless, over the past five years cable stocks have outperformed the overall market, generating an average annual return in ex- cess of 30 percent. One reason for this strong performance is that each of these companies has generated a strong cash flow.

Besides their growth in cash flow, there are at least two other reasons cable stocks have performed so well despite weak earnings. First, many believe that the cable companies will be-

come the dominant providers of Internet service, which if true will lead to much higher growth in the future. Second, in recent years cable companies have become acquisition targets. For ex- ample, AT&T recently acquired cable giant Tele-Communications Inc. and Media One. This takeover activity has helped bid up the prices of all cable stocks.

To be sure, many analysts take a more sanguine view of the cable industry’s future prospects. Cable companies continue to face increased competition from digital satellite companies, and other technologies are emerging to compete with cable for providing high-speed Internet access. Finally, despite their growth potential, it is clear that to compete in the years ahead the cable companies will have to continue making large capital expenditures. As a result, much of the cash flow will not be available to pay dividends to shareholders — rather, it will be required for investments that are necessary to maintain existing revenues. So, while cash flow will probably continue to be an important determinant of cable stock values, more and more analysts are insisting that these companies must also begin to generate positive earnings.

SELF-TEST QUESTIONS

Differentiate between net cash flow and accounting profit.

In accounting, the emphasis is on net income. What is emphasized in fi- nance, and why is that item emphasized?

Assuming that depreciation is its only noncash cost, how can someone cal- culate a business’s cash flow?

S TAT E M E N T O F C A S H F L OW S

Net cash flow represents the amount of cash a business generates for its share- holders in a given year. However, the fact that a company generates high cash

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flow does not necessarily mean that the amount of cash reported on its balance sheet will also be high. The cash flow may be used in a variety of ways. For ex- ample, the firm may use its cash flow to pay dividends, to increase inventories, to finance accounts receivable, to invest in fixed assets, to reduce debt, or to buy back common stock. Indeed, the company’s cash position as reported on the balance sheet is affected by a great many factors, including the following:

1. Cash flow. Other things held constant, a positive net cash flow will lead to more cash in the bank. However, as we discuss below, other things are generally not held constant.

2. Changes in working capital. Net working capital, which is discussed in detail in Chapter 15, is defined as current assets minus current liabilities. Increases in current assets other than cash, such as inventories and ac- counts receivable, decrease cash, whereas decreases in these accounts in- crease cash. For example, if inventories are to increase, the firm must use some of its cash to buy the additional inventory, whereas if inventories decrease, this generally means the firm is selling off inventories and not replacing them, hence generating cash. On the other hand, increases in current liabilities such as accounts payable increase cash, whereas de- creases in these accounts decrease it. For example, if payables increase, the firm has received additional credit from its suppliers, which saves cash, but if payables decrease, this means the firm has used cash to pay off its suppliers.

3. Fixed assets. If a company invests in fixed assets, this will reduce its cash position. On the other hand, the sale of fixed assets will increase cash.

4. Security transactions. If a company issues stock or bonds during the year, the funds raised will enhance its cash position. On the other hand, if it uses cash to buy back outstanding debt or equity, or pays dividends to its shareholders, this will reduce cash.

Each of the above factors is reflected in the statement of cash flows, which summarizes the changes in a company’s cash position. The statement separates activities into three categories:

1. Operating activities, which includes net income, depreciation, and changes in current assets and current liabilities other than cash and short-term debt.

2. Investing activities, which includes investments in or sales of fixed assets. 3. Financing activities, which includes cash raised during the year by issuing

short-term debt, long-term debt, or stock. Also, since dividends paid or cash used to buy back outstanding stock or bonds reduces the company’s cash, such transactions are included here.

Accounting texts explain how to prepare the statement of cash flows, but the statement is used to help answer questions such as these: Is the firm gen- erating enough cash to purchase the additional assets required for growth? Is the firm generating any extra cash that can be used to repay debt or to invest in new products? Will inadequate cash flows force the company to issue more stock? Such information is useful both for managers and investors, so the statement of cash flows is an important part of the annual report. Financial

Statement of Cash Flows A statement reporting the impact of a firm’s operating, investing, and financing activities on cash flows over an accounting period.

51

managers generally use this statement, along with the cash budget, when fore- casting their companies’ cash positions. This issue is considered in more detail in Chapter 15.

Table 2-4 is Allied’s statement of cash flows as it would appear in the com- pany’s annual report. The top part of the table shows cash flows generated by and used in operations — for Allied, operations provided net cash flows of minus $2.5 million. The operating cash flows are generated in the normal course of business, and this amount is determined by adjusting the net income figure to account for depreciation and amortization plus other cash flows re- lated to operations. Allied’s day-to-day operations in 2001 provided $257.5 mil- lion; however, the increase in receivables and inventories more than offset this amount, resulting in a negative $2.5 million cash flow from operations.

The second section shows long-term fixed-assets investing activities. Allied purchased fixed assets totaling $230 million; this was the only long-term in- vestment it made during 2001.

S TAT E M E N T O F C A S H F L OW S

T A B L E 2 - 4

OPERATING ACTIVITIES

Net income before preferred dividends $117.5 Additions (Sources of Cash)

Depreciation and amortizationa 100.0 Increase in accounts payable 30.0 Increase in accruals 10.0

Subtractions (Uses of Cash)

Increase in accounts receivable (60.0) Increase in inventories (200.0)

Net cash provided by operating activities ($ 2.5) LONG-TERM INVESTING ACTIVITIES

Cash used to acquire fixed assetsb ($230.0) FINANCING ACTIVITIES

Increase in notes payable $ 50.0 Increase in bonds 174.0 Payment of common and preferred dividends (61.5)

Net cash provided by financing activities $162.5 Net decrease in cash and marketable securities ($ 70.0) Cash and securities at beginning of year 80.0 Cash and securities at end of year $ 10.0

aDepreciation and amortization are noncash expenses that were deducted when calculating net income. They must be added back to show the actual cash flow from operations. bThe net increase in fixed assets is $130 million; however, this net amount is after deducting the year’s depreciation expense. Depreciation expense must be added back to find the actual expenditures on fixed assets. From the company’s income statement, we see that the 2001 depreciation expense is $100 million; thus, expenditures on fixed assets were actually $230 million.

Allied Food Products: Statement of Cash Flows for 2001 (Millions of Dollars)

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Allied’s financing activities, shown in the third section, include borrowing from banks (notes payable), selling new bonds, and paying dividends on its common and preferred stock. Allied raised $224 million by borrowing, but it paid $61.5 million in preferred and common dividends, so its net inflow of funds from financing activities was $162.5 million.

When all of the sources and uses of cash are totaled, we see that Allied’s cash outflows exceeded its cash inflows by $70 million during 2001. It met that shortfall by drawing down its cash and marketable securities holdings by $70 million, as confirmed by Table 2-1, the firm’s balance sheet.

Allied’s statement of cash flows should be worrisome to its managers and to outside analysts. The company had a $2.5 million cash shortfall from opera- tions, it spent $230 million on new fixed assets, and it paid out another $61.5 million in dividends. It covered these cash outlays by borrowing heavily and by selling off most of its marketable securities. Obviously, this situation cannot continue year after year, so something will have to be done. In Chapter 3, we will consider some of the actions Allied’s financial staff might recommend to ease the cash flow problem.

SELF-TEST QUESTIONS

What is the statement of cash flows, and what types of questions does it answer?

Identify and briefly explain the three different categories of activities shown in the statement of cash flows.

M O D I F Y I N G AC C O U N T I N G DATA F O R M A N AG E R I A L D E C I S I O N S

Thus far in the chapter we have focused on financial statements as they are pre- pared by accountants and presented in the annual report. However, these state- ments are designed more for use by creditors and tax collectors than for man- agers and equity (stock) analysts. Therefore, certain modifications are used for corporate decision making and stock valuation purposes. In the following sec- tions we discuss how financial analysts combine stock prices and accounting data to evaluate and reward managerial performance.

OPERAT ING ASSETS AND OPERAT ING CAPITAL

Different firms have different financial structures, different tax situations, and different amounts of nonoperating assets. These differences affect traditional accounting measures such as the rate of return on equity. They can cause two firms, or two divisions within a single firm, that actually have similar operations to appear to be operated with different efficiency. This is important, because if managerial compensation systems are to function properly, operating managers must be judged and compensated for those things that are under their control,

53

not on the basis of things outside their control. Therefore, to judge managerial performance, we need to compare managers’ ability to generate operating income (or EBIT) with the operating assets under their control.

The first step in modifying the traditional accounting framework is to divide total assets into two categories, operating assets, which consist of the cash and marketable securities, accounts receivable, inventories, and fixed assets necessary to operate the business, and nonoperating assets, which would include cash and marketable securities above the level required for normal operations, in- vestments in subsidiaries, land held for future use, and the like. Moreover, oper- ating assets are further divided into working capital and fixed assets such as plant and equipment. Obviously, if a manager can generate a given amount of profits and cash flows with a relatively small investment in operating assets, that reduces the amount of capital investors must put up and thus increases the rate of return on that capital.

The primary source of capital for business is investors — stockholders, bond- holders, and lenders such as banks. Investors must be paid for the use of their money, with payment coming as interest in the case of debt and as dividends plus capital gains in the case of stock. So, if a company acquires more assets than it actually needs, and thus raises too much capital, then its capital costs will be unnecessarily high.

Must all of the capital used to acquire assets be obtained from investors? The answer is no, because some of the funds will come from suppliers and be reported as accounts payable, while other funds will come as accrued wages and ac- crued taxes, which amount to short-term loans from workers and tax authorities. Generally, both accounts payable and accruals are “free” in the sense that no explicit fee is charged for their use. Therefore, if a firm needs $100 million of current assets, but it has $10 million of accounts payable and another $10 mil- lion of accrued wages and taxes, then its investor-supplied capital would be only $80 million.

Those current assets used in operations are called operating working cap- ital, and operating working capital less accounts payable and accruals is called net operating working capital. Therefore, net operating working capital is the working capital acquired with investor-supplied funds.6 Here is a workable definition in equation form:

(2-3)Net operating working capital � All current assets � All current

liabilities that do not charge interest

.

M O D I F Y I N G AC C O U N T I N G DATA F O R M A N AG E R I A L D E C I S I O N S

Operating Assets The cash and marketable securities, accounts receivable, inventories, and fixed assets necessary to operate the business.

Nonoperating Assets Cash and marketable securities above the level required for normal operations, investments in subsidiaries, land held for future use, and other nonessential assets.

Operating Working Capital Current assets used in operations.

Net Operating Working Capital Operating working capital less accounts payable and accruals. It is the working capital acquired with investor-supplied funds.

6 Note that the term “capital” can be given two meanings. First, when accountants use the term “capital,” they typically mean the sum of long-term debt, preferred stock, and common equity, or perhaps those items plus interest-bearing short-term debt. However, when economists use the term, they generally mean assets used in production, as in “labor plus capital.” If all funds were raised from long-term sources, and if all assets were operating assets, then money capital would equal operating assets, and the accountants’ capital would always equal the economists’ capital. When you encounter the term “capital” in the business and financial literature, it can mean either asset capital or money capital. For example, in Coca-Cola’s operating manuals, which explain to its employees how Coke wants the company to be operated, capital means “assets financed by investor- supplied capital.” However, in most accounting and finance textbooks, and in the traditional finance literature, “capital” means investor-supplied capital, not assets. It might be easier if we picked one meaning and then used it consistently in this book. However, that would be misleading, because both meanings are encountered in practice. Therefore, we shall use the term “capital” in both ways. However, you should be able to figure out which definition is implied from the context in which the term is used.

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Now think about how these concepts can be used in practice. First, all companies must carry some cash to “grease the wheels” of their operations. Companies continuously cash checks from customers and write checks to sup- pliers, employees, and so on. Because inflows and outflows do not coincide per- fectly, a company must keep some cash and marketable securities in its bank ac- count. In other words, some cash and marketable securities is required to conduct operations. The same is true for most other current assets, such as in- ventory and accounts receivable, which are required for normal operations. Our measure of operating working capital assumes that cash and marketable securi- ties on the balance sheet represent the amount that is required under normal operations. However, in some instances companies have large holdings of cash and marketable securities that they are holding as a reserve for some contin- gency, or as a “parking place” for funds prior to an acquisition, a major captial investment program, or the like. In such instances, the excess cash and mar- ketable securities should not be viewed as part of operating working capital.

Looking at the other side of the balance sheet, some current liabilities — es- pecially accounts payable and accruals — arise in the normal course of opera- tions. Moreover, each dollar of these current liabilities is a dollar that the com- pany does not have to raise from investors to acquire current assets. Therefore, when finding the net operating working capital, we deduct these current liabil- ities from the operating current assets. Other current liabilities that charge in- terest, such as notes payable to banks, are treated as investor-supplied capital and thus are not deducted when calculating net operating working capital.

We can apply these definitions to Allied, using the balance sheet data given back in Table 2-1. Here is the net operating working capital for 2001:

� ($10 � $375 � $615) � ($60 � $140)

� $800 million.

Allied’s total operating capital for 2001 was

(2-4)

Now note that Allied’s net operating working capital a year earlier, at year- end 2000, was

and, since it had $870 million of fixed assets, its total operating capital was

Therefore, Allied increased its operating capital from $1,520 to $1,800 million, or by $280 million, during 2001. Furthermore, most of this increase went into working capital, which rose by $150 million. This 23 percent increase in net operating working capital, when sales only rose 5 percent (from $2,850 to

� $1,520 million.

Total operating capital � $650 � $870

� $650 million,

Net operating working capital � ($80 � $315 � $415) � ($30 � $130)

� $1,800 million.

� $800 � $1,000

� Net fixed assets Total operating capital � Net operating working capital

Net operating working capital

� ° Cash andmarketable securities

� Accounts receivable � Inventories¢ � °Accountspayable � Accruals¢

55

$3,000 million), should set off warning bells in your head: What caused Allied to tie up so much additional cash in working capital? Are inventories not mov- ing? Are receivables not being collected and thus building up? We will address these questions in detail later in the chapter.

NET OPERAT ING PROFIT AFTER TAXES (NOPAT)

If two companies have different amounts of debt, hence different interest charges, they could have identical operating performances but different net in- comes — the one with more debt would have a lower net income. Net income is certainly important, but as the example below shows, net income does not al- ways reflect the true performance of a company’s operations or the effectiveness of its operating managers and employees. A better measurement for comparing managers’ performance is net operating profit after taxes, or NOPAT, which is the amount of profit a company would generate if it had no debt and held no nonoperating assets. NOPAT is defined as follows:7

(2-5)

Using data from the income statement in Table 2-2, Allied’s 2001 NOPAT was

Thus, Allied generated an after-tax profit of $170.3 million from its operations. This was a little better than the 2000 NOPAT of $263(0.6) � $157.8 million. However, the income statements in Table 2-2 show that Allied’s earnings per share declined from 2000 to 2001. This decrease in EPS was caused by an in- crease in interest expense, not by a decrease in operating profit. See Table 2-2. Moreover, the balance sheets in Table 2-1 show that debt increased from 2000 to 2001. But why did Allied increase its debt? The reason was that Allied’s in- vestment in operating capital increased dramatically from 2000 to 2001, and that increase was financed primarily with debt.

FREE CASH FLOW

Earlier in the chapter we defined net cash flow as being equal to net income plus noncash adjustments, typically net income plus depreciation and amortiza- tion. Note, though, that cash flows cannot be maintained over time unless de- preciating fixed assets are replaced and new products are developed, so man- agement is not completely free to use cash flows however it chooses. Therefore, we now define another term, free cash flow, which is the cash flow actually available for distribution to all investors (stockholders and debtholders) after the company has made all the investments in fixed assets, new products, and working cap- ital necessary to sustain ongoing operations.

NOPAT � $283.8(1 � 0.4) � $283.8(0.6) � $170.3 million.

NOPAT � EBIT(1 � Tax rate).

M O D I F Y I N G AC C O U N T I N G DATA F O R M A N AG E R I A L D E C I S I O N S

Net Operating Profit After Taxes (NOPAT) The profit a company would generate if it had no debt and held no nonoperating assets.

7 For firms with a more complicated tax situation, it is better to define NOPAT as follows: NOPAT � (Net income before preferred dividends) � (Net interest expense)(1 � Tax rate). Also, if firms are able to defer paying some of their taxes, perhaps by the use of accelerated depreciation, then NOPAT should be adjusted to reflect the taxes that the company actually paid on its operating in- come. For additional information see Tom Copeland, Tim Koller, and Jack Murrin, Valuation: Mea- suring and Managing the Value of Companies, 3rd edition (New York: John Wiley & Sons, Inc., 2000); and G. Bennett Stewart III, The Quest for Value (New York: HarperCollins Publishers, Inc., 1991).

Free Cash Flow The cash flow actually available for distribution to all investors (stockholders and debtholders) after the company has made all the investments in fixed assets, new products, and working capital necessary to sustain ongoing operations.

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When you studied income statements in accounting, the emphasis probably was on the firm’s net income, which is its accounting profit. However, we began this chapter by telling you that the value of a company’s operations is deter- mined by the stream of cash flows that the operations will generate now and in the future. As the statement of cash flows shows, accounting profit and cash flow can be quite different.

To be more specific, the value of a company’s operations depends on all the future expected free cash flows (FCF), defined as after-tax operating profit minus the amount of investment in working capital and fixed assets necessary to sustain the business. Thus, free cash flow represents the cash that is actually available for distribution to investors. Therefore, the way for managers to make their companies more valuable is to increase their free cash flow.

CALCULAT ING FREE CASH FLOW

As shown earlier in the chapter, Allied had a 2001 NOPAT of $170.3 million. Its operating cash flow is NOPAT plus any noncash adjustments as shown on the statement of cash flows. For Allied, where depreciation is the only noncash charge, the 2001 operating cash flow is8

Operating cash flow � NOPAT � Depreciation (2-6)

� $170.3 � $100

� $270.3 million.

Please note that this definition of operating cash flow is calculated on an after- tax basis. As shown earlier in the chapter, Allied had $1,520 million of operating assets, or operating capital, at the end of 2000, but $1,800 million at the end of 2001. Therefore, during 2001 it made a net investment in operating capital of

Net investment in operating capital � $1,800 � $1,520 � $280 million.

Fixed assets rose from $870 to $1,000 million, or by $130 million. However, Allied took $100 million of depreciation, so its gross investment in fixed assets was $130 � $100 � $230 million for the year. With this background, we find the gross investment in operating capital as follows:

Gross investment � Net investment � Depreciation

� $280 � $100 � $380 million.

Allied’s free cash flow in 2001 was

FCF � Operating cash flow � Gross investment in operating capital (2-7)

� $270.3 � $380

� �$109.7 million.

Operating Cash Flow Equal to NOPAT plus any noncash adjustments, calculated on an after-tax basis.

8 In those instances in which operating costs include an amortization expense, operating cash flow would also need to include an adjustment for the amortization charge. However, in practice, only a small percentage of firms report amortization expenses on their income statements. Moreover, the accounting and tax treatments of amortization charges are often quite complex. For these rea- sons, we have chosen to disregard amortization expenses when calculating operating cash flow and free cash flow. See Copeland, Koller, and Murrin, Valuation: Measuring and Managing the Value of Companies, for a more detailed discussion of how to incorporate amortization expenses into the calculation of free cash flow.

57

If we subtract depreciation from both operating cash flow and gross investment in operating capital in Equation 2-7, we obtain the following algebraically equivalent expression for free cash flow:

FCF � NOPAT � Net investment in operating capital (2-7a)

� $170.3 � $280

� �$109.7 million.

Even though Allied had a positive NOPAT, its very high investment in op- erating capital resulted in a negative free cash flow. Since free cash flow is what is available for distribution to investors, not only was there nothing for in- vestors, but investors actually had to provide more money to Allied to keep the business going. Investors provided most of the required new money as debt.

Is a negative free cash flow always bad? The answer is, “Not necessarily. It depends on why the free cash flow was negative.” If FCF was negative because NOPAT was negative, this is bad, because the company is probably experienc- ing operating problems. Exceptions to this might be startup companies, or companies that are incurring significant current expenses to launch a new product line. Also, many high-growth companies have positive NOPAT but negative free cash flow due to investments in operating assets needed to sup- port growth. There is nothing wrong with profitable growth, even if it causes negative cash flows in the short term.

M VA A N D E VA

SELF-TEST QUESTIONS

What is net operating working capital?

What is total operating capital?

What is NOPAT? Why might it be a better performance measure than net in- come?

What is free cash flow? Why is free cash flow the most important determi- nant of a firm’s value?

M VA A N D E VA

Neither traditional accounting data nor the modified data discussed in the pre- ceding section bring in stock prices. Since the primary goal of management is to maximize the firm’s stock price, we need to bring stock prices into the pic- ture. Financial analysts have therefore developed two new performance mea- sures, MVA, or Market Value Added, and EVA, or Economic Value Added. These concepts are discussed in this section.9

9 The concepts of EVA and MVA were developed by Joel Stern and Bennett Stewart, co-founders of the consulting firm Stern Stewart & Company. Stern Stewart copyrighted the terms “EVA” and “MVA,” so other consulting firms have given other names to these values. Still, EVA and MVA are the terms most commonly used in practice.

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MARKET VALUE ADDED (MVA)

The primary goal of most firms is to maximize shareholders’ wealth. This goal obviously benefits shareholders, but it also helps to ensure that scarce resources are allocated efficiently, which benefits the economy. Shareholder wealth is maximized by maximizing the difference between the market value of the firm’s stock and the amount of equity capital that was supplied by share- holders. This difference is called the Market Value Added (MVA):

MVA � Market value of stock � Equity capital supplied by shareholders

� (Shares outstanding)(Stock price) � Total common equity. (2-8) To illustrate, consider our illustrative company, Allied Food Products. In

2001, its total market equity value was $1,150 million, while its balance sheet showed that stockholders had put up only $896 million. Thus, Allied’s MVA was $1,150 � $896 � $254 million. This $254 million represents the difference between the money that Allied’s stockholders have invested in the corporation since its founding — including retained earnings — versus the cash they could get if they sold the business. The higher its MVA, the better the job manage- ment is doing for the firm’s shareholders.

ECONOMIC VALUE ADDED (EVA)

Whereas MVA measures the effects of managerial actions since the very incep- tion of a company, Economic Value Added (EVA) focuses on managerial ef- fectiveness in a given year. The basic formula for EVA is as follows:

EVA � Net operating profit after taxes, or NOPAT � After-tax dollar cost of capital used to support operations

� EBIT(1 � Corporate tax rate) � (Total investor-supplied operating capital)(After-tax percentage cost of capital). (2-9)

Total investor-supplied operating capital is the sum of the interest-bearing debt, preferred stock, and common equity used to acquire the company’s net operat- ing assets, that is, its net operating working capital plus net plant and equipment.

EVA is an estimate of a business’s true economic profit for the year, and it dif- fers sharply from accounting profit.10 EVA represents the residual income that re- mains after the cost of all capital, including equity capital, has been deducted, whereas accounting profit is determined without imposing a charge for equity capital. As we will discuss more completely in Chapter 10, equity capital has a cost, because funds provided by shareholders could have been invested elsewhere where they would have earned a return. Shareholders give up the opportunity to invest funds elsewhere when they provide capital to the firm. The return they could earn elsewhere in investments of equal risk represents the cost of equity cap- ital. This cost is an opportunity cost rather than an accounting cost, but it is quite real nevertheless.

Note that when calculating EVA we do not add back depreciation. Although it is not a cash expense, depreciation is a cost, and it is therefore deducted when

Economic Value Added (EVA) Value added to shareholders by management during a given year.

If you want to read more about EVA and MVA, surf over to http:// www.sternstewart.com and hear about it from the

people that invented it, Stern Stewart & Co. While you are there, you may like to take a look at a video of executives describing how EVA has helped them, which can be found at http:// www.sternstewart.com/evaabout/ comments.shtml. To see the video, you will need Real Player, which can be downloaded for free from http:// www.realplayer.com.

10 The most important reason EVA differs from accounting profit is that the cost of equity capital is deducted when EVA is calculated. Other factors that could lead to differences include adjust- ments that might be made to depreciation, to research and development costs, to inventory valua- tions, and so on. See Stewart, The Quest for Value.

Market Value Added (MVA) The difference between the market value of the firm’s stock and the amount of equity capital investors have supplied.

59

determining both net income and EVA. Our calculation of EVA assumes that the true economic depreciation of the company’s fixed assets exactly equals the depreciation used for accounting and tax purposes. If this were not the case, ad- justments would have to be made to obtain a more accurate measure of EVA.

EVA provides a good measure of the extent to which the firm has added to shareholder value. Therefore, if managers focus on EVA, this will help to ensure that they operate in a manner that is consistent with maximizing shareholder wealth. Note too that EVA can be determined for divisions as well as for the com- pany as a whole, so it provides a useful basis for determining managerial compen- sation at all levels. As a result of all this, EVA is being used by an increasing num- ber of firms as the primary basis for determining managerial compensation.

Table 2-5 shows how Allied’s MVA and EVA are calculated. The stock price was $23 per share at year-end 2001, down from $26 per share at the end of 2000; its percentage after-tax cost of capital was 10.3 percent in 2000 and 10.0 percent in 2001, and its tax rate was 40 percent. Other data in Table 2-5 were given in the basic financial statements provided earlier in the chapter.

Note first that the lower stock price and the higher book value of equity (due to retaining earnings during 2001) combined to reduce the MVA. The 2001 MVA is still positive, but $460 � $254 � $206 million of stockholders’ value was lost during 2001.

EVA for 2000 was just barely positive, and in 2001 it was negative. Operat- ing income (NOPAT) rose, but EVA still declined, primarily because the amount of capital rose more sharply than NOPAT — by about 18 percent ver- sus 8 percent — and the cost of this increased capital pulled EVA down.

Recall also that net income fell somewhat from 2000 to 2001, but not nearly so dramatically as the decline in EVA. Net income does not reflect the amount

M VA A N D E VA

T A B L E 2 - 5

2001 2000

MVA CALCULATION

Price per share $23.0 $26.0 Number of shares (millions) 50 50 Market value of equity $1,150.0 $1,300.0 Book value of equity 896.0 840.0 MVA � Market value � Book value $ 254.0 $ 460.0 EVA CALCULATION

EBIT $283.8 $263.0 Tax rate 40% 40% NOPAT � EBIT (1 � T) $170.3 $157.8 Total investor-supplied operating capitala $1,800.0 $1,520.0 After-tax cost of capital (%) 10.0% 10.3% Dollar cost of capital $180.0 $156.6 EVA � NOPAT � Capital cost ($9.7) $1.2

a Investor-supplied operating capital equals the sum of notes payable, long-term debt, preferred stock, and common equity. It could also be calculated as total liabilities and equity minus accounts payable and accruals.

MVA and EVA for Allied (Millions of Dollars)

MANY FIRMS ADOPT EVA IN AN ATTEMPT TO ENHANCE SHAREHOLDER WEALTH

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of equity capital employed, but EVA does. Because of this omission, net income is not as useful as EVA for setting corporate goals and measuring managerial performance.

We will have more to say about both MVA and EVA later in the book, but we can close this section with two observations. First, there is a relationship between MVA and EVA, but it is not a direct one. If a company has a history of negative EVAs, then its MVA will probably be negative, and vice versa if it has a history of positive EVAs. However, the stock price, which is the key in- gredient in the MVA calculation, depends more on expected future perfor- mance than on historical performance. Therefore, a company with a history of negative EVAs could have a positive MVA, provided investors expect a turn- around in the future.

The second observation is that when EVAs or MVAs are used to evaluate managerial performance as part of an incentive compensation program, EVA is the measure that is typically used. The reasons are (1) EVA shows the value added during a given year, whereas MVA reflects performance over the com- pany’s entire life, perhaps even including times before the current managers were born, and (2) EVA can be applied to individual divisions or other units of a large corporation, whereas MVA must be applied to the entire corporation.

According to Fortune magazine, “Economic Value Added(EVA)” is today’s hottest financial idea. Developed and pop- ularized by the consulting firm Stern Stewart & Co., EVA helps managers ensure that a given business unit is adding to stock- holder value, while investors can use it to spot stocks that are likely to increase in value. Right now, relatively few managers and investors are using EVA, so those who do use it have a competitive advantage. However, Fortune thinks this situation won’t last long, as more managers and investors are catching the EVA fever every day.

What exactly is EVA? EVA is a way to measure an operation’s true profitability. The cost of debt capital (interest expense) is deducted when calculating net income, but no cost is deducted to account for the cost of common equity. Therefore, in an eco- nomic sense, net income overstates “true” income. EVA over- comes this flaw in conventional accounting.

EVA is found by taking the after-tax operating profit and subtracting the annual cost of all the capital a firm uses. Such highly successful giants as Coca-Cola, AT&T, Quaker Oats, Briggs & Stratton, and CSX have jumped on the EVA bandwagon and attribute much of their success to its use. According to AT&T fi- nancial executive William H. Kurtz, EVA played a major role in AT&T’s decision to acquire McCaw Cellular. In addition, AT&T made EVA the primary measure of its business unit managers’ performance.

Surprisingly, many corporate executives have no idea how much capital they are using or what that capital costs. The cost

of debt capital is easy to determine because it shows up in fi- nancial statements as interest expense; however, the cost of eq- uity capital, which is actually much larger than the cost of debt capital, does not appear in financial statements. As a result, managers often regard equity as free capital, even though it ac- tually has a high cost. So, until a management team determines its cost of capital, it cannot know whether it is covering all costs and thereby adding value to the firm.

Although EVA is perhaps the most widely discussed concept in finance today, it is not completely new; the need to earn more than the cost of capital is actually one of the oldest ideas in business. However, the idea is often lost because of a mis- guided focus on conventional accounting.

One of EVA’s greatest virtues is its direct link to stock prices. AT&T found an almost perfect correlation between its EVA and its stock price. Moreover, security analysts have found that stock prices track EVA far more closely than other factors such as earnings per share, operating margin, or return on equity. This correlation occurs because EVA is what investors really care about, namely, the net cash return on their capital. Therefore, more and more security analysts are calculating companies’ EVAs and using them to help identify good buys in the stock market.

SOURCES: “The Real Key to Creating Wealth,” Fortune, September 20, 1993, 38–44; and “America’s Wealth Creators,” Fortune, November 22, 1999, 275.

61T H E F E D E R A L I N C O M E TA X SY S T E M

SELF-TEST QUESTIONS

Define the terms “Market Value Added (MVA)” and “Economic Value Added (EVA).”

How does EVA differ from accounting profit?

T H E F E D E R A L I N C O M E TA X SY S T E M

The value of any financial asset (including stocks, bonds, and mortgages), as well as most real assets such as plants or even entire firms, depends on the stream of cash flows produced by the asset. Cash flows from an asset consist of usable income plus depreciation, and usable income means income after taxes.

Our tax laws can be changed by Congress, and in recent years changes have occurred frequently. Indeed, a major change has occurred, on average, every three to four years since 1913, when our federal income tax system began. Fur- ther, certain parts of our tax system are tied to the inflation rate, so changes occur automatically each year, depending on the rate of inflation during the previous year. Therefore, although this section will give you a good back- ground on the basic nature of our tax system, you should consult current rate schedules and other data published by the Internal Revenue Service (available in U.S. post offices) before you file your personal or business tax returns.

Currently (2001), federal income tax rates for individuals go up to 39.6 per- cent, and, when Social Security, Medicare, and state and city income taxes are included, the marginal tax rate on an individual’s income can easily exceed 50 percent. Business income is also taxed heavily. The income from partnerships and proprietorships is reported by the individual owners as personal income and, consequently, is taxed at federal-plus-state rates going up to 50 percent or more. Corporate profits are subject to federal income tax rates of up to 39 per- cent, plus state income taxes. Furthermore, corporations pay taxes and then dis- tribute after-tax income to their stockholders as dividends, which are also taxed. So, corporate income is really subject to double taxation. Because of the magni- tude of the tax bite, taxes play a critical role in many financial decisions.

As this text is being written, a Republican Congress and administration con- tinue to debate the merits of different changes in the tax laws. Even in the un- likely event that no explicit changes are made in the tax laws, changes will still occur because certain aspects of the tax calculation are tied to the inflation rate. Thus, by the time you read this chapter, tax rates and other factors will almost certainly be different from those we provide. Still, if you understand this sec- tion, you will understand the basics of our tax system, and you will know how to operate under the revised tax code.

Taxes are so complicated that university law schools offer master’s degrees in taxation to lawyers, many of whom are also CPAs. In a field complicated enough to warrant such detailed study, only the highlights can be covered in a book such as this. This is really enough, though, because business managers and investors should and do rely on tax specialists rather than trusting their

A web site of interest concerning federal tax law is http:// www.taxsites.com/ federal.html. From this

home page one can visit other sites that provide summaries of recent tax legislation or current information on corporate and individual tax rates.

For these reasons, MVA is used primarily to evaluate top corporate officers over periods of five to 10 years, or longer.

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own limited knowledge. Still, it is important to know the basic elements of the tax system as a starting point for discussions with tax experts.

INDIV IDUAL INCOME TAXES

Individuals pay taxes on wages and salaries, on investment income (dividends, interest, and profits from the sale of securities), and on the profits of propri-

T A B L E 2 - 6

Single Individuals

YOU PAY THIS PLUS THIS PERCENTAGE AVERAGE TAX AMOUNT ON THE BASE ON THE EXCESS RATE AT TOP

IF YOUR TAXABLE INCOME IS OF THE BRACKET OVER THE BASE OF BRACKET

Up to $26,250 $ 0 15.0% 15.0% $26,250–$63,550 3,937.50 28.0 22.6 $63,550–$132,600 14,381.50 31.0 27.0 $132,600–$288,350 35,787.00 36.0 31.9 Over $288,350 91,857.00 39.6 39.6

Married Couples Filing Joint Returns

YOU PAY THIS PLUS THIS PERCENTAGE AVERAGE TAX AMOUNT ON THE BASE ON THE EXCESS RATE AT TOP

IF YOUR TAXABLE INCOME IS OF THE BRACKET OVER THE BASE OF BRACKET

Up to $43,850 $ 0 15.0% 15.0% $43,850–$105,950 6,577.50 28.0 22.6 $105,950–$161,450 23,965.50 31.0 25.5 $161,450–$288,350 41,170.50 36.0 30.1 Over $288,350 86,854.50 39.6 39.6

NOTES: a. These are the tax rates in April 2001. The income ranges at which each tax rate takes effect, as well as the ranges for the additional taxes discussed below, are indexed with inflation each year, so they will change from those shown in the table.

b. The average tax rate approaches 39.6 percent as taxable income rises without limit. At $1 million of taxable income, the average tax rates for single individuals and married couples filing joint returns are 37.4 percent and 36.9 percent, respectively, while at $10 million they are 39.4 and 39.3 percent, respectively.

c. In 2000, a personal exemption of $2,800 per person or dependent could be deducted from gross income to determine taxable income. Thus, a husband and wife with two children would have a 2000 exemption of 4 � $2,800 � $11,200. The amount of the exemption is scheduled to increase with inflation. However, if gross income exceeds certain limits ($193,400 for joint returns and $128,950 for single individuals in 2000), the exemption is phased out, and this has the effect of raising the effective tax rate on incomes over the specified limit by about 0.5 percent per family member, or 2.0 percent for a family of four. In addition, taxpayers can claim itemized deductions for charitable contributions and certain other items, but these deductions are reduced if the gross income exceeds $128,950 (for both single individuals and joint returns), and this raises the effective tax rate for high- income taxpayers by another 1 percent or so. The combined effect of the loss of exemptions and the reduction of itemized deductions is about 3 percent, so the marginal federal tax rate for high-income individuals goes up to about 42.6 percent.

In addition, there is the Social Security tax, which amounts to 6.2 percent (12.4 percent for a self- employed person) on up to $76,200 of earned income, plus a 1.45 percent Medicare payroll tax (2.9 percent for self-employed individuals) on all earned income. Finally, older high-income taxpayers who receive Social Security payments must pay taxes on 85 percent of their Social Security receipts, up from 50 percent in 1994. All of this pushes the effective tax rate up even further.

Individual Tax Rates in April 2001

etorships and partnerships. Our tax rates are progressive — that is, the higher one’s income, the larger the percentage paid in taxes. Table 2-6 gives the tax rates for single individuals and married couples filing joint returns under the rate schedules that were in effect in April 2001.

1. Taxable income is defined as gross income less a set of exemptions and deductions that are spelled out in the instructions to the tax forms indi- viduals must file. When filing a tax return in 2001 for the tax year 2000, each taxpayer received an exemption of $2,800 for each dependent, in- cluding the taxpayer, which reduces taxable income. However, this ex- emption is indexed to rise with inflation, and the exemption is phased out (taken away) for high-income taxpayers. Also, certain expenses including mortgage interest paid, state and local income taxes paid, and charitable contributions, can be deducted and thus be used to reduce taxable in- come, but again, high-income taxpayers lose most of these deductions.

2. The marginal tax rate is defined as the tax rate on the last unit of in- come. Marginal rates begin at 15 percent and rise to 39.6 percent. Note, though, that when consideration is given to the phase-out of exemptions and deductions, to Social Security and Medicare taxes, and to state taxes, the marginal tax rate can actually exceed 50 percent.

3. One can calculate average tax rates from the data in Table 2-6. For ex- ample, if Jill Smith, a single individual, had taxable income of $35,000, her tax bill would be $3,937.50 � ($35,000 � $26,250)(0.28) � $3,937.50 � $2,450 � $6,387.50. Her average tax rate would be $6,387.50/$35,000 � 18.25% versus a marginal rate of 28 percent. If Jill received a raise of $1,000, bringing her income to $36,000, she would have to pay $280 of it as taxes, so her after-tax raise would be $720. In addition, her Social Se- curity and Medicare taxes would increase by $76.50, which would cut her net raise to $643.50.

4. As indicated in the notes to the table, the tax code indexes tax brackets to inflation to avoid the bracket creep that occurred several years ago and that in reality raised tax rates substantially.11

Ta xe s o n D i v i d e n d a n d I n t e r e s t I n c o m e Dividend and interest income received by individuals from corporate securities is added to other income and thus is taxed at rates going up to about 50 per- cent.12 Since corporations pay dividends out of earnings that have already been

63T H E F E D E R A L I N C O M E TA X SY S T E M

Marginal Tax Rate The tax rate applicable to the last unit of a person’s income.

Average Tax Rate Taxes paid divided by taxable income.

Bracket Creep A situation that occurs when progressive tax rates combine with inflation to cause a greater portion of each taxpayer’s real income to be paid as taxes.

11 For example, if you were single and had a taxable income of $26,250, your tax bill would be $3,937.50. Now suppose inflation caused prices to double and your income, being tied to a cost-of- living index, rose to $52,500. Because our tax rates are progressive, if tax brackets were not indexed, your taxes would jump to $11,287.50. Your after-tax income would thus increase from $22,312.50 to $41,212.50, but, because prices have doubled, your real income would decline from $22,312.50 to $20,606.25 (calculated as one-half of $41,212.50). You would be in a higher tax bracket, so you would be paying a higher percentage of your real income in taxes. If this happened to everyone, and if Con- gress failed to change tax rates sufficiently, real disposable incomes would decline because the federal government would be taking a larger share of the national product. This is called the federal gov- ernment’s “inflation dividend.” However, since tax brackets are now indexed, if your income doubled due to inflation, your tax bill would double, but your after-tax real income would remain constant at $22,312.50. Bracket creep was a real problem until the 1980s, when indexing put an end to it. 12 You do not pay Social Security and Medicare taxes on interest, dividends, and capital gains, only on earned income, but state taxes are generally imposed on dividends, interest, and capital gains.

Taxable Income Gross income minus exemptions and allowable deductions as set forth in the Tax Code.

Progressive Tax A tax system where the tax rate is higher on higher incomes. The personal income tax in the United States, which goes from 0 percent on the lowest increments of income to 39.6 percent, is progressive.

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taxed, there is double taxation of corporate income — income is first taxed at the corporate rate, and when what is left is paid out as dividends, it is taxed again at the personal rate.

It should be noted that under U.S. tax laws, interest on most state and local government bonds, called municipals or “munis,” is not subject to federal income taxes. Thus, investors get to keep all of the interest received from most munici- pal bonds but only a fraction of the interest received from bonds issued by cor- porations or by the U.S. government. This means that a lower-yielding muni can provide the same after-tax return as a higher-yielding corporate bond. For ex- ample, a taxpayer in the 39.6 percent marginal tax bracket who could buy a muni that yielded 5.5 percent would have to receive a before-tax yield of 9.11 percent on a corporate or U.S. Treasury bond to have the same after-tax income:

If we know the yield on the taxable bond, we can use the following equation to find the equivalent yield on a muni:

The exemption from federal taxes stems from the separation of federal and state powers, and its primary effect is to help state and local governments bor- row at lower rates than they otherwise could.

Munis always yield less than corporate bonds with similar risk, maturity, and liquidity. Because of this, it would make no sense for someone in a zero or very low tax bracket to buy munis. Therefore, most munis are owned by high- bracket investors.

C a p i ta l G a i n s v e r s u s O rd i n a r y I n c o m e Assets such as stocks, bonds, and real estate are defined as capital assets. If you buy a capital asset and later sell it for more than your purchase price, the profit is called a capital gain; if you suffer a loss, it is called a capital loss. An asset sold within one year of the time it was purchased produces a short-term gain or loss and one held for more than a year produces a long-term gain or loss. Thus, if you buy 100 shares of Disney stock for $42 per share and sell it for $52 per share, you make a capital gain of 100 � $10, or $1,000. However, if you sell the stock for $32 per share, you will have a $1,000 capital loss. Depending on how long you held the stock, you will have a short-term or long-term gain or loss.13

If you sell the stock for exactly $42 per share, you make neither a gain nor a loss; you simply get your $4,200 back, and no tax is due.

� 9.11% (1 � 0.396) � 9.11%(0.604) � 5.5%.

Equivalent yield on muni � °Pre-tax yieldon taxable bond

¢ (1 � Marginal tax rate)

� 5.5%

1 � 0.396 � 9.11%.

Equivalent pre-tax yieldon taxable bond � Yield on muni

1 � Marginal tax rate

13 If you have a net capital loss (capital losses exceed capital gains) for the year, you can currently deduct only up to $3,000 of this loss against your other income (for example, salary, interest, and dividends). This $3,000 loss limitation is not applicable to losses on the sale of business assets, which by definition are not capital assets.

Capital Gain or Loss The profit (loss) from the sale of a capital asset for more (less) than its purchase price.

65

Short-term capital gains are added to such ordinary income as wages, divi- dends, and interest and then are taxed at the same rate as ordinary income. However, long-term capital gains are taxed differently. The top rate on long- term gains is 20 percent. Thus, if in 2000 you were in the 39.6 percent tax bracket, any short-term gains you earned would be taxed just like ordinary in- come, but your long-term gains would be taxed at 20 percent. Thus, capital gains on assets held for more than 12 months are better than ordinary income for many people because the tax bite is smaller.14

Capital gains tax rates have varied over time, but they have generally been lower than rates on ordinary income. The reason is simple — Congress wants the economy to grow, for growth we need investment in productive assets, and low capital gains tax rates encourage investment. To see why, suppose you owned a company that earned $1 million after corporate taxes. Because it is your company, you could have it pay out the entire $1 million profit as divi- dends, or you could have it retain and reinvest all or part of the income to ex- pand the business. If it paid dividends, they would be taxable to you at a rate of 39.6 percent. However, if the company reinvests its income, that reinvestment should cause the company’s earnings and stock price to increase. Then, if you wait for one year and then sell some of your stock at a now-higher price, you will have earned capital gains, but they will be taxed at only 20 percent. Fur- ther, you can postpone the capital gains tax indefinitely by simply not selling the stock.

It should be clear that a lower tax rate on capital gains will encourage in- vestment. The owners of small businesses will want to reinvest income to get capital gains, as will stockholders in large corporations. Individuals with money to invest will understand the tax advantages associated with investing in newly formed companies versus buying bonds, so new ventures will have an easier time attracting equity capital. All in all, lower capital gains tax rates stimulate capital formation and investment.15

CORPORATE INCOME TAXES

The corporate tax structure, shown in Table 2-7, is relatively simple. To illus- trate, if a firm had $65,000 of taxable income, its tax bill would be

Taxes � $7,500 � 0.25($15,000)

� $7,500 � $3,750 � $11,250,

T H E F E D E R A L I N C O M E TA X SY S T E M

14 The Tax Code governing capital gains is very complex, and we have illustrated only the most common provision. 15 Fifty percent of any capital gains on the newly issued stock of certain small companies is excluded from taxation, provided the small-company stock is held for five years or longer. The remaining 50 percent of the gain is taxed at a rate of 20 percent for most taxpayers. Thus, if one bought newly issued stock from a qualifying small company and held it for at least five years, any capital gains would be taxed at a maximum rate of 10 percent for most taxpayers. This provision was designed to help small businesses attract equity capital.

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and its average tax rate would be $11,250/$65,000 � 17.3%. Note that cor- porate income above $18,333,333 has an average and marginal tax rate of 35 percent.16

I n t e r e s t a n d D i v i d e n d I n c o m e R e c e i ve d by a C o r p o ra t i o n Interest income received by a corporation is taxed as ordinary income at regu- lar corporate tax rates. However, 70 percent of the dividends received by one corpora- tion from another is excluded from taxable income, while the remaining 30 percent is

T A B L E 2 - 7

IT PAYS THIS PLUS THIS PERCENTAGE IF A CORPORATION’S AMOUNT ON THE BASE ON THE EXCESS AVERAGE TAX RATE TAXABLE INCOME IS OF THE BRACKET OVER THE BASE AT TOP OF BRACKET

Up to $50,000 $ 0 15% 15.0% $50,000–$75,000 7,500 25 18.3 $75,000–$100,000 13,750 34 22.3 $100,000–$335,000 22,250 39 34.0 $335,000–$10,000,000 113,900 34 34.0 $10,000,000–$15,000,000 3,400,000 35 34.3 $15,000,000–$18,333,333 5,150,000 38 35.0 Over $18,333,333 6,416,667 35 35.0

Corporate Tax Rates as of January 2001

16 Prior to 1987, many large, profitable corporations such as General Electric and Boeing paid no income taxes. The reasons for this were as follows: (1) expenses, especially depreciation, were de- fined differently for calculating taxable income than for reporting earnings to stockholders, so some companies reported positive profits to stockholders but losses — hence no taxes — to the Internal Revenue Service; and (2) some companies that did have tax liabilities used various tax credits to offset taxes that would otherwise have been payable. This situation was effectively elim- inated in 1987.

The principal method used to eliminate this situation is the Alternative Minimum Tax (AMT). Under the AMT, both corporate and individual taxpayers must figure their taxes in two ways, the “regular” way and the AMT way, and then pay the higher of the two. The AMT is calculated as follows: (1) Figure your regular taxes. (2) Take your taxable income under the regular method and then add back certain items, especially income on certain municipal bonds, depreciation in excess of straight-line depreciation, certain research and drilling costs, itemized or standard deductions (for individuals), and a number of other items. (3) The income determined in (2) is defined as AMT income, and it must then be multiplied by the AMT tax rate to determine the tax due under the AMT system. An individual or corporation must then pay the higher of the regular tax or the AMT tax. In 2000, there were two AMT tax rates for individuals (26 percent and 28 percent, depending on the level of AMT income and filing status). Most corporations have an AMT of 20 percent. However, there is no AMT for very small companies, defined as those that have had average sales of less than $5 million for the last three years and whose average sales continue to be less than $7.5 million.

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taxed at the ordinary tax rate.17 Thus, a corporation earning more than $18,333,333 and paying a 35 percent marginal tax rate would pay only (0.30)(0.35) � 0.105 � 10.5% of its dividend income as taxes, so its effective tax rate on dividends received would be 10.5 percent. If this firm had $10,000 in pre-tax dividend income, its after-tax dividend income would be $8,950:

� Before-tax income � (Before-tax income)(Effective tax rate)

� Before-tax income(1 � Effective tax rate)

� $10,000 [1 � (0.30)(0.35)]

� $10,000(1 � 0.105) � $10,000(0.895) � $8,950.

If the corporation pays its own after-tax income out to its stockholders as dividends, the income is ultimately subjected to triple taxation: (1) the original corporation is first taxed, (2) the second corporation is then taxed on the divi- dends it received, and (3) the individuals who receive the final dividends are taxed again. This is the reason for the 70 percent exclusion on intercorporate dividends.

If a corporation has surplus funds that can be invested in marketable secu- rities, the tax factor favors investment in stocks, which pay dividends, rather than in bonds, which pay interest. For example, suppose GE had $100,000 to invest, and it could buy either bonds that paid interest of $8,000 per year or preferred stock that paid dividends of $7,000. GE is in the 35 percent tax bracket; therefore, its tax on the interest, if it bought bonds, would be 0.35($8,000) � $2,800, and its after-tax income would be $5,200. If it bought preferred (or common) stock, its tax would be 0.35[(0.30)($7,000)] � $735, and its after-tax income would be $6,265. Other factors might lead GE to in- vest in bonds, but the tax factor certainly favors stock investments when the investor is a corporation.18

I n t e r e s t a n d D i v i d e n d s Pa i d by a C o r p o ra t i o n A firm’s operations can be financed with either debt or equity capital. If it uses debt, it must pay interest on this debt, whereas if it uses equity, it is expected to

After-tax income � Before-tax income � Taxes

T H E F E D E R A L I N C O M E TA X SY S T E M

17 The size of the dividend exclusion actually depends on the degree of ownership. Corporations that own less than 20 percent of the stock of the dividend-paying company can exclude 70 percent of the dividends received; firms that own more than 20 percent but less than 80 percent can exclude 80 percent of the dividends; and firms that own more than 80 percent can exclude the entire divi- dend payment. We will, in general, assume a 70 percent dividend exclusion. 18 This illustration demonstrates why corporations favor investing in lower-yielding preferred stocks over higher-yielding bonds. When tax consequences are considered, the yield on the pre- ferred stock, [1 � 0.35(0.30)](7.0%) � 6.265%, is higher than the yield on the bond, (1 � 0.35)(8.0%) � 5.200%. Also, note that corporations are restricted in their use of borrowed funds to purchase other firms’ preferred or common stocks. Without such restrictions, firms could en- gage in tax arbitrage, whereby the interest on borrowed funds reduces taxable income on a dollar- for-dollar basis, but taxable income is increased by only $0.30 per dollar of dividend income. Thus, current tax laws reduce the 70 percent dividend exclusion in proportion to the amount of borrowed funds used to purchase the stock.

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pay dividends to the equity investors (stockholders). The interest paid by a cor- poration is deducted from its operating income to obtain its taxable income, but dividends paid are not deductible. Therefore, a firm needs $1 of pre-tax in- come to pay $1 of interest, but if it is in the 40 percent federal-plus-state tax bracket, it must earn $1.67 of pre-tax income to pay $1 of dividends:

Working backward, if a company has $1.67 in pre-tax income, it must pay $0.67 in taxes [(0.4)($1.67) � $0.67]. This leaves it with after-tax income of $1.00.

Table 2-8 shows the situation for a firm with $10 million of assets, sales of $5 million, and $1.5 million of earnings before interest and taxes (EBIT). As shown in Column 1, if the firm were financed entirely by bonds, and if it made interest payments of $1.5 million, its taxable income would be zero, taxes would be zero, and its investors would receive the entire $1.5 million. (The term in- vestors includes both stockholders and bondholders.) However, as shown in Column 2, if the firm had no debt and was therefore financed only by stock, all of the $1.5 million of EBIT would be taxable income to the corporation, the tax would be $1,500,000(0.40) � $600,000, and investors would receive only $0.9 million versus $1.5 million under debt financing. The rate of return to in- vestors on their $10 million investment is therefore much higher if debt is used.

Of course, it is generally not possible to finance exclusively with debt capi- tal, and the risk of doing so would offset the benefits of the higher expected in- come. Still, the fact that interest is a deductible expense has a profound effect on the way businesses are financed — our corporate tax system favors debt financing over eq- uity financing. This point is discussed in more detail in Chapters 10 and 13.

C o r p o ra t e C a p i ta l G a i n s Before 1987, corporate long-term capital gains were taxed at lower rates than corporate ordinary income, so the situation was similar for corporations and

Pre-tax income needed to pay $1 of dividends �

$1 1 � Tax rate

� $1

0.60 � $1.67.

T A B L E 2 - 8

USE BONDS USE STOCK (1) (2)

Sales $5,000,000 $5,000,000 Operating costs 3,500,000 3,500,000

Earnings before interest and taxes (EBIT) $1,500,000 $1,500,000 Interest 1,500,000 0

Taxable income $ 0 $1,500,000 Federal-plus-state taxes (40%) 0 600,000 After-tax income $ 0 $ 900,000 Income to investors $1,500,000 $ 900,000 Rate of return on $10 million of assets 15.0% 9.0%

Returns to Investors under Bond and Stock Financing

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individuals. Under current law, however, corporations’ capital gains are taxed at the same rates as their operating income.

C o r p o ra t e L o s s C a r r y - B a c k a n d C a r r y - Fo r wa rd Ordinary corporate operating losses can be carried back (carry-back) to each of the preceding 2 years and forward (carry-forward) for the next 20 years and used to offset taxable income in those years. For example, an operating loss in 2002 could be carried back and used to reduce taxable income in 2000 and 2001, and forward, if necessary, and used in 2003, 2004, and so on, to the year 2022. The loss is typically applied first to the earliest year, then to the next earliest year, and so on, until losses have been used up or the 20-year carry-forward limit has been reached.

To illustrate, suppose Apex Corporation had $2 million of pre-tax profits (taxable income) in 2000 and 2001, and then, in 2002, Apex lost $12 million. Also, assume that Apex’s federal-plus-state tax rate is 40 percent. As shown in Table 2-9, the company would use the carry-back feature to recompute its taxes for 2000, using $2 million of the 2002 operating losses to reduce the 2000 pre-tax profit to zero. This would permit it to recover the taxes paid in 2000. Therefore, in 2002 Apex would receive a refund of its 2000 taxes be- cause of the loss experienced in 2002. Because $10 million of the unrecovered losses would still be available, Apex would repeat this procedure for 2001. Thus, in 2002 the company would pay zero taxes for 2002 and also would re- ceive a refund for taxes paid in 2000 and 2001. Apex would still have $8 mil- lion of unrecovered losses to carry forward, subject to the 20-year limit. This $8 million could be used until the entire $12 million loss had been used to offset taxable income. The purpose of permitting this loss treatment is to avoid penalizing corporations whose incomes fluctuate substantially from year to year.

T H E F E D E R A L I N C O M E TA X SY S T E M

T A B L E 2 - 9

2000 2001

Original taxable income $2,000,000 $2,000,000 Carry-back credit � 2,000,000 � 2,000,000 Adjusted profit $ 0 $ 0 Taxes previously paid (40%) 800,000 800,000 Difference � Tax refund $ 800,000 $ 800,000

Total refund check received in 2003: $800,000 � $800,000 � $1,600,000 Amount of loss carry-forward available for use in 2003–2022:

2002 loss $12,000,000 Carry-back losses used 4,000,000 Carry-forward losses still available $ 8,000,000

Apex Corporation: Calculation of Loss Carry-Back and Carry-Forward for 2000–2001 Using a $12 Million 2002 Loss

Tax Loss Carry-Back and Carry-Forward Ordinary corporate operating losses can be carried backward for 2 years or forward for 20 years to offset taxable income in a given year.

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I m p ro p e r A c c u m u l a t i o n to Avo i d Pa y m e n t o f D i v i d e n d s Corporations could refrain from paying dividends and thus permit their stock- holders to avoid personal income taxes on dividends. To prevent this, the Tax Code contains an improper accumulation provision that states that earnings accumulated by a corporation are subject to penalty rates if the purpose of the ac- cumulation is to enable stockholders to avoid personal income taxes. A cumulative total of $250,000 (the balance sheet item “retained earnings”) is by law exempted from the improper accumulation tax for most corporations. This is a benefit primarily to small corporations.

The improper accumulation penalty applies only if the retained earnings in excess of $250,000 are shown by the IRS to be unnecessary to meet the reasonable needs of the business. A great many companies do indeed have legitimate reasons for retaining more than $250,000 of earnings. For example, earnings may be retained and used to pay off debt, to finance growth, or to provide the corpo- ration with a cushion against possible cash drains caused by losses. How much a firm should properly accumulate for uncertain contingencies is a matter of judgment. We shall consider this matter again in Chapter 14, which deals with corporate dividend policy.

C o n s o l i d a t e d C o r p o ra t e Ta x R e t u r n s If a corporation owns 80 percent or more of another corporation’s stock, it can aggregate income and file one consolidated tax return; thus, the losses of one company can be used to offset the profits of another. (Similarly, one division’s

Improper Accumulation Retention of earnings by a business for the purpose of enabling stockholders to avoid personal income taxes.

Many multinational corporations have found aninteresting but controversial way to reduce their tax burdens: By shifting some of their opera-

tions to countries with low or nonexistent taxes, they can sig- nificantly reduce their total tax bills. Over the years, several countries have passed tax laws that make the countries tax havens designed to attract foreign investment. Notable exam- ples include the Bahamas, Grand Cayman, and the Netherlands Antilles.

Rupert Murdoch, chairman of global media giant News Cor- poration, has in some years paid virtually no taxes on his U.S. businesses, despite the fact that these businesses represent roughly 70 percent of his total operating profit. How has Mur- doch been able to reduce his tax burden? By shifting profits to a News Corp. subsidiary that is incorporated in the Netherlands Antilles. As Murdoch puts it, “Moving assets around like that is one of the advantages of being global.”

While activities such as Murdoch’s are legal, some have questioned their ethics. Clearly, shareholders want corporations to take legal steps to reduce taxes. Indeed, many argue that managers have a fiduciary responsibility to take such actions whenever they are cost effective. Moreover, citizens of the var- ious tax havens benefit from foreign investment. Who loses? Obviously, the United States loses tax revenue whenever a do- mestic corporation establishes a subsidiary in a tax haven. Ul- timately, this loss of tax revenue either reduces services or raises the tax burden on other corporations and individuals. Nevertheless, even the U.S. government is itself somewhat am- bivalent about the establishment of off-shore subsidiaries — it does not like to lose tax revenues, but it does like to encour- age foreign investment.

TAX HAVENS

To learn more about tax havens, check out http:// www.escapeartist.com for an in-depth analysis into tax havens, including

country profiles and indexes of offshore banks and foreign markets.

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losses can be used to offset another division’s profits.) No business ever wants to incur losses (you can go broke losing $1 to save 35¢ in taxes), but tax offsets do help make it more feasible for large, multidivisional corporations to under- take risky new ventures or ventures that will suffer losses during a develop- mental period.

TAXAT ION OF SMALL BUSINESSES : S CORPORAT IONS

The Tax Code provides that small businesses that meet certain restrictions as spelled out in the code may be set up as corporations and thus receive the ben- efits of the corporate form of organization — especially limited liability — yet still be taxed as proprietorships or partnerships rather than as corporations. These corporations are called S corporations. (“Regular” corporations are called C corporations.) If a corporation elects S corporation status for tax pur- poses, all of the business’s income is reported as personal income by its stock- holders, on a pro rata basis, and thus is taxed at the rates that apply to individ- uals. This is an important benefit to the owners of small corporations in which all or most of the income earned each year will be distributed as dividends, be- cause then the income is taxed only once, at the individual level.

D E P R E C I AT I O N

SELF-TEST QUESTIONS

Explain what is meant by this statement: “Our tax rates are progressive.”

Are tax rates progressive for all income ranges?

Explain the difference between marginal tax rates and average tax rates.

What is a “municipal bond,” and how are these bonds taxed?

What are capital gains and losses, and how are they taxed relative to ordi- nary income?

How does the federal income tax system treat corporate dividends received by a corporation versus those received by an individual? Why is this dis- tinction made?

What is the difference in the tax treatment of interest and dividends paid by a corporation? Does this difference favor debt or equity financing?

Briefly explain how tax loss carry-back and carry-forward procedures work.

S Corporation A small corporation that, under Subchapter S of the Internal Revenue Code, elects to be taxed as a proprietorship or a partnership yet retains limited liability and other benefits of the corporate form of organization.

D E P R E C I AT I O N

Depreciation plays an important role in income tax calculations — the larger the depreciation, the lower the taxable income, the lower the tax bill, hence the higher the cash flow from operations. Congress specifies, in the Tax Code, both the life over which assets can be depreciated for tax purposes and the methods of depreciation that can be used. We will discuss in detail how depreciation is calculated, and how it affects income and cash flows, when we take up capital budgeting in Chapters 11 and 12.

C H A P T E R 2 � F I N A N C I A L S TAT E M E N TS , C A S H F L O W, A N D TA X E S72

The primary purposes of this chapter were (1) to describe the basic financial statements, (2) to present some background information on cash flows, and (3) to provide an overview of the federal income tax system. The key concepts cov- ered are listed below.

� The four basic statements contained in the annual report are the balance sheet, the income statement, the statement of retained earnings, and the statement of cash flows. Investors use the information provided in these statements to form expectations about the future levels of earnings and dividends, and about the firm’s riskiness.

� The balance sheet shows assets on the left-hand side and liabilities and equity, or claims against assets, on the right-hand side. The balance sheet may be thought of as a snapshot of the firm’s financial position at a par- ticular point in time.

� The income statement reports the results of operations over a period of time, and it shows earnings per share as its “bottom line.”

� The statement of retained earnings shows the change in retained earn- ings between the balance sheet dates. Retained earnings represent a claim against assets, not assets per se.

� The statement of cash flows reports the impact of operating, investing, and financing activities on cash flows over an accounting period.

� Net cash flow differs from accounting profit because some of the rev- enues and expenses reflected in accounting profits may not have been re- ceived or paid out in cash during the year. Depreciation is typically the largest noncash item, so net cash flow is often expressed as net income plus depreciation. Investors are at least as interested in a firm’s projected net cash flow as in reported earnings because it is cash, not paper profit, that is paid out as dividends and plowed back into the business to produce growth.

� Net operating working capital is defined as the difference between the current assets necessary to operate the business and those current liabili- ties on which no interest is charged (generally, accounts payable and ac- cruals). Thus, net operating working capital is the working capital ac- quired with investor-supplied funds.

� Operating assets are the cash and marketable securities, accounts receiv- able, inventories, and fixed assets necessary to operate the business.

� NOPAT is net operating profit after taxes. It is the after-tax profit a com- pany would have if it had no debt and no investments in nonoperating as- sets. Since it excludes the effects of financial decisions, it is a better mea- sure of operating performance than is net income.

� Operating cash flow arises from normal operations, and it is the differ- ence between cash revenues and cash costs, including taxes on operating income. Operating cash flow differs from net cash flow because operating cash flow does not include either interest income or interest expense. It is equal to NOPAT plus any noncash adjustments.

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� Free cash flow (FCF) is the amount of cash flow remaining after a company makes the asset investments necessary to support operations. In other words, FCF is the amount of cash flow available for distribution to investors, so the value of a company is directly related to its ability to generate free cash flow.

� Market Value Added (MVA) represents the difference between the market value of a firm’s stock and the amount of equity its investors have supplied.

� Economic Value Added (EVA) is the difference between after-tax oper- ating profit and the total cost of capital, including the cost of equity capi- tal. EVA is an estimate of the value created by management during the year, and it differs substantially from accounting profit because no charge for the use of equity capital is reflected in accounting profit.

� The value of any asset depends on the stream of after-tax cash flows it produces. Tax rates and other aspects of our tax system are changed by Congress every year or so.

� In the United States, tax rates are progressive — the higher one’s income, the larger the percentage paid in taxes.

� Assets such as stocks, bonds, and real estate are defined as capital assets. If a capital asset is sold for more than its cost, the profit is called a capital gain. If the asset is sold for a loss, it is called a capital loss. Assets held for more than a year provide long-term gains or losses.

� Operating income paid out as dividends is subject to double taxation: the income is first taxed at the corporate level, and then shareholders must pay personal taxes on their dividends.

� Interest income received by a corporation is taxed as ordinary income; however, 70 percent of the dividends received by one corporation from an- other are excluded from taxable income. The reason for this exclusion is that corporate dividend income is ultimately subjected to triple taxation.

� Because interest paid by a corporation is a deductible expense while div- idends are not, our tax system favors debt over equity financing.

� Ordinary corporate operating losses can be carried back to each of the preceding 2 years and forward for the next 20 years and used to offset tax- able income in those years.

� S corporations are small businesses that have the limited-liability benefits of the corporate form of organization yet are taxed as a partnership or a proprietorship.

Q U E S T I O N S

2-1 What four statements are contained in most annual reports? 2-2 If a “typical” firm reports $20 million of retained earnings on its balance sheet, could its

directors declare a $20 million cash dividend without any qualms whatsoever? 2-3 Explain the following statement: “While the balance sheet can be thought of as a snap-

shot of the firm’s financial position at a point in time, the income statement reports on operations over a period of time.”

2-4 Differentiate between accounting income and net cash flow. Why might these two num- bers differ?

2-5 Differentiate between operating cash flow and net cash flow. Why might these two numbers differ?

Q U E S T I O N S

C H A P T E R 2 � F I N A N C I A L S TAT E M E N TS , C A S H F L O W, A N D TA X E S74

2-6 What do the numbers on financial statements actually represent? 2-7 Who are some of the basic users of financial statements, and how do they use them? 2-8 What is operating capital, and why is it important? 2-9 Explain the difference between NOPAT and net income. Which is a better measure of

the performance of a company’s operations? 2-10 What is free cash flow? Why is it the most important measure of cash flow? 2-11 In what way does the Tax Code discourage corporations from paying high dividends to

their shareholders? 2-12 What does double taxation of corporate income mean? 2-13 If you were starting a business, what tax considerations might cause you to prefer to set

it up as a proprietorship or a partnership rather than as a corporation? 2-14 Explain how the federal income tax structure affects the choice of financing (use of debt

versus equity) of U.S. business firms. 2-15 For someone planning to start a new business, is the average or the marginal tax rate

more relevant? 2-16 How might it be possible for a company to generate positive net accounting income yet

have a negative EVA?

S E L F - T E S T P R O B L E M S ( S O L U T I O N S A P P E A R I N A P P E N D I X B )

Define each of the following terms: a. Annual report; balance sheet; income statement b. Common stockholders’ equity, or net worth; retained earnings c. Statement of retained earnings; statement of cash flows d. Depreciation; tangible assets; amortization; intangible assets; EBITDA e. Accounting profit; net cash flow; operating cash flow f. Operating assets; nonoperating assets g. Operating working capital; net operating working capital h. Net operating profit after taxes (NOPAT); free cash flow i. Market Value Added (MVA); Economic Value Added (EVA) j. Progressive tax; taxable income k. Marginal and average tax rates l. Bracket creep

m. Capital gain or loss n. Tax loss carry-back and carry-forward o. Improper accumulation p. S corporation

Last year Rattner Robotics had $5 million in operating income (EBIT). The company had a net depreciation expense of $1 million and an interest expense of $1 million; its corporate tax rate was 40 percent. The company has $14 million in current assets and $4 million in non-interest-bearing current liabilities; it has $15 million in net plant and equipment. It estimates that it has an after-tax cost of capital of 10 percent. Assume that Rattner’s only noncash item was depreciation. a. What was the company’s net income for the year? b. What was the company’s net cash flow? c. What was the company’s net operating profit after taxes (NOPAT)? d. What was the company’s operating cash flow? e. If operating capital in the previous year was $24 million what was the company’s free

cash flow (FCF) for the year? f. What was the company’s Economic Value Added (EVA)?

Mary Henderson is planning to start a new business, MH Enterprises, and she must decide whether to incorporate or to do business as a sole proprietorship. Under either form, Henderson will initially own 100 percent of the firm, and tax considerations are important to her. She plans to finance the firm’s expected growth by drawing a salary

ST-3 Effect of form of organization on

taxes

ST-2 Net income, cash flow, and EVA

ST-1 Key terms

75

just sufficient for her family living expenses, which she estimates will be about $40,000, and by retaining all other income in the business. Assume that as a married woman with one child, she files a joint return. She has income tax exemptions of 3 � $2,800 � $8,400, and she estimates that her itemized deductions for each of the 3 years will be $9,700. She expects MH Enterprises to grow and to earn income of $52,700 in 2002, $90,000 in 2003, and $150,000 in 2004. Which form of business organization will allow Henderson to pay the lowest taxes (and retain the most income) during the period from 2002 to 2004? Assume that the tax rates given in the chapter are applica- ble for all future years. (Social Security taxes would also have to be paid, but ignore them.)

S TA R T E R P R O B L E M S

Little Books Inc. recently reported net income of $3 million. Its operating income (EBIT) was $6 million, and the company pays a 40 percent tax rate. What was the com- pany’s interest expense for the year? [Hint: Divide $3 million by (1 � T) � 0.6 to find taxable income.] Kendall Corners Inc. recently reported net income of $3.1 million. The company’s de- preciation expense was $500,000. What is the company’s approximate net cash flow? As- sume the firm has no amortization expense. An investor recently purchased a corporate bond that yields 9 percent. The investor is in the 36 percent tax bracket. What is the bond’s after-tax yield? Joe and Jane Keller are a married couple who file a joint income tax return. The cou- ple’s taxable income was $102,000. How much federal taxes did they owe? Use the tax tables given in the chapter. Corporate bonds issued by Johnson Corporation currently yield 8 percent. Municipal bonds of equal risk currently yield 6 percent. At what tax rate would an investor be in- different between these two bonds? Kordell Company recently reported $170,000 in operating income (EBIT). The com- pany’s total operating capital is $800,000. The company’s after-tax cost of that capital is 11.625 percent, and the company is in the 40 percent tax bracket. What is Kordell’s EVA? In its most recent financial statements, Newhouse Inc. reported $50 million of net in- come and $810 million of retained earnings. The previous year, its balance sheet showed $780 million of retained earnings. What were the total dividends paid to shareholders during the most recent year? Pearson Brothers recently reported an EBITDA of $7.5 million and $1.8 million of net income. The company has $2.0 million of interest expense and the corporate tax rate is 40 percent. What was the company’s depreciation and amortization expense?

E X A M - T Y P E P R O B L E M S

The problems included in this section are set up in such a way that they could be used as multiple-choice exam problems. The Talley Corporation had a 2001 taxable income of $365,000 from operations after all operating costs but before (1) interest charges of $50,000, (2) dividends received of $15,000, (3) dividends paid of $25,000, and (4) income taxes. What is the firm’s income tax liability and its after-tax income? What are the company’s marginal and average tax rates on taxable income? The Wendt Corporation had $10.5 million of taxable income from operations in 2001. a. What is the company’s federal income tax bill for the year? b. Assume the firm receives an additional $1 million of interest income from some

bonds it owns. What is the tax on this interest income?

2-10 Corporate tax liability

2-9 Corporate tax liability

2-8 Income statement

2-7 Statement of retained earnings

2-6 EVA

2-5 After-tax yield

2-4 Personal taxes

2-3 After-tax yield

2-2 Net cash flow

2-1 Income statement

E X A M - T Y P E P R O B L E M S

C H A P T E R 2 � F I N A N C I A L S TAT E M E N TS , C A S H F L O W, A N D TA X E S76

c. Now assume that Wendt does not receive the interest income but does receive an ad- ditional $1 million as dividends on some stock it owns. What is the tax on this divi- dend income?

The Shrieves Corporation has $10,000 that it plans to invest in marketable securities. It is choosing between AT&T bonds, which yield 7.5 percent, state of Florida muni bonds, which yield 5 percent, and AT&T preferred stock, with a dividend yield of 6 percent. Shrieves’ corporate tax rate is 35 percent, and 70 percent of the dividends received are tax exempt. Assuming that the investments are equally risky and that Shrieves chooses strictly on the basis of after-tax returns, which security should be selected? What is the after-tax rate of return on the highest-yielding security? Your personal tax rate is 36 percent. You can invest in either corporate bonds that yield 9 percent or municipal bonds (of equal risk) that yield 7 percent. Which investment should you choose? (Ignore state income taxes.)

The Klaven Corporation has operating income (EBIT) of $750,000. The company’s de- preciation expense is $200,000. Klaven is 100 percent equity financed, and it faces a 40 percent tax rate. What are its net income, its net cash flow, and its operating cash flow?

Which of the following actions will, all else equal, increase the amount of cash on a company’s balance sheet? a. The company issues $2 million in new common stock. b. The company invests $3 million in new plant and equipment. c. The company generates negative net income and negative net cash flow during the

year. d. The company increases the dividend paid on its common stock.

Bailey Corporation recently reported the following income statement (dollars are in thousands):

Sales $14,000,000 Operating costs excluding depreciation and amortization 7,000,000 EBITDA $ 7,000,000 Depreciation and amortization 3,000,000 EBIT $ 4,000,000 Interest 1,500,000 EBT $ 2,500,000 Taxes (40%) 1,000,000 Net income $ 1,500,000

Bailey’s total operating capital is $20 billion and its after-tax cost of capital is 10 percent. Therefore, Bailey’s total after-tax dollar cost of operating capital is $2 billion. During the past year, Bailey made a $1.3 billion net investment in its operating captial. a. What is Bailey’s NOPAT for the year? b. What is Bailey’s net cash flow for the year? c. What is Bailey’s operating cash flow for the year? d. What is Bailey’s free cash flow for the year? e. What is Bailey’s EVA for the year?

P R O B L E M S

Note: By the time this book is published, Congress might have changed rates and/or other provi- sions of current tax law — as noted in the chapter, such changes occur fairly often. Work all prob- lems on the assumption that the information in the chapter is applicable.

2-15 Cash flow

2-14 Balance sheet

2-13 Cash flow

2-12 After-tax yield

2-11 After-tax yield

The Smythe-Davidson Corporation just issued its annual report. The current year’s balance sheet and income statement as they appeared in the annual report are given below. Answer the questions that follow based on information given in the financial statements.

Smythe-Davidson Corporation: Balance Sheet as of December 31, 2001 (Millions of Dollars)

ASSETS LIABILITIES AND EQUITY

Cash and marketable securities $ 15 Accounts payable $ 120 Accounts receivable 515 Notes payable 220 Inventories 880 Accruals 280

Total current assets $1,410 Total current liabilities $ 620 Net plant and equipment 2,590 Long-term bonds 1,520

Total debt $2,140 Preferred stock (800,000 shares) 80 Common stock (100 million shares) 260 Retained earnings 1,520

Common equity $1,780 Total assets $4,000 Total liabilities and equity $4,000

Smythe-Davidson Corporation: Income Statement for Year Ending December 31, 2001 (Millions of Dollars)

Sales $6,250 Operating costs excluding depreciation 5,230 EBITDA $1,020 Depreciation 220 EBIT $ 800 Less: Interest 180 EBT $ 620 Taxes (40%) 248 Net income before preferred dividends $ 372 Preferred dividends 8 Net income available to common stockholders $ 364 Common dividends paid $ 146 Earnings per share $3.64

a. Assume that all of the firm’s revenues were received in cash during the year and that all costs except depreciation were paid in cash during the year. What is the firm’s net cash flow available to common stockholders for the year? How is this number differ- ent from the accounting profit reported by the firm?

b. Construct the firm’s Statement of Retained Earnings for December 31, 2001. c. How much money has the firm reinvested in itself over the years instead of paying

out dividends? d. At the present time, how large a check could the firm write without it bouncing? e. How much money must the firm pay its current creditors within the next year?

2-16 Financial statements

77P R O B L E M S

C H A P T E R 2 � F I N A N C I A L S TAT E M E N TS , C A S H F L O W, A N D TA X E S78

The Menendez Corporation expects to have sales of $12 million in 2002. Costs other than depreciation are expected to be 75 percent of sales, and depreciation is expected to be $1.5 million. All sales revenues will be collected in cash, and costs other than depre- ciation must be paid for during the year. Menendez’s federal-plus-state tax rate is 40 per- cent. a. Set up an income statement. What is Menendez’s expected net cash flow? b. Suppose Congress changed the tax laws so that Menendez’s depreciation expenses

doubled. No changes in operations occurred. What would happen to reported profit and to net cash flow?

c. Now suppose that Congress, instead of doubling Menendez’s depreciation, reduced it by 50 percent. How would profit and net cash flow be affected?

d. If this were your company, would you prefer Congress to cause your depreciation ex- pense to be doubled or halved? Why?

e. In the situation in which depreciation doubled, would this possibly have an adverse effect on the company’s stock price and on its ability to borrow money?

Last year Martin Motors reported the following income statement:

Sales $2,000,000 Cost of goods sold 1,200,000 EBITDA $ 800,000 Depreciation 500,000 Operating income (EBIT) $ 300,000 Interest expense 100,000 Taxable income (EBT) $ 200,000 Taxes (40%) 80,000 Net income $ 120,000

The company’s CEO, Joe Lawrence, was unhappy with the firm’s performance. This year, he would like to see net income doubled to $240,000. Depreciation, interest ex- pense, and the tax rate will all remain constant, and the cost of goods sold will also re- main at 60 percent of sales. How much sales revenue must the company generate to achieve the CEO’s net income target? You have just obtained financial information for the past 2 years for Powell Panther Corporation. Answer the following questions.

Powell Panther Corporation: Income Statements for Year Ending December 31 (Millions of Dollars)

2001 2000

Sales $1,200.0 $1,000.0 Operating costs excluding depreciation 1,020.0 850.0 EBITDA $ 180.0 $ 150.0 Depreciation 30.0 25.0 Earnings before interest and taxes $ 150.0 $ 125.0 Less: Interest 21.7 20.2 Earnings before taxes $ 128.3 $ 104.8 Taxes (40%) 51.3 41.9 Net income available to common stockholders $ 77.0 $ 62.9 Common dividends $ 60.5 $ 46.4

2-19 Free cash flow

2-18 Income statement

2-17 Income and cash flow analysis

79

Powell Panther Corporation: Balance Sheets as of December 31 (Millions of Dollars)

2001 2000

ASSETS

Cash and marketable securities $ 12.0 $ 10.0 Accounts receivable 180.0 150.0 Inventories 180.0 200.0

Total current assets $372.0 $360.0 Net plant and equipment 300.0 250.0 Total assets $672.0 $610.0

LIABILITIES AND EQUITY

Accounts payable $108.0 $ 90.0 Notes payable 67.0 51.5 Accruals 72.0 60.0

Total current liabilities $247.0 $201.5 Long-term bonds 150.0 150.0

Total debt $397.0 $351.5 Common stock (50 million shares) 50.0 50.0 Retained earnings 225.0 208.5

Common equity $275.0 $258.5 Total liabilities and equity $672.0 $610.0

a. What is the net operating profit after taxes (NOPAT) for 2001? b. What are the amounts of net operating working capital for 2000 and 2001? c. What are the amounts of total operating capital for 2000 and 2001? d. What is the free cash flow for 2001? e. How can you explain the large increase in dividends in 2001? The Herrmann Company has made $150,000 before taxes during each of the last 15 years, and it expects to make $150,000 a year before taxes in the future. However, in 2001 the firm incurred a loss of $650,000. The firm will claim a tax credit at the time it files its 2001 income tax return, and it will receive a check from the U.S. Treasury. Show how it calculates this credit, and then indicate the firm’s tax liability for each of the next 5 years. Assume a 40 percent tax rate on all income to ease the calculations. The projected taxable income of the McAlhany Corporation, formed in 2002, is indi- cated in the table below. (Losses are shown in parentheses.) What is the corporate tax li- ability for each year? Assume a constant federal-plus-state tax rate of 40 percent.

YEAR TAXABLE INCOME

2002 ($ 95,000,000) 2003 70,000,000 2004 55,000,000 2005 80,000,000 2006 (150,000,000)

Susan Visscher has operated her small restaurant as a sole proprietorship for several years, but projected changes in her business’s income have led her to consider incorpo- rating. Visscher is married and has two children. Her family’s only income, an annual salary of $52,000, is from operating the business. (The business actually earns more than $52,000, but Susan reinvests the additional earnings in the business.) She itemizes de- ductions, and she is able to deduct $8,600. These deductions, combined with her four personal exemptions for 4 � $2,800 � $11,200, give her a taxable income of $52,000 �

2-22 Form of organization

2-21 Loss carry-back, carry-forward

2-20 Loss carry-back, carry-forward

P R O B L E M S

C H A P T E R 2 � F I N A N C I A L S TAT E M E N TS , C A S H F L O W, A N D TA X E S80

$8,600 � $11,200. (Assume the personal exemption remains at $2,800.) Of course, her actual taxable income, if she does not incorporate, would be higher by the amount of reinvested income. Visscher estimates that her business earnings before salary and taxes for the period 2002 to 2004 will be:

YEAR EARNINGS BEFORE SALARY AND TAXES

2002 $ 70,000 2003 $ 95,000 2004 $110,000

a. What would her total taxes (corporate plus personal) be in each year under (1) A non-S corporate form of organization? (2002 tax � $7,530.) (2) A proprietorship? (2002 tax � $8,356.)

b. Should Visscher incorporate? Discuss. Mary Jarvis, a single individual, has this situation for the year 2001: salary of $82,000; dividend income of $12,000; interest on Disney bonds of $5,000; interest on state of Florida municipal bonds of $10,000; proceeds of $22,000 from the sale of Disney stock purchased in 1999 at a cost of $9,000; and proceeds of $22,000 from the November 2001 sale of Disney stock purchased in October 2001 at a cost of $21,000. Jarvis gets one exemption ($2,800), and she has allowable itemized deductions of $6,000; these amounts will be deducted from her gross income to determine her taxable income. a. What is Jarvis’s federal tax liability for 2001? b. What are her marginal and average tax rates? c. If she had $5,000 to invest and was offered a choice of either state of Florida bonds

with a yield of 6 percent or more Disney bonds with a yield of 8 percent, which should she choose, and why?

d. At what marginal tax rate would Jarvis be indifferent in her choice between the Florida and Disney bonds?

S P R E A D S H E E T P R O B L E M

Laiho Industries’ 2000 and 2001 balance sheets (in thousands of dollars) are shown below:

2001 2000

Cash $102,850 $ 89,725 Accounts receivable 103,365 85,527 Inventories 38,444 34,982

Total current assets $244,659 $210,234 Net fixed assets 67,165 42,436 Total assets $311,824 $252,670

Accounts payable $ 30,761 $ 23,109 Accruals 30,477 22,656 Notes payable 16,717 14,217

Total current liabilities $ 77,955 $ 59,982 Long-term debt 76,264 63,914

Total liabilities $154,219 $123,896 Common stock 100,000 90,000 Retained earnings 57,605 38,774

Total common equity $157,605 $128,774 Total liabilities and equity $311,824 $252,670

2-24 Financial statements, EVA, and MVA

2-23 Personal taxes

81

a. The company’s sales for 2001 were $455,150,000, and EBITDA was 15 percent of sales. Furthermore, depreciation amounted to 11 percent of net fixed assets, interest charges were $8,575,000, the state-plus-federal corporate tax rate was 40 percent, and Laiho pays 40 percent of its net income out in dividends. Given this information, construct Laiho’s 2001 income statement. (Hint: You might find it easiest to select the balance sheets, then copy them, and then paste them to an Excel worksheet. You might have to move the data around some in the worksheet to get things lined up properly.)

b. Next, construct the firm’s statement of retained earnings for the year ending De- cember 31, 2001, and then its 2001 statement of cash flows.

c. Calculate net operating working capital, total operating capital, net operating profit after taxes, operating cash flow, and free cash flow for 2001.

d. Calculate the firm’s EVA and MVA for 2001. Assume that Laiho had 10 million shares outstanding, that the year-end closing stock price was $17.25 per share, and its after-tax cost of capital was 12 percent.

C Y B E R P R O B L E M

The information related to the cyberproblems is likely to change over time, due to the release of new information and the ever-changing nature of the World Wide Web. With these changes in mind, we will periodically update these problems on the textbook’s web site. To avoid problems, please check for these updates before proceeding with the cyberproblems. A manager’s primary goal is to maximize the value of his or her firm’s stock. The stock’s value is calculated as the present value of the firm’s future cash flow stream. A study of a firm’s financial statements provides clues to its past, present, and likely fu- ture performance. Managers must understand financial statements because their ac- tions have a direct impact on them. Managers and investors alike need to know how to read and interpret financial statements.

Let’s examine Minnesota Mining and Manufacturing (otherwise known as 3M) Company’s financial statements as reported in its 1999 annual report, which can be found at www.mmm.com/profile/finance/report.html.

2-25 Financial statements, cash

flow, and taxes

D’LEON INC., PART I

2-26 SECTION I: Financial Statements Donna Jamison, a 1996 graduate of the University of Florida with four years of banking experience, was recently brought in as assistant to the chairman of the board of D’Leon Inc., a small food pro- ducer that operates in north Florida and whose specialty is high-quality pecan and other nut products sold in the snack- foods market. D’Leon’s president, Al Watkins, decided in 2000 to undertake a major expansion and to “go national” in competition with Frito-Lay, Eagle, and other major snack- food companies. Watkins felt that D’Leon’s products were of a higher quality than the competition’s, that this quality dif- ferential would enable it to charge a premium price, and that the end result would be greatly increased sales, profits, and stock price.

The company doubled its plant capacity, opened new sales offices outside its home territory, and launched an ex- pensive advertising campaign. D’Leon’s results were not satisfactory, to put it mildly. Its board of directors, which consisted of its president and vice-president plus its major stockholders (who were all local business people), was most upset when directors learned how the expansion was going. Suppliers were being paid late and were unhappy, and the bank was complaining about the deteriorating situation and threatening to cut off credit. As a result, Watkins was in- formed that changes would have to be made, and quickly, or he would be fired. Also, at the board’s insistence Donna Jamison was brought in and given the job of assistant to Fred

Campo, a retired banker who was D’Leon’s chairman and largest stockholder. Campo agreed to give up a few of his golfing days and to help nurse the company back to health, with Jamison’s help.

Jamison began by gathering the financial statements and other data given in Tables IC2-1, IC2-2, IC2-3, and IC2-4. Assume that you are Jamison’s assistant, and you must help her answer the following questions for Campo. (Note: We will continue with this case in Chapter 3, and you will feel more comfortable with the analysis there, but answering these questions will help prepare you for Chapter 3. Provide clear explanations, not just yes or no answers!)

a. What effect did the expansion have on sales, net operat- ing profit after taxes (NOPAT), net operating working capital (NOWC), total investor-supplied operating cap- ital, and net income?

b. What effect did the company’s expansion have on its net cash flow, operating cash flow, and free cash flow?

c. Jamison also has asked you to estimate D’Leon’s EVA. She estimates that the after-tax cost of capital was 10 percent in 2000 and 13 percent in 2001.

d. Looking at D’Leon’s stock price today, would you conclude that the expansion increased or decreased MVA?

e. D’Leon purchases materials on 30-day terms, meaning that it is supposed to pay for purchases within 30 days of receipt. Judging from its 2001 balance sheet, do you think D’Leon pays suppliers on time? Explain. If not, what problems might this lead to?

C H A P T E R 2 � F I N A N C I A L S TAT E M E N TS , C A S H F L O W, A N D TA X E S82

a. Look at 3M’s consolidated balance sheet. Did 3M have more or less cash on De- cember 31, 1999, than it did on December 31, 1998? How does this affect the firm’s liquidity?

b. What was 3M’s method for valuing inventory in fiscal year 1999? Refer to the “notes to consolidated financial statements” where the firm’s accounting policies are discussed.

c. What is 3M’s total common equity or net worth as of year-end 1999? Is this amount larger or smaller than year-end 1998? (Note that as of December 31, 1999, 3M had no preferred stock.)

d. Look at 3M’s consolidated statement of income, which appears before its balance sheet in the annual report. What was 3M’s operating income in 1999? Did oper- ating income increase in 1999 when compared against 1998?

e. What was 3M’s net income available to common stockholders for fiscal years 1997, 1998, and 1999?

f. What was 3M’s reported “basic” and “diluted” earnings per common share (after the extraordinary loss) in 1998 and 1999? (Note that “basic” EPS uses the average number of shares actually outstanding in the EPS calculation, whereas “diluted” EPS assumes that all warrants issued with bonds and all convertibles are exercised and converted into common stock. Warrants and convertibles are discussed briefly in Chapter 8.)

83I N T E G R AT E D C A S E

f. D’Leon spends money for labor, materials, and fixed as- sets (depreciation) to make products, and still more money to sell those products. Then, it makes sales that result in receivables, which eventually result in cash in- flows. Does it appear that D’Leon’s sales price exceeds its costs per unit sold? How does this affect the cash balance?

g. Suppose D’Leon’s sales manager told the sales staff to start offering 60-day credit terms rather than the 30-day terms now being offered. D’Leon’s competitors react by offering similar terms, so sales remain constant. What effect would this have on the cash account? How would the cash account be affected if sales doubled as a result of the credit policy change?

h. Can you imagine a situation in which the sales price ex- ceeds the cost of producing and selling a unit of output, yet a dramatic increase in sales volume causes the cash balance to decline?

i. Did D’Leon finance its expansion program with inter- nally generated funds (additions to retained earnings plus depreciation) or with external capital? How does the choice of financing affect the company’s financial strength?

j. Refer to Tables IC2-2 and IC2-4. Suppose D’Leon broke even in 2001 in the sense that sales revenues

equaled total operating costs plus interest charges. Would the asset expansion have caused the company to experience a cash shortage that required it to raise exter- nal capital?

k. If D’Leon started depreciating fixed assets over 7 years rather than 10 years, would that affect (1) the physical stock of assets, (2) the balance sheet account for fixed as- sets, (3) the company’s reported net income, and (4) its cash position? Assume the same depreciation method is used for stockholder reporting and for tax calculations, and the accounting change has no effect on assets’ phys- ical lives.

l. Explain how earnings per share, dividends per share, and book value per share are calculated, and what they mean. Why does the market price per share not equal the book value per share?

m. The 2001 income statement shows negative taxes, that is, a tax credit. Given the tax refund received in 2001, what can you conclude about the amount of taxes paid in the previous 2 years?

SECTION II: Taxes n. Working with Jamison has required you to put in a lot

of overtime, so you have had very little time to spend on

T A B L E I C 2 - 1

2001 2000

ASSETS

Cash $ 7,282 $ 57,600 Accounts receivable 632,160 351,200 Inventories 1,287,360 715,200

Total current assets $1,926,802 $1,124,000 Gross fixed assets 1,202,950 491,000 Less accumulated depreciation 263,160 146,200

Net fixed assets $ 939,790 $ 344,800 Total assets $2,866,592 $1,468,800

LIABILITIES AND EQUITY

Accounts payable $ 524,160 $ 145,600 Notes payable 636,808 200,000 Accruals 489,600 136,000

Total current liabilities $1,650,568 $ 481,600 Long-term debt 723,432 323,432 Common stock (100,000 shares) 460,000 460,000 Retained earnings 32,592 203,768

Total equity $ 492,592 $ 663,768 Total liabilities and equity $2,866,592 $1,468,800

Balance Sheets

your private finances. It’s now April 1, and you have only two weeks left to file your income tax return. You have managed to get all the information together that you will need to complete your return. D’Leon paid you a salary of $45,000, and you received $3,000 in dividends from common stock that you own. You are single, so

your personal exemption is $2,800, and your itemized deductions are $5,150. (1) On the basis of the information above and the April

2001 individual tax rate schedule, what is your tax li- ability?

(2) What are your marginal and average tax rates?

C H A P T E R 2 � F I N A N C I A L S TAT E M E N TS , C A S H F L O W, A N D TA X E S84

T A B L E I C 2 - 3

Balance of retained earnings, 12/31/00 $203,768 Add: Net income, 2001 (160,176) Less: Dividends paid (11,000)

Balance of retained earnings, 12/31/01 $ 32,592

Statement of Retained Earnings, 2001

T A B L E I C 2 - 2

2001 2000

Sales $6,034,000 $3,432,000 Cost of goods sold 5,528,000 2,864,000 Other expenses 519,988 358,672 Total operating costs excluding depreciation $6,047,988 $3,222,672 EBITDA ($13,988) $ 209,328 Depreciation 116,960 18,900 EBIT ($ 130,948) $ 190,428 Interest expense 136,012 43,828 EBT ($ 266,960) $ 146,600 Taxes (40%) (106,784)a 58,640 Net income ($ 160,176) $ 87,960

EPS ($ 1.602) $ 0.880 DPS $ 0.110 $ 0.220 Book value per share $ 4.926 $ 6.638 Stock price $ 2.25 $ 8.50 Shares outstanding 100,000 100,000 Tax rate 40.00% 40.00% Lease payments 40,000 40,000 Sinking fund payments 0 0

aThe firm had sufficient taxable income in 1999 and 2000 to obtain its full tax refund in 2001.

Income Statements

o. Assume that a corporation has $100,000 of taxable in- come from operations plus $5,000 of interest income and $10,000 of dividend income. What is the company’s tax liability?

p. Assume that after paying your personal income tax as calculated in part n, you have $5,000 to invest. You have

narrowed your investment choices down to California bonds with a yield of 7 percent or equally risky Exxon Mobil bonds with a yield of 10 percent. Which one should you choose and why? At what marginal tax rate would you be indifferent to the choice between Califor- nia and Exxon Mobil bonds?

85I N T E G R AT E D C A S E

T A B L E I C 2 - 4

OPERATING ACTIVITIES

Net income ($ 160,176) Additions (Sources of Cash)

Depreciation 116,960 Increase in accounts payable 378,560 Increase in accruals 353,600 Subtractions (Uses of Cash)

Increase in accounts receivable (280,960) Increase in inventories (572,160)

Net cash provided by operating activities ($ 164,176) LONG-TERM INVESTING ACTIVITIES

Cash used to acquire fixed assets ($ 711,950) FINANCING ACTIVITIES

Increase in notes payable $ 436,808 Increase in long-term debt 400,000 Payment of cash dividends (11,000)

Net cash provided by financing activities $ 825,808 Sum: net decrease in cash ($ 50,318) Plus: cash at beginning of year 57,600 Cash at end of year $ 7,282

Statement of Cash Flows, 2001

6

SOURCE: Jerry Arcieri/SABA

CHAPTER

A na l y s i s o f F i na nc i a l S t a t e me n t s3

NOTE: We have covered this chapter both early in the course and toward the end. Early coverage gives students an overview of how financial decisions affect financial statements and results, and thus of what financial management is all about. Later coverage, after students have an understanding of stock valu-

cautioned investors that future sales and earnings might

be weaker than expected.

Until this recent decline, Gap stock had performed

quite well — shareholders have realized a 387 percent

cumulative return over the past five years. Following

this report, many analysts announced that they were

downgrading their opinion of Gap stock. However, other

analysts argued that Gap might still be an attractive

investment for long-term investors due to its long-term

track record and its ability in the past to recover from

slumping sales.

Wall Street’s response to Gap’s announcement brings

home several important points. First, investors and others

outside the company use reported earnings and other

financial statement data to determine a company’s value.

Second, analysts are primarily concerned about future

performance — past performance is useful only to the

extent that it provides information about the company’s

future. Finally, analysts go beyond reported profits and

dig into the details of the financial statements.

So, while many people regard financial statements as

“just accounting,” they really are much more. As you

will see in this chapter, the statements provide a wealth

of information that is used for a wide variety of

purposes by managers, investors, lenders, customers,

suppliers, and regulators. An analysis of its statements

can highlight a company’s strengths and shortcomings,

hortly after the markets closed on August 30,

2000, Gap Inc. reported a 14 percent decline

in its monthly same-store sales. The markets

responded quickly, and Gap’s stock price fell sharply

in overnight trading. At the end of the following

trading day, the stock’s price was $22 per share, almost

a 60 percent decline from its 52-week high of

$53.75.

While the opening of new stores enabled Gap to

report a 6 percent increase in overall sales, the market

clearly focused on the disappointing decline in same-

store sales. Analysts pouring over the company’s

financial data were also concerned about a weakening

economy, the company’s recent difficulties in managing

its inventory, and the possibility that higher

distribution costs and increased competition might

lower future operating margins. An even closer look at

the data showed that declines in same-store sales

occurred at not only the flagship stores but also at the

company’s Banana Republic and Old Navy units. The

more than 20 percent drop in same-store sales for Old

Navy was particularly alarming, since analysts had

assumed that Old Navy would be a major contributor to

the company’s future growth. Adding more fuel to the

fire, the company indicated that distribution problems

would limit the inventory that Old Navy stores would

have for their back-to-school sales. Thus, the company

T H E GA P WA R N S WA L L S T R E E T

GAP INC.

$

S

87

ation, risk analysis, capital budgeting, capital structure, and working capital management, helps stu- dents appreciate why ratios are the way they are, and how they are used for different purposes. Depending on students’ backgrounds, instructors may want to cover the chapter early or late.

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS88

The primary goal of financial management is to maximize the stock price, not to

maximize accounting measures such as net income or EPS. However, accounting

data do influence stock prices, and to understand why a company is performing the

way it is and to forecast where it is heading, one needs to evaluate the accounting

information reported in the financial statements. Chapter 2 described the primary

financial statements and showed how they change as a firm’s operations undergo

change. Now, in Chapter 3, we show how financial statements are used by managers

to improve performance, by lenders to evaluate the likelihood of collecting on

loans, and by stockholders to forecast earnings, dividends, and stock prices.

If management is to maximize a firm’s value, it must take advantage of the

firm’s strengths and correct its weaknesses. Financial statement analysis involves

(1) comparing the firm’s performance with that of other firms in the same indus-

try and (2) evaluating trends in the firm’s financial position over time. These stud-

ies help management identify deficiencies and then take actions to improve per-

formance. In this chapter, we focus on how financial managers (and investors)

evaluate a firm’s current financial position. Then, in the remaining chapters, we

examine the types of actions management can take to improve future performance

and thus increase its stock price.

This chapter should, for the most part, be a review of concepts you learned in

accounting. However, accounting focuses on how financial statements are made,

whereas our focus is on how they are used by management to improve the firm’s

performance and by investors when they set values on the firm’s stock and bonds.

Like Chapter 2, a spreadsheet model accompanies this chapter. You are encouraged

to use the model and follow along with the textbook examples. �

strategic decisions as the sale of a division, a major

marketing program, or a plant expansion are likely to

affect future financial performance. �

and this information can be used by management to

improve performance and by others to forecast future

results. As you will see both here and in Chapter 4,

financial analysis can be used to predict how such

89

R AT I O A N A LY S I S

Financial statements report both on a firm’s position at a point in time and on its operations over some past period. However, the real value of financial statements lies in the fact that they can be used to help predict future earnings and dividends. From an investor’s standpoint, predicting the future is what finan- cial statement analysis is all about, while from management’s standpoint, financial statement analysis is useful both to help anticipate future conditions and, more impor- tant, as a starting point for planning actions that will improve the firm’s future per- formance.

Financial ratios are designed to help one evaluate a financial statement. For example, Firm A might have debt of $5,248,760 and interest charges of $419,900, while Firm B might have debt of $52,647,980 and interest charges of $3,948,600. Which company is stronger? The burden of these debts, and the companies’ ability to repay them, can best be evaluated (1) by comparing each firm’s debt to its assets and (2) by comparing the interest it must pay to the in- come it has available for payment of interest. Such comparisons are made by ratio analysis.

In the paragraphs that follow, we will calculate the Year 2001 financial ratios for Allied Food Products, using data from the balance sheets and income state- ments given in Tables 2-1 and 2-2 back in Chapter 2. We will also evaluate the ratios in relation to the industry averages.1 Note that all dollar amounts in the ratio calculations are in millions.

L I Q U I D I T Y R AT I O S

A liquid asset is one that trades in an active market and hence can be quickly converted to cash at the going market price, and a firm’s “liquidity position” deals with this question: Will the firm be able to pay off its debts as they come due over the next year or so? As shown in Table 2-1 in Chapter 2, Al- lied has debts totaling $310 million that must be paid off within the coming year. Will it have trouble satisfying those obligations? A full liquidity analysis requires the use of cash budgets, but by relating the amount of cash and other current assets to current obligations, ratio analysis provides a quick, easy-to- use measure of liquidity. Two commonly used liquidity ratios are discussed in this section.

L I Q U I D I T Y R AT I O S

1 In addition to the ratios discussed in this section, financial analysts also employ a tool known as common size balance sheets and income statements. To form a common size balance sheet, one simply divides each asset and liability item by total assets and then expresses the result as a per- centage. The resultant percentage statement can be compared with statements of larger or smaller firms, or with those of the same firm over time. To form a common size income state- ment, one simply divides each income statement item by sales. With a spreadsheet, this is triv- ially easy.

Liquid Asset An asset that can be converted to cash quickly without having to reduce the asset’s price very much.

Liquidity Ratios Ratios that show the relationship of a firm’s cash and other current assets to its current liabilities.

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ABIL I TY TO MEET SHORT-TERM OBLIGAT IONS: THE CURRENT RATIO

The current ratio is calculated by dividing current assets by current liabilities:

Industry average � 4.2 times.

Current assets normally include cash, marketable securities, accounts receiv- able, and inventories. Current liabilities consist of accounts payable, short-term notes payable, current maturities of long-term debt, accrued taxes, and other accrued expenses (principally wages).

If a company is getting into financial difficulty, it begins paying its bills (ac- counts payable) more slowly, borrowing from its bank, and so on. If current li- abilities are rising faster than current assets, the current ratio will fall, and this could spell trouble. Because the current ratio provides the best single indicator of the extent to which the claims of short-term creditors are covered by assets that are expected to be converted to cash fairly quickly, it is the most commonly used measure of short-term solvency.

Allied’s current ratio is well below the average for its industry, 4.2, so its liq- uidity position is relatively weak. Still, since current assets are scheduled to be converted to cash in the near future, it is highly probable that they could be liq- uidated at close to their stated value. With a current ratio of 3.2, Allied could liquidate current assets at only 31 percent of book value and still pay off cur- rent creditors in full.2

Although industry average figures are discussed later in some detail, it should be noted at this point that an industry average is not a magic number that all firms should strive to maintain — in fact, some very well-managed firms will be above the average while other good firms will be below it. However, if a firm’s ra- tios are far removed from the averages for its industry, an analyst should be con- cerned about why this variance occurs. Thus, a deviation from the industry aver- age should signal the analyst (or management) to check further.

QUICK, OR ACID TEST, RAT IO

The quick, or acid test, ratio is calculated by deducting inventories from cur- rent assets and then dividing the remainder by current liabilities:

Industry average � 2.1 times.

� $385 $310

� 1.2 times.

Quick, or acid test, ratio � Current assets � Inventories

Current liabilities

� $1,000 $310

� 3.2 times.

Current ratio � Current assets

Current liabilities

2 1/3.2 � 0.31, or 31 percent. Note that 0.31($1,000) � $310, the amount of current liabilities.

Quick (Acid Test) Ratio This ratio is calculated by deducting inventories from current assets and dividing the remainder by current liabilities.

Current Ratio This ratio is calculated by dividing current assets by current liabilities. It indicates the extent to which current liabilities are covered by those assets expected to be converted to cash in the near future.

A S S E T M A N AG E M E N T R AT I O S

The second group of ratios, the asset management ratios, measures how ef- fectively the firm is managing its assets. These ratios are designed to answer this question: Does the total amount of each type of asset as reported on the balance sheet seem reasonable, too high, or too low in view of current and pro- jected sales levels? When they acquire assets, Allied and other companies must borrow or obtain capital from other sources. If a firm has too many assets, its cost of capital will be too high, hence its profits will be depressed. On the other hand, if assets are too low, profitable sales will be lost. Ratios that analyze the different types of assets are described in this section.

EVALUAT ING INVENTORIES : THE INVENTORY TURNOVER RATIO

The inventory turnover ratio is defined as sales divided by inventories:

As a rough approximation, each item of Allied’s inventory is sold out and re- stocked, or “turned over,” 4.9 times per year. “Turnover” is a term that orig- inated many years ago with the old Yankee peddler, who would load up his wagon with goods, then go off on his route to peddle his wares. The mer- chandise was called “working capital” because it was what he actually sold, or “turned over,” to produce his profits, whereas his “turnover” was the number

Industry average � 9.0 times.

� $3,000 $615

� 4.9 times.

Inventory turnover ratio � Sales

Inventories

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Inventories are typically the least liquid of a firm’s current assets, hence they are the assets on which losses are most likely to occur in the event of liquidation. Therefore, a measure of the firm’s ability to pay off short-term obligations without relying on the sale of inventories is important.

The industry average quick ratio is 2.1, so Allied’s 1.2 ratio is low in com- parison with other firms in its industry. Still, if the accounts receivable can be collected, the company can pay off its current liabilities without having to liq- uidate its inventory.

A S S E T M A N AG E M E N T R AT I O S

SELF-TEST QUESTIONS

Identify two ratios that are used to analyze a firm’s liquidity position, and write out their equations.

What are the characteristics of a liquid asset? Give some examples.

Which current asset is typically the least liquid?

Asset Management Ratios A set of ratios that measure how effectively a firm is managing its assets.

Inventory Turnover Ratio This ratio is calculated by dividing sales by inventories.

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of trips he took each year. Annual sales divided by inventory equaled turnover, or trips per year. If he made 10 trips per year, stocked 100 pans, and made a gross profit of $5 per pan, his annual gross profit would be (100)($5)(10) � $5,000. If he went faster and made 20 trips per year, his gross profit would double, other things held constant. So, his turnover directly affected his profits.

Allied’s turnover of 4.9 times is much lower than the industry average of 9 times. This suggests that Allied is holding too much inventory. Excess in- ventory is, of course, unproductive, and it represents an investment with a low or zero rate of return. Allied’s low inventory turnover ratio also makes us question the current ratio. With such a low turnover, we must wonder whether the firm is actually holding obsolete goods not worth their stated value.3

Note that sales occur over the entire year, whereas the inventory figure is for one point in time. For this reason, it is better to use an average inventory mea- sure.4 If the firm’s business is highly seasonal, or if there has been a strong up- ward or downward sales trend during the year, it is especially useful to make some such adjustment. To maintain comparability with industry averages, how- ever, we did not use the average inventory figure.

EVALUAT ING RECE IVABLES: THE DAYS SALES OUTSTANDING

Days sales outstanding (DSO), also called the “average collection period” (ACP), is used to appraise accounts receivable, and it is calculated by dividing accounts receivable by average daily sales to find the number of days’ sales that are tied up in receivables. Thus, the DSO represents the average length of time that the firm must wait after making a sale before receiving cash, which is the average collection period. Allied has 46 days sales outstanding, well above the 36-day industry average:

Industry average � 36 days.

� $375

$3,000/365 �

$375 $8.2192

� 45.625 days � 46 days.

DSO � Days sales

outstanding �

Receivables Average sales per day

� Receivables

Annual sales/365

3 A problem arises calculating and analyzing the inventory turnover ratio. Sales are stated at mar- ket prices, so if inventories are carried at cost, as they generally are, the calculated turnover over- states the true turnover ratio. Therefore, it would be more appropriate to use cost of goods sold in place of sales in the formula’s numerator. However, established compilers of financial ratio statistics such as Dun & Bradstreet use the ratio of sales to inventories carried at cost. To develop a figure that can be compared with those published by Dun & Bradstreet and similar organizations, it is necessary to measure inventory turnover with sales in the numerator, as we do here. 4 Preferably, the average inventory value should be calculated by summing the monthly figures dur- ing the year and dividing by 12. If monthly data are not available, one can add the beginning and ending figures and divide by 2. Both methods adjust for growth but not for seasonal effects.

Days Sales Outstanding (DSO) This ratio is calculated by dividing accounts receivable by average sales per day; indicates the average length of time the firm must wait after making a sale before it receives cash.

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Note that in this calculation we used a 365-day year. Other analysts use a 360-day year for this calculation. If Allied had calculated its DSO using a 360- day year, its DSO would have been reduced slightly to 45 days.5

The DSO can also be evaluated by comparison with the terms on which the firm sells its goods. For example, Allied’s sales terms call for payment within 30 days, so the fact that 46 days’ sales, not 30 days’, are outstanding indicates that customers, on the average, are not paying their bills on time. This deprives Al- lied of funds that it could use to invest in productive assets. Moreover, in some instances the fact that a customer is paying late may signal that the customer is in financial trouble, in which case Allied may have a hard time ever collecting the receivable. Therefore, if the trend in DSO over the past few years has been rising, but the credit policy has not been changed, this would be strong evidence that steps should be taken to expedite the collection of accounts receivable.

EVALUAT ING FIXED ASSETS : THE FIXED ASSETS TURNOVER RATIO

The fixed assets turnover ratio measures how effectively the firm uses its plant and equipment. It is the ratio of sales to net fixed assets:

Allied’s ratio of 3.0 times is equal to the industry average, indicating that the firm is using its fixed assets about as intensively as are other firms in its indus- try. Therefore, Allied seems to have about the right amount of fixed assets in relation to other firms.

A potential problem can exist when interpreting the fixed assets turnover ratio. Recall from accounting that fixed assets reflect the historical costs of the assets. Inflation has caused the value of many assets that were purchased in the past to be seriously understated. Therefore, if we were comparing an old firm that had acquired many of its fixed assets years ago at low prices with a new company that had acquired its fixed assets only recently, we would probably find that the old firm had the higher fixed assets turnover ratio. However, this would be more reflective of the difficulty accountants have in dealing with in- flation than of any inefficiency on the part of the new firm. The accounting profession is trying to devise ways of making financial statements reflect cur- rent values rather than historical values. If balance sheets were actually stated on a current value basis, this would help us make better comparisons, but at the

Industry average � 3.0 times.

� $3,000 $1,000

� 3.0 times.

Fixed assets turnover ratio � Sales

Net fixed assets

A S S E T M A N AG E M E N T R AT I O S

Fixed Assets Turnover Ratio The ratio of sales to net fixed assets.

5 It would be better to use average receivables, either an average of the monthly figures or (Begin- ning receivables � Ending receivables)/2 � ($315 � $375)/2 � $345 in the formula. Had the an- nual average receivables been used, Allied’s DSO on a 365-day basis would have been $345.00/$8.2192 � 41.975 days, or approximately 42 days. The 42-day figure is the more accurate one, but because the industry average was based on year-end receivables, we used 46 days for our comparison. The DSO is discussed further in Chapter 15.

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moment the problem still exists. Since financial analysts typically do not have the data necessary to make adjustments, they simply recognize that a problem exists and deal with it judgmentally. In Allied’s case, the issue is not a serious one because all firms in the industry have been expanding at about the same rate, hence the balance sheets of the comparison firms are reasonably compa- rable.6

EVALUAT ING TOTAL ASSETS : THE TOTAL ASSETS TURNOVER RATIO

The final asset management ratio, the total assets turnover ratio, measures the turnover of all the firm’s assets; it is calculated by dividing sales by total assets:

Allied’s ratio is somewhat below the industry average, indicating that the com- pany is not generating a sufficient volume of business given its total assets in- vestment. Sales should be increased, some assets should be disposed of, or a combination of these steps should be taken.

Industry average � 1.8 times.

� $3,000 $2,000

� 1.5 times.

Total assets turnover ratio � Sales

Total assets

Total Assets Turnover Ratio This ratio is calculated by dividing sales by total assets.

SELF-TEST QUESTIONS

Identify four ratios that are used to measure how effectively a firm is man- aging its assets, and write out their equations.

How might rapid growth distort the inventory turnover ratio?

What potential problem might arise when comparing different firms’ fixed as- sets turnover ratios?

D E BT M A N AG E M E N T R AT I O S

The extent to which a firm uses debt financing, or financial leverage, has three important implications: (1) By raising funds through debt, stockholders can maintain control of a firm while limiting their investment. (2) Creditors look to the equity, or owner-supplied funds, to provide a margin of safety, so the higher the proportion of the total capital that was provided by stockholders, the less the risk faced by creditors. (3) If the firm earns more on investments financed with borrowed funds than it pays in interest, the return on the owners’ capital is magnified, or “leveraged.”

Financial Leverage The use of debt financing.

6 See FASB #89, Financial Reporting and Changing Prices (December 1986), for a discussion of the effects of inflation on financial statements.

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To understand better how financial leverage affects risk and return, consider Table 3-1. Here we analyze two companies that are identical except for the way they are financed. Firm U (for “unleveraged”) has no debt, whereas Firm L (for “leveraged”) is financed with half equity and half debt that costs 15 percent. Both companies have $100 of assets and $100 of sales, and their expected oper- ating income (also called earnings before interest and taxes, or EBIT) is $30. Thus, both firms expect to earn $30, before taxes, on their assets. Of course, things could turn out badly, in which case EBIT would be lower. Thus, in the

D E BT M A N AG E M E N T R AT I O S

T A B L E 3 - 1

FIRM U (UNLEVERAGED)

Current assets $ 50 Debt $ 0 Fixed assets 50 Common equity 100 Total assets $100 Total liabilities and equity $100

EXPECTED BAD CONDITIONS CONDITIONS

(1) (2)

Sales $100.00 $82.50 Operating costs 70.00 80.00

Operating income (EBIT) $ 30.00 $ 2.50 Interest 0.00 0.00

Earnings before taxes (EBT) $ 30.00 $ 2.50 Taxes (40%) 12.00 1.00

Net income (NI) $ 18.00 $ 1.50 ROEU � NI/Common equity � NI/$100 � 18.00% 1.50%

FIRM L (LEVERAGED)

Current assets $ 50 Debt (interest � 15%) $ 50 Fixed assets 50 Common equity 50 Total assets $100 Total liabilities and equity $100

EXPECTED BAD CONDITIONS CONDITIONS

(1) (2)

Sales $100.00 $82.50 Operating costs 70.00 80.00

Operating income (EBIT) $ 30.00 $ 2.50 Interest (15%) 7.50 7.50

Earnings before taxes (EBT) $ 22.50 ($ 5.00) Taxes (40%) 9.00 (2.00)

Net income (NI) $ 13.50 ($ 3.00) ROEL � NI/Common equity � NI/$50 � 27.00% (6.00%)

Effects of Financial Leverage on Stockholders’ Returns

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second column of the table, we show EBIT declining from $30 to $2.50 under bad conditions.

Even though both companies’ assets produce the same expected EBIT, under normal conditions Firm L should provide its stockholders with a return on eq- uity of 27 percent versus only 18 percent for Firm U. This difference is caused by Firm L’s use of debt, which “leverages up” its expected rate of return to stock- holders. There are two reasons for the leveraging effect: (1) Since interest is de- ductible, the use of debt lowers the tax bill and leaves more of the firm’s operat- ing income available to its investors. (2) If operating income as a percentage of assets exceeds the interest rate on debt, as it generally does, then a company can use debt to acquire assets, pay the interest on the debt, and have something left over as a “bonus” for its stockholders. For our hypothetical firms, these two ef- fects combine to push Firm L’s expected rate of return on equity up far above that of Firm U. Thus, debt can “leverage up” the rate of return on equity.

However, financial leverage can cut both ways. As we show in Column 2, if sales are lower and costs are higher than were expected, the return on assets will also be lower than was expected. Under these conditions, the leveraged firm’s return on equity falls especially sharply, and losses occur. Under the “bad con- ditions” in Table 3-1, the debt-free firm still shows a profit, but Firm L shows a loss and thus has a negative return on equity. This occurs because Firm L needs cash to service its debt, while Firm U does not. Firm U, because of its strong balance sheet, could ride out the recession and be ready for the next boom. Firm L, on the other hand, must pay interest of $7.50 regardless of its level of sales. Since in the recession its operations do not generate enough income to meet the interest payments, cash would be depleted, and the firm probably would need to raise additional funds. Because it would be running a loss, Firm L would have a hard time selling stock to raise capital, and its losses would cause lenders to raise the interest rate, increasing L’s problems still further. As a result, Firm L just might not survive to enjoy the next boom.

We see, then, that firms with relatively high debt ratios have higher expected returns when the economy is normal, but they are exposed to risk of loss when the economy goes into a recession. Therefore, decisions about the use of debt require firms to balance higher expected returns against increased risk. Determining the optimal amount of debt is a complicated process, and we defer a discussion of this topic until Chapter 13. For now, we simply look at two procedures analysts use to examine the firm’s debt: (1) They check the balance sheet to determine the proportion of total funds represented by debt, and (2) they review the income statement to see how well fixed charges are covered by operating profits.

HOW THE FIRM IS FINANCED: TOTAL DEBT TO TOTAL ASSETS

The ratio of total debt to total assets, generally called the debt ratio, measures the percentage of funds provided by creditors:

Industry average � 40.0%.

� $310 � $754

$2,000 �

$1,064 $2,000

� 53.2%.

Debt ratio � Total debt Total assets

Debt Ratio The ratio of total debt to total assets.

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Total debt includes both current liabilities and long-term debt. Creditors pre- fer low debt ratios because the lower the ratio, the greater the cushion against creditors’ losses in the event of liquidation. Stockholders, on the other hand, may want more leverage because it magnifies expected earnings.

Allied’s debt ratio is 53.2 percent, which means that its creditors have sup- plied more than half the total financing. As we will discuss in Chapter 13, there are a variety of factors that determine a company’s optimal debt ratio. Never- theless, the fact that Allied’s debt ratio exceeds the industry average raises a red flag and may make it costly for Allied to borrow additional funds without first raising more equity capital. Creditors may be reluctant to lend the firm more money, and management would probably be subjecting the firm to the risk of bankruptcy if it sought to increase the debt ratio any further by borrowing ad- ditional funds.7

ABIL I TY TO PAY INTEREST: T IMES-INTEREST-EARNED RATIO

The times-interest-earned (TIE) ratio is determined by dividing earnings before interest and taxes (EBIT in Table 2-2) by the interest charges:

The TIE ratio measures the extent to which operating income can decline be- fore the firm is unable to meet its annual interest costs. Failure to meet this obligation can bring legal action by the firm’s creditors, possibly resulting in bankruptcy. Note that earnings before interest and taxes, rather than net in- come, is used in the numerator. Because interest is paid with pre-tax dollars, the firm’s ability to pay current interest is not affected by taxes.

Allied’s interest is covered 3.2 times. Since the industry average is 6 times, Allied is covering its interest charges by a relatively low margin of safety. Thus, the TIE ratio reinforces the conclusion from our analysis of the debt ratio that Allied would face difficulties if it attempted to borrow additional funds.

ABIL I TY TO SERVICE DEBT: EBITDA COVERAGE RATIO

The TIE ratio is useful for assessing a company’s ability to meet interest charges on its debt, but this ratio has two shortcomings: (1) Interest is not the only fixed financial charge — companies must also reduce debt on schedule, and many firms lease assets and thus must make lease payments. If they fail to repay debt or meet lease payments, they can be forced into bankruptcy.

Industry average � 6.0 times.

� $283.8

$88 � 3.2 times.

Times-interest-earned (TIE) ratio � EBIT

Interest charges

D E BT M A N AG E M E N T R AT I O S

7 The ratio of debt to equity is also used in financial analysis. The debt-to-assets (D/A) and debt- to-equity (D/E) ratios are simply transformations of each other:

D/E � D/A

1 � D/A , D/A �

D/E 1 � D/E

.

Times-Interest-Earned (TIE) Ratio The ratio of earnings before interest and taxes (EBIT) to interest charges; a measure of the firm’s ability to meet its annual interest payments.

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(2) EBIT does not represent all the cash flow available to service debt, espe- cially if a firm has high depreciation and/or amortization charges. To account for these deficiencies, bankers and others have developed the EBITDA cover- age ratio, defined as follows:8

Allied had $283.8 million of operating income (EBIT), presumably all cash. Noncash charges of $100 million for depreciation and amortization (the DA part of EBITDA) were deducted in the calculation of EBIT, so they must be added back to find the cash flow available to service debt. Also, lease payments of $28 million were deducted before getting the $283.8 million of EBIT.9 That $28 million was available to meet financial charges, hence it must be added back, bringing the total available to cover fixed financial charges to $411.8 mil- lion. Fixed financial charges consisted of $88 million of interest, $20 million of sinking fund payments, and $28 million for lease payments, for a total of $136 million.10 Therefore, Allied covered its fixed financial charges by 3.0 times. However, if operating income declines, the coverage will fall, and operating in- come certainly can decline. Moreover, Allied’s ratio is well below the industry average, so again, the company seems to have a relatively high level of debt.

The EBITDA coverage ratio is most useful for relatively short-term lenders such as banks, which rarely make loans (except real estate-backed loans) for longer than about five years. Over a relatively short period, depreciation- generated funds can be used to service debt. Over a longer time, those funds must be reinvested to maintain the plant and equipment or else the company cannot remain in business. Therefore, banks and other relatively short-term lenders focus on the EBITDA coverage ratio, whereas long-term bondholders focus on the TIE ratio.

Industry average � 4.3 times.

� $283.8 � $100 � $28

$88 � $20 � $28 �

$411.8 $136

� 3.0 times.

EBITDA coverage ratio � EBITDA � Lease payments

Interest � Principal payments � Lease payments

8 Different analysts define the EBITDA coverage ratio in different ways. For example, some would omit the lease payment information, and others would “gross up” principal payments by dividing them by (1 � T) because these payments are not tax deductions, hence must be made with after- tax cash flows. We included lease payments because, for many firms, they are quite important, and failing to make them can lead to bankruptcy just as surely as can failure to make payments on “reg- ular” debt. We did not gross up principal payments because, if a company is in financial difficulty, its tax rate will probably be zero, hence the gross up is not necessary whenever the ratio is really important. 9 Lease payments are included in the numerator because, unlike interest, they were deducted when EBITDA was calculated. We want to find all the funds that were available to service debt, so lease payments must be added to the EBIT and DA to find the funds that could be used to service debt and meet lease payments. To illustrate this, suppose EBIT before lease payments was $100, lease payments were $100, and DA was zero. After lease payments, EBIT would be $100 � $100 � $0. Yet lease payments of $100 were made, so obviously there was cash to make those payments. The available cash was the reported EBIT of $0 plus the $100 of lease payments. 10 A sinking fund is a required annual payment designed to reduce the balance of a bond or pre- ferred stock issue. A sinking fund payment is like the principal repayment portion of the payment on an amortized loan, but sinking funds are used for publicly traded bond issues, whereas amorti- zation payments are used for bank loans and other private loans.

EBITDA Coverage Ratio A ratio whose numerator includes all cash flows available to meet fixed financial charges and whose denominator includes all fixed financial charges.

99P R O F I TA B I L I T Y R AT I O S

SELF-TEST QUESTIONS

How does the use of financial leverage affect stockholders’ control position?

In what way do taxes influence a firm’s willingness to finance with debt?

In what way does the decision to use debt involve a risk-versus-return trade- off?

Explain the following statement: “Analysts look at both balance sheet and income statement ratios when appraising a firm’s financial condition.”

Name three ratios that are used to measure the extent to which a firm uses financial leverage, and write out their equations.

P R O F I TA B I L I T Y R AT I O S

Profitability is the net result of a number of policies and decisions. The ratios examined thus far provide useful clues as to the effectiveness of a firm’s opera- tions, but the profitability ratios show the combined effects of liquidity, asset management, and debt on operating results.

PROFIT MARGIN ON SALES

The profit margin on sales, calculated by dividing net income by sales, gives the profit per dollar of sales:

Allied’s profit margin is below the industry average of 5 percent. This sub-par result occurs because costs are too high. High costs, in turn, generally occur because of inefficient operations. However, Allied’s low profit margin is also a result of its heavy use of debt. Recall that net income is income after interest. Therefore, if two firms have identical operations in the sense that their sales, operating costs, and EBIT are the same, but if one firm uses more debt than the other, it will have higher interest charges. Those interest charges will pull net income down, and since sales are constant, the result will be a relatively low profit margin. In such a case, the low profit margin would not indicate an op- erating problem, just a difference in financing strategies. Thus, the firm with the low profit margin might end up with a higher rate of return on its stock- holders’ investment due to its use of financial leverage. We will see exactly how profit margins and the use of debt interact to affect stockholder returns shortly, when we examine the Du Pont model.

Industry average � 5.0%.

� $113.5 $3,000

� 3.8%.

Profit marginon sales �

Net income available to common stockholders

Sales

Profitability Ratios A group of ratios that show the combined effects of liquidity, asset management, and debt on operating results.

Profit Margin on Sales This ratio measures net income per dollar of sales; it is calculated by dividing net income by sales.

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BASIC EARNING POWER (BEP)

The basic earning power (BEP) ratio is calculated by dividing earnings be- fore interest and taxes (EBIT) by total assets:

This ratio shows the raw earning power of the firm’s assets, before the influence of taxes and leverage, and it is useful for comparing firms with different tax sit- uations and different degrees of financial leverage. Because of its low turnover

Industry average � 17.2%.

� $283.8 $2,000

� 14.2%.

Basic earning power ratio (BEP) � EBIT

Total assets

You must be a good financial detective to analyze financialstatements, especially if the company operates overseas. Despite attempts to standardize accounting practices, there are many differences in the way financial information is re- ported in different countries, and these differences create headaches for investors trying to make cross-border company comparisons.

A study by two Rider College accounting professors demon- strated that huge differences can exist. The professors devel- oped a computer model to evaluate the net income of a hypo- thetical but typical company operating in different countries. Applying the standard accounting practices of each country, the hypothetical company would have reported net income of $34,600 in the United States, $260,600 in the United Kingdom, and $240,600 in Australia.

Such variances occur for a number of reasons. In most coun- tries, including the United States, an asset’s balance sheet value is reported at original cost less any accumulated depreci- ation. However, in some countries, asset values are adjusted to reflect current market prices. Also, inventory valuation methods vary from country to country, as does the treatment of goodwill. Other differences arise from the treatment of leases, research and development costs, and pension plans.

These differences arise from a variety of legal, historical, cultural, and economic factors. For example, in Germany and

Japan large banks are the key source of both debt and equity capital, whereas in the United States public capital markets are most important. As a result, U.S. corporations disclose a great deal of information to the public, while German and Japanese corporations use very conservative accounting practices that appeal to the banks.

The accounting profession has long recognized that inter- national accounting differences exist, and it has taken steps toward making international comparisons easier. The Interna- tional Accounting Standards Committee (IASC) was formed for the purpose of bringing financial accounting and reporting standards into closer conformity on a global basis. This com- mittee, whose recognition and acceptance is growing, is cur- rently working on projects to produce the first globally recog- nized accounting standards. A global accounting structure would enable investors and practitioners around the world to read and understand financial reports produced anywhere in the world. So, as you can see, the IASC’s task is a very im- portant one. It remains to be seen whether the IASC’s lofty goal will be achieved.

SOURCE: “All Accountants Soon May Speak the Same Language,” The Wall Street

Journal, August 29, 1995, A15.

INTERNATIONAL ACCOUNTING DIFFERENCES CREATE HEADACHES FOR INVESTORS

Basic Earning Power (BEP) Ratio This ratio indicates the ability of the firm’s assets to generate operating income; calculated by dividing EBIT by total assets.

101

ratios and low profit margin on sales, Allied is not earning as high a return on its assets as is the average food-processing company.11

RETURN ON TOTAL ASSETS

The ratio of net income to total assets measures the return on total assets (ROA) after interest and taxes:

Allied’s 5.7 percent return is well below the 9 percent average for the industry. This low return results from (1) the company’s low basic earning power plus (2) high interest costs resulting from its above-average use of debt, both of which cause its net income to be relatively low.

RETURN ON COMMON EQUITY

Ultimately, the most important, or “bottom line,” accounting ratio is the ratio of net income to common equity, which measures the return on common eq- uity (ROE):

Stockholders invest to get a return on their money, and this ratio tells how well they are doing in an accounting sense. Allied’s 12.7 percent return is below the 15 percent industry average, but not as far below as the return on total assets. This somewhat better result is due to the company’s greater use of debt, a point that is analyzed in detail later in the chapter.

Industry average � 15.0%.

� $113.5 $896

� 12.7%.

Return oncommon equity � ROE �

Net income available to common stockholders

Common equity

Industry average � 9.0%.

� $113.5 $2,000

� 5.7%.

Return ontotal assets � ROA �

Net income available to common stockholders

Total assets

P R O F I TA B I L I T Y R AT I O S

11 Notice that EBIT is earned throughout the year, whereas the total assets figure is an end-of-the- year number. Therefore, it would be conceptually better to calculate this ratio as EBIT/Average as- sets � EBIT/[(Beginning assets � Ending assets)/2]. We have not made this adjustment because the published ratios used for comparative purposes do not include it. However, when we construct our own comparative ratios, we do make the adjustment. Incidentally, the same adjustment would also be appropriate for the next two ratios, ROA and ROE.

Return on Common Equity (ROE) The ratio of net income to common equity; measures the rate of return on common stockholders’ investment.

Return on Total Assets (ROA) The ratio of net income to total assets.

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS102

M A R K E T VA L U E R AT I O S

A final group of ratios, the market value ratios, relates the firm’s stock price to its earnings, cash flow, and book value per share. These ratios give manage- ment an indication of what investors think of the company’s past performance and future prospects. If the liquidity, asset management, debt management, and profitability ratios all look good, then the market value ratios will be high, and the stock price will probably be as high as can be expected.

PRICE/EARNINGS RATIO

The price/earnings (P/E) ratio shows how much investors are willing to pay per dollar of reported profits. Allied’s stock sells for $23, so with an EPS of $2.27 its P/E ratio is 10.1:

As we will see in Chapter 9, P/E ratios are higher for firms with strong growth prospects, other things held constant, but they are lower for riskier firms. Since Allied’s P/E ratio is below the average for other food processors, this suggests that the company is regarded as being somewhat riskier than most, as having poorer growth prospects, or both.

PRICE/CASH FLOW RATIO

In some industries, stock price is tied more closely to cash flow rather than net income. Consequently, investors often look at the price/cash flow ratio:

Industry average � 6.8 times.

� $23.00 $4.27

� 5.4 times.

Price/cash flow � Price per share

Cash flow per share

Industry average � 12.5 times.

� $23.00 $2.27

� 10.1 times.

Price/earnings (P/E) ratio � Price per share

Earnings per share

Market Value Ratios A set of ratios that relate the firm’s stock price to its earnings, cash flow, and book value per share.

Price/Earnings (P/E) Ratio The ratio of the price per share to earnings per share; shows the dollar amount investors will pay for $1 of current earnings.

Price/Cash Flow Ratio The ratio of price per share divided by cash flow per share; shows the dollar amount investors will pay for $1 of cash flow.

SELF-TEST QUESTIONS

Identify and write out the equations for four ratios that show the combined effects of liquidity, asset management, and debt management on profitability.

Why is the basic earning power ratio useful?

Why does the use of debt lower the ROA?

What does ROE measure? Since interest expense lowers profits, does using debt lower ROE?

103

The calculation for cash flow per share was shown in Chapter 2, but just to re- fresh your memory, cash flow per share is calculated as net income plus depre- ciation and amortization divided by common shares outstanding.

Allied’s price/cash flow ratio is also below the industry average, once again suggesting that its growth prospects are below average, its risk is above average, or both.

Note that some analysts look at multiples beyond just the price/earnings and the price/cash flow ratios. For example, depending on the industry, some may look at measures such as price/sales, price/customers, or price/EBITDA per share. Ultimately, though, value depends on earnings and cash flows, so if these “exotic” ratios do not forecast future EPS and cash flow, they may turn out to be misleading.

MARKET/BOOK RATIO

The ratio of a stock’s market price to its book value gives another indication of how investors regard the company. Companies with relatively high rates of re- turn on equity generally sell at higher multiples of book value than those with low returns. First, we find Allied’s book value per share:

Now we divide the market price per share by the book value to get a market/ book (M/B) ratio of 1.3 times:

Investors are willing to pay less for a dollar of Allied’s book value than for one of an average food-processing company.

The average company followed by the Value Line Investment Survey had a market/book ratio of about 4.28 in early 2001. Since M/B ratios typically ex- ceed 1.0, this means that investors are willing to pay more for stocks than their accounting book values. This situation occurs primarily because asset values, as reported by accountants on corporate balance sheets, do not reflect either in- flation or “goodwill.” Thus, assets purchased years ago at preinflation prices are carried at their original costs, even though inflation might have caused their ac- tual values to rise substantially, and successful going concerns have a value greater than their historical costs.

If a company earns a low rate of return on its assets, then its M/B ratio will be relatively low versus an average company. Thus, some airlines, which have not fared well in recent years, sell at M/B ratios below 1.0, while very successful

Industry average � 1.7 times.

� $23.00 $17.92

� 1.3 times.

Market/book ratio � M/B � Market price per share Book value per share

� $896

50 � $17.92.

Book value per share � Common equity

Shares outstanding

M A R K E T VA L U E R AT I O S

Market/Book (M/B) Ratio The ratio of a stock’s market price to its book value.

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS104

eBAY’S FINANCIAL STATEMENTS

If you examine the financial statements of a typical Internetretailer, you will quickly see that these companies are very different from their traditional “bricks and mortar” counter- parts. For example, look at the 1998 year-end balance sheet of the online auctioneer, eBay Inc., shown in millions of dollars:

ASSETS:

Cash and marketable securities $72.1 Accounts receivable 6.4 Other current assets 4.8

Total current assets $83.3 Net property and equipment 7.8 Other assets 1.3

Total assets $92.4 LIABILITIES AND EQUITY:

Total current liabilities $ 8.0 Total shareholders’ equity 84.4

Total liabilities and shareholders’ equity $92.4

During the year ending March 31, 1999, eBay generated net income of $8.15 million. At first glance, eBay may look like a somewhat sleepy company with modest profitability (ROE less than 10 percent), a strong balance sheet (lots of cash and lit- tle debt), and limited growth opportunities (because the com- pany does not have much plant and equipment that can be used to generate future sales). However, midway through 1999, eBay’s market capitalization (its stock price multiplied by the number of shares outstanding) was a whopping $17.6 billion! What makes this even more incredible is the fact that eBay’s market capitalization had fallen dramatically from a high of $30 billion just two months earlier.

Why does the market value eBay so highly? Clearly, the market is forecasting that eBay will have phenomenal growth over the next several years. Many believe that online auctions will continue to grow, and eBay’s costs should grow more slowly than its revenues. This should translate into strong

earnings growth. Moreover, many proponents of eBay argue that the company is unlikely to face much in the way of seri- ous competition, because it has the advantage of being the first major player in this market. After all, if you want to auc- tion off that old baseball card, wouldn’t you want to use the company that has the longest track record and the most po- tential bidders?

Critics suggest that while eBay is a great company, its price has gotten way ahead of its value, and it is due for a fall once the hype dies down. These critics also contend that it is fool- ish to think that eBay won’t face serious competition. For ex- ample, Internet retailer Amazon.com has already leapt into the online auction market, and it threatens to be a serious com- petitor in the years ahead.

Over 18 months later in mid-2000, eBay’s total assets had increased more than ten-fold to just over $1 billion, yet its market capitalization had fallen to $13 billion. Here are some key items from eBay’s mid-2000 balance sheet, shown again in millions of dollars:

ASSETS:

Total current assets $ 369.2 Net property and equipment 123.5 Other assets 579.0

Total assets $1,071.7

LIABILITIES AND EQUITY:

Total current liabilities $ 111.1 Long-term debt and leases 14.7 Other liabilities and minority interests 20.7 Total shareholders’ equity 925.2

Total liabilities and shareholders’ equity $1,071.7

The more recent balance sheet numbers confirm that eBay has grown tremendously in a short period of time and that the company’s operations are transforming over time. These changes will undoubtedly continue in the future.

firms such as Microsoft (which makes the operating systems for virtually all PCs) achieve high rates of return on their assets, causing their market values to be well in excess of their book values. In February 2001, Microsoft’s book value per share was $8.71 versus a market price of $64.69, so its market/book ratio was $64.69/$8.71 � 7.43 times.

T R E N D A N A LY S I S

It is important to analyze trends in ratios as well as their absolute levels, for trends give clues as to whether a firm’s financial condition is likely to improve or to deteriorate. To do a trend analysis, one simply plots a ratio over time, as shown in Figure 3-1. This graph shows that Allied’s rate of return on common equity has been declining since 1998, even though the industry average has been relatively stable. All the other ratios could be an- alyzed similarly.

105T R E N D A N A LY S I S

SELF-TEST QUESTIONS

Describe three ratios that relate a firm’s stock price to its earnings, cash flow, and book value per share, and write out their equations.

How do market value ratios reflect what investors think about a stock’s risk and expected rate of return?

What does the price/earnings (P/E) ratio show? If one firm’s P/E ratio is lower than that of another, what are some factors that might explain the difference?

How is book value per share calculated? Explain how inflation and “good- will” could cause book values to deviate from market values.

F I G U R E 3 - 1 Rate of Return on Common Equity, 1997–2001

16

14

12

10

ROE (%)

1997 1998 1999 2000 2001

Industry

Allied

Trend Analysis An analysis of a firm’s financial ratios over time; used to estimate the likelihood of improvement or deterioration in its financial condition.

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS106

T Y I N G T H E R AT I O S TO G E T H E R : T H E D U P O N T C H A R T A N D E Q UAT I O N

Table 3-2 summarizes Allied’s ratios, and Figure 3-2 shows how the return on equity is affected by asset turnover, the profit margin, and leverage. The chart depicted in Figure 3-2 is called a modified Du Pont chart because that com- pany’s managers developed this approach for evaluating performance. Working from the bottom up, the left-hand side of the chart develops the profit margin on sales. The various expense items are listed and then summed to obtain Al- lied’s total cost, which is subtracted from sales to obtain the company’s net in- come. When we divide net income by sales, we find that 3.8 percent of each sales dollar is left over for stockholders. If the profit margin is low or trending down, one can examine the individual expense items to identify and then cor- rect problems.

The right-hand side of Figure 3-2 lists the various categories of assets, totals them, and then divides sales by total assets to find the number of times Allied “turns its assets over” each year. The company’s total assets turnover ratio is 1.5 times.

The profit margin times the total assets turnover is called the Du Pont equation, and it gives the rate of return on assets (ROA):

(3-1)

Allied made 3.8 percent, or 3.8 cents, on each dollar of sales, and assets were “turned over” 1.5 times during the year. Therefore, the company earned a re- turn of 5.7 percent on its assets.

If the company were financed only with common equity, the rate of return on assets (ROA) and the return on equity (ROE) would be the same because total assets would equal common equity:

This equality holds if and only if Total assets � Common equity, that is, if the company uses no debt. Allied does use debt, so its common equity is less than total assets. Therefore, the return to the common stockholders (ROE) must be greater than the ROA of 5.7 percent. Specifically, the rate of return on assets

ROA � Net income Total assets

� Net income

Common equity � ROE.

� 3.8% � 1.5 � 5.7%.

� Net income

Sales �

Sales Total assets

ROA � Profit margin � Total assets turnover

Du Pont Equation A formula which shows that the rate of return on assets can be found as the product of the profit margin times the total assets turnover.

Du Pont Chart A chart designed to show the relationships among return on investment, asset turnover, profit margin, and leverage.

SELF-TEST QUESTIONS

How does one do a trend analysis?

What important information does a trend analysis provide?

107T Y I N G T H E R AT I O S TO G E T H E R : T H E D U P O N T C H A R T A N D E Q UAT I O N

T A B L E 3 - 2

INDUSTRY RATIO FORMULA FOR CALCULATION CALCULATION RATIO AVERAGE COMMENT

LIQUIDITY

Current � 3.2� 4.2� Poor

� 1.2� 2.1� Poor

ASSET MANAGEMENT

� 4.9� 9.0� Poor

� 46 days 36 days Poor

� 3.0� 3.0� OK

� 1.5� 1.8�

DEBT MANAGEMENT

� 53.2% 40.0% High (risky)

� 3.2� 6.0� Low (risky)

� 3.0� 4.3� Low (risky)

PROFITABILITY

� 3.8% 5.0% Poor

� 14.2% 17.2% Poor

� 5.7% 9.0% Poor

� 12.7% 15.0% Poor

MARKET VALUE

� 10.1� 12.5� Low

� 5.4� 6.8� Low

� 1.3� 1.7� Low $23.00 $17.92

Market price per share Book value per share

Market/book (M/B)

$23.00 $4.27

Price per share Cash flow per share

Price/cash flow

$23.00 $2.27

Price per share Earnings per share

Price/earnings (P/E)

$113.5 $896

Net income available to common stockholders Common equity

Return on common equity (ROE)

$113.5 $2,000

Net income available to common stockholders Total assets

Return on total assets (ROA)

$283.8 $2,000

Earnings before interest and taxes (EBIT) Total assets

Basic earning power (BEP)

$113.5 $3,000

Net income available to common stockholders Sales

Profit margin on sales

$411.8 $136

EBITDA � Lease payments Interest � Principal payments � Lease payments

EBITDA coverage

$283.8 $88

Earnings before interest and taxes (EBIT) Interest charges

Times-interest- earned (TIE)

$1,064 $2,000

Total debt Total assets

Total debt to total assets

Somewhat low

$3,000 $2,000

Sales Total assets

Total assets turnover

$3,000 $1,000

Sales Net fixed assets

Fixed assets turnover

$375 $8.2192

Receivables Annual sales/365

Days sales outstanding (DSO)

$3,000 $615

Sales Inventories

Inventory turnover

$385 $310

Current assets � Inventories Current liabilities

Quick, or acid, test

$1,000 $310

Current assets Current liabilities

Allied Food Products: Summary of Financial Ratios (Millions of Dollars)

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS108

(ROA) can be multiplied by the equity multiplier, which is the ratio of assets to common equity:

Firms that use a large amount of debt financing (more leverage) will necessar- ily have a high equity multiplier — the more the debt, the less the equity, hence the higher the equity multiplier. For example, if a firm has $1,000 of assets and is financed with $800, or 80 percent debt, then its equity will be $200, and its equity multiplier will be $1,000/$200 � 5. Had it used only $200 of debt, then its equity would have been $800, and its equity multiplier would have been only $1,000/$800 � 1.25.12

Equity multiplier � Total assets

Common equity .

12 Expressed algebraically,

Here D is debt, E is equity, A is total assets, and A/E is the equity multiplier. This equation ignores preferred stock.

Debt ratio � D A

� A � E

A �

A A

� E A

� 1 � 1

Equity multiplier .

Depreciation $100

Taxes $78.3

Total Costs $2,886.5

Interest plus Preferred Dividends

$92

Other Operating Costs $2,616.2

(Labor, overhead, etc.)

Subtracted from

Sales $3,000

Profit Margin: Earnings as a Percent of Sales 3.8%

Divided into

Net Income $113.5

Sales $3,000

Multiplied by

Multiplied by

Return on Equity 12.7%

Return on Assets 5.7% Assets/Equity = $2,000/$896

Total Assets Turnover 1.5

Sales $3,000

Divided by

Fixed Assets $1,000

Added to

Cash and Marketable

Securities $10

Accounts Receivable

$375 Inventories

$615

Current Assets $1,000

Total Assets $2,000

= 2.23

F I G U R E 3 - 2 Modified Du Pont Chart for Allied Food Products (Millions of Dollars)

109

Allied’s return on equity (ROE) depends on its ROA and its use of lever- age:13

(3-2)

� 5.7% � $2,000/$896

� 5.7% � 2.23

� 12.7%.

Now we can combine Equations 3-1 and 3-2 to form the Extended Du Pont Equation, which shows how the profit margin, the assets turnover ratio, and the equity multiplier combine to determine the ROE:

ROE � (Profit margin) (Total assets turnover) (Equity multiplier)

(3-3)

For Allied, we have

ROE � (3.8%) (1.5) (2.23)

� 12.7%.

The 12.7 percent rate of return could, of course, be calculated directly: both Sales and Total assets cancel, leaving Net income/Common equity � $113.5/ $896 � 12.7%. However, the Du Pont equation shows how the profit margin, the total assets turnover, and the use of debt interact to determine the return on equity.14

Allied’s management can use the Du Pont system to analyze ways of im- proving performance. Focusing on the left, or “profit margin,” side of its modified Du Pont chart, Allied’s marketing people can study the effects of raising sales prices (or lowering them to increase volume), of moving into new products or markets with higher margins, and so on. The company’s cost ac- countants can study various expense items and, working with engineers, pur- chasing agents, and other operating personnel, seek ways to hold down costs. On the “turnover” side, Allied’s financial analysts, working with both produc- tion and marketing people, can investigate ways to reduce the investment in

� Net income

Sales �

Sales Total assets

� Total assets

Common equity .

� Net income Total assets

� Total assets

Common equity

ROE � ROA � Equity multiplier

T Y I N G T H E R AT I O S TO G E T H E R : T H E D U P O N T C H A R T A N D E Q UAT I O N

13 Note that we could also find the ROE by “grossing up” the ROA, that is, by dividing the ROA by the common equity fraction: ROE � ROA/Equity fraction � 5.7%/0.448 � 12.7%. The two procedures are algebraically equivalent. 14 Another frequently used ratio is the following:

The numerator shows the dollar returns to investors, the denominator shows the total amount of money investors have put up, and the ratio itself shows the rate of return on all investors’ capital. This ratio is especially important in the public utility industries, where regulators are concerned about the companies’ using their monopoly positions to earn excessive returns on investors’ capi- tal. In fact, regulators try to set utility prices (service rates) at levels that will force the return on in- vestors’ capital to equal a company’s cost of capital as defined in Chapter 10.

Rate of return on investors' capital � Net income � Interest

Debt � Equity .

C O M PA R AT I V E R AT I O S A N D “ B E N C H M A R K I N G ”

Ratio analysis involves comparisons — a company’s ratios are compared with those of other firms in the same industry, that is, to industry aver- age figures. However, like most firms, Allied’s managers go one step further — they also compare their ratios with those of a smaller set of leading food companies. This technique is called benchmarking, and the companies used for the comparison are called benchmark companies. Allied’s management benchmarks against Campbell Soup, a leading manufacturer of canned soups; Dean Foods, a processor of canned and frozen vegetables; Dole Food Com- pany, a processor of fruits and vegetables; H.J. Heinz, which makes ketchup and other products; Flowers Industries, a producer of bakery and snack-food goods; Sara Lee, a manufacturer of baked goods; and Hershey Foods Corp., a producer of chocolates, nonchocolate confectionary products, and pasta. Ratios are calculated for each company. Then the ratios are listed in de- scending order, as shown below for the profit margin on sales (as reported

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS110

various types of assets. At the same time, the treasury staff can analyze the ef- fects of alternative financing strategies, seeking to hold down interest expense and the risk of debt while still using leverage to increase the rate of return on equity.

As a result of such an analysis, Ellen Jackson, Allied’s president, recently an- nounced a series of moves designed to cut operating costs by more than 20 per- cent per year. Jackson and Allied’s other executives have a strong incentive for improving the company’s financial performance, because their compensation is based to a large extent on how well the company does. Allied’s executives re- ceive a salary that is sufficient to cover their living costs, but their compensa- tion package also includes “performance shares” that will be awarded if and only if the company meets or exceeds target levels for earnings and the stock price. These target levels are based on Allied’s performance relative to other food companies. So, if Allied does well, then Jackson and the other executives — and the stockholders — will also do well. But if things deteriorate, Jackson could be looking for a new job.

Benchmarking The process of comparing a particular company with a group of “benchmark” companies.

SELF-TEST QUESTIONS

Explain how the extended, or modified, Du Pont equation and chart can be used to reveal the basic determinants of ROE.

What is the equity multiplier?

How can management use the Du Pont system to analyze ways of improving the firm’s performance?

111C O M PA R AT I V E R AT I O S A N D “ B E N C H M A R K I N G ”

SELF-TEST QUESTIONS

Differentiate between trend analysis and comparative ratio analysis.

Why is it useful to do a comparative ratio analysis?

What is benchmarking?

on the firms’ latest quarterly financial statements for 2000 by Hoover’s On- line):

PROFIT MARGIN

Campbell Soup 10.0% Sara Lee 6.0 Hershey Foods 4.8 Allied Food Products 3.8 Heinz 3.8 Dole Food Company 3.5 Dean Foods 2.6 Flowers Industries 0.6

The benchmarking setup makes it easy for Allied’s management to see exactly where the company stands relative to its competition. As the data show, Allied is in the middle of its benchmark group with respect to its profit margin, so the company has room for improvement. Other ratios are analyzed similarly.

Comparative ratios are available from a number of sources, including Value Line. Table 3-3 presents a list of key ratios for a variety of industries covered by Value Line. Useful ratios are also compiled by Dun and Bradstreet (D&B) and the Annual Statement Studies published by Robert Morris Associates, which is the national association of bank loan officers. Also, financial statement data for thousands of publicly owned corporations are available on magnetic tapes and diskettes, and since brokerage houses, banks, and other financial institutions have access to these data, security analysts can and do generate comparative ra- tios tailored to their specific needs.

Each of the data-supplying organizations uses a somewhat different set of ratios designed for its own purposes. For example, D&B deals mainly with small firms, many of which are proprietorships, and it sells its services pri- marily to banks and other lenders. Therefore, D&B is concerned largely with the creditor’s viewpoint, and its ratios emphasize current assets and liabilities, not market value ratios. So, when you select a comparative data source, you should be sure that your emphasis is similar to that of the agency whose ra- tios you plan to use. Additionally, there are often definitional differences in the ratios presented by different sources, so before using a source, be sure to verify the exact definitions of the ratios to ensure consistency with your own work.

A great link for comparative ratios is http://finance. yahoo.com. Here you can find stock quotes, detailed company profiles, company

ratios, and comparative ratios.

112

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U S E S A N D L I M I TAT I O N S O F R AT I O A N A LY S I S

As noted earlier, ratio analysis is used by three main groups: (1) managers, who employ ratios to help analyze, control, and thus improve their firms’ opera- tions; (2) credit analysts, including bank loan officers and bond rating analysts, who analyze ratios to help ascertain a company’s ability to pay its debts; and (3) stock analysts, who are interested in a company’s efficiency, risk, and growth prospects. In later chapters we will look more closely at the basic factors that underlie each ratio, which will give you a better idea about how to interpret and use ratios. Note, though, that while ratio analysis can provide useful informa- tion concerning a company’s operations and financial condition, it does have limitations that necessitate care and judgment. Some potential problems are listed below:

1. Many large firms operate different divisions in different industries, and for such companies it is difficult to develop a meaningful set of industry averages. Therefore, ratio analysis is more useful for small, narrowly fo- cused firms than for large, multidivisional ones.

2. Most firms want to be better than average, so merely attaining average performance is not necessarily good. As a target for high-level perfor- mance, it is best to focus on the industry leaders’ ratios. Benchmarking helps in this regard.

3. Inflation may have badly distorted firms’ balance sheets — recorded val- ues are often substantially different from “true” values. Further, since in- flation affects both depreciation charges and inventory costs, profits are also affected. Thus, a ratio analysis for one firm over time, or a com- parative analysis of firms of different ages, must be interpreted with judgment.

4. Seasonal factors can also distort a ratio analysis. For example, the inven- tory turnover ratio for a food processor will be radically different if the balance sheet figure used for inventory is the one just before versus just after the close of the canning season. This problem can be minimized by using monthly averages for inventory (and receivables) when calculating turnover ratios.

5. Firms can employ “window dressing” techniques to make their finan- cial statements look stronger. To illustrate, a Chicago builder borrowed on a two-year basis on December 29, 2001, held the proceeds of the loan as cash for a few days, and then paid off the loan ahead of time on January 2, 2002. This improved his current and quick ratios, and made his year-end 2001 balance sheet look good. However, the improvement was strictly window dressing; a week later the balance sheet was back at the old level.

6. Different accounting practices can distort comparisons. As noted earlier, inventory valuation and depreciation methods can affect financial state- ments and thus distort comparisons among firms. Also, if one firm leases a substantial amount of its productive equipment, then its assets may ap- pear low relative to sales because leased assets often do not appear on the balance sheet. At the same time, the liability associated with the lease

U S E S A N D L I M I TAT I O N S O F R AT I O A N A LY S I S

“Window Dressing” Techniques Techniques employed by firms to make their financial statements look better than they really are.

To find quick information about a company, link to http://www. marketguide.com. Here you can find company

profiles, stock price and share information, and several key ratios.

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS114

obligation may not be shown as a debt. Therefore, leasing can artificially improve both the turnover and the debt ratios. However, the accounting profession has taken steps to reduce this problem.

7. It is difficult to generalize about whether a particular ratio is “good” or “bad.” For example, a high current ratio may indicate a strong liquid- ity position, which is good, or excessive cash, which is bad (because ex- cess cash in the bank is a nonearning asset). Similarly, a high fixed as- sets turnover ratio may denote either a firm that uses its assets efficiently or one that is undercapitalized and cannot afford to buy enough assets.

8. A firm may have some ratios that look “good” and others that look “bad,” making it difficult to tell whether the company is, on balance, strong or weak. However, statistical procedures can be used to analyze the net effects of a set of ratios. Many banks and other lending organizations use such procedures to analyze firms’ financial ratios, and then to classify them ac- cording to their probability of getting into financial trouble.15

Ratio analysis is useful, but analysts should be aware of these problems and make adjustments as necessary. Ratio analysis conducted in a mechanical, un- thinking manner is dangerous, but used intelligently and with good judgment, it can provide useful insights into a firm’s operations. Your judgment in inter- preting a set of ratios is bound to be weak at this point, but it will improve as you go through the remainder of the book.

SELF-TEST QUESTIONS

List three types of users of ratio analysis. Would the different users empha- size the same or different types of ratios? Explain.

List several potential problems with ratio analysis.

15 The technique used is discriminant analysis. For a detailed discussion, see Edward I. Altman, “Fi- nancial Ratios, Discriminant Analysis, and the Prediction of Corporate Bankruptcy,” Journal of Fi- nance, September 1968, 589–609. For a summary, see Eugene F. Brigham and Phillip R. Daves, In- termediate Financial Management, 7th ed. (Fort Worth, TX: Harcourt College Publishers, 2002), Chapter 24 Extensions.

P R O B L E M S W I T H R O E

In Chapter 1 we said that managers should strive to maximize shareholder wealth. If a firm takes steps to improve its ROE, does it mean that shareholder wealth will also increase? Not necessarily, for despite its widespread use and the fact that ROE and shareholder wealth are often highly correlated, some prob- lems can arise when firms use ROE as the sole measure of performance.

First, ROE does not consider risk. While shareholders clearly care about re- turns, they also care about risk. To illustrate this point, consider two divisions

CALCULATING EVA

115P R O B L E M S W I T H R O E

To better understand the idea behind EVA and how it is con-nected to ROE, let’s look at Keller Electronics. Keller has $100,000 in investor-supplied operating capital, which, in turn, consists of $50,000 of long-term debt and $50,000 of common equity. The company has no preferred stock or notes payable. The long-term debt has a 10 percent interest rate. However, since the company is in the 40 percent tax bracket and interest expense is tax deductible, the after-tax cost of debt is only 6 percent. On the basis of their assessment of the company’s risk, shareholders require a 14 percent return. This 14 percent return is what shareholders could expect to earn if they were to take their money elsewhere and invest in stocks that have the same risk as Keller. Keller’s overall cost of capital is a weighted aver- age of the cost of debt and equity, and it is 10 percent, found as 0.50(6%) � 0.50(14%) � 10%. The total dollar cost of cap- ital per year is 0.10($100,000) � $10,000.

Now let’s look at Keller’s income statement. Its operating in- come, EBIT, is $20,000, and its interest expense is 0.10($50,000) � $5,000. Therefore, its taxable income is $20,000 � $5,000 � $15,000. Taxes equal 40 percent of tax- able income, or 0.4($15,000) � $6,000, so the firm’s net in- come is $9,000, and its return on equity, ROE, is $9,000/$50,000 � 18%.

Now what is Keller’s EVA? Recall from Chapter 2 that the basic formula for EVA is:

EVA � EBIT (1 � Corporate tax rate) � (Total investor- supplied operating capital)(After-tax percentage cost of capital)

� $20,000 (1 � 0.40) � ($100,000)(0.10) � $2,000.

This $2,000 EVA indicates that Keller provided its shareholders with $2,000 more than they could have earned elsewhere by in- vesting in other stocks with the same risk as Keller’s stock. To see where this $2,000 comes from, let’s trace what happens to the money:

� The firm generates $20,000 in operating income. � $6,000 goes to the government to pay taxes, leaving

$14,000. � $5,000 goes to the bondholders in the form of interest

payments, thus leaving $9,000. � $7,000 is what Keller’s shareholders expected to earn:

0.14($50,000) � $7,000. Note that this $7,000 payment is not a requirement to stay in business — companies can stay in business as long as they pay their bills and their taxes. However, this $7,000 is what shareholders expected to earn, and it is the amount the firm must earn if it is to avoid reducing shareholder wealth.

� What’s left over, the $2,000, is EVA. In this case, Keller’s management created wealth because it provided share- holders with a return greater than what they presumably would have earned on alternative investments with the same risk as Keller’s stock.

SOME ADDITIONAL POINTS � In practice, it is often necessary to make several adjust-

ments in order to arrive at a “better” measure of EVA. The adjustments deal with leased assets, depreciation, and other accounting details.

� Shareholders may not immediately receive the $9,000 that Keller made for them this year (the $7,000 that shareholders expected plus the $2,000 of EVA). Keller can either pay its earnings out as dividends or keep them in the firm as retained earnings. In either event, the $9,000 is shareholders’ money. The factors influenc- ing the dividend payout decision are discussed in Chap- ter 14.

THE CONNECTION BETWEEN ROE AND EVA We said that EVA is different from the traditional accounting measure of profit in that EVA explicitly considers not just the interest cost of debt but also the cost of equity. Indeed, using the simple example above, we could also express EVA as net in- come minus the dollar cost of equity:

EVA � Net income � [(Equity capital) (Cost of equity capital)]

� $9,000 � [($50,000)(0.14)]

� $2,000.

Note that this is the same number we calculated before when we used the other formula for calculating EVA. Note also that the expression above could be rewritten as follows:

EVA � (Equity capital)[Net income/Equity capital � Cost of equity capital],

or simply as:

EVA � (Equity capital)(ROE � Cost of equity capital).

This last expression implies that EVA depends on three factors: rate of return, as reflected in ROE; risk, which affects the cost of equity; and size, which is measured by the amount of eq- uity capital employed. Recall that earlier in this chapter we said that shareholder value depends on risk, return, and the amount of capital invested. This final equation illustrates this point.

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS116

SELF-TEST QUESTION

If a firm takes steps to improve its ROE, does this mean that shareholder wealth will also increase? Explain.

within the same firm. Division S has very stable cash flows and a predictable 15 percent ROE. Division R, on the other hand, has a 16 percent expected ROE, but its cash flows are very risky, so the expected ROE may not materialize. If managers were compensated solely on the basis of ROE, and if the expected ROEs were actually achieved, then Division R’s manager would receive a higher bonus than Division S’s manager, even though Division S may actually create more value for shareholders as a result of its lower risk.

Second, ROE does not consider the amount of invested capital. To illustrate this point, let’s consider a rather extreme example. A large company has $1 in- vested in Project A, which has an ROE of 50 percent, and $1 million invested in Project B, which has a 40 percent ROE. The projects are equally risky, and the two returns are both well above the cost the company had to pay for the capital invested in the projects. In this example, Project A has a higher ROE, but since it is so small, it does little to enhance shareholder wealth. Project B, on the other hand, has the lower ROE, but it adds much more to shareholder value.

Consider one last problem with ROE. Assume that you manage a division of a large firm. The firm uses ROE as the sole measure of performance, and it de- termines bonuses on the basis of ROE. Toward the end of the fiscal year, your division’s ROE is an impressive 45 percent. Now you have an opportunity to invest in a large, low-risk project that has an estimated ROE of 35 percent, which is well above the cost of the capital you need to make the investment. Even though this project is profitable, you might be reluctant to make the in- vestment because it would reduce your division’s average ROE, and therefore reduce the size of your year-end bonus.

These three examples suggest that a project’s return must be combined with its risk and size to determine its effect on shareholder value. To the extent that ROE focuses only on rate of return, increasing ROE may in some cases be in- consistent with increasing shareholder wealth. With this in mind, academics, practitioners, and consultants have tried to develop alternative measures that overcome ROE’s potential problems when it is used as the sole gauge of per- formance. One such measure is Economic Value Added (EVA). In Chapter 2, we showed how to calculate EVA. For a discussion of the connection between ROE and EVA, see the accompanying box, “Calculating EVA.”

Students might want to refer to AAII’s educational web site at http:// www.aaii.org. The site provides information on

investing basics, financial planning, portfolio management, and the like, so individuals can manage their own assets more effectively.

L O O K I N G B E YO N D T H E N U M B E R S

Hopefully, working through this chapter has helped your understanding of fi- nancial statements and improved your ability to interpret accounting numbers. These important and basic skills are necessary when making business decisions, when evaluating performance, and when forecasting likely future developments.

Sound financial analysis involves more than just calculating numbers — good analysis requires that certain qualitative factors be considered when eval-

117L O O K I N G B E YO N D T H E N U M B E R S

Financial ratio analysis is especially useful for small busi-nesses, and readily available sources provide comparative data by firm size. For example, Robert Morris Associates pro- vides comparative ratios for a number of small-firm classes, down to a size range of zero to $250,000 in annual sales. Nev- ertheless, analyzing a small firm’s statements presents some unique problems. We examine here some of those problems from the standpoint of a bank loan officer, one of the most frequent users of ratio analysis.

When evaluating a small-business credit prospect, a banker is essentially making a prediction about the company’s ability to repay its debt. In making this prediction, the banker will be especially concerned about indicators of liquidity and about continuing prospects for profitability. Bankers like to do busi- ness with a new customer if it appears that loans can be paid off on time and that the company will remain in business and therefore continue to be a customer for some years to come. Thus, both short-run and long-run viability are of interest to the banker. Note too that the banker’s perceptions about the business are important to the owner-manager, because the bank will probably be the firm’s primary source of funds.

The first problem the banker is likely to encounter is that, unlike the bank’s bigger customers, the small firm may not have audited financial statements. Further, the statements that are available may have been produced on an irregular basis (for ex- ample, in some months or quarters but not in others). If the firm is young, it may have historical financial statements for only one year, or perhaps none at all. Also, the financial state- ments may not have been produced by a reputable accounting firm but by the owner’s brother-in-law.

The poor quality of its financial data may therefore be a hin- drance for a small business that is attempting to establish a banking relationship. This could keep the firm from getting credit even though it is really on solid financial ground. There- fore, it is in the owner’s interest to make sure that the firm’s fi- nancial data are credible, even if it is more expensive to do so. Furthermore, if the banker is uncomfortable with the data, the firm’s management should also be uncomfortable: Because many managerial decisions depend on the numbers in the firm’s ac- counting statements, those numbers should be as accurate as possible.

For a given set of financial ratios, a small firm may be riskier than a larger one. Small firms often produce a single product, rely heavily on a single customer, or both. For example, several

years ago a company called Yard Man Inc. manufactured and sold lawn equipment. Most of Yard Man’s sales were to Sears, so most of its revenues and profits were due to its Sears account. When Sears decided to drop Yard Man as a supplier, the com- pany was left without its most important customer. Yard Man is no longer in business. Because large firms typically have a broad customer base, they are not as exposed to the sudden loss of a large portion of their business.

A similar danger applies to a single-product company. Just as the loss of a key customer can be disastrous for a small busi- ness, so can a shift in the tides of consumer interest in a par- ticular fad. For example, Coleco manufactured and sold the ex- tremely popular Cabbage Patch dolls. The phenomenal popularity of the dolls was a great boon for Coleco. However, the public is fickle — one can never predict when such a fad will die out, leaving the company with a great deal of capacity to make a product that no one will buy, and with a large amount of overvalued inventory. Exactly that situation hit Coleco, and it was forced into bankruptcy.

Extending credit to a small company, especially to a small owner-managed company, often involves yet another risk that is less of a problem for larger firms — dependence on a single key individual whose unexpected death could cause the company to fail. Similarly, if the company is family owned and managed, there is typically one key decision maker, even though several other family members may be involved in helping to manage the company. In the case of the family business, the loss of the top person may not wipe out the company, but it often creates the serious problem of who will assume the leadership role. The loss of a key family member is often a highly emotional event, and it is not at all unusual for it to be followed by an ugly and protracted struggle for control of the business. It is in the fam- ily’s interest, and certainly in the creditors’ interests, to see that a plan of management succession is clearly specified before trouble arises. If no good plan can be worked out, perhaps the firm should be forced to carry “key person insurance,” payable to the bank and used to retire the loan in the event of the key person’s death.

In summary, to determine the creditworthiness of a small firm, the financial analyst must “look beyond the ratios” and analyze the viability of the firm’s products, customers, manage- ment, and market. Still, ratio analysis is the first step in such a credit analysis.

FINANCIAL ANALYSIS IN THE SMALL FIRM

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS118

SELF-TEST QUESTION

What are some qualitative factors analysts should consider when evaluating a company’s likely future financial performance?

uating a company. These factors, as summarized by the American Association of Individual Investors (AAII), include the following:

1. Are the company’s revenues tied to one key customer? If so, the company’s per- formance may decline dramatically if the customer goes elsewhere. On the other hand, if the relationship is firmly entrenched, this might actu- ally stabilize sales.

2. To what extent are the company’s revenues tied to one key product? Companies that rely on a single product may be more efficient and focused, but a lack of diversification increases risk. If revenues come from several different products, the overall bottom line will be less affected by a drop in the de- mand for any one product.

3. To what extent does the company rely on a single supplier? Depending on a sin- gle supplier may lead to unanticipated shortages, which investors and po- tential creditors should consider.

4. What percentage of the company’s business is generated overseas? Companies with a large percentage of overseas business are often able to realize higher growth and larger profit margins. However, firms with large over- seas operations find that the value of their operations depends in large part on the value of the local currency. Thus, fluctuations in currency markets create additional risks for firms with large overseas operations. Also, the potential stability of the region is important.

5. Competition. Generally, increased competition lowers prices and profit margins. In forecasting future performance, it is important to assess both the likely actions of the current competition and the likelihood of new competitors in the future.

6. Future prospects. Does the company invest heavily in research and devel- opment? If so, its future prospects may depend critically on the success of new products in the pipeline. For example, the market’s assessment of a computer company depends on how next year’s products are shaping up. Likewise, investors in pharmaceutical companies are interested in knowing whether the company has developed any potential blockbuster drugs that are doing well in the required tests.

7. Legal and regulatory environment. Changes in laws and regulations have important implications for many industries. For example, when forecast- ing the future of tobacco companies, it is crucial to factor in the effects of proposed regulations and pending or likely lawsuits. Likewise, when as- sessing banks, telecommunications firms, and electric utilities, analysts need to forecast both the extent to which these industries will be regu- lated in the future, and the ability of individual firms to respond to changes in regulation.

119T Y I N G I T A L L TO G E T H E R

The primary purpose of this chapter was to discuss techniques used by in- vestors and managers to analyze financial statements. The key concepts covered are listed below.

� Financial statement analysis generally begins with a set of financial ra- tios designed to reveal the strengths and weaknesses of a company as com- pared with other companies in the same industry, and to show whether its financial position has been improving or deteriorating over time.

� Liquidity ratios show the relationship of a firm’s current assets to its cur- rent liabilities, and thus its ability to meet maturing debts. Two commonly used liquidity ratios are the current ratio and the quick, or acid test, ratio.

� Asset management ratios measure how effectively a firm is managing its assets. These ratios include inventory turnover, days sales outstanding, fixed assets turnover, and total assets turnover.

� Debt management ratios reveal (1) the extent to which the firm is fi- nanced with debt and (2) its likelihood of defaulting on its debt obliga- tions. They include the debt ratio, times-interest-earned ratio, and EBITDA coverage ratio.

� Profitability ratios show the combined effects of liquidity, asset manage- ment, and debt management policies on operating results. They include the profit margin on sales, the basic earning power ratio, the return on total assets, and the return on common equity.

� Market value ratios relate the firm’s stock price to its earnings, cash flow, and book value per share, thus giving management an indication of what investors think of the company’s past performance and future prospects. These include the price/earnings ratio, price/cash flow ratio, and the market/book ratio.

� Trend analysis, where one plots a ratio over time, is important, because it reveals whether the firm’s condition is improving or deteriorating over time.

� The Du Pont system is designed to show how the profit margin on sales, the assets turnover ratio, and the use of debt interact to determine the rate of return on equity. The firm’s management can use the Du Pont system to analyze ways of improving the firm’s performance.

� Benchmarking is the process of comparing a particular company with a group of “benchmark” companies.

� ROE is important, but it does not take account of either the amount of in- vestment or risk. Economic Value Added (EVA) adds these factors to the analysis.

� In analyzing a small firm’s financial position, ratio analysis is a useful start- ing point. However, the analyst must also (1) examine the quality of the financial data, (2) ensure that the firm is sufficiently diversified to with- stand shifts in customers’ buying habits, and (3) determine whether the firm has a plan for the succession of its management.

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS120

Ratio analysis has limitations, but used with care and judgment, it can be very helpful.

Q U E S T I O N S

3-1 Financial ratio analysis is conducted by four groups of analysts: managers, equity in- vestors, long-term creditors, and short-term creditors. What is the primary emphasis of each of these groups in evaluating ratios?

3-2 Why would the inventory turnover ratio be more important when analyzing a grocery chain than an insurance company?

3-3 Over the past year, M. D. Ryngaert & Co. has realized an increase in its current ratio and a drop in its total assets turnover ratio. However, the company’s sales, quick ratio, and fixed assets turnover ratio have remained constant. What explains these changes?

3-4 Profit margins and turnover ratios vary from one industry to another. What differences would you expect to find between a grocery chain such as Safeway and a steel company? Think particularly about the turnover ratios, the profit margin, and the Du Pont equation.

3-5 How does inflation distort ratio analysis comparisons, both for one company over time (trend analysis) and when different companies are compared? Are only balance sheet items or both balance sheet and income statement items affected?

3-6 If a firm’s ROE is low and management wants to improve it, explain how using more debt might help.

3-7 How might (a) seasonal factors and (b) different growth rates distort a comparative ratio analysis? Give some examples. How might these problems be alleviated?

3-8 Why is it sometimes misleading to compare a company’s financial ratios with other firms that operate in the same industry?

3-9 Indicate the effects of the transactions listed in the following table on total current as- sets, current ratio, and net income. Use (�) to indicate an increase, (�) to indicate a decrease, and (0) to indicate either no effect or an indeterminate effect. Be prepared to state any necessary assumptions, and assume an initial current ratio of more than 1.0. (Note: A good accounting background is necessary to answer some of these questions; if yours is not strong, just answer the questions you can handle.)

TOTAL EFFECT CURRENT CURRENT ON NET ASSETS RATIO INCOME

a. Cash is acquired through issuance of additional common stock. ��������������� ��������������� ���������������

b. Merchandise is sold for cash. ��������������� ��������������� ��������������� c. Federal income tax due for the previous

year is paid. ��������������� ��������������� ��������������� d. A fixed asset is sold for less than book value. ��������������� ��������������� ��������������� e. A fixed asset is sold for more than book value. ��������������� ��������������� ��������������� f. Merchandise is sold on credit. ��������������� ��������������� ��������������� g. Payment is made to trade creditors for

previous purchases. ��������������� ��������������� ��������������� h. A cash dividend is declared and paid. ��������������� ��������������� ��������������� i. Cash is obtained through short-term bank

loans. ��������������� ��������������� ��������������� j. Short-term notes receivable are sold at a

discount. ��������������� ��������������� ��������������� k. Marketable securities are sold below cost. ��������������� ��������������� ��������������� l. Advances are made to employees. ��������������� ��������������� ���������������

m. Current operating expenses are paid. ��������������� ��������������� ��������������� n. Short-term promissory notes are issued to

trade creditors in exchange for past due accounts payable. ��������������� ��������������� ���������������

121

o. Ten-year notes are issued to pay off accounts payable. ��������������� ��������������� ���������������

p. A fully depreciated asset is retired. ��������������� ��������������� ��������������� q. Accounts receivable are collected. ��������������� ��������������� ��������������� r. Equipment is purchased with short-term

notes. ��������������� ��������������� ��������������� s. Merchandise is purchased on credit. ��������������� ��������������� ��������������� t. The estimated taxes payable are increased. ��������������� ��������������� ���������������

3-10 Johnson Electric doubled its EVA last year, yet its return on equity declined. What could explain these changes?

S E L F - T E S T P R O B L E M S ( S O L U T I O N S A P P E A R I N A P P E N D I X B )

Define each of the following terms: a. Liquidity ratios: current ratio; quick, or acid test, ratio b. Asset management ratios: inventory turnover ratio; days sales outstanding (DSO);

fixed assets turnover ratio; total assets turnover ratio c. Financial leverage: debt ratio; times-interest-earned (TIE) ratio; EBITDA coverage

ratio d. Profitability ratios: profit margin on sales; basic earning power (BEP) ratio; return on

total assets (ROA); return on common equity (ROE) e. Market value ratios: price/earnings (P/E) ratio; price/cash flow ratio; market/book

(M/B) ratio f. Trend analysis; comparative ratio analysis; benchmarking g. Du Pont chart; Du Pont equation; book value per share h. “Window dressing”; seasonal effects on ratios K. Billingsworth & Co. had earnings per share of $4 last year, and it paid a $2 dividend. Total retained earnings increased by $12 million during the year, while book value per share at year-end was $40. Billingsworth has no preferred stock, and no new common stock was issued during the year. If Billingsworth’s year-end debt (which equals its total liabilities) was $120 million, what was the company’s year-end debt/assets ratio? The following data apply to A.L. Kaiser & Company (millions of dollars):

Cash and marketable securities $100.00 Fixed assets $283.50 Sales $1,000.00 Net income $50.00 Quick ratio 2.0� Current ratio 3.0� DSOa 40.55 days ROE 12% aCalculation is based on a 365-day year.

Kaiser has no preferred stock — only common equity, current liabilities, and long-term debt. a. Find Kaiser’s (1) accounts receivable (A/R), (2) current liabilities, (3) current assets,

(4) total assets, (5) ROA, (6) common equity, and (7) long-term debt. b. In part a, you should have found Kaiser’s accounts receivable (A/R) � $111.1 million.

If Kaiser could reduce its DSO from 40.55 days to 30.4 days while holding other things constant, how much cash would it generate? If this cash were used to buy back common stock (at book value), thus reducing the amount of common equity, how would this affect (1) the ROE, (2) the ROA, and (3) the total debt/total assets ratio?

ST-3 Ratio analysis

ST-2 Debt ratio

ST-1 Key terms

S E L F - T E S T P R O B L E M S

TOTAL EFFECT CURRENT CURRENT ON NET ASSETS RATIO INCOME

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS122

S TA R T E R P R O B L E M S

Ace Industries has current assets equal to $3 million. The company’s current ratio is 1.5, and its quick ratio is 1.0. What is the firm’s level of current liabilities? What is the firm’s level of inventories? Baker Brothers has a DSO of 40 days. The company’s annual sales are $7,300,000. What is the level of its accounts receivable? Assume there are 365 days in a year. Bartley Barstools has an equity multiplier of 2.4. The company’s assets are financed with some combination of long-term debt and common equity. What is the company’s debt ratio? Doublewide Dealers has an ROA of 10 percent, a 2 percent profit margin, and a return on equity equal to 15 percent. What is the company’s total assets turnover? What is the firm’s equity multiplier? Jaster Jets has $10 billion in total assets. The left side of its balance sheet consists of $1 billion in current liabilities, $3 billion in long-term debt, and $6 billion in common eq- uity. The company has 800 million shares of common stock outstanding, and its stock price is $32 per share. What is Jaster’s market/book ratio?

E X A M - T Y P E P R O B L E M S

The problems included in this section are set up in such a way that they could be used as multiple-choice exam problems. Graser Trucking has $12 billion in assets, and its tax rate is 40 percent. The company’s basic earning power (BEP) ratio is 15 percent, and its return on assets (ROA) is 5 per- cent. What is Graser’s times-interest-earned (TIE) ratio? Assume you are given the following relationships for the Brauer Corporation:

Sales/total assets 1.5� Return on assets (ROA) 3% Return on equity (ROE) 5%

Calculate Brauer’s profit margin and debt ratio. The Petry Company has $1,312,500 in current assets and $525,000 in current liabilities. Its initial inventory level is $375,000, and it will raise funds as additional notes payable and use them to increase inventory. How much can Petry’s short-term debt (notes payable) increase without pushing its current ratio below 2.0? What will be the firm’s quick ratio after Petry has raised the maximum amount of short-term funds? The Kretovich Company had a quick ratio of 1.4, a current ratio of 3.0, an inventory turnover of 6 times, total current assets of $810,000, and cash and marketable securities of $120,000 in 2001. What were Kretovich’s annual sales and its DSO for that year? As- sume there are 365 days in a year. The H.R. Pickett Corporation has $500,000 of debt outstanding, and it pays an interest rate of 10 percent annually. Pickett’s annual sales are $2 million, its average tax rate is 30 percent, and its net profit margin on sales is 5 percent. If the company does not main- tain a TIE ratio of at least 5 times, its bank will refuse to renew the loan, and bankruptcy will result. What is Pickett’s TIE ratio? Willis Publishing has $30 billion in total assets. The company’s basic earning power (BEP) ratio is 20 percent, and its times-interest-earned ratio is 8.0. Willis’ depreciation and amortization expense totals $3.2 billion. It has $2 billion in lease payments and $1 billion must go toward principal payments on outstanding loans and long-term debt. What is Willis’ EBITDA coverage ratio? Midwest Packaging’s ROE last year was only 3 percent, but its management has devel- oped a new operating plan designed to improve things. The new plan calls for a total debt ratio of 60 percent, which will result in interest charges of $300,000 per year. Man- agement projects an EBIT of $1,000,000 on sales of $10,000,000, and it expects to have

3-12 Return on equity

3-11 EBITDA coverage ratio

3-10 Times-interest-earned ratio

3-9 Ratio calculations

3-8 Liquidity ratios

3-7 Ratio calculations

3-6 Ratio calculations

3-5 Market to book ratio

3-4 Du Pont analysis

3-3 Debt ratio

3-2 Days sales outstanding

3-1 Liquidity ratios

123

a total assets turnover ratio of 2.0. Under these conditions, the tax rate will be 34 per- cent. If the changes are made, what return on equity will the company earn? Central City Construction Company, which is just being formed, needs $1 million of as- sets, and it expects to have a basic earning power ratio of 20 percent. Central City will own no securities, so all of its income will be operating income. If it chooses to, Central City can finance up to 50 percent of its assets with debt, which will have an 8 percent interest rate. Assuming a 40 percent federal-plus-state tax rate on all taxable income, what is the difference between its expected ROE if Central City finances with 50 percent debt versus its expected ROE if it finances entirely with common stock? Which of the following statements is most correct? (Hint: Work Problem 3-13 before answering 3-14, and consider the solution setup for 3-13 as you think about 3-14.) a. If a firm’s expected basic earning power (BEP) is constant for all of its assets and ex-

ceeds the interest rate on its debt, then adding assets and financing them with debt will raise the firm’s expected rate of return on common equity (ROE).

b. The higher its tax rate, the lower a firm’s BEP ratio will be, other things held con- stant.

c. The higher the interest rate on its debt, the lower a firm’s BEP ratio will be, other things held constant.

d. The higher its debt ratio, the lower a firm’s BEP ratio will be, other things held con- stant.

e. Statement a is false, but statements b, c, and d are all true. Lloyd and Daughters Inc. has sales of $200,000, a net income of $15,000, and the fol- lowing balance sheet:

Cash $ 10,000 Accounts payable $ 30,000 Receivables 50,000 Other current liabilities 20,000 Inventories 150,000 Long-term debt 50,000 Net fixed assets 90,000 Common equity 200,000

Total assets $300,000 Total liabilities and equity $300,000

a. The company’s new owner thinks that inventories are excessive and can be lowered to the point where the current ratio is equal to the industry average, 2.5�, without affecting either sales or net income. If inventories are sold off and not replaced so as to reduce the current ratio to 2.5�, if the funds generated are used to reduce com- mon equity (stock can be repurchased at book value), and if no other changes occur, by how much will the ROE change?

b. Now suppose we wanted to take this problem and modify it for use on an exam, that is, to create a new problem that you have not seen to test your knowledge of this type of problem. How would your answer change if (1) We doubled all the dollar amounts? (2) We stated that the target current ratio was 3�? (3) We stated that the target was to achieve an inventory turnover ratio of 2� rather than a current ratio of 2.5�? (Hint: Compare the ROE obtained with an inventory turnover ratio of 2� to the original ROE obtained before any changes are considered.) (4) We said that the company had 10,000 shares of stock outstanding, and we asked how much the change in part a would increase EPS? (5) What would your answer to (4) be if we changed the original problem to state that the stock was selling for twice book value, so com- mon equity would not be reduced on a dollar-for-dollar basis?

c. Now explain how we could have set the problem up to have you focus on changing accounts receivable, or fixed assets, or using the funds generated to retire debt (we would give you the interest rate on outstanding debt), or how the original problem could have stated that the company needed more inventories and it would finance them with new common equity or with new debt.

P R O B L E M S

Complete the balance sheet and sales information in the table that follows for Hoffmeis- ter Industries using the following financial data:

3-16 Balance sheet analysis

3-15 Return on equity

3-14 Conceptual: Return on equity

3-13 Return on equity

P R O B L E M S

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS124

Debt ratio: 50% Quick ratio: 0.80� Total assets turnover: 1.5� Days sales outstanding: 36.5 daysa

Gross profit margin on sales: (Sales � Cost of goods sold)/Sales � 25% Inventory turnover ratio: 5� a Calculation is based on a 365-day year.

BALANCE SHEET

Cash ������������������� Accounts payable ������������� Accounts receivable ������������������� Long-term debt 60,000 Inventories ������������������� Common stock ������������� Fixed assets ������������������� Retained earnings 97,500 Total assets $300,000 Total liabilities and equity

�������������

Sales ������������������� Cost of goods sold �������������

Data for Barry Computer Company and its industry averages follow. a. Calculate the indicated ratios for Barry. b. Construct the extended Du Pont equation for both Barry and the industry. c. Outline Barry’s strengths and weaknesses as revealed by your analysis. d. Suppose Barry had doubled its sales as well as its inventories, accounts receivable,

and common equity during 2001. How would that information affect the validity of your ratio analysis? (Hint: Think about averages and the effects of rapid growth on ratios if averages are not used. No calculations are needed.)

Barry Computer Company: Balance Sheet as of December 31, 2001 (In Thousands)

Cash $ 77,500 Accounts payable $ 129,000 Receivables 336,000 Notes payable 84,000 Inventories 241,500 Other current liabilities 117,000

Total current assets $ 655,000 Total current liabilities $ 330,000 Net fixed assets 292,500 Long-term debt 256,500

Common equity 361,000 Total assets $ 947,500 Total liabilities and equity $ 947,500

Barry Computer Company: Income Statement for Year Ended December 31, 2001 (In Thousands)

Sales $1,607,500 Cost of goods sold

Materials $717,000 Labor 453,000 Heat, light, and power 68,000 Indirect labor 113,000 Depreciation 41,500 1,392,500

Gross profit $ 215,000 Selling expenses 115,000 General and administrative expenses 30,000

Earnings before interest and taxes (EBIT) $ 70,000

3-17 Ratio analysis

125

Interest expense 24,500 Earnings before taxes (EBT) $ 45,500

Federal and state income taxes (40%) 18,200 Net income $ 27,300

RATIO BARRY INDUSTRY AVERAGE

Current assets/current liabilities ������������������� 2.0� Days sales outstandinga ������������������� 35 days Sales/inventories ������������������� 6.7� Sales/total assets ������������������� 3.0� Net income/sales ������������������� 1.2% Net income/total assets ������������������� 3.6% Net income/common equity ������������������� 9.0% Total debt/total assets ������������������� 60.0% a Calculation is based on a 365-day year.

The Ferri Furniture Company, a manufacturer and wholesaler of high-quality home fur- nishings, has been experiencing low profitability in recent years. As a result, the board of directors has replaced the president of the firm with a new president, Helen Adams, who has asked you to make an analysis of the firm’s financial position using the Du Pont chart. In addition to the information given below, you have been informed by the new president that the firm has no lease payments but has a $2 million sinking fund payment on its debt. The most recent industry average ratios, and Ferri’s financial statements, are as follows:

INDUSTRY AVERAGE RATIOS

Current ratio 2� Sales/fixed assets 6� Debt/total assets 30% Sales/total assets 3� Times interest earned 7� Profit margin on sales 3% EBITDA coverage 9� Return on total assets 9% Sales/inventory 10� Return on common equity 12.9% Days sales outstandinga 24 days a Calculation is based on a 365-day year.

Ferri Furniture Company: Balance Sheet as of December 31, 2001 (Millions of Dollars)

Cash $ 45 Accounts payable $ 45 Marketable securities 33 Notes payable 45 Net receivables 66 Other current liabilities 21 Inventories 159 Total current liabilities $111

Total current assets $303 Long-term debt 24 Total liabilities $135

Gross fixed assets 225 Less depreciation 78 Common stock 114

Net fixed assets $147 Retained earnings 201 Total stockholders’ equity $315

Total assets $450 Total liabilities and equity $450

3-18 Du Pont analysis

P R O B L E M S

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS126

Ferri Furniture Company: Income Statement for Year Ended December 31, 2001 (Millions of Dollars)

Net sales $795.0 Cost of goods sold 660.0

Gross profit $135.0 Selling expenses 73.5 EBITDA $ 61.5 Depreciation expense 12.0

Earnings before interest and taxes (EBIT) $ 49.5 Interest expense 4.5

Earnings before taxes (EBT) $ 45.0 Taxes (40%) 18.0 Net income $ 27.0

a. Calculate those ratios that you think would be useful in this analysis. b. Construct an extended Du Pont equation for Ferri, and compare the company’s ra-

tios to the industry average ratios. c. Do the balance sheet accounts or the income statement figures seem to be primarily

responsible for the low profits? d. Which specific accounts seem to be most out of line in relation to other firms in the

industry? e. If Ferri had a pronounced seasonal sales pattern, or if it grew rapidly during the year,

how might that affect the validity of your ratio analysis? How might you correct for such potential problems?

The Corrigan Corporation’s forecasted 2002 financial statements follow, along with some industry average ratios. a. Calculate Corrigan’s 2002 forecasted ratios, compare them with the industry average

data, and comment briefly on Corrigan’s projected strengths and weaknesses. b. What do you think would happen to Corrigan’s ratios if the company initiated cost-

cutting measures that allowed it to hold lower levels of inventory and substantially decreased the cost of goods sold? No calculations are necessary. Think about which ratios would be affected by changes in these two accounts.

Corrigan Corporation: Forecasted Balance Sheet as of December 31, 2002

Cash $ 72,000 Accounts receivable 439,000 Inventories 894,000

Total current assets $1,405,000 Land and building 238,000 Machinery 132,000 Other fixed assets 61,000 Total assets $1,836,000

Accounts and notes payable $ 432,000 Accruals 170,000

Total current liabilities $ 602,000 Long-term debt 404,290 Common stock 575,000 Retained earnings 254,710 Total liabilities and equity $1,836,000

3-19 Ratio analysis

127

Corrigan Corporation: Forecasted Income Statement for Year Ended December 31, 2002

Sales $4,290,000 Cost of goods sold 3,580,000

Gross operating profit $ 710,000 General administrative and selling expenses 236,320 Depreciation 159,000 Miscellaneous 134,000

Earnings before taxes (EBT) $ 180,680 Taxes (40%) 72,272 Net income $ 108,408

PER-SHARE DATA

EPS $4.71 Cash dividends $0.95 Market price (average) $23.57 P/E ratio 5� Number of shares outstanding 23,000

INDUSTRY FINANCIAL RATIOS (2002)a

Quick ratio 1.0� Current ratio 2.7� Inventory turnoverb 7.0� Days sales outstandingc 32 days Fixed assets turnoverb 13.0� Total assets turnoverb 2.6� Return on assets 9.1% Return on equity 18.2% Debt ratio 50.0% Profit margin on sales 3.5% P/E ratio 6.0� Price/cash flow ratio 3.5� a Industry average ratios have been constant for the past 4 years. b Based on year-end balance sheet figures. c Calculation is based on a 365-day year.

S P R E A D S H E E T P R O B L E M

This problem requires you to analyze the financial data given back in the spreadsheet problem for Chapter 2.

Laiho Industries’ common stock has increased in price from $14.75 to $17.25 from the end of 2000 to the end of 2001, and its shares outstanding increased from 9 to 10 million shares during that same period. Laiho has annual lease payments of $75,000 (which are included in operating costs on the income statement), but no sinking fund payments are required. Now answer the following questions.

Using Laiho Industries’ financial statements as given in the Chapter 2 spreadsheet problem, perform a ratio analysis for 2000 and 2001. Consider its liquidity, asset man- agement, debt management, profitability, and market value ratios. (Hint: If you worked the Chapter 2 problem and saved your file, you can rename that file something like

3-20 Ratio analysis

S P R E A D S H E E T P R O B L E M

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS128

The information related to the cyberproblems is likely to change over time, due to the release of new information and the ever-changing nature of the World Wide Web. With these changes in mind, we will periodically update these problems on the textbook’s web site. To avoid problems, please check for these updates before proceeding with the cyberproblems.

Chapter 3 demonstrates the various ways that managers and investors use financial statements. The following cyberproblem addresses the financial statement analysis of Brady Corporation. Use the company’s web site at www.bradycorp.com to navigate through this cyberproblem.

Brady Corporation is a leader in identification, safety, and material solutions. In 1998, the firm was hit hard by faltering foreign markets, so it embarked upon an ag- gressive campaign to redesign its cost structure. The firm believes this will help it to enhance future stockholder value. Brady follows the concept of Shareholder Value Enhancement (SVE), which is improved through increased sales, cost control, and effective use and control of assets.

3-21 Using ratio analysis as a tool

a. Review Brady Corporation’s consolidated statements of income. Its 1999 annual report is found at www.bradycorp.com/1999annual/splash.htm. Calculate and interpret Brady’s gross margin (calculated as [Net sales � Cost of goods sold]/Net sales) for 1997, 1998, and 1999. What conclusions, if any, can you draw from an-

Prob-03 and then perform the necessary calculations with the data generated for Chap- ter 2. This will save you from having to re-enter data.) a. Has Laiho’s liquidity position improved or worsened? Explain. b. Has Laiho’s ability to manage its assets improved or worsened? Explain. c. How has Laiho’s profitability changed during the last year? d. Perform an extended Du Pont analysis for Laiho for 2000 and 2001.

D’LEON INC., PART II

3-22 Financial Statement Analysis Part I of this case, pre- sented in Chapter 2, discussed the situation that D’Leon Inc., a regional snack-foods producer, was in after an expan- sion program. D’Leon had increased plant capacity and un- dertaken a major marketing campaign in an attempt to “go

national.” Thus far, sales have not been up to the forecasted level, costs have been higher than were projected, and a large loss occurred in 2001 rather than the expected profit. As a result, its managers, directors, and investors are con- cerned about the firm’s survival.

Donna Jamison was brought in as assistant to Fred Campo, D’Leon’s chairman, who had the task of getting the

129I N T E G R AT E D C A S E

alyzing these gross margins? (Hint: Have manufacturing costs as a percentage of sales increased, decreased, or remained level during this period?)

b. Calculate and interpret the firm’s profit margin for 1997, 1998, and 1999. Has the firm’s profit margin improved or worsened during this period? Why?

c. Calculate Brady’s TIE ratio for 1997, 1998, and 1999, and interpret your results. d. Look at Brady’s balance sheets for 1998 and 1999. Calculate the firm’s current and

quick ratios, and comment on any changes in its liquidity position. e. Using both the income statements and balance sheets, calculate Brady’s total as-

sets turnover for 1998 and 1999, and interpret your results.

T A B L E I C 3 - 1

2002E 2001 2000

ASSETS

Cash $ 85,632 $ 7,282 $ 57,600 Accounts receivable 878,000 632,160 351,200 Inventories 1,716,480 1,287,360 715,200

Total current assets $2,680,112 $1,926,802 $1,124,000 Gross fixed assets 1,197,160 1,202,950 491,000 Less accumulated depreciation 380,120 263,160 146,200

Net fixed assets $ 817,040 $ 939,790 $ 344,800 Total assets $3,497,152 $2,866,592 $1,468,800

LIABILITIES AND EQUITY

Accounts payable $ 436,800 $ 524,160 $ 145,600 Notes payable 300,000 636,808 200,000 Accruals 408,000 489,600 136,000

Total current liabilities $1,144,800 $1,650,568 $ 481,600 Long-term debt 400,000 723,432 323,432 Common stock 1,721,176 460,000 460,000 Retained earnings 231,176 32,592 203,768

Total equity $1,952,352 $ 492,592 $ 663,768 Total liabilities and equity $3,497,152 $2,866,592 $1,468,800

NOTE: “E” indicates estimated. The 2002 data are forecasts.

Balance Sheets

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS130

company back into a sound financial position. D’Leon’s 2000 and 2001 balance sheets and income statements, together with projections for 2002, are given in Tables IC3-1 and IC3-2. In addition, Table IC3-3 gives the company’s 2000 and 2001 financial ratios, together with industry average data. The 2002 projected financial statement data represent Jamison’s and Campo’s best guess for 2002 results, assuming that some new financing is arranged to get the company “over the hump.”

Jamison examined monthly data for 2001 (not given in the case), and she detected an improving pattern during the year. Monthly sales were rising, costs were falling, and large losses in the early months had turned to a small profit by December. Thus, the annual data look somewhat worse than final monthly data. Also, it appears to be taking longer for the advertising program to get the message across, for the new sales offices to generate sales, and for the new manufac- turing facilities to operate efficiently. In other words, the lags between spending money and deriving benefits were longer than D’Leon’s managers had anticipated. For these reasons, Jamison and Campo see hope for the company — provided it can survive in the short run.

Jamison must prepare an analysis of where the company is now, what it must do to regain its financial health, and what actions should be taken. Your assignment is to help her answer the following questions. Provide clear explanations, not yes or no answers. a. Why are ratios useful? What are the five major cate-

gories of ratios? b. Calculate D’Leon’s 2002 current and quick ratios based

on the projected balance sheet and income statement data. What can you say about the company’s liquidity position in 2000, 2001, and as projected for 2002? We often think of ratios as being useful (1) to managers to help run the business, (2) to bankers for credit analysis, and (3) to stockholders for stock valuation. Would these different types of analysts have an equal interest in the liquidity ratios?

c. Calculate the 2002 inventory turnover, days sales out- standing (DSO), fixed assets turnover, and total assets turnover. How does D’Leon’s utilization of assets stack up against other firms in its industry?

d. Calculate the 2002 debt, times-interest-earned, and EBITDA coverage ratios. How does D’Leon compare

C H A P T E R 3 � A N A LY S IS O F F I N A N C I A L S TAT E M E N TS

T A B L E I C 3 - 2

2002E 2001 2000

Sales $7,035,600 $6,034,000 $3,432,000 Cost of goods sold 5,875,992 5,528,000 2,864,000 Other expenses 550,000 519,988 358,672 Total operating costs

excluding depreciation $6,425,992 $6,047,988 $3,222,672 EBITDA $ 609,608 ($ 13,988) $ 209,328 Depreciation 116,960 116,960 18,900

EBIT $ 492,648 ($ 130,948) $ 190,428 Interest expense 70,008 136,012 43,828

EBT $ 422,640 ($ 266,960) $ 146,600 Taxes (40%) 169,056 (106,784)a 58,640 Net income $ 253,584 ($ 160,176) $ 87,960

EPS $1.014 ($1.602) $0.880 DPS $0.220 $0.110 $0.220 Book value per share $7.809 $4.926 $6.638 Stock price $12.17 $2.25 $8.50 Shares outstanding 250,000 100,000 100,000 Tax rate 40.00% 40.00% 40.00% Lease payments 40,000 40,000 40,000 Sinking fund payments 0 0 0

NOTE: “E” indicates estimated. The 2002 data are forecasts. aThe firm had sufficient taxable income in 1999 and 2000 to obtain its full tax refund in 2001.

Income Statements

with the industry with respect to financial leverage? What can you conclude from these ratios?

e. Calculate the 2002 profit margin, basic earning power (BEP), return on assets (ROA), and return on equity (ROE). What can you say about these ratios?

f. Calculate the 2002 price/earnings ratio, price/cash flow ratio, and market/book ratio. Do these ratios indicate that investors are expected to have a high or low opinion of the company?

g. Use the extended Du Pont equation to provide a sum- mary and overview of D’Leon’s financial condition as projected for 2002. What are the firm’s major strengths and weaknesses?

h. Use the following simplified 2002 balance sheet to show, in general terms, how an improvement in the DSO would tend to affect the stock price. For example, if the company could improve its collection procedures and thereby lower its DSO from 45.6 days to the 32-day in- dustry average without affecting sales, how would that change “ripple through” the financial statements (shown in thousands below) and influence the stock price?

Accounts receivable $ 878 Debt $1,545 Other current assets 1,802 Net fixed assets 817 Equity 1,952

Total assets $3,497 Liabilities plus equity $3,497

i. Does it appear that inventories could be adjusted, and, if so, how should that adjustment affect D’Leon’s prof- itability and stock price?

j. In 2001, the company paid its suppliers much later than the due dates, and it was not maintaining financial ratios at levels called for in its bank loan agreements. There- fore, suppliers could cut the company off, and its bank could refuse to renew the loan when it comes due in 90 days. On the basis of data provided, would you, as a credit manager, continue to sell to D’Leon on credit? (You could demand cash on delivery, that is, sell on terms of COD, but that might cause D’Leon to stop buying from your company.) Similarly, if you were the bank loan officer, would you recommend renewing the loan or de- mand its repayment? Would your actions be influenced if, in early 2002, D’Leon showed you its 2002 projec- tions plus proof that it was going to raise over $1.2 mil- lion of new equity capital?

k. In hindsight, what should D’Leon have done back in 2000? l. What are some potential problems and limitations of fi-

nancial ratio analysis? m. What are some qualitative factors analysts should con-

sider when evaluating a company’s likely future financial performance?

131I N T E G R AT E D C A S E

T A B L E I C 3 - 3

2002E 2001 2000 INDUSTRY AVERAGE

Current 1.2� 2.3� 2.7� Quick 0.4� 0.8� 1.0� Inventory turnover 4.7� 4.8� 6.1� Days sales outstanding (DSO)a 38.2 37.4 32.0 Fixed assets turnover 6.4� 10.0� 7.0� Total assets turnover 2.1� 2.3� 2.6� Debt ratio 82.8% 54.8% 50.0% TIE �1.0� 4.3� 6.2� EBITDA coverage 0.1� 3.0� 8.0� Profit margin �2.7% 2.6% 3.5% Basic earning power �4.6% 13.0% 19.1% ROA �5.6% 6.0% 9.1% ROE �32.5% 13.3% 18.2% Price/earnings �1.4� 9.7� 14.2� Price/cash flow �5.2� 8.0� 11.0� Market/book 0.5� 1.3� 2.4� Book value per share $4.93 $6.64 n.a.

NOTE: “E” indicates estimated. The 2002 data are forecasts. a Calculation is based on a 365-day year.

Ratio Analysis

SOURCE: © Silver Image.

CHAPTER

F i na nc i a l P l a n n i ng a nd F o r e c a s t i ng4

32

To Disney Owners and Fellow Cast Members:

I am looking out the window and can see the

seasons change (yes, the seasons do change in Los

Angeles—the eucalyptus leaves droop more and the

sprinklers go on less often). I am reminded that our

rhythms are set by the seasons and that any number

of human endeavors are ruled by the calendar. Such

as this annual report. Every 12 months we compile

it, and every 12 months I sit down to write you this

letter.

There’s just one problem with this annual

exercise: It implies that businesses can be run in

neat 12-month chunks of time. Unfortunately, the

business cycle has its own seasons, which are not

ruled by the orderly and predictable orbit of the

earth around the sun. Indeed, at Disney we live by a

60-month calendar. We set our goals over rolling

five-year timelines. In this context, each year is

more like a season. Some are sunny and some are

overcast, but each is merely a period of passage and

not a destination. Our five-year calendars force us to

think long-term. They make us devise strategies that

add value, not squeeze profits.

Eisner went on to tell shareholders that the

company’s long-run forecast remained promising. After

n early 1998, corporations were reporting earnings

for 1997. Simultaneously, security analysts were

issuing their forecasts of earnings for 1998. Stock

prices were extremely volatile, moving up with a good

earnings surprise—that is, where reported EPS was

higher than analysts had been expecting—and down

with unpleasant surprises. Corporate executives know

that these reactions will occur, so they generally try to

give analysts early warnings when unpleasant surprises

are likely to occur. The logic is that unpleasant surprises

increase uncertainty about the future, so a stock will

react less negatively to low earnings if the drop is

anticipated than if it is a complete surprise.

Corporate finance staffs also review their own

internal plans and forecasts during the first part of the

year. Firms’ formal plans are generally completed in the

fall and then go into effect at the start of the year, so

early in the year information starts coming in that

indicates how the year is shaping up.

For executives at Walt Disney Co., 1998 was a

particularly difficult year. After several years of

outstanding performance, Disney’s earnings fell, causing

a sharp drop in its stock price. Trying to address

investors’ concerns, Disney’s Chairman and Chief

Executive, Michael Eisner, began his annual letter to

shareholders with the following words:

F O R E C A S T I N G D IS N E Y ’ S F U T U R E

WALT DISNEY CO.

$

I

133

C H A P T E R 4 � F I N A N C I A L P L A N N I N G A N D F O R E C A S T I N G134

Chapters 2 and 3 described what financial statements are and showed how both

managers and investors analyze them to evaluate a firm’s past performance. While

this is clearly important, it is even more important to look ahead and to antici-

pate what is likely to happen in the future. So, both managers and investors need

to understand how to forecast future results.

Managers make pro forma, or projected, financial statements and then use

them in four ways: (1) By looking at projected statements, they can assess

whether the firm’s anticipated performance is in line with the firm’s own general

targets and with investors’ expectations. For example, if the projected financial

statements indicate that the forecasted return on equity is well below the indus-

try average, managers should investigate the cause and then seek a remedy. (2) Pro

forma statements can be used to estimate the effect of proposed operating

changes. Therefore, financial managers spend a lot of time doing “what if” analy-

Pro Forma (Projected) Financial Statements Financial statements that forecast the company’s financial position and performance over a period of years.

Eisner’s assurances, many analysts are still lukewarm

about Disney’s future prospects. Many others, though,

are betting that the company’s stock will continue to

rebound. Unfortunately, no crystal ball exists for

predicting the future. Instead, both corporate insiders

and investors must base decisions on their own financial

forecasts. While forecasting is necessarily somewhat

subjective, we discuss in this chapter some basic

principles that will improve financial forecasts. By the

time you finish the chapter, you will have a good idea

about how to forecast future results for Disney or any

other company. �

SOURCE: Walt Disney Co.’s 1998 and 1999 Annual Reports.

acknowledging that Disney had problems in its

entertainment and broadcasting divisions, he went on

to state that the company was taking steps to cut costs

and to improve operations. Eisner also stated that

Disney’s earnings had been hampered because it had

begun a series of expensive new projects, including

Disney’s Animal Kingdom, its Cruise Line, the launching

of ESPN Magazine, and the renovation of Anaheim

Stadium. However, he argued that they were laying the

groundwork for future profitability.

In the two years that have followed since Eisner

wrote this letter, Disney continued to have its ups and

downs. Its stock price struggled throughout most of

1999, but it rebounded a bit in early 2001. In his most

recent letter to shareholders, Eisner spoke optimistically

about the company’s future. However, in spite of

135

ses. (3) Managers use pro forma statements to anticipate the firm’s future financ-

ing needs. (4) Projected financial statements are used to estimate future free cash

flows, which determine the company’s overall value. Thus, managers forecast free

cash flows under different operating plans, forecast their capital requirements, and

then choose the plan that maximizes shareholder value.

Security analysts make the same types of projections, forecasting future earn-

ings, cash flows, and stock prices. Of course, managers have more information

about the company than security analysts, and managers are the ones who make

the decisions that determine the future. However, analysts influence investors, and

investors determine the future of managers. To illustrate, suppose an influential

analyst at a firm such as Goldman Sachs concludes, on the basis of a comparative

financial analysis, that a particular firm’s managers are less effective than others

in the industry. The analyst’s negative report could lead stockholders to revolt and

replace management. Or, the report might lead a firm that specializes in taking

over underperforming firms to buy stock in the company and then launch a hostile

takeover designed to change management, improve cash flows, and make a large

capital gain.

We will have more to say about investors’ and analysts’ use of projections in

Chapter 9, when we discuss how stock prices are determined. First, though, in this

chapter we explain how to create and use pro forma financial statements. We begin

with the strategic plan, which provides a foundation for pro forma statements. �

S T R AT E G I C P L A N S

Our primary objective in this book is to explain what managers can do to make their companies more valuable. Managers must understand how investors de- termine the values of stocks and bonds if they are to identify, evaluate, and im- plement projects that meet or exceed investor expectations. However, value creation is impossible unless the company has a well-articulated plan. As Yogi Berra once said, “You’ve got to be careful if you don’t know where you’re going, because you might not get there.”

Companies begin with a mission statement, which is in many ways a con- densed version of their strategic plan. Figure 4-1 shows the mission statement of Coca-Cola, which we use to illustrate some of the key elements of strategic plans.

S T R AT E G I C P L A N S

Mission Statement A condensed version of a firm’s strategic plan.

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CORPORATE PURPOSE

Both mission statements and strategic plans usually begin with a statement of the overall corporate purpose. Coca-Cola is very clear about its corporate pur- pose: “. . . maximize share-owner value over time.”

F I G U R E 4 - 1 The Mission Statement of the Coca-Cola Company(http://www.thecoca-colacompany.com/tccc/mission.html)

137

This same corporate purpose is increasingly common for U.S. compa- nies, but that has not always been the case. For example, Varian Associates, Inc., a New York Stock Exchange company with sales of almost $2 billion, was, in 1990, regarded as one of the most technologically advanced elec- tronics companies. However, Varian’s management was more concerned with developing new technology than with marketing it, and its stock price was lower than it had been 10 years earlier. Some of the larger stockholders were intensely unhappy with the state of affairs, and management was faced with the threat of a proxy fight or forced merger. In 1991, management an- nounced a change in policy and stated that it would, in the future, empha- size both technological excellence and profitability, rather than focusing pri- marily on technology. Earnings improved dramatically, and the stock price rose from $6.75 to more than $60 within four years of that change in cor- porate purpose.

A corporate focus on creating wealth for the company’s owners is not yet as common abroad as it is in the United States. For example, Veba AG, one of Germany’s largest companies, created a stir in 1996 when it stated in its annual report that “Our commitment is to create value for you, our share- holders.” This was quite different from the usual German model, in which companies have representatives from labor on their boards of directors and which explicitly state their commitments to a variety of stakeholders. As one might expect, Veba’s stock has consistently outperformed the average German stock. As the trend in international investing continues, more and more non- U.S. companies are adopting a corporate purpose similar to that of Coke and Veba.

CORPORATE SCOPE

Its corporate scope defines a firm’s lines of business and geographic area of oper- ations. As Coca-Cola’s mission statement indicates, the company limits its products to soft drinks, but on a global geographic scale. Pepsi-Cola recently followed Coke’s lead — it restricted its scope by spinning off its food service businesses.

Several recent studies have found that the market tends to value focused firms more highly than it does diversified firms.1 Nokia is an example of a company that has taken steps in recent years to sharpen its corporate focus. While most investors think of Nokia as a company that specializes in the wireless phone market, it has actually been around for more than 135 years, and until recently, Nokia was involved in a wide range of different industries. However, over the past decade, the Finnish conglomerate has sold off many of its less productive divisions. Investors have generally applauded the com- pany’s more focused strategy — Nokia’s stock has risen nearly 2,000 percent over the past five years, and the company currently has a $200 billion market capitalization.

S T R AT E G I C P L A N S

1 See, for example, Philip G. Berger and Eli Ofek, “Diversification’s Effect on Firm Value,” Journal of Financial Economics, Vol. 37, No. 1, 39–66 (1995); and Larry Lang and René Stulz, “Tobin’s Q, Corporate Diversification, and Firm Performance,” Journal of Political Economy, Vol. 102, Issue 6, 1248–1280 (1994).

C H A P T E R 4 � F I N A N C I A L P L A N N I N G A N D F O R E C A S T I N G138

It is important to recognize that when it comes to corporate scope, one size doesn’t fit all. For example, General Electric has investments in a large number of different areas, yet it is widely recognized as one of the best-managed and highly-valued industrial companies in the world.

CORPORATE OBJECT IVES

The corporate purpose states the general philosophy of the business, but it does not provide managers with operational objectives. The statement of corpo- rate objectives sets forth specific goals to guide management. Most organiza- tions have both qualitative and quantitative objectives. For example, Coca- Cola’s mission statement lists six corporate objectives, including becoming “the best marketers in the world” and “leading as a model corporate citizen.” However, these statements are qualitative, hence hard to measure, so the ob- jectives need to be restated in quantitative terms, such as attaining a 50 per- cent market share, a 20 percent ROE, a 10 percent earnings growth rate, or a $100 million economic value added (EVA). Coca-Cola doesn’t list its quanti- tative objectives in its mission statement, but it has them in its detailed strate- gic plan. Moreover, executive bonuses are based on achieving the quantitative objectives.

CORPORATE STRATEGIES

Once a firm has defined its purpose, scope, and objectives, it must develop a strategy for achieving its goals. Corporate strategies are broad approaches rather than detailed plans. For example, one airline may have a strategy of offering no-frills service between a limited number of cities, while another’s strategy may be to offer “staterooms in the sky.” Broadly speaking, a company’s strategy often has several dimensions including whether (1) to invest overseas, (2) to in- vest in new lines of business and new technologies, and/or (3) to focus on a broad or narrow portion of the customer market. In any event, strategies should be both attainable and compatible with the firm’s purpose, scope, and objectives.

SELF-TEST QUESTIONS

What are pro forma financial statements?

What are four ways that pro forma financial statements are used by man- agers?

Briefly describe the nature and use of the following corporate planning terms: (1) corporate purpose, (2) corporate scope, (3) corporate objectives, and (4) corporate strategies.

139

O P E R AT I N G P L A N S

Operating plans provide detailed implementation guidance, based on the cor- porate strategy, to help meet the corporate objectives. These plans can be de- veloped for any time horizon, but like Disney, most companies use a five-year horizon. A five-year plan is most detailed for the first year, with each succeed- ing year’s plan becoming less specific. The plan explains in considerable detail who is responsible for each particular function, when specific tasks are to be ac- complished, sales and profit targets, and the like.

Table 4-1 summarizes the annual planning schedule of Allied Food Prod- ucts. This schedule illustrates the fact that for larger companies, the planning process is essentially continuous. Next, Table 4-2 outlines the key elements of Allied’s five-year plan. A full outline would require several pages, but Table 4-2 does provide insights into the format and content of a five-year plan. It should be noted that large, multidivisional companies such as General Electric break down their operating plans by divisions. Thus, each division has its own goals, mission, and plan for meeting its objectives, and these plans are then consoli- dated to form the corporate plan.2

O P E R AT I N G P L A N S

T A B L E 4 - 1

MONTHS ACTION

April–May Planning department analyzes general economic and industry factors. Marketing department prepares sales forecast for each product group.

June–July Engineering department prepares cost estimates for new processing/distribution facilities and plant modernization programs.

August–September Financial analysts evaluate proposed capital expenditures, divisional operating plans, and proposed sources and uses of funds.

October–November Five-year plan is finalized by planning department, reviewed by divisional officers, and put into “semifinal” form.

December Five-year plan is approved by the executive committee and then submitted to the board of directors for final approval.

Allied Food Products: Annual Planning Schedule

2 For more on the corporate planning process, see Benton E. Gup, Guide to Strategic Planning (New York: McGraw-Hill, 1980).

SELF-TEST QUESTIONS

What is the purpose of a firm’s operating plan?

What is the most common time horizon for operating plans?

Briefly describe the contents of a typical operating plan.

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T H E F I N A N C I A L P L A N

The financial planning process can be broken down into six steps:

1. Project financial statements and use these projections to analyze the ef- fects of the operating plan on projected profits and various financial ra- tios. The projections can also be used to monitor operations after the plan has been finalized and put into effect. Rapid awareness of deviations from the plan is essential in a good control system, which, in turn, is es- sential to corporate success in a changing world.

T A B L E 4 - 2 Allied Food Products: Five-Year Operating Plan Outline

Part 1. Corporate purpose Part 2. Corporate scope Part 3. Corporate objectives Part 4. Projected business environment Part 5. Corporate strategies Part 6. Summary of projected business results Part 7. Product line plans and policies

a. Marketing b. Processing/distribution c. Finance

1. Working capital (a) Overall working capital policy (b) Cash and marketable securities (c) Inventory management (d) Credit policy and receivables management

2. Dividend policy 3. Capital structure policy 4. Financial forecast

(a) Capital budget (b) Cash budget (c) Pro forma financial statements (d) External financing requirements (e) Financial condition analysis

5. Accounting plan 6. Control plan

d. Administrative and personnel e. Research and development f. New products

141

2. Determine the funds needed to support the five-year plan. This includes funds for plant and equipment as well as for inventories and receivables, for R&D programs, and for major advertising campaigns.

3. Forecast funds availability over the next five years. This involves estimat- ing the funds to be generated internally as well as those to be obtained from external sources. Any constraints on operating plans imposed by fi- nancial restrictions must be incorporated into the plan; constraints in- clude restrictions on the debt ratio, the current ratio, and the coverage ratios.

4. Establish and maintain a system of controls to govern the allocation and use of funds within the firm. In essence, this involves making sure that the basic plan is carried out properly.

5. Develop procedures for adjusting the basic plan if the economic forecasts upon which the plan was based do not materialize. For example, if the economy turns out to be stronger than was forecasted, then these new conditions must be recognized and reflected in higher production sched- ules, larger marketing quotas, and the like, and as rapidly as possible. Thus, Step 5 is really a “feedback loop” that triggers modifications to the financial plan.

6. Establish a performance-based management compensation system. It is critically important that such a system rewards managers for doing what stockholders want them to do —maximize share prices.

In the remainder of this chapter, we discuss how firms use computerized fi- nancial planning models to implement the three key components of the finan- cial plan: (1) the sales forecast, (2) pro forma financial statements, and (3) the external financing plan.

C O M P U T E R I Z E D F I N A N C I A L P L A N N I N G M O D E L S

SELF-TEST QUESTION

What are the six steps of the financial planning process?

C O M P U T E R I Z E D F I N A N C I A L P L A N N I N G M O D E L S

Although financial forecasting as described in this chapter can be done with a calculator, virtually all corporate forecasts are made using computerized fore- casting models. Most forecasting models are based on a spreadsheet program such as Microsoft Excel. Spreadsheets have two major advantages over pencil- and-paper calculations. First, it is much faster to construct a spreadsheet model than to make a “by-hand” forecast if the forecast period extends beyond a year or two. Second, and more important, with a spreadsheet model you can change inputs and instantaneously recompute the projected financial statements and ratios, thus making it easy for managers to determine the effects of changes in variables such as unit sales, labor costs, and sales prices.

In this chapter, we developed forecasted financial statements for Allied Food Products with an Excel model. The model is provided on the CD-ROM for the

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book, under the filename 04MODEL.xls. You do not have to understand the model to understand the chapter, but working through the model will give you a better feel for the forecasting process.3

SELF-TEST QUESTION

What are the two major advantages of spreadsheet models over pencil-and- paper calculations?

Sales Forecast A forecast of a firm’s unit and dollar sales for some future period; it is generally based on recent sales trends plus forecasts of the economic prospects for the nation, region, industry, and so forth.

3 There are small rounding differences between “by-hand” answers and those obtained using the spreadsheet. The spreadsheet carries calculations out to more decimal places and thus is somewhat more accurate than “by-hand” calculations.

SA L E S F O R E C A S T S

The sales forecast generally starts with a review of sales during the past five to ten years, expressed in a graph such as that in Figure 4-2. The first part of the graph shows five years of historical sales for Allied. The graph could have con- tained 10 years of sales data, but Allied focuses on sales figures for the latest five years because the firm’s studies have shown that its future growth is more closely related to recent events than to the distant past.

Allied had its ups and downs during the period from 1997 to 2001. In 1999, poor weather in California’s fruit-producing regions resulted in low produc- tion, which caused 1999 sales to fall below the 1998 level. Then, a bumper crop in 2000 pushed sales up by 15 percent, an unusually high growth rate for a ma- ture food processor. Based on a regression analysis, Allied’s forecasters deter- mined that the average annual growth rate in sales over the past five years was 9.1 percent. On the basis of this historical sales trend, on planned new-product introductions, and on Allied’s forecast for the economy, the firm’s planning committee projects a 10 percent sales growth rate during 2002, to sales of $3,300 million. Here are some of the factors Allied considered in developing its sales forecast:

1. Allied Food Products is divided into three divisions: canned foods, frozen foods, and packaged foods such as dried fruits. Sales growth is seldom the same for each of the divisions, so to begin the forecasting process, divi- sional projections are made on the basis of historical growth, and then the divisional forecasts are combined to produce a “first approximation” cor- porate sales forecast.

2. Next, the level of economic activity in each of the company’s marketing areas is forecasted—for example, how strong will the economies be in each of Allied’s six domestic and two foreign distribution territories, and what population changes are forecasted in each area?

3. Allied’s planning committee also looks at the firm’s probable market share in each distribution territory. Consideration is given to such factors as the firm’s production and distribution capacity, its competitors’ capacities,

143SA L E S F O R E C A S T S

new-product introductions that are planned by Allied or its competitors, and potential changes in shelf-space allocations, which are vital for food sales. Pricing strategies are also considered—for example, does the com- pany have plans to raise prices to boost margins, or to lower prices to in- crease market share and take advantage of economies of scale? Obviously, such factors could greatly affect future sales.

4. Allied’s foreign sales present unique forecasting problems. In particular, its planners must consider how exchange rate fluctuations would affect sales. Allied must also consider the effects of trade agreements, govern- mental policies, and the like.

5. Allied’s planners must also consider the effects of inflation on prices. Over the next five years, the inflation rate for food products is expected to average 3 to 4 percent, and Allied plans to increase prices, on average, by a like amount. In addition, the firm expects to expand its market share in certain products, resulting in a 4 percent growth rate in unit sales. The combination of unit sales growth and increases in sales prices has resulted in historical revenue growth rates in the 8 to 10 percent range, and this same situation is expected in the future.

F I G U R E 4 - 2 Allied Food Products: 2002 Sales Projection (Millions of Dollars)

3,000

2,000

1,000

0

Net Sales ($)

1997 1998 1999 2000 2001 2002

Projected

Regression Line

YEAR SALES

1997 $2,058 1998 2,534 1999 2,472 2000 2,850 2001 3,000 2002 3,300 (Projected)

F I N A N C I A L S TAT E M E N T F O R E C A S T I N G : T H E P E R C E N T O F SA L E S M E T H O D

Once sales have been forecasted, we must forecast future balance sheets and in- come statements. The most commonly used technique is the percent of sales method, which begins with the sales forecast, expressed as an annual growth rate in dollar sales revenues. Although we showed only one year in our earlier exam- ple, Allied’s managers actually forecasted sales for eight years, with these results:

YEAR 2002 2003 2004 2005 2006 2007 2008 2009

Growth rate in sales 10% 10% 10% 10% 9% 8% 7% 7%

This eight-year period is called the explicit forecast period, with the eighth year being the forecast horizon.

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6. Advertising campaigns, promotional discounts, credit terms, and the like also affect sales, so probable developments for these items are also fac- tored in.

7. Forecasts are made for each division, both in the aggregate and on an individual product basis. The individual product sales forecasts are summed, and this sum is compared with the aggregated division forecasts. Differences are reconciled, and the end result is a sales forecast for the company as a whole but with breakdowns by the three divisions and by individual products.

If the sales forecast is off, the consequences can be serious. First, if the market expands more than Allied has geared up for, the company will not be able to meet demand. Its customers will end up buying competitors’ products, and Allied will lose market share. On the other hand, if its projections are overly optimistic, Allied could end up with too much plant, equipment, and inventory. This would mean low turnover ratios, high costs for depreciation and storage, and write-offs of spoiled inventory. All of this would result in low profits, a low rate of return on equity, and a depressed stock price. If Allied had financed an unnecessary expansion with debt, high interest charges would compound its problems. Thus, an accurate sales forecast is critical to the firm’s well-being.4

4 A sales forecast is actually the expected value of a probability distribution, so there are many possible levels of sales. Because any sales forecast is subject to uncertainty, financial planners are just as in- terested in the degree of uncertainty inherent in the sales forecast, as measured by the standard de- viation, as in the expected level of sales.

SELF-TEST QUESTIONS

List some factors that should be considered when developing a sales fore- cast.

Explain why an accurate sales forecast is critical to profitability.

Percent of Sales Method A method of forecasting future financial statements that expresses each account as a percentage of sales. These percentages can be constant, or they can change over time.

145

The initially forecasted growth rate is 10 percent, but high growth attracts competitors, and eventually the market becomes saturated. Therefore, popula- tion growth and inflation determine the long-term sales growth rate for most companies. Reasonable values for the long-term sales growth rate are from 5 to 7 percent for companies in mature industries. Allied’s managers believe that a long-term sales growth rate of 7 percent is reasonable. Its managers also believe that competition will drive their growth rate down to this level within seven or eight years, so they have chosen an eight-year forecast period.

Companies often have what is called a competitive advantage period, during which they can grow at rates higher than the long-term growth rate. For com- panies with proprietary technology or strong brand identities, such as Mi- crosoft or Coca-Cola, the competitive advantage period might be as long as 20 years. For companies that produce commodities or that are in highly competi- tive industries, the competitive advantage period might be as short as two or three years, or even be nonexistent.

To summarize, most financial plans have a forecast period of at least 5 years, with 5 to 15 years, depending on the expected length of the competitive ad- vantage period, being most common.

Many items on the income statement and balance sheet are often assumed to increase proportionally with sales. For example, the inventories-to-sales ratio might increase 20 percent, receivables/sales might increase 15 percent, variable costs might increase 60 percent of sales, and so forth. Then, as sales increase, items that are tied to sales also increase, and the values of those items for a particular year are estimated as percentages of the forecasted sales for that year. The remaining items on the forecasted statements — items that are not tied directly to sales — are set at “reasonable” levels.

Note that if the forecasted percentage of sales for each item is the same as the percentage for the prior year, then each item will grow at the same rate as sales. While the financial statement forecasting method often begins by assum- ing that many key items will grow at the same rate as projected sales, it is im- portant to recognize that this method can be easily adjusted to allow different income statement and balance sheet items to grow at different rates. This process is particularly straightforward whenever a spreadsheet is used to de- velop the forecast. With this understanding in mind, we explain in the follow- ing section how to use this method to forecast Allied’s financial statements.

STEP 1. FORECASTED INCOME STATEMENT

First, we forecast the income statement for the coming year. This statement is needed to estimate both income and the addition to retained earnings. Table 4-3 shows the forecast for 2002. Sales are forecasted to grow by 10 percent. The forecast of sales for 2002, shown in Row 1 of Column 3, is calculated by mul- tiplying the 2001 sales, shown in Column 1, by (1 � growth rate) � 1.1. The result is a 2002 forecast of $3,300 million.

The percent of sales method assumes initially that all costs except deprecia- tion are a specified percentage of sales. For 2001, Allied’s ratio of costs to sales is 87.2 percent ($2,616/$3,000 � 0.872). Thus, for each dollar of sales in 2001, Allied incurred 87.2 cents of costs. Initially, the company’s managers assume that the cost structure will remain unchanged in 2002. Later in the chapter we explore the impact of an improvement in the cost structure, but for now we as- sume that costs will equal 87.2 percent of sales. See Column 3, Row 2.

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Allied’s managers assume that depreciation will be a fixed percentage of net plant and equipment. For 2001, the ratio of depreciation to net plant and equipment is 10 percent ($100/$1,000 � 0.10), and Allied’s managers believe that this is a good estimate of future depreciation. As we discuss in the next sec- tion, the forecasted net plant and equipment for 2002 is $1,100. Therefore, the forecasted depreciation for 2002 is 0.10($1,100) � $110.

Total operating costs, shown in Row 4, are the sum of costs and deprecia- tion. EBIT is found by subtraction, while the interest charges in Column 3 are simply carried over from Column 1.

Earnings before taxes (EBT) is then calculated, as is net income before pre- ferred dividends. Preferred dividends are carried over from the 2001 column, and they will remain constant unless Allied decides to issue additional preferred stock. Net income available to common is then calculated, after which the 2002 dividends are forecasted as follows. The 2001 dividend per share is $1.15, and this dividend is expected to increase by about 8 percent, to $1.25. Since there are 50 million shares outstanding, the projected dividends are $1.25(50) � $62.5 million, rounded to $63 million.

To complete the forecasted income statement, the $63 million of projected dividends are subtracted from the $131 million projected net income, and the result is the first-pass projection of the addition to retained earnings, $131 � $63 � $68 million.

T A B L E 4 - 3 Allied Food Products: Actual 2001 and Projected 2002 IncomeStatements (Millions of Dollars)

ACTUAL FORECAST 2002 2001a BASIS FORECAST (1) (2) (3)

1. Sales $3,000 1.1 � 2001 Sales � $3,300 2. Costs except depreciation 2,616 0.872 � 2002 Sales � 2,878 3. Depreciation 100 0.1 � 2002 Net plant � 110 4. Total operating costs $2,716 $2,988 5. EBIT $ 284 $ 312 6. Interest 88 → 88b

7. Earnings before taxes (EBT) $ 196 $ 224 8. Taxes (40%) 78 89 9. NI before preferred dividends $ 118 $ 135

10. Dividends to preferred 4 → 4b

11. NI available to common $ 114 $ 131 12. Dividends to common $ 58 $ 63c

13. Addition to retained earnings $ 56 $ 68

a To reduce clutter, the income statement as shown previously in Chapter 2 is rounded to whole numbers. b Indicates a 2001 amount carried over for the 2002 forecast. Indicated in Column 2 by an arrow. c See the text for explanation of dividends.

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STEP 2. FORECAST THE BALANCE SHEET

The assets shown on Allied’s balance sheet must increase if sales are to increase. For example, companies such as Allied write and deposit checks every day. Be- cause they don’t know exactly when all of these checks will clear, they can’t predict exactly what the balance in their checking accounts will be on any given day. Therefore, they must maintain a balance of cash and marketable se- curities to avoid overdrawing their accounts. We discuss cash management in more detail in Chapter 15, but for now we simply assume that the cash required to support the company’s operations is proportional to its sales. Allied’s 2001 ratio of cash to sales was approximately 0.33 percent ($10/$3,000 � 0.003333), and its managers believe this ratio will remain constant in 2002. Therefore, the forecasted cash balance for 2002, shown in Column 3 of Table 4-4, is 0.003333($3,300) � $11 million.

Unless a company changes its credit policy or has a change in its types of customers, accounts receivable will increase proportionately with sales. Allied’s 2001 ratio of accounts receivable to sales was $375/$3,000 � 0.125 � 12.5%. Later, we examine the effect of a change in credit policy, but for now we assume a constant credit policy and customer base. Therefore, the forecasted accounts receivable for 2002 is 0.125($3,300) � $412.5 million, rounded to $412 million as shown in Column 3 of Table 4-4.

As sales increase, companies generally need more inventory. For Allied, the 2001 ratio of inventory to sales is $615/$3,000 � 20.5%. Assuming no change in Allied’s inventory management, the forecasted inventory for 2002 is 0.205($3,300) � $676.5 million, rounded to $677 million as shown in Column 3 of Table 4-4.

It might be reasonable to assume that cash, accounts receivable, and inven- tory grow proportionally with sales, but will the amount of net plant and equip- ment go up and down as sales go up and down? The correct answer could be yes or no. When companies acquire plant and equipment, they often install greater capacity than they currently need, due to economies of scale. For ex- ample, it was economically better for GM to build the Saturn automobile plant with a capacity of about 320,000 cars per year than to build the plant with a ca- pacity of only 50,000 cars per year and then add capacity each year. Saturn’s sales were far below 320,000 units for the first few years of production, so it was possible to increase sales during those years without also increasing plant and equipment. Even if a factory is at its maximum rated capacity, most companies can produce additional units by reducing the amount of downtime due to scheduled maintenance, by running machinery at a higher than optimal speed, or by running a second (or third) shift. Therefore, there is not necessarily a close relationship between sales and net plant and equipment in the short term.

However, for some companies there is a fixed relationship between sales and plant and equipment, even in the short term. For example, new stores in many retail chains achieve the same sales during their first year as the chain’s existing stores. The only way these retailers can grow is by adding new stores, which re- sults in a strong proportional relationship between fixed assets and sales.

In the long run, there is a relatively close relationship between sales and fixed assets for all companies: No company can continue to increase sales unless it even- tually adds capacity. Therefore, as a first approximation it is reasonable to assume that the long-term ratio of net plant and equipment to sales will be constant.

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For the first years of a forecast, managers generally use the actual planned dollars of investment in plant and equipment. If those estimates are not avail- able, it is reasonable to assume an approximately constant ratio of net plant and equipment to sales. For Allied, the ratio of net plant and equipment to sales for 2001 is $1,000/$3,000 � 33.33%. Allied’s net plant and equipment have grown fairly steadily in the past, and its managers expect steady future growth. There- fore, they forecast net plant and equipment for 2002 to be 0.3333($3,300) � $1,100 million.

Once the individual asset accounts have been forecasted, they can be summed to complete the asset section of the balance sheet. For Allied, the total current assets forecasted for 2002 are $11 � $412 � $677 � $1,100 million, and fixed as- sets add another $1,100 million. Therefore, as Table 4-4 shows, Allied will need total assets of $2,200 million to support $3,300 million of sales in 2002.

If Allied’s assets are to increase, its liabilities and equity must also increase — the additional assets must be financed. Some items on the liability side can be

T A B L E 4 - 4 Allied Food Products: Actual 2001 and Projected 2002 Balance Sheets (Millions of Dollars)

2 0 0 2 F O R E C A S TACTUAL FORECAST 2001 BASIS FIRST PASS AFNa SECOND PASS (1) (2) (3) (4) (5)

Cash and marketable securities $ 10 0.33% � 2002 Sales � $ 11 → $ 11 Accounts receivable 375 12.5% � 2002 Sales � 412 → 412 Inventories 615 20.5% � 2002 Sales � 677 → 677

Total current assets $1,000 $1,100 $1,100 Net plant and equipment 1,000 33.33% � 2002 Sales � 1,100 → 1,100 Total assets $2,000 $2,200 $2,200

Accounts payable $ 60 2% � 2002 Sales � $ 66 → $ 66 Notes payable 110 → 110b �28 138 Accruals 140 4.67% � 2002 Sales � 154 → 154

Total current liabilities $ 310 $ 330 $ 358 Long-term bonds 754 → 754b �28 782

Total debt $1,064 $1,084 $1,140 Preferred stock 40 → 40b → 40 Common stock 130 → 130b �56 186 Retained earnings 766 �68c 834 → 834

Total common equity $ 896 $ 964 $1,020 Total liabilities and equity $2,000 $2,088 �112 $2,200

Additional funds needed (AFN) $ 112

a AFN stands for “Additional Funds Needed.” This figure is determined at the bottom of Column 3. Then, Column 4 shows how the required $112 of AFN will be raised. b Indicates a 2001 amount carried over as the first-pass forecast. Arrows also indicate items whose values are carried over from one pass to another. c From Line 13 in Column 3 of Table 4-3.

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expected to increase spontaneously with sales, producing what are called spon- taneously generated funds. For example, as sales increase, so will Allied’s pur- chases of raw materials, and those larger purchases will spontaneously lead to a higher level of accounts payable. For Allied, the 2001 ratio of accounts payable to sales is $60/$3,000 � 0.02 � 2%. Allied’s managers assume that their payables policy will not change, so the forecasted accounts payable for 2002 is 0.02($3,300) � $66 million.

More sales will require more labor, and higher sales should also result in higher taxable income and thus taxes. Therefore, accrued wages and taxes will both increase. For Allied, the 2001 ratio of accruals to sales is $140/$3,000 � 0.0467 � 4.67%. If this ratio does not change, then the forecasted level of ac- cruals for 2002 will be 0.0467($3,300) � $154 million.

Retained earnings will also increase, but not at the same rate as sales: The new balance for retained earnings will be the old level plus the addition to re- tained earnings, which we calculated in Step 1. Also, notes payable, long-term bonds, preferred stock, and common stock will not rise spontaneously with sales — rather, the projected levels of these accounts will depend on financing decisions, as we discuss later.

In summary, (1) higher sales must be supported by additional assets, (2) some of the asset increases can be financed by spontaneous increases in accounts payable and accruals, and by retained earnings, but (3) any shortfall must be fi- nanced from external sources, using some combination of debt, preferred stock, and common stock.

The spontaneously increasing liabilities (accounts payable and accruals) are forecasted and shown in Column 3 of Table 4-4, the first-pass forecast. Then, those liability and equity accounts whose values reflect conscious management decisions — notes payable, long-term bonds, preferred stock, and common stock — are initially set at their 2001 levels. Thus, 2002 notes payable are ini- tially set at $110 million, the long-term bond account is forecasted at $754 mil- lion, and so on. The 2002 value for the retained earnings (RE) account is ob- tained by adding the projected addition to retained earnings as developed in the 2002 income statement (see Table 4-3) to the 2001 ending balance:

2002 RE � 2001 RE � 2002 forecasted addition to RE

� $766 � $68 � $834 million.

The forecast of total assets as shown in Column 3 (first-pass forecast) of Table 4-4 is $2,200 million, which indicates that Allied must add $200 million of new assets in 2002 to support the higher sales level. However, the forecasted liability and equity accounts as shown in the lower portion of Column 3 rise by only $88 million, to $2,088 million. Since the balance sheet must balance, Al- lied must raise an additional $2,200 � $2,088 � $112 million, which we define as Additional Funds Needed (AFN). The AFN will be raised by some com- bination of borrowing from the bank as notes payable, issuing long-term bonds, and selling new common stock.

STEP 3. RAIS ING THE ADDIT IONAL FUNDS NEEDED

Allied’s financial staff will raise the needed funds based on several factors, in- cluding the firm’s target capital structure, the effect of short-term borrowing on the current ratio, conditions in the debt and equity markets, and restrictions

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Spontaneously Generated Funds Funds that are obtained automatically from routine business transactions.

Additional Funds Needed (AFN) Funds that a firm must raise externally through borrowing or by selling new common or preferred stock.

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imposed by existing debt agreements. The financial staff, after considering all of the relevant factors, decided on the following financing mix to raise the needed $112 million:

A M O U N T O F N E W C A P I TA L

PERCENT DOLLARS (MILLIONS) INTEREST RATE

Notes payable 25% $ 28 8% Long-term bonds 25 28 10 Common stock 50 56 —

100% $112

5 For a thorough discussion of financing feedbacks, see Eugene F. Brigham and Phillip R. Daves, Intermediate Financial Management, 7th ed. (Fort Worth, TX: Harcourt College Publishers, 2002), Chapter 8.

These amounts, which are shown in Column 4 of Table 4-4, are added to the initially forecasted account totals as shown in Column 3 to generate the second-pass balance sheet. Thus, in Column 5 the notes payable account in- creases to $110 � $28 � $138 million, long-term bonds rise to $754 � $28 � $782 million, and common stock increases to $130 � $56 � $186 million. Then, the balance sheet is in balance.

A COMPLICAT ION: FINANCING FEEDBACKS

Our projected financial statements are incomplete in one sense — they do not reflect the fact that interest must be paid on the debt used to help finance the AFN, and that dividends will be paid on the shares issued to raise the common stock portion of the AFN. Those payments would lower net income and re- tained earnings shown in the projected statements. One could take account of these financing feedback effects by adding columns to Tables 4-3 and 4-4 and then making further adjustments. The adjustments are not difficult, but they do in- volve a good bit of arithmetic. In view of the fact that all of the data are based on forecasts, and since the adjustments add substantially to the work but relatively little to the accuracy of the forecasts, we leave them to later finance courses.5

ANALYS IS OF THE FORECAST

The 2002 forecast as developed above is only the first part of Allied’s total fore- casting process. We must go on to analyze the projected statements to deter- mine whether the forecast meets the firm’s financial targets as set forth in the five-year financial plan. If the statements do not meet the targets, then ele- ments of the forecast must be changed.

Table 4-5 shows Allied’s actual ratios for 2001, its projected 2002 ratios, and the latest industry average ratios. (The table also shows a “Revised Forecast for 2002” column, which we will discuss later. Disregard the revised data for now.) The firm’s financial condition at the close of 2001 was weak, with many ratios

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well below the industry averages. For example, Allied’s current ratio, based on Column 1 of Table 4-4, was only 3.2 versus 4.2 for an average food processor.

The “Inputs” section shown on the top three rows of the table provides data on three of the model’s key drivers: (1) costs (excluding depreciation) as a per- centage of sales, (2) accounts receivable as a percentage of sales, and (3) inven- tories as a percentage of sales. The preliminary forecast in Column 2 assumes these variables remain constant. While Allied’s cost-to-sales ratio is only slightly worse than the industry average, its ratios of accounts receivable to sales and inventories to sales are significantly higher than those of its competi- tors. Its investment in inventories and receivables is too high, causing its re- turns on assets, equity, and invested capital as shown in the lower part of the table to be too low. Therefore, Allied should make operational changes de- signed to reduce its current assets.

The “Key Ratios” section of Table 4-5 for the forecast period provides more details regarding the firm’s weaknesses. Allied’s asset management ratios are much

T A B L E 4 - 5 Model Inputs, AFN, and Key Ratios

PRELIMINARY REVISED INDUSTRY ACTUAL FORECAST FOR FORECAST FOR AVERAGE 2001 2002 2002a 2001 (1) (2) (3) (4)

MODEL INPUTS

Costs (excluding depreciation) as percentage of sales 87.2% 87.2% 86.0% 87.1% Accounts receivable as percentage of sales 12.5 12.5 11.8 10.0 Inventories as percentage of sales 20.5 20.5 16.7 11.1 MODEL OUTPUTS

NOPAT (net operating profit after taxes) $170.3 $187.3 $211.2 Net operating working capital $800.0 $880.0 $731.5 Total operating capital $1,800.0 $1,980.0 $1,831.5 Free cash flow (FCF) ($109.7) $7.3 $179.7 AFN $112 ($60) KEY RATIOS

Current ratio 3.2� 3.1� 3.5� 4.2� Inventory turnover 4.9� 4.9� 6.0� 9.0� Days sales outstanding (365-day basis) 45.6 45.6 43.1 36.0 Total assets turnover 1.5� 1.5� 1.6� 1.8� Debt ratio 53.2% 51.8% 49.9% 40.0% Profit margin 3.8% 4.0% 4.7% 5.0% Return on assets 5.7% 5.9% 7.5% 9.0% Return on equity 12.7% 12.8% 15.6% 15.0% Return on invested capital (NOPAT/Total operating capital) 9.5% 9.5% 11.5% 11.4%

a The “Revised” data show ratios after policy changes related to asset levels, as discussed later, have been incorporated into the forecast. All of the surplus AFN is used to pay off notes payable.

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worse than the industry averages. For example, its total assets turnover ratio is 1.5 versus an industry average of 1.8. Its poor asset management ratios drag down the return on invested capital (9.5 percent for Allied versus 11.4 percent for the in- dustry average). Furthermore, Allied must carry more than the average amount of debt to support its excessive assets, and the extra interest expense reduces its profit margin to 4.0 percent versus 5.0 percent for the industry. Much of the debt is short term, and this results in a current ratio of 3.1 versus the 4.2 industry average. These problems will persist unless management takes action to improve things.

After reviewing its preliminary forecast, management decided to take three steps to improve its financial condition: (1) It decided to lay off some workers and close certain operations. It forecasted that these steps would lower operat- ing costs (excluding depreciation) from the current 87.2 to 86 percent of sales as shown in Column 3 of Table 4-5. (2) By screening credit customers more closely and by being more aggressive in collecting past-due accounts, the company be- lieves it can reduce the ratio of accounts receivable-to-sales from 12.5 to 11.8 percent. (3) Finally, management thinks it can reduce the inventories-to-sales ratio from 20.5 to 16.7 percent through the use of tighter inventory controls.6

These projected operational changes were then used to create a revised set of forecasted statements for 2002. We do not show the new financial state- ments, but the revised ratios are shown in the third column of Table 4-5. You can see the details in the chapter spreadsheet model, 04MODEL.xls. Here are the highlights of the revised forecast:

1. The reduction in operating costs improved the 2002 NOPAT, or net op- erating profit after taxes, by $23.9 million. Even more impressive, the im- provements in the receivables policy and in inventory management re- duced receivables and inventories by $148.5 million. The net result of the increase in NOPAT and the reduction of current assets was a very large increase in free cash flow for 2002, from a previously estimated $7.3 mil- lion to $179.7 million. Although we do not show it, the improvements in operations also led to significantly higher free cash flow for each year in the whole forecast period.

2. The profit margin improved to 4.7 percent. However, the firm’s profit margin still lagged the industry average because its high debt ratio re- sults in higher-than-average interest payments.

3. The increase in the profit margin resulted in an increase in projected re- tained earnings. More importantly, by tightening inventory controls and reducing the days sales outstanding, Allied projected a reduction in in- ventories and receivables. Taken together, these actions resulted in a neg- ative AFN of $60 million, which means that Allied would actually gener- ate $60 million more from internal operations during 2002 than it needs for new assets. All of this $60 million of surplus funds would be used to reduce short-term debt, which would lead to a decrease in the forecasted debt ratio from 51.8 to 49.9 percent. The debt ratio would still be well above the industry average, but this is a step in the right direction.

4. The indicated changes would also affect Allied’s current ratio, which would improve from 3.1 to 3.5.

6 We will discuss receivables and inventory management in detail in Chapter 15.

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5. These actions would also raise the rate of return on assets from 5.9 to 7.5 percent, and they would boost the return on equity from 12.8 to 15.6 percent, which is even higher than the industry average.

Although Allied’s managers believe that the revised forecast is achievable, they are not sure of this. Accordingly, they wanted to know how variations in sales would affect the forecast. Therefore, a spreadsheet model was run using several different sales growth rates, and the results were analyzed to see how the ratios would change under different growth scenarios. To illustrate, if the sales growth rate increased from 10 to 20 percent, the additional funding requirement would change dramatically, from a $60 million surplus to an $87 million shortfall.

The spreadsheet model was also used to evaluate dividend policy. If Allied decided to reduce its dividend growth rate, then additional funds would be gen- erated, and those funds could be invested in plant, equipment, and inventories; used to reduce debt; or used to repurchase stock.

The model was also used to evaluate financing alternatives. For example, Al- lied could use the forecasted $60 million of surplus funds to retire long-term bonds rather than to reduce short-term debt. Under this financing alternative, the current ratio would drop from 3.5 to 2.9, but the firm’s interest coverage ratio would rise, assuming that the firm’s long-term debt carries a higher inter- est rate than its notes payable.

We see, then, that forecasting is an iterative process, both in the way the fi- nancial statements are generated and the way the financial plan is developed. For planning purposes, the financial staff develops a preliminary forecast based on a continuation of past policies and trends. This provides a starting point, or “baseline” forecast. Next, the projections are modified to see what effects alter- native operating plans would have on the firm’s earnings and financial condi- tion. This results in a revised forecast. Then alternative operating plans are ex- amined under different sales growth scenarios, and the model is used to evaluate both dividend policy and capital structure decisions.

The spreadsheet model can be used to analyze alternative working capital policies —that is, to see the effects of changes in cash management, credit pol- icy, inventory policy, and the use of different types of short-term credit. We will examine Allied’s working capital policy within the framework of the company’s financial model later, but in the remainder of this chapter, we consider some other aspects of the financial forecasting process.

FORECAST ING FREE CASH FLOW

The spreadsheet model can also be used to estimate Allied’s free cash flow. Re- call from Chapter 2, Equation 2-7, that free cash flow is calculated as follows:

FCF � Operating cash flow � Gross investment in operating capital.

Alternatively, FCF can be calculated using Equation 2-7a:

FCF � NOPAT � Net investment in operating capital.

Recall also that free cash flow represents the amount of cash generated in a given year minus the amount of cash needed to finance the additional capital ex- penditures and operating working capital needed to support the firm’s growth.

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The detailed spreadsheet model is not provided in the text, but its key out- puts were shown in the “Model Outputs” section back in Table 4-5. We see that before the operating changes Allied forecasted a slight increase in NOPAT (net operating profit after taxes), but it projected a very large increase in net oper- ating working capital and in total operating capital. The net result is a very low level of free cash flow, only $7.3 million. Although we do not show projections of the full financial statements for all eight years of the explicit forecast hori- zon, here are the initially projected free cash flows (FCFs):

YEARS 2002 2003 2004 2005 2006 2007 2008 2009

FCF 7.3 8.4 8.9 9.8 34.6 63.7 96.9 103.7

As we will see in Chapter 9, investors and financial managers use such fore- casts to estimate the firm’s stock price. Thus, this model helps managers mea- sure the expected changes in the determinants of value under different strate- gic and operating alternatives.

SELF-TEST QUESTIONS

What is the AFN, and how is the percent of sales method used to estimate it?

Why do accounts payable and accruals provide “spontaneous funds” to a growing firm?

Would payables and accruals provide spontaneous funds to a no-growth firm? One that is declining?

Why do retained earnings not grow at the same rate as sales? In answering this question, think about a firm whose sales are not growing (g � 0%), but that is profitable and does not pay out all of its earnings as dividends.

T H E A F N F O R M U L A

Most firms forecast their capital requirements by constructing pro forma income statements and balance sheets as described above. However, if the ratios are ex- pected to remain constant, then the following formula can be used to forecast fi- nancial requirements. Here we apply the formula to Allied based on the 2001 data, not the revised data, as the revised data do not assume constant ratios.

Additional Required Spontaneous Increase in funds � increase � increase in � retained

needed in assets liabilities earnings

AFN � (A*/S0)�S � (L*/S0)�S � MS1(RR). (4-1)

Here

AFN � additional funds needed. A* � assets that are tied directly to sales, hence which must increase if sales

are to increase. Note that A designates total assets and A* designates those assets that must increase if sales are to increase. When the firm

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is operating at full capacity, as is the case here, A* � A. Often, though, A* and A are not equal, and either the equation must be modified or we must use the projected financial statement method.

S0 � sales during the last year. A*/S0 � percentage of required assets to sales, which also shows the required

dollar increase in assets per $1 increase in sales. A*/S0 � $2,000/$3,000 � 0.6667 for Allied. Thus, for every $1 increase in sales, assets must increase by about 67 cents.

L* � liabilities that increase spontaneously. L* is normally much less than total liabilities (L). Spontaneous liabilities include accounts payable and accruals, but not bank loans and bonds.

L*/S0 � liabilities that increase spontaneously as a percentage of sales, or spon- taneously generated financing per $1 increase in sales. L*/S0 � ($60 � $140)/$3,000 � 0.0667 for Allied. Thus, every $1 increase in sales generates about 7 cents of spontaneous financing.

S1 � total sales projected for next year. Note that S0 designates last year’s sales, and S1 � $3,300 million for Allied.

�S � change in sales � S1 � S0 � $3,300 million � $3,000 million � $300 million for Allied.

M � profit margin, or profit per $1 of sales. M � $114/$3,000 � 0.0380 for Allied. So, Allied earns 3.8 cents on each dollar of sales.

RR � retention ratio, which is the percentage of net income that is retained. For Allied, RR � $56/$114 � 0.491. RR is also equal to 1 � payout ratio, since the retention ratio and the payout ratio must total to 1.0 � 100%.

Inserting values for Allied into Equation 4-1, we find the additional funds needed to be $118 million:

Required Spontaneous Increase AFN � asset � liability � in retained

increase increase earnings

�0.667(�S) � 0.067(�S) � 0.038(S1)(0.491)

� 0.667($300 million) � 0.067($300 million) � 0.038($3,300 million)(0.491)

� $200 million � $20 million � $62 million

� $118 million.

To increase sales by $300 million, the formula suggests that Allied must in- crease assets by $200 million. The $200 million of new assets must be financed in some manner. Of the total, $20 million will come from a spontaneous in- crease in liabilities, while another $62 million will be obtained from retained earnings. The remaining $118 million must be raised from external sources. This value is an approximation, but it is only slightly different from the initial AFN figure ($112 million) we developed in Table 4-4.7

This equation shows that external financing requirements depend on five key factors:

T H E A F N F O R M U L A

7 If Table 4-4 had been extended to include financing feedbacks, the forecasted AFN would have been $119 million, which is very close to the formula AFN.

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� Sales growth (DS). Rapidly growing companies require large increases in assets, other things held constant.

� Capital intensity (A*/S0). The amount of assets required per dollar of sales, A*/S0 in Equation 4-1, is called the capital intensity ratio. This ratio has a major effect on capital requirements. Companies with higher assets-to- sales ratios require more assets for a given increase in sales, hence a greater need for external financing.

� Spontaneous liabilities-to-sales ratio (L*/S0). Companies that spontaneously generate a large amount of liabilities from accounts payable and accruals will have a relatively small need for external financing.

� Profit margin (M). The higher the profit margin, the larger the net income available to support increases in assets, hence the lower the need for ex- ternal financing.

� Retention ratio (RR). Companies that retain more of their earnings as op- posed to paying them out as dividends will generate more retained earn- ings and thus have less need for external financing.

Note that Equation 4-1 provides an accurate forecast only for companies whose ratios are all expected to remain constant. It is useful to obtain a quick “back of the envelope” estimate of external financing requirements for nonconstant ratio companies, but in the planning process one should calculate the actual addi- tional funds needed by the projected financial statement method.

Capital Intensity Ratio The amount of assets required per dollar of sales (A*/S0).

SELF-TEST QUESTIONS

If all ratios are expected to remain constant, a formula can be used to fore- cast AFN. Give the formula and briefly explain it.

How do the following factors affect external capital requirements?

(1) Retention ratio.

(2) Capital intensity.

(3) Profit margin.

(4) Dividend payout ratio.

F O R E C A S T I N G F I N A N C I A L R E Q U I R E M E N T S W H E N T H E BA L A N C E S H E E T R AT I O S A R E S U B J E C T TO C H A N G E

Both the AFN formula and the projected financial statement method as we ini- tially used it assume that the ratios of assets and liabilities to sales (A*/S0 and L*/S0) remain constant over time. This, in turn, requires the assumption that each “spontaneous” asset and liability item increases at the same rate as sales. In graph form, this implies the type of relationship shown in Panel a of Figure 4-3, a relationship that is (1) linear and (2) passes through the origin. Under those conditions, if the company’s sales increase from $200 million to $400 mil- lion, or by 100 percent, inventory will also increase by 100 percent, from $100 million to $200 million.

157F O R E C A S T I N G F I N A N C I A L R E Q U I R E M E N T S W H E N T H E BA L A N C E S H E E T R AT I O S A R E S U B J E C T TO C H A N G E

The assumption of constant ratios and identical growth rates is appropriate at times, but there are times when it is incorrect. Three such conditions are de- scribed in the following sections.

ECONOMIES OF SCALE

There are economies of scale in the use of many kinds of assets, and when economies occur, the ratios are likely to change over time as the size of the firm increases. For example, retailers often need to maintain base stocks of different inventory items, even if current sales are quite low. As sales expand, inventories may then grow less rapidly than sales, so the ratio of inventory to sales (I/S) de- clines. This situation is depicted in Panel b of Figure 4-3. Here we see that the

F I G U R E 4 - 3 Four Possible Ratio Relationships (Millions of Dollars)

Capacity

300

225

150

75

0 100 200 300 Sales ($)

Excess Capacity (Temporary)

FA/S

50

Fixed Assets

($)

A

B

d. Lumpy Assets

Sales ($)4002000

100

200

Inventory ($)

a. Constant Ratios

I/S

I/S

100/200 = 0.50 = 50%

200/400 = 0.50 = 50%

Base Stock

300/200 = 1.50 = 150%

2000 400 Sales ($)

400/400 = 1.00 = 100%

Inventory ($)

b. Economies of Scale; Declining Ratios

I/S

300

400

2000 400 Sales ($)

Inventory ($)

c. Curvilinear Relationship

300

424

C H A P T E R 4 � F I N A N C I A L P L A N N I N G A N D F O R E C A S T I N G158

inventory/sales ratio is 1.5, or 150 percent, when sales are $200 million, but the ratio declines to 1.0 when sales climb to $400 million.

The relationship in Panel b is linear, but nonlinear relationships often exist. Indeed, if the firm uses one popular model for establishing inventory levels (the EOQ model), its inventories will rise with the square root of sales. This situa- tion is shown in Panel c of Figure 4-3, which shows a curved line whose slope decreases at higher sales levels. In this situation, very large increases in sales would require very little additional inventory.

LUMPY ASSETS

In many industries, technological considerations dictate that if a firm is to be competitive, it must add fixed assets in large, discrete units; such assets are often referred to as lumpy assets. In the paper industry, for example, there are strong economies of scale in basic paper mill equipment, so when a paper company expands capacity, it must do so in large, lumpy increments. This type of situation is depicted in Panel d of Figure 4-3. Here we assume that the minimum economically efficient plant has a cost of $75 million, and that such a plant can produce enough output to reach a sales level of $100 million. If the firm is to be competitive, it simply must have at least $75 million of fixed assets.

Lumpy assets have a major effect on the fixed assets/sales (FA/S) ratio at dif- ferent sales levels and, consequently, on financial requirements. At Point A in Panel d, which represents a sales level of $50 million, the fixed assets are $75 million, so the ratio FA/S � $75/$50 � 1.5. Sales can expand by $50 million, out to $100 million, with no additions to fixed assets. At that point, represented by Point B, the ratio FA/S � $75/$100 � 0.75. However, since the firm is op- erating at capacity (sales of $100 million), even a small increase in sales would require a doubling of plant capacity, so a small projected sales increase would bring with it a very large financial requirement.8

EXCESS ASSETS DUE TO FORECAST ING ERRORS

Panels a, b, c, and d of Figure 4-3 all focus on target, or projected, relationships between sales and assets. Actual sales, however, are often different from pro- jected sales, and the actual assets-to-sales ratio at a given time may be quite different from the planned ratio. To illustrate, the firm depicted in Panel b of

Lumpy Assets Assets that cannot be acquired in small increments but must be obtained in large, discrete units.

8 Several other points should be noted about Panel d of Figure 4-3. First, if the firm is operating at a sales level of $100 million or less, any expansion that calls for a sales increase above $100 million would require a doubling of the firm’s fixed assets. A much smaller percentage increase would be in- volved if the firm were large enough to be operating a number of plants. Second, firms generally go to multiple shifts and take other actions to minimize the need for new fixed asset capacity as they approach Point B. However, these efforts can only go so far, and eventually a fixed asset expansion will be required. Third, firms often make arrangements to share excess capacity with other firms in their industry. For example, the situation in the electric utility industry is very much like that de- picted in Panel d. However, electric companies often build jointly owned plants, or else they “take turns” building plants, and then they buy power from or sell power to other utilities to avoid build- ing new plants that would be underutilized.

159

Figure 4-3 might, when its sales are at $200 million and its inventories at $300 million, project a sales expansion to $400 million and then increase its inventories to $400 million in anticipation of the higher sales. However, sup- pose an unforeseen economic downturn held sales to only $300 million. Ac- tual inventories would then be $400 million, but inventories of only $350 mil- lion would be needed to support actual sales of $300 million. Thus, inventories would be $50 million larger than needed. Then, when the firm makes its forecast for the following year, it must recognize that sales could ex- pand by $100 million with no increase whatever in inventories, but that any sales expansion beyond $100 million would require additional financing to in- crease inventories.

OT H E R T E C H N I Q U E S F O R F O R E C A S T I N G F I N A N C I A L S TAT E M E N T S

SELF-TEST QUESTION

Describe three conditions under which the assumption that each “sponta- neous” asset and liability item increases at the same rate as sales is not correct.

OT H E R T E C H N I Q U E S F O R F O R E C A S T I N G F I N A N C I A L S TAT E M E N T S

If any of the conditions noted above (economies of scale, excess capacity, or lumpy assets) apply, the A*/S0 ratio will not be a constant, and the constant growth forecasting methods as discussed thus far should not be used. Rather, other techniques must be used to forecast asset levels and additional financing requirements. Two of these methods — linear regression and excess capacity adjustments — are discussed in the following sections.

SIMPLE LINEAR REGRESS ION

If we assume that the relationship between a certain type of asset and sales is linear, then we can use simple linear regression techniques to estimate the re- quirements for that type of asset for any given sales increase. For example, Al- lied’s sales, inventories, and receivables during the last five years are shown in the lower section of Figure 4-4, and both current asset items are plotted in the upper section as a scatter diagram versus sales. Estimated regression equations, determined using a financial calculator or a spreadsheet, are also shown with each graph. For example, the estimated relationship between inventories and sales (in millions of dollars) is

Inventories � �$35.7 � 0.186(Sales).

The plotted points are not very close to the regression line, which indicates that changes in inventory are affected by factors other than changes in sales. In fact, the correlation coefficient between inventories and sales is only 0.71, indicating that there is only a moderate linear relationship between these two

C H A P T E R 4 � F I N A N C I A L P L A N N I N G A N D F O R E C A S T I N G160

variables. Still, the regression relationship is strong enough to provide a rea- sonable basis for forecasting the target inventory level, as described below.

We can use the regression relationship between inventories and sales to fore- cast 2002 inventory levels. Since 2002 sales are projected at $3,300 million, 2002 inventories should be $578 million:

Inventories � �$35.7 � 0.186($3,300) � $578 million.

This is $99 million less than the preliminary forecast based on the projected fi- nancial statement method. The difference occurs because the projected finan- cial statement method assumed that the ratio of inventories to sales would re- main constant, when in fact it will probably decline. Note also that although our graphs show linear relationships, we could have easily used a nonlinear re- gression model had such a relationship been indicated.

After analyzing the regression results, Allied’s managers decided that a new forecast of AFN should be developed assuming a lower days sales outstanding and a higher inventory turnover ratio. Management recognized that the 2001 levels of these accounts were above the industry averages, hence that the pre- liminary results projected for 2002 back in Table 4-4 were unnecessarily high. When simple linear regression was used to forecast the receivables and inven- tories accounts, this caused the 2002 levels to reflect both the average relation- ships of these accounts to sales over the five-year period and the trend in the variables’ values. In contrast, the projected financial statement method we de- veloped earlier assumed that the nonoptimal 2001 relationships would remain constant in 2002 and beyond. These new assumptions were largely responsible for the improved forecasts shown in Column 3 of Table 4-5.

YEAR SALES INVENTORIES ACCOUNTS RECEIVABLE

1997 $2,058 $387 $268 1998 2,534 398 297 1999 2,472 409 304 2000 2,850 415 315 2001 3,000 615 375

F I G U R E 4 - 4 Allied Food Products: Linear Regression Models (Millions of Dollars)

Sales ($)3,0002,7502,5002,2502,0000

400

350

300

250

200

Receivables ($)

Receivables = 62 + 0.097 (Sales)

Sales ($)3,0002,7502,5002,2502,0000

700

600

500

400

300

Inventories ($)

Inventories = –35.7 + 0.186 (Sales)

161

EXCESS CAPACITY ADJUSTMENTS

Consider again the Allied example set forth in Tables 4-3 and 4-4, but now as- sume that excess capacity exists in fixed assets. Specifically, assume that fixed as- sets in 2001 were being utilized to only 96 percent of capacity. If fixed assets had been used to full capacity, 2001 sales could have been as high as $3,125 mil- lion versus the $3,000 million in actual sales:

(4-2)

This suggests that Allied’s target fixed assets/sales ratio should be 32 percent rather than 33.3 percent:

(4-3)

Therefore, if sales are to increase to $3,300 million, then fixed assets would have to increase to $1,056 million:

Required level of fixed assets � (Target fixed assets/Sales)(Projected sales) (4-4)

� 0.32($3,300) � $1,056 million.

We previously forecasted that Allied would need to increase fixed assets at the same rate as sales, or by 10 percent. That meant an increase from $1,000 million to $1,100 million, or by $100 million. Now we see that the actual re- quired increase is only from $1,000 million to $1,056 million, or by $56 mil- lion. Thus, the capacity-adjusted forecast is $100 million � $56 million � $44 million less than the earlier forecast. With a smaller fixed asset requirement, the projected AFN would decline from an estimated $112 million to $112 mil- lion � $44 million � $68 million.

Note also that when excess capacity exists, sales can grow to the capacity sales as determined above with no increase whatever in fixed assets, but sales beyond that level will require fixed asset additions as calculated in our example. The same situation could occur with respect to inventories, and the required additions would be determined in exactly the same manner as for fixed assets. Theoretically, the same situation could occur with other types of assets. How- ever, as a practical matter excess capacity normally exists only with respect to fixed assets and inventories.

� $1,000 $3,125

� 0.32 � 32%.

Target fixed assets/Sales � Actual fixed assets Full capacity sales

Full capacity

sales �

Actual sales Percentage of capacity at which fixed assets

were operated

� $3,000 million

0.96 � $3,125 million.

OT H E R T E C H N I Q U E S F O R F O R E C A S T I N G F I N A N C I A L S TAT E M E N T S

SELF-TEST QUESTIONS

If sales are to double, would it be more important to use the regression method of forecasting asset requirements if the true situation were like that in Panel a or that in Panel b of Figure 4-3?

If excess capacity exists, how will that affect the AFN?

C H A P T E R 4 � F I N A N C I A L P L A N N I N G A N D F O R E C A S T I N G162

This chapter described techniques for forecasting financial statements, which is a crucial part of the financial planning process. As we will see throughout the rest of the book, both investors and corporations regularly use forecasting tech- niques to help value a company’s stock, to estimate the benefits of potential projects, and to estimate how changes in capital structure, dividend policy, and working capital policy will influence shareholder value. The key concepts cov- ered are listed below.

� To make their firms more valuable, managers must identify, evaluate, and implement projects that meet or exceed investor expectations. However, value creation for a firm is impossible unless a company has a well-articu- lated strategic plan.

� The firm’s strategic plan begins with a mission statement. � Key elements of a firm’s strategic plan include corporate purpose, cor-

porate scope, corporate objectives, and corporate strategies. � Operating plans provide detailed implementation guidance to help meet

corporate objectives. � The financial planning process can be divided into six steps: (1) project

financial statements and analyze them; (2) determine the funds needed to support the 5-year plan; (3) forecast funds availability over the next five years; (4) establish and maintain a system of controls for the allocation and use of funds; (5) develop procedures for adjusting the basic plan if the eco- nomic forecasts don’t materialize; and (6) establish a performance-based management compensation system.

� Virtually all corporate forecasts are made using computerized forecast- ing models based on spreadsheet programs. Spreadsheets have two major advantages over pencil-and-paper calculations: (1) Spreadsheet models are faster than by-hand calculations and (2) models can be instantaneously re- calculated making it easier to determine the effects of changes in variables.

� Financial forecasting generally begins with a forecast of the firm’s sales, in terms of both units and dollars.

� Either the projected, or pro forma, financial statement method or the AFN formula method can be used to forecast financial requirements. The financial statement method is more reliable, and it also provides ra- tios that can be used to evaluate alternative business plans.

� A firm can determine its additional funds needed (AFN) by estimating the amount of new assets necessary to support the forecasted level of sales and then subtracting from that amount the spontaneous funds that will be generated from operations. The firm can then plan how to raise the AFN most efficiently.

� The higher a firm’s sales growth rate, the greater will be its need for additional financing. In addition, the greater the firm’s capital intensity ratio, the greater the need for external financing. Similarly, the smaller its retention ratio, the greater its need for additional funds. However, the higher the profit margin, the lower the need for external financing.

163

� Adjustments must be made if economies of scale exist in the use of assets, if excess capacity exists, or if assets must be added in lumpy increments.

� Linear regression and excess capacity adjustments can be used to fore- cast asset requirements in situations in which assets are not expected to grow at the same rate as sales.

The type of forecasting described in this chapter is important for several rea- sons. First, if the projected operating results are unsatisfactory, management can “go back to the drawing board,” reformulate its plans, and develop more reasonable targets for the coming year. Second, it is possible that the funds re- quired to meet the sales forecast simply cannot be obtained. If so, it is obviously better to know this in advance and to scale back the projected level of opera- tions than to suddenly run out of cash and have operations grind to a halt. And third, even if the required funds can be raised, it is desirable to plan for their acquisition well in advance.

Q U E S T I O N S

4-1 Certain liability and net worth items generally increase spontaneously with increases in sales. Put a check (�) by those items that typically increase spontaneously:

Accounts payable ��������������� Notes payable to banks ��������������� Accrued wages ��������������� Accrued taxes ��������������� Mortgage bonds ��������������� Common stock ��������������� Retained earnings ���������������

4-2 The following equation can, under certain assumptions, be used to forecast financial re- quirements:

AFN � (A*/S0)(�S) � (L*/S0)(�S) � MS1(RR).

Under what conditions does the equation give satisfactory predictions, and when should it not be used?

4-3 Assume that an average firm in the office supply business has a 6 percent after-tax profit margin, a 40 percent debt/assets ratio, a total assets turnover of 2 times, and a dividend payout ratio of 40 percent. Is it true that if such a firm is to have any sales growth (g � 0), it will be forced either to borrow or to sell common stock (that is, it will need some nonspontaneous, external capital even if g is very small)?

4-4 Is it true that computerized corporate planning models were a fad during the 1990s but, because of a need for flexibility in corporate planning, they have been dropped by most firms in the millennium?

4-5 Suppose a firm makes the following policy changes. If the change means that external, nonspontaneous financial requirements (AFN) will increase, indicate this by a (�); indi- cate a decrease by a (�); and indicate indeterminate or no effect by a (0). Think in terms of the immediate, short-run effect on funds requirements. a. The dividend payout ratio is increased. ��������������� b. The firm contracts to buy, rather than make, certain components used in

its products. ��������������� c. The firm decides to pay all suppliers on delivery, rather than after a

30-day delay, to take advantage of discounts for rapid payment. ��������������� d. The firm begins to sell on credit (previously all sales had been on a cash

basis). ���������������

Q U E S T I O N S

C H A P T E R 4 � F I N A N C I A L P L A N N I N G A N D F O R E C A S T I N G164

e. The firm’s profit margin is eroded by increased competition; sales are steady. ���������������

f. Advertising expenditures are stepped up. ��������������� g. A decision is made to substitute long-term mortgage bonds for

short-term bank loans. ��������������� h. The firm begins to pay employees on a weekly basis (previously it had

paid at the end of each month). ���������������

S E L F - T E S T P R O B L E M S ( S O L U T I O N S A P P E A R I N A P P E N D I X B )

Define each of the following terms: a. Mission statement b. Sales forecast c. Percent of sales method d. Spontaneously generated funds e. Pro forma financial statement f. Additional funds needed (AFN); AFN formula g. Capital intensity ratio h. Lumpy assets Weatherford Industries Inc. has the following ratios: A*/S0 � 1.6; L*/S0 � 0.4; profit margin � 0.10; and retention ratio � 0.55, or 55 percent. Sales last year were $100 mil- lion. Assuming that these ratios will remain constant, use the AFN formula to determine the maximum growth rate Weatherford can achieve without having to employ non- spontaneous external funds. Suppose Weatherford’s financial consultants report (1) that the inventory turnover ratio is sales/inventory � 3 times versus an industry average of 4 times and (2) that Weatherford could reduce inventories and thus raise its turnover to 4 without affect- ing sales, the profit margin, or the other asset turnover ratios. Under these condi- tions, use the AFN formula to determine the amount of additional funds Weather- ford would require during each of the next 2 years if sales grew at a rate of 20 percent per year.

S TA R T E R P R O B L E M S

Carter Corporation’s sales are expected to increase from $5 million in 2001 to $6 mil- lion in 2002, or by 20 percent. Its assets totaled $3 million at the end of 2001. Carter is at full capacity, so its assets must grow in proportion to projected sales. At the end of 2001, current liabilities are $1 million, consisting of $250,000 of accounts payable, $500,000 of notes payable, and $250,000 of accruals. The after-tax profit margin is fore- casted to be 5 percent, and the forecasted retention ratio is 30 percent. Use this infor- mation to answer Problems 4-1, 4-2, and 4-3. Use the AFN formula to forecast Carter’s additional funds needed for the coming year. What would the additional funds needed be if the company’s year-end 2001 assets had been $4 million? Assume that all other numbers are the same. Why is this AFN differ- ent from the one you found in Problem 4-1? Is the company’s “capital intensity” the same or different? Return to the assumption that the company had $3 million in assets at the end of 2001, but now assume that the company pays no dividends. Under these assumptions, what would be the additional funds needed for the coming year? Why is this AFN different from the one you found in Problem 4-1? Jasper Furnishings has $300 million in sales. The company expects that its sales will increase 12 percent this year. Jasper’s CFO uses a simple linear regression to forecast the company’s inventory level for a given level of projected sales. On the basis of re-

4-4 Linear regression

4-3 AFN formula

4-2 AFN formula

4-1 AFN formula

ST-3 Additional funds needed

ST-2 Growth rate

ST-1 Key terms

165

cent history, the estimated relationship between inventories and sales (in millions of dollars is

Inventories � $25 � 0.125(Sales).

Given the estimated sales forecast and the estimated relationship between invento- ries and sales, what is your forecast of the company’s year-end inventory turnover ratio? Walter Industries has $5 billion in sales and $1.7 billion in fixed assets. Currently, the company’s fixed assets are operating at 90 percent of capacity. a. What level of sales could Walter Industries have obtained if it had been operating at

full capacity? b. What is Walter’s target fixed assets/sales ratio? c. If Walter’s sales increase 12 percent, how large of an increase in fixed assets would

the company need in order to meet its target fixed assets/sales ratio? Austin Grocers recently reported the following income statement (in millions of dol- lars):

Sales $700 Operating costs 500 EBIT $200 Interest 40 EBT $160 Taxes (40%) 64 Net income $96

Dividends $32 Addition to retained earnings $64

This year the company is forecasting a 25 percent increase in sales, and it expects that its year-end operating costs will equal 70 percent of sales. Austin’s tax rate, interest ex- pense, and dividend payout ratio are all expected to remain constant. a. What is Austin’s projected 2002 net income? b. What is the expected growth rate in Austin’s dividends?

E X A M - T Y P E P R O B L E M S

The problems included in this section are set up in such a way that they could be used as multiple-choice exam problems. At the end of last year, Roberts Inc. reported the following income statement (in mil- lions of dollars):

Sales $3,000 Operating costs excluding depreciation 2,450 EBITDA $ 550 Depreciation 250 EBIT $ 300 Interest 125 EBT $ 175 Taxes (40%) 70 Net income $ 105

4-7 Pro forma income statement

4-6 Pro forma income statement

4-5 Excess capacity

E X A M - T Y P E P R O B L E M S

C H A P T E R 4 � F I N A N C I A L P L A N N I N G A N D F O R E C A S T I N G166

Looking ahead to the following year, the company’s CFO has assembled the following information: � Year-end sales are expected to be 10 percent higher than the $3 billion in sales gen-

erated last year. � Year-end operating costs excluding depreciation are expected to equal 80 percent of

year-end sales. � Depreciation is expected to increase at the same rate as sales. � Interest costs are expected to remain unchanged. � The tax rate is expected to remain at 40 percent. On the basis of this information, what will be the forecast for Roberts’ year-end net income? Adel Sporting Goods recently reported the following income statement and balance sheet.

INCOME STATEMENT

Sales $4,200 Operating costs 3,780 EBIT $ 420 Interest 120 EBT $ 300 Taxes (40%) 120 Net income $ 180

Dividends paid $ 0 Addition to retained earnings $ 180 BALANCE SHEET

Cash and marketable securities $ 42 Accounts receivable 336 Inventories 441

Current assets $ 819 Net fixed assets 2,562 Total assets $3,381

Accounts payable and accruals $ 168 Notes payable 250

Current liabilities $ 418 Long-term debt 700 Common stock 400 Retained earnings 1,863 Total liabilities and equity $3,381

In developing its forecast for the upcoming year, the company has assembled the following information: � Sales are expected to increase 8 percent this upcoming year. � Operating costs are expected to remain at 90 percent of sales. � Cash and marketable securities are expected to remain at 1 percent of sales. � Accounts receivable are expected to remain at 8 percent of sales. � Due to excess capacity, the company expects that its year-end inventories will remain

at current levels. � Fixed assets are expected to remain at 61 percent of sales.

4-8 Pro forma statements

and ratios

167

� Spontaneous liabilities (accounts payable and accruals) are expected to increase at the same rate as sales.

� The company will continue to pay a zero dividend, and its tax rate will remain at 40 percent.

� The company anticipates that any additional funds needed will be raised in the fol- lowing manner: 25 percent notes payable, 25 percent long-term debt, and 50 percent common stock.

a. On the basis of the assumptions listed above, construct Adel’s pro forma income state- ment and balance sheet. Assume that there are no financial feedback effects. (That is, as- sume interest will remain unchanged even though the company may increase its debt.)

b. On the basis of this forecast, describe changes from the prior year that Adel should expect in its return on equity, inventory turnover ratio, and profit margin.

At year-end 2001, total assets for Ambrose Inc. were $1.2 million and accounts payable were $375,000. Sales, which in 2001 were $2.5 million, are expected to increase by 25 percent in 2002. Total assets and accounts payable are proportional to sales, and that relationship will be maintained. Ambrose typically uses no current liabilities other than accounts payable. Common stock amounted to $425,000 in 2001, and retained earn- ings were $295,000. Ambrose plans to sell new common stock in the amount of $75,000. The firm’s profit margin on sales is 6 percent; 60 percent of earnings will be retained. a. What was Ambrose’s total debt in 2001? b. How much new, long-term debt financing will be needed in 2002? (Hint: AFN �

New stock � New long-term debt.) The Flint Company’s sales are forecasted to increase from $1,000 in 2001 to $2,000 in 2002. Here is the December 31, 2001, balance sheet:

Cash $ 100 Accounts payable $ 50 Accounts receivable 200 Notes payable 150 Inventories 200 Accruals 50

Total current assets $ 500 Total current liabilities $ 250 Net fixed assets 500 Long-term debt 400

Common stock 100 Retained earnings 250

Total assets $1,000 Total liabilities and equity $1,000

Flint’s fixed assets were used to only 50 percent of capacity during 2001, but its current assets were at their proper levels. All assets except fixed assets increase in proportion to sales, and fixed assets would also increase proportionally with sales if the current excess capacity did not exist. Flint’s after-tax profit margin is forecasted to be 5 percent, and its payout ratio will be 60 percent. What is Flint’s additional funds needed (AFN) for the coming year? Pierce Furnishings generated $2.0 million in sales during 2001, and its year-end total as- sets were $1.5 million. Also, at year-end 2001, current liabilities were $500,000, consist- ing of $200,000 of notes payable, $200,000 of accounts payable, and $100,000 of accru- als. Looking ahead to 2002, the company estimates that its assets must increase by 75 cents for every $1 increase in sales. Pierce’s profit margin is 5 percent, and its retention ratio is 40 percent. How large a sales increase can the company achieve without having to raise funds externally?

P R O B L E M S

Tozer Computers makes bulk purchases of small computers, stocks them in conveniently located warehouses, and ships them to its chain of retail stores. Tozer’s balance sheet as of December 31, 2001, is shown here (in millions of dollars):

4-12 Pro forma statements and ratios

4-11 Sales increase

4-10 Additional funds needed

4-9 Long-term financing needed

P R O B L E M S

C H A P T E R 4 � F I N A N C I A L P L A N N I N G A N D F O R E C A S T I N G168

Cash $ 3.5 Accounts payable $ 9.0 Receivables 26.0 Notes payable 18.0 Inventories 58.0 Accruals 8.5

Total current assets $ 87.5 Total current liabilities $ 35.5 Net fixed assets 35.0 Mortgage loan 6.0

Common stock 15.0 Retained earnings 66.0

Total assets $122.5 Total liabilities and equity $122.5

Sales for 2001 were $350 million, while net income for the year was $10.5 million. Tozer paid dividends of $4.2 million to common stockholders. The firm is operating at full ca- pacity. Assume that all ratios remain constant. a. If sales are projected to increase by $70 million, or 20 percent, during 2002, use the

AFN equation to determine Tozer’s projected external capital requirements. b. Construct Tozer’s pro forma balance sheet for December 31, 2002. Assume that all

external capital requirements are met by bank loans and are reflected in notes payable.

c. Now calculate the following ratios, based on your projected December 31, 2002, bal- ance sheet. Tozer’s 2001 ratios and industry average ratios are shown here for com- parison:

TOZ E R C O M P U T E R S I N D U S T R Y AV E R AG E

12/31/02 12/31/01 12/31/01

Current ratio ��������������� 2.5� 3� Debt/total assets ��������������� 33.9% 30% Rate of return on equity ��������������� 13.0% 12%

d. Now assume that Tozer grows by the same $70 million but that the growth is spread over 5 years —that is, that sales grow by $14 million each year. (1) Calculate total additional financial requirements over the 5-year period. (Hint:

Use 2001 ratios, �S � $70, but total sales for the 5-year period.) (2) Construct a pro forma balance sheet as of December 31, 2006, using notes

payable as the balancing item. (3) Calculate the current ratio, total debt/total assets ratio, and rate of return on eq-

uity as of December 31, 2006. [Hint: Be sure to use total sales, which amount to $1,960 million, to calculate retained earnings, but 2006 profits to calculate the rate of return on equity —that is, return on equity � (2006 profits)/(12/31/06 equity).]

e. Do the plans outlined in parts b and/or d seem feasible to you? That is, do you think Tozer could borrow the required capital, and would the company be raising the odds on its bankruptcy to an excessive level in the event of some temporary misfortune?

Cooley Textile’s 2001 financial statements are shown below.

Cooley Textile: Balance Sheet as of December 31, 2001 (Thousands of Dollars)

Cash $ 1,080 Accounts payable $ 4,320 Receivables 6,480 Accruals 2,880 Inventories 9,000 Notes payable 2,100

Total current assets $16,560 Total current liabilities $ 9,300 Net fixed assets 12,600 Mortgage bonds 3,500

Common stock 3,500 Retained earnings 12,860

Total assets $29,160 Total liabilities and equity $29,160

4-13 Additional funds needed

169

Cooley Textile: Income Statement for December 31, 2001 (Thousands of Dollars)

Sales $36,000 Operating costs 32,440 Earnings before interest and taxes $ 3,560 Interest 560 Earnings before taxes $ 3,000 Taxes (40%) 1,200 Net income $ 1,800 Dividends (45%) $810 Addition to retained earnings $990

Suppose 2002 sales are projected to increase by 15 percent over 2001 sales. Determine the additional funds needed. Assume that the company was operating at full capacity in 2001, that it cannot sell off any of its fixed assets, and that any required financing will be borrowed as notes payable. Also, assume that assets, spontaneous liabilities, and operat- ing costs are expected to increase in proportion to sales. Use the projected financial statement method to develop a pro forma balance sheet and income statement for December 31, 2002. Use the pro forma income statement to determine the addition to retained earnings. Krogh Lumber’s 2001 financial statements are shown below.

Krogh Lumber: Balance Sheet as of December 31, 2001 (Thousands of Dollars)

Cash $ 1,800 Accounts payable $ 7,200 Receivables 10,800 Notes payable 3,472 Inventories 12,600 Accruals 2,520

Total current assets $25,200 Total current liabilities $13,192 Mortgage bonds 5,000 Common stock 2,000

Net fixed assets 21,600 Retained earnings 26,608 Total assets $46,800 Total liabilities and equity $46,800

Krogh Lumber: Income Statement for December 31, 2001 (Thousands of Dollars)

Sales $36,000 Operating costs 30,783 Earnings before interest and taxes $ 5,217 Interest 1,017 Earnings before taxes $ 4,200 Taxes (40%) 1,680 Net income $ 2,520 Dividends (60%) $1,512 Addition to retained earnings 1,008

a. Assume that the company was operating at full capacity in 2001 with regard to all items except fixed assets; fixed assets in 2001 were being utilized to only 75 percent of capacity. By what percentage could 2002 sales increase over 2001 sales without the need for an increase in fixed assets?

b. Now suppose 2002 sales increase by 25 percent over 2001 sales. How much addi- tional external capital will be required? Assume that Krogh cannot sell any fixed

4-14 Excess capacity

P R O B L E M S

C H A P T E R 4 � F I N A N C I A L P L A N N I N G A N D F O R E C A S T I N G170

assets. (Hint: Use the projected financial statement method to develop a pro forma income statement and balance sheet as in Tables 4-3 and 4-4.) Assume that any re- quired financing is borrowed as notes payable. Use a pro forma income statement to determine the addition to retained earnings. (Another hint: Notes payable � $6,021.)

c. Suppose the industry average DSO and inventory turnover ratio are 90 days and 3.33, respectively, and that Krogh Lumber matches these figures in 2002 and then uses the funds released to reduce equity. (It pays a special dividend out of retained earnings.) What would this do to the rate of return on year-end 2002 equity? Use the balance sheet and income statement as developed in part b.

Morrissey Technologies Inc.’s 2001 financial statements are shown below.

Morrissey Technologies Inc.: Balance Sheet as of December 31, 2001

Cash $ 180,000 Accounts payable $ 360,000 Receivables 360,000 Notes payable 156,000 Inventories 720,000 Accruals 180,000

Total current assets $1,260,000 Total current liabilities $ 696,000 Fixed assets 1,440,000 Common stock 1,800,000

Retained earnings 204,000 Total assets $2,700,000 Total liabilities and equity $2,700,000

Morrissey Technologies Inc.: Income Statement for December 31, 2001

Sales $3,600,000 Operating costs 3,279,720 EBIT $ 320,280 Interest 20,280 EBT $ 300,000 Taxes (40%) 120,000 Net income $ 180,000 PER SHARE DATA:

Common stock price $24.00 Earnings per share (EPS) $ 1.80 Dividends per share (DPS) $ 1.08

a. Suppose that in 2002 sales increase by 10 percent over 2001 sales and that 2002 DPS will increase to $1.12. Construct the pro forma financial statements using the pro- jected financial statement method. Use AFN to balance the pro forma balance sheet. How much additional capital will be required? Assume the firm operated at full ca- pacity in 2001.

b. If the profit margin were to remain at 5 percent and the dividend payout rate were to remain at 60 percent, at what growth rate in sales would the additional financing requirements be exactly zero? (Hint: Set AFN equal to zero and solve for g.)

4-15 Additional funds needed

171S P R E A D S H E E T P R O B L E M

The 2001 balance sheet and income statement for the Lewis Company are shown below.

Lewis Company: Balance Sheet as of December 31, 2001 (Thousands of Dollars)

Cash $ 80 Accounts payable $ 160 Accounts receivable 240 Accruals 40 Inventories 720 Notes payable 252

Total current assets $1,040 Total current liabilities $ 452 Fixed assets 3,200 Long-term debt 1,244

Total debt $1,696 Common stock 1,605 Retained earnings 939

Total assets $4,240 Total liabilities and equity $4,240

Lewis Company: Income Statement for December 31, 2001 (Thousands of Dollars)

Sales $8,000 Operating costs 7,450 EBIT $ 550 Interest 150 EBT $ 400 Taxes (40%) 160 Net income $ 240 PER SHARE DATA:

Common stock price $16.96 Earnings per share (EPS) $ 1.60 Dividends per share (DPS) $ 1.04

a. The firm operated at full capacity in 2001. It expects sales to increase by 20 percent during 2002 and expects 2002 dividends per share to increase to $1.10. Use the projected financial statement method to determine how much outside financing is re- quired, developing the firm’s pro forma balance sheet and income statement, and use AFN as the balancing item.

b. If the firm must maintain a current ratio of 2.3 and a debt ratio of 40 percent, how much financing will be obtained using notes payable, long-term debt, and common stock?

S P R E A D S H E E T P R O B L E M

Laiho Industries’ financial planners must forecast the company’s financial results for the coming year. The forecast will be based on the percent of sales method, and any addi- tional funds needed will be obtained by using a mix of notes payable, long-term debt, and common stock. No preferred stock will be issued. Data for the problem, including Laiho Industries’ balance sheet and income statement, can be found in the spreadsheet problem for Chapter 2. Use these data to answer the following questions.

4-17 Forecasting financial statements

4-16 External financing requirements

C H A P T E R 4 � F I N A N C I A L P L A N N I N G A N D F O R E C A S T I N G172

a. Laiho Industries has had the following sales since 1996. Assuming the historical trend continues, what will sales be in 2002?

YEAR SALES

1996 $129,215,000 1997 180,901,000 1998 235,252,000 1999 294,065,000 2000 396,692,000 2001 455,150,000

Base your forecast on a spreadsheet regression analysis of the 1996–2001 sales, and in- clude the summary output of the regression in your answer. By what percentage are sales predicted to increase in 2002 over 2001? Is the sales growth rate increasing or decreasing?

b. Laiho’s management believes that the firm will actually experience a 20 percent in- crease in sales during 2002. Use the Chapter 2 spreadsheet problem to obtain the company’s 2001 financial statements, then use those statements to construct 2002 pro forma financial statements. Assume that any additional funds needed (AFN) will be raised as follows: notes payable, 25 percent; long-term debt, 50 percent; and new common stock, 25 percent.

c. Now create a graph that shows the sensitivity of AFN to the sales growth rate. To make this graph, compare the AFN at sales growth rates of 5, 10, 15, 20, 25, and 30 percent.

d. Calculate net operating working capital (NOWC), total operating capital, NOPAT, and operating cash flow (OCF) for 2001 and 2002. Also, calculate the free cash flow (FCF) for 2002.

e. Suppose Laiho’s management does not believe that accounts receivable and invento- ries should remain as a constant percentage of sales. Rather, they think that current assets should be predicted by using a regression analysis of recent levels versus sales. Use the following data on accounts receivable, inventories, and sales to run regres- sions to estimate the necessary levels of accounts receivable and inventories for 2002.

YEAR SALESa INVENTORIESa A/Ra

1996 $129,215 $12,341 $ 24,764 1997 180,901 16,763 39,589 1998 235,252 20,564 53,764 1999 294,065 25,324 64,864 2000 396,692 35,997 98,568 2001 455,150 38,444 103,365

a In thousands of dollars.

The information related to the cyberproblems is likely to change over time, due to the release of new information and the ever-changing nature of the World Wide Web. With these changes in mind, we will periodically update these problems on the textbook’s web site. To avoid problems, please check for these updates before proceeding with the cyberproblems. A sales forecast usually begins with a forecast of a firm’s unit and dollar sales for some future period, and it is generally based on recent sales trends plus forecasts of the economic prospects for the nation, region, industry, and so forth. Analysts at

4-18 Financial forecasting—using

analysts’ reports

173C Y B E R P R O B L E M

investment research firms also make forecasts of companies’ current and likely fu- ture financial performances. These analysts must piece together information that includes forecasts of the overall economy and the level and direction of interest rates. Moreover, they must examine economic and competitive conditions in spe- cific industries including sales, costs, margins, profits, and cash flows for specific firms. In this cyberproblem, you will look at analysts’ forecasts of earnings and recommendations about the investment potential of specific firms based on their forecasts of the firms’ performances. Use the Zacks Investment Research web site, which can be found at my.zacks.com. a. Sun Microsystems has enjoyed dramatic increases in sales, earnings, and stock

prices, and many employees and investors have become millionaires in a very short time. What were Sun Microsystems’ actual earnings last quarter? Was there an earnings surprise? If so, what was it? What are the analysts’ consensus estimates for the (1) current quarter, (2) current fiscal year, and (3) next fiscal year? What was the average broker recommendation for Sun Microsystems, and was there any change from the previous average recommendation? To answer this question, enter Sun Microsystems’ stock symbol and request “All Reports.” If you do not know Sun Microsystems’ stock symbol, you can use Zack’s “Ticker Lookup” function.

b. Access Sun Microsystems’ company report, as prepared by Zacks. What per- centage of Sun Microsystems’ shareholders are institutional investors and insid- ers? What was the stock’s 52-week high and low? What was the stock’s price change during the past year?

c. Access Zack’s long-term outlook of Sun Microsystems and discuss it. d. Examine analysts’ predictions about future earnings and investment potential

for software companies Oracle and Microsoft. How do analysts generate earn- ings predictions and make recommendations?

C H A P T E R 4 � F I N A N C I A L P L A N N I N G A N D F O R E C A S T I N G174

T A B L E I C 4 - 1

A. 2001 BALANCE SHEET

Cash and securities $ 20 Accounts payable and accruals $ 100 Accounts receivable 240 Notes payable 100 Inventories 240 Total current liabilities $ 200

Total current assets $ 500 Long-term debt 100 Net fixed assets 500 Common stock 500

Retained earnings 200 Total assets $ 1,000 Total liabilities and equity $1,000

B. 2001 INCOME STATEMENT

Sales $2,000.00 Less: Variable costs 1,200.00

Fixed costs 700.00 Earnings before interest and taxes (EBIT) $ 100.00 Interest 16.00 Earnings before taxes (EBT) $ 84.00 Taxes (40%) 33.60 Net income $ 50.40

Dividends (30%) $ 15.12 Addition to retained earnings $ 35.28 C. KEY RATIOS NWC INDUSTRY COMMENT

Basic earning power 10.00% 20.00% Profit margin 2.52 4.00 Return on equity 7.20 15.60 Days sales outstanding (365 days) 43.80 days 32.00 days Inventory turnover 8.33� 11.00� Fixed assets turnover 4.00 5.00 Total assets turnover 2.00 2.50 Debt/assets 30.00% 36.00% Times interest earned 6.25� 9.40� Current ratio 2.50 3.00 Payout ratio 30.00% 30.00%

Financial Statements and Other Data on NWC (Millions of Dollars)

NEW WORLD CHEMICALS INC.

4-19 Financial Forecasting Sue Wilson, the new finan- cial manager of New World Chemicals (NWC), a Cali- fornia producer of specialized chemicals for use in fruit orchards, must prepare a financial forecast for 2002. NWC’s 2001 sales were $2 billion, and the marketing de- partment is forecasting a 25 percent increase for 2002.

Wilson thinks the company was operating at full capacity in 2001, but she is not sure about this. The 2001 finan- cial statements, plus some other data, are given in Table IC4-1.

Assume that you were recently hired as Wilson’s assistant, and your first major task is to help her develop the forecast.

175

She asked you to begin by answering the following set of questions. a. Assume (1) that NWC was operating at full capacity in

2001 with respect to all assets, (2) that all assets must grow proportionally with sales, (3) that accounts payable and accruals will also grow in proportion to sales, and (4) that the 2001 profit margin and dividend payout will be maintained. Under these conditions, what will the company’s financial requirements be for the coming year? Use the AFN equation to answer this question.

b. Now estimate the 2002 financial requirements using the projected financial statement approach. Disregard the as- sumptions in part a, and now assume (1) that each type of asset, as well as payables, accruals, and fixed and variable costs, grow in proportion to sales; (2) that NWC was oper- ating at full capacity; (3) that the payout ratio is held con- stant at 30 percent; and (4) that external funds needed are financed 50 percent by notes payable and 50 percent by long-term debt. (No new common stock will be issued.)

c. Why do the two methods produce somewhat different AFN forecasts? Which method provides the more accu- rate forecast?

d. Calculate NWC’s forecasted ratios, and compare them with the company’s 2001 ratios and with the industry av- erages. How does NWC compare with the average firm in its industry, and is the company expected to improve during the coming year?

e. Calculate NWC’s free cash flow for 2002. f. Suppose you now learn that NWC’s 2001 receivables and

inventories were in line with required levels, given the firm’s credit and inventory policies, but that excess capac- ity existed with regard to fixed assets. Specifically, fixed assets were operated at only 75 percent of capacity. (1) What level of sales could have existed in 2001 with

the available fixed assets? What would the fixed assets- to-sales ratio have been if NWC had been operating at full capacity?

(2) How would the existence of excess capacity in fixed assets affect the additional funds needed during 2002?

g. Without actually working out the numbers, how would you expect the ratios to change in the situation where excess capacity in fixed assets exists? Explain your rea- soning.

h. On the basis of comparisons between NWC’s days sales outstanding (DSO) and inventory turnover ratios with the industry average figures, does it appear that NWC is operating efficiently with respect to its inventories and

I N T E G R AT E D C A S E

accounts receivable? If the company were able to bring these ratios into line with the industry averages, what ef- fect would this have on its AFN and its financial ratios? (Note: Inventories and receivables will be discussed in detail in Chapter 15.)

i. The relationship between sales and the various types of assets is important in financial forecasting. The financial statement method, under the assumption that each asset item grows proportionally with sales, leads to an AFN forecast that is reasonably close to the forecast using the AFN equation. Explain how each of the following factors would affect the accuracy of financial forecasts based on the AFN equation: (1) excess capacity; (2) base stocks of assets, such as shoes in a shoe store; (3) economies of scale in the use of assets; and (4) lumpy assets.

j. (1) How could regression analysis be used to detect the presence of the situations described above and then to improve the financial forecasts? Plot a graph of the following data, which is for a typical well- managed company in NWC’s industry to illustrate your answer.

YEAR SALES INVENTORIES

1999 $1,280 $118 2000 1,600 138 2001 2,000 162 2002E 2,500 192

(2) On the same graph that plots the above data, draw a line that shows how the regression line would have to appear to justify the use of the AFN formula and the projected financial statement forecasting method. As a part of your answer, show the growth rate in inven- tories that results from a 10 percent increase in sales from a sales level of (a) $200 and (b) $2,000 based on both the actual regression line and a hypothetical re- gression line, which is linear and which goes through the origin.

k. How would changes in these items affect the AFN? (1) The dividend payout ratio, (2) the profit margin, (3) the capital intensity ratio, and (4) if NWC begins buying from its suppliers on terms that permit it to pay after 60 days rather than after 30 days. (Consider each item sep- arately and hold all other things constant.)

SOURCE: Accessed November 1999. © 1999 Charles Schwab & Co., Inc. www.schwab.com

CHAPTER

T he F i na nc i a l E n v i r o n me n t : Ma r ke t s , I n s t i t u t i o n s , a nd I n t e r e s t R a t e s

5

76

To take a look at the online ventures of Charles Schwab and Merrill Lynch, check out their web sites at http://www.schwab.com

and http://askmerrill.ml.com. You can test the Schwab customer experience or take a tour of Merrill Lynch Online.

brokerage powerhouse Merrill Lynch has seen its stock

rise more than 350 percent over the past five years.

During this same period, Charles Schwab, the leader in

online trading, has seen its stock rise by nearly 900

percent! The Internet has enabled online brokers such

as Schwab, E*Trade, DLJDirect, and Datek to offer

investors the opportunity to trade stocks at a small

fraction of the price traditionally charged by full-service

firms such as Merrill Lynch. While online trading was

virtually nonexistent just a couple of years ago, there

are now an estimated 160 online brokers serving more

than 13 million customers. Some estimate that by 2003

there will be more than 40 million online accounts.

The same forces that dramatically affected the

brokerage industry have had similar effects on other

industries. Companies such as Barnes and Noble and Toys

Us have been presented with new and aggressive

competition from the likes of Amazon.com and eToys Inc.

Likewise, changing technology has altered the way

millions of consumers purchase airline tickets, hotel

rooms, and automobiles. Consequently, financial

managers must understand today’s technological

environment and be ready to change operations as the

environment evolves. �

R

inancial managers and investors don’t operate in a

vacuum — they make decisions within a large and

complex financial environment. This environment

includes financial markets and institutions, tax and

regulatory policies, and the state of the economy. The

environment both defines the available financial

alternatives and affects the outcomes of various

decisions. Therefore, it is crucial that financial managers

and investors have a good understanding of the

environment in which they operate.

Good financial decisions require an understanding of

the current direction of the economy, interest rates, and

the stock market — but figuring out what’s likely to

happen is no trivial matter. Recently, the financial

environment has been extraordinarily favorable to

financial managers and investors: The economy has not

seen a recession for nearly 10 years; interest rates and

inflation have remained relatively low; and the stock

market has boomed throughout most of the past decade.

At the same time, the financial environment has

undergone tremendous changes, presenting financial

managers and investors with both opportunities and

risks.

Consider Charles Schwab and Merrill Lynch.

Benefiting from the strong stock market, traditional

S C H WA B A N D M E R R I L L LY N C H C O M P E T E I N A C H A N G I N G E N V I R O N M E N T

CHARLES SCHWAB AND MERRILL LYNCH

$

F

177

C H A P T E R 5 � T H E F I N A N C I A L E N V I R O N M E N T: M A R K E TS , I N S T I T U T IO N S , A N D I N T E R E S T R AT E S178

In earlier chapters we discussed financial statements and showed how financial

managers and others analyze them to see where their firms have been and are

headed. Financial managers also need to understand the environment and markets

within which businesses operate. Therefore, this chapter describes the markets

where capital is raised, securities are traded, and stock prices are established, as

well as the institutions that operate in these markets. In the process, we also ex-

plore the principal factors that determine the level of interest rates. �

T H E F I N A N C I A L M A R K E T S

Businesses, individuals, and governments often need to raise capital. For example, suppose Carolina Power & Light (CP&L) forecasts an increase in the demand for electricity in North Carolina, and the company decides to build a new power plant. Because CP&L almost certainly will not have the $1 billion or so necessary to pay for the plant, the company will have to raise this capital in the financial markets. Or suppose Mr. Fong, the proprietor of a San Francisco hardware store, decides to expand into appliances. Where will he get the money to buy the initial inventory of TV sets, washers, and freezers? Similarly, if the Johnson family wants to buy a home that costs $100,000, but they have only $20,000 in savings, how can they raise the additional $80,000? If the city of New York wants to borrow $200 million to finance a new sewer plant, or the federal government needs money to meet its needs, they too need access to the capital markets.

On the other hand, some individuals and firms have incomes that are greater than their current expenditures, so they have funds available to invest. For exam- ple, Carol Hawk has an income of $36,000, but her expenses are only $30,000, and in 2000 Ford Motor Company had accumulated roughly $21 billion of cash and marketable securities, which it has available for future investments.

TYPES OF MARKETS

People and organizations wanting to borrow money are brought together with those having surplus funds in the financial markets. Note that “markets” is plural — there are a great many different financial markets in a developed economy such as ours. Each market deals with a somewhat different type of instrument in terms of the instrument’s maturity and the assets backing it. Also, different markets serve different types of customers, or operate in different parts of the country. For these reasons it is often useful to classify markets along various dimensions:

1. Physical asset vs. Financial asset markets. Physical asset markets (also called “tangible” or “real” asset markets) are those for such products as

179

wheat, autos, real estate, computers, and machinery. Financial asset markets, on the other hand, deal with stocks, bonds, notes, mortgages, and other claims on real assets, as well as with derivative securities whose values are de- rived from changes in the prices of other assets.

2. Spot vs. Futures markets. Spot markets are markets in which assets are bought or sold for “on-the-spot” delivery (literally, within a few days). Futures markets are markets in which participants agree today to buy or sell an asset at some future date. For example, a farmer may enter into a futures contract in which he agrees today to sell 5,000 bushels of soy- beans six months from now at a price of $5 a bushel. In contrast, an in- ternational food producer looking to buy soybeans in the future may enter into a futures contract in which it agrees to buy soybeans three months from now.

3. Money vs. Capital markets. Money markets are the markets for short- term, highly liquid debt securities. The New York and London money markets have long been the world’s largest, but Tokyo is rising rapidly. Capital markets are the markets for intermediate- or long-term debt and corporate stocks. The New York Stock Exchange, where the stocks of the largest U.S. corporations are traded, is a prime example of a capital mar- ket. There is no hard and fast rule on this, but when describing debt mar- kets, “short term” generally means less than one year, “intermediate term” means one to five years, and “long term” means more than five years.

4. Primary vs. Secondary markets. Primary markets are the markets in which corporations raise new capital. If Microsoft were to sell a new issue of common stock to raise capital, this would be a primary market trans- action. The corporation selling the newly created stock receives the pro- ceeds from the sale in a primary market transaction. Secondary markets are markets in which existing, already outstanding, securities are traded among investors. Thus, if Jane Doe decided to buy 1,000 shares of AT&T stock, the purchase would occur in the secondary market. The New York Stock Exchange is a secondary market, since it deals in out- standing, as opposed to newly issued, stocks and bonds. Secondary mar- kets also exist for mortgages, various other types of loans, and other fi- nancial assets. The corporation whose securities are being traded is not involved in a secondary market transaction and, thus, does not receive any funds from such a sale.

The initial public offering (IPO) market is a subset of the primary market. Here firms “go public” by offering shares to the public for the first time. Microsoft had its IPO in 1986. Previously, Bill Gates and other insiders owned all the shares. In many IPOs, the insiders sell some of their shares plus the company sells new shares to raise additional capital.

5. Private vs. Public markets. Private markets, where transactions are worked out directly between two parties, are differentiated from public markets, where standardized contracts are traded on organized exchanges. Bank loans and private placements of debt with insurance companies are examples of private market transactions. Since these transactions are pri- vate, they may be structured in any manner that appeals to the two parties. By contrast, securities that are issued in public markets (for example, com- mon stock and corporate bonds) are ultimately held by a large number of individuals. Public securities must have fairly standardized contractual

T H E F I N A N C I A L M A R K E T S

Money Markets The financial markets in which funds are borrowed or loaned for short periods (less than one year).

Capital Markets The financial markets for stocks and for intermediate- or long- term debt (one year or longer).

Primary Markets Markets in which corporations raise capital by issuing new securities.

Secondary Markets Markets in which securities and other financial assets are traded among investors after they have been issued by corporations.

Initial Public Offering (IPO) Market The market in which firms “go public” by offering shares to the public.

Private Markets Markets in which transactions are worked out directly between two parties.

Public Markets Markets in which standardized contracts are traded on organized exchanges.

Spot Markets The markets in which assets are bought or sold for “on-the-spot” delivery.

Futures Markets The markets in which participants agree today to buy or sell an asset at some future date.

C H A P T E R 5 � T H E F I N A N C I A L E N V I R O N M E N T: M A R K E TS , I N S T I T U T IO N S , A N D I N T E R E S T R AT E S180

features, both to appeal to a broad range of investors and also because pub- lic investors cannot afford the time to study unique, nonstandardized con- tracts. Their diverse ownership also ensures that public securities are rela- tively liquid. Private market securities are, therefore, more tailor-made but less liquid, whereas public market securities are more liquid but subject to greater standardization.

Other classifications could be made, but this breakdown is sufficient to show that there are many types of financial markets. Also, note that the distinctions among markets are often blurred and unimportant, except as a general point of reference. For example, it makes little difference if a firm borrows for 11, 12, or 13 months, hence, whether we have a “money” or “capital” market transaction. You should recognize the big differences among types of markets, but don’t get hung up trying to distinguish them at the boundaries.

A healthy economy is dependent on efficient transfers of funds from people who are net savers to firms and individuals who need capital. Without efficient

T A B L E 5 - 1

ORIGINAL INTEREST RATE INSTRUMENT MARKET MAJOR PARTICIPANTS RISKINESS MATURITY ON 12/29/00a

(1) (2) (3) (4) (5) (6)

U.S. Treasury bills Money Sold by U.S. Treasury to Default-free 91 days to 1 year 5.7% finance federal expenditures

Bankers’ Money A firm’s promise to pay, Low degree of risk Up to 180 days 6.3 acceptances guaranteed by a bank if guaranteed by a

strong bank Commercial Money Issued by financially secure Low default risk Up to 270 days 6.4 paper firms to large investors Negotiable Money Issued by major Default risk depends Up to 1 year 6.3 certificates of money-center commercial on the strength of deposit (CDs) banks to large investors the issuing bank Money market Money Invest in Treasury bills, CDs, Low degree of risk No specific 6.0 mutual funds and commercial paper; held maturity

by individuals and businesses (instant liquidity) Eurodollar market Money Issued by banks outside U.S. Default risk depends Up to 1 year 6.3 time deposits on the strength of

the issuing bank Consumer credit Money Issued by banks/credit Risk is variable Variable Variable loans unions/finance companies to

individuals U.S. Treasury Capital Issued by U.S. government No default risk, but 2 to 30 years 5.5 notes and bonds price will decline if

interest rates rise

a The yields reported on money market mutual funds and bankers’ acceptances are from The Wall Street Journal. All other data are from the Federal Reserve Statistical Release. Money market rates assume a 3-month maturity. The corporate bond rate is for AAA-rated bonds.

Summary of Major Market Instruments, Market Participants, and Security Characteristics

S E C U R I T Y C H A R AC T E R I S T I C S

181

transfers, the economy simply could not function: Carolina Power & Light could not raise capital, so Raleigh’s citizens would have no electricity; the John- son family would not have adequate housing; Carol Hawk would have no place to invest her savings; and so on. Obviously, the level of employment and pro- ductivity, hence our standard of living, would be much lower. Therefore, it is absolutely essential that our financial markets function efficiently — not only quickly, but also at a low cost.1

Table 5-1 gives a listing of the most important instruments traded in the various financial markets. The instruments are arranged from top to bottom in

T H E F I N A N C I A L M A R K E T S

1 As the countries of the former Soviet Union and other Eastern European nations move toward cap- italism, just as much attention must be paid to the establishment of cost-efficient financial markets as to electrical power, transportation, communications, and other infrastructure systems. Economic efficiency is simply impossible without a good system for allocating capital within the economy.

Students can access current and historical interest rates and economic data as well as regional economic data for

the states of Arkansas, Illinois, Indiana, Kentucky, Mississippi, Missouri, and Tennessee from the Federal Reserve Economic Data (FRED) site at http://www.stls.frb.org/fred/.

S E C U R I T Y C H A R AC T E R I S T I C S

T A B L E 5 - 1

ORIGINAL INTEREST RATE INSTRUMENT MARKET MAJOR PARTICIPANTS RISKINESS MATURITY ON 12/29/00a

(1) (2) (3) (4) (5) (6)

Mortgages Capital Borrowings from commercial Risk is variable Up to 30 years 7.1% banks and S&Ls by individuals and businesses

State and local Capital Issued by state and local Riskier than U.S. Up to 30 years 5.1 government bonds governments to individuals government

and institutional investors securities, but exempt from most taxes

Corporate bonds Capital Issued by corporations to Riskier than U.S. Up to 40 yearsb 7.2 individuals and institutional government securities, investors but less risky than

preferred and common stocks; varying degree of risk within bonds depending on strength of issuer

Leases Capital Similar to debt in that firms Risk similar to Generally 3 to Similar to can lease assets rather than corporate bonds 20 years bond yields borrow and then buy the assets

Preferred stocks Capital Issued by corporations to Riskier than corporate Unlimited 7 to 9% individuals and institutional bonds, but less risky investors than common stock

Common stocksc Capital Issued by corporations to Risky Unlimited 10 to 15% individuals and institutional investors

b Just recently, a few corporations have issued 100-year bonds; however, the majority have issued bonds with maturities less than 40 years. c Common stocks are expected to provide a “return” in the form of dividends and capital gains rather than interest. Of course, if you buy a stock, your actual return may be considerably higher or lower than your expected return. For example, Nasdaq stocks on average provided a negative return of 39.3 percent in 2000, but that was well below the return most investors expected.

continued

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ascending order of typical length of maturity. As we go through the book, we will look in much more detail at many of the instruments listed in Table 5-1. For example, we will see that there are many varieties of corporate bonds, rang- ing from “plain vanilla” bonds to bonds that are convertible into common stocks to bonds whose interest payments vary depending on the inflation rate. Still, the table gives an idea of the characteristics and costs of the instruments traded in the major financial markets.

RECENT TRENDS

Financial markets have experienced many changes during the last two decades. Technological advances in computers and telecommunications, along with the globalization of banking and commerce, have led to deregulation, and this has increased competition throughout the world. The result is a much more effi- cient, internationally linked market, but one that is far more complex than ex- isted a few years ago. While these developments have been largely positive, they have also created problems for policy makers. At a recent conference, Fed- eral Reserve Board Chairman Alan Greenspan stated that modern financial markets “expose national economies to shocks from new and unexpected sources, and with little if any lag.” He went on to say that central banks must develop new ways to evaluate and limit risks to the financial system. Large amounts of capital move quickly around the world in response to changes in in- terest and exchange rates, and these movements can disrupt local institutions and economies.

With globalization has come the need for greater cooperation among regu- lators at the international level. Various committees are currently working to improve coordination, but the task is not easy. Factors that complicate coordi- nation include (1) the differing structures among nations’ banking and securi- ties industries, (2) the trend in Europe toward financial service conglomerates, and (3) a reluctance on the part of individual countries to give up control over their national monetary policies. Still, regulators are unanimous about the need to close the gaps in the supervision of worldwide markets.

Another important trend in recent years has been the increased use of de- rivatives. A derivative is any security whose value is derived from the price of some other “underlying” asset. An option to buy IBM stock is a derivative, as is a contract to buy Japanese yen six months from now. The value of the IBM option depends on the price of IBM’s stock, and the value of the Japanese yen “future” depends on the exchange rate between yen and dollars. The market for derivatives has grown faster than any other market in recent years, pro- viding corporations with new opportunities but also exposing them to new risks.

Derivatives can be used either to reduce risks or to speculate. Suppose an importer’s net income tends to fall whenever the dollar falls relative to the yen. That company could reduce its risk by purchasing derivatives that in- crease in value whenever the dollar declines. This would be called a hedging operation, and its purpose is to reduce risk exposure. Speculation, on the other hand, is done in the hope of high returns, but it raises risk exposure. For ex- ample, Procter & Gamble recently disclosed that it lost $150 million on de- rivative investments, and Orange County (California) went bankrupt as a re- sult of its treasurer’s speculation in derivatives.

Derivative Any financial asset whose value is derived from the value of some other “underlying” asset.

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The size and complexity of derivatives transactions concern regulators, aca- demics, and members of Congress. Fed Chairman Greenspan noted that, in theory, derivatives should allow companies to manage risk better, but that it is not clear whether recent innovations have “increased or decreased the inherent stability of the financial system.”

F I N A N C I A L I N S T I T U T I O N S

SELF-TEST QUESTIONS

Distinguish between physical asset markets and financial asset markets.

What is the difference between spot and futures markets?

Distinguish between money and capital markets.

What is the difference between primary and secondary markets?

Differentiate between private and public markets.

Why are financial markets essential for a healthy economy?

What is a derivative, and how is its value related to that of an “underlying asset”?

F I N A N C I A L I N S T I T U T I O N S

Transfers of capital between savers and those who need capital take place in the three different ways diagrammed in Figure 5-1:

1. Direct transfers of money and securities, as shown in the top section, occur when a business sells its stocks or bonds directly to savers, without going through any type of financial institution. The business delivers its securi- ties to savers, who in turn give the firm the money it needs.

2. As shown in the middle section, transfers may also go through an invest- ment banking house such as Merrill Lynch, which underwrites the issue. An underwriter serves as a middleman and facilitates the issuance of securi- ties. The company sells its stocks or bonds to the investment bank, which in turn sells these same securities to savers. The businesses’ securities and the savers’ money merely “pass through” the investment banking house. However, the investment bank does buy and hold the securities for a pe- riod of time, so it is taking a risk — it may not be able to resell them to savers for as much as it paid. Because new securities are involved and the corporation receives the proceeds of the sale, this is a primary market transaction.

3. Transfers can also be made through a financial intermediary such as a bank or mutual fund. Here the intermediary obtains funds from savers in ex- change for its own securities. The intermediary then uses this money to purchase and then hold businesses’ securities. For example, a saver might give dollars to a bank, receiving from it a certificate of deposit, and then the bank might lend the money to a small business in the form of a mort- gage loan. Thus, intermediaries literally create new forms of capital — in this case, certificates of deposit, which are both safer and more liquid

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than mortgages and thus are better securities for most savers to hold. The existence of intermediaries greatly increases the efficiency of money and capital markets.

In our example, we assume that the entity needing capital is a business, and specifically a corporation, but it is easy to visualize the demander of capital as a home purchaser, a government unit, and so on.

Direct transfers of funds from savers to businesses are possible and do occur on occasion, but it is generally more efficient for a business to enlist the services of an investment banking house such as Merrill Lynch, Salomon Smith Bar- ney, Morgan Stanley Dean Witter, or Goldman Sachs. Such organizations (1) help corporations design securities with features that are currently attractive to investors, (2) then buy these securities from the corporation, and (3) resell them to savers. Although the securities are sold twice, this process is really one pri- mary market transaction, with the investment banker acting as a facilitator to help transfer capital from savers to businesses.

The financial intermediaries shown in the third section of Figure 5-1 do more than simply transfer money and securities between firms and savers — they literally create new financial products. Since the intermediaries are generally large, they gain economies of scale in analyzing the creditwor- thiness of potential borrowers, in processing and collecting loans, and in pooling risks and thus helping individual savers diversify, that is, “not putting all their financial eggs in one basket.” Further, a system of specialized in- termediaries can enable savings to do more than just draw interest. For ex- ample, individuals can put money into banks and get both interest income and a convenient way of making payments (checking), or put money into life

Business

Business

Business

1. Direct Transfers

2. Indirect Transfers through Investment Bankers

3. Indirect Transfers through a Financial Intermediary

Savers

Savers

SaversFinancialIntermediary

Investment Banking Houses

Securities (Stocks or Bonds)

Dollars

Securities

Dollars

Securities

Dollars

Intermediary’s Securities

Dollars

Business’s Securities

Dollars

F I G U R E 5 - 1 Diagram of the Capital Formation Process

Investment Banking House An organization that underwrites and distributes new investment securities and helps businesses obtain financing.

Financial Intermediaries Specialized financial firms that facilitate the transfer of funds from savers to demanders of capital.

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insurance companies and get both interest income and protection for their beneficiaries.

In the United States and other developed nations, a set of specialized, highly efficient financial intermediaries has evolved. The situation is changing rapidly, however, and different types of institutions are performing services that were formerly reserved for others, causing institutional distinctions to become blurred. Still, there is a degree of institutional identity, and here are the major classes of intermediaries:

1. Commercial banks, the traditional “department stores of finance,” serve a wide variety of savers and borrowers. Historically, commercial banks were the major institutions that handled checking accounts and through which the Federal Reserve System expanded or contracted the money supply. Today, however, several other institutions also provide checking services and significantly influence the money supply. Conversely, commercial banks are providing an ever-widening range of services, including stock brokerage services and insurance.

2. Savings and loan associations (S&Ls), which have traditionally served indi- vidual savers and residential and commercial mortgage borrowers, take the funds of many small savers and then lend this money to home buyers and other types of borrowers. In the 1980s, the S&L industry experienced se- vere problems when (1) short-term interest rates paid on savings accounts rose well above the returns being earned on the existing mortgages held by S&Ls and (2) commercial real estate suffered a severe slump, resulting in high mortgage default rates. Together, these events forced many S&Ls to either merge with stronger institutions or close their doors.

3. Mutual savings banks, which are similar to S&Ls, operate primarily in the northeastern states, accept savings primarily from individuals, and lend mainly on a long-term basis to home buyers and consumers.

4. Credit unions are cooperative associations whose members are supposed to have a common bond, such as being employees of the same firm. Mem- bers’ savings are loaned only to other members, generally for auto pur- chases, home improvement loans, and home mortgages. Credit unions are often the cheapest source of funds available to individual borrowers.

5. Pension funds are retirement plans funded by corporations or government agencies for their workers and administered primarily by the trust de- partments of commercial banks or by life insurance companies. Pension funds invest primarily in bonds, stocks, mortgages, and real estate.

6. Life insurance companies take savings in the form of annual premiums; in- vest these funds in stocks, bonds, real estate, and mortgages; and finally make payments to the beneficiaries of the insured parties. In recent years, life insurance companies have also offered a variety of tax-deferred savings plans designed to provide benefits to the participants when they retire.

7. Mutual funds are corporations that accept money from savers and then use these funds to buy stocks, long-term bonds, or short-term debt in- struments issued by businesses or government units. These organizations pool funds and thus reduce risks by diversification. They also achieve eco- nomies of scale in analyzing securities, managing portfolios, and buying and selling securities. Different funds are designed to meet the objectives

F I N A N C I A L I N S T I T U T I O N S

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of different types of savers. Hence, there are bond funds for those who desire safety, stock funds for savers who are willing to accept significant risks in the hope of higher returns, and still other funds that are used as interest-bearing checking accounts (the money market funds). There are literally thousands of different mutual funds with dozens of different goals and purposes.

Mutual funds have grown more rapidly than any other institution in recent years, in large part because of a change in the way corporations provide for employees’ retirement. Before the 1980s, most corporations said, in effect, “Come work for us, and when you retire, we will give you a retirement income based on the salary you were earning during the last five years before you retired.” The company was then responsible for set- ting aside funds each year to make sure that it had the money available to pay the agreed-upon retirement benefits. That situation is changing rapidly. Today, new employees are likely to be told, “Come work for us, and we will give you some money each payday that you can invest for your future retirement. You can’t get the money until you retire (without paying a huge tax penalty), but if you invest wisely, you can retire in com- fort.” Most workers know they don’t know how to invest wisely, so they turn their retirement funds over to a mutual fund. Hence, mutual funds are growing rapidly. Excellent information on the objectives and past per- formances of the various funds are provided in publications such as Value Line Investment Survey and Morningstar Mutual Funds, which are available in most libraries.

Financial institutions have historically been heavily regulated, with the pri- mary purpose of this regulation being to ensure the safety of the institutions and thus to protect investors. However, these regulations — which have taken the form of prohibitions on nationwide branch banking, restrictions on the types of assets the institutions can buy, ceilings on the interest rates they can pay, and limitations on the types of services they can provide — have tended to impede the free flow of capital and thus have hurt the efficiency of our capital markets. Recognizing this fact, Congress has authorized some major changes, and more are on the horizon.

The result of the ongoing regulatory changes has been a blurring of the dis- tinctions between the different types of institutions. Indeed, the trend in the United States today is toward huge financial service corporations, which own banks, S&Ls, investment banking houses, insurance companies, pension plan operations, and mutual funds, and which have branches across the country and around the world. Examples of financial service corporations, most of which started in one area but have now diversified to cover most of the financial spectrum, include Merrill Lynch, American Express, Citigroup, Fidelity, and Prudential.

Panel a of Table 5-2 lists the ten largest U.S. bank and thrift holding com- panies, and Panel b shows the leading world banking companies. Among the world’s 10 largest, only two (Citigroup and Bank of America) are from the United States. While U.S. banks have grown dramatically as a result of recent mergers, they are still small by global standards. Panel c of the table lists the 10 leading underwriters in terms of dollar volume of new issues. Five of the top underwriters are also major commercial banks or are part of bank holding com-

Financial Service Corporation A firm that offers a wide range of financial services, including investment banking, brokerage operations, insurance, and commercial banking.

Money Market Fund A mutual fund that invests in short-term, low-risk securities and allows investors to write checks against their accounts.

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T H E S TO C K M A R K E T

As noted earlier, secondary markets are those in which outstanding, previously issued securities are traded. By far the most active secondary market, and the most important one to financial managers, is the stock market, where the prices

T H E S TO C K M A R K E T

T A B L E 5 - 2

Panel a Panel b Panel c

U.S. BANK AND THRIFT HOLDING COMPANIESa WORLD BANKING COMPANIESb LEADING GLOBAL UNDERWRITERSc

Citigroup Inc. Deutsche Bank AG (Frankfurt) Merrill Lynch Bank of America Corp. Citigroup (New York) Salomon Smith Barney Chase Manhattan Corp. BNP Paribas (Paris) Morgan Stanley Dean Witter Bank One Corp. Bank of Tokyo-Mitsubishi Ltd. (Tokyo) Credit Suisse First Boston J. P. Morgan & Co. Bank of America (Charlotte) J. P. Morgan First Union Corp. UBS AG Group (Zurich) Goldman Sachs Wells Fargo & Co. HSBC Holdings PLC (London) Deutsche Bank Washington Mutual Inc. Fuji Bank Ltd. (Tokyo) Lehman Brothers Fleet Boston Financial Corp. Sumitomo Bank Ltd. (Osaka) UBS Warburg SunTrust Banks Inc. HypoVereinsbank AG (Munich) Banc of America Securities

NOTES: a Ranked by total assets as of June 30, 2000. SOURCE: Compiled by American Banker from bank and thrift holding company second quarter 2000 reports. b Ranked by total assets as of December 31, 1999. SOURCE: “Top 50 World Banking Companies in Assets,” American Banker.com, September 15, 2000. c Ranked by dollar amount raised through new issues in 2000. For this ranking, the lead underwriter (manager) is given credit for the entire issue.

10 Largest U.S. Bank and Thrift Holding Companies and World Banking Companies and Top 10 Leading Underwriters

SELF-TEST QUESTIONS

Identify three different ways capital is transferred between savers and bor- rowers.

What is the difference between a commercial bank and an investment bank?

Distinguish between investment banking houses and financial intermedi- aries.

List the major types of intermediaries and briefly describe the primary func- tion of each.

panies, which confirms the continued blurring of distinctions among different types of financial institutions.

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of firms’ stocks are established. Since the primary goal of financial management is to maximize the firm’s stock price, a knowledge of the stock market is im- portant to anyone involved in managing a business.

While the two leading stock markets today are the New York Stock Ex- change and the Nasdaq stock market, stocks are actually traded using a vari- ety of market procedures. However, there are just two basic types of stock markets: (1) physical location exchanges, which include the New York Stock Ex- change (NYSE), the American Stock Exchange (AMEX), and several regional stock exchanges, and (2) electronic dealer-based markets that include the Nasdaq stock market, the less formal over-the-counter market, and the re- cently developed electronic communications networks (ECNs). (See the Technology Matters box entitled, “Online Trading Systems.”) Because the physical location exchanges are easier to describe and understand, we con- sider them first.

THE PHYSICAL LOCAT ION STOCK EXCHANGES

The physical location exchanges are tangible physical entities. Each of the larger ones occupies its own building, has a limited number of members, and has an elected governing body — its board of governors. Members are said to have “seats” on the exchange, although everybody stands up. These seats, which are bought and sold, give the holder the right to trade on the exchange. There are currently 1,366 seats on the New York Stock Exchange, and on April 25, 2000, a seat on the NYSE sold for $1.7 million, which was down from the previous high of $2.6 million.

Most of the larger investment banking houses operate brokerage departments, and they own seats on the exchanges and designate one or more of their offi- cers as members. The exchanges are open on all normal working days, with the members meeting in a large room equipped with telephones and other elec- tronic equipment that enable each member to communicate with his or her firm’s offices throughout the country.

Like other markets, security exchanges facilitate communication between buyers and sellers. For example, Merrill Lynch (the largest brokerage firm) might receive an order in its Atlanta office from a customer who wants to buy shares of AT&T stock. Simultaneously, Morgan Stanley Dean Witter’s Denver office might receive an order from a customer wishing to sell shares of AT&T. Each broker communicates electronically with the firm’s representative on the NYSE. Other brokers throughout the country are also communicating with their own exchange members. The exchange members with sell orders offer the shares for sale, and they are bid for by the members with buy orders. Thus, the exchanges operate as auction markets.2

You can access the home pages of the major U.S. stock markets by typing http://www.nyse.com or

http://www.nasdaq.com. These sites provide background information as well as the opportunity to obtain individual stock quotes.

Physical Location Exchanges Formal organizations having tangible physical locations that conduct auction markets in designated (“listed”) securities.

2 The NYSE is actually a modified auction market, wherein people (through their brokers) bid for stocks. Originally — about 200 years ago — brokers would literally shout, “I have 100 shares of Erie for sale; how much am I offered?” and then sell to the highest bidder. If a broker had a buy order, he or she would shout, “I want to buy 100 shares of Erie; who’ll sell at the best price?” The same general situation still exists, although the exchanges now have members known as specialists who facilitate the trading process by keeping an inventory of shares of the stocks in which they specialize. If a buy order comes in at a time when no sell order arrives, the

(footnote continues)

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THE OVER-THE-COUNTER AND THE NASDAQ STOCK MARKETS

While the stocks of most large companies trade on the NYSE, a larger number of stocks trade off the exchange in what has traditionally been referred to as the over-the-counter market (OTC). An explanation of the term “over-the- counter” will help clarify how this term arose. As noted earlier, the exchanges operate as auction markets — buy and sell orders come in more or less simulta- neously, and exchange members match these orders. If a stock is traded infre- quently, perhaps because the firm is new or small, few buy and sell orders come in, and matching them within a reasonable amount of time would be difficult. To avoid this problem, some brokerage firms maintain an inventory of such

T H E S TO C K M A R K E T

ONLINE TRADING SYSTEMS

The forces described in the vignette that led to online trad-ing have also promoted online trading systems that bypass the traditional exchanges. These systems, known as electronic communications networks (ECNs), use technology to bring buy- ers and sellers together electronically. Bob Mazzarella, president of Fidelity Brokerage Services Inc., estimates that ECNs have al- ready captured 20 to 35 percent of Nasdaq’s trading volume. In- stinet, the first and largest ECN, has a stake with Goldman Sachs, J. P. Morgan, and E*Trade in another network, Archipel- ago, which recently announced plans to form its own exchange. Likewise, Charles Schwab recently announced plans to join with Fidelity Investments, Donaldson, Lufkin & Jenrette, and Spear, Leeds & Kellogg to develop another ECN.

ECNs will accelerate the move toward 24-hour trading. Large clients who want to trade after the other markets have closed

may utilize an ECN, bypassing the NYSE and Nasdaq. The move toward faster, cheaper, and continuous trading obviously bene- fits investors, but it does present regulators, who try to ensure that all investors have access to a “level playing field,” with a number of headaches.

Because of the threat from ECNs and the need to raise cap- ital and increase flexibility, both the NYSE and Nasdaq plan to convert from privately held, member-owned businesses to stockholder-owned, for-profit corporations. This suggests that the financial landscape will continue to undergo dramatic changes in the upcoming years.

SOURCES: Katrina Brooker, “Online Investing: It’s Not Just for Geeks Anymore,” Fortune, December 21, 1998, 89–98; and “Fidelity, Schwab Part of Deal to Create Nasdaq Challenger,” The Milwaukee Journal Sentinel, July 22, 1999, 1.

(Footnote 2 continued) specialist will sell off some inventory. Similarly, if a sell order comes in, the specialist will buy and add to inventory. The specialist sets a bid price (the price the specialist will pay for the stock) and an asked price (the price at which shares will be sold out of inventory). The bid and asked prices are set at levels designed to keep the inventory in balance. If many buy orders start coming in because of favorable developments or sell orders come in because of unfavorable events, the specialist will raise or lower prices to keep supply and demand in balance. Bid prices are somewhat lower than asked prices, with the difference, or spread, representing the specialist’s profit margin.

Special facilities are available to help institutional investors such as mutual funds or pension funds sell large blocks of stock without depressing their prices. In essence, brokerage houses that cater to institutional clients will purchase blocks (defined as 10,000 or more shares) and then resell the stock to other institutions or individuals. Also, when a firm has a major announcement that is likely to cause its stock price to change sharply, it will ask the exchanges to halt trading in its stock until the announcement has been made and digested by investors. Thus, when Texaco announced that it planned to acquire Getty Oil, trading was halted for one day in both Texaco and Getty stocks.

Over-the-Counter Market A large collection of brokers and dealers, connected electronically by telephones and computers, that provides for trading in unlisted securities.

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stocks and stand prepared to make a market for these stocks. These “dealers” buy when individual investors want to sell, and then sell part of their inventory when investors want to buy. At one time, the inventory of securities was kept in a safe, and the stocks, when bought and sold, were literally passed over the counter.

Today, these markets are often referred to as dealer markets. A dealer mar- ket is defined to include all facilities that are needed to conduct security trans- actions not made on the physical location exchanges. These facilities include (1) the relatively few dealers who hold inventories of these securities and who are said to “make a market” in these securities; (2) the thousands of brokers who act as agents in bringing the dealers together with investors; and (3) the computers, terminals, and electronic networks that provide a communication link between dealers and brokers. The dealers who make a market in a particular stock quote the price at which they will pay for the stock (the bid price) and the price at which they will sell shares (the ask price). Each dealer’s prices, which are ad- justed as supply and demand conditions change, can be read off computer screens all across the world. The bid-ask spread, which is the difference between bid and ask prices, represents the dealer’s markup, or profit. The dealer’s risk increases if the stock is more volatile, or if the stock trades infrequently. Gen- erally, we would expect volatile, infrequently traded stocks to have wider spreads in order to compensate the dealers for assuming the risk of holding them in inventory.

Brokers and dealers who participate in the over-the-counter market are members of a self-regulatory body known as the National Association of Securities Dealers (NASD), which licenses brokers and oversees trading practices. The computerized network used by the NASD is known as the NASD Automated Quotation System.

Nasdaq started as just a quotation system, but it has grown to become an organized securities market with its own listing requirements. Over the past decade the competition between the NYSE and Nasdaq has become increas- ingly fierce. In an effort to become more competitive with the NYSE and with international markets, the Nasdaq and the AMEX merged in 1998 to form the Nasdaq-Amex Market Group, which might best be referred to as an organized investment network. This investment network is often referred to as Nasdaq, but stocks continue to be traded and reported separately on the two markets. Increased competition among global stock markets assuredly will result in similar alliances among other exchanges and markets in the future.

Since most of the largest companies trade on the NYSE, the market capital- ization of NYSE-traded stocks is much higher than for stocks traded on Nas- daq ($11.4 trillion compared with $3.6 trillion at year-end 2000). However, re- ported volume (number of shares traded) is often larger on Nasdaq, and more companies are listed on Nasdaq.3

Interestingly, many high-tech companies such as Microsoft and Intel have remained on Nasdaq even though they easily meet the listing requirements of the NYSE. At the same time, however, other high-tech companies such as Gateway 2000, America Online, and Iomega have left Nasdaq for the NYSE.

3 One transaction on Nasdaq generally shows up as two separate trades (the buy and the sell). This “double counting” makes it difficult to compare the volume between stock markets.

Dealer Market Includes all facilities that are needed to conduct security transactions not conducted on the physical location exchanges.

A VERY EXPENSIVE BEER

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Despite these defections, Nasdaq’s growth over the past decade has been im- pressive. In the years ahead, the competition will no doubt remain fierce.

T H E C O S T O F M O N E Y

Afew summers ago, two professors met for a beer at an aca-demic conference. During their conversation, the professors, William Christie of Vanderbilt University and Paul Schultz of Ohio State University, decided it would be interesting to see how prices are set for Nasdaq stocks. The results of their study were startling to many, and they produced a real firestorm in the investment community.

When looking through data on the bid/asked spreads set by Nasdaq market makers, Christie and Schultz found that the mar- ket makers routinely avoided posting quotes that had “odd- eighths fractions,” that is, �18�, �38�, �58�, and �78�. For example, if a mar- ket maker were to use odd-eighths quotes, he might offer to buy a stock for 10�12� a share and sell it for 10�58�, thus providing a “spread,” or profit, of �18� point (10�58� � 10�12� � �18�). The spread be- tween the two prices is the market maker’s compensation for providing a market and taking the risk associated with holding an inventory of a given stock. Note that if he or she avoided odd-eighths fractions, then the offer price would be 10�34� (which is 10�68�), so the spread would be 10�68� � 10�12� � �14�, or twice as high as if he or she made an odd-eighths quote.

What amazed Christie and Schultz was the fact that this practice was so widespread — even for widely followed stocks

such as Apple Computer and Lotus Development. The professors concluded that the evidence strongly suggested that there had to be tacit collusion among Nasdaq dealers designed to keep spreads artificially high. The National Association of Securities Dealers (NASD) originally denied the accusations. Others have come forward to provide a justification for the practice.

The publicity surrounding the study led the Securities and Exchange Commission (SEC) to investigate. Without admitting guilt, the NASD settled with the SEC, and, as part of the agree- ment, the dealers agreed to spend $100 million during the next five years to improve their enforcement practices. These allega- tions have also led to a civil class-action suit. In a dramatic de- velopment, several of the nation’s largest securities firms have reached an agreement to pay more than $1 billion in damages — which is believed to be the largest antitrust settlement in history. All of this explains why the professors’ beers turned out to be so expensive.

SOURCES: William Christie, “An Expensive Beer for the N.A.S.D.,” The New York Times, August 25, 1996, Sec. 3, 12; and Michael Rapoport, “Securities Firms’ Settlement Wins Backing from Judge,” The Wall Street Journal Interactive Edition, December 30, 1997.

SELF-TEST QUESTIONS

What are the differences between the physical location exchanges and the Nasdaq stock market?

What is the bid-ask spread?

T H E C O S T O F M O N E Y

Capital in a free economy is allocated through the price system. The interest rate is the price paid to borrow debt capital. With equity capital, investors expect to receive dividends and capital gains, whose sum is the cost of equity money. The factors that affect supply of and demand for investment capital, hence the cost of money, are discussed in this section.

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MEASURING THE MARKET

Astock index is designed to show the performance of thestock market. The problem is that there are many stock in- dexes, and it is difficult to determine which index best reflects market actions. Some are designed to represent the whole eq- uity market, some to track the returns of certain industry sectors, and others to track the returns of small-cap, mid-cap, or large-cap stocks. We discuss below three of the leading indexes.

DOW JONES INDUSTRIAL AVERAGE Unveiled in 1896 by Charles H. Dow, the Dow Jones Industrial Average (DJIA) provided a benchmark for comparing individual stocks with the overall market and for comparing the market with other economic indicators. The industrial average began with just 10 stocks, was expanded in 1916 to 20 stocks, and then to 30 in 1928. Also, in 1928 The Wall Street Journal edi- tors began adjusting it for stock splits, and making substitu- tions. Today, the DJIA still includes 30 companies. They repre- sent almost a fifth of the market value of all U.S. stocks, and all are both leading companies in their industries and widely held by individual and institutional investors.

S&P 500 INDEX Created in 1926, the S&P 500 Index is widely regarded as the standard for measuring large-cap U.S. stock market perfor- mance. The stocks in the S&P 500 are selected by the Standard & Poor’s Index Committee for being the leading companies in the leading industries, and for accurately reflecting the U.S. stock market. It is value weighted, so the largest companies (in

terms of value) have the greatest influence. The S&P 500 Index is used by 97 percent of all U.S. money managers and pension plan sponsors, and approximately $700 billion is managed so as to obtain the same performance as this index (that is, in in- dexed funds).

NASDAQ COMPOSITE INDEX The Nasdaq Composite Index measures the performance of all common stocks listed on the Nasdaq stock market. Currently, it includes more than 5,000 companies, and because many of the technology-sectored companies are traded on the computer- based Nasdaq exchange, this index is generally regarded as an economic indicator of the high-tech industry. Microsoft, Intel, and Cisco Systems are the three largest Nasdaq companies, and they comprise a high percentage of the index’s value-weighted market capitalization. For this reason, substantial movements in the same direction by these three companies can move the entire index.

RECENT PERFORMANCE The accompanying figure plots the value that an investor would now have if he or she had invested $1.00 in each of the three indexes on August 31, 1979. The returns on the three indexes are compared to an investment strategy that only invests in T- bills. Every year, the proceeds from that T-bill investment are reinvested at the current one-year T-bill rate. Over the past 20 years each of these indexes has performed quite well, which re- flects the spectacular rise in the stock market. During this pe-

The four most fundamental factors affecting the cost of money are (1) pro- duction opportunities, (2) time preferences for consumption, (3) risk, and (4) inflation. To see how these factors operate, visualize an isolated island com- munity where the people live on fish. They have a stock of fishing gear that permits them to survive reasonably well, but they would like to have more fish. Now suppose Mr. Crusoe had a bright idea for a new type of fishnet that would enable him to double his daily catch. However, it would take him a year to per- fect his design, to build his net, and to learn how to use it efficiently, and Mr. Crusoe would probably starve before he could put his new net into operation. Therefore, he might suggest to Ms. Robinson, Mr. Friday, and several others that if they would give him one fish each day for a year, he would return two fish a day during all of the next year. If someone accepted the offer, then the fish that Ms. Robinson or one of the others gave to Mr. Crusoe would consti- tute savings; these savings would be invested in the fishnet; and the extra fish the net produced would constitute a return on the investment.

Production Opportunities The returns available within an economy from investments in productive (cash-generating) assets.

Time Preferences for Consumption The preferences of consumers for current consumption as opposed to saving for future consumption.

Risk In a financial market context, the chance that an investment will provide a low or negative return.

193

Obviously, the more productive Mr. Crusoe thought the new fishnet would be, the more he could afford to offer potential investors for their savings. In this example, we assume that Mr. Crusoe thought he would be able to pay, and thus he offered, a 100 percent rate of return — he offered to give back two fish for every one he received. He might have tried to attract savings for less — for example, he might have decided to offer only 1.5 fish next year for every one he received this year, which would represent a 50 percent rate of return to Ms. Robinson and the other potential savers.

How attractive Mr. Crusoe’s offer appeared to a potential saver would de- pend in large part on the saver’s time preference for consumption. For example, Ms. Robinson might be thinking of retirement, and she might be willing to trade fish today for fish in the future on a one-for-one basis. On the other hand, Mr. Friday might have a wife and several young children and need his current fish, so he might be unwilling to “lend” a fish today for anything less than three fish next year. Mr. Friday would be said to have a high time

T H E C O S T O F M O N E Y

SOURCES: Yahoo! Finance, Nasdaq, and FRED Database.

Value of $1 Investment

30

25

20

15

10

5

0 19811979

Year

1983 1985 1987 1989 1991 1993 1995 1997 1999 2001

Nasdaq

S&P

DJIA

T-bills

Growth of a $1 Investment Made on August 31, 1979

riod the average annualized returns of these indexes ranged from 12.0 percent for the S&P 500 to 13.5 percent for the Nas- daq. The Nasdaq’s relatively strong performance occurred pri-

marily after 1992, reflecting the fact that it includes a large number of technology stocks, a sector that has performed ex- traordinarily well in recent years.

Inflation The amount by which prices increase over time.

I N T E R E S T R AT E L E V E L S

Capital is allocated among borrowers by interest rates: Firms with the most profitable investment opportunities are willing and able to pay the most for capital, so they tend to attract it away from inefficient firms or from those whose products are not in demand. Of course, our economy is not completely free in the sense of being influenced only by market forces. Thus, the federal government has agencies that help designated individuals or groups obtain credit on favorable terms. Among those eligible for this kind of assistance are small businesses, certain minorities, and firms willing to build plants in areas with high unemployment. Still, most capital in the U.S. economy is allocated through the price system.

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preference for current consumption and Ms. Robinson a low time preference. Note also that if the entire population were living right at the subsistence level, time preferences for current consumption would necessarily be high, ag- gregate savings would be low, interest rates would be high, and capital forma- tion would be difficult.

The risk inherent in the fishnet project, and thus in Mr. Crusoe’s ability to repay the loan, would also affect the return investors would require: the higher the perceived risk, the higher the required rate of return. Also, in a more com- plex society there are many businesses like Mr. Crusoe’s, many goods other than fish, and many savers like Ms. Robinson and Mr. Friday. Therefore, peo- ple use money as a medium of exchange rather than barter with fish. When money is used, its value in the future, which is affected by inflation, comes into play: the higher the expected rate of inflation, the larger the required return. We discuss this point in detail later in the chapter.

Thus, we see that the interest rate paid to savers depends in a basic way (1) on the rate of return producers expect to earn on invested capital, (2) on savers’ time preferences for current versus future consumption, (3) on the riskiness of the loan, and (4) on the expected future rate of inflation. Producers’ expected returns on their business investments set an upper limit on how much they can pay for savings, while consumers’ time preferences for consumption establish how much consumption they are willing to defer, hence how much they will save at different rates of interest offered by producers.4 Higher risk and higher inflation also lead to higher interest rates.

SELF-TEST QUESTIONS

What is the price paid to borrow money called?

What are the two items whose sum is the “price” of equity capital?

What four fundamental factors affect the cost of money?

4 The term “producers” is really too narrow. A better word might be “borrowers,” which would in- clude corporations, home purchasers, people borrowing to go to college, or even people borrowing to buy autos or to pay for vacations. Also, the wealth of a society and its demographics influence its people’s ability to save and thus their time preferences for current versus future consumption.

195I N T E R E S T R AT E L E V E L S

5 The letter “k” is the traditional symbol for interest rates and the cost of equity, but “i” is used fre- quently today because this term corresponds to the interest rate key on financial calculators. There- fore, in Chapter 7, when we discuss calculators, the term “i” will be used for the interest rate.

Figure 5-2 shows how supply and demand interact to determine interest rates in two capital markets. Markets A and B represent two of the many capital mar- kets in existence. The going interest rate, which can be designated as either k or i, but for purposes of our discussion is designated as k, is initially 10 percent for the low-risk securities in Market A.5 Borrowers whose credit is strong enough to borrow in this market can obtain funds at a cost of 10 percent, and investors who want to put their money to work without much risk can obtain a 10 percent re- turn. Riskier borrowers must obtain higher-cost funds in Market B. Investors who are more willing to take risks invest in Market B, expecting to earn a 12 per- cent return but also realizing that they might actually receive much less.

If the demand for funds declines, as it typically does during business reces- sions, the demand curves will shift to the left, as shown in Curve D2 in Market A. The market-clearing, or equilibrium, interest rate in this example declines to 8 percent. Similarly, you should be able to visualize what would happen if the Fed- eral Reserve tightened credit: The supply curve, S1, would shift to the left, and this would raise interest rates and lower the level of borrowing in the economy.

Capital markets are interdependent. For example, if Markets A and B were in equilibrium before the demand shift to D2 in Market A, then investors were willing to accept the higher risk in Market B in exchange for a risk premium of 12% � 10% � 2%. After the shift to D2, the risk premium would initially in- crease to 12% � 8% � 4%. Immediately, though, this much larger premium

F I G U R E 5 - 2 Interest Rates as a Function of Supply and Demand for Funds

k = 10A

8

D1

D2

S1

Interest Rate, k (%)

Market A: Low-Risk Securities

0 Dollars 0 Dollars

Interest Rate, k (%)

k = 12B

Market B: High-Risk Securities

S1

D1

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would induce some of the lenders in Market A to shift to Market B, which would, in turn, cause the supply curve in Market A to shift to the left (or up) and that in Market B to shift to the right. The transfer of capital between mar- kets would raise the interest rate in Market A and lower it in Market B, thus bringing the risk premium back closer to the original 2 percent.

There are many capital markets in the United States. U.S. firms also invest and raise capital throughout the world, and foreigners both borrow and lend in the United States. There are markets for home loans; farm loans; business loans; federal, state, and local government loans; and consumer loans. Within each category, there are regional markets as well as different types of submar- kets. For example, in real estate there are separate markets for first and second mortgages and for loans on single-family homes, apartments, office buildings, shopping centers, vacant land, and so on. Within the business sector there are dozens of types of debt and also several different markets for common stocks.

There is a price for each type of capital, and these prices change over time as shifts occur in supply and demand conditions. Figure 5-3 shows how long- and short-term interest rates to business borrowers have varied since the early

F I G U R E 5 - 3 Long- and Short-Term Interest Rates, 1961-2000

Interest Rate (%)

Long-Term Rates

Short-Term Rates

19851961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1987 1989

18

16

14

12

10

8

6

4

2

0 1991 1993 1995 1997 1999

18

16

14

12

10

8

6

4

2

0

NOTES:

a. The shaded areas designate business recessions. b. Short-term rates are measured by three- to six-month loans to very large, strong corporations, and long-term rates are measured by AAA corporate bonds.

SOURCE: Federal Reserve Bulletin.

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1960s. Notice that short-term interest rates are especially prone to rise during booms and then fall during recessions. (The shaded areas of the chart indicate recessions.) When the economy is expanding, firms need capital, and this de- mand for capital pushes rates up. Also, inflationary pressures are strongest dur- ing business booms, and that also exerts upward pressure on rates. Conditions are reversed during recessions such as the one in 1990 and 1991. Slack business reduces the demand for credit, the rate of inflation falls, and the result is a drop in interest rates. Furthermore, the Federal Reserve deliberately lowers rates during recessions to help stimulate the economy.

These tendencies do not hold exactly — the period after 1984 is a case in point. The price of oil fell dramatically in 1985 and 1986, reducing inflationary pressures on other prices and easing fears of serious long-term inflation. Ear- lier, these fears had pushed interest rates to record levels. The economy from 1984 to 1987 was strong, but the declining fears of inflation more than offset the normal tendency of interest rates to rise during good economic times, and the net result was lower interest rates.6

The relationship between inflation and long-term interest rates is high- lighted in Figure 5-4, which plots rates of inflation along with long-term inter- est rates. In the early 1960s, inflation averaged 1 percent per year, and interest rates on high-quality, long-term bonds averaged 4 percent. Then the Vietnam War heated up, leading to an increase in inflation, and interest rates began an upward climb. When the war ended in the early 1970s, inflation dipped a bit, but then the 1973 Arab oil embargo led to rising oil prices, much higher infla- tion rates, and sharply higher interest rates.

Inflation peaked at about 13 percent in 1980, but interest rates continued to increase into 1981 and 1982, and they remained quite high until 1985, because people were afraid inflation would start to climb again. Thus, the “inflationary psychology” created during the 1970s persisted to the mid-1980s.

Gradually, though, people began to realize that the Federal Reserve was se- rious about keeping inflation down, that global competition was keeping U.S. auto producers and other corporations from raising prices as they had in the past, and that constraints on corporate price increases were diminishing labor unions’ ability to push through cost-increasing wage hikes. As these realizations set in, interest rates declined.

The gap between the current interest rate and the current inflation rate is defined as the “current real rate of interest.” It is called the “real rate” because it shows how much investors really earned after taking out the effects of infla- tion. The real rate was extremely high during the mid-1980s, but it averaged about 4 percent during the 1990s.

In recent years, inflation has been running at about 3 percent a year. How- ever, long-term interest rates have been volatile, because investors are not sure if inflation is truly under control or is getting ready to jump back to the higher levels of the 1980s. In the years ahead, we can be sure that the level of interest rates will vary (1) with changes in the current rate of inflation and (2) with changes in expectations about future inflation.

I N T E R E S T R AT E L E V E L S

6 Short-term rates are responsive to current economic conditions, whereas long-term rates primar- ily reflect long-run expectations for inflation. As a result, short-term rates are sometimes above and sometimes below long-term rates. The relationship between long-term and short-term rates is called the term structure of interest rates, and it is discussed later in the chapter.

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T H E D E T E R M I N A N T S O F M A R K E T I N T E R E S T R AT E S

In general, the quoted (or nominal) interest rate on a debt security, k, is com- posed of a real risk-free rate of interest, k*, plus several premiums that reflect inflation, the riskiness of the security, and the security’s marketability (or liq- uidity). This relationship can be expressed as follows:

Quoted interest rate � k � k* � IP � DRP � LP � MRP. (5-1)

SELF-TEST QUESTIONS

How are interest rates used to allocate capital among firms?

What happens to market-clearing, or equilibrium, interest rates in a capital market when the demand for funds declines? What happens when inflation increases or decreases?

Why does the price of capital change during booms and recessions?

How does risk affect interest rates?

F I G U R E 5 - 4 Relationship between Annual Inflation Rates and Long-Term Interest Rates, 1961-2000

NOTES:

a. Interest rates are those on AAA long-term corporate bonds. b. Inflation is measured as the annual rate of change in the Consumer Price Index (CPI).

SOURCE: Federal Reserve Bulletin.

Percent

16

14

12

10

8

6

4

2

0

Long-Term Interest Rates

Inflation

1985198319811979197719751973197119691967196519631961 1987 1989 1991 1995 1997 19991993

16

14

12

10

8

6

4

2

0

199T H E D E T E R M I N A N T S O F M A R K E T I N T E R E S T R AT E S

Here

k � the quoted, or nominal, rate of interest on a given security.7 There are many different securities, hence many different quoted interest rates.

k* � the real risk-free rate of interest. k* is pronounced “k-star,” and it is the rate that would exist on a riskless security if zero inflation were ex- pected.

kRF � k* � IP, and it is the quoted risk-free rate of interest on a security such as a U.S. Treasury bill, which is very liquid and also free of most risks. Note that kRF includes the premium for expected inflation, because kRF � k* � IP.

IP � inflation premium. IP is equal to the average expected inflation rate over the life of the security. The expected future inflation rate is not necessarily equal to the current inflation rate, so IP is not necessarily equal to current inflation as reported in Figure 5-4.

DRP � default risk premium. This premium reflects the possibility that the issuer will not pay interest or principal at the stated time and in the stated amount. DRP is zero for U.S. Treasury securities, but it rises as the riskiness of issuers increases.

LP � liquidity, or marketability, premium. This is a premium charged by lenders to reflect the fact that some securities cannot be converted to cash on short notice at a “reasonable” price. LP is very low for Trea- sury securities and for securities issued by large, strong firms, but it is relatively high on securities issued by very small firms.

MRP � maturity risk premium. As we will explain later, longer-term bonds, even Treasury bonds, are exposed to a significant risk of price declines, and a maturity risk premium is charged by lenders to reflect this risk.

As noted above, since kRF � k* � IP, we can rewrite Equation 5-1 as follows:

Nominal, or quoted, rate � k � kRF � DRP � LP � MRP.

We discuss the components whose sum makes up the quoted, or nominal, rate on a given security in the following sections.

THE REAL RISK-FREE RATE OF INTEREST, k*

The real risk-free rate of interest, k*, is defined as the interest rate that would exist on a riskless security if no inflation were expected, and it may be thought of as the rate of interest on short-term U.S. Treasury securities in an in- flation-free world. The real risk-free rate is not static — it changes over time depending on economic conditions, especially (1) on the rate of return corpo- rations and other borrowers expect to earn on productive assets and (2) on people’s time preferences for current versus future consumption. Borrowers’

7 The term nominal as it is used here means the stated rate as opposed to the real rate, which is ad- justed to remove inflation effects. If you had bought a 10-year Treasury bond in February 2001, the quoted, or nominal, rate would be about 5.2 percent, but if inflation averages 2.5 percent over the next 10 years, the real rate would be about 5.2% � 2.5% � 2.7%.

Real Risk-Free Rate of Interest, k* The rate of interest that would exist on default-free U.S. Treasury securities if no inflation were expected.

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expected returns on real asset investments set an upper limit on how much they can afford to pay for borrowed funds, while savers’ time preferences for con- sumption establish how much consumption they are willing to defer, hence the amount of funds they will lend at different interest rates. It is difficult to mea- sure the real risk-free rate precisely, but most experts think that k* has fluctu- ated in the range of 1 to 5 percent in recent years.8 The best estimate of k* is the rate of return on indexed Treasury bonds, which are discussed in a box later in the chapter.

THE NOMINAL, OR QUOTED, RISK-FREE RATE OF INTEREST, kRF

The nominal, or quoted, risk-free rate, kRF, is the real risk-free rate plus a premium for expected inflation: kRF � k* � IP. To be strictly correct, the risk- free rate should mean the interest rate on a totally risk-free security — one that has no risk of default, no maturity risk, no liquidity risk, no risk of loss if infla- tion increases, and no risk of any other type. There is no such security, hence there is no observable truly risk-free rate. However, there is one security that is free of most risks — an indexed U.S. Treasury security. These securities are free of default, maturity, and liquidity risks, and also of risk due to changes in the general level of interest rates.9

If the term “risk-free rate” is used without either the modifier “real” or the modifier “nominal,” people generally mean the quoted (nominal) rate, and we will follow that convention in this book. Therefore, when we use the term risk- free rate, kRF, we mean the nominal risk-free rate, which includes an inflation premium equal to the average expected inflation rate over the life of the secu- rity. In general, we use the T-bill rate to approximate the short-term risk-free rate, and the T-bond rate to approximate the long-term risk-free rate. So, whenever you see the term “risk-free rate,” assume that we are referring either to the quoted U.S. T-bill rate or to the quoted T-bond rate.

INFLAT ION PREMIUM (IP)

Inflation has a major impact on interest rates because it erodes the purchasing power of the dollar and lowers the real rate of return on investments. To illus-

8 The real rate of interest as discussed here is different from the current real rate as discussed in connection with Figure 5-4. The current real rate is the current interest rate minus the current (or latest past) inflation rate, while the real rate, without the word “current,” is the current interest rate minus the expected future inflation rate over the life of the security. For example, suppose the cur- rent quoted rate for a one-year Treasury bill is 5 percent, inflation during the latest year was 2 per- cent, and inflation expected for the coming year is 4 percent. Then the current real rate would be 5% � 2% � 3%, but the expected real rate would be 5% � 4% � 1%. The rate on a 10-year bond would be related to the expected inflation rate over the next 10 years, and so on. In the press, the term “real rate” generally means the current real rate, but in economics and finance, hence in this book unless otherwise noted, the real rate means the one based on expected inflation rates. 9 Indexed Treasury securities are the closest thing we have to a riskless security, but even they are not totally riskless, because k* itself can change and cause a decline in the prices of these securities. For example, between October 1998 and January 2000, the price of one indexed Treasury security declined from 98 to 89, or by almost 10 percent. The cause was an increase in the real rate on long- term securities from 3.7 percent to 4.4 percent. One year later, the real rate on long-term securi- ties has dropped to 3.5 percent.

Nominal (Quoted) Risk-Free Rate, kRF The rate of interest on a security that is free of all risk; kRF is proxied by the T-bill rate or the T-bond rate. kRF includes an inflation premium.

201

trate, suppose you saved $1,000 and invested it in a Treasury bill that matures in one year and pays a 5 percent interest rate. At the end of the year, you will receive $1,050 — your original $1,000 plus $50 of interest. Now suppose the inflation rate during the year is 10 percent, and it affects all items equally. If gas had cost $1 per gallon at the beginning of the year, it would cost $1.10 at the end of the year. Therefore, your $1,000 would have bought $1,000/$1 � 1,000 gallons at the beginning of the year, but only $1,050/$1.10 � 955 gallons at the end. In real terms, you would be worse off — you would receive $50 of interest, but it would not be sufficient to offset inflation. You would thus be better off buying 1,000 gallons of gas (or some other storable asset such as land, timber, apartment buildings, wheat, or gold) than buying the Treasury bill.

Investors are well aware of all this, so when they lend money, they build in an inflation premium (IP) equal to the average expected inflation rate over the life of the security. As discussed previously, for a short-term, default-free U.S. Treasury bill, the actual interest rate charged, kT-bill, would be the real risk-free rate, k*, plus the inflation premium (IP):

kT-bill � kRF � k* � IP.

Therefore, if the real risk-free rate of interest were k* � 2.8%, and if inflation were expected to be 2 percent (and hence IP � 2%) during the next year, then the quoted rate of interest on one-year T-bills would be 2.8% � 2% � 4.8%. Indeed, in February 2001, the expected one-year inflation rate was about 2 per- cent, and the yield on one-year T-bills was about 4.8 percent, so the real risk- free rate on short-term securities at that time was 2.8 percent.

It is important to note that the inflation rate built into interest rates is the inflation rate expected in the future, not the rate experienced in the past. Thus, the latest reported figures might show an annual inflation rate of 3.3 percent, but that is for the past year. If people on the average expect a 6 percent infla- tion rate in the future, then 6 percent would be built into the current interest rate. Note also that the inflation rate reflected in the quoted interest rate on any security is the average rate of inflation expected over the security’s life. Thus, the inflation rate built into a one-year bond is the expected inflation rate for the next year, but the inflation rate built into a 30-year bond is the average rate of inflation expected over the next 30 years.10

Expectations for future inflation are closely, but not perfectly, correlated with rates experienced in the recent past. Therefore, if the inflation rate re- ported for last month increased, people would tend to raise their expectations for future inflation, and this change in expectations would cause an increase in interest rates.

T H E D E T E R M I N A N T S O F M A R K E T I N T E R E S T R AT E S

Inflation Premium (IP) A premium equal to expected inflation that investors add to the real risk-free rate of return.

10 To be theoretically precise, we should use a geometric average. Also, since millions of investors are active in the market, it is impossible to determine exactly the consensus expected inflation rate. Survey data are available, however, which give us a reasonably good idea of what investors expect over the next few years. For example, in 1980 the University of Michigan’s Survey Re- search Center reported that people expected inflation during the next year to be 11.9 percent and that the average rate of inflation expected over the next 5 to 10 years was 10.5 percent. Those expectations led to record-high interest rates. However, the economy cooled in 1981 and 1982, and, as Figure 5-4 showed, actual inflation dropped sharply after 1980. This led to grad- ual reductions in the expected future inflation rate. In February 2001, as we write this, the ex- pected inflation rate for the next year is about 2 percent, and the expected long-term inflation rate is about 2.5 percent. As inflationary expectations change, so do quoted market interest rates.

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Note that Germany, Japan, and Switzerland have over the past 3.5 or so years had lower inflation rates than the United States, hence their interest rates have generally been lower than ours. Italy and most South American countries have experienced high inflation, and that is reflected in their inter- est rates.

DEFAULT RISK PREMIUM (DRP)

The risk that a borrower will default on a loan, which means not pay the inter- est or the principal, also affects the market interest rate on a security: the greater the default risk, the higher the interest rate. Treasury securities have no default risk, hence they carry the lowest interest rates on taxable securities in the United States. For corporate bonds, the higher the bond’s rating, the lower its default risk, and, consequently, the lower its interest rate.11 Here are some representative interest rates on long-term bonds during November 2000:

RATE DRP

U.S. Treasury 5.8% — AAA 7.5 1.7% AA 7.8 2.0 A 8.1 2.3 BBB 8.3 2.5

The difference between the quoted interest rate on a T- bond and that on a corporate bond with similar maturity, liquidity, and other features is the default risk premium (DRP). Therefore, if the bonds listed above were otherwise similar, the default risk premium would be DRP � 7.5% � 5.8% � 1.7 per- centage points for AAA corporate bonds, 7.8% � 5.8% � 2.0 percentage points for AA, 8.1% � 5.8% � 2.3 percentage points for A corporate bonds, and so forth. Default risk premiums vary somewhat over time, but the Novem- ber 2000 figures are representative of levels in recent years.

LIQUIDITY PREMIUM (LP)

A “liquid” asset can be converted to cash quickly and at a “fair market value.” Financial assets are generally more liquid than real assets. Because liquidity is important, investors include liquidity premiums (LPs) when market rates of securities are established. Although it is difficult to accurately measure liquidity premiums, a differential of at least two and probably four or five percentage points exists between the least liquid and the most liquid financial assets of sim- ilar default risk and maturity.

Default Risk Premium (DRP) The difference between the interest rate on a U.S. Treasury bond and a corporate bond of equal maturity and marketability.

Liquidity Premium (LP) A premium added to the equilibrium interest rate on a security if that security cannot be converted to cash on short notice and at close to “fair market value.”

11 Bond ratings, and bonds’ riskiness in general, are discussed in detail in Chapter 8. For now, merely note that bonds rated AAA are judged to have less default risk than bonds rated AA, while AA bonds are less risky than A bonds, and so on. Ratings are designated AAA or Aaa, AA or Aa, and so forth, depending on the rating agency. In this book, the designations are used inter- changeably.

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MATURITY RISK PREMIUM (MRP)

U.S. Treasury securities are free of default risk in the sense that one can be vir- tually certain that the federal government will pay interest on its bonds and will also pay them off when they mature. Therefore, the default risk premium on Treasury securities is essentially zero. Further, active markets exist for Treasury securities, so their liquidity premiums are also close to zero. Thus, as a first ap- proximation, the rate of interest on a Treasury bond should be the risk-free rate, kRF, which is equal to the real risk-free rate, k*, plus an inflation premium, IP. However, an adjustment is needed for long-term Treasury bonds. The prices of long-term bonds decline sharply whenever interest rates rise, and since interest rates can and do occasionally rise, all long-term bonds, even Trea- sury bonds, have an element of risk called interest rate risk. As a general rule, the bonds of any organization, from the U.S. government to Continental Air- lines, have more interest rate risk the longer the maturity of the bond.12 There- fore, a maturity risk premium (MRP), which is higher the longer the years to maturity, must be included in the required interest rate.

The effect of maturity risk premiums is to raise interest rates on long-term bonds relative to those on short-term bonds. This premium, like the others, is difficult to measure, but (1) it varies somewhat over time, rising when interest rates are more volatile and uncertain, then falling when interest rates are more stable, and (2) in recent years, the maturity risk premium on 30-year T-bonds appears to have generally been in the range of one or two percentage points.13

We should mention that although long-term bonds are heavily exposed to in- terest rate risk, short-term bills are heavily exposed to reinvestment rate risk. When short-term bills mature and the funds are reinvested, or “rolled over,” a de- cline in interest rates would necessitate reinvestment at a lower rate, and this would result in a decline in interest income. To illustrate, suppose you had $100,000 invested in one-year T-bills, and you lived on the income. In 1981, short-term rates were about 15 percent, so your income would have been about $15,000. However, your income would have declined to about $9,000 by 1983, and to just $4,800 by 2001. Had you invested your money in long-term T-bonds, your income (but not the value of the principal) would have been stable.14 Thus, although “investing short” preserves one’s principal, the interest income provided by short-term T-bills is less stable than the interest income on long-term bonds.

T H E D E T E R M I N A N T S O F M A R K E T I N T E R E S T R AT E S

12 For example, if someone had bought a 30-year Treasury bond for $1,000 in 1998, when the long- term interest rate was 5.25 percent, and held it until 2001, when long-term T-bond rates were about 5.5 percent, the value of the bond would have declined to about $965. That would represent a loss of 3.5 percent, and it demonstrates that long-term bonds, even U.S. Treasury bonds, are not riskless. However, had the investor purchased short-term T-bills in 1998 and subsequently rein- vested the principal each time the bills matured, he or she would still have had $1,000. This point will be discussed in detail in Chapter 8. 13 The MRP for long-term bonds has averaged 1.4 percent over the last 73 years. See Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2000 Yearbook (Chicago: Ibbotson Associates, 2000). 14 Long-term bonds also have some reinvestment rate risk. If one is saving and investing for some future purpose, say, to buy a house or for retirement, then to actually earn the quoted rate on a long-term bond, the interest payments must be reinvested at the quoted rate. However, if interest rates fall, the interest payments must be reinvested at a lower rate; thus, the realized return would be less than the quoted rate. Note, though, that reinvestment rate risk is lower on a long-term bond than on a short-term bond because only the interest payments (rather than interest plus prin- cipal) on the long-term bond are exposed to reinvestment rate risk. Zero coupon bonds, which are discussed in Chapter 8, are completely free of reinvestment rate risk during their life.

Interest Rate Risk The risk of capital losses to which investors are exposed because of changing interest rates.

Maturity Risk Premium (MRP) A premium that reflects interest rate risk.

Reinvestment Rate Risk The risk that a decline in interest rates will lead to lower income when bonds mature and funds are reinvested.

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A NEW, ALMOST RISKLESS TREASURY BOND

Investors who purchase bonds must constantly worry aboutinflation. If inflation turns out to be greater than expected, bonds will provide a lower-than-expected real return. To protect themselves against expected increases in inflation, investors build an inflation risk premium into their required rate of re- turn. This raises borrowers’ costs.

In order to provide investors with an inflation-protected bond, and also to reduce the cost of debt to the government, on January 29, 1997, the U.S. Treasury issued $7 billion of 10- year inflation-indexed bonds. These initial bonds paid an inter- est rate of 3.375 percent plus an additional amount to offset inflation. At the end of each six-month period, the principal (originally set at par, or $1,000) is adjusted by the inflation rate. For example, during the first six-month interest period, in- flation (as measured by the CPI) was 1.085 percent. The infla- tion-adjusted principal was then calculated as $1,000(1 � in- flation) � $1,000 � 1.01085 � $1,010.85. So, on July 15, 1997, each bond paid interest of 0.03375/2 � $1,010.85 � $17.06. Note that the interest rate is divided by two because interest is paid twice a year.

By January 15, 1998, a bit more inflation had occurred, and the inflation-adjusted principal was up to $1,019.69, so on January 15, 1998, each bond paid interest of 0.03375/2 � $1,019.69 � $17.21. Thus, the total return during the first year consisted of $17.06 � $17.21 � $34.27 of interest and $1,019.69 � $1,000.00 � $19.69 of “capital gains,” or $34.27 � $19.69 � $53.96 in total. Thus, the total return was $53.96/$1,000 � 5.396%.

This same adjustment process will continue each year until the bonds mature on January 15, 2007, at which time they will pay the adjusted maturity value. Thus, the cash income pro- vided by the bonds rises by exactly enough to cover inflation, producing a real, inflation-adjusted rate of 3.375 percent. Fur- ther, since the principal also rises by the inflation rate, it too is protected from inflation. The accompanying table gives the inflation-adjusted principal and interest paid during the life of these 33⁄8 percent coupon, 10-year, inflation-indexed bonds:

DATE INFLATION-ADJUSTED PRINCIPAL INTEREST PAID

7/15/97 $1,010.85 $17.06 1/15/98 1,019.69 17.21 7/15/98 1,026.51 17.32 1/15/99 1,035.12 17.47 7/15/99 1,049.01 17.70 1/15/00 1,061.92 17.92 7/15/00 1,080.85 18.24 1/15/01 1,098.52 18.54

SOURCE: Bureau of the Public Debt’s Online, Historical Reference CPI Numbers and Daily Index Ratios for 3�38�%, 10-year note due January 15, 2007, at http://www.publicdebt.treas.gov/of/ofhiscpi.htm.

The Treasury regularly conducts auctions to issue indexed bonds. The 3.375 percent rate was based on the relative supply

SELF-TEST QUESTIONS

Write out an equation for the nominal interest rate on any debt security.

Distinguish between the real risk-free rate of interest, k*, and the nominal, or quoted, risk-free rate of interest, kRF.

How is inflation dealt with when interest rates are determined by investors in the financial markets?

Does the interest rate on a T-bond include a default risk premium? Explain.

Distinguish between liquid and illiquid assets, and identify some assets that are liquid and some that are illiquid.

Briefly explain the following statement: “Although long-term bonds are heavily exposed to interest rate risk, short-term bills are heavily exposed to reinvestment rate risk. The maturity risk premium reflects the net effects of these two opposing forces.”

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T H E T E R M S T R U C T U R E O F I N T E R E S T R AT E S

The term structure of interest rates describes the relationship between long- and short-term rates. The term structure is important to corporate treasurers who must decide whether to borrow by issuing long- or short-term debt and to investors who must decide whether to buy long- or short-term bonds. Thus, it is important to understand (1) how long- and short-term rates relate to each other and (2) what causes shifts in their relative positions.

Interest rates for bonds with different maturities can be found in a variety of publications, including The Wall Street Journal and the Federal Reserve Bulletin, and on a number of web sites, including Bloomberg, Yahoo, and CNN Finan- cial. From interest rate data obtained from these sources, we can construct the term structure at a given point in time. For example, the tabular section below Figure 5-5 presents interest rates for different maturities on three different

T H E T E R M S T R U C T U R E O F I N T E R E S T R AT E S

and demand for the issue, and it will remain constant over the life of the bond. However, new bonds are issued periodically, and their “coupon” real rates depend on the market at the time the bond is auctioned. In January 2001, 10-year indexed secu- rities had a real rate of 3.5 percent.

Federal Reserve Board Chairman Greenspan lobbied in favor of the indexed bonds on the grounds that they would help him and the Fed make better estimates of investors’ expectations about inflation. He did not explain his reasoning (to our knowl- edge), but it might have gone something like this:

� We know that interest rates in general are determined as follows:

k � k* � IP � MRP � DRP � LP.

� For Treasury bonds, DRP and LP are essentially zero, so for a 10-year bond the rate is

kRF � k* � IP � MRP.

The reason the MRP is not zero is that if inflation increases, interest rates will rise and the price of the bonds will decline. Therefore, “regular” 10-year bonds are exposed to maturity risk, hence a maturity risk premium is built into their market interest rate.

� The indexed bonds are protected against inflation — if inflation increases, then so will their dollar returns, and as a result, their price will not decline in real terms. Therefore, indexed bonds should have no MRP, hence their market return is

kRF � k* � 0 � 0 � k*.

In other words, the market rate on indexed bonds is the real rate.

� The difference between the yield on a regular 10-year bond and that on an indexed bond is the sum of the 10- year bonds’ IP and MRP. The yield on regular 10-year bonds was 6.80 percent when the indexed bonds were issued, and the indexed bonds’ yield was 3.375 percent. The difference, 3.425 percent, is the average expected inflation rate over the next 10 years plus the MRP for 10- year bonds.

� The 10-year MRP is about 1.0 percent, and it has been relatively stable in recent years. Therefore, the expected rate of inflation in January 1997 was about 2.425 percent (3.425% � 1.00% � 2.425%).

The interest received and the increase in principal are taxed each year as interest income, even though cash from the appre- ciation will not be received until the bond matures. Therefore, these bonds are especially suitable for individual retirement ac- counts (IRAs), which are not taxed until funds are withdrawn.

Keep in mind, though, that despite their protection against inflation, indexed bonds are not completely riskless. The real rate of interest can change, and if k* rises, the price of the in- dexed bonds will decline. This just confirms one more time that there is no such thing as a free lunch or a riskless security!

SOURCES: “Inflation Notes Will Offer Fed Forecast Tool,” The Wall Street Journal, February 3, 1997, C1; and The Wall Street Journal, January 6, 2000, C21.

Term Structure of Interest Rates The relationship between bond yields and maturities.

Students can find current U.S. Treasury yield curve graphs and other global and domestic interest rate information at Bloomberg

markets’ site at http://www. bloomberg.com/markets/index.html.

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dates. The set of data for a given date, when plotted on a graph such as that in Figure 5-5 is called the yield curve for that date.

The yield curve changes both in position and in slope over time. In March 1980, all rates were relatively high, and since short-term rates were higher than long-term rates, the yield curve was downward sloping. However, by August 1999, all rates had fallen, and because short-term rates were lower than long- term rates, the yield curve was upward sloping. Six months later, in February 2000, all rates were higher, and the yield curve had become humped —medium- term rates were higher than both short- and long-term rates. If the current

Yield Curve A graph showing the relationship between bond yields and maturities.

F I G U R E 5 - 5 U.S. Treasury Bond Interest Rates on Different Dates

Interest Rate (%)

16

14

12

10

8

6

4

2

0 1 5 10 30

Years to Maturity

Short Term Intermediate Term

Long Term

Yield Curve for March 1980

Yield Curve for August 1999

Yield Curve for February 2000

I N T E R E S T R AT E

TERM TO MATURITY MARCH 1980 AUGUST 1999 FEBRUARY 2000

6 months 15.0% 5.1% 6.0% 1 year 14.0 5.2 6.2 5 years 13.5 5.8 6.7 10 years 12.8 5.9 6.7 30 years 12.3 6.0 6.3

207W H AT D E T E R M I N E S T H E S H A P E O F T H E Y I E L D C U R V E ?

yield curve (February 2001) were graphed on Figure 5-5, it would be downward sloping for short-term securities but upward sloping for longer-term securities. The data points would plot close to the August 1999 yield curve.

Figure 5-5 shows yield curves for U.S. Treasury securities, but we could have constructed curves for corporate bonds issued by AT&T, IBM, Delta Airlines, or any other company that borrows money over a range of maturi- ties. Had we constructed corporate curves and plotted them on Figure 5-5, they would have been above those for Treasury securities because corporate yields include default risk premiums. However, the corporate yield curves would have had the same general shape as the Treasury curves. Also, the riskier the corporation, the higher its yield curve, so Delta Airlines, which has a lower bond rating than either AT&T or IBM, would have a higher yield curve than those of AT&T and IBM.

Historically, in most years long-term rates have been above short-term rates, so the yield curve usually slopes upward. For this reason, people often call an upward-sloping yield curve a “normal” yield curve and a yield curve that slopes downward an inverted, or “abnormal,” curve. Thus, in Figure 5-5 the yield curve for March 1980 was inverted and the one for August 1999 was normal. However, the February 2000 curve was humped, which means that interest rates on medium-term maturities were higher than rates on both short- and long-term maturities. We explain in detail in the next section why an upward slope is the normal situation, but briefly, the reason is that short- term securities have less interest rate risk than longer-term securities, hence smaller MRPs. Therefore, short-term rates are normally lower than long-term rates.

“Normal” Yield Curve An upward-sloping yield curve.

Inverted (“Abnormal”) Yield Curve A downward-sloping yield curve.

Humped Yield Curve A yield curve where interest rates on medium-term maturities are higher than rates on both short- and long-term maturities.

SELF-TEST QUESTIONS

What is a yield curve, and what information would you need to draw this curve?

Distinguish among the shapes of a “normal” yield curve, an “abnormal” curve, and a “humped” curve.

W H AT D E T E R M I N E S T H E S H A P E O F T H E Y I E L D C U R V E ?

Since maturity risk premiums are positive, then if other things were held con- stant, long-term bonds would have higher interest rates than short-term bonds. However, market interest rates also depend on expected inflation, default risk, and liquidity, and each of these factors can vary with maturity.

Expected inflation has an especially important effect on the yield curve’s shape. To see why, consider U.S. Treasury securities. Because Treasuries have

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essentially no default or liquidity risk, the yield on a Treasury bond that ma- tures in t years can be found using the following equation:

kT � k*t � IPt � MRPt.

While the real risk-free rate, k*, may vary somewhat over time because of changes in the economy and demographics, these changes are random rather than predictable, so it is reasonable to assume that k* will remain constant. However, the inflation premium, IP, does vary significantly over time, and in a somewhat predictable manner. Recall that the inflation premium is simply the

F I G U R E 5 - 6 Illustrative Treasury Yield Curves

Interest Rate (%)

8

7

6

5

4

3

2

1

0 2010 30 Years to Maturity

Maturity Risk Premium

Inflation Premium

Real Risk- Free Rate

When Inflation Is Expected to Increasea.

Interest Rate (%)

8

7

6

5

4

3

2

1

0 2010 30 Years to Maturity

Maturity Risk Premium

Inflation Premium

Real Risk- Free Rate

When Inflation Is Expected to Decreaseb.

W I T H I N C R E A S I N G W I T H D E C R E A S I N G E X P E C T E D I N F L AT I O N E X P E C T E D I N F L AT I O N

MATURITY k* IP MRP YIELD MATURITY k* IP MRP YIELD

1 year 2.50% 3.00% 0.00% 5.50% 1 year 2.50% 5.00% 0.00% 7.50% 5 years 2.50 3.40 0.18 6.08 5 years 2.50 4.60 0.18 7.28 10 years 2.50 4.00 0.28 6.78 10 years 2.50 4.00 0.28 6.78 20 years 2.50 4.50 0.42 7.42 20 years 2.50 3.50 0.42 6.42 30 years 2.50 4.67 0.53 7.70 30 years 2.50 3.33 0.53 6.36

209

average level of expected inflation over the life of the bond. Thus, if the mar- ket expects inflation to increase in the future, the inflation premium will be higher the longer the bond’s maturity. On the other hand, if the market expects inflation to decline in the future, long-term bonds will have a smaller inflation premium than short-term bonds. Finally, if investors consider long-term bonds riskier than short-term bonds, the maturity risk premium will increase with ma- turity.

Panel a of Figure 5-6 shows the yield curve when inflation is expected to in- crease. Here long-term bonds have higher yields for two reasons: (1) Inflation is expected to be higher in the future, and (2) there is a positive maturity risk premium. Panel b of Figure 5-6 shows the yield curve when inflation is ex- pected to decline, causing the yield curve to be downward sloping. Downward sloping yield curves often foreshadow an economic downturn, because weaker economic conditions tend to be correlated with declining inflation, which in turn leads to lower long-term rates.

Now let’s consider the yield curve for corporate bonds. Recall that corporate bonds include a default-risk premium (DRP) and a liquidity premium (LP). Therefore, the yield on a corporate bond that matures in t years can be ex- pressed as follows:

kC � k*t � IPt � MRPt � DRPt � LPt.

A corporate bond’s default and liquidity risks are affected by its maturity. For example, the default risk on Coca-Cola’s short-term debt is very small, since there is almost no chance that Coca-Cola will go bankrupt over the next few years. However, Coke has some 100-year bonds, and while the odds of Coke defaulting on these bonds still might not be that high, the default risk on these bonds is considerably higher than that on its short-term debt.

Longer-term corporate bonds are also less liquid than shorter-term debt, hence the liquidity premium rises as maturity lengthens. The primary reason for this is that, for the reasons discussed earlier, short-term debt has less de- fault risk, so a buyer can buy short-term debt without having to do as much credit checking as would be necessary for long-term debt. Thus, people can move into and out of short-term corporate debt much more rapidly than long-term debt. The end result is that short-term corporate debt is more liq- uid, hence has a smaller liquidity premium than the same company’s long- term debt.

Figure 5-7 shows yield curves for two hypothetical corporate bonds, an AA-rated bond with minimal default risk and a BBB-rated bond with more default risk, along with the yield curve for Treasury securities as taken from Panel a of Figure 5-6. Here we assume that inflation is expected to increase, so the Treasury yield curve is upward sloping. Because of their additional de- fault and liquidity risk, corporate bonds always trade at a higher yield than Treasury bonds with the same maturity, and BBB-rated bonds trade at higher yields than AA-rated bonds. Finally, note that the yield spread between cor- porate bonds and Treasury bonds is larger the longer the maturity. This oc- curs because longer-term corporate bonds have more default and liquidity risk than shorter-term bonds, and both of these premiums are absent in Treasury bonds.

W H AT D E T E R M I N E S T H E S H A P E O F T H E Y I E L D C U R V E ?

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SELF-TEST QUESTIONS

How do maturity risk premiums affect the yield curve?

If the rate of inflation is expected to increase, would this increase or de- crease the slope of the yield curve?

If the rate of inflation is expected to remain constant in the future, would the yield curve slope up, down, or be horizontal?

Explain why corporate bonds’ default and liquidity premiums are likely to in- crease with maturity.

Explain why corporate bonds always trade at higher yields than Treasury bonds and why BBB-rated bonds always trade at higher yields than AA-rated bonds.

F I G U R E 5 - 7 Corporate and Treasury Yield Curves

Interest Rate (%)

12

10

8

6

4

2

0 2010 30

Years to Maturity

BBB-Rated Bond

AA-Rated Bond

Treasury Bond

I N T E R E S T R AT E

TERM TO MATURITY TREASURY BOND AA-RATED BOND BBB-RATED BOND

1 year 5.5% 6.7% 7.4% 5 years 6.1 7.4 8.1 10 years 6.8 8.2 9.1 20 years 7.4 9.2 10.2 30 years 7.7 9.8 11.1

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U S I N G T H E Y I E L D C U R V E TO E S T I M AT E F U T U R E I N T E R E S T R AT E S 1 5

In the last section we saw that the shape of the yield curve depends primarily on two factors: (1) expectations about future inflation and (2) the relative riski- ness of securities with different maturities. We also saw how to calculate the yield curve, given inflation and maturity-related risks. In practice, this process often works in reverse: Investors and analysts plot the yield curve and then use information embedded in it to estimate the market’s expectations regarding fu- ture inflation and risk.

This process of using the yield curve to estimate future expected interest rates is straightforward, provided (1) we focus on Treasury securities, and (2) we assume that all Treasury securities have the same risk; that is, there is no maturity risk premium. Some academics and practitioners contend that this second assumption is reasonable, at least as an approximation. They argue that the market is dominated by large bond traders who buy and sell securi- ties of different maturities each day, that these traders focus only on short- term returns, and that they are not concerned with risk. According to this view, a bond trader is just as willing to buy a 30-year bond to pick up a short-term profit as he would be to buy a three-month security. Strict pro- ponents of this view argue that the shape of the yield curve is therefore de- termined only by market expectations about future interest rates, thus their position has been called the pure expectations theory of the term structure of interest rates.

The pure expectations theory (which is sometimes simply referred to as the “expectations theory”) assumes that investors establish bond prices and in- terest rates strictly on the basis of expectations for interest rates. This means that they are indifferent with respect to maturity in the sense that they do not view long-term bonds as being riskier than short-term bonds. If this were true, then the maturity risk premium (MRP) would be zero, and long-term in- terest rates would simply be a weighted average of current and expected fu- ture short-term interest rates. For example, if 1-year Treasury bills currently yield 7 percent, but 1-year bills were expected to yield 7.5 percent a year from now, investors would expect to earn an average of 7.25 percent over the next two years:16

According to the expectations theory, this implies that a 2-year Treasury note purchased today should also yield 7.25 percent. Similarly, if 10-year bonds yield 9 percent today, and if 5-year bonds are expected to yield 7.5 percent 10 years from now, then investors should expect to earn 9 percent for 10 years

7% � 7.5% 2

� 7.25%.

U S I N G T H E Y I E L D C U R V E TO E S T I M AT E F U T U R E I N T E R E S T R AT E S

Expectations Theory A theory which states that the shape of the yield curve depends on investors’ expectations about future interest rates.

15 This section is relatively technical, but instructors can omit it without loss of continuity. 16 Technically, we should be using geometric averages rather than arithmetic averages, but the dif- ferences are not material in this example. For a discussion of this point, see Robert C. Radcliffe, Investment: Concepts, Analysis, and Strategy, 5th ed. (Reading, MA: Addison-Wesley, 1997), Chapter 5.

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and 7.5 percent for 5 years, for an average return of 8.5 percent over the next 15 years:

Consequently, a 15-year bond should yield this same return, 8.5 percent. To understand the logic behind this averaging process, ask yourself what

would happen if long-term yields were not an average of expected short-term yields. For example, suppose 2-year bonds yielded only 7 percent, not the 7.25 percent calculated above. Bond traders would be able to earn a profit by adopt- ing the following trading strategy:

1. Borrow money for two years at a cost of 7 percent. 2. Invest the money in a series of 1-year bonds. The expected return over

the 2-year period would be (7.0 � 7.5)/2 � 7.25%.

In this case, bond traders would rush to borrow money (demand funds) in the 2-year market and invest (or supply funds) in the 1-year market. Recall from Figure 5-2 that an increase in the demand for funds raises interest rates, whereas an increase in the supply of funds reduces interest rates. Therefore, bond traders’ actions would push up the 2-year yield but reduce the yield on 1-year bonds. The net effect would be to bring about a market equilibrium in which 2-year rates were a weighted average of expected future 1-year rates.

Under these assumptions, we can “back out” of the yield curve the bond market’s best guess about future interest rates. If, for example, you observe that Treasury securities with 1- and 2-year maturities yield 7 percent and 8 percent, respectively, this information can be used to calculate the market’s forecast of what 1-year rates will yield one year from now. If the pure expectations theory is correct, the rate on 2-year bonds is the average of the current 1-year rate and the 1-year rate expected a year from now. Since the current 1-year rate is 7 per- cent, this implies that the 1-year rate one year from now is expected to be 9 percent:

X � 16% � 7% � 9% � 1-year yield expected next year.

The preceding analysis was based on the assumption that the maturity risk premium is zero. However, most evidence suggests that there is a positive ma- turity risk premium, so the MRP should be taken into account.

For example, assume once again that 1- and 2-year maturities yield 7 percent and 8 percent, respectively, but now assume that the maturity risk premium on the 2-year bond is 0.5 percent. This maturity risk premium implies that the ex- pected return on 2-year bonds (8 percent) is 0.5 percent higher than the ex- pected returns from buying a series of 1-year bonds (7.5 percent). With this background, we can use the following two-step procedure to back out X, the expected 1-year rate one year from now:

Step 1: 2-year yield � MRP on 2-year bond � 8.0% � 0.5% � 7.5%.

Step 2: 7.5% � (7.0% � X%)/2 X � 15.0% � 7.0% � 8.0%.

2-year yield � 8% � 7% � X%

2

9% � 9% � � � � � 9% � 7.5% � � � � � 7.5% 15

� 10(9%) � 5(7.5%)

15 � 8.5%.

213

Therefore, the yield next year on a 1-year T-bond should be 8 percent, up from 7 percent this year.

I N V E S T I N G OV E R S E A S

SELF-TEST QUESTIONS

What key assumption underlies the pure expectations theory?

Assuming that the pure expectations theory is correct, how are long-term in- terest rates calculated?

According to the pure expectations theory, what would happen if long-term rates were not an average of expected short-term rates?

I N V E S T I N G OV E R S E A S

Investors should consider additional risk factors before investing overseas. First there is country risk, which refers to the risk that arises from investing or doing business in a particular country. This risk depends on the country’s eco- nomic, political, and social environment. Countries with stable economic, so- cial, political, and regulatory systems provide a safer climate for investment, and therefore less country risk, than less stable nations. Examples of country risk in- clude the risk associated with changes in tax rates, regulations, currency con- version, and exchange rates. Country risk also includes the risk that property will be expropriated without adequate compensation, as well as new host coun- try stipulations about local production, sourcing or hiring practices, and dam- age or destruction of facilities due to internal strife.

A second point to keep in mind when investing overseas is that more often than not the security will be denominated in a currency other than the dollar, which means that the value of your investment will depend on what happens to exchange rates. This is known as exchange rate risk. For example, if a U.S. in- vestor purchases a Japanese bond, interest will probably be paid in Japanese yen, which must then be converted into dollars if the investor wants to spend his or her money in the United States. If the yen weakens relative to the dollar, then it will buy fewer dollars, hence the investor will receive fewer dollars when it comes time to convert. Alternatively, if the yen strengthens relative to the dollar, the investor will earn higher dollar returns. It therefore follows that the effective rate of return on a foreign investment will depend on both the per- formance of the foreign security and on what happens to exchange rates over the life of the investment.

Country Risk The risk that arises from investing or doing business in a particular country.

Exchange Rate Risk The risk that exchange rate changes will reduce the number of dollars provided by a given amount of a foreign currency.

SELF-TEST QUESTIONS

What is country risk?

What is exchange rate risk?

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Various forecasting services measure the level of country riskin different countries and provide indexes that measure fac- tors such as each country’s expected economic performance, access to world capital markets, political stability, and level of internal conflict. Country risk analysts use sophisticated mod- els to measure it, thus providing corporate managers and over- seas investors with a way to judge both the relative and ab- solute risk of investing in a given country. A sample of recent country risk estimates compiled by Institutional Investor is presented in the following table. The higher the country’s score, the lower its estimated country risk. The maximum pos- sible score is 100.

The countries with the least amount of country risk all have strong, market-based economies, ready access to worldwide capital markets, relatively little social unrest, and a stable po- litical climate. Switzerland’s top ranking may surprise you, but that country’s ranking is the result of its strong economic per- formance. You may also be surprised that the United States was not ranked in the top five — it is ranked sixth.

Arguably, there are fewer surprises when looking at the bot- tom five. Each of these countries has considerable social and political unrest, and none has embraced a market-based eco- nomic system. Clearly, an investment in any of these countries is a risky proposition.

MEASURING COUNTRY RISK

Top Five Countries (Least Amount of Country Risk)

TOTAL SCORE RANK COUNTRY (MAXIMUM POSSIBLE � 100)

1 Switzerland 95.6 2 Germany 94.6 3 Netherlands 94.5 4 Luxembourg 93.9 5 France 93.6

Bottom Five Countries (Greatest Amount of Country Risk)

TOTAL SCORE RANK COUNTRY (MINIMUM POSSIBLE � 0)

141 Sudan 8.7 142 Liberia 8.6 143 Afghanistan 6.5 144 Sierra Leone 6.4 145 North Korea 6.2

Students can access the home page of Institutional Investor magazine by typing

http://www.iimagazine.com. Although the site requires users to register, the site is free to use. (Some data sets and articles are available only to subscribers.) The country risk rankings can be found by clicking on “Research and Rankings,” shown on the top of the screen, and then clicking on “Country Credit” in the middle of the screen.

OT H E R FAC TO R S T H AT I N F L U E N C E I N T E R E S T R AT E L E V E L S

In addition to inflationary expectations, other factors also influence both the general level of interest rates and the shape of the yield curve. The four most important factors are (1) Federal Reserve policy; (2) the federal budget deficit or surplus; (3) international factors, including the foreign trade balance and in- terest rates in other countries; and (4) the level of business activity.

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FEDERAL RESERVE POLICY

As you probably learned in your economics courses, (1) the money supply has a major effect on both the level of economic activity and the inflation rate, and (2) in the United States, the Federal Reserve Board controls the money supply. If the Fed wants to stimulate the economy, as it did in 1995, it increases growth in the money supply. The initial effect of such an action is to cause interest rates to decline. However, a larger money supply may also lead to an increase in the expected inflation rate, which, in turn, could push interest rates up. The reverse holds if the Fed tightens the money supply.

To illustrate, in 1981 inflation was quite high, so the Fed tightened up the money supply. The Fed deals primarily in the short-term end of the market, so this tightening had the direct effect of pushing short-term rates up sharply. At the same time, the very fact that the Fed was taking strong action to reduce in- flation led to a decline in expectations for long-run inflation, which led to a de- cline in long-term bond yields.

In 1991, the situation was just the reverse. To combat the recession, the Fed took steps to reduce interest rates. Short-term rates fell, and long-term rates also dropped, but not as sharply. These lower rates benefitted heavily indebted businesses and individual borrowers, and home mortgage refinancings put ad- ditional billions of dollars into consumers’ pockets. Savers, of course, lost out, but the net effect of lower interest rates was a stronger economy. Lower rates encourage businesses to borrow for investment, stimulate the housing market, and bring down the value of the dollar relative to other currencies, which helps U.S. exporters and thus lowers the trade deficit.

During periods when the Fed is actively intervening in the markets, the yield curve may be temporarily distorted. Short-term rates will be temporar- ily “too low” if the Fed is easing credit, and “too high” if it is tightening credit. Long-term rates are not affected as much by Fed intervention. For ex- ample, the fear of rising inflation led the Federal Reserve to increase short- term interest rates six times during 1994. While short-term rates rose by nearly 4 percentage points, long-term rates increased by only 1.5 percentage points.

BUDGET DEF IC I TS OR SURPLUSES

If the federal government spends more than it takes in from tax revenues, it runs a deficit, and that deficit must be covered either by borrowing or by print- ing money (increasing the money supply). If the government borrows, this added demand for funds pushes up interest rates. If it prints money, this in- creases expectations for future inflation, which also drives up interest rates. Thus, the larger the federal deficit, other things held constant, the higher the level of interest rates. Whether long- or short-term rates are more affected de- pends on how the deficit is financed, so we cannot state, in general, how deficits will affect the slope of the yield curve.

Over the past several decades, the federal government routinely ran large budget deficits. However, in 1999, for the first time in recent memory, the gov- ernment had a budget surplus, and further surpluses are projected on into the future. As a result, the government is buying back some of the outstanding Treasury securities. If these surpluses become a reality, the government would

OT H E R FAC TO R S T H AT I N F L U E N C E I N T E R E S T R AT E L E V E L S

The home page for the Board of Governors of the Federal Reserve System can be found at http:// www.federalreserve.

gov/. You can access general information about the Federal Reserve, including press releases, speeches, and monetary policy.

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become a net supplier of funds rather than a net borrower of funds. All else equal, this would tend to reduce interest rates.

INTERNAT IONAL FACTORS

Businesses and individuals in the United States buy from and sell to people and firms in other countries. If we buy more than we sell (that is, if we im- port more than we export), we are said to be running a foreign trade deficit. When trade deficits occur, they must be financed, and the main source of fi- nancing is debt. In other words, if we import $200 billion of goods but export only $100 billion, we run a trade deficit of $100 billion, and we would prob- ably borrow the $100 billion.17 Therefore, the larger our trade deficit, the more we must borrow, and as we increase our borrowing, this drives up in- terest rates. Also, foreigners are willing to hold U.S. debt if and only if the rate paid on this debt is competitive with interest rates in other countries. Therefore, if the Federal Reserve attempts to lower interest rates in the United States, causing our rates to fall below rates abroad, then foreigners will sell U.S. bonds, those sales will depress bond prices, and the result will be higher U.S. rates. Thus, if the trade deficit is large relative to the size of the overall economy, it may hinder the Fed’s ability to combat a recession by low- ering interest rates.

The United States has been running annual trade deficits since the mid- 1970s, and the cumulative effect of these deficits is that the United States has become the largest debtor nation of all time. As a result, our interest rates are very much influenced by interest rates in other countries around the world (higher rates abroad lead to higher U.S. rates). Because of all this, U.S. corpo- rate treasurers — and anyone else who is affected by interest rates — must keep up with developments in the world economy.

BUSINESS ACT IV I TY

Figure 5-3, presented earlier, can be examined to see how business conditions influence interest rates. Here are the key points revealed by the graph:

1. Because inflation increased from 1961 to 1981, the general tendency dur- ing that period was toward higher interest rates. However, since the 1981 peak, the trend has generally been downward.

2. Until 1966, short-term rates were almost always below long-term rates. Thus, in those years the yield curve was almost always “normal” in the sense that it was upward sloping.

3. The shaded areas in the graph represent recessions, during which (1) both the demand for money and the rate of inflation tend to fall and (2) the Federal Reserve tends to increase the money supply in an effort to stimulate the economy. As a result, there is a tendency for interest

17 The deficit could also be financed by selling assets, including gold, corporate stocks, entire com- panies, and real estate. The United States has financed its massive trade deficits by all of these means in recent years, but the primary method has been by borrowing from foreigners.

217I N T E R E S T R AT E S A N D B U S I N E S S D E C I S I O N S

rates to decline during recessions. Currently, in early 2001, there are continued signs that the economy has begun to weaken. In response to these signs of economic weakness, the Federal Reserve has instituted a se- ries of interest rate cuts. At the same time, there are also signs that infla- tion has begun to increase. These concerns about inflation may limit the Fed’s ability to cut rates further.

4. During recessions, short-term rates decline more sharply than long- term rates. This occurs because (1) the Fed operates mainly in the short-term sector, so its intervention has the strongest effect there, and (2) long-term rates reflect the average expected inflation rate over the next 20 to 30 years, and this expectation generally does not change much, even when the current inflation rate is low because of a recession or high because of a boom. So, short-term rates are more volatile than long-term rates.

SELF-TEST QUESTIONS

Other than inflationary expectations, name some additional factors that in- fluence interest rates, and explain the effects of each.

How does the Fed stimulate the economy? How does the Fed affect interest rates? Does the Fed have complete control over U.S. interest rates; that is, can it set rates at any level it chooses?

I N T E R E S T R AT E S A N D B U S I N E S S D E C I S I O N S

The yield curve for August 1999, shown earlier in Figure 5-5, indicates how much the U.S. government had to pay in 1999 to borrow money for one year, five years, ten years, and so on. A business borrower would have had to pay somewhat more, but assume for the moment that we are back in August 1999 and that the yield curve for that year also applies to your company. Now suppose your company has decided (1) to build a new plant with a 30- year life that will cost $1 million and (2) to raise the $1 million by selling an issue of debt (or borrowing) rather than by selling stock. If you borrowed in 1999 on a short-term basis — say, for one year — your interest cost for that year would be only 5.2 percent, or $52,000. On the other hand, if you used long-term (30-year) financing, your cost would be 6.0 percent, or $60,000. Therefore, at first glance, it would seem that you should use short-term debt.

However, this could prove to be a horrible mistake. If you use short-term debt, you will have to renew your loan every year, and the rate charged on each new loan will reflect the then-current short-term rate. Interest rates could re- turn to their previous highs, in which case you would be paying 14 percent, or $140,000, per year. Those high interest payments would cut into, and perhaps eliminate, your profits. Your reduced profitability could easily increase your firm’s risk to the point where its bond rating would be lowered, causing lenders

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to increase the risk premium built into the interest rate they charge. That would force you to pay an even higher rate, which would further reduce your profitability, worrying lenders even more, and making them reluctant to renew your loan. If your lenders refused to renew the loan and demanded its repay- ment, as they would have every right to do, you might have to sell assets at a loss, which could lead to bankruptcy.

On the other hand, if you used long-term financing in 1999, your interest costs would remain constant at $60,000 per year, so an increase in interest rates in the economy would not hurt you. You might even be able to buy up some of your bankrupt competitors at bargain prices — bankruptcies increase dramati- cally when interest rates rise, primarily because many firms do use too much short-term debt.

Does all this suggest that firms should always avoid short-term debt? Not necessarily. If inflation falls over the next few years, so will interest rates. If you had borrowed on a long-term basis for 6.0 percent in August 1999, your com- pany would be at a major disadvantage if it were locked into 6.0 percent debt while its competitors (who used short-term debt in 1999 and thus rode interest rates down in subsequent years) had a borrowing cost of only 3 or 4 percent.

Financing decisions would be easy if we could make accurate forecasts of fu- ture interest rates. Unfortunately, predicting interest rates with consistent ac- curacy is somewhere between difficult and impossible — people who make a living by selling interest rate forecasts say it is difficult, but many others say it is impossible.

Even if it is difficult to predict future interest rate levels, it is easy to predict that interest rates will fluctuate — they always have, and they always will. This being the case, sound financial policy calls for using a mix of long- and short- term debt, as well as equity, to position the firm so that it can survive in any in- terest rate environment. Further, the optimal financial policy depends in an im- portant way on the nature of the firm’s assets — the easier it is to sell off assets to generate cash, the more feasible it is to use large amounts of short-term debt. This makes it more feasible for a firm to finance its current assets such as inventories than its fixed assets such as buildings with short-term debt. We will return to this issue later in the book, when we discuss working capital policy.

Changes in interest rates also have implications for savers. For example, if you had a 401(k) plan — and someday you almost certainly will — you would probably want to invest some of your money in a bond mutual fund. You could choose a fund that had an average maturity of 25 years, 20 years, and so on, down to only a few months (a money market fund). How would your choice af- fect your investment results, hence your retirement income? First, your annual interest income would be affected. For example, if the yield curve were upward sloping, as it normally is, you would earn more interest if you choose a fund that held long-term bonds. Note, though, that if you choose a long-term fund and interest rates then rose, the market value of the bonds in the fund would decline. For example, as we will see in Chapter 8, if you had $100,000 in a fund whose average bond had a maturity of 25 years and a coupon rate of 6 percent, and if interest rates then rose from 6 percent to 10 percent, the market value of your fund would decline from $100,000 to about $64,000. On the other hand, if rates declined, your fund would increase in value. In any event, your choice of maturity would have a major effect on your investment performance, hence your future income.

219T Y I N G I T A L L TO G E T H E R

SELF-TEST QUESTIONS

If short-term interest rates are lower than long-term rates, why might a bor- rower still choose to finance with long-term debt?

Explain the following statement: “The optimal financial policy depends in an important way on the nature of the firm’s assets.”

In this chapter, we discussed the nature of financial markets, the types of in- stitutions that operate in these markets, how interest rates are determined, and some of the ways interest rates affect business decisions. In later chapters we will use this information to help value different investments, and to better understand corporate financing and investing decisions. The key concepts covered are listed below:

� There are many different types of financial markets. Each market serves a different region or deals with a different type of security.

� Physical asset markets, also called tangible or real asset markets, are those for such products as wheat, autos, and real estate.

� Financial asset markets deal with stocks, bonds, notes, mortgages, and other claims on real assets.

� Spot markets and futures markets are terms that refer to whether the assets are bought or sold for “on-the-spot” delivery or for delivery at some future date.

� Money markets are the markets for debt securities with maturities of less than one year.

� Capital markets are the markets for long-term debt and corporate stocks. � Primary markets are the markets in which corporations raise new capital. � Secondary markets are markets in which existing, already outstanding,

securities are traded among investors. � A derivative is a security whose value is derived from the price of some

other “underlying” asset. � Transfers of capital between borrowers and savers take place (1) by direct

transfers of money and securities; (2) by transfers through investment banking houses, which act as middlemen; and (3) by transfers through fi- nancial intermediaries, which create new securities.

� Among the major classes of intermediaries are commercial banks, sav- ings and loan associations, mutual savings banks, credit unions, pen- sion funds, life insurance companies, and mutual funds.

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� One result of ongoing regulatory changes has been a blurring of the dis- tinctions between the different financial institutions. The trend in the United States has been toward financial service corporations that offer a wide range of financial services, including investment banking, broker- age operations, insurance, and commercial banking.

� The stock market is an especially important market because this is where stock prices (which are used to “grade” managers’ performances) are established.

� There are two basic types of stock markets — the physical location ex- changes (like the NYSE) and the electronic dealer-based markets (that include the Nasdaq and the over-the-counter market).

� Capital is allocated through the price system — a price must be paid to “rent” money. Lenders charge interest on funds they lend, while equity investors receive dividends and capital gains in return for letting firms use their money.

� Four fundamental factors affect the cost of money: (1) production op- portunities, (2) time preferences for consumption, (3) risk, and (4) in- flation.

� The risk-free rate of interest, kRF, is defined as the real risk-free rate, k*, plus an inflation premium, IP, hence kRF � k* � IP.

� The nominal (or quoted) interest rate on a debt security, k, is composed of the real risk-free rate, k*, plus premiums that reflect inflation (IP), de- fault risk (DRP), liquidity (LP), and maturity risk (MRP):

k � k* � IP � DRP � LP � MRP.

� If the real risk-free rate of interest and the various premiums were constant over time, interest rates would be stable. However, both the real rate and the premiums — especially the premium for expected infla- tion — do change over time, causing market interest rates to change. Also, Federal Reserve intervention to increase or decrease the money sup- ply, as well as international currency flows, leads to fluctuations in interest rates.

� The relationship between the yields on securities and the securities’ ma- turities is known as the term structure of interest rates, and the yield curve is a graph of this relationship.

� The shape of the yield curve depends on two key factors: (1) expectations about future inflation and (2) perceptions about the relative riskiness of securities with different maturities.

� The yield curve is normally upward sloping — this is called a normal yield curve. However, the curve can slope downward (an inverted yield curve) if the inflation rate is expected to decline. The yield curve can also be humped, which means that interest rates on medium- term maturities are higher than rates on both short- and long-term maturities.

� Because interest rate levels are difficult if not impossible to predict, sound financial policy calls for using a mix of short- and long-term debt, and also for positioning the firm to survive in any future interest rate environ- ment.

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Q U E S T I O N S

5-1 What are financial intermediaries, and what economic functions do they perform? 5-2 Suppose interest rates on residential mortgages of equal risk were 7 percent in Califor-

nia and 9 percent in New York. Could this differential persist? What forces might tend to equalize rates? Would differentials in borrowing costs for businesses of equal risk lo- cated in California and New York be more or less likely to exist than differentials in res- idential mortgage rates? Would differentials in the cost of money for New York and Cal- ifornia firms be more likely to exist if the firms being compared were very large or if they were very small? What are the implications of all this for the pressure now being put on Congress to permit banks to engage in nationwide branching?

5-3 What would happen to the standard of living in the United States if people lost faith in the safety of our financial institutions? Why?

5-4 How does a cost-efficient capital market help to reduce the prices of goods and services? 5-5 Which fluctuate more, long-term or short-term interest rates? Why? 5-6 Suppose you believe that the economy is just entering a recession. Your firm must raise

capital immediately, and debt will be used. Should you borrow on a long-term or a short-term basis? Why?

5-7 Suppose the population of Area Y is relatively young while that of Area O is relatively old, but everything else about the two areas is equal. a. Would interest rates likely be the same or different in the two areas? Explain. b. Would a trend toward nationwide branching by banks and savings and loans, and the de-

velopment of nationwide diversified financial corporations, affect your answer to part a? 5-8 Suppose a new process was developed that could be used to make oil out of seawater.

The equipment required is quite expensive, but it would, in time, lead to very low prices for gasoline, electricity, and other types of energy. What effect would this have on in- terest rates?

5-9 Suppose a new and much more liberal Congress and administration were elected, and their first order of business was to take away the independence of the Federal Reserve System, and to force the Fed to greatly expand the money supply. What effect would this have a. On the level and slope of the yield curve immediately after the announcement? b. On the level and slope of the yield curve that would exist two or three years in the

future? 5-10 It is a fact that the federal government (1) encouraged the development of the savings

and loan industry; (2) virtually forced the industry to make long-term, fixed-interest-rate mortgages; and (3) forced the savings and loans to obtain most of their capital as de- posits that were withdrawable on demand. a. Would the savings and loans have higher profits in a world with a “normal” or an in-

verted yield curve? b. Would the savings and loan industry be better off if the individual institutions sold

their mortgages to federal agencies and then collected servicing fees or if the institu- tions held the mortgages that they originated?

5-11 Suppose interest rates on Treasury bonds rose from 7 to 14 percent as a result of higher interest rates in Europe. What effect would this have on the price of an average com- pany’s common stock?

5-12 What does it mean when it is said that the United States is running a trade deficit? What impact will a trade deficit have on interest rates?

5-13 What are the two leading stock exchanges in the United States today? 5-14 Differentiate between dealer markets and stock markets that have a physical location.

S E L F - T E S T P R O B L E M S ( S O L U T I O N S A P P E A R I N A P P E N D I X B )

Define each of the following terms: a. Money market; capital market b. Primary market; secondary market; initial public offering (IPO) market c. Private markets; public markets d. Spot market; futures market

ST-1 Key terms

S E L F - T E S T P R O B L E M S

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e. Derivatives f. Investment banking house; financial service corporation g. Financial intermediary h. Mutual fund; money market fund i. Physical location exchanges; dealer market; over-the-counter market j. Production opportunities; time preferences for consumption; risk; inflation

k. Real risk-free rate of interest, k*; nominal (quoted) risk-free rate of interest, kRF l. Inflation premium (IP)

m. Default risk premium (DRP) n. Liquidity; liquidity premium (LP) o. Interest rate risk; maturity risk premium (MRP) p. Reinvestment rate risk; country risk q. Term structure of interest rates; yield curve r. “Normal” yield curve; inverted (“abnormal”) yield curve; humped yield curve s. Expectations theory t. Foreign trade deficit; exchange rate risk

Assume that it is January 1, 2002. The rate of inflation is expected to be 4 percent throughout 2002. However, increased government deficits and renewed vigor in the economy are then expected to push inflation rates higher. Investors expect the inflation rate to be 5 percent in 2003, 6 percent in 2004, and 7 percent in 2005. The real risk- free rate, k*, is expected to remain at 2 percent over the next 5 years. Assume that no maturity risk premiums are required on bonds with 5 years or less to maturity. The cur- rent interest rate on 5-year T-bonds is 8 percent. a. What is the average expected inflation rate over the next 4 years? b. What should be the prevailing interest rate on 4-year T-bonds? c. What is the implied expected inflation rate in 2006, or Year 5, given that Treasury

bonds which mature in that year yield 8 percent?

S TA R T E R P R O B L E M S

The real risk-free rate of interest is 3 percent. Inflation is expected to be 2 percent this year and 4 percent during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Trea- sury securities? A Treasury bond that matures in 10 years has a yield of 6 percent. A 10-year corporate bond has a yield of 8 percent. Assume that the liquidity premium on the corporate bond is 0.5 percent. What is the default risk premium on the corporate bond? One-year Treasury securities yield 5 percent. The market anticipates that 1 year from now, 1-year Treasury securities will yield 6 percent. If the pure expectations theory is correct, what should be the yield today for 2-year Treasury securities? The real risk-free rate is 3 percent, and inflation is expected to be 3 percent for the next 2 years. A 2-year Treasury security yields 6.2 percent. What is the maturity risk pre- mium for the 2-year security?

E X A M - T Y P E P R O B L E M S

The problems included in this section are set up in such a way that they could be used as multiple- choice exam problems. Interest rates on 1-year Treasury securities are currently 5.6 percent, while 2-year Trea- sury securities are yielding 6 percent. If the pure expectations theory is correct, what does the market believe will be the yield on 1-year securities 1 year from now? Interest rates on 4-year Treasury securities are currently 7 percent, while interest rates on 6-year Treasury securities are currently 7.5 percent. If the pure expectations theory is correct, what does the market believe that 2-year securities will be yielding 4 years from now? The real risk-free rate is 3 percent. Inflation is expected to be 3 percent this year, 4 per- cent next year, and then 3.5 percent thereafter. The maturity risk premium is estimated to be 0.0005 � (t � 1), where t � number of years to maturity. What is the nominal in- terest rate on a 7-year Treasury note?

5-7 Expected rate of interest

5-6 Expected rate of interest

5-5 Expected rate of interest

5-4 Maturity risk premium

5-3 Expected rate of interest

5-2 Default risk premium

5-1 Expected rate of interest

ST-2 Inflation rates

223

Suppose the annual yield on a 2-year Treasury bond is 4.5 percent, while that on a 1- year bond is 3 percent. k* is 1 percent, and the maturity risk premium is zero. a. Using the expectations theory, forecast the interest rate on a 1-year bond during the

second year. (Hint: Under the expectations theory, the yield on a 2-year bond is equal to the average yield on 1-year bonds in Years 1 and 2.)

b. What is the expected inflation rate in Year 1? Year 2? Assume that the real risk-free rate is 2 percent and that the maturity risk premium is zero. If the nominal rate of interest on 1-year bonds is 5 percent and that on comparable-risk 2- year bonds is 7 percent, what is the 1-year interest rate that is expected for Year 2? What inflation rate is expected during Year 2? Comment on why the average interest rate during the 2-year period differs from the 1-year interest rate expected for Year 2. Assume that the real risk-free rate, k*, is 3 percent and that inflation is expected to be 8 percent in Year 1, 5 percent in Year 2, and 4 percent thereafter. Assume also that all Treasury bonds are highly liquid and free of default risk. If 2-year and 5-year Treasury bonds both yield 10 percent, what is the difference in the maturity risk premiums (MRPs) on the two bonds; that is, what is MRP5 minus MRP2? Due to a recession, the inflation rate expected for the coming year is only 3 percent. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3 percent. Assume that the real risk-free rate is k* � 2% for all maturities and that the expectations theory fully explains the yield curve, so there are no maturity risk premiums. If 3-year Treasury bonds yield 2 percentage points more than 1-year bonds, what inflation rate is expected after Year 1?

P R O B L E M S

Suppose you and most other investors expect the inflation rate to be 7 percent next year, to fall to 5 percent during the following year, and then to remain at a rate of 3 percent thereafter. Assume that the real risk-free rate, k*, will remain at 2 percent and that ma- turity risk premiums on Treasury securities rise from zero on very short-term bonds (those that mature in a few days) to a level of 0.2 percentage point for 1-year securities. Furthermore, maturity risk premiums increase 0.2 percentage point for each year to ma- turity, up to a limit of 1.0 percentage point on 5-year or longer-term T-bonds. a. Calculate the interest rate on 1-, 2-, 3-, 4-, 5-, 10-, and 20-year Treasury securities,

and plot the yield curve. b. Now suppose Exxon Mobil, an AAA-rated company, had bonds with the same matu-

rities as the Treasury bonds. As an approximation, plot an Exxon Mobil yield curve on the same graph with the Treasury bond yield curve. (Hint: Think about the de- fault risk premium on Exxon Mobil’s long-term versus its short-term bonds.)

c. Now plot the approximate yield curve of Long Island Lighting Company, a risky nu- clear utility.

The following yields on U.S. Treasury securities were taken from The Wall Street Jour- nal in September 1999:

TERM RATE

6 months 5.1% 1 year 5.5 2 years 5.6 3 years 5.7 4 years 5.8 5 years 6.0 10 years 6.1 20 years 6.5 30 years 6.3

Plot a yield curve based on these data.

5-13 Yield curves

5-12 Yield curves

5-11 Interest rates

5-10 Maturity risk premium

5-9 Expected rate of interest

5-8 Expected rate of interest

P R O B L E M S

C H A P T E R 5 � T H E F I N A N C I A L E N V I R O N M E N T: M A R K E TS , I N S T I T U T IO N S , A N D I N T E R E S T R AT E S224

In late 1980, the U.S. Commerce Department released new figures that showed that in- flation was running at an annual rate of close to 15 percent. At the time, the prime rate of interest was 21 percent, a record high. However, many investors expected the new Reagan administration to be more effective in controlling inflation than the Carter ad- ministration had been. Moreover, many observers believed that the extremely high in- terest rates and generally tight credit, which resulted from the Federal Reserve System’s attempts to curb the inflation rate, would shortly bring about a recession, which, in turn, would lead to a decline in the inflation rate and also in the interest rate. Assume that at the beginning of 1981, the expected inflation rate for 1981 was 13 percent; for 1982, 9 percent; for 1983, 7 percent; and for 1984 and thereafter, 6 percent. a. What was the average expected inflation rate over the 5-year period 1981–1985?

(Use the arithmetic average.) b. What average nominal interest rate would, over the 5-year period, be expected to

produce a 2 percent real risk-free rate of return on 5-year Treasury securities? c. Assuming a real risk-free rate of 2 percent and a maturity risk premium that starts at

0.1 percent and increases by 0.1 percent each year, estimate the interest rate in Jan- uary 1981 on bonds that mature in 1, 2, 5, 10, and 20 years, and draw a yield curve based on these data.

d. Describe the general economic conditions that could be expected to produce an upward-sloping yield curve.

e. If the consensus among investors in early 1981 had been that the expected inflation rate for every future year was 10 percent (that is, It � It�1 � 10% for t � 1 to �), what do you think the yield curve would have looked like? Consider all the factors that are likely to affect the curve. Does your answer here make you question the yield curve you drew in part c?

S P R E A D S H E E T P R O B L E M

a. Suppose you are considering two possible investment opportunities: a 12-year Trea- sury bond and a 7-year, A-rated corporate bond. The current real risk-free rate is 4 percent, and inflation is expected to be 2 percent for the next two years, 3 percent for the following four years, and 4 percent thereafter. The maturity risk premium is estimated by this formula: MRP � 0.1%(t � 1). The liquidity premium for the corporate bond is estimated to be 0.7 percent. Finally, you may determine the de- fault risk premium, given the company’s bond rating, from the default risk premium table in the text. What yield would you predict for each of these two investments?

b. Given the following Treasury bond yield information from the September 27, 1999, Wall Street Journal, construct a graph of the yield curve as of that date.

MATURITY YIELD

1 year 5.37% 2 years 5.47 3 years 5.65 4 years 5.71 5 years 5.64 10 years 5.75 20 years 6.33 30 years 5.94

c. Based on the information about the corporate bond that was given in part a, calcu- late yields and then construct a new yield curve graph that shows both the Treasury and the corporate bonds.

d. Using the Treasury yield information above, calculate the following forward rates: (1) The 1-year rate, 1 year from now. (2) The 5-year rate, 5 years from now. (3) The 10-year rate, 10 years from now. (4) The 10-year rate, 20 years from now.

5-15 Analyzing interest rates

5-14 Inflation and interest rates

225C Y B E R P R O B L E M

a. Construct four distinct Treasury yield curves using monthly interest rate data for February 1982, 1988, 1993, and 1998. Use the constant maturity interest rates for maturities of 3 months, 6 months, 1 year, 5 years, 10 years, and 30 years.

b. Examine the yield curves you have constructed. What could explain the large vari- ation in the 3-month, risk-free rate over the different time periods?

The information related to the cyberproblems is likely to change over time, due to the release of new information and the ever-changing nature of the World Wide Web. With these changes in mind, we will periodically update these problems on the textbook’s web site. To avoid problems, please check for these updates before proceeding with the cyberproblems. The yield curve is a graph of the term structure of interest rates, which is the rela- tionship of yield and maturity for securities of similar risk. When we think of the yield curve we typically think of the Treasury yield curve as found each day in fi- nancial publications such as The Wall Street Journal. The yield curve changes in both level and shape due to a variety of monetary, economic, and political factors that were discussed in Chapter 5. The Federal Reserve is a useful site for obtaining actual economic and monetary data. Along with other data, you can obtain histori- cal interest rates at this site to construct a yield curve and analyze changes in inter- est rates.

To access information from the Federal Reserve, you will be using FRED (the Federal Reserve Economic Database). First, you must connect to the Federal Reserve Bank of St. Louis web site, which can be found at www.stls.frb.org. From this web page, click on data (near the bottom of the screen), and then select monthly interest rates from the list of database categories. On this page, you will find links to all of the information needed for this cyberproblem.

5-16 Financial environment

SMYTH BARRY & COMPANY

5-17 Financial Markets, Institutions, and Interest Rates Assume that you recently graduated with a degree in fi- nance and have just reported to work as an investment ad- visor at the brokerage firm of Smyth Barry & Co. Your first assignment is to explain the nature of the U.S. financial markets to Michelle Varga, a professional tennis player who has just come to the United States from Mexico. Varga is a highly ranked tennis player who expects to invest substan- tial amounts of money through Smyth Barry. She is also very bright, and, therefore, she would like to understand in general terms what will happen to her money. Your boss has developed the following set of questions that you must ask and answer to explain the U.S. financial system to Varga. a. What is a market? Differentiate between the following

types of markets: physical asset vs. financial markets, spot vs. futures markets, money vs. capital markets, primary vs. secondary markets, and public vs. private markets.

b. What is an initial public offering (IPO) market? c. If Apple Computer decided to issue additional common

stock, and Varga purchased 100 shares of this stock from Merrill Lynch, the underwriter, would this transaction be a primary market transaction or a secondary market transaction? Would it make a difference if Varga pur- chased previously outstanding Apple stock in the dealer market?

d. Describe the three primary ways in which capital is transferred between savers and borrowers.

e. What are the two leading stock markets? Describe the two basic types of stock markets.

f. What do we call the price that a borrower must pay for debt capital? What is the price of equity capital? What are the four most fundamental factors that affect the cost

of money, or the general level of interest rates, in the economy?

g. What is the real risk-free rate of interest (k*) and the nominal risk-free rate (kRF)? How are these two rates measured?

h. Define the terms inflation premium (IP), default risk premium (DRP), liquidity premium (LP), and maturity risk premium (MRP). Which of these premiums is in- cluded when determining the interest rate on (1) short- term U.S. Treasury securities, (2) long-term U.S. Trea- sury securities, (3) short-term corporate securities, and (4) long-term corporate securities? Explain how the pre- miums would vary over time and among the different se- curities listed above.

i. What is the term structure of interest rates? What is a yield curve?

j. Suppose most investors expect the inflation rate to be 5 percent next year, 6 percent the following year, and 8 percent thereafter. The real risk-free rate is 3 percent. The maturity risk premium is zero for bonds that mature in 1 year or less, 0.1 percent for 2-year bonds, and then the MRP increases by 0.1 percent per year thereafter for 20 years, after which it is stable. What is the interest rate on 1-year, 10-year, and 20-year Treasury bonds? Draw a yield curve with these data. What factors can explain why this constructed yield curve is upward sloping?

k. At any given time, how would the yield curve facing an AAA-rated company compare with the yield curve for U.S. Treasury securities? At any given time, how would the yield curve facing a BB-rated company compare with the yield curve for U.S. Treasury securities? Draw a graph to illustrate your answer.

l. What is the pure expectations theory? What does the pure expectations theory imply about the term structure of interest rates?

C H A P T E R 5 � T H E F I N A N C I A L E N V I R O N M E N T: M A R K E TS , I N S T I T U T IO N S , A N D I N T E R E S T R AT E S226

c. (1) Contrast the slope of the February 1982 yield curve with that of February 1993. What do we call a yield curve that has the same shape as the 1982 yield curve? (2) Why might the 1982 yield curve be downward sloping? What does this indicate? (3) What does the 1993 yield curve illustrate about long-term versus short-term interest rates?

d. Contrast the yield curves of 1993 and 1998. Note that the 1998 yield curve is al- most flat, while the 1993 yield curve has a very steep slope. What could account for this difference in slopes?

e. Pretend that you are an investor back in 1988, and you have no knowledge of fu- ture interest rates, except the information given in the yield curve. Use the 1988 yield curve to determine the expected yield on 5-year Treasury bonds five years from 1988 (or the 5-year bond rate in 1993). Then, compare that figure to the actual 5-year bond rate in 1993. Did investors under- or overestimate future in- flation in 1988?

m. Suppose that you observe the following term structure for Treasury securities:

MATURITY YIELD

1 year 6.0% 2 years 6.2 3 years 6.4 4 years 6.5 5 years 6.5

Assume that the pure expectations theory of the term structure is correct. (This implies that you can use the yield curve given above to “back out” the market’s ex- pectations about future interest rates.) What does the market expect will be the interest rate on 1-year securi- ties one year from now? What does the market expect will be the interest rate on 3-year securities two years from now?

n. Finally, Varga is also interested in investing in countries other than the United States. Describe the various types of risks that arise when investing overseas.

227I N T E G R AT E D C A S E

SOURCE: Beard, William Holbrook (1823–1900). New York Historical Society/The Bridgeman Art Library International, Ltd.

CHAPTER

R i s k a nd R a t e s o f R e t u r n6

30

around, you’re not tied to the fickleness of a given

market, stock, or industry. . . . Correlation, in

portfolio-manager speak, helps you diversify properly

because it describes how closely two investments track

each other. If they move in tandem, they’re likely to

suffer from the same bad news. So, you should combine

assets with low correlations.”

U.S. investors tend to think of “the stock market” as

the U.S. stock market. However, U.S. stocks amount to

only 35 percent of the value of all stocks. Foreign

markets have been quite profitable, and they are not

perfectly correlated with U.S. markets. Therefore, global

diversification offers U.S. investors an opportunity to

raise returns and at the same time reduce risk. However,

foreign investing brings some risks of its own, most

notably “exchange rate risk,” which is the danger that

exchange rate shifts will decrease the number of dollars

a foreign currency will buy.

Although the central thrust of the Business Week

article was on ways to measure and then reduce risk, it

did point out that some recently created instruments

that are actually extremely risky have been marketed as

low-risk investments to naive investors. For example,

several mutual funds have advertised that their

portfolios “contain only securities backed by the U.S.

government” but then failed to highlight that the funds

themselves are using financial leverage, are investing in

f someone had invested $1,000 in a portfolio of

large-company stocks in 1925 and then reinvested

all dividends received, his or her investment would

have grown to $2,845,697 by 1999. Over the same

time period, a portfolio of small-company stocks would

have grown even more, to $6,641,505. But if instead he

or she had invested in long-term government bonds, the

$1,000 would have grown to only $40,219, and to a

measly $15,642 for short-term bonds.

Given these numbers, why would anyone invest in

bonds? The answer is, “Because bonds are less risky.”

While common stocks have over the past 74 years

produced considerably higher returns, (1) we cannot be

sure that the past is a prologue to the future, and (2)

stock values are more likely to experience sharp declines

than bonds, so one has a greater chance of losing

money on a stock investment. For example, in 1990 the

average small-company stock lost 21.6 percent of its

value, and large-company stocks also suffered losses.

Bonds, though, provided positive returns that year, as

they almost always do.

Of course, some stocks are riskier than others, and

even in years when the overall stock market goes up,

many individual stocks go down. Therefore, putting all

your money into one stock is extremely risky. According

to a Business Week article, the single best weapon

against risk is diversification: “By spreading your money

NO PA I N NO GA I N

$

I

231

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N232

In this chapter, we start from the basic premise that investors like returns and dis-

like risk. Therefore, people will invest in risky assets only if they expect to receive

higher returns. We define precisely what the term risk means as it relates to in-

vestments, we examine procedures managers use to measure risk, and we discuss

the relationship between risk and return. Then, in Chapters 7, 8, and 9, we extend

these relationships to show how risk and return interact to determine security

prices. Managers must understand these concepts and think about them as they

plan the actions that will shape their firms’ futures.

As you will see, risk can be measured in different ways, and different conclu-

sions about an asset’s riskiness can be reached depending on the measure used.

Risk analysis can be confusing, but it will help if you remember the following:

1. All financial assets are expected to produce cash flows, and the riskiness of an asset is judged in terms of the riskiness of its cash flows.

2. The riskiness of an asset can be considered in two ways: (1) on a stand- alone basis, where the asset’s cash flows are analyzed by themselves, or (2) in a portfolio context, where the cash flows from a number of assets are com- bined, and then the consolidated cash flows are analyzed.1 There is an im- portant difference between stand-alone and portfolio risk, and an asset that has a great deal of risk if held by itself may be much less risky if it is held as part of a larger portfolio.

3. In a portfolio context, an asset’s risk can be divided into two components: (a) diversifiable risk, which can be diversified away and thus is of little con-

1 A portfolio is a collection of investment securities. If you owned some General Motors stock, some Exxon Mobil stock, and some IBM stock, you would be holding a three-stock portfolio. Because di- versification lowers risk, most stocks are held in portfolios.

SOURCES: “Figuring Risk: It’s Not So Scary,” Business Week, November 1, 1993, 154–155; “T-Bill Trauma and the Meaning of Risk,” The Wall Street Journal, February 12, 1993, C1; and Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2000 Yearbook (Chicago: Ibbotson Associates, 2000).

“derivatives,” or are taking some other action that

boosts current yields but exposes investors to huge

risks.

When you finish this chapter, you should understand

what risk is, how it is measured, and what actions can

be taken to minimize it, or at least to ensure that you

are adequately compensated for bearing it. �

233

cern to diversified investors, and (b) market risk, which reflects the risk of a general stock market decline and which cannot be eliminated by diversifi- cation, hence does concern investors. Only market risk is relevant — diver- sifiable risk is irrelevant to rational investors because it can be eliminated.

4. An asset with a high degree of relevant (market) risk must provide a rela- tively high expected rate of return to attract investors. Investors in general are averse to risk, so they will not buy risky assets unless those assets have high expected returns.

5. In this chapter, we focus on financial assets such as stocks and bonds, but the concepts discussed here also apply to physical assets such as computers, trucks, or even whole plants. �

I N V E S T M E N T R E T U R N S

With most investments, an individual or business spends money today with the expectation of earning even more money in the future. The concept of return provides investors with a convenient way of expressing the financial perfor- mance of an investment. To illustrate, suppose you buy 10 shares of a stock for $1,000. The stock pays no dividends, but at the end of one year, you sell the stock for $1,100. What is the return on your $1,000 investment?

One way of expressing an investment return is in dollar terms. The dollar return is simply the total dollars received from the investment less the amount invested:

Dollar return � Amount received � Amount invested

� $1,100 � $1,000

� $100.

If at the end of the year you had sold the stock for only $900, your dollar re- turn would have been �$100.

Although expressing returns in dollars is easy, two problems arise: (1) To make a meaningful judgment about the return, you need to know the scale (size) of the investment; a $100 return on a $100 investment is a good return (assuming the investment is held for one year), but a $100 return on a $10,000 investment would be a poor return. (2) You also need to know the timing of the return; a $100 return on a $100 investment is a very good return if it occurs after one year, but the same dollar return after 20 years would not be very good.

The solution to the scale and timing problems is to express investment results as rates of return, or percentage returns. For example, the rate of return on the 1-year stock investment, when $1,100 is received after one year, is 10 percent:

The rate of return calculation “standardizes” the return by considering the re- turn per unit of investment. In this example, the return of 0.10, or 10 percent, indicates that each dollar invested will earn 0.10($1.00) � $0.10. If the rate of

� 0.10 � 10%.

� Dollar return

Amount invested �

$100 $1,000

Rate of return � Amount received � Amount invested

Amount invested

I N V E S T M E N T R E T U R N S

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N234

return had been negative, this would indicate that the original investment was not even recovered. For example, selling the stock for only $900 results in a �10 percent rate of return, which means that each dollar invested lost 10 cents.

Note also that a $10 return on a $100 investment produces a 10 percent rate of return, while a $10 return on a $1,000 investment results in a rate of return of only 1 percent. Thus, the percentage return takes account of the size of the investment.

Expressing rates of return on an annual basis, which is typically done in practice, solves the timing problem. A $10 return after one year on a $100 in- vestment results in a 10 percent annual rate of return, while a $10 return after five years yields only a 1.9 percent annual rate of return. We will discuss all this in detail in Chapter 7, which deals with the time value of money.

Although we illustrated return concepts with one outflow and one inflow, in later chapters we demonstrate that rate of return concepts can easily be applied in situations where multiple cash flows occur over time. For example, when Intel makes an investment in new chip-making technology, the investment is made over several years and the resulting inflows occur over even more years. For now, it is sufficient to recognize that the rate of return solves the two major problems associated with dollar returns, size and timing. Therefore, the rate of return is the most common measure of investment performance.

SELF-TEST QUESTIONS

Differentiate between dollar return and rate of return.

Why is the rate of return superior to the dollar return in terms of account- ing for the size of investment and the timing of cash flows?

S TA N D - A L O N E R I S K

Risk is defined in Webster’s as “a hazard; a peril; exposure to loss or injury.” Thus, risk refers to the chance that some unfavorable event will occur. If you engage in skydiving, you are taking a chance with your life — skydiving is risky. If you bet on the horses, you are risking your money. If you invest in specula- tive stocks (or, really, any stock), you are taking a risk in the hope of making an appreciable return.

An asset’s risk can be analyzed in two ways: (1) on a stand-alone basis, where the asset is considered in isolation, and (2) on a portfolio basis, where the asset is held as one of a number of assets in a portfolio. Thus, an asset’s stand-alone risk is the risk an investor would face if he or she held only this one asset. Ob- viously, most assets are held in portfolios, but it is necessary to understand stand-alone risk in order to understand risk in a portfolio context.

To illustrate the riskiness of financial assets, suppose an investor buys $100,000 of short-term Treasury bills with an expected return of 5 percent. In this case, the rate of return on the investment, 5 percent, can be estimated quite precisely, and the investment is defined as being essentially risk free. However, if the $100,000 were invested in the stock of a company just being organized to prospect for oil in the mid-Atlantic, then the investment’s return could not be

Risk The chance that some unfavorable event will occur.

Stand-Alone Risk The risk an investor would face if he or she held only one asset.

235

estimated precisely. One might analyze the situation and conclude that the ex- pected rate of return, in a statistical sense, is 20 percent, but the investor should also recognize that the actual rate of return could range from, say, �1,000 per- cent to �100 percent. Because there is a significant danger of actually earning much less than the expected return, the stock would be relatively risky.

No investment will be undertaken unless the expected rate of return is high enough to compensate the investor for the perceived risk of the investment. In our example, it is clear that few if any investors would be willing to buy the oil company’s stock if its expected return were the same as that of the T-bill.

Risky assets rarely produce their expected rates of return — generally, risky assets earn either more or less than was originally expected. Indeed, if assets al- ways produced their expected returns, they would not be risky. Investment risk, then, is related to the probability of actually earning a low or negative return — the greater the chance of a low or negative return, the riskier the investment. However, risk can be defined more precisely, and we do so in the next section.

PROBABIL I TY DISTR IBUT IONS

An event’s probability is defined as the chance that the event will occur. For ex- ample, a weather forecaster might state, “There is a 40 percent chance of rain today and a 60 percent chance that it will not rain.” If all possible events, or outcomes, are listed, and if a probability is assigned to each event, the listing is called a probability distribution. For our weather forecast, we could set up the following probability distribution:

OUTCOME PROBABILITY (1) (2)

Rain 0.4 � 40% No rain 0.6 � 60%

1.0 � 100%

The possible outcomes are listed in Column 1, while the probabilities of these outcomes, expressed both as decimals and as percentages, are given in Col- umn 2. Notice that the probabilities must sum to 1.0, or 100 percent.

Probabilities can also be assigned to the possible outcomes (or returns) from an investment. If you buy a bond, you expect to receive interest on the bond plus a return of your original investment, and those payments will provide you with a rate of return on your investment. The possible outcomes from this in- vestment are (1) that the issuer will make the required payments or (2) that the issuer will default on the payments. The higher the probability of default, the riskier the bond, and the higher the risk, the higher the required rate of return. If you invest in a stock instead of buying a bond, you will again expect to earn a return on your money. A stock’s return will come from dividends plus capital gains. Again, the riskier the stock — which means the higher the probability that the firm will fail to perform as you expected — the higher the expected re- turn must be to induce you to invest in the stock.

With this in mind, consider the possible rates of return (dividend yield plus capital gain or loss) that you might earn next year on a $10,000 investment in the stock of either Martin Products Inc. or U.S. Water Company. Martin man-

S TA N D - A L O N E R I S K

Probability Distribution A listing of all possible outcomes, or events, with a probability (chance of occurrence) assigned to each outcome.

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N236

ufactures and distributes computer terminals and equipment for the rapidly growing data transmission industry. Because it faces intense competition, its new products may or may not be competitive in the marketplace, so its future earnings cannot be predicted very well. Indeed, some new company could de- velop better products and literally bankrupt Martin. U.S. Water, on the other hand, supplies an essential service, and because it has city franchises that pro- tect it from competition, its sales and profits are relatively stable and pre- dictable.

The rate-of-return probability distributions for the two companies are shown in Table 6-1. There is a 30 percent chance of strong demand, in which case both companies will have high earnings, pay high dividends, and enjoy capital gains. There is a 40 percent probability of normal demand and moder- ate returns, and there is a 30 percent probability of weak demand, which will mean low earnings and dividends as well as capital losses. Notice, however, that Martin Products’ rate of return could vary far more widely than that of U.S. Water. There is a fairly high probability that the value of Martin’s stock will drop substantially, resulting in a 70 percent loss, while there is no chance of a loss for U.S. Water.2

EXPECTED RATE OF RETURN

If we multiply each possible outcome by its probability of occurrence and then sum these products, as in Table 6-2, we have a weighted average of outcomes. The weights are the probabilities, and the weighted average is the expected rate of return, k̂ , called “k-hat.”3 The expected rates of return for both Mar- tin Products and U.S. Water are shown in Table 6-2 to be 15 percent. This type of table is known as a payoff matrix.

T A B L E 6 - 1

R AT E O F R E T U R N O N S TO C K I F T H I S D E M A N D O C C U R S

DEMAND FOR THE PROBABILITY OF THIS COMPANY’S PRODUCTS DEMAND OCCURRING MARTIN PRODUCTS U.S. WATER

Strong 0.3 100% 20% Normal 0.4 15 15 Weak 0.3 (70) 10

1.0

Probability Distributions for Martin Products and U.S. Water

2 It is, of course, completely unrealistic to think that any stock has no chance of a loss. Only in hy- pothetical examples could this occur. To illustrate, the price of Columbia Gas’s stock dropped from $34.50 to $20.00 in just three hours a few years ago. All investors were reminded that any stock is exposed to some risk of loss, and those investors who bought Columbia Gas learned that lesson the hard way. 3 In Chapters 8 and 9, we will use kd and ks to signify the returns on bonds and stocks, respectively. However, this distinction is unnecessary in this chapter, so we just use the general term, k, to sig- nify the expected return on an investment.

Expected Rate of Return, k̂ The rate of return expected to be realized from an investment; the weighted average of the probability distribution of possible results.

237

The expected rate of return calculation can also be expressed as an equation that does the same thing as the payoff matrix table:4

Expected rate of return � k̂ � P1k1 � P2k2 � � � � � Pnkn

. (6-1)

Here ki is the ith possible outcome, Pi is the probability of the ith outcome, and n is the number of possible outcomes. Thus, k̂ is a weighted average of the pos- sible outcomes (the ki values), with each outcome’s weight being its probability of occurrence. Using the data for Martin Products, we obtain its expected rate of return as follows:

k̂ � P1(k1) � P2(k2) � P3(k3)

� 0.3(100%) � 0.4(15%) � 0.3(�70%)

� 15%.

U.S. Water’s expected rate of return is also 15 percent:

k̂ � 0.3(20%) � 0.4(15%) � 0.3(10%)

� 15%.

We can graph the rates of return to obtain a picture of the variability of pos- sible outcomes; this is shown in the Figure 6-1 bar charts. The height of each bar signifies the probability that a given outcome will occur. The range of probable returns for Martin Products is from �70 to �100 percent, with an ex- pected return of 15 percent. The expected return for U.S. Water is also 15 per- cent, but its range is much narrower.

Thus far, we have assumed that only three situations can exist: strong, nor- mal, and weak demand. Actually, of course, demand could range from a deep de- pression to a fantastic boom, and there are an unlimited number of possibilities

� a n

i�1 Piki

S TA N D - A L O N E R I S K

T A B L E 6 - 2

M A R T I N P R O D U C T S U . S . WAT E R

DEMAND FOR PROBABILITY RATE OF RETURN RATE OF RETURN THE COMPANY’S OF THIS DEMAND IF THIS DEMAND PRODUCT: IF THIS DEMAND PRODUCT: PRODUCTS OCCURRING OCCURS (2) � (3) OCCURS (2) � (5)

(1) (2) (3) � (4) (5) � (6)

Strong 0.3 100% 30% 20% 6% Normal 0.4 15 6 15 6 Weak 0.3 (70) (21)1 10 13%

1.0 k̂ � 15% k̂ � 15%

Calculation of Expected Rates of Return: Payoff Matrix

4 The second form of the equation is simply a shorthand expression in which sigma (�) means “sum up,” or add the values of n factors. If i � 1, then Piki � P1k1; if i � 2, then Piki � P2k2; and so

on until i � n, the last possible outcome. The symbol simply says, “Go through the following

process: First, let i � 1 and find the first product; then let i � 2 and find the second product; then continue until each individual product up to i � n has been found, and then add these individual products to find the expected rate of return.”

a n

i�1

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N238

in between. Suppose we had the time and patience to assign a probability to each possible level of demand (with the sum of the probabilities still equaling 1.0) and to assign a rate of return to each stock for each level of demand. We would have a table similar to Table 6-1, except that it would have many more entries in each column. This table could be used to calculate expected rates of return as shown previously, and the probabilities and outcomes could be ap- proximated by continuous curves such as those presented in Figure 6-2. Here we have changed the assumptions so that there is essentially a zero probability that Martin Products’ return will be less than �70 percent or more than 100 percent, or that U.S. Water’s return will be less than 10 percent or more than 20 percent, but virtually any return within these limits is possible.

The tighter, or more peaked, the probability distribution, the more likely it is that the actual outcome will be close to the expected value, and, consequently, the less likely it is that the actual return will end up far below the expected return. Thus, the tighter the probability distribution, the lower the risk assigned to a stock. Since U.S. Water has a relatively tight probability distribution, its actual return is likely to be closer to its 15 percent expected return than is that of Martin Products.

MEASURING STAND-ALONE RISK: THE STANDARD DEVIAT ION

Risk is a difficult concept to grasp, and a great deal of controversy has sur- rounded attempts to define and measure it. However, a common definition, and one that is satisfactory for many purposes, is stated in terms of probability distri-

F I G U R E 6 - 1 Probability Distributions of Martin Products’ and U.S. Water’s Rates of Return

Probability of Occurrence

a. Martin Products

Rate of Return (%)

100150–70

0.4

0.3

0.2

0.1

Expected Rate of Return

Probability of Occurrence

b. U.S. Water

Rate of Return (%)

20150 10

0.4

0.3

0.2

0.1

Expected Rate of Return

239

butions such as those presented in Figure 6-2: The tighter the probability distribu- tion of expected future returns, the smaller the risk of a given investment. According to this definition, U.S. Water is less risky than Martin Products because there is a smaller chance that its actual return will end up far below its expected return.

To be most useful, any measure of risk should have a definite value — we need a measure of the tightness of the probability distribution. One such mea- sure is the standard deviation, the symbol for which is �, pronounced “sigma.” The smaller the standard deviation, the tighter the probability distribution, and, accordingly, the lower the riskiness of the stock. To calculate the standard deviation, we proceed as shown in Table 6-3, taking the following steps:

1. Calculate the expected rate of return:

For Martin, we previously found k̂ � 15%. 2. Subtract the expected rate of return (k̂) from each possible outcome (ki)

to obtain a set of deviations about k̂ as shown in Column 1 of Table 6-3:

Deviationi � ki � k̂ .

Expected rate of return � k̂ � a n

i�1 Pik i.

S TA N D - A L O N E R I S K

F I G U R E 6 - 2 Continuous Probability Distributions of Martin Products’ and U.S. Water’s Rates of Return

Probability Density

U.S. Water

Martin Products

100150–70

Expected Rate of Return

Rate of Return (%)

NOTE: The assumptions regarding the probabilities of various outcomes have been changed from those in Figure 6-1. There the probability of obtaining exactly 15 percent was 40 percent; here it is much smaller because there are many possible outcomes instead of just three. With continuous distributions, it is more appropriate to ask what the probability is of obtaining at least some specified rate of return than to ask what the probability is of obtaining exactly that rate. This topic is covered in detail in statistics courses.

Standard Deviation, � A statistical measure of the variability of a set of observations.

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N240

3. Square each deviation, then multiply the result by the probability of oc- currence for its related outcome, and then sum these products to obtain the variance of the probability distribution as shown in Columns 2 and 3 of the table:

(6-2)

4. Finally, find the square root of the variance to obtain the standard devia- tion:

(6-3)

Thus, the standard deviation is essentially a weighted average of the deviations from the expected value, and it provides an idea of how far above or below the expected value the actual value is likely to be. Martin’s standard deviation is seen in Table 6-3 to be � � 65.84%. Using these same procedures, we find U.S. Water’s standard deviation to be 3.87 percent. Martin Products has the larger standard deviation, which indicates a greater variation of returns and thus a greater chance that the expected return will not be realized. Therefore, Martin Products is a riskier investment than U.S. Water when held alone.

If a probability distribution is normal, the actual return will be within �1 standard deviation of the expected return 68.26 percent of the time. Figure 6-3 illustrates this point, and it also shows the situation for �2� and �3�. For Martin Products, k̂� 15% and � � 65.84%, whereas k̂� 15% and � � 3.87% for U.S. Water. Thus, if the two distributions were normal, there would be a 68.26 percent probability that Martin’s actual return would be in the range of 15 � 65.84 percent, or from �50.84 to 80.84 percent. For U.S. Water, the 68.26 percent range is 15 � 3.87 percent, or from 11.13 to 18.87 percent. With such a small �, there is only a small probability that U.S. Water’s return would be significantly less than expected, so the stock is not very risky. For the aver- age firm listed on the New York Stock Exchange, � has generally been in the range of 35 to 40 percent in recent years.5

Standard deviation � � � B ani�1 (ki � k̂)2Pi.

Variance � �2 � a n

i�1 (k i � k̂)

2Pi.

T A B L E 6 - 3

ki � k̂ (ki � k̂) 2 (ki � k̂)

2Pi (1) (2) (3)

100 � 15 � 85 7,225 (7,225)(0.3) � 2,167.5 15 � 15 � 0 0 (0)(0.4) � 0.0

�70 � 15 � �85 7,225 (7,225)(0.3) � 2,167.5 Variance � �2 � 4,335.0

Standard deviation � � � ���2� � �4�,3�3�5� � 65.84%.

Calculating Martin Products’ Standard Deviation

Variance, �2

The square of the standard deviation.

Wilshire Associates provides a download site for various returns series for indexes such as the Wilshire 5000 and the

Wilshire 4500 at http:// www.wilshire.com/indexes/wilshire_ indexes.htm in Microsoft ExcelTM

format.

5 In the example, we described the procedure for finding the mean and standard deviation when the data are in the form of a known probability distribution. If only sample returns data over some past period are available, the standard deviation of returns can be estimated using this formula:

(footnote continues)

241S TA N D - A L O N E R I S K

F I G U R E 6 - 3 Probability Ranges for a Normal Distribution

+3σ+2σ+1σ–1σ k–2σ–3σ ˆ

68.26%

95.46% 99.74%

NOTES: a. The area under the normal curve always equals 1.0, or 100 percent. Thus, the areas under any pair of

normal curves drawn on the same scale, whether they are peaked or flat, must be equal. b. Half of the area under a normal curve is to the left of the mean, indicating that there is a 50

percent probability that the actual outcome will be less than the mean, and half is to the right of k, indicating a 50 percent probability that it will be greater than the mean.

c. Of the area under the curve, 68.26 percent is within �1� of the mean, indicating that the probability is 68.26 percent that the actual outcome will be within the range k � 1� to k � 1�.

d. Procedures exist for finding the probability of other ranges. These procedures are covered in statistics courses.

e. For a normal distribution, the larger the value of �, the greater the probability that the actual outcome will vary widely from, and hence perhaps be far below, the expected, or most likely, outcome. Since the probability of having the actual result turn out to be far below the expected result is one definition of risk, and since � measures this probability, we can use � as a measure of risk. This definition may not be a good one, however, if we are dealing with an asset held in a diversified portfolio. This point is covered later in the chapter.

(6-3a)

Here k� t (“k bar t”) denotes the past realized rate of return in Period t, and k� Avg is the average an- nual return earned during the last n years. Here is an example:

YEAR k —

t

1999 15% 2000 �5 2001 20

� B3502 � 13.2%. Estimated � (or S) �C (15 � 10)2 � (�5 � 10)2 � (20 � 10)23 � 1

kAvg � (15 � 5 � 20)

3 � 10.0%.

Estimated � � S �R a n

t�1 (kt � kAvg)

2

n � 1 .

(footnote continues)

(Footnote 5 continued)

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N242

MEASURING STAND-ALONE RISK: THE COEFF IC IENT OF VARIAT ION

If a choice has to be made between two investments that have the same expected returns but different standard deviations, most people would choose the one with the lower standard deviation and, therefore, the lower risk. Similarly, given a choice between two investments with the same risk (standard deviation) but different expected returns, investors would generally prefer the investment with the higher expected return. To most people, this is common sense — return is “good,” risk is “bad,” and, consequently, investors want as much return and as little risk as possible. But how do we choose between two investments if one has the higher expected return but the other the lower standard deviation? To help answer this question, we use another measure of risk, the coefficient of varia- tion (CV), which is the standard deviation divided by the expected return:

(6-4)

The coefficient of variation shows the risk per unit of return, and it provides a more meaningful basis for comparison when the expected returns on two alternatives are not the same. Since U.S. Water and Martin Products have the same expected return, the coefficient of variation is not necessary in this case. The firm with the larger standard deviation, Martin, must have the larger coefficient of variation when the means are equal. In fact, the coefficient of variation for Martin is 65.84/15 � 4.39 and that for U.S. Water is 3.87/15 � 0.26. Thus, Martin is almost 17 times riskier than U.S. Water on the basis of this criterion.

For a case where the coefficient of variation is necessary, consider Projects X and Y in Figure 6-4. These projects have different expected rates of return and different standard deviations. Project X has a 60 percent expected rate of return and a 15 percent standard deviation, while Project Y has an 8 percent expected return but only a 3 percent standard deviation. Is Project X riskier, on a rela- tive basis, because it has the larger standard deviation? If we calculate the coef- ficients of variation for these two projects, we find that Project X has a coeffi- cient of variation of 15/60 � 0.25, and Project Y has a coefficient of variation of 3/8 � 0.375. Thus, we see that Project Y actually has more risk per unit of return than Project X, in spite of the fact that X’s standard deviation is larger. Therefore, even though Project Y has the lower standard deviation, according to the coefficient of variation it is riskier than Project X.

Project Y has the smaller standard deviation, hence the more peaked proba- bility distribution, but it is clear from the graph that the chances of a really low

Coefficient of variation � CV � �

k̂ .

Coefficient of Variation (CV) Standardized measure of the risk per unit of return; calculated as the standard deviation divided by the expected return.

The historical � is often used as an estimate of the future �. Much less often, and generally incor- rectly, k� Avg for some past period is used as an estimate of k, the expected future return. Because past variability is likely to be repeated, � may be a good estimate of future risk, but it is much less rea- sonable to expect that the past level of return (which could have been as high as �100% or as low as �50%) is the best expectation of what investors think will happen in the future.

Equation 6-3a is built into all financial calculators, and it is very easy to use. We simply enter the rates of return and press the key marked S (or Sx) to get the standard deviation. Note, though, that calculators have no built-in formula for finding � where probabilistic data are involved; there you must go through the process outlined in Table 6-3 and Equation 6-3. The same situation holds for computer spreadsheet programs.

(Footnote 5 continued)

243

return are higher for Y than for X because X’s expected return is so high. Be- cause the coefficient of variation captures the effects of both risk and return, it is a better measure for evaluating risk in situations where investments have sub- stantially different expected returns.

RISK AVERS ION AND REQUIRED RETURNS

Suppose you have worked hard and saved $1 million, which you now plan to in- vest. You can buy a 5 percent U.S. Treasury note, and at the end of one year you will have a sure $1.05 million, which is your original investment plus $50,000 in interest. Alternatively, you can buy stock in R&D Enterprises. If R&D’s research programs are successful, your stock will increase in value to $2.1 million. How- ever, if the research is a failure, the value of your stock will go to zero, and you will be penniless. You regard R&D’s chances of success or failure as being 50-50, so the expected value of the stock investment is 0.5($0) � 0.5($2,100,000) � $1,050,000. Subtracting the $1 million cost of the stock leaves an expected profit of $50,000, or an expected (but risky) 5 percent rate of return:

Thus, you have a choice between a sure $50,000 profit (representing a 5 per- cent rate of return) on the Treasury note and a risky expected $50,000 profit (also representing a 5 percent expected rate of return) on the R&D Enterprises stock. Which one would you choose? If you choose the less risky investment, you are

� $50,000

$1,000,000 � 5%.

� $1,050,000 � $1,000,000

$1,000,000

Expected rate of return � Expected ending value � Cost

Cost

S TA N D - A L O N E R I S K

F I G U R E 6 - 4 Comparison of Probability Distributions and Rates of Return for Projects X and Y

0 8 60

Probability Density

Project Y

Project X

Expected Rate of Return (%)

THE TRADE-OFF BETWEEN RISK AND RETURN

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N244

risk averse. Most investors are indeed risk averse, and certainly the average investor is risk averse with regard to his or her “serious money.” Because this is a well-documented fact, we shall assume risk aversion throughout the remainder of the book.

What are the implications of risk aversion for security prices and rates of re- turn? The answer is that, other things held constant, the higher a security’s risk, the lower its price and the higher its required return. To see how risk aversion af- fects security prices, look back at Figure 6-2 and consider again U.S. Water and

The table accompanying this box summarizes the historicaltrade-off between risk and return for different classes of in- vestments from 1926 through 1999. As the table shows, those assets that produced the highest average returns also had the highest standard deviations and the widest ranges of returns. For example, small-company stocks had the highest average an- nual return, 17.6 percent, but their standard deviation of re- turns, 33.6 percent, was also the highest. By contrast, U.S. Treasury bills had the lowest standard deviation, 3.2 percent, but they also had the lowest average return, 3.8 percent.

When deciding among alternative investments, one needs to be aware of the trade-off between risk and return. While there is certainly no guarantee that history will repeat itself, returns observed in the past are a good starting point for estimating investments’ returns in the future. Likewise, the standard devi- ations of past returns provide useful insights into the risks of

different investments. For T-bills, however, the standard devia- tion needs to be interpreted carefully. Note that the table shows that Treasury bills have a positive standard deviation, which indicates some risk. However, if you invested in a one- year Treasury bill and held it for the full year, your realized re- turn would be the same regardless of what happened to the economy that year, and thus the standard deviation of your re- turn would be zero. So, why does the table show a 3.2 percent standard deviation for T-bills, which indicates some risk? In fact, a T-bill is riskless if you hold it for one year, but if you in- vest in a rolling portfolio of one-year T-bills and hold the port- folio for a number of years, your investment income will vary depending on what happens to the level of interest rates in each year. So, while you can be sure of the return you will earn on a T-bill in a given year, you cannot be sure of the return you will earn on a portfolio of T-bills over a period of time.

Risk Aversion Risk-averse investors dislike risk and require higher rates of return as an inducement to buy riskier securities.

Selected Realized Returns, 1926–1999

AVERAGE RETURN STANDARD DEVIATION

Small-company stocks 17.6% 33.6% Large-company stocks 13.3 20.1 Long-term corporate bonds 5.9 8.7 Long-term goverment bonds 5.5 9.3 U.S. Treasury bills 3.8 3.2

Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2000 Yearbook (Chicago: Ibbotson Associates, 2000), 14.

245

Martin Products stocks. Suppose each stock sold for $100 per share and each had an expected rate of return of 15 percent. Investors are averse to risk, so under these conditions there would be a general preference for U.S. Water. People with money to invest would bid for U.S. Water rather than Martin stock, and Martin’s stockholders would start selling their stock and using the money to buy U.S. Water. Buying pressure would drive up U.S. Water’s stock, and selling pres- sure would simultaneously cause Martin’s price to decline.

These price changes, in turn, would cause changes in the expected rates of re- turn on the two securities. Suppose, for example, that U.S. Water’s stock price was bid up from $100 to $150, whereas Martin’s stock price declined from $100 to $75. This would cause U.S. Water’s expected return to fall to 10 percent, while Mar- tin’s expected return would rise to 20 percent. The difference in returns, 20% � 10% � 10%, is a risk premium, RP, which represents the additional compensa- tion investors require for assuming the additional risk of Martin stock.

This example demonstrates a very important principle: In a market dominated by risk-averse investors, riskier securities must have higher expected returns, as esti- mated by the marginal investor, than less risky securities. If this situation does not exist, buying and selling in the market will force it to occur. We will consider the question of how much higher the returns on risky securities must be later in the chapter, after we see how diversification affects the way risk should be measured. Then, in Chapters 8 and 9, we will see how risk-adjusted rates of return affect the prices investors are willing to pay for different securities.

S TA N D - A L O N E R I S K

Risk Premium, RP The difference between the expected rate of return on a given risky asset and that on a less risky asset.

SELF-TEST QUESTIONS

What does “investment risk” mean?

Set up an illustrative probability distribution for an investment.

What is a payoff matrix?

Which of the two stocks graphed in Figure 6-2 is less risky? Why?

How does one calculate the standard deviation?

Which is a better measure of risk if assets have different expected returns: (1) the standard deviation or (2) the coefficient of variation? Why?

Explain the following statement: “Most investors are risk averse.”

How does risk aversion affect rates of return?

R I S K I N A P O R T F O L I O C O N T E X T

In the preceding section, we considered the riskiness of assets held in isolation. Now we analyze the riskiness of assets held in portfolios. As we shall see, an asset held as part of a portfolio is less risky than the same asset held in isolation. Accordingly, most financial assets are held as parts of portfolios. Banks, pension funds, insurance companies, mutual funds, and other financial institutions are

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N246

required by law to hold diversified portfolios. Even individual investors — at least those whose security holdings constitute a significant part of their total wealth — generally hold portfolios, not the stock of only one firm. This being the case, from an investor’s standpoint the fact that a particular stock goes up or down is not very important; what is important is the return on his or her port- folio, and the portfolio’s risk. Logically, then, the risk and return of an individual se- curity should be analyzed in terms of how that security affects the risk and return of the portfolio in which it is held.

To illustrate, Pay Up Inc. is a collection agency company that operates na- tionwide through 37 offices. The company is not well known, its stock is not very liquid, its earnings have fluctuated quite a bit in the past, and it doesn’t pay a dividend. All this suggests that Pay Up is risky and that its required rate of re- turn, k, should be relatively high. However, Pay Up’s required rate of return in 2001, and all other years, was quite low in comparison to those of most other companies. This indicates that investors regard Pay Up as being a low-risk company in spite of its uncertain profits. The reason for this counterintuitive fact has to do with diversification and its effect on risk. Pay Up’s earnings rise during recessions, whereas most other companies’ earnings tend to decline when the economy slumps. It’s like fire insurance — it pays off when other things go bad. Therefore, adding Pay Up to a portfolio of “normal” stocks tends to stabilize returns on the entire portfolio, thus making the portfolio less risky.

PORTFOLIO RETURNS

The expected return on a portfolio, k̂p, is simply the weighted average of the expected returns on the individual assets in the portfolio, with the weights being the fraction of the total portfolio invested in each asset:

k̂p � w1k̂1 � w2k̂2 � � � � � wnk̂n

(6-5)

Here the k̂ i’s are the expected returns on the individual stocks, the wi’s are the weights, and there are n stocks in the portfolio. Note (1) that wi is the fraction of the portfolio’s dollar value invested in Stock i (that is, the value of the in- vestment in Stock i divided by the total value of the portfolio) and (2) that the wi’s must sum to 1.0.

Assume that in August 2001, a security analyst estimated that the following returns could be expected on the stocks of four large companies:

EXPECTED RETURN, k̂

Microsoft 12.0% General Electric 11.5 Pfizer 10.0 Coca-Cola 9.5

If we formed a $100,000 portfolio, investing $25,000 in each stock, the ex- pected portfolio return would be 10.75%:

� a n

i�1 wik̂i.

Expected Return on a Portfolio, k̂p The weighted average of the expected returns on the assets held in the portfolio.

247

k̂p � w1k̂1 � w2k̂2 � w3k̂3 � w4k̂4 � 0.25(12%) � 0.25(11.5%) � 0.25(10%) � 0.25(9.5%)

� 10.75%.

Of course, after the fact and a year later, the actual realized rates of return, k�, on the individual stocks — the k� i, or “k-bar,” values — will almost certainly be different from their expected values, so k� p will be different from k̂ p � 10.75%. For example, Coca-Cola stock might double in price and provide a return of �100%, whereas Microsoft stock might have a terrible year, fall sharply, and have a return of �75%. Note, though, that those two events would be some- what offsetting, so the portfolio’s return might still be close to its expected re- turn, even though the individual stocks’ actual returns were far from their ex- pected returns.

PORTFOLIO RISK

As we just saw, the expected return on a portfolio is simply the weighted aver- age of the expected returns on the individual assets in the portfolio. However, unlike returns, the riskiness of a portfolio, �p, is generally not the weighted average of the standard deviations of the individual assets in the portfolio; the portfolio’s risk will be smaller than the weighted average of the assets’ �’s. In fact, it is theoretically possible to combine stocks that are individually quite risky as measured by their standard deviations and to form a portfolio that is completely riskless, with �p � 0.

To illustrate the effect of combining assets, consider the situation in Figure 6-5. The bottom section gives data on rates of return for Stocks W and M in- dividually, and also for a portfolio invested 50 percent in each stock. The three top graphs show plots of the data in a time series format, and the lower graphs show the probability distributions of returns, assuming that the future is ex- pected to be like the past. The two stocks would be quite risky if they were held in isolation, but when they are combined to form Portfolio WM, they are not risky at all. (Note: These stocks are called W and M because the graphs of their returns in Figure 6-5 resemble a W and an M.)

The reason Stocks W and M can be combined to form a riskless portfolio is that their returns move countercyclically to each other — when W’s returns fall, those of M rise, and vice versa. The tendency of two variables to move to- gether is called correlation, and the correlation coefficient, r, measures this tendency.6 In statistical terms, we say that the returns on Stocks W and M are perfectly negatively correlated, with r � �1.0.

The opposite of perfect negative correlation, with r � �1.0, is perfect positive correlation, with r � �1.0. Returns on two perfectly positively correlated stocks

R I S K I N A P O R T F O L I O C O N T E X T

Realized Rate of Return, k� The return that was actually earned during some past period. The actual return (k� ) usually turns out to be different from the expected return (k̂) except for riskless assets.

Correlation The tendency of two variables to move together.

Correlation Coefficient, r A measure of the degree of relationship between two variables.

6 The correlation coefficient, r, can range from �1.0, denoting that the two variables move up and down in perfect synchronization, to �1.0, denoting that the variables always move in exactly op- posite directions. A correlation coefficient of zero indicates that the two variables are not related to each other — that is, changes in one variable are independent of changes in the other.

It is easy to calculate correlation coefficients with a financial calculator. Simply enter the returns on the two stocks and then press a key labeled “r.” For W and M, r � �1.0.

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N248

F I G U R E 6 - 5 Rate of Return Distributions for Two Perfectly Negatively Correlated Stocks (r � �1.0) and for Portfolio WM

k (%) W _

a. Rates of Return

Stock W

2001

25

0

–10

15

k (%)M _

Stock M

2001

25

0

–10

15

k (%)p _

Portfolio WM

2001

25

0

–10

15

Percent150

(= k )W

Probability Density

Stock W

b. Probability Distributions of Returns

Percent150

Probability Density

Stock M

Percent150

Probability Density

Portfolio WM

(= k )M (= k )pˆ ˆˆ

STOCK W STOCK M PORTFOLIO WM YEAR (k�W) (k�M) (k�p)

1997 40.0% (10.0%) 15.0% 1998 (10.0) 40.0 15.0 1999 35.0 (5.0) 15.0 2000 (5.0) 35.0 15.0 2001 15.0% 15.0% 15.0%

Average return 15.0% 15.0% 15.0% Standard deviation 22.6% 22.6% 0.0%

249

(M and M�) would move up and down together, and a portfolio consisting of two such stocks would be exactly as risky as the individual stocks. This point is illustrated in Figure 6-6, where we see that the portfolio’s standard deviation is equal to that of the individual stocks. Thus, diversification does nothing to reduce risk if the portfolio consists of perfectly positively correlated stocks.

Figures 6-5 and 6-6 demonstrate that when stocks are perfectly negatively correlated (r � �1.0), all risk can be diversified away, but when stocks are per- fectly positively correlated (r � �1.0), diversification does no good whatsoever. In reality, most stocks are positively correlated, but not perfectly so. On aver- age, the correlation coefficient for the returns on two randomly selected stocks would be about �0.6, and for most pairs of stocks, r would lie in the range of �0.5 to �0.7. Under such conditions, combining stocks into portfolios reduces risk but does not eliminate it completely. Figure 6-7 illustrates this point with two stocks whose correlation coefficient is r � �0.67. The portfolio’s average return is 15 percent, which is exactly the same as the average return for each of the two stocks, but its standard deviation is 20.6 percent, which is less than the standard deviation of either stock. Thus, the portfolio’s risk is not an average of the risks of its individual stocks — diversification has reduced, but not eliminated, risk.

From these two-stock portfolio examples, we have seen that in one extreme case (r � �1.0), risk can be completely eliminated, while in the other extreme case (r � �1.0), diversification does nothing to limit risk. The real world lies between these extremes, so in general combining two stocks into a portfolio re- duces, but does not eliminate, the riskiness inherent in the individual stocks.

What would happen if we included more than two stocks in the portfolio? As a rule, the riskiness of a portfolio will decline as the number of stocks in the portfo- lio increases. If we added enough partially correlated stocks, could we completely eliminate risk? In general, the answer is no, but the extent to which adding stocks to a portfolio reduces its risk depends on the degree of correlation among the stocks: The smaller the positive correlation coefficients, the lower the risk in a large portfolio. If we could find a set of stocks whose correlations were zero or negative, all risk could be eliminated. In the real world, where the correlations among the individual stocks are generally positive but less than �1.0, some, but not all, risk can be eliminated.

To test your understanding, would you expect to find higher correlations be- tween the returns on two companies in the same or in different industries? For example, would the correlation of returns on Ford’s and General Motors’ stocks be higher, or would the correlation coefficient be higher between either Ford or GM and AT&T, and how would those correlations affect the risk of portfo- lios containing them?

Answer: Ford’s and GM’s returns have a correlation coefficient of about 0.9 with one another because both are affected by auto sales, but their correlation is only about 0.6 with AT&T.

Implications: A two-stock portfolio consisting of Ford and GM would be less well diversified than a two-stock portfolio consisting of Ford or GM, plus AT&T. Thus, to minimize risk, portfolios should be diversified across industries.

Before leaving this section we should issue a warning — in the real world, it is impossible to find stocks like W and M, whose returns are expected to be per- fectly negatively correlated. Therefore, it is impossible to form completely riskless stock portfolios. Diversification can reduce risk, but it cannot eliminate it. The real world is closer to the situation depicted in Figure 6-7.

R I S K I N A P O R T F O L I O C O N T E X T

STOCK M STOCK M� PORTFOLIO MM� YEAR (k�M) (k�M�) (k�p)

1997 (10.0%) (10.0%) (10.0%) 1998 40.0 40.0 40.0 1999 (5.0) (5.0) (5.0) 2000 35.0 35.0 35.0 2001 15.0% 15.0% 15.0%

Average return 15.0% 15.0% 15.0% Standard deviation 22.6% 22.6% 22.6%

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N250

F I G U R E 6 - 6 Rate of Return Distributions for Two Perfectly Positively Correlated Stocks (r � �1.0) and for Portfolio MM�

k (%)M _

a. Rates of Return

Stock M

2001

25

0

–10

15

k (%) _

Stock M´

2001

25

0

–10

15

k (%)p _

Portfolio MM´

2001

25

0

–10

15

Percent150

(= k )M

Probability Density

b. Probability Distributions of Returns

Percent150

Probability Density

Percent150

Probability Density

(= k )M (= k )p ˆ ˆ ˆ

M

STOCK W STOCK Y PORTFOLIO WY YEAR (k�W) (k�Y) (k�p)

1997 40.0% 28.0% 34.0% 1998 (10.0) 20.0 5.0 1999 35.0 41.0 38.0 2000 (5.0) (17.0) (11.0) 2001 15.0% 3.0% 9.0%

Average return 15.0% 15.0% 15.0% Standard deviation 22.6% 22.6% 20.6%

251R I S K I N A P O R T F O L I O C O N T E X T

k (%)W _

a. Rates of Return

Stock W

2001

25

0

–15

15

k (%)Y _

Stock Y

2001

25

0

–15

15

k (%)p _

Portfolio WY

2001

25

0

–15

15

b. Probability Distributions of Returns

Percent150

Probability Density

(= k )pˆ

Portfolio WY

Stocks W and Y

F I G U R E 6 - 7 Rate of Return Distributions for Two Partially Correlated Stocks (r � �0.67) and for Portfolio WY

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N252

DIVERS IF IABLE RISK VERSUS MARKET RISK

As noted above, it is difficult if not impossible to find stocks whose expected re- turns are negatively correlated — most stocks tend to do well when the national economy is strong and badly when it is weak.7 Thus, even very large portfolios end up with a substantial amount of risk, but not as much risk as if all the money were invested in only one stock.

To see more precisely how portfolio size affects portfolio risk, consider Fig- ure 6-8, which shows how portfolio risk is affected by forming larger and larger portfolios of randomly selected New York Stock Exchange (NYSE) stocks. Standard deviations are plotted for an average one-stock portfolio, a two-stock portfolio, and so on, up to a portfolio consisting of all 2,000-plus common stocks that were listed on the NYSE at the time the data were graphed. The graph illustrates that, in general, the riskiness of a portfolio consisting of large- company stocks tends to decline and to approach some limit as the size of the portfolio increases. According to data accumulated in recent years, �1, the stan- dard deviation of a one-stock portfolio (or an average stock), is approximately 35 percent. A portfolio consisting of all stocks, which is called the market portfolio, would have a standard deviation, �M, of about 20.4 percent, which is shown as the horizontal dashed line in Figure 6-8.

Thus, almost half of the riskiness inherent in an average individual stock can be eliminated if the stock is held in a reasonably well-diversified portfolio, which is one containing 40 or more stocks. Some risk always remains, however, so it is virtually impossible to diversify away the effects of broad stock market movements that affect almost all stocks.

The part of a stock’s risk that can be eliminated is called diversifiable risk, while the part that cannot be eliminated is called market risk.8 The fact that a large part of the riskiness of any individual stock can be eliminated is vitally important, because rational investors will eliminate it and thus render it irrel- evant.

Diversifiable risk is caused by such random events as lawsuits, strikes, suc- cessful and unsuccessful marketing programs, winning or losing a major con- tract, and other events that are unique to a particular firm. Since these events are random, their effects on a portfolio can be eliminated by diversification — bad events in one firm will be offset by good events in another. Market risk, on the other hand, stems from factors that systematically affect most firms: war, inflation, recessions, and high interest rates. Since most stocks are negatively affected by these factors, market risk cannot be eliminated by diversification.

We know that investors demand a premium for bearing risk; that is, the higher the riskiness of a security, the higher its expected return must be to in- duce investors to buy (or to hold) it. However, if investors are primarily con- cerned with the riskiness of their portfolios rather than the riskiness of the indi-

7 It is not too hard to find a few stocks that happened to have risen because of a particular set of circumstances in the past while most other stocks were declining, but it is much harder to find stocks that could logically be expected to go up in the future when other stocks are falling. 8 Diversifiable risk is also known as company-specific, or unsystematic, risk. Market risk is also known as nondiversifiable, or systematic, or beta, risk; it is the risk that remains after diversification.

Market Portfolio A portfolio consisting of all stocks.

Diversifiable Risk That part of a security’s risk associated with random events; it can be eliminated by proper diversification.

Market Risk That part of a security’s risk that cannot be eliminated by diversification.

253

vidual securities in the portfolio, how should the riskiness of an individual stock be measured? One answer is provided by the Capital Asset Pricing Model (CAPM), an important tool used to analyze the relationship between risk and rates of return.9 The primary conclusion of the CAPM is this: The relevant risk- iness of an individual stock is its contribution to the riskiness of a well-diversified port- folio. In other words, the riskiness of General Electric’s stock to a doctor who

R I S K I N A P O R T F O L I O C O N T E X T

F I G U R E 6 - 8 Effects of Portfolio Size on Portfolio Risk for Average Stocks

35

30

25

15

10

5

0

= 20.4

101 20 30 40 2,000+ Number of Stocks

in the Portfolio

σ M

Portfolio's Stand- Alone Risk:

Declines as Stocks

Are Added

Portfolio's Market Risk: Remains Constant

Diversifiable Risk

Portfolio Risk, σp (%)

Minimum Attainable Risk in a Portfolio of Average Stocks

Capital Asset Pricing Model (CAPM) A model based on the proposition that any stock’s required rate of return is equal to the risk-free rate of return plus a risk premium that reflects only the risk remaining after diversification.

9 Indeed, the 1990 Nobel Prize was awarded to the developers of the CAPM, Professors Harry Markowitz and William F. Sharpe. The CAPM is a relatively complex subject, and only its basic el- ements are presented in this text. For a more detailed discussion, see any standard investments text- book.

The basic concepts of the CAPM were developed specifically for common stocks, and, there- fore, the theory is examined first in this context. However, it has become common practice to ex- tend CAPM concepts to capital budgeting and to speak of firms having “portfolios of tangible as- sets and projects.” Capital budgeting is discussed in Chapters 11 and 12.

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N254

has a portfolio of 40 stocks or to a trust officer managing a 150-stock portfolio is the contribution the GE stock makes to the portfolio’s riskiness. The stock might be quite risky if held by itself, but if half of its risk can be eliminated by diversification, then its relevant risk, which is its contribution to the portfolio’s risk, is much smaller than its stand-alone risk.

A simple example will help make this point clear. Suppose you are offered the chance to flip a coin once. If a head comes up, you win $20,000, but if a tail comes up, you lose $16,000. This is a good bet — the expected return is 0.5($20,000) � 0.5(�$16,000) � $2,000. However, it is a highly risky proposition, because you have a 50 percent chance of losing $16,000. Thus, you might well refuse to make the bet. Alternatively, suppose you were of- fered the chance to flip a coin 100 times, and you would win $200 for each head but lose $160 for each tail. It is possible that you would flip all heads and win $20,000, and it is also possible that you would flip all tails and lose $16,000, but the chances are very high that you would actually flip about 50 heads and about 50 tails, winning a net of about $2,000. Although each in- dividual flip is a risky bet, collectively you have a low-risk proposition be- cause most of the risk has been diversified away. This is the idea behind holding portfolios of stocks rather than just one stock, except that with stocks all of the risk cannot be eliminated by diversification — those risks re- lated to broad, systematic changes in the stock market will remain.

Are all stocks equally risky in the sense that adding them to a well- diversified portfolio would have the same effect on the portfolio’s riskiness? The answer is no. Different stocks will affect the portfolio differently, so dif- ferent securities have different degrees of relevant risk. How can the relevant risk of an individual stock be measured? As we have seen, all risk except that re- lated to broad market movements can, and presumably will, be diversified away. After all, why accept risk that can be easily eliminated? The risk that remains after diversifying is market risk, or the risk that is inherent in the market, and it can be measured by the degree to which a given stock tends to move up or down with the market. In the next section, we develop a measure of a stock’s market risk, and then, in a later section, we introduce an equation for determining the required rate of return on a stock, given its market risk.

THE CONCEPT OF BETA

The tendency of a stock to move up and down with the market is reflected in its beta coefficient, b. Beta is a key element of the CAPM. An average-risk stock is defined as one that tends to move up and down in step with the general mar- ket as measured by some index such as the Dow Jones Industrials, the S&P 500, or the New York Stock Exchange Index. Such a stock will, by definition, be as- signed a beta, b, of 1.0, which indicates that, in general, if the market moves up by 10 percent, the stock will also move up by 10 percent, while if the market falls by 10 percent, the stock will likewise fall by 10 percent. A portfolio of such b � 1.0 stocks will move up and down with the broad market averages, and it will be just as risky as the averages. If b � 0.5, the stock is only half as volatile as the market — it will rise and fall only half as much — and a portfolio of such stocks will be half as risky as a portfolio of b � 1.0 stocks. On the other hand, if b � 2.0, the stock is twice as volatile as an average stock, so a portfolio of

Beta Coefficient, b A measure of market risk, which is the extent to which the returns on a given stock move with the stock market.

Relevant Risk The risk of a security that cannot be diversified away, or its market risk. This reflects a security’s contribution to the riskiness of a portfolio.

255

such stocks will be twice as risky as an average portfolio. The value of such a portfolio could double — or halve — in a short time, and if you held such a portfolio, you could quickly go from millionaire to pauper.

Figure 6-9 graphs the relative volatility of three stocks. The data below the graph assume that in 1999 the “market,” defined as a portfolio consisting of all stocks, had a total return (dividend yield plus capital gains yield) of kM � 10%, and Stocks H, A, and L (for High, Average, and Low risk) also all had returns of 10 percent. In 2000, the market went up sharply, and the return on the mar- ket portfolio was k� M � 20%. Returns on the three stocks also went up: H soared to 30 percent; A went up to 20 percent, the same as the market; and L only went up to 15 percent. Now suppose the market dropped in 2001, and the market return was k� M � �10%. The three stocks’ returns also fell, H plunging to �30 percent, A falling to �10 percent, and L going down only to k� L � 0%. Thus, the three stocks all moved in the same direction as the mar- ket, but H was by far the most volatile; A was just as volatile as the market; and L was less volatile.

Beta measures a stock’s volatility relative to an average stock, which by definition has b � 1.0, and a stock’s beta can be calculated by plotting a line like those in Figure 6-9. The slopes of the lines show how each stock moves in response to a movement in the general market — indeed, the slope coefficient of such a “regression line” is defined as a beta coefficient. (Procedures for actually calcu- lating betas are described in Appendix 6A.) Betas for literally thousands of companies are calculated and published by Merrill Lynch, Value Line, and nu- merous other organizations, and the beta coefficients of some well-known com- panies are shown in Table 6-4. Most stocks have betas in the range of 0.50 to 1.50, and the average for all stocks is 1.0 by definition.

Theoretically, it is possible for a stock to have a negative beta. In this case, the stock’s returns would tend to rise whenever the returns on other stocks fall. In practice, we have never seen a stock with a negative beta. For example, Value Line follows more than 1,700 stocks, and not one has a negative beta. Keep in mind, though, that a stock in a given year may move counter to the overall market, even though the stock’s beta is positive. If a stock has a positive beta, we would expect its return to increase whenever the overall stock market rises. However, company-specific factors may cause the stock’s realized return to de- cline, even though the market’s return is positive.

If a stock whose beta is greater than 1.0 is added to a b � 1.0 portfolio, then the portfolio’s beta, and consequently its riskiness, will increase. Conversely, if a stock whose beta is less than 1.0 is added to a b � 1.0 portfolio, the portfo- lio’s beta and risk will decline. Thus, since a stock’s beta measures its contribution to the riskiness of a portfolio, beta is the theoretically correct measure of the stock’s riskiness.

The preceding analysis of risk in a portfolio context is part of the Capital Asset Pricing Model (CAPM), and we can summarize our discussion to this point as follows:

1. A stock’s risk consists of two components, market risk and diversifiable risk.

2. Diversifiable risk can be eliminated by diversification, and most investors do indeed diversify, either by holding large portfolios or by purchasing

R I S K I N A P O R T F O L I O C O N T E X T

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N256

The size of the global stock market has grown steadily overthe last several decades, and it passed the $15 trillion mark during 1995. U.S. stocks account for approximately 41 percent of this total, whereas the Japanese and European markets con- stitute roughly 25 and 26 percent, respectively. The rest of the world makes up the remaining 8 percent. Although the U.S. eq- uity market has long been the world’s biggest, its share of the world total has decreased over time.

The expanding universe of securities available internation- ally suggests the possibility of achieving a better risk-return trade-off than could be obtained by investing solely in U.S. se- curities. So, investing overseas might lower risk and simultane- ously increase expected returns. The potential benefits of diver- sification are due to the facts that the correlation between the returns on U.S. and international securities is fairly low, and re- turns in developing nations are often quite high.

Figure 6-8, presented earlier, demonstrated that an investor can significantly reduce the risk of his or her portfolio by hold- ing a large number of stocks. The figure accompanying this box suggests that investors may be able to reduce risk even further by holding a large portfolio of stocks from all around the world, given the fact that the returns of domestic and international stocks are not perfectly correlated.

Despite the apparent benefits from investing overseas, the typical U.S. investor still dedicates less than 10 percent of his or her portfolio to foreign stocks — even though foreign stocks represent roughly 60 percent of the worldwide equity market.

Researchers and practitioners alike have struggled to under- stand this reluctance to invest overseas. One explanation is that investors prefer domestic stocks because they have lower transaction costs. However, this explanation is not completely convincing, given that recent studies have found that investors buy and sell their overseas stocks more frequently than they trade their domestic stocks. Other explanations for the domes- tic bias focus on the additional risks from investing overseas (for example, exchange rate risk) or suggest that the typical U.S. investor is uninformed about international investments and/or views international investments as being extremely risky or uncertain. More recently, other analysts have argued that as world capital markets have become more integrated, the corre- lation of returns between different countries has increased, and hence the benefits from international diversification have de- clined. A third explanation is that U.S. corporations are them- selves investing more internationally, hence U.S. investors are de facto obtaining international diversification.

Whatever the reason for the general reluctance to hold in- ternational assets, it is a safe bet that in the future U.S. in- vestors will shift more and more of their assets to overseas in- vestments.

SOURCE: Kenneth Kasa, “Measuring the Gains from International Portfolio Diversi- fication,” Federal Reserve Bank of San Francisco Weekly Letter, Number 94-14, April 8, 1994.

THE BENEFITS OF DIVERSIFYING OVERSEAS

shares in a mutual fund. We are left, then, with market risk, which is caused by general movements in the stock market and which reflects the fact that most stocks are systematically affected by events like war, recessions, and inflation. Market risk is the only relevant risk to a rational, diversified in- vestor because such an investor would eliminate diversifiable risk.

3. Investors must be compensated for bearing risk — the greater the riski- ness of a stock, the higher its required return. However, compensation is required only for risk that cannot be eliminated by diversification. If risk premiums existed on stocks due to diversifiable risk, well-diversified investors would start buying those securities (which would not be espe- cially risky to such investors) and bidding up their prices, and the stocks’ final (equilibrium) expected returns would reflect only nondiversifiable market risk.

If this point is not clear, an example may help clarify it. Suppose half of Stock A’s risk is market risk (it occurs because Stock A moves up and down with the market), while the other half of A’s risk is diversifiable. You

257

hold only Stock A, so you are exposed to all of its risk. As compensation for bearing so much risk, you want a risk premium of 8 percent over the 10 percent T-bond rate. Thus, your required return is kA � 10% � 8% � 18%. But suppose other investors, including your professor, are well diversified; they also hold Stock A, but they have eliminated its di- versifiable risk and thus are exposed to only half as much risk as you. Therefore, their risk premium will be only half as large as yours, and their required rate of return will be kA � 10% � 4% � 14%.

If the stock were yielding more than 14 percent in the market, diver- sified investors, including your professor, would buy it. If it were yielding 18 percent, you would be willing to buy it, but well-diversified investors would bid its price up and its yield down, hence you could not buy it at a price low enough to provide you with an 18 percent return. In the end, you would have to accept a 14 percent return or else keep your money in the bank. Thus, risk premiums in a market populated by rational, diver- sified investors can reflect only market risk.

R I S K I N A P O R T F O L I O C O N T E X T

U.S. Stocks

U.S. and International Stocks

Number of Stocks in the Portfolio

Portfolio Risk, σp (%)

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N258

4. The market risk of a stock is measured by its beta coefficient, which is an index of the stock’s relative volatility. Some benchmark betas follow:

b � 0.5: Stock is only half as volatile, or risky, as an average stock. b � 1.0: Stock is of average risk. b � 2.0: Stock is twice as risky as an average stock.

Return on Stock i, k (%)

30

20

10

–10

–20

–30

3020100–10–20

X

Stock H, High Risk: b = 2.0

Stock A, Average Risk: b = 1.0

Stock L, Low Risk: b = 0.5

Return on the Market, kM(%)

i

_

_

F I G U R E 6 - 9 Relative Volatility of Stocks H, A, and L

YEAR k�H k�A k�L k�M

1999 10% 10% 10% 10% 2000 30 20 15 20 2001 (30) (10) 0 (10)

NOTE: These three stocks plot exactly on their regression lines. This indicates that they are exposed only to market risk. Mutual funds that concentrate on stocks with betas of 2, 1, and 0.5 would have patterns similar to those shown in the graph.

259

5. A portfolio consisting of low-beta securities will itself have a low beta, be- cause the beta of a portfolio is a weighted average of its individual secu- rities’ betas:

(6-6)

Here bp is the beta of the portfolio, and it shows how volatile the portfo- lio is in relation to the market; wi is the fraction of the portfolio invested in the ith stock; and bi is the beta coefficient of the ith stock. For exam- ple, if an investor holds a $100,000 portfolio consisting of $33,333.33 in- vested in each of three stocks, and if each of the stocks has a beta of 0.7, then the portfolio’s beta will be bp � 0.7:

bp � 0.3333(0.7) � 0.3333(0.7) � 0.3333(0.7) � 0.7.

Such a portfolio will be less risky than the market, so it should experience relatively narrow price swings and have relatively small rate-of-return fluctuations. In terms of Figure 6-9, the slope of its regression line would be 0.7, which is less than that for a portfolio of average stocks.

Now suppose one of the existing stocks is sold and replaced by a stock with bi � 2.0. This action will increase the beta of the portfolio from bp1 � 0.7 to bp2 � 1.13:

bp2 � 0.3333(0.7) � 0.3333(0.7) � 0.3333(2.0)

� 1.13.

� a n

i�1 wibi.

bp � w1b1 � w2b2 � � � � � wnbn

R I S K I N A P O R T F O L I O C O N T E X T

T A B L E 6 - 4

STOCK BETA

Merrill Lynch 1.85 America Online 1.60 General Electric 1.25 Microsoft Corp. 1.00 Coca-Cola 1.00 IBM 1.00 Procter & Gamble 0.85 Energen Corp.a 0.80 Heinz 0.70 Empire District Electric 0.45

a Energen is a gas distribution company. It has a monopoly in much of Alabama, and its prices are adjusted every three months so as to keep its profits relatively constant.

SOURCE: Value Line, September 2000, CD-ROM.

Illustrative List of Beta Coefficients

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N260

Had a stock with bi � 0.2 been added, the portfolio beta would have de- clined from 0.7 to 0.53. Adding a low-beta stock, therefore, would reduce the riskiness of the portfolio. Consequently, adding new stocks to a port- folio can change the riskiness of that portfolio.

6. Since a stock’s beta coefficient determines how the stock affects the riskiness of a diversified portfolio, beta is the most relevant measure of any stock’s risk.

SELF-TEST QUESTIONS

Explain the following statement: “An asset held as part of a portfolio is gen- erally less risky than the same asset held in isolation.”

What is meant by perfect positive correlation, perfect negative correlation, and zero correlation?

In general, can the riskiness of a portfolio be reduced to zero by increasing the number of stocks in the portfolio? Explain.

What is an average-risk stock? What will be its beta?

Why is beta the theoretically correct measure of a stock’s riskiness?

If you plotted the returns on a particular stock versus those on the Dow Jones Index over the past five years, what would the slope of the regression line you obtained indicate about the stock’s market risk?

T H E R E L AT I O N S H I P B E T W E E N R I S K A N D R AT E S O F R E T U R N

In the preceding section, we saw that under the CAPM theory, beta is the ap- propriate measure of a stock’s relevant risk. Now we must specify the relation- ship between risk and return: For a given level of risk as measured by beta, what rate of return will investors require to compensate them for bearing that risk? To begin, let us define the following terms:

k̂ i � expected rate of return on the ith stock. ki � required rate of return on the ith stock. Note

that if k̂ i is less than ki, you would not pur- chase this stock, or you would sell it if you owned it. If k̂ i were greater than ki, you would want to buy the stock, because it looks like a bargain. You would be indifferent if k̂ i � ki.

k� � realized, after-the-fact return. One obvi- ously does not know k� at the time he or she is considering the purchase of a stock.

kRF � risk-free rate of return. In this context, kRF is generally measured by the return on long- term U.S. Treasury bonds.

261R I S K I N A P O R T F O L I O C O N T E X T

IS THE DOW JONES HEADING TO 36,000?

In the 18-year period since 1982, the Dow Jones IndustrialAverage has risen from 777 to over 10,526, or an increase of approximately 1,255 percent! Although millions of investors have profited from this increase, many analysts believe that stocks are now overvalued. These analysts point to record P/E ratios as an indication that stock prices are too high. Federal Reserve Chairman Alan Greenspan made the same point, warn- ing about the dangers of “irrational exuberance.”

In sharp contrast to this bearish perspective, James Glass- man and Kevin Hassett, co-authors of a book, Dow 36,000, make the following argument:

Using sensible assumptions, we are comfortable with stock prices rising to three or four times their current levels. Our calculations show that with earnings growing at the same rate as the gross domestic product and Treasury bond yields below 6 percent, a perfectly reasonable level for the Dow would be 36,000 — tomorrow, not 10 or 20 years from now.

How do Glassman and Hassett reach this conclusion? They claim that the market risk premium (kM � kRF) has declined, and that it will continue to decline in the future. Investors require a risk premium for bearing risk, and the size of that premium depends on the average investor’s degree of risk aversion. From 1926 through 1999, large-company stocks have produced average an- nual returns of 13.3 percent, while the returns on long-term government bonds have averaged 5.5 percent, suggesting a risk premium of 13.3% � 5.5% � 7.8%. However, Glassman and Hassett make the following assertion:

What has happened since 1982, and especially during the past four years, is that investors have become calmer and smarter. They are requiring a much smaller extra return, or “risk premium,” from stocks to compensate for their fear. That premium, which has averaged about 7 percent in mod- ern history, is now around 3 percent. We believe that it is headed for its proper level: zero. That means that stock prices should rise accordingly.

A declining risk premium leads to a lower required return on stocks. This, in turn, implies that stock prices should rise be- cause the same cash flows will then be discounted at a lower rate. To support their argument, Glassman and Hassett cite re- search by Jeremy Siegel of the University of Pennsylvania’s Whar- ton School. In his best-selling book, Stocks for the Long Run, Siegel documents that over the long run stocks have not been riskier than bonds. Indeed, based on his research, Siegel con- cludes that, “The safest long-term investment for the preserva- tion of purchasing power has clearly been stocks, not bonds.”

Siegel acknowledges that stocks are riskier for short-term in- vestors. This point is confirmed when we compare the average annual standard deviation of stock market returns (20 percent) with that of bonds (9 percent). The higher volatility of stocks occurs because stocks get hit harder than bonds in the short run when the economy weakens or inflation increases. However, stocks have always eventually recovered, and over longer peri- ods they have outperformed bonds.

Glassman and Hassett contend that more and more investors are viewing stocks as long-term investments, and they are con- vinced that the long-run risk of stocks is fairly low. This has led investors to put increasing amounts of money in the stock mar- ket, pushing up stock prices and driving stocks’ returns even higher. These positive results, in turn, lower the perceived risk- iness of stocks, and that leads to still more buying and further stock market gains.

To put all of this in perspective, we need to address three important points. First, the relevant market risk premium is for- ward looking — it is based on investors’ perceptions of the rel- ative riskiness of stocks versus bonds in the future, and it will change over time. Most analysts acknowledge that the risk pre- mium has fallen, but few agree with Glassman and Hassett that it is or should be zero. Most believe that investors require a premium in the neighborhood of at least 3 to 5 percent as an inducement for holding stocks. Moreover, the risk premium would probably rise sharply if something led to a sustained market decline.

Second, if the risk premium were to stabilize at a relatively low level, then investors would receive low stock returns in the future. For example, if the T-bond yield were 5 percent and the market risk premium were 3 percent, then the required return on the market would be 8 percent. In this situation, it would be unreasonable to expect stock returns of 12 to 13 percent in the future.

Third, investors should be concerned with real returns, which take inflation into account. For example, suppose the risk-free nominal rate of return were 5.5 percent and the mar- ket risk premium were 3 percent. Here, the expected nominal return on an average stock would be 8.5 percent. If inflation were 3.5 percent, the real return would be only 5.0 percent. Correctly looking at things in terms of real returns suggests that with low market risk premiums, stocks will have a hard time competing with inflation-indexed Treasury securities, which currently provide investors with only a slightly lower real return with considerably less risk.

SOURCE: James K. Glassman and Kevin A. Hassett, “Stock Prices Are Still Far Too Low,” The Wall Street Journal, March 17, 1999, A26.

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N262

bi � beta coefficient of the ith stock. The beta of an average stock is bA � 1.0.

kM � required rate of return on a portfolio con- sisting of all stocks, which is called the mar- ket portfolio. kM is also the required rate of return on an average (bA � 1.0) stock.

RPM � (kM � kRF) � risk premium on “the market,” and also on an average (b � 1.0) stock. This is the addi- tional return over the risk-free rate required to compensate an average investor for as- suming an average amount of risk. Average risk means a stock whose bi � bA � 1.0.

RPi � (kM � kRF)bi � (RPM)bi � risk premium on the ith stock. The stock’s risk premium will be less than, equal to, or greater than the premium on an average stock, RPM, depending on whether its beta is less than, equal to, or greater than 1.0. If bi � bA � 1.0, then RPi � RPM.

The market risk premium, RPM, shows the premium investors require for bearing the risk of an average stock. The size of this premium depends on the perceived risk of the stock market and investors’ degree of risk aversion. Let us assume that at the current time Treasury bonds yield kRF � 6% and an average share of stock has a required rate of return of kM � 11%. Therefore, the mar- ket risk premium is 5 percent calculated as:

RPM � kM � kRF � 11% � 6% � 5%.

It should be noted that the risk premium of an average stock, kM � kRF, is hard to measure because it is impossible to obtain precise estimates of the expected future return of the market, kM.

10 Given the difficulty of estimating future market returns, analysts often look to historical data to estimate the market risk premium. Historical data suggest that the market risk premium varies somewhat from year to year, and it has generally ranged from 4 to 8 percent.

While historical estimates might be a good starting point for estimating the market risk premium, historical estimates may be misleading if investors’ atti- tudes toward risk change considerably over time. (See the Industry Practice Box entitled “Estimating the Market Risk Premium.”) Indeed, many analysts have argued that the market risk premium has fallen in recent years because an in- creasing number of investors have been willing to bear the risks of the stock market. If this claim is correct, the market risk premium may be considerably lower than what would be implied using historical data. (See the Industry Prac- tice Box entitled “Is the Dow Jones Heading to 36,000?” for a discussion of

Market Risk Premium, RPM The additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk.

10 This concept, as well as other aspects of the CAPM, is discussed in more detail in Chapter 3 of Eugene F. Brigham and Phillip R. Daves, Intermediate Financial Management, 7th ed. (Fort Worth, TX: Harcourt College Publishers, 2002). Chapter 3 of Intermediate Financial Management also dis- cusses the assumptions embodied in the CAPM framework. Some of these are unrealistic, and be- cause of this the theory does not hold exactly.

263

how changes in investor risk aversion may have influenced the market risk pre- mium and stock returns in recent years.)

While the market risk premium represents the risk premium for the entire stock market, the risk premium on individual stocks will vary. For example, if one stock were twice as risky as another, its risk premium would be twice as high, while if its risk were only half as much, its risk premium would be half as large. Further, we can measure a stock’s relative riskiness by its beta coeffi- cient. If we know the market risk premium, RPM, and the stock’s risk as mea- sured by its beta coefficient, bi, we can find the stock’s risk premium as the product (RPM)bi. For example, if bi � 0.5 and RPM � 5%, then RPi is 2.5 percent:

Risk premium for Stock i � RPi � (RPM)bi (6-7)

� (5%)(0.5)

� 2.5%.

As the discussion in Chapter 5 implied, the required return for any invest- ment can be expressed in general terms as

Required return � Risk-free return � Premium for risk.

Here the risk-free return includes a premium for expected inflation, and we as- sume that the assets under consideration have similar maturities and liquidity. Under these conditions, the required return for Stock i can be written as follows:

ki � kRF � (kM � kRF)bi (6-8)

� kRF � (RPM)bi � 6% � (11% � 6%)(0.5)

� 6% � 5%(0.5)

� 8.5%.

Equation 6-8 is called the Security Market Line (SML). If some other Stock j were riskier than Stock i and had bj � 2.0, then its re-

quired rate of return would be 16 percent:

k j � 6% � (5%)2.0 � 16%.

An average stock, with b � 1.0, would have a required return of 11 percent, the same as the market return:

kA � 6% � (5%)1.0 � 11% � kM.

As noted above, Equation 6-8 is called the Security Market Line (SML) equation, and it is often expressed in graph form, as in Figure 6-10, which shows the SML when kRF � 6% and kM � 11%. Note the following points:

1. Required rates of return are shown on the vertical axis, while risk as measured by beta is shown on the horizontal axis. This graph is quite different from the one shown in Figure 6-9, where the returns on in- dividual stocks were plotted on the vertical axis and returns on the market index were shown on the horizontal axis. The slopes of the

SML Equation: Required return

on Stock i �

Risk-free rate

� aMarket risk premium

b aStock i's beta

b

T H E R E L AT I O N S H I P B E T W E E N R I S K A N D R AT E S O F R E T U R N

Security Market Line (SML) The line on a graph that shows the relationship between risk as measured by beta and the required rate of return for individual securities. Equation 6-8 is the equation for the SML.

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N264

three lines in Figure 6-9 were used to calculate the three stocks’ betas, and those betas were then plotted as points on the horizontal axis of Figure 6-10.

2. Riskless securities have bi � 0; therefore, kRF appears as the vertical axis intercept in Figure 6-10. If we could construct a portfolio that had a beta of zero, it would have an expected return equal to the risk-free rate.

3. The slope of the SML (5% in Figure 6-10) reflects the degree of risk aversion in the economy — the greater the average investor’s aversion to risk, then (a) the steeper the slope of the line, (b) the greater the

ESTIMATING THE MARKET RISK PREMIUM

The Capital Asset Pricing Model (CAPM) is more than just atheory describing the trade-off between risk and return. The CAPM is also widely used in practice. As we will see in Chapter 9, investors use the CAPM to determine the discount rate for valuing stocks. Later, in Chapter 10, we will also see that cor- porate managers use the CAPM to estimate the cost of equity fi- nancing.

The market risk premium is an important component of the CAPM. In practice, what we would ideally like to use in the CAPM is the expected market risk premium, which gives an in- dication of investors’ future returns. Unfortunately, we cannot direcly observe investors’ expectations. Instead, academicians and practitioners often use an historical estimate of the mar- ket risk premium as a proxy for the expected risk premium.

Historical premiums are found by taking the differences be- tween actual returns of the overall stock market and the risk- free rate. Ibbotson Associates provide perhaps the most com- prehensive estimates of historical risk premiums. Their estimates indicate that the equity risk premium has averaged about 8 percent a year over the past 75 years.

Analysts have pointed out some of the shortcomings of using an historical estimate as a proxy for the expected risk premium. First, historical estimates may be very misleading at times when the market risk premium is changing. As we men- tioned in an earlier box entitled “Is the Dow Jones Heading to 36,000?,” many analysts believe that the expected risk premium has fallen in recent years. It is important to recognize that a sharp drop in the expected risk premium (perhaps because of lower perceived risk and/or declining risk aversion) pushes up stock prices, and that ironically increases the observed (histor-

ical) risk premium. In this situation, an analyst would be se- riously missing the boat if he used the historical risk premium to approximate the expected risk premium. To further illustrate this point, the strong performance in the stock market over the past several years has produced high historical premiums — in- deed, Ibbotson Associates estimate that the market risk pre- mium averaged 22.3 percent a year during the period between 1995 and 1999. Nobody would seriously suggest that future in- vestors require a 22.3 percent premium to invest in the stock market! Given these concerns, Ibbotson and others suggest that historical estimates are more reliable if estimated over longer time intervals.

A second concern is that historical estimates may be biased upward because they only include the returns of firms that have survived and do not take into account the performances of fail- ing firms. Stephen Brown, William Goetzmann, and Stephen Ross discussed the implications of this “survivorship bias” in a 1995 Journal of Finance article. Putting these ideas into prac- tice, Tom Copeland, Tim Koller, and Jack Murrin have recently suggested that this “survivorship bias” increases historical re- turns by 11⁄2 to 2 percent a year. For that reason, they suggest that practitioners trying to estimate a forward-looking expected risk premium subtract 11⁄2 to 2 percent from their historical risk premium estimates.

SOURCES: Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2000 Yearbook (Chicago: Ibbotson Associates, 2000); Stephen J. Brown, William N. Goetzmann, and Stephen A. Ross, “Survival,” The Journal of Finance, Vol. 50, No. 3, July 1995, 853–873; and Tom Copeland, Tim Koller, and Jack Murrin, Valuation: Measuring and Managing the Value of Companies, 3rd edition, (New York: McKinsey & Com- pany, 2000).

265T H E R E L AT I O N S H I P B E T W E E N R I S K A N D R AT E S O F R E T U R N

11 Students sometimes confuse beta with the slope of the SML. This is a mistake. The slope of any straight line is equal to the “rise” divided by the “run,” or (Y1 � Y0)/(X1 � X0). Consider Figure 6-10. If we let Y � k and X � beta, and we go from the origin to b � 1.0, we see that the slope is (kM � kRF)/(bM � bRF) � (11% � 6%)/(1 � 0) � 5%. Thus, the slope of the SML is equal to (kM � kRF), the market risk premium. In Figure 6-10, ki � 6% � 5%bi, so a doubling of beta (for example, from 1.0 to 2.0) would produce a 5 percentage point increase in ki.

F I G U R E 6 - 1 0 The Security Market Line (SML)

A

Relatively Risky Stock’s Risk Premium: 10%

Market Risk Premium: 5%. Applies Also to an Average Stock, and Is the Slope Coefficient in the SML Equation

Safe Stock’s Risk Premium: 2.5%

Risk-Free Rate, kRF

0 0.5 1.0 1.5 2.0 Risk, b i

k = 16

k = k = 11

k = 8.5

k = 6

Required Rate of Return (%)

High

M

Low

RF

SML: k = k + (k – k ) b ii RF M RF

= 6% + (11% – 6%) b i

= 6% + (5%) b i

risk premium for all stocks, and (c) the higher the required rate of return on all stocks.11 These points are discussed further in a later section.

4. The values we worked out for stocks with bi � 0.5, bi � 1.0, and bi � 2.0 agree with the values shown on the graph for kLow, kA, and kHigh.

Both the Security Market Line and a company’s position on it change over time due to changes in interest rates, investors’ aversion to risk, and individual companies’ betas. Such changes are discussed in the following sections.

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N266

THE IMPACT OF INFLAT ION

As we learned in Chapter 5, interest amounts to “rent” on borrowed money, or the price of money. Thus, kRF is the price of money to a riskless borrower. We also learned that the risk-free rate as measured by the rate on U.S. Treasury securities is called the nominal, or quoted, rate, and it consists of two elements: (1) a real infla- tion-free rate of return, k*, and (2) an inflation premium, IP, equal to the anticipated rate of inflation.12 Thus, kRF � k* � IP. The real rate on long-term Treasury bonds has historically ranged from 2 to 4 percent, with a mean of about 3 percent. There- fore, if no inflation were expected, long-term Treasury bonds would yield about 3 percent. However, as the expected rate of inflation increases, a premium must be added to the real risk-free rate of return to compensate investors for the loss of purchasing power that results from inflation. Therefore, the 6 percent kRF shown in Figure 6-10 might be thought of as consisting of a 3 percent real risk-free rate of return plus a 3 percent inflation premium: kRF � k* � IP � 3% � 3% � 6%.

If the expected inflation rate rose by 2 percent, to 3% � 2% � 5%, this would cause kRF to rise to 8 percent. Such a change is shown in Figure 6-11. Notice that under the CAPM, the increase in kRF leads to an equal increase in the rate of return on all risky assets, because the same inflation premium is built into the required rate of return of both riskless and risky assets.13 For example, the rate of return on an average stock, kM, increases from 11 to 13 percent. Other risky securities’ returns also rise by two percentage points.

CHANGES IN RISK AVERS ION

The slope of the Security Market Line reflects the extent to which investors are averse to risk — the steeper the slope of the line, the greater the average in- vestor’s risk aversion. Suppose investors were indifferent to risk; that is, they were not risk averse. If kRF were 6 percent, then risky assets would also provide an expected return of 6 percent, because if there were no risk aversion, there would be no risk premium, and the SML would graph as a horizontal line. As risk aversion increases, so does the risk premium, and this causes the slope of the SML to become steeper.

Figure 6-12 illustrates an increase in risk aversion. The market risk premium rises from 5 to 7.5 percent, causing kM to rise from kM1 � 11% to kM2 � 13.5%. The returns on other risky assets also rise, and the effect of this shift in risk aversion is more pronounced on riskier securities. For example, the re- quired return on a stock with bi � 0.5 increases by only 1.25 percentage points, from 8.5 to 9.75 percent, whereas that on a stock with bi � 1.5 increases by 3.75 percentage points, from 13.5 to 17.25 percent.

12 Long-term Treasury bonds also contain a maturity risk premium, MRP. Here we include the MRP in k* to simplify the discussion. 13 Recall that the inflation premium for any asset is equal to the average expected rate of inflation over the asset’s life. Thus, in this analysis we must assume either that all securities plotted on the SML graph have the same life or else that the expected rate of future inflation is constant.

It should also be noted that kRF in a CAPM analysis can be proxied by either a long-term rate (the T-bond rate) or a short-term rate (the T-bill rate). Traditionally, the T-bill rate was used, but in recent years there has been a movement toward use of the T-bond rate because there is a closer relationship between T-bond yields and stocks than between T-bill yields and stocks. See Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2000 Yearbook (Chicago: Ibbotson Associates, 2000) for a discussion.

267

CHANGES IN A STOCK ’S BETA COEFF IC IENT

As we shall see later in the book, a firm can influence its market risk, hence its beta, through changes in the composition of its assets and also through its use of debt. A company’s beta can also change as a result of external factors such as increased competition in its industry, the expiration of basic patents, and the like. When such changes occur, the required rate of return also changes, and, as we shall see in Chapter 9, this will affect the firm’s stock price. For example, consider Allied Food Products, with a beta of 1.40. Now suppose some action occurred that caused Allied’s beta to increase from 1.40 to 2.00. If the condi- tions depicted in Figure 6-10 held, Allied’s required rate of return would in- crease from 13 to 16 percent:

k1 � kRF � (kM � kRF)bi � 6% � (11% � 6%)1.40

� 13%

to

k2 � 6% � (11% � 6%)2.0

� 16%.

As we shall see in Chapter 9, this change would have a dramatic impact on Al- lied’s stock price.

T H E R E L AT I O N S H I P B E T W E E N R I S K A N D R AT E S O F R E T U R N

F I G U R E 6 - 1 1 Shift in the SML Caused by an Increase in Inflation

0 0.5 1.0 1.5 2.0 Risk, b i

kM2 = 13

kM1 = 11

kRF2 = 8

Required Rate of Return (%)

kRF1 = 6

k* = 3

Original IP = 3%

�Increase in Anticipated Inflation, IP = 2%

Real Risk-Free Rate of Return, k*

SML2 = 8% + 5%(bi)

SML1 = 6% + 5%(bi)

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N268

SELF-TEST QUESTIONS

Differentiate among the expected rate of return (k̂ ), the required rate of re- turn (k), and the realized, after-the-fact return (k� ) on a stock. Which would have to be larger to get you to buy the stock, k̂ or k? Would k̂ , k, and k� typ- ically be the same or different? Explain.

What are the differences between the relative volatility graph (Figure 6-9), where “betas are made,” and the SML graph (Figure 6-10), where “betas are used”? Discuss both how the graphs are constructed and the information they convey.

What happens to the SML graph in Figure 6-10 when inflation increases or decreases?

What happens to the SML graph when risk aversion increases or decreases? What would the SML look like if investors were indifferent to risk, that is, if they had zero risk aversion?

How can a firm influence its market risk as reflected in its beta?

F I G U R E 6 - 1 2 Shift in the SML Caused by Increased Risk Aversion

0 0.5 1.0 1.5 2.0 Risk, b i

kM2 = 13.5

kRF = 6

Required Rate of Return (%)

New Market Risk Premium, kM2 – kRF = 7.5%

Original Market Risk Premium, kM1 – kRF = 5%

8.5 9.75

kM1 = 11

17.25

SML2 = 6% + 7.5%(bi)

SML1 = 6% + 5%(bi)

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P H Y S I C A L A S S E T S V E R S U S S E C U R I T I E S

In a book on financial management for business firms, why do we spend so much time discussing the riskiness of stocks? Why not begin by looking at the riskiness of such business assets as plant and equipment? The reason is that, for a management whose primary goal is stock price maximization, the over- riding consideration is the riskiness of the firm’s stock, and the relevant risk of any physical asset must be measured in terms of its effect on the stock’s risk as seen by in- vestors. For example, suppose Goodyear Tire Company is considering a major investment in a new product, recapped tires. Sales of recaps, hence earnings on the new operation, are highly uncertain, so on a stand-alone basis the new venture appears to be quite risky. However, suppose returns in the recap business are negatively correlated with Goodyear’s regular operations — when times are good and people have plenty of money, they buy new tires, but when times are bad, they tend to buy more recaps. Therefore, returns would be high on regular operations and low on the recap division during good times, but the opposite would occur during recessions. The result might be a pattern like that shown earlier in Figure 6-5 for Stocks W and M. Thus, what appears to be a risky investment when viewed on a stand-alone basis might not be very risky when viewed within the context of the company as a whole.

This analysis can be extended to the corporation’s stockholders. Because Goodyear’s stock is owned by diversified stockholders, the real issue each time management makes an asset investment is this: How will this investment affect the risk of our stockholders? Again, the stand-alone risk of an individual proj- ect may look quite high, but viewed in the context of the project’s effect on stockholders’ risk, it may not be very large. We will address this issue again in Chapter 10, where we examine the effects of capital budgeting on companies’ beta coefficients and thus on stockholders’ risks.

P H Y S I C A L A S S E T S V E R S U S S E C U R I T I E S

SELF-TEST QUESTIONS

Explain the following statement: “The stand-alone risk of an individual proj- ect may be quite high, but viewed in the context of a project’s effect on stockholders’ risk, the project’s true risk may not be very large.”

How would the correlation between returns on a project and returns on the firm’s other assets affect the project’s risk?

S O M E C O N C E R N S A B O U T B E TA A N D T H E C A P M

The Capital Asset Pricing Model (CAPM) is more than just an abstract theory described in textbooks — it is also widely used by analysts, investors, and corpo- rations. However, despite the CAPM’s intuitive appeal, a number of recent stud- ies have raised concerns about its validity. In particular, a recent study by Eu- gene Fama of the University of Chicago and Kenneth French of Yale found no

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N270

historical relationship between stocks’ returns and their market betas, confirm- ing a position long held by a number of professors and stock market analysts.14

If beta does not determine returns, what does? Fama and French found two variables that are consistently related to stock returns: (1) the firm’s size and (2) its market/book ratio. After adjusting for other factors, they found that smaller firms have provided relatively high returns, and that returns are higher on stocks with low market/book ratios. By contrast, they found no relationship between a stock’s beta and its return.

As an alternative to the traditional CAPM, researchers and practitioners have begun to look to more general multi-beta models that encompass the CAPM and address its shortcomings. The multi-beta model is an attractive generalization of the traditional CAPM model’s insight that market risk — risk that cannot be diversified away — underlies the pricing of assets. In the multi- beta model, market risk is measured relative to a set of risk factors that deter- mine the behavior of asset returns, whereas the CAPM gauges risk only relative to the market return. It is important to note that the risk factors in the multi- beta model are all nondiversifiable sources of risk. Empirical research investi- gating the relationship between economic risk factors and security returns is ongoing, but it has discovered several systematic empirical risk factors, includ- ing the bond default premium, the bond term structure premium, and inflation.

Practitioners and academicians have long recognized the limitations of the CAPM, and they are constantly looking for ways to improve it. The multi- beta model is a potential step in that direction. Although the CAPM repre- sents a significant step forward in security pricing theory, it does have some deficiencies when applied in practice, hence estimates of ki found through use of the SML may be subject to considerable error.

SELF-TEST QUESTION

Are there any reasons to question the validity of the CAPM? Explain.

14 See Eugene F. Fama and Kenneth R. French, “The Cross-Section of Expected Stock Returns,” Journal of Finance, Vol. 47, 1992, 427–465; and Eugene F. Fama and Kenneth R. French, “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics, Vol. 33, 1993, 3–56.

VO L AT I L I T Y V E R S U S R I S K

Before closing this chapter, we should note that volatility does not necessarily imply risk. For example, suppose a company’s sales and earnings fluctuate widely from month to month, from year to year, or in some other manner. Does this imply that the company is risky in either the stand-alone or portfolio sense? If the fluctuations follow seasonal or cyclical patterns, as for an ice cream distributor or a steel company, they can be predicted, hence volatility would not signify much in the way of risk. If the ice cream company’s earnings dropped about as much as they normally did in the winter, this would not concern in-

271VO L AT I L I T Y V E R S U S R I S K

SELF-TEST QUESTIONS

Does earnings volatility necessarily imply risk? Explain.

Why is stock price volatility more likely to imply risk than earnings volatility?

In this chapter, we described the trade-off between risk and return. We began by discussing how to calculate risk and return for both individual as- sets and portfolios. In particular, we differentiated between stand-alone risk and risk in a portfolio context, and we explained the benefits of diversifica- tion. Finally, we developed the CAPM, which explains how risk affects rates of return. In the chapters that follow, we will give you the tools to estimate the required rates of return for bonds, preferred stock, and common stock, and we will explain how firms use these returns to develop their costs of capital. As you will see, the cost of capital is an important element in the firm’s capital budgeting process. The key concepts covered in this chapter are listed below.

vestors, so the company’s stock price would not be affected. Similarly, if the steel company’s earnings fell during a recession, this would not be a surprise, so the company’s stock price would not fall nearly as much as its earnings. There- fore, earnings volatility does not necessarily imply investment risk.

Now consider some other company, say, Wal-Mart. In 1995 Wal-Mart’s earnings declined for the first time in its history. That decline worried investors — they were concerned that Wal-Mart’s era of rapid growth had ended. The result was that Wal-Mart’s stock price declined more than its earnings. Again, we conclude that while a downturn in earnings does not necessarily imply risk, it could, depending on conditions.

Now let’s consider stock price volatility as opposed to earnings volatility. Is stock price volatility more likely to imply risk than earnings volatility? The an- swer is a loud yes! Stock prices vary because investors are uncertain about the future, especially about future earnings. So, if you see a company whose stock price fluctuates relatively widely (which will result in a high beta), you can bet that its future earnings are relatively unpredictable. Thus, biotech companies have less predictable earnings than utilities, biotechs’ stock prices are volatile, and they have relatively high betas.

To conclude, keep two points in mind: (1) Earnings volatility does not nec- essarily signify risk — you have to think about the cause of the volatility before reaching any conclusion as to whether earnings volatility indicates risk. (2) Stock price volatility does signify risk.

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N272

� Risk can be defined as the chance that some unfavorable event will occur. � The riskiness of an asset’s cash flows can be considered on a stand-

alone basis (each asset by itself ) or in a portfolio context, where the investment is combined with other assets and its risk is reduced through diversification.

� Most rational investors hold portfolios of assets, and they are more con- cerned with the riskiness of their portfolios than with the riskiness of in- dividual assets.

� The expected return on an investment is the mean value of its probabil- ity distribution of returns.

� The greater the probability that the actual return will be far below the ex- pected return, the greater the stand-alone risk associated with an asset. Two measures of stand-alone risk are the standard deviation and the co- efficient of variation.

� The average investor is risk averse, which means that he or she must be compensated for holding risky assets. Therefore, riskier assets have higher required returns than less risky assets.

� An asset’s risk consists of (1) diversifiable risk, which can be eliminated by diversification, plus (2) market risk, which cannot be eliminated by di- versification.

� The relevant risk of an individual asset is its contribution to the riskiness of a well-diversified portfolio, which is the asset’s market risk. Since market risk cannot be eliminated by diversification, investors must be compensated for bearing it.

� The Capital Asset Pricing Model is a model based on the proposition that any stock’s required rate of return is equal to the risk-free rate of re- turn plus a risk premium that reflects only the risk remaining after diver- sification.

� A stock’s beta coefficient, b, is a measure of its market risk. Beta mea- sures the extent to which the stock’s returns move relative to the market.

� A high-beta stock is more volatile than an average stock, while a low-beta stock is less volatile than an average stock. An average stock has b � 1.0.

� The beta of a portfolio is a weighted average of the betas of the indi- vidual securities in the portfolio.

� The Security Market Line (SML) equation shows the relationship be- tween a security’s market risk and its required rate of return. The return required for any security i is equal to the risk-free rate plus the market risk premium times the security’s beta: ki � kRF � (kM � kRF)bi.

� Even though the expected rate of return on a stock is generally equal to its required return, a number of things can happen to cause the required rate of return to change: (1) the risk-free rate can change because of changes in either real rates or anticipated inflation, (2) a stock’s beta can change, and (3) investors’ aversion to risk can change.

� Because returns on assets in different countries are not perfectly corre- lated, global diversification may result in lower risk for multinational companies and globally diversified portfolios.

273

In the next three chapters, we will see how a security’s rate of return affects its value. Then, in the remainder of the book, we will examine the ways in which a firm’s management can influence a stock’s riskiness and hence its price.

Q U E S T I O N S

6-1 The probability distribution of a less risky expected return is more peaked than that of a riskier return. What shape would the probability distribution have for (a) completely certain returns and (b) completely uncertain returns?

6-2 Security A has an expected return of 7 percent, a standard deviation of expected returns of 35 percent, a correlation coefficient with the market of �0.3, and a beta coefficient of �0.5. Security B has an expected return of 12 percent, a standard deviation of returns of 10 percent, a correlation with the market of 0.7, and a beta coefficient of 1.0. Which se- curity is riskier? Why?

6-3 Suppose you owned a portfolio consisting of $250,000 worth of long-term U.S. govern- ment bonds. a. Would your portfolio be riskless? b. Now suppose you hold a portfolio consisting of $250,000 worth of 30-day Treasury

bills. Every 30 days your bills mature, and you reinvest the principal ($250,000) in a new batch of bills. Assume that you live on the investment income from your port- folio and that you want to maintain a constant standard of living. Is your portfolio truly riskless?

c. Can you think of any asset that would be completely riskless? Could someone de- velop such an asset? Explain.

6-4 A life insurance policy is a financial asset. The premiums paid represent the investment’s cost. a. How would you calculate the expected return on a life insurance policy? b. Suppose the owner of a life insurance policy has no other financial assets — the per-

son’s only other asset is “human capital,” or lifetime earnings capacity. What is the correlation coefficient between returns on the insurance policy and returns on the policyholder’s human capital?

c. Life insurance companies have to pay administrative costs and sales representatives’ commissions; hence, the expected rate of return on insurance premiums is generally low, or even negative. Use the portfolio concept to explain why people buy life in- surance in spite of negative expected returns.

6-5 If investors’ aversion to risk increased, would the risk premium on a high-beta stock in- crease more or less than that on a low-beta stock? Explain.

6-6 If a company’s beta were to double, would its expected return double? 6-7 Is it possible to construct a portfolio of stocks that has an expected return equal to the

risk-free rate? 6-8 A stock had a 12 percent return last year, a year in which the overall stock market de-

clined in value. Does this mean that the stock has a negative beta?

S E L F - T E S T P R O B L E M S ( S O L U T I O N S A P P E A R I N A P P E N D I X B )

Define the following terms, using graphs or equations to illustrate your answers wher- ever feasible: a. Stand-alone risk; risk; probability distribution b. Expected rate of return, k̂ c. Continuous probability distribution d. Standard deviation, �; variance, �2; coefficient of variation, CV e. Risk aversion; realized rate of return, k� f. Risk premium for Stock i, RPi; market risk premium, RPM g. Capital Asset Pricing Model (CAPM)

ST-1 Key terms

S E L F - T E S T P R O B L E M S

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N274

h. Expected return on a portfolio, k̂p; market portfolio i. Correlation coefficient, r; correlation j. Market risk; diversifiable risk; relevant risk k. Beta coefficient, b; average stock’s beta, bA l. Security Market Line (SML); SML equation

m. Slope of SML as a measure of risk aversion Stocks A and B have the following historical returns:

YEAR STOCK A’S RETURNS, kA STOCK B’S RETURNS, kB

1997 (10.00%) (3.00%) 1998 18.50 21.29 1999 38.67 44.25 2000 14.33 3.67 2001 33.00 28.30

a. Calculate the average rate of return for each stock during the period 1997 through 2001. Assume that someone held a portfolio consisting of 50 percent of Stock A and 50 percent of Stock B. What would have been the realized rate of return on the port- folio in each year from 1997 through 2001? What would have been the average re- turn on the portfolio during this period?

b. Now calculate the standard deviation of returns for each stock and for the portfolio. Use Equation 6-3a in Footnote 5.

c. Looking at the annual returns data on the two stocks, would you guess that the cor- relation coefficient between returns on the two stocks is closer to 0.9 or to �0.9?

d. If you added more stocks at random to the portfolio, which of the following is the most accurate statement of what would happen to �p? (1) �p would remain constant. (2) �p would decline to somewhere in the vicinity of 21 percent. (3) �p would decline to zero if enough stocks were included.

ECRI Corporation is a holding company with four main subsidiaries. The percentage of its business coming from each of the subsidiaries, and their respective betas, are as follows:

SUBSIDIARY PERCENTAGE OF BUSINESS BETA

Electric utility 60% 0.70 Cable company 25 0.90 Real estate 10 1.30 International/special projects 5 1.50

a. What is the holding company’s beta? b. Assume that the risk-free rate is 6 percent and the market risk premium is 5 percent.

What is the holding company’s required rate of return? c. ECRI is considering a change in its strategic focus; it will reduce its reliance on the

electric utility subsidiary, so the percentage of its business from this subsidiary will be 50 percent. At the same time, ECRI will increase its reliance on the international/ special projects division, so the percentage of its business from that subsidiary will rise to 15 percent. What will be the shareholders’ required rate of return if ECRI adopts these changes?

ST-3 Beta and required rate of return

ST-2 Realized rates of return

275

S TA R T E R P R O B L E M S

A stock’s expected return has the following distribution:

RATE OF RETURN DEMAND FOR THE PROBABILITY OF THIS IF THIS DEMAND COMPANY’S PRODUCTS DEMAND OCCURRING OCCURS

Weak 0.1 (50%) Below average 0.2 ( 5) Average 0.4 16 Above average 0.2 25 Strong 0.1 60

1.0

Calculate the stock’s expected return, standard deviation, and coefficient of variation. An individual has $35,000 invested in a stock that has a beta of 0.8 and $40,000 invested in a stock with a beta of 1.4. If these are the only two investments in her portfolio, what is her portfolio’s beta? Assume that the risk-free rate is 5 percent and the market risk premium is 6 percent. What is the expected return for the overall stock market? What is the required rate of return on a stock that has a beta of 1.2? Assume that the risk-free rate is 6 percent and the expected return on the market is 13 percent. What is the required rate of return on a stock that has a beta of 0.7? A stock has a required return of 11 percent. The risk-free rate is 7 percent, and the mar- ket risk premium is 4 percent. a. What is the stock’s beta? b. If the market risk premium increases to 6 percent, what will happen to the stock’s re-

quired rate of return? Assume the risk-free rate and the stock’s beta remain un- changed.

E X A M - T Y P E P R O B L E M S

The problems included in this section are set up in such a way that they could be used as multiple- choice exam problems. The market and Stock J have the following probability distributions:

PROBABILITY kM kJ

0.3 15% 20% 0.4 9 5 0.3 18 12

a. Calculate the expected rates of return for the market and Stock J. b. Calculate the standard deviations for the market and Stock J. c. Calculate the coefficients of variation for the market and Stock J. Stocks X and Y have the following probability distributions of expected future returns:

PROBABILITY X Y

0.1 (10%) (35%) 0.2 2 0 0.4 12 20 0.2 20 25 0.1 38 45

6-7 Expected returns

6-6 Expected returns

6-5 Beta and required rate of return

6-4 Required rate of return

6-3 Expected and required rates of return

6-2 Portfolio beta

6-1 Expected return

E X A M - T Y P E P R O B L E M S

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N276

a. Calculate the expected rate of return, k̂, for Stock Y. (k̂X � 12%.) b. Calculate the standard deviation of expected returns for Stock X. (That for Stock

Y is 20.35 percent.) Now calculate the coefficient of variation for Stock Y. Is it possible that most investors might regard Stock Y as being less risky than Stock X? Explain.

Suppose kRF � 5%, kM � 10%, and kA � 12%. a. Calculate Stock A’s beta. b. If Stock A’s beta were 2.0, what would be A’s new required rate of return? Suppose kRF � 9%, kM � 14%, and bi � 1.3. a. What is ki, the required rate of return on Stock i? b. Now suppose kRF (1) increases to 10 percent or (2) decreases to 8 percent. The slope

of the SML remains constant. How would this affect kM and ki? c. Now assume kRF remains at 9 percent but kM (1) increases to 16 percent or (2) falls

to 13 percent. The slope of the SML does not remain constant. How would these changes affect ki?

Suppose you hold a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio beta is equal to 1.12. Now, suppose you have decided to sell one of the stocks in your portfolio with a beta equal to 1.0 for $7,500 and to use these proceeds to buy another stock for your portfolio. Assume the new stock’s beta is equal to 1.75. Calculate your portfolio’s new beta. Suppose you are the money manager of a $4 million investment fund. The fund consists of 4 stocks with the following investments and betas:

STOCK INVESTMENT BETA

A $ 400,000 1.50 B 600,000 (0.50) C 1,000,000 1.25 D 2,000,000 0.75

If the market’s required rate of return is 14 percent and the risk-free rate is 6 percent, what is the fund’s required rate of return? You have a $2 million portfolio consisting of a $100,000 investment in each of 20 dif- ferent stocks. The portfolio has a beta equal to 1.1. You are considering selling $100,000 worth of one stock that has a beta equal to 0.9 and using the proceeds to purchase an- other stock that has a beta equal to 1.4. What will be the new beta of your portfolio fol- lowing this transaction? Stock R has a beta of 1.5, Stock S has a beta of 0.75, the expected rate of return on an average stock is 13 percent, and the risk-free rate of return is 7 percent. By how much does the required return on the riskier stock exceed the required return on the less risky stock? Stock X has an expected return of 10 percent, a beta coefficient of 0.9, and a standard deviation of expected returns of 35 percent. Stock Y has an expected return of 12.5 per- cent, a beta coefficient of 1.2, and a standard deviation of expected returns of 25 percent. The risk-free rate is 6 percent, and the market risk premium is 5 percent. a. Calculate each stock’s coefficient of variation. b. Which stock is riskier for diversified investors? c. Calculate each stock’s required rate of return. d. On the basis of the two stocks’ expected and required returns, which stock would be

most attractive to a diversified investor? e. Calculate the required return of a portfolio that has $7,500 invested in Stock X and

$2,500 invested in Stock Y. f. If the market risk premium increased to 6 percent, which of the two stocks would

have the largest increase in their required return?

6-14 Evaluating risk and return

6-13 Required rate of return

6-12 Portfolio beta

6-11 Portfolio required return

6-10 Portfolio beta

6-9 Required rate of return

6-8 Required rate of return

277

P R O B L E M S

Suppose you won the Florida lottery and were offered (1) $0.5 million or (2) a gamble in which you would receive $1 million if a head were flipped but zero if a tail came up. a. What is the expected value of the gamble? b. Would you take the sure $0.5 million or the gamble? c. If you choose the sure $0.5 million, are you a risk averter or a risk seeker? d. Suppose you actually take the sure $0.5 million. You can invest it in either a U.S.

Treasury bond that will return $537,500 at the end of a year or a common stock that has a 50-50 chance of being either worthless or worth $1,150,000 at the end of the year. (1) What is the expected dollar profit on the stock investment? (The expected profit

on the T-bond investment is $37,500.) (2) What is the expected rate of return on the stock investment? (The expected rate

of return on the T-bond investment is 7.5 percent.) (3) Would you invest in the bond or the stock? (4) Exactly how large would the expected profit (or the expected rate of return) have

to be on the stock investment to make you invest in the stock, given the 7.5 per- cent return on the bond?

(5) How might your decision be affected if, rather than buying one stock for $0.5 million, you could construct a portfolio consisting of 100 stocks with $5,000 invested in each? Each of these stocks has the same return characteristics as the one stock — that is, a 50-50 chance of being worth either zero or $11,500 at year-end. Would the correlation between returns on these stocks matter?

The Kish Investment Fund, in which you plan to invest some money, has total capital of $500 million invested in five stocks:

STOCK INVESTMENT STOCK’S BETA COEFFICIENT

A $160 million 0.5 B 120 million 2.0 C 80 million 4.0 D 80 million 1.0 E 60 million 3.0

The beta coefficient for a fund like Kish Investment can be found as a weighted average of the fund’s investments. The current risk-free rate is 6 percent, whereas market returns have the following estimated probability distribution for the next period:

PROBABILITY MARKET RETURN

0.1 7% 0.2 9 0.4 11 0.2 13 0.1 15

a. What is the estimated equation for the Security Market Line (SML)? (Hint: First de- termine the expected market return.)

b. Calculate the fund’s required rate of return for the next period. c. Suppose Bridget Nelson, the president, receives a proposal for a new stock. The in-

vestment needed to take a position in the stock is $50 million, it will have an expected

6-16 Security Market Line

6-15 Expected returns

P R O B L E M S

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N278

return of 15 percent, and its estimated beta coefficient is 2.0. Should the new stock be purchased? At what expected rate of return should the fund be indifferent to pur- chasing the stock?

Stocks A and B have the following historical returns:

YEAR STOCK A’S RETURNS, kA STOCK B’S RETURNS, kB

1997 (18.00%) (14.50%) 1998 33.00 21.80 1999 15.00 30.50 2000 (0.50) (7.60) 2001 27.00 26.30

a. Calculate the average rate of return for each stock during the period 1997 through 2001.

b. Assume that someone held a portfolio consisting of 50 percent of Stock A and 50 percent of Stock B. What would have been the realized rate of return on the portfo- lio in each year from 1997 through 2001? What would have been the average return on the portfolio during this period?

c. Calculate the standard deviation of returns for each stock and for the portfolio. d. Calculate the coefficient of variation for each stock and for the portfolio. e. If you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the

portfolio? Why? You have observed the following returns over time:

YEAR STOCK X STOCK Y MARKET

1997 14% 13% 12% 1998 19 7 10 1999 �16 �5 �12 2000 3 1 1 2001 20 11 15

Assume that the risk-free rate is 6 percent and the market risk premium is 5 percent. a. What are the betas of Stocks X and Y? (Hint: See Appendix 6A.) b. What are the required rates of return for Stocks X and Y? c. What is the required rate of return for a portfolio consisting of 80 percent of Stock

X and 20 percent of Stock Y? d. If Stock X’s expected return is 22 percent, is Stock X under- or overvalued?

S P R E A D S H E E T P R O B L E M

Bartman Industries’ stock prices and dividends, along with the Wilshire 5000 Index, are shown below for the period 1995-2000. The Wilshire 5000 data are adjusted to include dividends.

BA R T M A N I N D U S T R I E S R E Y N O L D S I N C O R P O R AT E D W I L S H I R E 5 0 0 0

YEAR STOCK PRICE DIVIDEND STOCK PRICE DIVIDEND INCLUDES DIVS.

2000 $17.250 $1.15 $48.750 $3.00 11,663.98 1999 14.750 1.06 52.300 2.90 8,785.70 1998 16.500 1.00 48.750 2.75 8,679.98 1997 10.750 0.95 57.250 2.50 6,434.03 1996 11.375 0.90 60.000 2.25 5,602.28 1995 7.625 0.85 55.750 2.00 4,705.97

6-19 Evaluating risk and return

6-18 Financial calculator needed; Expected

and required rates of return

6-17 Realized rates of return

279

a. Use the data given to calculate annual returns for Bartman, Reynolds, and the Wilshire 5000 Index, and then calculate average returns over the 5-year period. (Hint: Remember, returns are calculated by subtracting the beginning price from the ending price to get the capital gain or loss, adding the dividend to the capital gain or loss, and dividing the result by the beginning price. Assume that dividends are al- ready included in the index. Also, you cannot calculate the rate of return for 1995 be- cause you do not have 1994 data.)

b. Calculate the standard deviations of the returns for Bartman, Reynolds, and the Wilshire 5000. (Hint: Use the sample standard deviation formula given in Footnote 5 to this chapter, which corresponds to the STDEV function in Excel.)

c. Now calculate the coefficients of variation for Bartman, Reynolds, and the Wilshire 5000.

d. Construct a scatter diagram graph that shows Bartman’s and Reynolds’ returns on the vertical axis and the market index’s returns on the horizontal axis.

e. Estimate Bartman’s and Reynolds’ betas by running regressions of their returns against the Wilshire 5000’s returns. Are these betas consistent with your graph?

f. The risk-free rate on long-term Treasury bonds is 6.04 percent. Assume that the av- erage annual return on the Wilshire 5000 is not a good estimate of the market’s re- quired return — it is too high, so use 11 percent as the expected return on the mar- ket. Now use the SML equation to calculate the two companies’ required returns.

g. If you formed a portfolio that consisted of 50 percent of Bartman stock and 50 per- cent of Reynolds stock, what would be the beta and the required return for the port- folio?

h. Suppose an investor wants to include Bartman Industries’ stock in his or her portfo- lio. Stocks A, B, and C are currently in the portfolio, and their betas are 0.769, 0.985, and 1.423, respectively. Calculate the new portfolio’s required return if it consists of 25 percent of Bartman, 15 percent of Stock A, 40 percent of Stock B, and 20 percent of Stock C.

C Y B E R P R O B L E M

The information related to the cyberproblems is likely to change over time, due to the release of new information and the ever-changing nature of the World Wide Web. With these changes in mind, we will periodically update these problems on the textbook’s web site. To avoid problems, please check for these updates before proceeding with the cyberproblems.

The tendency of a stock’s price to move up and down with the market is reflected in its beta coefficient. Therefore, beta is a measure of an investment’s market risk and is a key element of the CAPM.

In this exercise you will find betas using Yahoo!Finance, located at http:// finance.yahoo.com. To find a company’s beta, enter the desired stock symbol and request a basic quote. Once you have the basic quote, select the “Profile” option in the “More Info” section of the basic quote screen. Scroll down this page to find the stock’s beta. a. According to Yahoo!Finance, what is the beta for a company called ELXSI, whose

stock symbol is ELXS? b. From Yahoo!Finance obtain a report on MBNA America Bank’s holding company,

KRB, whose stock symbol is KRB. What is KRB’s beta? c. Obtain and view a report for Exxon Mobil Corporation and identify its beta. Use

Yahoo!Finance’s look-up feature to obtain Exxon Mobil’s trading symbol. To do this, click on symbol lookup, type part of the company name, say Exxon, and then click on Lookup. (Hint: You should find that the company’s stock symbol is XOM.)

d. Obtain and view a report on Ford Motor Company, and identify its beta. Use Yahoo!Finance’s look-up feature to obtain Ford’s trading symbol.

e. If you made an equal dollar investment in each of the four stocks above, ELXSI, KRB, Exxon Mobil, and Ford Motor Company, what would be your portfolio’s beta?

6-20 Risk and rates of return

MERRILL FINCH INC. 6-21 Risk and Return Assume that you recently graduated with a major in finance, and you just landed a job as a financial planner with Merrill Finch Inc., a large financial services cor- poration.Yourfirst assignment is to invest$100,000 foraclient. Because the funds are to be invested in a business at the end of 1 year, you have been instructed to plan for a 1-year holding pe- riod. Further, your boss has restricted you to the following in- vestment alternatives in the table below, shown with their probabilities and associated outcomes. (Disregard for now the items at the bottom of the data; you will fill in the blanks later.)

Merrill Finch’s economic forecasting staff has developed probability estimates for the state of the economy, and its se- curity analysts have developed a sophisticated computer pro- gram, which was used to estimate the rate of return on each alternative under each state of the economy. High Tech Inc. is an electronics firm; Collections Inc. collects past-due debts; and U.S. Rubber manufactures tires and various other rubber and plastics products. Merrill Finch also maintains a “market portfolio” that owns a market-weighted fraction of all publicly traded stocks; you can invest in that portfolio, and thus obtain average stock market results. Given the sit- uation as described, answer the following questions.

a. (1) Why is the T-bill’s return independent of the state of the economy? Do T-bills promise a completely risk-free return? (2) Why are High Tech’s returns expected to move with the economy whereas Collections’ are ex- pected to move counter to the economy?

b. Calculate the expected rate of return on each alternative and fill in the blanks on the row for k̂ in the table below.

c. You should recognize that basing a decision solely on ex- pected returns is only appropriate for risk-neutral indi- viduals. Since your client, like virtually everyone, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of returns. (1) Calculate this value for each alternative, and fill in the blank on the row for � in the table below. (2) What type of risk is measured by the standard deviation? (3) Draw a graph that shows roughly the shape of the probability distributions for High Tech, U.S. Rubber, and T-bills.

d. Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as being a better measure of stand-alone risk than the standard deviation when the alternatives being considered have widely dif- fering expected returns. Calculate the missing CVs, and

C H A P T E R 6 � R IS K A N D R AT E S O F R E T U R N280

281I N T E G R AT E D C A S E

R E T U R N S O N A LT E R N AT I V E I N V E S T M E N T S

E S T I M AT E D R AT E O F R E T U R N

STATE OF HIGH U.S. MARKET 2-STOCK THE ECONOMY PROBABILITY T-BILLS TECH COLLECTIONS RUBBER PORTFOLIO PORTFOLIO

Recession 0.1 8.0% (22.0%) 28.0% 10.0%* (13.0%) 3.0% Below average 0.2 8.0 (2.0) 14.7 (10.0) 1.0 Average 0.4 8.0 20.0 0.0 7.0 15.0 10.0 Above average 0.2 8.0 35.0 (10.0) 45.0 29.0 Boom 0.1 8.0 50.0 (20.0) 30.0 43.0 15.0 k̂ 1.7% 13.8% 15.0% � 0.0 13.4 18.8 15.3 3.3 CV 7.9 1.4 1.0 0.3 b �0.87 0.89

* Note that the estimated returns of U.S. Rubber do not always move in the same direction as the overall economy. For example, when the economy is below average, consumers purchase fewer tires than they would if the economy was stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a new car may choose to wait and instead purchase new tires for the car they currently own. Under these circumstances, we would expect U.S. Rubber’s stock price to be higher if there is a recession than if the economy was just below average.

fill in the blanks on the row for CV in the table above. Does the CV produce the same risk rankings as the stan- dard deviation?

e. Suppose you created a 2-stock portfolio by investing $50,000 in High Tech and $50,000 in Collections. (1) Cal- culate the expected return (k̂p), the standard deviation (�p), and the coefficient of variation (CVp) for this portfolio and fill in the appropriate blanks in the table above. (2) How does the riskiness of this 2-stock portfolio compare with the riskiness of the individual stocks if they were held in isolation?

f. Suppose an investor starts with a portfolio consisting of one randomly selected stock. What would happen (1) to the riskiness and (2) to the expected return of the port- folio as more and more randomly selected stocks were added to the portfolio? What is the implication for in- vestors? Draw a graph of the two portfolios to illustrate your answer.

g. (1) Should portfolio effects impact the way investors think about the riskiness of individual stocks? (2) If you decided to hold a 1-stock portfolio, and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all of your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying?

h. The expected rates of return and the beta coefficients of the alternatives as supplied by Merrill Finch’s computer program are as follows:

SECURITY RETURN (k̂) RISK (BETA)

High Tech 17.4% 1.30 Market 15.0 1.00 U.S. Rubber 13.8 0.89 T-bills 8.0 0.00 Collections 1.7 (0.87)

(1) What is a beta coefficient, and how are betas used in risk analysis? (2) Do the expected returns appear to be related to each alternative’s market risk? (3) Is it possible to choose among the alternatives on the basis of the in- formation developed thus far? Use the data given at the start of the problem to construct a graph that shows how the T-bill’s, High Tech’s, and Collections’ beta coeffi- cients are calculated. Then discuss what betas measure and how they are used in risk analysis.

i. The yield curve is currently flat, that is, long-term Treasury bonds also have an 8 percent yield. Conse- quently, Merrill Finch assumes that the risk-free rate is 8 percent. (1) Write out the Security Market Line (SML) equation, use it to calculate the required rate of return on each alternative, and then graph the relation- ship between the expected and required rates of return. (2) How do the expected rates of return compare with the required rates of return? (3) Does the fact that Col- lections has an expected return that is less than the T- bill rate make any sense? (4) What would be the market risk and the required return of a 50-50 portfolio of High Tech and Collections? Of High Tech and U.S. Rubber?

j. (1) Suppose investors raised their inflation expectations by 3 percentage points over current estimates as re- flected in the 8 percent risk-free rate. What effect would higher inflation have on the SML and on the returns re- quired on high- and low-risk securities? (2) Suppose in- stead that investors’ risk aversion increased enough to cause the market risk premium to increase by 3 percent- age points. (Inflation remains constant.) What effect would this have on the SML and on returns of high- and low-risk securities?

The CAPM is an ex ante model, which means that all of the variables represent before-the-fact, expected values. In particular, the beta coefficient used in the SML equation should reflect the expected volatility of a given stock’s return ver- sus the return on the market during some future period. However, people gen- erally calculate betas using data from some past period, and then assume that the stock’s relative volatility will be the same in the future as it was in the past.

To illustrate how betas are calculated, consider Figure 6A-1. The data at the bottom of the figure show the historical realized returns for Stock J and for the market over the last five years. The data points have been plotted on the scat- ter diagram, and a regression line has been drawn. If all the data points had fallen on a straight line, as they did in Figure 6-9 in Chapter 6, it would be easy to draw an accurate line. If they do not, as in Figure 6A-1, then you must fit the line either “by eye” as an approximation or with a calculator.

Recall what the term regression line, or regression equation, means: The equa- tion Y � a � bX � e is the standard form of a simple linear regression. It states that the dependent variable, Y, is equal to a constant, a, plus b times X, where b is the slope coefficient and X is the independent variable, plus an error term, e. Thus, the rate of return on the stock during a given time period (Y) depends on what happens to the general stock market, which is measured by X � k� M.

Once the data have been plotted and the regression line has been drawn on graph paper, we can estimate its intercept and slope, the a and b values in Y � a � bX. The intercept, a, is simply the point where the line cuts the vertical axis. The slope coefficient, b, can be estimated by the “rise-over-run” method. This involves calculating the amount by which k� J increases for a given increase in k� M. For example, we observe in Figure 6A-1 that k� J increases from �8.9 to �7.1 percent (the rise) when k� M increases from 0 to 10.0 percent (the run). Thus, b, the beta coefficient, can be measured as follows:

Note that rise over run is a ratio, and it would be the same if measured using any two arbitrarily selected points on the line.

The regression line equation enables us to predict a rate of return for Stock J, given a value of k� M. For example, if k� M � 15%, we would predict k� J � �8.9% � 1.6(15%) � 15.1%. However, the actual return would probably dif- fer from the predicted return. This deviation is the error term, eJ, for the year, and it varies randomly from year to year depending on company-specific fac- tors. Note, though, that the higher the correlation coefficient, the closer the points lie to the regression line, and the smaller the errors.

In actual practice, monthly, rather than annual, returns are generally used for k�J and k�M, and five years of data are often employed; thus, there would be

b � Beta � Rise Run

� �Y �X

� 7.1 � (�8.9) 10.0 � 0.0

� 16.0 10.0

� 1.6.

A P P E N D I X 6 A � C A L C U L AT I N G B E TA C O E F F I C I E N TS282

CALCULATING BETA COEFFICIENTS

6A

283A P P E N D I X 6 A � C A L C U L AT I N G B E TA C O E F F I C I E N TS

5 � 12 � 60 data points on the scatter diagram. Also, in practice one would use the least squares method for finding the regression coefficients a and b. This pro- cedure minimizes the squared values of the error terms, and it is discussed in statistics courses.

The least squares value of beta can be obtained quite easily with a financial calculator. The procedures that follow explain how to find the values of beta and the slope using either a Texas Instruments, a Hewlett-Packard, or a Sharp financial calculator.

F I G U R E 6 A - 1 Calculating Beta Coefficients

k _

∆

Historic Realized Returns on Stock J, kJ(%)

Historic Realized Returns on the Market, k (%)

302010

aJ = Intercept = –8.9% k = 8.9% + 7.1% = 16%

= 10% b = Rise

Run = = 16

10 = 1.6J

M J

J

–10 0

–20

–10

10

20

30

40

7.1

Year 3

Year 4

Year 5Year 1

= aJ + bJkM + eJ = –8.9 + 1.6kM + eJ

kJ _ __

Year 2

_

_

M

_

M ∆

k _

∆ k _

∆

YEAR MARKET (k�M) STOCK J (k�J)

1 23.8% 38.6% 2 (7.2) (24.7) 3 6.6 12.3 4 20.5 8.2 5 30.6% 40.1%

Average k� 14.9% 14.9% �k� 15.1% 26.5%

TEXAS INSTRUMENTS BA, BA-II, OR MBA CALCULATOR

1. Press until “STAT” shows in the display. 2. Enter the first X value (k� M � 23.8 in our example), press , and

then enter the first Y value (k� J � 38.6) and press . 3. Repeat Step 2 until all values have been entered. 4. Press to find the value of Y at X � 0, which is the value of the

Y intercept (a), �8.9219, and then press to display the value of the slope (beta), 1.6031.

5. You could also press to obtain the correlation coefficient, r, which is 0.9134.

Putting it all together, you should have this regression line:

k� J � �8.92 � 1.60k� M r � 0.9134.

HEWLETT-PACKARD 10B1

1. Press to clear your memory registers. 2. Enter the first X value (k� M � 23.8 in our example), press , and

then enter the first Y value (k� J � 38.6) and press . Be sure to enter the X variable first.

3. Repeat Step 2 until all values have been entered. 4. To display the vertical axis intercept, press 0 . Then �8.9219

should appear. 5. To display the beta coefficient, b, press . Then 1.6031 should

appear. 6. To obtain the correlation coefficient, press and then

to get r � 0.9134.

Putting it all together, you should have this regression line:

k� J � �8.92 � 1.60k� M r � 0.9134.

SHARP EL-733

1. Press until “STAT” shows in the lower right corner of the display.

2. Press to clear all memory registers. 3. Enter the first X value (k� M � 23.8 in our example) and press . (This

is the RM key; do not press the second F key at all.) Then enter the first Y value (k� J � 38.6), and press . (This is the M� key; again, do not press the second F key.)

DATA

(x,y)

CA2nd F

Mode2nd F

SWAPx̂,r

SWAP

ŷ,m

��

INPUT

Clear all

Corr2nd

x � y b/a2nd

��

x � y

Mode2nd

A P P E N D I X 6 A � C A L C U L AT I N G B E TA C O E F F I C I E N TS284

1 The Hewlett-Packard 17B calculator is even easier to use. If you have one, see Chapter 9 of the Owner’s Manual.

285A P P E N D I X 6 A � C A L C U L AT I N G B E TA C O E F F I C I E N TS

4. Repeat Step 3 until all values have been entered. 5. Press to find the value of Y at X � 0, which is the value of the

Y intercept (a), �8.9219, and then press to display the value of the slope (beta), 1.6031.

6. You can also press to obtain the correlation coefficient, r, which is 0.9134.

Putting it all together, you should have this regression line:

k� J � �8.92 � 1.60k� M r � 0.9134.

Beta coefficients can also be calculated with spreadsheet programs such as Excel. Simply input the returns data and then use the spreadsheet’s regression rou- tine to calculate beta. The model on the file named 06MODEL.xls calculates beta for our illustrative Stock J, and it produces exactly the same results as with the cal- culator. However, the spreadsheet is more flexible. First, the file can be retained, and when new data become available, they can be added and a new beta can be cal- culated quite rapidly. Second, the regression output can include graphs and sta- tistical information designed to give us an idea of how stable the beta coefficient is. In other words, while our beta was calculated to be 1.60, the “true beta” might actually be higher or lower, and the regression output can give us an idea of how large the error might be. Third, the spreadsheet can be used to calculate returns data from historical stock price and dividend information, and then the returns can be fed into the regression routine to calculate the beta coefficient. This is im- portant, because stock market data are generally provided in the form of stock prices and dividends, making it necessary to calculate returns. This can be a big job if a number of different companies and a number of time periods are involved.

P R O B L E M S

You are given the following set of data:

H I S TO R I C A L R AT E S O F R E T U R N ( k�)

YEAR STOCK Y (k�Y) NYSE (k�M)

1 3.0% 4.0% 2 18.2 14.3 3 9.1 19.0 4 (6.0) (14.7) 5 (15.3) (26.5) 6 33.1 37.2 7 6.1 23.8 8 3.2 (7.2) 9 14.8 6.6

10 24.1 20.5 11 18.0% 30.6%

Mean 9.8% 9.8% �k� 13.8 19.6

a. Construct a scatter diagram graph (on graph paper) showing the relationship between returns on Stock Y and the market as in Figure 6A-1; then draw a freehand approx-

6A-1 Beta coefficients and rates of return

r2nd F

b2nd F a2nd F

A P P E N D I X 6 A � C A L C U L AT I N G B E TA C O E F F I C I E N TS286

imation of the regression line. What is the approximate value of the beta coefficient? (If you have a calculator with statistical functions, use it to calculate beta.)

b. Give a verbal interpretation of what the regression line and the beta coefficient show about Stock Y’s volatility and relative riskiness as compared with other stocks.

c. Suppose the scatter of points had been more spread out but the regression line was exactly where your present graph shows it. How would this affect (1) the firm’s risk if the stock were held in a 1-asset portfolio and (2) the actual risk premium on the stock if the CAPM held exactly? How would the degree of scatter (or the correlation coef- ficient) affect your confidence that the calculated beta will hold true in the years ahead?

d. Suppose the regression line had been downward sloping and the beta coefficient had been negative. What would this imply about (1) Stock Y’s relative riskiness and (2) its probable risk premium?

e. Construct an illustrative probability distribution graph of returns (see Figure 6-7) for portfolios consisting of (1) only Stock Y, (2) 1 percent each of 100 stocks with beta coefficients similar to that of Stock Y, and (3) all stocks (that is, the distribution of re- turns on the market). Use as the expected rate of return the arithmetic mean as given previously for both Stock Y and the market, and assume that the distributions are normal. Are the expected returns “reasonable” — that is, is it reasonable that k̂Y � k̂M � 9.8%?

f. Now, suppose that in the next year, Year 12, the market return was 27 percent, but Firm Y increased its use of debt, which raised its perceived risk to investors. Do you think that the return on Stock Y in Year 12 could be approximated by this historical characteristic line?

k̂Y � 3.8% � 0.62(k̂M) � 3.8% � 0.62(27%) � 20.5%.

g. Now, suppose k� Y in Year 12, after the debt ratio was increased, had actually been 0 percent. What would the new beta be, based on the most recent 11 years of data (that is, Years 2 through 12)? Does this beta seem reasonable — that is, is the change in beta consistent with the other facts given in the problem?

You are given the following historical data on market returns, k� M, and the returns on Stocks A and B, k� A and k� B:

YEAR k�M k�A k�B

1 29.00% 29.00% 20.00% 2 15.20 15.20 13.10 3 (10.00) (10.00) 0.50 4 3.30 3.30 7.15 5 23.00 23.00 17.00 6 31.70 31.70 21.35

kRF, the risk-free rate, is 9 percent. Your probability distribution for kM for next year is as follows:

PROBABILITY kM

0.1 (14%) 0.2 0 0.4 15 0.2 25 0.1 44

6A-2 Security Market Line

287

a. Determine graphically the beta coefficients for Stocks A and B. b. Graph the Security Market Line, and give its equation. c. Calculate the required rates of return on Stocks A and B. d. Suppose a new stock, C, with k̂C � 18 percent and bC � 2.0, becomes available. Is

this stock in equilibrium; that is, does the required rate of return on Stock C equal its expected return? Explain. If the stock is not in equilibrium, explain how equilib- rium will be restored.

A P P E N D I X 6 A � C A L C U L AT I N G B E TA C O E F F I C I E N TS

SOURCE: © Zigy Kaluzny/Tony Stone Images.

CHAPTER T i me Va l u e o f Mo ne y 17

88

1 This chapter was written on the assumption that most students will have financial calculators. Calculators are relatively inexpensive, and students who cannot use them run the risk of being deemed obsolete and uncompeti- tive before they even graduate. Therefore, the chapter has been written to include a discussion of financial cal- culator solutions along with the regular calculator, and tabular and spreadsheet solutions. Those sections that re- quire the use of financial calculators, are identified, and instructors may choose to permit students to skip them.

requirement would increase to $110,765 in 10 years and

to $180,424 in 20 years. If inflation were 7 percent, her

Year 20 requirement would jump to $263,139! How

much wealth would Ms. Jones need at retirement to

maintain her standard of living, and how much would

she have had to save during each working year to

accumulate that wealth?

The answer depends on a number of factors,

including the rate she could earn on her savings, the

inflation rate, and when her savings program began.

Also, the answer would depend on how much she will

receive from Social Security and from her corporate

retirement plan, if she has one. (She might not receive

much from Social Security unless she is really down and

out.) Note, too, that her plans could be upset if the

inflation rate increased, if the return on her savings

changed, or if she lived beyond 20 years.

Fortune and other organizations have done studies

relating to the retirement issue, using the tools and

techniques described in this chapter. The general

conclusion is that most Americans have been putting

their heads in the sand — many of us have been

ignoring what is almost certainly going to be a huge

personal and social problem. But if you study this

chapter carefully, you can avoid the trap that seems to

be catching so many people. �

our reaction to the question in the title of this

vignette is probably, “First things first! I’m

worried about getting a job, not retiring!”

However, an awareness of the retirement situation

could help you land a job because (1) this is an

important issue today, (2) employers prefer to hire

people who know the issues, and (3) professors often

test students on time value of money with problems

related to saving for some future purpose, including

retirement. So read on.

A recent Fortune article began with some interesting

facts: (1) The U.S. savings rate is the lowest of any

industrial nation. (2) The ratio of U.S. workers to

retirees, which was 17 to 1 in 1950, is now down to 3.2

to 1, and it will decline to less than 2 to 1 after 2020.

(3) With so few people paying into the Social Security

System, and so many drawing funds out, Social Security

may soon be in serious trouble. The article concluded

that even people making $85,000 per year will have

trouble maintaining a reasonable standard of living after

they retire, and many of today’s college students will

have to support their parents.

If Ms. Jones, who earns $85,000, retires in 2001,

expects to live for another 20 years after retirement,

and needs 80 percent of her pre-retirement income, she

would require $68,000 during 2001. However, if

inflation amounts to 5 percent per year, her income

W I L L YO U B E A B L E TO R E T I R E ?

$

Y

289

Note also that tutorials on how to use several Hewlett-Packard, Texas Instruments, and Sharp calculators are provided in the Technology Supplement to this book, which is available to adopting instructors. We also discuss spreadsheets briefly in the chapter, and a more complete discussion is contained in the file 07MODEL.xls on the CD-ROM that accompanies the book. The spreadsheet material is also set up so that it can be either covered or skipped.

C H A P T E R 7 � T I M E VA L U E O F MO N E Y290

In Chapter 1, we saw that the primary goal of financial management is to maxi-

mize the value of the firm’s stock. We also saw that stock values depend in part

on the timing of the cash flows investors expect to receive from an investment —

a dollar expected soon is worth more than a dollar expected in the distant future.

Therefore, it is essential for financial managers to have a clear understanding of

the time value of money and its impact on stock prices. These concepts are dis-

cussed in this chapter, where we show how the timing of cash flows affects asset

values and rates of return.

The principles of time value analysis have many applications, ranging from set-

ting up schedules for paying off loans to decisions about whether to acquire new

equipment. In fact, of all the concepts used in finance, none is more important than

the time value of money, also called discounted cash flow (DCF) analysis. Since this

concept is used throughout the remainder of the book, it is vital that you under-

stand the material in this chapter before you move on to other topics. �

T I M E L I N E S

One of the most important tools in time value analysis is the time line, which is used by analysts to help visualize what is happening in a particular problem and then to help set up the problem for solution. To illustrate the time line concept, consider the following diagram:

Time 0 is today; Time 1 is one period from today, or the end of Period 1; Time 2 is two periods from today, or the end of Period 2; and so on. Thus, the num- bers above the tick marks represent end-of-period values. Often the periods are years, but other time intervals such as semiannual periods, quarters, months, or even days can be used. If each period on the time line represents a year, the in- terval from the tick mark corresponding to 0 to the tick mark corresponding to 1 would be Year 1, the interval from 1 to 2 would be Year 2, and so on. Note that each tick mark corresponds to the end of one period as well as the begin- ning of the next period. In other words, the tick mark at Time 1 represents the end of Year 1, and it also represents the beginning of Year 2 because Year 1 has just passed.

0Time: 1 2 3 4 5

Excellent retirement calculators are available at http://www. sovereignbank.com/ calculate/index.html. You

will need to scroll down the page until you see retirement calculators — there are 17 of them, each designed to answer a different question. Each one provides results, graphs, and explanations.

Time Line An important tool used in time value of money analysis; it is a graphical representation used to show the timing of cash flows.

291

Cash flows are placed directly below the tick marks, and interest rates are shown directly above the time line. Unknown cash flows, which you are trying to find in the analysis, are indicated by question marks. Now consider the fol- lowing time line:

Here the interest rate for each of the three periods is 5 percent; a single amount (or lump sum) cash outflow is made at Time 0; and the Time 3 value is an un- known inflow. Since the initial $100 is an outflow (an investment), it has a minus sign. Since the Period 3 amount is an inflow, it does not have a minus sign, which implies a plus sign. Note that no cash flows occur at Times 1 and 2. Note also that we generally do not show dollar signs on time lines to reduce clutter.

Now consider a different situation, where a $100 cash outflow is made today, and we will receive an unknown amount at the end of Time 2:

Here the interest rate is 5 percent during the first period, but it rises to 10 per- cent during the second period. If the interest rate is constant in all periods, we show it only in the first period, but if it changes, we show all the relevant rates on the time line.

Time lines are essential when you are first learning time value concepts, but even experts use time lines to analyze complex problems. We will be using time lines throughout the book, and you should get into the habit of using them when you work problems.

0 5% 10%

�100 ?

1 2

0 5%

�100Cash flows:

Time: 1 2 3

?

F U T U R E VA L U E

Outflow A cash deposit, cost, or amount paid. It has a minus sign.

Inflow A cash receipt.

SELF-TEST QUESTION

Draw a three-year time line to illustrate the following situation: (1) An out- flow of $10,000 occurs at Time 0. (2) Inflows of $5,000 then occur at the end of Years 1, 2, and 3. (3) The interest rate during all three years is 10 percent.

F U T U R E VA L U E

A dollar in hand today is worth more than a dollar to be received in the future because, if you had it now, you could invest it, earn interest, and end up with more than one dollar in the future. The process of going from today’s values, or present values (PVs), to future values (FVs) is called compounding. To il- lustrate, suppose you deposit $100 in a bank that pays 5 percent interest each year. How much would you have at the end of one year? To begin, we define the following terms:

Compounding The arithmetic process of determining the final value of a cash flow or series of cash flows when compound interest is applied.

C H A P T E R 7 � T I M E VA L U E O F MO N E Y292

PV � present value, or beginning amount, in your account. Here PV � $100. i � interest rate the bank pays on the account per year. The interest earned

is based on the balance at the beginning of each year, and we assume that it is paid at the end of the year. Here i � 5%, or, expressed as a decimal, i � 0.05. Throughout this chapter, we designate the interest rate as i (or I) because that symbol is used on most financial calculators. Note, though, that in later chapters we use the symbol k to denote interest rates because k is used more often in the financial literature.

INT � dollars of interest you earn during the year � Beginning amount � i. Here INT � $100(0.05) � $5.

FVn � future value, or ending amount, of your account at the end of n years. Whereas PV is the value now, or the present value, FVn is the value n years into the future, after the interest earned has been added to the ac- count.

n � number of periods involved in the analysis. Here n � 1.

In our example, n � 1, so FVn can be calculated as follows:

FVn � FV1 � PV � INT

� PV � PV(i)

� PV(1 � i)

� $100(1 � 0.05) � $100(1.05) � $105.

Thus, the future value (FV) at the end of one year, FV1, equals the present value multiplied by 1 plus the interest rate, so you will have $105 after one year.

What would you end up with if you left your $100 in the account for five years? Here is a time line set up to show the amount at the end of each year:

Note the following points: (1) You start by depositing $100 in the account — this is shown as an outflow at t � 0. (2) You earn $100(0.05) � $5 of interest during the first year, so the amount at the end of Year 1 (or t � 1) is $100 � $5 � $105. (3) You start the second year with $105, earn $5.25 on the now larger amount, and end the second year with $110.25. Your interest during Year 2, $5.25, is higher than the first year’s interest, $5, because you earned $5(0.05) � $0.25 interest on the first year’s interest. (4) This process continues, and because the beginning balance is higher in each succeeding year, the annual interest earned increases. (5) The total interest earned, $27.63, is reflected in the final balance at t � 5, $127.63.

Note that the value at the end of Year 2, $110.25, is equal to

FV2 � FV1(1 � i)

� PV(1 � i)(1 � i)

� PV(1 � i)2

� $100(1.05)2 � $110.25.

Future Value (FV) The amount to which a cash flow or series of cash flows will grow over a given period of time when compounded at a given interest rate. 0 5%

�100 FV1 � ? FV2 � ? FV3 � ? FV4 � ? FV5 � ?

1

5.00Interest earned:

Initial deposit:

Amount at the end of each period � FVn: 105.00

5.25

110.25

5.51

115.76

5.79

121.55

6.08

127.63

2 3 4 5

293

Continuing, the balance at the end of Year 3 is

FV3 � FV2(1 � i)

� PV(1 � i)3

� $100(1.05)3 � $115.76,

and

FV5 � $100(1.05) 5 � $127.63.

In general, the future value of an initial lump sum at the end of n years can be found by applying Equation 7-1:

FVn � PV(1 � i) n. (7-1)

Equation 7-1 and most other time value of money equations can be solved in four ways: numerically with a regular calculator, with interest tables, with a fi- nancial calculator, or with a computer spreadsheet program. Most advanced work in financial management will be done with a financial calculator or on a computer, but when learning basic concepts it is best to work through all the methods.

Numerical Solution

One can use a regular calculator and either multiply (1 � i) by itself n � 1 times or else use the exponential function to raise (1 � i) to the nth power. With most calculators, you would enter 1 � i � 1.05 and multiply it by itself four times, or else enter 1.05, then press the yx (exponential) function key, and then enter 5. In either case, your answer would be 1.2763 (if you set your cal- culator to display four decimal places), which you would multiply by $100 to get the final answer, $127.6282, which would be rounded to $127.63.

In certain problems, it is extremely difficult to arrive at a solution using a regular calculator. We will tell you this when we have such a problem, and in these cases we will not show a numerical solution. Also, at times we show the numerical solution just below the time line, as a part of the diagram, rather than in a separate section.

Interest Tables (Tabular Solution)

The Future Value Interest Factor for i and n (FVIFi,n) is defined as (1 � i)n, and these factors can be found by using a regular calculator as discussed above and then put into tables. Table 7-1 is illustrative, while Table A-3 in Appendix A at the back of the book contains FVIFi,n values for a wide range of i and n values.

Since (1 � i)n � FVIFi,n, Equation 7-1 can be rewritten as follows:

FVn � PV(FVIFi,n). (7-1a)

To illustrate, the FVIF for our five-year, 5 percent interest problem can be found in Table 7-1 by looking down the first column to Period 5, and then looking across that row to the 5 percent column, where we see that FVIF5%,5 � 1.2763. Then, the value of $100 after five years is found as follows:

FVn � PV(FVIFi,n)

� $100(1.2763) � $127.63.

F U T U R E VA L U E

Future Value Interest Factor for i and n (FVIFi,n) The future value of $1 left on deposit for n periods at a rate of i percent per period.

C H A P T E R 7 � T I M E VA L U E O F MO N E Y294

Before financial calculators became readily available (in the 1980s), such tables were used extensively, but they are rarely used today in the real world.

Financial Calculator Solution

Equation 7-1 and a number of other equations have been programmed directly into financial calculators, and these calculators can be used to find future val- ues. Note that calculators have five keys that correspond to the five most com- monly used time value of money variables:

Here

N � the number of periods. Some calculators use n rather than N. I � interest rate per period. Some calculators use i or I/YR rather than I.

PV � present value. PMT � payment. This key is used only if the cash flows involve a series of

equal, or constant, payments (an annuity). If there are no periodic payments in a particular problem, then PMT � 0.

FV � future value.

On some financial calculators, these keys are actually buttons on the face of the calculator, while on others they are shown on a screen after going into the time value of money (TVM) menu.

In this chapter, we deal with equations involving only four of the variables at any one time — three of the variables are known, and the calculator then solves for the fourth (unknown) variable. In the next chapter, when we deal with bonds, we will use all five variables in the bond valuation equation.2

T A B L E 7 - 1

PERIOD (n) 0% 5% 10% 15%

1 1.0000 1.0500 1.1000 1.1500 2 1.0000 1.1025 1.2100 1.3225 3 1.0000 1.1576 1.3310 1.5209 4 1.0000 1.2155 1.4641 1.7490 5 1.0000 1.2763 1.6105 2.0114 6 1.0000 1.3401 1.7716 2.3131 7 1.0000 1.4071 1.9487 2.6600 8 1.0000 1.4775 2.1436 3.0590 9 1.0000 1.5513 2.3579 3.5179

10 1.0000 1.6289 2.5937 4.0456

Future Value Interest Factors: FVIFi,n � (1 � i) n

2 The equation programmed into the calculators actually has five variables, one for each key. In this chapter, the value of one of the variables is always zero. It is a good idea to get into the habit of inputting

(footnote continues)

295

To find the future value of $100 after five years at 5 percent using a financial calculator, note that we must solve Equation 7-1:

FVn � PV(1 � i) n. (7-1)

The equation has four variables, FVn, PV, i, and n. If we know any three, we can solve for the fourth. In our example, we enter N � 5, I � 5, PV � 100, and PMT � 0. Then, when we press the FV key, we get the answer, FV � 127.63 (rounded to two decimal places).3

Many financial calculators require that all cash flows be designated as either inflows or outflows, with outflows being entered as negative numbers. In our il- lustration, you deposit, or put in, the initial amount (which is an outflow to you) and you take out, or receive, the ending amount (which is an inflow to you). If your calculator requires that you follow this sign convention, the PV would be entered as �100. Enter the �100 by keying in 100 and then pressing the “change sign” or �/� key. (If you entered 100, then the FV would appear as �127.63.) Also, on some calculators you are required to press a “Compute” key before pressing the FV key.

Sometimes the convention of changing signs can be confusing. For example, if you have $100 in the bank now and want to find out how much you will have after five years if your account pays 5 percent interest, the calculator will give you a negative answer, in this case �127.63, because the calculator assumes you are going to withdraw the funds. This sign convention should cause you no problem if you think about what you are doing.

We should also note that financial calculators permit you to specify the num- ber of decimal places that are displayed. Twelve significant digits are actually used in the calculations, but we generally use two places for answers when work- ing with dollars or percentages and four places when working with decimals. The nature of the problem dictates how many decimal places should be displayed.

Spreadsheet Solution

As noted back in Chapter 2, spreadsheet programs are ideally suited for solving many financial problems, including time value of money problems.4 With very little effort, the spreadsheet itself becomes a time line. Here is how the prob- lem would look in a spreadsheet:

F U T U R E VA L U E

a zero for the unused variable (whose value is automatically set equal to zero when you clear the calcu- lator’s memory); if you forget to clear your calculator, inputting a zero will help you avoid trouble. 3 Here we assume that compounding occurs once each year. Most calculators have a setting that can be used to designate the number of compounding periods per year. For example, the HP-10B comes preset with payments at 12 per year. You would need to change it to 1 per year to get FV � 127.63. With the HP-10B, you would do this by typing 1, pressing the gold key, and then pressing the P/YR key. 4 In this section, and in other sections and chapters, we discuss spreadsheet solutions to various fi- nancial problems. If a reader is not familiar with spreadsheets and has no interest in them, then these sections can be omitted. For those who are interested, 07MODEL.xls is the Excel file on the CD-ROM for this chapter that does the various calculations in the chapter. If you have the time, we highly recommend that you go through the models. This will give you practice with Excel, which will help tremendously in later courses, in the job market, and in the workplace. Also, going through the models will enhance your understanding of financial concepts.

(Footnote 2 continued)

A B C D E F G

1 Interest rate 0.05

2 Time 0 1 2 3 4 5

3 Cash flow �100

4 Future value 105.00 110.25 115.76 121.55 127.63

C H A P T E R 7 � T I M E VA L U E O F MO N E Y296

Cell B1 shows the interest rate, entered as a decimal number, 0.05. Row 2 shows the periods for the time line. With Microsoft Excel, you could enter 0 in Cell B2, then the formula �B2�1 in Cell C2, and then copy this formula into Cells D2 through G2 to produce the time periods shown on Row 2. Note that if your time line had many years, say, 50, you would simply copy the formula across more columns. Other procedures could also be used to enter the periods.

Row 3 shows the cash flows. In this case, there is only one cash flow, shown in Cell B3. Row 4 shows the future value of this cash flow at the end of each year. Cell C4 contains the formula for Equation 7-1. The formula could be written as ��$B$3*(11.05)^C2, but we wrote it as ��$B$3*(1�$B$1)^C2, which gives us the flexibility to change the interest rate in Cell B1 to see how the future value changes with changes in interest rates. Note that the formula has a minus sign for the PV (which is in Cell B3) to account for the minus sign of the cash flow. This formula was then copied into Cells D4 through G4. As Cell G4 shows, the value of $100 compounded for five years at 5 percent per year is $127.63.

You could also find the FV by putting the cursor on Cell G4, then clicking the function wizard, then Financial, then scrolling down to FV, and then clicking OK to bring up the FV dialog box. Then enter B1 or 0.05 for Rate, G2 or 5 for Nper, 0 or leave blank for Pmt because there are no periodic payments, B3 or �100 for PV, and 0 or leave blank for Type to indicate that payments occur at the end of the period. Then, when you click OK, you get the future value, $127.63.

Note that the dialog box prompts you to fill in the arguments in an equation. The equation itself, in Excel format, is FV(Rate,Nper,Pmt,PV,Type) � FV(0.05,5,0,�100,0). Rather than insert numbers, you could input cell refer- ences for Rate, Nper, Pmt, and PV. Either way, when Excel sees the equation, it knows to use our Equation 7-1 to fill in the specified arguments, and to de- posit the result in the cell where the cursor was located when you began the process. If someone really knows what they are doing and has memorized the formula, they can skip both the time line and the function wizard and just in- sert data into the formula to get the answer. But until you become an expert, we recommend that you use time lines to visualize the problem and the func- tion wizard to complete the formula.

COMPARING THE FOUR PROCEDURES

The first step in solving any time value problem is to understand the verbal de- scription of the problem well enough to diagram it on a time line. Woody Allen said that 90 percent of success is just showing up. With time value problems, 90 percent of success is correctly setting up the time line.

After you diagram the problem on a time line, your next step is to pick an approach to solve the problem. Which of the four approaches should you use

297

— numerical, tabular, financial calculator, or spreadsheet? In general, you should use the easiest approach. But which is easiest? The answer depends on the particular situation.

First, we would never recommend the tabular approach — it went out when calculators were invented some 20 years ago. Second, all business students should know Equation 7-1 by heart and should also know how to use a finan- cial calculator. So, for simple problems such as finding the future value of a sin- gle payment, it is probably easiest and quickest to use either the numerical ap- proach or a financial calculator.

For problems with more than a couple of cash flows, the numerical approach is usually too time consuming, so here either the calculator or spreadsheet ap- proaches would generally be used. Calculators are portable and quick to set up, but if many calculations of the same type must be done, or if you want to see how changes in an input such as the interest rate affect the future value, the spreadsheet approach is generally more efficient. If the problem has many ir- regular cash flows, or if you want to analyze many scenarios with different cash flows, then the spreadsheet approach is definitely the most efficient. The im- portant point is that you understand the various approaches well enough to make a rational choice, given the nature of the problem and the equipment you have available. In any event, you must understand the concepts behind the cal- culations and know how to set up time lines in order to work complex prob- lems. This is true for stock and bond valuation, capital budgeting, lease analy- sis, and many other important types of problems.

PROBLEM FORMAT

To help you understand the various types of time value problems, we generally use a standard format. First, we state the problem in words. Next, we diagram the problem on a time line. Then, beneath the time line, we show the equation that must be solved. Finally, we present four alternative procedures for solving the equation to obtain the answer: (1) use a regular calculator to obtain a nu- merical solution, (2) use the tables, (3) use a financial calculator, or (4) use a spreadsheet program. For some of the very easy problems, we will not show a spreadsheet solution, and for some difficult problems, we will not show numer- ical or tabular solutions because they are simply too inefficient.

To illustrate the format, consider again our five-year, 5 percent example:

Time Line:

Equation:

FVn � PV(1 � i) n � $100(1.05)5.

1. Numerical Solution

0 15%

� 1.05 � 1.05

105.00 110.25 115.76 121.55

� 1.05 � 1.05 � 1.05

2 3 4 5

� 127.63100

0 15% 2 3 4 5

FV�?�100

F U T U R E VA L U E

C H A P T E R 7 � T I M E VA L U E O F MO N E Y298

Using a regular calculator, raise 1.05 to the 5th power and multiply by $100 to get FV5 � $127.63.

2. Tabular Solution

Look up FVIF5%,5 in Table 7-1 or Table A-3 at the end of the book, and then multiply by $100:

FV5 � $100(FVIF5%,5) � $100(1.2763) � $127.63.

3. Financial Calculator Solution Inputs: 5 5 �100 0

Output: � 127.63

Note that the calculator diagram tells you to input N � 5, I � 5, PV � �100, and PMT � 0, and then to press the FV key to get the answer, 127.63. Inter- est rates are entered as percentages (5), not decimals (0.05). Also, note that in this particular problem, the PMT key does not come into play, as no constant series of payments is involved.5 Finally, you should recognize that small round- ing differences will often occur among the various solution methods because ta- bles use fewer significant digits (4) than do calculators (12), and also because rounding sometimes is done at intermediate steps in long problems.

4. Spreadsheet Solution

5 We input PMT � 0, but if you cleared the calculator before you started, the PMT register would already have been set to 0.

Cell G4 contains the formula for Equation 7-1: ��$B$3*(1�$B$1)^G2 or ��$B$3*(1�.05)^G2. You could also use Excel’s FV function to find the $127.63, following the procedures described in the previous section.

GRAPHIC VIEW OF THE COMPOUNDING PROCESS : GROWTH

Figure 7-1 shows how $1 (or any other lump sum) grows over time at various interest rates. The data used to plot the curves could be obtained from Table

A B C D E F G

1 Interest rate 0.05

2 Time 0 1 2 3 4 5

3 Cash flow �100

4 Future value 105.00 110.25 115.76 121.55 127.63

299

A-3, but we generated the data and then made the graph with a spreadsheet model. See 07MODEL.xls. The higher the rate of interest, the faster the rate of growth. The interest rate is, in fact, a growth rate: If a sum is deposited and earns 5 percent interest, then the funds on deposit will grow at a rate of 5 per- cent per period. Note also that time value concepts can be applied to anything that is growing — sales, population, earnings per share, your future salary, or whatever.

F U T U R E VA L U E

F I G U R E 7 - 1 Relationships among Future Value, Growth, Interest Rates, and Time

Future Value of $1

8 106420

1.0

2.0

3.0

4.0

5.0

i = 0%

i = 5%

i =10%

i =15%

Periods

SELF-TEST QUESTIONS

Explain what is meant by the following statement: “A dollar in hand today is worth more than a dollar to be received next year.”

What is compounding? Explain why earning “interest on interest” is called “compound interest.”

Explain the following equation: FV1 � PV � INT.

Set up a time line that shows the following situation: (1) Your initial deposit is $100. (2) The account pays 5 percent interest annually. (3) You want to know how much money you will have at the end of three years.

Write out an equation that could be used to solve the preceding problem.

What are the five TVM (time value of money) input keys on a financial cal- culator? List them (horizontally) in the proper order.

THE POWER OF COMPOUND INTEREST

C H A P T E R 7 � T I M E VA L U E O F MO N E Y300

P R E S E N T VA L U E

Suppose you have some extra cash, and you have a chance to buy a low-risk se- curity that will pay $127.63 at the end of five years. Your local bank is currently offering 5 percent interest on five-year certificates of deposit (CDs), and you regard the security as being exactly as safe as a CD. The 5 percent rate is de- fined as your opportunity cost rate, or the rate of return you could earn on an alternative investment of similar risk. How much should you be willing to pay for the security?

From the future value example presented in the previous section, we saw that an initial amount of $100 invested at 5 percent per year would be worth $127.63 at the end of five years. As we will see in a moment, you should be indifferent between $100 today and $127.63 at the end of five years. The $100 is defined as the present value, or PV, of $127.63 due in five years when the opportunity cost rate is 5 percent. If the price of the security were less than $100, you should buy it, because its price would then be less than the $100 you would have to spend on a similar-risk alternative to end up with $127.63 after five years. Conversely, if the security cost more than $100, you should not buy it, because you would have to invest only $100 in a similar- risk alternative to end up with $127.63 after five years. If the price were ex- actly $100, then you should be indifferent — you could either buy the secu- rity or turn it down. Therefore, $100 is defined as the security’s fair, or equilibrium, value.

In general, the present value of a cash flow due n years in the future is the amount which, if it were on hand today, would grow to equal the future amount. Since $100 would grow to $127.63 in five years at a 5 percent interest rate, $100 is the present value of $127.63 due in five years when the opportunity cost rate is 5 percent.

Opportunity Cost Rate The rate of return on the best available alternative investment of equal risk.

Present Value (PV) The value today of a future cash flow or series of cash flows.

Fair (Equilibrium) Value The price at which investors are indifferent between buying or selling a security.

You are 21 years old and have just graduated from college. Afterreading the introduction to this chapter, you decide to start investing in the stock market for your retirement. Your goal is to have $1 million when you retire at age 65. Assuming you earn a 10 percent annual rate on your stock investments, how much must you invest at the end of each year in order to reach your goal?

The answer is $1,532.24, but this amount depends critically on the return earned on your investments. If returns drop to 8 percent, your required annual contributions would rise to $2,801.52, while if returns rise to 12 percent, you would only need to put away $825.21 per year.

What if you are like most of us and wait until later to worry about retirement? If you wait until age 40, you will need to

save $10,168 per year to reach your $1 million goal, assuming you earn 10 percent, and $13,679 per year if you earn only 8 percent. If you wait until age 50 and then earn 8 percent, the required amount will be $36,830 per year.

While $1 million may seem like a lot of money, it won’t be when you get ready to retire. If inflation averages 5 percent a year over the next 44 years, your $1 million nest egg will be worth only $116,861 in today’s dollars. At an 8 percent rate of return, and assuming you live for 20 years after retirement, your annual retirement income in today’s dollars would be only $11,903 before taxes. So, after celebrating graduation and your new job, start saving!

301

Finding present values is called discounting, and it is simply the reverse of compounding — if you know the PV, you can compound to find the FV, while if you know the FV, you can discount to find the PV. When discounting, you would follow these steps:

Time Line:

Equation:

To develop the discounting equation, we begin with the future value equation, Equation 7-1:

FVn � PV(1 � i) n � PV(FVIFi,n). (7-1)

Next, we solve it for PV in several equivalent forms:

(7-2)

The last form of Equation 7-2 recognizes that the interest factor PVIFi,n is equal to the term in parentheses in the second version of the equation.

1. Numerical Solution

Divide $127.63 by 1.05 five times, or by (1.05)5, to find PV � $100.

2. Tabular Solution

The term in parentheses in Equation 7-2 is called the Present Value Interest Factor for i and n, or PVIFi,n, and Table A-1 in Appendix A contains present value interest factors for selected values of i and n. The value of PVIFi,n for i � 5% and n � 5 is 0.7835, so the present value of $127.63 to be received after five years when the appropriate interest rate is 5 percent is $100:

PV � $127.63(PVIF5%,5) � $127.63(0.7835) � $100.

3. Financial Calculator Solution

Inputs: 5 5 0 127.63

Output: � �100

Enter N � 5, I � 5, PMT � 0, and FV � 127.63, and then press PV to get PV � �100. This is the easy way!

0 15%

105.00 110.25 115.76 121.55 127.63 � 1.05 � 1.05 � 1.05 � 1.05 � 1.05

2 3 4 5

�100 �

PV � FVn

(1 � i)n � FVna 11 � ib

n

� FVn(PVIFi,n).

0 15% 2 3 4 5

127.63PV � ?

P R E S E N T VA L U E

Present Value Interest Factor for i and n (PVIFi,n) The present value of $1 due n periods in the future discounted at i percent per period.

Discounting The process of finding the present value of a cash flow or a series of cash flows; discounting is the reverse of compounding.

C H A P T E R 7 � T I M E VA L U E O F MO N E Y302

4. Spreadsheet Solution

You could enter the spreadsheet version of Equation 7-2 in Cell B4, �127.63/(1�0.05)^5, but you could also use the built-in spreadsheet PV func- tion. In Excel, you would put the cursor on Cell B4, then click the function wiz- ard, indicate that you want a Financial function, scroll down, and double click PV. Then, in the dialog box, enter B1 or 0.05 for Rate, G2 or 5 for Nper, 0 for Pmt (because there are no annual payments), G3 or 127.63 for FV, and 0 (or leave blank) for Type because the cash flow occurs at the end of the year. Then, press OK to get the answer, PV � $100.00.

GRAPHIC VIEW OF THE DISCOUNTING PROCESS

Figure 7-2 shows how the present value of $1 (or any other sum) to be received in the future diminishes as the years to receipt and the interest rate increase. Again, the data used to plot the curves could be obtained with a calculator, but we used a spreadsheet to calculate the data and make the graph. See 07MODEL.xls. The graph shows (1) that the present value of a sum to be re- ceived at some future date decreases and approaches zero as the payment date is extended further into the future, and (2) that the rate of decrease is greater the higher the interest (discount) rate. At relatively high interest rates, funds due in the future are worth very little today, and even at a relatively low dis- count rate, the present value of a sum due in the very distant future is quite small. For example, at a 20 percent discount rate, $1 million due in 100 years is worth approximately 1 cent today. (However, 1 cent would grow to almost $1 million in 100 years at 20 percent.)

SELF-TEST QUESTIONS

What is meant by the term “opportunity cost rate”?

What is discounting? How is it related to compounding?

How does the present value of an amount to be received in the future change as the time is extended and as the interest rate increases?

A B C D E F G

1 Interest rate 0.05

2 Time 0 1 2 3 4 5

3 Cash flow 0 0 0 0 127.63

4 Present value 100

303

S O LV I N G F O R I N T E R E S T R AT E A N D T I M E

At this point, you should realize that compounding and discounting are related, and that we have been dealing with one equation that can be solved for either the FV or the PV.

FV Form:

FVn � PV(1 � i) n. (7-1)

PV Form:

(7-2)

There are four variables in these equations — PV, FV, i, and n — and if you know the values of any three, you can find the value of the fourth. Thus far, we have always given you the interest rate (i) and the number of years (n), plus ei- ther the PV or the FV. In many situations, though, you will need to solve for either i or n, as we discuss below.

SOLVING FOR i

Suppose you can buy a security at a price of $78.35, and it will pay you $100 after five years. Here you know PV, FV, and n, and you want to find i, the in- terest rate you would earn if you bought the security. Problems such as this are solved as follows:

PV � FVn

(1 � i)n � FVna 11 � ib

n

.

S O LV I N G F O R I N T E R E S T R AT E A N D T I M E

F I G U R E 7 - 2 Relationships among Present Value, Interest Rates, and Time

Present Value of $1

8 106420

0.25

0.50

0.75

1.00

i = 15%

i = 10%

i = 5%

i = 0%

Periods

C H A P T E R 7 � T I M E VA L U E O F MO N E Y304

Time Line:

Equation:

FVn � PV(1 � i) n (7-1)

$100 � $78.35(1 � i)5. Solve for i.

1. Numerical Solution

Go through a trial-and-error process in which you insert different values of i into Equation 7-1 until you find a value that “works” in the sense that the right-hand side of the equation equals $100. The solution value is i � 0.05, or 5 percent. The trial-and-error procedure is extremely tedious and inefficient for most time value problems, so no one in the real world uses it.

2. Tabular Solution

FVn � PV(1 � i) n � PV(FVIFi,n)

$100 � $78.35(FVIFi,5)

FVIFi,5 � $100/$78.35 � 1.2763.

Find the value of the FVIF as shown above, and then look across the Period 5 row in Table A-3 until you find FVIF � 1.2763. This value is in the 5% col- umn, so the interest rate at which $78.35 grows to $100 over five years is 5 per- cent. This procedure can be used only if the interest rate is in the table; there- fore, it will not work for fractional interest rates or where n is not a whole number. Approximation procedures can be used, but they are laborious and in- exact.

3. Financial Calculator Solution Inputs: 5 �78.35 0 100

Output: � 5.0

Enter N � 5, PV � �78.35, PMT � 0, and FV � 100, and then press I to get I � 5%. This procedure is easy, and it can be used for any interest rate or for any value of n, including fractional values.

4. Spreadsheet Solution

0 1 2 3 4 5

100�78.35

i � ?

A B C D E F G

1 Time 0 1 2 3 4 5

2 Cash flow �78.35 0 0 0 0 100

3 Interest rate 5%

305

Most spreadsheets have a built-in function to find the interest rate. In Excel, you would put the cursor on Cell B3, then click the function wizard, indicate that you want a Financial function, scroll down to Rate, and click OK. Then, in the dialog box, enter G1 or 5 Nper, 0 for Pmt because there are no periodic payments, B2 or �78.35 for PV, G2 or 100 for FV, 0 for type, and leave “Guess” blank to let Excel decide where to start its iterations. Then, when you click OK, Excel solves for the interest rate, 5.00 percent. Excel also has other procedures that could be used to find the 5 percent, but for this problem the Rate function is easiest to apply.

SOLVING FOR n

Suppose you know that a security will provide a return of 5 percent per year, that it will cost $78.35, and that you will receive $100 at maturity, but you do not know when the security matures. Thus, you know PV, FV, and i, but you do not know n, the number of periods. Here is the situation:

Time Line:

Equation:

FVn � PV(1 � i) n (7-1)

$100 � $78.35(1.05)n. Solve for n.

1. Numerical Solution

Again, you could go through a trial-and-error process wherein you substitute different values for n into the equation. You would find (eventually) that n � 5 “works,” so 5 is the number of years it takes for $78.35 to grow to $100 if the interest rate is 5 percent.

2. Tabular Solution

FVn � PV(1 � i) n � PV(FVIFi,n)

$100 � $78.35(FVIF5%,n)

FVIF5%,n � $100/$78.35 � 1.2763.

Now look down the 5% column in Table A-3 until you find FVIF � 1.2763. This value is in Row 5, which indicates that it takes five years for $78.35 to grow to $100 at a 5 percent interest rate.

3. Financial Calculator Solution Inputs: 5 �78.35 0 100

Output: � 5.0

Enter I � 5, PV � �78.35, PMT � 0, and FV � 100, and then press N to get N � 5.

0 1 2 n � 1 n � ?

100�78.35

5%

S O LV I N G F O R I N T E R E S T R AT E A N D T I M E

C H A P T E R 7 � T I M E VA L U E O F MO N E Y306

4. Spreadsheet Solution

To solve this problem, starting with a new spreadsheet, you could enter the for- mula �78.35*(1.05)^B2 in Cell B4 and then use the goal-seeking function on the Tools menu to find a value for B2 that causes the value in B4 to equal 100. The value is 5.00. You could also use the Solver function on the Tools menu to solve the equation.

SELF-TEST QUESTIONS

Assuming that you are given PV, FV, and the time period, n, write out an equation that can be used to determine the interest rate, i.

Assuming that you are given PV, FV, and the interest rate, i, write out an equation that can be used to determine the time period, n.

Explain how a financial calculator can be used to solve for i and n.

F U T U R E VA L U E O F A N A N N U I T Y

An annuity is a series of equal payments made at fixed intervals for a specified number of periods. For example, $100 at the end of each of the next three years is a three-year annuity. The payments are given the symbol PMT, and they can occur at either the beginning or the end of each period. If the payments occur at the end of each period, as they typically do, the annuity is called an ordinary, or deferred, annuity. Payments on mortgages, car loans, and student loans are typically set up as ordinary annuities. If payments are made at the beginning of each period, the annuity is an annuity due. Rental payments for an apartment, life insurance premiums, and lottery payoffs are typically set up as annuities due. Since ordinary annuities are more common in finance, when the term “an- nuity” is used in this book, you should assume that the payments occur at the end of each period unless otherwise noted.

ORDINARY ANNUIT IES

An ordinary, or deferred, annuity consists of a series of equal payments made at the end of each period. If you deposit $100 at the end of each year for three years in a savings account that pays 5 percent interest per year, how much will you have at the end of three years? To answer this question, we must find the future value of the annuity, FVAn. Each payment is compounded out to the end of Period n, and the sum of the compounded payments is the future value of the annuity, FVAn.

Time Line: 0 5% 1 2 3

100 100 100 105 110.25 315.25FVA3 �

Annuity A series of payments of an equal amount at fixed intervals for a specified number of periods.

Ordinary (Deferred) Annuity An annuity whose payments occur at the end of each period.

Annuity Due An annuity whose payments occur at the beginning of each period.

FVAn The future value of an annuity over n periods.

307

Here we show the regular time line as the top portion of the diagram, but we also show how each cash flow is compounded to produce the value FVAn in the lower portion of the diagram.

Equation:

FVAn � PMT(1 � i) n�1 � PMT(1 � i)n�2 � PMT(1 � i)n�3 � � � �

� PMT(1 � i)0

(7-3)

� PMT(FVIFAi,n).

The first line of Equation 7-3 represents the application of Equation 7-1 to each individual payment of the annuity. In other words, each term is the com- pounded amount of a single payment, with the superscript in each term indi- cating the number of periods during which the payment earns interest. For ex- ample, because the first annuity payment was made at the end of Period 1, interest would be earned in Periods 2 through n only, so compounding would be for n � 1 periods rather than n periods. Compounding for the second an- nuity payment would be for Period 3 through Period n, or n � 2 periods, and so on. The last annuity payment is made at the end of the annuity’s life, so there is no time for interest to be earned. The second form of Equation 7-3 is just a shorthand version of the first. Finally, the third line shows the payment multi- plied by the Future Value Interest Factor for an Annuity (FVIFAi,n), which is the tabular approach.

1. Numerical Solution

The lower section of the time line shows the numerical solution, which in- volves using the first line of Equation 7-3. The future value of each cash flow is found, and those FVs are summed to find the FV of the annuity, $315.25. This is a tedious process for long annuities.

2. Tabular Solution

The summation term in Equation 7-3 is called the Future Value Interest Fac- tor for an Annuity (FVIFAi,n):

6

(7-3a)

FVIFAs have been calculated for various combinations of i and n, and Table A-4 in Appendix A contains a set of FVIFA factors. To find the answer to the

FVIFAi,n � a n

t�1 (1 � i)n�t.

� PMT a n

t�1 (1 � i)n�t

F U T U R E VA L U E O F A N A N N U I T Y

Future Value Interest Factor for an Annuity (FVIFAi,n) The future value interest factor for an annuity of n periods compounded at i percent.

6 Another form for Equation 7-3a is as follows:

This form is found by applying the algebra of geometric progressions. This equation is useful in situations when the required values of i and n are not in the tables and no financial calculator or computer is available.

FVIFAi,n � (1 � i)n � 1

i .

C H A P T E R 7 � T I M E VA L U E O F MO N E Y308

three-year, $100 annuity problem, first refer to Table A-4 and look down the 5% column to the third period; the FVIFA is 3.1525. Thus, the future value of the $100 annuity is $315.25:

FVAn � PMT(FVIFAi,n)

FVA3 � $100(FVIFA5%,3) � $100(3.1525) � $315.25.

3. Financial Calculator Solution Inputs: 3 5 0 � 100

Output: � 315.25

Note that in annuity problems, the PMT key is used in conjunction with the N and I keys, plus either the PV or the FV key, depending on whether you are trying to find the PV or the FV of the annuity. In our example, you want the FV, so press the FV key to get the answer, $315.25. Since there is no initial pay- ment, we input PV � 0.

4. Spreadsheet Solution

Most spreadsheets have a built-in function to find the future value of an annu- ity. In Excel, we could put the cursor on Cell E4, then click function wizard, Financial, FV, and OK to get the FV dialog box. Then, we would enter 0.05 or B1 for Rate, 3 or E2 for Nper, and �100 for Pmt. (Like the financial calcu- lator approach, the payment is entered as a negative number to show that it is a cash outflow.) We would leave PV blank because there is no initial payment, and we would leave Type blank to signify that payments come at the end of the periods. Then, when we clicked OK, we would get the FV of the annuity, $315.25. Note that it isn’t necessary to show the time line, since the FV func- tion doesn’t require you to input a range of cash flows. Still, the time line is useful to help visualize the problem.

ANNUIT IES DUE

Had the three $100 payments in the previous example been made at the begin- ning of each year, the annuity would have been an annuity due. On the time line, each payment would be shifted to the left one year; therefore, each payment would be compounded for one extra year.

A B C D E

1 Interest rate 0.05

2 Time 0 1 2 3

3 Cash flow 100 100 100

4 Future value 315.25

309

1. Time Line and Numerical Solution

Again, the time line is shown at the top of the diagram, and the values as cal- culated with a regular calculator are shown under Year 3. The future value of each cash flow is found, and those FVs are summed to find the FV of the an- nuity due. The payments occur earlier, so more interest is earned. Therefore, the future value of the annuity due is larger — $331.01 versus $315.25 for the ordinary annuity.

2. Tabular Solution

In an annuity due, each payment is compounded for one additional period, so the future value of the entire annuity is equal to the future value of an ordinary annuity compounded for one additional period. Here is the tabular solution:

FVAn (Annuity due) � PMT(FVIFAi,n)(1 � i) (7-3b)

� $100(3.1525)(1.05) � $331.01.

3. Financial Calculator Solution

Most financial calculators have a switch, or key, marked “DUE” or “BEG” that permits you to switch from end-of-period payments (ordinary annuity) to beginning-of-period payments (annuity due). When the beginning mode is ac- tivated, the display will normally show the word “BEGIN.” Thus, to deal with annuities due, switch your calculator to “BEGIN” and proceed as before:

BEGIN Inputs: 3 5 0 �100

Output: � 331.01

Enter N � 3, I � 5, PV � 0, PMT � �100, and then press FV to get the an- swer, $331.01. Since most problems specify end-of-period cash flows, you should always switch your calculator back to “END” mode after you work an annuity due problem.

4. Spreadsheet Solution

For the annuity due, proceed just as for the ordinary annuity except enter 1 for Type to indicate that we now have an annuity due. Then, when you click OK, the answer $331.01 will appear.

0 5% 1 2 3

100 100 100 105 110.25 115.76

331.01FVA3 (Annuity due) �

F U T U R E VA L U E O F A N A N N U I T Y

C H A P T E R 7 � T I M E VA L U E O F MO N E Y310

P R E S E N T VA L U E O F A N A N N U I T Y

Suppose you were offered the following alternatives: (1) a three-year annuity with payments of $100 or (2) a lump sum payment today. You have no need for the money during the next three years, so if you accept the annuity, you would deposit the payments in a bank account that pays 5 percent interest per year. Similarly, the lump sum payment would be deposited into a bank account. How large must the lump sum payment today be to make it equivalent to the annuity?

ORDINARY ANNUIT IES

If the payments come at the end of each year, then the annuity is an ordinary annuity, and it would be set up as follows:

Time Line:

The regular time line is shown at the top of the diagram, and the numerical so- lution values are shown in the left column. The PV of the annuity, PVAn, is $272.32.

Equation:

The general equation used to find the PV of an ordinary annuity is shown below:7

0 5% 1 2 3

100 100 100 95.24 90.70 86.38

272.32PVA3 �

SELF-TEST QUESTIONS

What is the difference between an ordinary annuity and an annuity due?

How do you modify the equation for determining the value of an ordinary annuity to find the value of an annuity due?

Other things held constant, which annuity has the greater future value: an ordinary annuity or an annuity due? Why?

Explain how financial calculators can be used to solve future value of annu- ity problems.

PVAn The present value of an annuity of n periods.

7 The summation term is called the PVIFA, and, using the geometric progression solution process, its value is found to be

PVIFAi,n � a n

t�1 a 1

1 � i b t �

1 � 1

(1 � i)n

i �

1 i

� 1

i(1 � i)n .

(footnote continues)

311

(7-4)

1. Numerical Solution

The present value of each cash flow is found and then summed to find the PV of the annuity. This procedure is shown in the lower section of the time line di- agram, where we see that the PV of the annuity is $272.32.

2. Tabular Solution

The summation term in Equation 7-4 is called the Present Value Interest Factor for an Annuity (PVIFAi,n), and values for the term at different values of i and n are shown in Table A-2 at the back of the book. Here is the equa- tion:

PVAn � PMT(PVIFAi,n). (7-4a)

To find the answer to the three-year, $100 annuity problem, simply refer to Table A-2 and look down the 5% column to the third period. The PVIFA is 2.7232, so the present value of the $100 annuity is $272.32:

PVAn � PMT(PVIFAi,n)

PVA3 � $100(PVIFA5%,3) � $100(2.7232) � $272.32.

3. Financial Calculator Solution Inputs: 3 5 �100 0

Output: � 272.32

Enter N � 3, I � 5, PMT � �100, and FV � 0, and then press the PV key to find the PV, $272.32.

4. Spreadsheet Solution

� PMTa n

t�1 a 1

1 � i b t.

PVAn � PMTa 11 � ib 1

� PMTa 1 1 � i

b2 � # # # � PMTa 1 1 � i

bn

P R E S E N T VA L U E O F A N A N N U I T Y

(Footnote 7 continued)

This form of the equation is useful for dealing with annuities when the values for i and n are not in the tables and no financial calculator or computer is available.

Present Value Interest Factor for an Annuity (PVIFAi,n) The present value interest factor for an annuity of n periods discounted at i percent.

A B C D E

1 Interest rate 0.05

2 Time 0 1 2 3

3 Cash flow 100 100 100

4 Present value $272.32

C H A P T E R 7 � T I M E VA L U E O F MO N E Y312

In Excel, put the cursor on Cell B4 and then click the function wizard, Finan- cial, PV, and OK. Then enter B1 or 0.05 for Rate, E2 or 3 for Nper, �100 for Pmt, 0 or leave blank for FV, and 0 or leave blank for Type. Then, when you click OK, you get the answer, $272.32.

One especially important application of the annuity concept relates to loans with constant payments, such as mortgages and auto loans. With such loans, called amortized loans, the amount borrowed is the present value of an ordinary annuity, and the payments constitute the annuity stream. We will examine con- stant payment loans in more depth in a later section of this chapter.

ANNUIT IES DUE

Had the three $100 payments in the preceding example been made at the be- ginning of each year, the annuity would have been an annuity due. Each pay- ment would be shifted to the left one year, so each payment would be dis- counted for one less year. Here is the time line setup:

1. Time Line and Numerical Solution

Again, we find the PV of each cash flow and then sum these PVs to find the PV of the annuity due. This procedure is illustrated in the lower section of the time line diagram. Since the cash flows occur sooner, the PV of the annuity due ex- ceeds that of the ordinary annuity, $285.94 versus $272.32.

2. Tabular Solution

In an annuity due, each payment is discounted for one less period. Since its payments come in faster, an annuity due is more valuable than an ordinary an- nuity. This higher value is found by multiplying the PV of an ordinary annuity by (1 � i):

PVAn (Annuity due) � PMT(PVIFAi,n)(1 � i) (7-4b)

� $100(2.7232)(1.05) � $285.94.

3. Financial Calculator Solution BEGIN

Inputs: 3 5 �100 0

Output: � 285.94

0 5% 1 2 3

100100 100 95.24 90.70

285.94PVA3 (Annuity due) �

313

Switch to the beginning-of-period mode, and then enter N � 3, I � 5, PMT � �100, and FV � 0, and then press PV to get the answer, $285.94. Again, since most problems deal with end-of-period cash flows, don’t forget to switch your calculator back to the “END” mode.

4. Spreadsheet Solution

For an annuity due, proceed exactly as for a regular annuity except enter 1 rather than 0 for Type to indicate that we now have an annuity due.

P E R P E T U I T I E S

SELF-TEST QUESTIONS

Which annuity has the greater present value: an ordinary annuity or an an- nuity due? Why?

Explain how financial calculators can be used to find the present value of annuities.

P E R P E T U I T I E S

Most annuities call for payments to be made over some finite period of time — for example, $100 per year for three years. However, some annuities go on in- definitely, or perpetually, and these are called perpetuities. The present value of a perpetuity is found by applying Equation 7-5.8

(7-5)

Perpetuities can be illustrated by some British securities issued after the Napoleonic Wars. In 1815, the British government sold a huge bond issue and used the proceeds to pay off many smaller issues that had been floated in prior years to pay for the wars. Since the purpose of the bonds was to consolidate past debts, the bonds were called consols. Suppose each consol promised to pay $100 per year in perpetuity. (Actually, interest was stated in pounds.) What would each bond be worth if the opportunity cost rate, or discount rate, was 5 percent? The answer is $2,000:

PV (Perpetuity) � $100 0.05

� $2,000 if i � 5%.

PV(Perpetuity) � Payment

Interest rate �

PMT i

.

8 The derivation of Equation 7-5 is given in the Web/CD Extension to Chapter 5 of Eugene F. Brigham and Phillip R. Daves, Intermediate Financial Management, 7th ed. (Fort Worth, TX: Har- court College Publishers, 2002).

Perpetuity A stream of equal payments expected to continue forever.

Consol A perpetual bond issued by the British government to consolidate past debts; in general, any perpetual bond.

C H A P T E R 7 � T I M E VA L U E O F MO N E Y314

Suppose the interest rate rose to 10 percent; what would happen to the consol’s value? The value would drop to $1,000:

We see that the value of a perpetuity changes dramatically when interest rates change. Perpetuities are discussed further in Chapter 9.

PV (Perpetuity) � $100 0.10

� $1,000 at i � 10%.

SELF-TEST QUESTIONS

What happens to the value of a perpetuity when interest rates increase?

What happens when interest rates decrease?

U N E V E N C A S H F L OW S T R E A M S

The definition of an annuity includes the words constant payment — in other words, annuities involve payments that are equal in every period. Although many financial decisions do involve constant payments, other important deci- sions involve uneven, or nonconstant, cash flows; for example, common stocks typically pay an increasing stream of dividends over time, and fixed asset in- vestments such as new equipment normally do not generate constant cash flows. Consequently, it is necessary to extend our time value discussion to in- clude uneven cash flow streams.

Throughout the book, we will follow convention and reserve the term pay- ment (PMT) for annuity situations where the cash flows are equal amounts, and we will use the term cash flow (CF) to denote uneven cash flows. Finan- cial calculators are set up to follow this convention, so if you are dealing with uneven cash flows, you will need to use the “cash flow register.”

PRESENT VALUE OF AN UNEVEN CASH FLOW STREAM

The PV of an uneven cash flow stream is found as the sum of the PVs of the individual cash flows of the stream. For example, suppose we must find the PV of the following cash flow stream, discounted at 6 percent:

The PV will be found by applying this general present value equation:

(7-6)� a n

t�1 CFta 11 � ib

t

� a n

t�1 CFt(PVIFi,t ).

PV � CF1a 11 � ib 1

� CF2a 11 � ib 2

� # # # � CFna 11 � ib n

0 16%

100

2

200

3

200

4

200

5

200

6

0

7

1,000PV � ?

Uneven Cash Flow Stream A series of cash flows in which the amount varies from one period to the next.

Payment (PMT) This term designates equal cash flows coming at regular intervals.

Cash Flow (CF) This term designates uneven cash flows.

315

We could find the PV of each individual cash flow using the numerical, tabular, financial calculator, or spreadsheet methods, and then sum these values to find the present value of the stream. Here is what the process would look like:

All we did was to apply Equation 7-6, show the individual PVs in the left col- umn of the diagram, and then sum these individual PVs to find the PV of the entire stream.

The present value of a cash flow stream can always be found by summing the present values of the individual cash flows as shown above. However, cash flow regularities within the stream may allow the use of shortcuts. For example, no- tice that the cash flows in periods 2 through 5 represent an annuity. We can use that fact to solve the problem in a slightly different manner:

Cash flows during Years 2 to 5 represent an ordinary annuity, and we find its PV at Year 1 (one period before the first payment). This PV ($693.02) must then be discounted back one more period to get its Year 0 value, $653.79.

Problems involving uneven cash flows can be solved in one step with most financial calculators. First, you input the individual cash flows, in chronological order, into the cash flow register. Cash flows are usually designated CF0, CF1, CF2, CF3, and so on. Next, you enter the interest rate, I. At this point, you have substituted in all the known values of Equation 7-6, so you only need to press the NPV key to find the present value of the stream. The calculator has been programmed to find the PV of each cash flow and then to sum these values to find the PV of the entire stream. To input the cash flows for this problem, enter 0 (because CF0 � 0), 100, 200, 200, 200, 200, 0, 1000 in that order into the cash flow register, enter I � 6, and then press NPV to obtain the answer, $1,413.19.

Two points should be noted. First, when dealing with the cash flow register, the calculator uses the term “NPV” rather than “PV.” The N stands for “net,” so NPV is the abbreviation for “Net Present Value,” which is simply the net present

0 16%

100

2

200

3

200

4

200

5

200

6

0

7

1,000

94.34

665.06 0.00

653.79 693.02

1,413.19

0 16%

100

2

200

3

200

4

200

5

200

6

0

7

1,000

94.34

665.06

149.45 0.00

158.42 167.92 178.00

1,413.19

U N E V E N C A S H F L OW S T R E A M S

C H A P T E R 7 � T I M E VA L U E O F MO N E Y316

value of a series of positive and negative cash flows. Our example has no negative cash flows, but if it did, we would simply input them with negative signs.9

The second point to note is that annuities can be entered into the cash flow register more efficiently by using the Nj key. (On some calculators, you are prompted to enter the number of times the cash flow occurs, and on still other calculators, the procedures for inputting data, as we discuss next, may be dif- ferent. You should consult your calculator manual or our Technology Supplement to determine the appropriate steps for your specific calculator.) In this illustra- tion, you would enter CF0 � 0, CF1 � 100, CF2 � 200, Nj � 4 (which tells the calculator that the 200 occurs 4 times), CF6 � 0, and CF7 � 1000. Then enter I � 6 and press the NPV key, and 1,413.19 will appear in the display. Also, note that amounts entered into the cash flow register remain in the register until they are cleared. Thus, if you had previously worked a problem with eight cash flows, and then moved to a problem with only four cash flows, the calculator would simply add the cash flows from the second problem to those of the first problem. Therefore, you must be sure to clear the cash flow register before starting a new problem.

Spreadsheets are especially useful for solving problems with uneven cash flows. Just as with a financial calculator, you must enter the cash flows in the spreadsheet:

9 To input a negative number, type in the positive number, then press the �/� key to change the sign to negative. If you begin by typing the minus sign, you make the mistake of subtracting the negative number from the last number that was entered in the calculator.

A B C D E F G H I

1 Interest rate 0.06

2 Time 0 1 2 3 4 5 6 7

3 Cash flow 100 200 200 200 200 0 1,000

4 Present value 1,413.19

To find the PV of these cash flows with Excel, put the cursor on Cell B4, click the function wizard, click Financial, scroll down to NPV, and click OK to get the dialog box. Then enter B1 or 0.06 for Rate and the range of cells containing the cash flows, C3:I3, for Value 1. N stands for Net, so the NPV is the net present value of a stream of cash flows, some of which may be negative. Now, when you click OK, you get the PV of the stream, $1,413.19. Note that you use the PV function if the cash flows (or payments) are constant, but the NPV function if they are not constant. Note too that one of the advantages of spreadsheets over financial calculators is that you can see the cash flows, which makes it easy to spot any typing errors.

317U N E V E N C A S H F L OW S T R E A M S

FUTURE VALUE OF AN UNEVEN CASH FLOW STREAM

The future value of an uneven cash flow stream (sometimes called the termi- nal value) is found by compounding each payment to the end of the stream and then summing the future values:

FVn � CF1(1 � i) n�1 � CF2(1 � i)

n�2 � � � � � CFn

(7-7)

The future value of our illustrative uneven cash flow stream is $2,124.92:

Some financial calculators have a net future value (NFV) key which, after the cash flows and interest rate have been entered, can be used to obtain the future value of an uneven cash flow stream. In any event, it is easy enough to compound the individual cash flows to the terminal year and then sum them to find the FV of the stream. Also, we are generally more interested in the present value of an asset’s cash flow stream than in the future value because the present value repre- sents today’s value, which is used to find the fair value of the asset. Finally, note that the cash flow stream’s net present value can be used to find its net future value: NFV � NPV (1 � i)n. Thus, in our example, you could find the PV of the stream, then find the FV of that PV, compounded for n periods at i percent. In the illustrative problem, find PV � 1,413.19 using the cash flow register and I � 6. Then enter N � 7, I � 6, PV � �1413.19, and PMT � 0, and then press FV to find FV � 2,124.92, which equals the NFV shown on the time line above.

SOLVING FOR i WITH UNEVEN CASH FLOW STREAMS

It is relatively easy to solve for i numerically or with the tables when the cash flows are lump sums or annuities. However, it is extremely difficult to solve for i if the cash flows are uneven, because then you would have to go through many tedious trial-and-error calculations. With a spreadsheet program or a financial calculator, though, it is easy to find the value of i. Simply input the CF values into the cash flow register and then press the IRR key. IRR stands for “internal rate of return,” which is the percentage return on an investment. We will defer further discussion of this calculation for now, but we will take it up later, in our discussion of capital budgeting methods in Chapter 11.10

0 16%

100

2

200

3

200

4

200

5

200

6

0

7

1,000

0 224.72

238.20 252.50

267.65 141.85

2,124.92

� a n

t�1 CFt(1 � i)

n�t � a n

t�1 CFt(FVIFi,n�t).

Terminal Value The future value of an uneven cash flow stream.

10 To obtain an IRR solution, at least one of the cash flows must have a negative sign, indicating that it is an investment. Since none of the CFs in our example were negative, the cash flow stream has no IRR. However, had we input a cost for CF0, say, �$1,000, we could have obtained an IRR, which would be the rate of return earned on the $1,000 investment. Here IRR would be 13.96 percent.

C H A P T E R 7 � T I M E VA L U E O F MO N E Y318

S E M I A N N UA L A N D OT H E R C O M P O U N D I N G P E R I O D S

In all of our examples thus far, we have assumed that interest is compounded once a year, or annually. This is called annual compounding. Suppose, how- ever, that you put $100 into a bank which states that it pays a 6 percent annual interest rate but that interest is credited each six months. This is called semi- annual compounding. How much would you have accumulated at the end of one year, two years, or some other period under semiannual compounding? Note that virtually all bonds pay interest semiannually, most stocks pay divi- dends quarterly, and most mortgages, student loans, and auto loans require monthly payments. Therefore, it is essential that you understand how to deal with nonannual compounding.

To illustrate semiannual compounding, assume that $100 is placed into an account at an interest rate of 6 percent and left there for three years. First, con- sider again what would happen under annual compounding:

FVn � PV(1 � i) n � $100(1.06)3

� $119.10.

We would, of course, get this same answer using the tables, a financial calcula- tor, or a spreadsheet.

How would things change if interest were paid semiannually rather than an- nually? First, whenever payments occur more frequently than once a year, or when interest is stated to be compounded more than once a year, then you must (1) convert the stated interest rate to a “periodic rate,” and (2) convert the num- ber of years to “number of periods,” as follows:

Periodic rate � Stated rate/Number of payments per year.

Number of periods � Number of years � Periods per year.

In our example, where we must find the value of $100 after three years when the stated interest rate is 6 percent, compounded semiannually (or twice a year), you would begin by making the following conversions:

Periodic rate � 6%/2 � 3%.

Periods � N � 3 � 2 � 6.

0 16% 2 3

FV�?�100

Annual Compounding The arithmetic process of determining the final value of a cash flow or series of cash flows when interest is added once a year.

Semiannual Compounding The arithmetic process of determining the final value of a cash flow or series of cash flows when interest is added twice a year.

SELF-TEST QUESTIONS

Give two examples of financial decisions that would typically involve uneven cash flows. (Hint: Think about a bond or a stock that you plan to hold for five years.)

What is meant by the term “terminal value”?

USING THE INTERNET FOR PERSONAL FINANCIAL PLANNING

319

In this situation, the investment will earn 3 percent every six months for six pe- riods, not 6 percent per year for three years. As we shall see, there is a signifi- cant difference between these two procedures.

You should make the conversions as your first step when working on such a problem because calculations must be done using the appropriate number of periods and periodic rate, not the number of years and stated rate. Periodic rates and num- ber of periods, not yearly rates and number of years, should normally be shown on time lines and entered into your calculator whenever you are dealing with nonannual compounding.11

With this background, we can now find the value of $100 after three years if it is held in an account that pays a stated rate of 6 percent, but with semiannual compounding. Here is the time line:

Time Line: 0 13% 2 3 4 5 6 6-month periods

FV � ?�100

S E M I A N N UA L A N D OT H E R C O M P O U N D I N G P E R I O D S

People continually face important financial decisions that re-quire an understanding of the time value of money. Should we buy or lease a car? How much and how soon do we need to save for our children’s education? What size house can we af- ford? Should we refinance our home mortgage? How much must we save in order to retire comfortably?

The answers to these questions are often complicated, and they depend on a number of factors, such as housing and edu- cation costs, interest rates, inflation, expected family income, and stock market returns. Hopefully, after completing this chap- ter, you will have a better idea of how to answer such ques- tions. Moreover, there are a number of online resources avail- able to help with financial planning.

A good place to start is http://www.smartmoney.com. Smartmoney is a personal finance magazine produced by the pub- lishers of The Wall Street Journal. If you go to Smartmoney’s web site you will find a section entitled “Tools.” This section has a

number of financial calculators, spreadsheets, and descriptive materials that cover a wide range of personal finance issues.

Another good place to look is Quicken’s web site, http://www.quicken.com. Here you will find several interesting sections that deal with a variety of personal finance issues. Within these sections you will find background articles plus spreadsheets and calculators that you can use to analyze your own situation.

Finally, http://www.financialengines.com is a great place to visit if you are focusing specifically on retirement planning. This web site, developed by Nobel Prize–winning financial econ- omist William Sharpe, considers a wide range of alternative sce- narios that might occur. This approach, which enables you to see a full range of potential outcomes, is much better than some of the more basic online calculators that give you simple answers to complicated questions.

11 With some financial calculators, you can enter the annual (nominal) rate and the number of com- pounding periods rather than make the conversion we recommend. We prefer making the conver- sion because it is easier to see the problem setup in a time line, and also because it is easy to forget to readjust your calculator after you change its settings and to then make an error on the next prob- lem because of the incorrect setting.

C H A P T E R 7 � T I M E VA L U E O F MO N E Y320

1. Equation and Numerical Solution

FVn � PV(1 � i) n � $100(1.03)6

� $100(1.1941) � $119.41.

Here i � rate per period � annual rate/compounding periods per year � 6%/ 2 � 3%, and n � the total number of periods � years � periods per year � 3 � 2 � 6.

2. Tabular Solution

FV6 � $100(FVIF3%,6) � $100(1.1941) � $119.41.

Look up FVIF for 3%, 6 periods in Table A-3 and complete the arithmetic.

3. Financial Calculator Solution

Inputs: 6 3 � 100 0

Output: � 119.41

Enter N � years � periods per year � 3 � 2 � 6, I � annual rate/periods per year � 6/2 � 3, PV � �100, and PMT � 0. Then press FV to find the answer, $119.41.

4. Spreadsheet Solution

The spreadsheet developed to find the future value of a lump sum under semi- annual compounding would look like the one for annual compounding, with two changes: The interest rate would be halved, and the time line would show twice as many periods. The future value under semiannual compounding, $119.41, would be larger than $119.10, the future value under annual com- pounding, because interest on interest is being earned more frequently.

Throughout the world economy, different compounding periods are used for different types of investments. For example, bank accounts generally pay in- terest daily; most bonds pay interest semiannually; and stocks generally pay div- idends quarterly.12 If we are to properly compare securities with different com- pounding periods, we need to put them on a common basis. This requires us to distinguish between nominal, or quoted, interest rates and effective, or equivalent, annual rates.13

The nominal, or quoted, or stated, interest rate in our example is 6 percent. The effective (or equivalent) annual rate (EAR, also called EFF%) is defined as the

12 Some banks and savings and loans even pay interest compounded continuously. Continuous com- pounding is discussed in Appendix 7A. 13 The term nominal rate as it is used here has a different meaning than the way it was used in Chapter 5. There, nominal interest rates referred to stated market rates as opposed to real (zero in- flation) rates. In this chapter, the term nominal rate means the stated, or quoted, annual rate as op- posed to the effective annual rate. In both cases, though, nominal means stated, or quoted, as opposed to some adjusted rate.

Nominal (Quoted, or Stated) Interest Rate The contracted, or quoted, or stated, interest rate.

Effective (Equivalent) Annual Rate (EFF% or EAR) The annual rate of interest actually being earned, as opposed to the quoted rate. Also called the “equivalent annual rate.”

321

rate that would produce the same ending (future) value if annual compounding had been used. In our example, the effective annual rate is the once-a-year rate that would produce an FV of $119.41 at the end of Year 3. Here is a time line of the situation:

Our task now is to find the effective annual rate, EAR or EFF%, that is equiv- alent to 6 percent with semiannual compounding.

We can determine the effective annual rate, given the nominal rate and the number of compounding periods per year, by solving this equation:

(7-8)

Here iNom is the nominal, or quoted, interest rate, and m is the number of com- pounding periods per year. For example, to find the effective annual rate if the nominal rate is 6 percent and semiannual compounding is used, we have14

� (1.03)2 � 1.0

� 1.0609 � 1.0 � 0.0609 � 6.09%.

The points made about semiannual compounding can be generalized as follows. When compounding occurs more frequently than once a year, we can use a modified version of Equation 7-1 to find the future value of any lump sum:

Annual compounding: FVn � PV(1 � i) n. (7-1)

(7-9)

Here iNom is the nominal, or quoted, rate, m is the number of times compound- ing occurs per year, and n is the number of years. For example, when banks pay daily interest, the value of m is set at 365 and Equation 7-9 is applied.15

To illustrate further the effect of compounding monthly rather than annu- ally, consider the interest rate charged on credit cards. Many banks charge 1.5 percent per month, and, in their advertising, they state that the Annual Per- centage Rate (APR) is 1.5% � 12 � 18%. However, the “true” rate is the ef- fective annual rate of 19.6 percent:

More frequent compounding: FVn � PVa1 � iNomm b mn

.

Effective annual rate � EAR (or EFF%) � a1 � 0.06 2 b2 � 1.0

Effective annual rate � EAR (or EFF%) � a1 � iNom m bm � 1.0.

0 1EAR (or EFF%) 2 3 Years

�100 119.41

S E M I A N N UA L A N D OT H E R C O M P O U N D I N G P E R I O D S

14 Most financial calculators are programmed to find the EAR or, given the EAR, to find the nom- inal rate. This is called “interest rate conversion,” and you simply enter the nominal rate and the number of compounding periods per year and then press the EFF% key to find the effective an- nual rate. 15 To illustrate, the future value of $1 invested at 10 percent for 1 year under daily compounding is $1.1052:

Note also that banks sometimes use 360 as the number of days per year for this and other calculations.

FVn � $1a1 � 0.10365 b 365(1)

� $1(1.105156) � $1.1052.

Annual Percentage Rate (APR) The periodic rate � the number of periods per year.

C H A P T E R 7 � T I M E VA L U E O F MO N E Y322

� (1.015)12 � 1.0

� 0.196 � 19.6%.

Semiannual and other compounding periods can also be used for discount- ing, and for both lump sums and annuities. First, consider the case where we want to find the PV of an ordinary annuity of $100 per year for three years when the interest rate is 8 percent, compounded annually:

Time Line:

1. Numerical Solution

Find the PV of each cash flow and sum them. The PV of the annuity is $257.71.

2. Tabular Solution

PVAn � PMT(PVIFAi,n)

� $100(PVIFA8%,3) � $100(2.5771) � $257.71.

3. Financial Calculator Solution Inputs: 3 8 100 0

Output: � �257.71

4. Spreadsheet Solution

A spreadsheet could be developed as we did earlier in the chapter in our dis- cussion of the present value of an annuity. Rows would be set up to show the interest rate (8 percent), time (t � 0 through t � 3), and cash flows (100 at t � 1 through t � 3). Then the present value of the annuity, $257.71, could be de- termined using the Excel PV function.

Now, let’s change the situation to semiannual compounding, where the annu- ity calls for payments of $50 each six months rather than $100 per year, and the rate is 8 percent, compounded semiannually. Here is the time line:

Time Line:

0 14% 2 3 4 5 6 6-month periods

PV � ? 50 50 50 50 50 50

0 18% 2 3

PV � ? 100 100 100

Effective annual rate � EAR (or EFF%) � a1 � 0.18 12 b12 � 1.0

323

1. Numerical Solution

Find the PV of each cash flow by discounting at 4 percent. Treat each tick mark on the time line as a period, so there are six periods. The PV of the annuity is $262.11 versus $257.71 under annual compounding.

2. Tabular Solution

PVAn � PMT(PVIFAi,n)

� $50(PVIFA4%,6) � $50(5.2421) � $262.11.

3. Financial Calculator Solution Inputs: 6 4 50 0

Output: � �262.11

4. Spreadsheet Solution

The spreadsheet developed to find the present value of an annuity under semi- annual compounding would look like the one for annual compounding, but the interest rate and annuity payment would be halved, and the time line would have twice as many periods.

The annuity value with semiannual compounding is $262.11, which is greater than the annual annuity value. The reason is that the semiannual pay- ments come in sooner, so the $50 semiannual annuity is more valuable than the $100 annual annuity.

C O M PA R I S O N O F D I F F E R E N T T Y P E S O F I N T E R E S T R AT E S

SELF-TEST QUESTIONS

What changes must you make in your calculations to determine the future value of an amount that is being compounded at 8 percent semiannually versus one being compounded annually at 8 percent?

Why is semiannual compounding better than annual compounding from a saver’s standpoint? What about a borrower’s standpoint?

Define the terms “annual percentage rate,” “effective (or equivalent) annual rate,” and “nominal interest rate.”

How does the term “nominal rate” as used in this chapter differ from the term as it was used in Chapter 5?

C O M PA R I S O N O F D I F F E R E N T T Y P E S O F I N T E R E S T R AT E S

Finance deals with three types of interest rates: nominal rates, iNom; periodic rates, iPER; and effective annual rates, EAR or EFF%. Therefore, it is essen- tial that you understand what each one is and when it should be used.

C H A P T E R 7 � T I M E VA L U E O F MO N E Y324

1. Nominal, or quoted, rate. This is the rate that is quoted by banks, bro- kers, and other financial institutions. So, if you talk with a banker, broker, mortgage lender, auto finance company, or student loan officer about rates, the nominal rate is the one he or she will normally quote you. However, to be meaningful, the quoted nominal rate must also include the number of compounding periods per year. For example, a bank might offer 6 percent, compounded quarterly, on CDs, or a mutual fund might offer 5 percent, compounded monthly, on its money market account.

The nominal rate on loans to consumers is also called the Annual Per- centage Rate (APR). If a credit card issuer quotes an APR of 18 percent, monthly, this means an interest rate of 18%/12 � 1.5 percent per month.

Nominal rates can be compared with one another, but only if the in- struments being compared use the same number of compounding periods per year. Thus, you could compare the quoted yields on two bonds if they both pay interest semiannually. However, to compare a 6 percent, annual payment CD with a 5 percent, daily payment money market fund, we would need to put both instruments on an effective (or equivalent) annual rate (EAR) basis as discussed later in this section.

Note that the nominal rate is never shown on a time line, and it is never used as an input in a financial calculator (unless compounding occurs only once a year, in which case iNom � periodic rate � EAR). If more frequent compounding occurs, you should use the periodic rate as discussed below.

2. Periodic rate, iPER. This is the rate charged by a lender or paid by a bor- rower each period. It can be a rate per year, per six-month period, per quarter, per month, per day, or per any other time interval. For example, a bank might charge 1.5 percent per month on its credit card loans, or a finance company might charge 3 percent per quarter on installment loans. We find the periodic rate as follows:

Periodic rate, iPER � iNom/m, (7-10)

which implies that

Nominal annual rate � iNom � (Periodic rate)(m). (7-11)

Here iNom is the nominal annual rate and m is the number of compound- ing periods per year. To illustrate, consider a finance company loan at 3 percent per quarter:

Nominal annual rate � iNom � (Periodic rate)(m) � (3%)(4) � 12%,

or

Periodic rate � iNom/m � 12%/4 � 3% per quarter.

If there is only one payment per year, or if interest is added only once a year, then m � 1, and the periodic rate is equal to the nominal rate.

The periodic rate is the rate that is generally shown on time lines and used in calculations.16 To illustrate use of the periodic rate, suppose you make the

16 The only exception is in situations where (1) annuities are involved and (2) the payment periods do not correspond to the compounding periods. If an annuity is involved and if its payment peri- ods do not correspond to the compounding periods — for example, if you are making quarterly payments into a bank account to build up a specified future sum, but the bank pays interest on a

(footnote continued)

325

following eight quarterly payments of $100 each into an account that pays a nominal rate of 12 percent, compounded quarterly. How much would you have after two years?

Time Line and Equation:

1. Numerical Solution

Compound each $100 payment at 12/4 � 3 percent for the appropriate number of periods, and then sum these individual FVs to find the FV of the payment stream, $889.23.

2. Tabular Solution

Look up FVIFA for 3%, 8 periods, in Table A-4, and complete the arith- metic:

FVAn � PMT(FVIFAi,n)

� $100(FVIFA3%,8) � $100(8.8923) � $889.23.

3. Financial Calculator Solution Inputs: 8 3 0 �100

Output: � 889.23

Input N � 2 � 4 � 8, I � 12/4 � 3, PV � 0, and PMT � �100, and then press the FV key to get FV � $889.23.

4. Spreadsheet Solution

A spreadsheet could be developed as we did earlier in the chapter in our discussion of the future value of an annuity. Rows would be set up to show

FVAn � a n

t�1 PMT(1 � i)n�t � a

8

t�1 $100(1.03)8�t.

0 Quarters13% 2 3 4 5 6

�100

FV � ?

�100�100�100�100�100�100�100

7 8

C O M PA R I S O N O F D I F F E R E N T T Y P E S O F I N T E R E S T R AT E S

daily basis — then the calculations are more complicated. For such problems, one can proceed in two alternative ways. (1) Determine the periodic (daily) interest rate by dividing the nominal rate by 360 (or 365 if the bank uses a 365-day year), then compound each payment over the exact num- ber of days from the payment date to the terminal point, and then sum the compounded payments to find the future value of the annuity. This is what would generally be done in the real world, be- cause with a computer, it would be a simple process. (2) Calculate the EAR based on daily com- pounding, then find the corresponding nominal rate based on quarterly compounding (because the annuity payments are made quarterly), then find the quarterly periodic rate, and then use that rate with standard annuity procedures. The second procedure is faster with a calculator, but hard to ex- plain and generally not used in practice given the ready availability of computers.

(Footnote 16 continues)

F R AC T I O N A L T I M E P E R I O D S 1 7

In all the examples used thus far in the chapter, we have assumed that payments occur at either the beginning or the end of periods, but not at some date within a period. However, we often encounter situations that require compounding or

C H A P T E R 7 � T I M E VA L U E O F MO N E Y326

the interest rate, time, cash flow, and future value of the annuity. The in- terest rate used in the spreadsheet would be the periodic interest rate (iNom/m) and the number of time periods shown would be (m)(n).

3. Effective (or equivalent) annual rate (EAR). This is the annual rate that produces the same result as if we had compounded at a given peri- odic rate m times per year. The EAR is found as follows:

(7-8)

You could also use the interest conversion feature of a financial calculator. In the EAR equation, iNom/m is the periodic rate, and m is the number

of periods per year. For example, suppose you could borrow using either a credit card that charges 1 percent per month or a bank loan with a 12 percent quoted nominal interest rate that is compounded quarterly. Which should you choose? To answer this question, the cost rate of each alternative must be expressed as an EAR:

Credit card loan: EAR � (1 � 0.01)12 � 1.0 � (1.01)12 � 1.0

� 1.126825 � 1.0 � 0.126825 � 12.6825%.

Bank loan: EAR � (1 � 0.03)4 � 1.0 � (1.03)4 � 1.0

� 1.125509 � 1.0 � 0.125509 � 12.5509%.

Thus, the credit card loan is slightly more costly than the bank loan. This result should have been intuitive to you — both loans have the same 12 percent nominal rate, yet you would have to make monthly payments on the credit card versus quarterly payments under the bank loan.

The EAR rate is not used in calculations. However, it should be used to compare the effective cost or rate of return on loans or investments when payment periods differ, as in the credit card versus bank loan example.

EAR (or EFF%) � a1 � iNom m bm � 1.0.

SELF-TEST QUESTIONS

Define the nominal (or quoted) rate, the periodic rate, and the effective an- nual rate.

How are the nominal rate, the periodic rate, and the effective annual rate related?

What is the one situation where all three of these rates will be the same?

Which rate should be shown on time lines and used in calculations?

17 This section is relatively technical, but it can be omitted without loss of continuity.

327A M O R T I Z E D L OA N S

discounting over fractional periods. For example, suppose you deposited $100 in a bank that adds interest to your account daily, that is, uses daily compound- ing, and pays a nominal rate of 10 percent with a 360-day year. How much will be in your account after nine months? The answer is $107.79:18

Periodic rate � iPER � 0.10/360 � 0.00027778 per day.

Number of days � 0.75(360) � 270.

Ending amount � $100(1.00027778)270 � $107.79.

Now suppose you borrow $100 from a bank that charges 10 percent per year “simple interest,” which means annual rather than daily compounding, but you borrow the $100 for only 270 days. How much interest would you have to pay for the use of $100 for 270 days? Here we would calculate a daily interest rate, iPER, as above, but multiply by 270 rather than use it as an exponent:

Interest owed � $100(0.00027778)(270) � $7.50 interest charged.

You would owe the bank a total of $107.50 after 270 days. This is the proce- dure most banks actually use to calculate interest on loans, except that they generally require you to pay the interest on a monthly basis rather than after 270 days.

Finally, let’s consider a somewhat different situation. Say an Internet access firm had 100 customers at the end of 2001, and its customer base is expected to grow steadily at the rate of 10 percent per year. What is the estimated customer base nine months into the new year? This problem would be set up exactly like the bank account with daily compounding, and the estimate would be 107.79 customers, rounded to 108.

The most important thing in problems like these, as in all time value prob- lems, is to be careful! Think about what is involved in a logical, systematic manner, draw a time line if it would help you visualize the situation, and then apply the appropriate equations.

A M O R T I Z E D L OA N S

One of the most important applications of compound interest involves loans that are paid off in installments over time. Included are automobile loans, home mortgage loans, student loans, and most business loans other than very short- term loans and long-term bonds. If a loan is to be repaid in equal periodic amounts (monthly, quarterly, or annually), it is said to be an amortized loan.19

Table 7-2 illustrates the amortization process. A firm borrows $1,000, and the loan is to be repaid in three equal payments at the end of each of the next three years. (In this case, there is only one payment per year, so years � periods and the stated rate � periodic rate.) The lender charges a 6 percent

18 Here we assumed a 360-day year, and we also assumed that the nine months all have 30 days. In real-world calculations, the bank’s computer (and many financial calculators) would have a built-in calendar, and if you input the beginning and ending dates, the computer or calculator would tell you the exact number of days, taking account of 30-day months, 31-day months, and 28- or 29-day months. 19 The word amortized comes from the Latin mors, meaning “death,” so an amortized loan is one that is “killed off” over time.

Amortized Loan A loan that is repaid in equal payments over its life.

C H A P T E R 7 � T I M E VA L U E O F MO N E Y328

interest rate on the loan balance that is outstanding at the beginning of each year. The first task is to determine the amount the firm must repay each year, or the constant annual payment. To find this amount, recognize that the $1,000 represents the present value of an annuity of PMT dollars per year for three years, discounted at 6 percent:

Time Line and Equation:

Here we know everything except PMT, so we can solve the equation for PMT.

1. Numerical Solution

You could follow the trial-and-error procedure, inserting values for PMT in the equation until you found a value that “worked” and caused the right side of the equation to equal $1,000. This would be a tedious process, but you would even- tually find PMT � $374.11.

2. Tabular Solution

Substitute in known values and look up PVIFA for 6%, 3 periods in Table A-2:

PVAn � PMT(PVIFAi,n)

$1,000 � PMT(PVIFA6%,3) � PMT(2.6730)

PMT � $1,000/2.6730 � $374.11.

$1,000 � a 3

t�1

PMT (1.06)t

.

PV � PMT

(1 � i)1 �

PMT (1 � i)2

� PMT

(1 � i)3 � a

3

t�1

PMT (1 � i)t

0 16% 2 3

1,000 PMT PMT PMT

T A B L E 7 - 2

BEGINNING REPAYMENT REMAINING AMOUNT PAYMENT INTERESTa OF PRINCIPALb BALANCE

YEAR (1) (2) (3) (2) � (3) � (4) (1) � (4) � (5)

1 $1,000.00 $ 374.11 $ 60.00 $ 314.11 $685.89 2 685.89 374.11 41.15 332.96 352.93 3 352.93 374.11 21.18 352.93 0.00

$1,122.33 $122.33 $1,000.00

aInterest is calculated by multiplying the loan balance at the beginning of the year by the interest rate. Therefore, interest in Year 1 is $1,000(0.06) � $60; in Year 2 it is $685.89(0.06) � $41.15; and in Year 3 it is $352.93(0.06) � $21.18. bRepayment of principal is equal to the payment of $374.11 minus the interest charge for each year.

Loan Amortization Schedule, 6 Percent Interest Rate

3. Financial Calculator Solution

Inputs: 3 6 1000 0

Output: � �374.11

Enter N � 3, I � 6, PV � 1000, and FV � 0, and then press the PMT key to find PMT � �$374.11.

4. Spreadsheet Solution

The spreadsheet is ideal for developing amortization tables. The setup is similar to Table 7-2, but you would want to include “input” cells for the interest rate, principal value, and the length of the loan. This would make the spreadsheet flex- ible in the sense that the loan terms could be changed and a new amortization table would be recalculated instantly. Then use the function wizard to find the payment. If you had I � 6% in B1, N � 3 in B2, and PV � 1000 in B3, then the function �PMT(B1, B2, B3) would find the payment, $374.11.

Therefore, the firm must pay the lender $374.11 at the end of each of the next three years, and the percentage cost to the borrower, which is also the rate of return to the lender, will be 6 percent. Each payment consists partly of interest and partly of repayment of principal. This breakdown is given in the amorti- zation schedule shown in Table 7-2. The interest component is largest in the first year, and it declines as the outstanding balance of the loan decreases. For tax purposes, a business borrower or homeowner reports the interest compo- nent shown in Column 3 as a deductible cost each year, while the lender reports this same amount as taxable income.

Financial calculators are programmed to calculate amortization tables — you simply enter the input data, and then press one key to get each entry in Table 7-2. If you have a financial calculator, it is worthwhile to read the appropriate section of the calculator manual and learn how to use its amortization feature. As we show in the model for this chapter, with a spreadsheet such as Excel, it is easy to set up and print out a full amortization schedule.

329T Y I N G I T A L L TO G E T H E R

SELF-TEST QUESTIONS

To construct an amortization schedule, how do you determine the amount of the periodic payments?

How do you determine the amount of each payment that goes to interest and to principal?

Financial decisions often involve situations in which someone pays money at one point in time and receives money at some later time. Dollars paid or re- ceived at two different points in time are different, and this difference is

Amortization Schedule A table showing precisely how a loan will be repaid. It gives the required payment on each payment date and a breakdown of the payment, showing how much is interest and how much is repayment of principal.

C H A P T E R 7 � T I M E VA L U E O F MO N E Y330

F I G U R E 7 - 3 Illustration for Chapter Summary (i � 4%, Annual Compounding)

0 Years4% 1 2 3

1,000 1,000 1,000.00 1,040.00 1,081.60

3,121.60Future value �

961.50 924.60 889.00

2,775.10Present value �

recognized and accounted for by time value of money (TVM) analysis. We sum- marize below the types of TVM analysis and the key concepts covered in this chapter, using the data shown in Figure 7-3 to illustrate the various points. Refer to the figure constantly, and try to find in it an example of the points cov- ered as you go through this summary.

� Compounding is the process of determining the future value (FV) of a cash flow or a series of cash flows. The compounded amount, or future value, is equal to the beginning amount plus the interest earned.

� Future value: FVn � PV(1 � i) n � PV(FVIFi,n).

(single payment)

Example: $1,000 compounded for 1 year at 4 percent:

FV1 � $1,000(1.04) 1 � $1,040.

� Discounting is the process of finding the present value (PV) of a future cash flow or a series of cash flows; discounting is the reciprocal, or reverse, of compounding.

� Present value: PV � � � FVn(PVIFi,n). (single payment)

Example: $1,000 discounted back for 2 years at 4 percent:

PV �

� An annuity is defined as a series of equal periodic payments (PMT) for a specified number of periods.

� Future value: (annuity)

FVAn �PMT(1� i) n�1 �PMT(1� i)n�2 �PMT(1� i)n�3�����PMT(1� i)0

� PMT(FVIFAi,n).

� PMTa n

t�1 (1 � i)n�t

$1,000 (1.04)2

� $1,000a 1 1.04 b2 � $1,000(0.9246) � $924.60.

FVna 11 � ib nFVn

(1 � i)n

331

Example: FVA of 3 payments of $1,000 when i � 4%:

FVA3 � $1,000(3.1216) � $3,121.60.

� Present value: (annuity)

� PMT(PVIFAi,n).

Example: PVA of 3 payments of $1,000 when i � 4% per period:

PVA3 � $1,000(2.7751) � $2,775.10.

� An annuity whose payments occur at the end of each period is called an ordinary annuity. The formulas above are for ordinary annuities.

� If each payment occurs at the beginning of the period rather than at the end, then we have an annuity due. In Figure 7-3, the payments would be shown at Years 0, 1, and 2 rather than at Years 1, 2, and 3. The PV of each payment would be larger, because each payment would be discounted back one year less, so the PV of the annuity would also be larger. Similarly, the FV of the annuity due would also be larger because each payment would be compounded for an extra year. The following formulas can be used to convert the PV and FV of an ordinary annuity to an annuity due:

PVA (annuity due) � PVA of an ordinary annuity � (1 � i).

Example: PVA of 3 beginning-of-year payments of $1,000 when i � 4%:

PVA (annuity due) � $1,000(2.7751)(1.04) � $2,886.10.

Example: FVA of 3 beginning-of-year payments of $1,000 when i � 4%:

FVA (annuity due) � FVA of an ordinary annuity � (1 � i).

FVA (annuity due) � $1,000(3.1216)(1.04) � $3,246.46.

� If the time line in Figure 7-3 were extended out forever so that the $1,000 payments went on forever, we would have a perpetuity whose value could be found as follows:

� If the cash flows in Figure 7-3 were unequal, we could not use the annuity formulas. To find the PV or FV of an uneven series, find the PV or FV of each individual cash flow and then sum them. Note, though, that if some of the cash flows constitute an annuity, then the annuity formula can be used to calculate the present or future value of that part of the cash flow stream.

� Financial calculators have built-in programs that perform all of the op- erations discussed in this chapter. It would be useful for you to buy such a calculator and to learn how to use it.

� Spreadsheet programs are especially useful for problems with many un- even cash flows. They are also very useful if you want to solve a problem re- peatedly with different inputs. See 07MODEL.xls on the CD-ROM that

Value of perpetuity � PMT

i �

$1,000 0.04

� $25,000.

� PMTa n

t�1 c 1 1 � i

d t PVAn �

PMT (1 � i)1

� PMT

(1 � i)2 � � � � �

PMT (1 � i)n

T Y I N G I T A L L TO G E T H E R

C H A P T E R 7 � T I M E VA L U E O F MO N E Y332

accompanies this text for spreadsheet models of the topics covered in this chapter.

� TVM calculations generally involve equations that have four variables, and if you know three of the values, you (or your calculator) can solve for the fourth.

� If you know the cash flows and the PV (or FV) of a cash flow stream, you can determine the interest rate. For example, in the Figure 7-3 illustra- tion, if you were given the information that a loan called for 3 payments of $1,000 each, and that the loan had a value today of PV � $2,775.10, then you could find the interest rate that caused the sum of the PVs of the payments to equal $2,775.10. Since we are dealing with an annuity, you could proceed as follows: a. With a financial calculator, enter N � 3, PV � 2775.10, PMT �

�1000, FV � 0, and then press the I key to find I � 4%. b. To use the tables, first recognize that PVAn � $2,775.10 �

$1,000(PVIFAi,3). Then solve for PVIFAi,3:

PVIFAi,3 � $2,775.10/$1,000 � 2.7751.

Look up 2.7751 in Table A-2, in the third row. It is in the 4% column, so the interest rate must be 4 percent. If the factor did not appear in the table, this would indicate that the interest rate was not a whole number. In that case, you could not use this procedure to find the exact rate. In practice, though, this is not a problem, because in business people use fi- nancial calculators or computers to find interest rates.

� Thus far in this section we have assumed that payments are made, and in- terest is earned, annually. However, many contracts call for more frequent payments; for example, mortgage and auto loans call for monthly pay- ments, and most bonds pay interest semiannually. Similarly, most banks compute interest daily. When compounding occurs more frequently than once a year, this fact must be recognized. We can use the Figure 7-3 ex- ample to illustrate semiannual compounding. First, recognize that the 4 percent stated rate is a nominal rate that must be converted to a periodic rate, and the number of years must be converted to periods:

iPER � Stated rate/Periods per year � 4%/2 � 2%.

Periods � Years � Periods per year � 3 � 2 � 6.

The periodic rate and number of periods would be used for calculations and shown on time lines.

If the $1,000 per-year payments were actually payable as $500 each 6 months, you would simply redraw Figure 7-3 to show 6 payments of $500 each, but you would also use a periodic interest rate of 4%/2 � 2% for determining the PV or FV of the payments.

� If we are comparing the costs of loans that require payments more than once a year, or the rates of return on investments that pay interest more frequently, then the comparisons should be based on equivalent (or ef- fective) rates of return using this formula:

Effective annual rate � EAR (or EFF%) � � 1.0.a1 � iNom m bm

333

For semiannual compounding, the effective annual rate is 4.04 percent:

� 1.0 � (1.02)2 � 1.0 � 1.0404 � 1.0 � 0.0404 � 4.04%.

� The general equation for finding the future value for any number of com- pounding periods per year is:

where

iNom � quoted interest rate. m � number of compounding periods per year. n � number of years.

� An amortized loan is one that is paid off in equal payments over a spec- ified period. An amortization schedule shows how much of each pay- ment constitutes interest, how much is used to reduce the principal, and the unpaid balance at each point in time.

The concepts covered in this chapter will be used throughout the remainder of the book. For example, in Chapters 8 and 9, we apply present value con- cepts to find the values of bonds and stocks, and we see that the market prices of securities are established by determining the present values of the cash flows they are expected to provide. In later chapters, the same basic concepts are applied to corporate decisions involving expenditures on capital assets, to the types of capital that should be used to pay for assets, and so forth.

Q U E S T I O N S

7-1 What is an opportunity cost rate? How is this rate used in time value analysis, and where is it shown on a time line? Is the opportunity rate a single number that is used in all sit- uations?

7-2 An annuity is defined as a series of payments of a fixed amount for a specific number of periods. Thus, $100 a year for 10 years is an annuity, but $100 in Year 1, $200 in Year 2, and $400 in Years 3 through 10 does not constitute an annuity. However, the second series contains an annuity. Is this statement true or false?

7-3 If a firm’s earnings per share grew from $1 to $2 over a 10-year period, the total growth would be 100 percent, but the annual growth rate would be less than 10 percent. True or false? Explain.

7-4 Would you rather have a savings account that pays 5 percent interest compounded semi- annually or one that pays 5 percent interest compounded daily? Explain.

7-5 To find the present value of an uneven series of cash flows, you must find the PVs of the individual cash flows and then sum them. Annuity procedures can never be of use, even if some of the cash flows constitute an annuity (for example, $100 each for Years 3, 4, 5, and 6), because the entire series is not an annuity. Is this statement true or false? Ex- plain.

7-6 The present value of a perpetuity is equal to the payment on the annuity, PMT, divided by the interest rate, i: PV � PMT/i. What is the sum, or future value, of a perpetuity of PMT dollars per year? (Hint: The answer is infinity, but explain why.)

FVn � PVa1 � iNomm b mn

,

a1 � 0.04 2 b2

Q U E S T I O N S

C H A P T E R 7 � T I M E VA L U E O F MO N E Y334

S E L F - T E S T P R O B L E M S ( S O L U T I O N S A P P E A R I N A P P E N D I X B )

Define each of the following terms: a. PV; i; INT; FVn; n; PVAn; FVAn; PMT; m; iNom b. FVIFi,n; PVIFi,n; FVIFAi,n; PVIFAi,n c. Opportunity cost rate; fair (equilibrium) value d. Annuity; lump sum payment; cash flow; uneven cash flow stream e. Ordinary (deferred) annuity; annuity due f. Perpetuity; consol g. Outflow; inflow; time line h. Compounding; discounting i. Annual, semiannual, quarterly, monthly, and daily compounding j. Effective (equivalent) annual rate (EAR); nominal (quoted) interest rate; Annual Per-

centage Rate (APR); periodic rate k. Amortization schedule; principal component versus interest component of a pay-

ment; amortized loan l. Terminal value

Assume that it is now January 1, 2002. On January 1, 2003, you will deposit $1,000 into a savings account that pays 8 percent. a. If the bank compounds interest annually, how much will you have in your account on

January 1, 2006? b. What would your January 1, 2006, balance be if the bank used quarterly compound-

ing rather than annual compounding? c. Suppose you deposited the $1,000 in 4 payments of $250 each on January 1 of 2003,

2004, 2005, and 2006. How much would you have in your account on January 1, 2006, based on 8 percent annual compounding?

d. Suppose you deposited 4 equal payments in your account on January 1 of 2003, 2004, 2005, and 2006. Assuming an 8 percent interest rate, how large would each of your payments have to be for you to obtain the same ending balance as you calculated in part a?

Assume that it is now January 1, 2002, and you will need $1,000 on January 1, 2006. Your bank compounds interest at an 8 percent annual rate. a. How much must you deposit on January 1, 2003, to have a balance of $1,000 on Jan-

uary 1, 2006? b. If you want to make equal payments on each January 1 from 2003 through 2006 to

accumulate the $1,000, how large must each of the 4 payments be? c. If your father were to offer either to make the payments calculated in part b

($221.92) or to give you a lump sum of $750 on January 1, 2003, which would you choose?

d. If you have only $750 on January 1, 2003, what interest rate, compounded annually, would you have to earn to have the necessary $1,000 on January 1, 2006?

e. Suppose you can deposit only $186.29 each January 1 from 2003 through 2006, but you still need $1,000 on January 1, 2006. What interest rate, with annual com- pounding, must you seek out to achieve your goal?

f. To help you reach your $1,000 goal, your father offers to give you $400 on Janu- ary 1, 2003. You will get a part-time job and make 6 additional payments of equal amounts each 6 months thereafter. If all of this money is deposited in a bank that pays 8 percent, compounded semiannually, how large must each of the 6 payments be?

g. What is the effective annual rate being paid by the bank in part f? h. Reinvestment rate risk was defined in Chapter 5 as being the risk that maturing secu-

rities (and coupon payments on bonds) will have to be reinvested at a lower rate of interest than they were previously earning. Is there a reinvestment rate risk involved in the preceding analysis? If so, how might this risk be eliminated?

Bank A pays 8 percent interest, compounded quarterly, on its money market account. The managers of Bank B want its money market account to equal Bank A’s effective an- nual rate, but interest is to be compounded on a monthly basis. What nominal, or quoted, rate must Bank B set?

ST-4 Effective annual rates

ST-3 Time value of money

ST-2 Future value

ST-1 Key terms

335

S TA R T E R P R O B L E M S

If you deposit $10,000 in a bank account that pays 10 percent interest annually, how much money will be in your account after 5 years? What is the present value of a security that promises to pay you $5,000 in 20 years? Assume that you can earn 7 percent if you were to invest in other securities of equal risk. If you deposit money today into an account that pays 6.5 percent interest, how long will it take for you to double your money?

John Roberts has $42,180.53 in a brokerage account, and he plans to contribute an ad- ditional $5,000 to the account at the end of every year. The brokerage account has an expected annual return of 12 percent. If John’s goal is to accumulate $250,000 in the ac- count, how many years will it take for John to reach his goal?

Your parents are planning to retire in 18 years. They currently have $250,000, and they would like to have $1,000,000 when they retire. What annual rate of interest would they have to earn on their $250,000 in order to reach their goal, assuming they save no more money? What is the future value of a 5-year ordinary annuity that promises to pay you $300 each year? The rate of interest is 7 percent. What is the future value of a 5-year annuity due that promises to pay you $300 each year? Assume that all payments are reinvested at 7 percent a year, until Year 5. What is the future value of a 5-year annuity due that promises to pay you $300 each year? Assume that all payments are reinvested at 7 percent a year, until Year 4. An investment pays you $100 at the end of each of the next 3 years. The investment will then pay you $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If the interest rate earned on the investment is 8 percent, what is its present value? What is its future value? An investment pays you 9 percent interest, compounded quarterly. What is the periodic rate of interest? What is the nominal rate of interest? What is the effective rate of in- terest? You are thinking about buying a car, and a local bank is willing to lend you $20,000 to buy the car. Under the terms of the loan, it will be fully amortized over 5 years (60 months), and the nominal rate of interest will be 12 percent, with interest paid monthly. What would be the monthly payment on the loan? What would be the effective rate of interest on the loan?

E X A M - T Y P E P R O B L E M S

The problems included in this section are set up in such a way that they could be used as multiple-choice exam problems. Which amount is worth more at 14 percent, compounded annually: $1,000 in hand today or $2,000 due in 6 years? Shalit Corporation’s 2001 sales were $12 million. Sales were $6 million 5 years earlier (in 1996). a. To the nearest percentage point, at what rate have sales been growing? b. Suppose someone calculated the sales growth for Shalit Corporation in part a as fol-

lows: “Sales doubled in 5 years. This represents a growth of 100 percent in 5 years, so, dividing 100 percent by 5, we find the growth rate to be 20 percent per year.” Ex- plain what is wrong with this calculation.

Washington-Atlantic invests $4 million to clear a tract of land and to set out some young pine trees. The trees will mature in 10 years, at which time Washington-Atlantic plans to sell the forest at an expected price of $8 million. What is Washington-Atlantic’s ex- pected rate of return?

7-14 Expected rate of return

7-13 Growth rates

7-12 Present value comparison

7-11 Loan amortization and effective interest rate

7-10 Comparison of interest rates

7-9 Present and future value

of a cash flow stream

7-8 Future value of an annuity

7-7 Future value of an annuity due

7-6 Future value of an annuity

7-5 Effective rate of interest

7-4 Financial calculator needed;

Reaching a financial goal

7-3 Financial calculator needed;

Time for a lump sum to double

7-2 Present value

7-1 Future value

E X A M - T Y P E P R O B L E M S

C H A P T E R 7 � T I M E VA L U E O F MO N E Y336

Your broker offers to sell you a note for $13,250 that will pay $2,345.05 per year for 10 years. If you buy the note, what interest rate (to the closest percent) will you be earning? A mortgage company offers to lend you $85,000; the loan calls for payments of $8,273.59 per year for 30 years. What interest rate is the mortgage company charging you? To complete your last year in business school and then go through law school, you will need $10,000 per year for 4 years, starting next year (that is, you will need to withdraw the first $10,000 one year from today). Your rich uncle offers to put you through school, and he will deposit in a bank paying 7 percent interest, compounded annually, a sum of money that is sufficient to provide the 4 payments of $10,000 each. His deposit will be made today. a. How large must the deposit be? b. How much will be in the account immediately after you make the first withdrawal?

After the last withdrawal? While you were a student in college, you borrowed $12,000 in student loans at an in- terest rate of 9 percent, compounded annually. If you repay $1,500 per year, how long, to the nearest year, will it take you to repay the loan? You need to accumulate $10,000. To do so, you plan to make deposits of $1,250 per year, with the first payment being made a year from today, in a bank account that pays 12 per- cent interest, compounded annually. Your last deposit will be less than $1,250 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal, and how large will the last deposit be? A rookie quarterback is in the process of negotiating his first contract. The team’s gen- eral manager has offered him three possible contracts. Each of the contracts lasts for 4 years. All of the money is guaranteed and is paid at the end of each year. The terms of each of the contracts are listed below:

CONTRACT 1 CONTRACT 2 CONTRACT 3 PAYMENTS PAYMENTS PAYMENTS

Year 1 $3 million $2 million $7 million Year 2 3 million 3 million 1 million Year 3 3 million 4 million 1 million Year 4 3 million 5 million 1 million

The quarterback discounts all cash flows at 10 percent. Which of the three contracts of- fers him the most value? What is the present value of a perpetuity of $100 per year if the appropriate discount rate is 7 percent? If interest rates in general were to double and the appropriate discount rate rose to 14 percent, what would happen to the present value of the perpetuity? Assume that you inherited some money. A friend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling some securities that call for 4 payments, $50 at the end of each of the next 3 years, plus a payment of $1,050 at the end of Year 4. Your friend says she can get you some of these securities at a cost of $900 each. Your money is now invested in a bank that pays an 8 percent nominal (quoted) interest rate, but with quarterly compounding. You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the se- curities is the same as that on your bank deposit. You must calculate the value of the se- curities to decide whether they are a good investment. What is their present value to you? Assume that your aunt sold her house on December 31, and that she took a mortgage in the amount of $10,000 as part of the payment. The mortgage has a quoted (or nominal) interest rate of 10 percent, but it calls for payments every 6 months, beginning on June 30, and the mortgage is to be amortized over 10 years. Now, one year later, your aunt must file Schedule B of her tax return with the IRS, informing them of the interest that was included in the 2 payments made during the year. (This interest will be income to your aunt and a deduction to the buyer of the house.) To the closest dollar, what is the total amount of interest that was paid during the first year?

7-23 Loan amortization

7-22 Financial calculator needed; PV and effective annual rate

7-21 Present value of a perpetuity

7-20 Present value of a cash flow stream

7-19 Reaching a financial goal

7-18 Repaying a loan

7-17 Required lump sum payment

7-16 Effective rate of interest

7-15 Effective rate of interest

337E X A M - T Y P E P R O B L E M S

Your company is planning to borrow $1,000,000 on a 5-year, 15%, annual payment, fully amortized term loan. What fraction of the payment made at the end of the second year will represent repayment of principal? a. It is now January 1, 2002. You plan to make 5 deposits of $100 each, one every 6

months, with the first payment being made today. If the bank pays a nominal interest rate of 12 percent, but uses semiannual compounding, how much will be in your ac- count after 10 years?

b. Ten years from today you must make a payment of $1,432.02. To prepare for this payment, you will make 5 equal deposits, beginning today and for the next 4 quar- ters, in a bank that pays a nominal interest rate of 12 percent, quarterly compound- ing. How large must each of the 5 payments be?

As the manager of Oaks Mall Jewelry, you want to sell on credit, giving customers 3 months in which to pay. However, you will have to borrow from the bank to carry the accounts receivable. The bank will charge a nominal 15 percent, but with monthly com- pounding. You want to quote a nominal rate to your customers (all of whom are ex- pected to pay on time) that will exactly cover your financing costs. What nominal an- nual rate should you quote to your credit customers? Assume that your father is now 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires, that is, until he is 85. He wants a fixed re- tirement income that has the same purchasing power at the time he retires as $40,000 has today (he realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will begin the day he retires, 10 years from today, and he will then get 24 additional annual payments. Inflation is expected to be 5 percent per year from today forward; he currently has $100,000 saved up; and he expects to earn a return on his savings of 8 percent per year, annual compounding. To the near- est dollar, how much must he save during each of the next 10 years (with deposits being made at the end of each year) to meet his retirement goal? The prize in last week’s Florida lottery was estimated to be worth $35 million. If you were lucky enough to win, the state will pay you $1.75 million per year over the next 20 years. Assume that the first installment is received immediately. a. If interest rates are 8 percent, what is the present value of the prize? b. If interest rates are 8 percent, what is the future value after 20 years? c. How would your answers change if the payments were received at the end of each

year? Your client is 40 years old and wants to begin saving for retirement. You advise the client to put $5,000 a year into the stock market. You estimate that the market’s return will be, on average, 12 percent a year. Assume the investment will be made at the end of the year. a. If the client follows your advice, how much money will she have by age 65? b. How much will she have by age 70? You are serving on a jury. A plaintiff is suing the city for injuries sustained after falling down an uncovered manhole. In the trial, doctors testified that it will be 5 years before the plaintiff is able to return to work. The jury has already decided in favor of the plain- tiff, and has decided to grant the plaintiff an award to cover the following items: (1) Recovery of 2 years of back-pay ($34,000 in 2000, and $36,000 in 2001). Assume

that it is December 31, 2001, and that all salary is received at year end. This recov- ery should include the time value of money.

(2) The present value of 5 years of future salary (2002–2006). Assume that the plaintiff’s salary would increase at a rate of 3 percent a year.

(3) $100,000 for pain and suffering. (4) $20,000 for court costs. Assume an interest rate of 7 percent. What should be the size of the settlement? You just started your first job, and you want to buy a house within 3 years. You are cur- rently saving for the down payment. You plan to save $5,000 the first year. You also anticipate that the amount you save each year will rise by 10 percent a year as your salary increases over time. Interest rates are assumed to be 7 percent, and all savings occur at year end. How much money will you have for a down payment in 3 years? A 15-year security has a price of $340.4689. The security pays $50 at the end of each of the next 5 years, and then it pays a different fixed cash flow amount at the end of each

7-32 Required annuity payment

7-31 Future value

7-30 Present value

7-29 Future value of an annuity

7-28 Value of an annuity

7-27 Financial calculator needed; Required annuity payments

7-26 Nominal rate of return

7-25 Nonannual compounding

7-24 Loan amortization

C H A P T E R 7 � T I M E VA L U E O F MO N E Y338

of the following 10 years. Interest rates are 9 percent. What is the annual cash flow amount between Years 6 and 15? An investment pays $20 semiannually for the next 2 years. The investment has a 7 per- cent nominal interest rate, and interest is compounded quarterly. What is the future value of the investment?

P R O B L E M S

Find the following values, using the equations, and then work the problems using a finan- cial calculator or the tables to check your answers. Disregard rounding differences. (Hint: If you are using a financial calculator, you can enter the known values, and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can “override” the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in parts b and d, and in many other situations, to see how changes in input variables affect the output variable.) Assume that compound- ing/discounting occurs once a year. a. An initial $500 compounded for 1 year at 6 percent. b. An initial $500 compounded for 2 years at 6 percent. c. The present value of $500 due in 1 year at a discount rate of 6 percent. d. The present value of $500 due in 2 years at a discount rate of 6 percent. Use the tables or a financial calculator to find the following values. See the hint for Problem 7-34. Assume that compounding/discounting occurs once a year. a. An initial $500 compounded for 10 years at 6 percent. b. An initial $500 compounded for 10 years at 12 percent. c. The present value of $500 due in 10 years at a 6 percent discount rate. d. The present value of $1,552.90 due in 10 years at a 12 percent discount rate and at a

6 percent rate. Give a verbal definition of the term present value, and illustrate it using a time line with data from this problem. As a part of your answer, explain why pres- ent values are dependent upon interest rates.

To the closest year, how long will it take $200 to double if it is deposited and earns the following rates? [Notes: (1) See the hint for Problem 7-34. (2) This problem cannot be solved exactly with some financial calculators. For example, if you enter PV � �200, FV � 400, and I � 7 in an HP-12C, and then press the N key, you will get 11 years for part a. The correct answer is 10.2448 years, which rounds to 10, but the calculator rounds up. However, the HP-10B and HP-17B give the correct answer. You should look up FVIF � $400/$200 � 2 in the tables for parts a, b, and c, but figure out part d.] Assume that compounding occurs once a year. a. 7 percent. b. 10 percent. c. 18 percent. d. 100 percent. Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1; that is, they are ordinary annuities. (Note: See the hint to Prob- lem 7-34. Also, note that you can leave values in the TVM register, switch to “BEG,” press FV, and find the FV of the annuity due.) Assume that compounding occurs once a year. a. $400 per year for 10 years at 10 percent. b. $200 per year for 5 years at 5 percent. c. $400 per year for 5 years at 0 percent. d. Now rework parts a, b, and c assuming that payments are made at the beginning of

each year; that is, they are annuities due. Find the present value of the following ordinary annuities (see note to Problem 7-37). As- sume that discounting occurs once a year. a. $400 per year for 10 years at 10 percent. b. $200 per year for 5 years at 5 percent. c. $400 per year for 5 years at 0 percent. d. Now rework parts a, b, and c assuming that payments are made at the beginning of

each year; that is, they are annuities due. a. Find the present values of the following cash flow streams. The appropriate interest

rate is 8 percent, compounded annually. (Hint: It is fairly easy to work this problem 7-39

Uneven cash flow stream

7-38 Present value of an annuity

7-37 Future value of an annuity

7-36 Time for a lump sum to double

7-35 Present and future values

for different interest rates

7-34 Present and future values

for different periods

7-33 Financial calculator needed;

Nonannual compounding

339

dealing with the individual cash flows. However, if you have a financial calculator, read the section of the manual that describes how to enter cash flows such as the ones in this problem. This will take a little time, but the investment will pay huge divi- dends throughout the course. Note that if you do work with the cash flow register, you must enter CF0 � 0.)

YEAR CASH STREAM A CASH STREAM B

1 $100 $300 2 400 400 3 400 400 4 400 400 5 300 100

b. What is the value of each cash flow stream at a 0 percent interest rate, compounded annually?

Find the interest rates, or rates of return, on each of the following: a. You borrow $700 and promise to pay back $749 at the end of 1 year. b. You lend $700 and receive a promise to be paid $749 at the end of 1 year. c. You borrow $85,000 and promise to pay back $201,229 at the end of 10 years. d. You borrow $9,000 and promise to make payments of $2,684.80 per year for 5 years. Find the amount to which $500 will grow under each of the following conditions: a. 12 percent compounded annually for 5 years. b. 12 percent compounded semiannually for 5 years. c. 12 percent compounded quarterly for 5 years. d. 12 percent compounded monthly for 5 years. Find the present value of $500 due in the future under each of the following conditions: a. 12 percent nominal rate, semiannual compounding, discounted back 5 years. b. 12 percent nominal rate, quarterly compounding, discounted back 5 years. c. 12 percent nominal rate, monthly compounding, discounted back 1 year. Find the future values of the following ordinary annuities: a. FV of $400 each 6 months for 5 years at a nominal rate of 12 percent, compounded

semiannually. b. FV of $200 each 3 months for 5 years at a nominal rate of 12 percent, compounded

quarterly. c. The annuities described in parts a and b have the same amount of money paid into

them during the 5-year period, and both earn interest at the same nominal rate, yet the annuity in part b earns $101.75 more than the one in part a over the 5 years. Why does this occur?

The First City Bank pays 7 percent interest, compounded annually, on time deposits. The Second City Bank pays 6 percent interest, compounded quarterly. a. Based on effective, or equivalent, interest rates, in which bank would you prefer to

deposit your money? b. Could your choice of banks be influenced by the fact that you might want to with-

draw your funds during the year as opposed to at the end of the year? In answering this question, assume that funds must be left on deposit during the entire com- pounding period in order for you to receive any interest.

a. Set up an amortization schedule for a $25,000 loan to be repaid in equal installments at the end of each of the next 5 years. The interest rate is 10 percent, compounded annually.

b. How large must each annual payment be if the loan is for $50,000? Assume that the interest rate remains at 10 percent, compounded annually, and that the loan is paid off over 5 years.

c. How large must each payment be if the loan is for $50,000, the interest rate is 10 percent, compounded annually, and the loan is paid off in equal installments at the end of each of the next 10 years? This loan is for the same amount as the loan in part b, but the payments are spread out over twice as many periods. Why are these pay- ments not half as large as the payments on the loan in part b?

7-45 Amortization schedule

7-44 Effective versus nominal interest rates

7-43 Future value of an annuity for various

compounding periods

7-42 Present value for various

compounding periods

7-41 Future value for various

compounding periods

7-40 Effective rate of interest

P R O B L E M S

C H A P T E R 7 � T I M E VA L U E O F MO N E Y340

The Jackson family is interested in buying a home. The family is applying for a $125,000, 30-year mortgage. Under the terms of the mortgage, they will receive $125,000 today to help purchase their home. The loan will be fully amortized over the next 30 years. Current mortgage rates are 8 percent. Interest is compounded monthly and all payments are due at the end of the month. a. What is the monthly mortgage payment? b. What portion of the mortgage payments made during the first year will go toward

interest? c. What will be the remaining balance on the mortgage after 5 years? d. How much could the Jacksons borrow today if they were willing to have a $1,200

monthly mortgage payment? (Assume that the interest rate and the length of the loan remain the same.)

Assume that AT&T’s pension fund managers are considering two alternative securities as investments: (1) Security Z (for zero intermediate year cash flows), which costs $422.41 today, pays nothing during its 10-year life, and then pays $1,000 after 10 years or (2) Security B, which has a cost today of $1,000 and which pays $80 at the end of each of the next 9 years and then $1,080 at the end of Year 10. a. What is the rate of return on each security? b. Assume that the interest rate AT&T’s pension fund managers can earn on the fund’s

money falls to 6 percent, compounded annually, immediately after the securities are purchased and is expected to remain at that level for the next 10 years. What would the price of each security change to, what would the fund’s profit be on each security, and what would be the percentage profit (profit divided by cost) for each security?

c. Assuming that the cash flows for each security had to be reinvested at the new 6 per- cent market interest rate, (1) what would be the value attributable to each security at the end of 10 years and (2) what “actual, after-the-fact” rate of return would the fund have earned on each security? (Hint: The “actual” rate of return is found as the in- terest rate that causes the PV of the compounded Year 10 amount to equal the orig- inal cost of the security.)

d. Now assume all the facts as given in parts b and c, except assume that the interest rate rose to 12 percent rather than fell to 6 percent. What would happen to the profit fig- ures as developed in part b and to the “actual” rates of return as determined in part c? Explain your results.

A father is planning a savings program to put his daughter through college. His daugh- ter is now 13 years old. She plans to enroll at the university in 5 years, and it should take her 4 years to complete her education. Currently, the cost per year (for everything — food, clothing, tuition, books, transportation, and so forth) is $12,500, but a 5 percent annual inflation rate in these costs is forecasted. The daughter recently received $7,500 from her grandfather’s estate; this money, which is invested in a bank account paying 8 percent interest, compounded annually, will be used to help meet the costs of the daugh- ter’s education. The remaining costs will be met by money the father will deposit in the savings account. He will make 6 equal deposits to the account, one deposit in each year from now until his daughter starts college. These deposits will begin today and will also earn 8 percent interest, compounded annually. a. What will be the present value of the cost of 4 years of education at the time the

daughter becomes 18? [Hint: Calculate the future value of the cost (at 5%) for each year of her education, then discount 3 of these costs back (at 8%) to the year in which she turns 18, then sum the 4 costs.]

b. What will be the value of the $7,500 that the daughter received from her grand- father’s estate when she starts college at age 18? (Hint: Compound for 5 years at an 8 percent annual rate.)

c. If the father is planning to make the first of 6 deposits today, how large must each de- posit be for him to be able to put his daughter through college? (Hint: An annuity due assumes interest is earned on all deposits; however, the 6th deposit earns no in- terest — therefore, the deposits are an ordinary annuity.)

S P R E A D S H E E T P R O B L E M

Answer the following questions, using a spreadsheet model to do the calculations. a. Find the FV of $1,000 invested to earn 10 percent after 5 years. Answer this question

by using a math formula and also by using the Excel function wizard.

7-49 Time value of money

7-48 Required annuity payments

7-47 Effective rates of return

7-46 Financial calculator needed;

Amortization schedule

341

b. Now create a table that shows the FV at 0 percent, 5 percent, and 20 percent for 0, 1, 2, 3, 4, and 5 years. Then create a graph with years on the horizontal axis and FV on the vertical axis to display your results.

c. Find the PV of $1,000 due in 5 years if the discount rate is 10 percent. Again, work the problem with a formula and also by using the function wizard.

d. A security has a cost of $1,000 and will return $2,000 after 5 years. What rate of re- turn does the security provide?

e. Suppose California’s population is 30 million people, and its population is expected to grow by 2 percent per year. How long would it take for the population to double?

f. Find the PV of an annuity that pays $1,000 at the end of each of the next 5 years if the interest rate is 15 percent. Then find the FV of that same annuity.

g. How would the PV and FV of the annuity change if it were an annuity due rather than an ordinary annuity?

h. What would the FV and the PV for parts a and c be if the interest rate were 10 percent with semiannual compounding rather than 10 percent with annual compounding?

i. Find the PV and the FV of an investment that makes the following end-of-year pay- ments. The interest rate is 8 percent.

YEAR PAYMENT

1 $100 2 200 3 400

j. Suppose you bought a house and took out a mortgage for $50,000. The interest rate is 8 percent, and you must amortize the loan over 10 years with equal end-of-year payments. Set up an amortization schedule that shows the annual payments and the amount of each payment that goes to pay off the principal and the amount that con- stitutes interest expense to the borrower and interest income to the lender. (1) Create a graph that shows how the payments are divided between interest and

principal repayment over time. (2) Suppose the loan called for 10 years of monthly payments, with the same origi-

nal amount and the same nominal interest rate. What would the amortization schedule show now?

k. Refer to Problem 7-48. Solve this problem using a spreadsheet model.

C Y B E R P R O B L E M

The information related to the cyberproblems is likely to change over time, due to the release of new information and the ever-changing nature of the World Wide Web. With these changes in mind, we will periodically update these problems on the textbook’s web site. To avoid problems, please check for these updates before proceeding with the cyberproblems. In managing one’s own finances, as well as those of a business, there are numerous decision situations where applications of Time Value of Money (TVM) concepts and methods help one assess the financial consequences of alternative courses of action. One such situation is the decision to prepay part or all of one’s mortgage or loan bal- ance by making extra periodic principal payments. As one makes extra principal payments, the loan balance is reduced faster. This means you pay less interest over the life of the loan and the loan will be repaid earlier (that is, fewer payments). For example, a person might decide to pay $50 per month extra (that is, if their mort- gage payment was $900 per month, they might pay $950 each month, $50 extra) on a mortgage loan. The extra payment of $50 would be applied each month to reduce the principal balance. However, there are important factors to consider before making this decision. For example, if the mortgage loan is on the person’s primary residence, the interest on the loan may be tax deductible. As you know from previ- ous text chapters, this reduces the net, after-tax cost of the loan.

7-50 Prepayment versus

investment analysis

To consider the financial consequences of this decision, visit the web site www.interest.com/hugh/calc, which offers various web calculators free, including a prepayment versus investment scenario analysis. Before using this web site, you will need to amortize the loan you will use as input data for the analysis.

Suppose you purchase a home for $150,000 and obtain a 90 percent mortgage loan, 30-year maturity, at a fixed annual interest rate of 8 percent, with deferred monthly payments. What is the monthly payment for principal and interest (P&I) on this loan?

The loan amount is $150,000 � 0.90 � $135,000. The calculator keystrokes follow. N � 360 (30 years � 12 months per year); I � 8.0/12 � 0.6667; PV � �135000; FV � 0 (the loan will be paid off at maturity); solve for PMT � $990.62. (Note: If you enter the interest rate at 0.6667 percent per month you get the payment above. If you carry full precision on your calculator, the PMT � $990.58.)

The data you will need for the prepayment scenario include the following. Loan balance: $135,000 Current payment: $990.62 Additional payment: $50.00 Loan interest rate: 8.0% Loan interest deductibility: Yes Investment rate return: 6.00%* Tax bracket: 30.00% Investment type: After-tax

*The investment rate return is your opportunity cost estimate. It is the annual rate you think you can earn on the $50 extra principal payment if you did not make extra principal payments on your mortgage but instead, invested it.

Now visit the web site www.interest.com/hugh/calc, and select Prepayment ver- sus Investment. a. After 12 months of making extra payments, what will be the loan balance? b. After 12 months of making the regular payment and investing the $50, what will

be the loan balance? c. Under the regular payment and investing option, excluding the tax due on the in-

terest earned, what is the investment balance after 12 months? d. Compare the scenarios of investment versus prepayment by examining the 60th

payment, which occurs at the end of the 5th year. What is the difference between the (1) interest portion of that payment, (2) tax deduction for interest, and (3) principal balance? Finally, how much is in the investment account?

C H A P T E R 7 � T I M E VA L U E O F MO N E Y342

FIRST NATIONAL BANK

7-51 Time Value of Money Analysis Assume that you are nearing graduation and that you have applied for a job with a local bank, First National Bank. As part of the bank’s eval- uation process, you have been asked to take an examination that covers several financial analysis techniques. The first section of the test addresses time value of money analysis. See how you would do by answering the following questions.

a. Draw time lines for (1) a $100 lump sum cash flow at the end of Year 2, (2) an ordinary annuity of $100 per year for 3 years, and (3) an uneven cash flow stream of �$50, $100, $75, and $50 at the end of Years 0 through 3.

b. (1) What is the future value of an initial $100 after 3 years if it is invested in an account paying 10 percent, annual compounding?

343I N T E G R AT E D C A S E

(2) What is the present value of $100 to be received in 3 years if the appropriate interest rate is 10 percent, an- nual compounding?

c. We sometimes need to find how long it will take a sum of money (or anything else) to grow to some specified amount. For example, if a company’s sales are growing at a rate of 20 percent per year, how long will it take sales to double?

d. What is the difference between an ordinary annuity and an annuity due? What type of annuity is shown below? How would you change it to the other type of annuity?

e. (1) What is the future value of a 3-year ordinary annuity of $100 if the appropriate interest rate is 10 percent, annual compounding?

(2) What is the present value of the annuity? (3) What would the future and present values be if the

annuity were an annuity due? f. What is the present value of the following uneven cash

flow stream? The appropriate interest rate is 10 percent, compounded annually.

g. What annual interest rate will cause $100 to grow to $125.97 in 3 years?

h. A 20-year-old student wants to begin saving for her re- tirement. Her plan is to save $3 a day. Every day she places $3 in a drawer. At the end of each year, she invests the accumulated savings ($1,095) in an online stock ac- count that has an expected annual return of 12 percent. (1) If she keeps saving in this manner, how much will

she have accumulated by age 65? (2) If a 40-year-old investor began saving in this manner,

how much would he have by age 65?

0 Years1 2 3

1000 300 300

4

�50

0 1 2 3

100 100 100

(3) How much would the 40-year-old investor have to save each year to accumulate the same amount at age 65 as the 20-year-old investor described above?

i. (1) Will the future value be larger or smaller if we com- pound an initial amount more often than annually, for example, every 6 months, or semiannually, hold- ing the stated interest rate constant? Why?

(2) Define (a) the stated, or quoted, or nominal, rate, (b) the periodic rate, and (c) the effective annual rate (EAR).

(3) What is the effective annual rate corresponding to a nominal rate of 10 percent, compounded semiannu- ally? Compounded quarterly? Compounded daily?

(4) What is the future value of $100 after 3 years under 10 percent semiannual compounding? Quarterly compounding?

j. When will the effective annual rate be equal to the nom- inal (quoted) rate?

k. (1) What is the value at the end of Year 3 of the follow- ing cash flow stream if the quoted interest rate is 10 percent, compounded semiannually?

(2) What is the PV of the same stream? (3) Is the stream an annuity? (4) An important rule is that you should never show a

nominal rate on a time line or use it in calculations unless what condition holds? (Hint: Think of annual compounding, when iNom � EAR � iPER.) What would be wrong with your answer to parts k (1) and k (2) if you used the nominal rate, 10 percent, rather than the periodic rate, iNom/2 � 10%/2 � 5%?

l. (1) Construct an amortization schedule for a $1,000, 10 percent, annual compounding loan with 3 equal in- stallments.

(2) What is the annual interest expense for the bor- rower, and the annual interest income for the lender, during Year 2?

0 Periods2

100 100 1000

4 6

A P P E N D I X 7 A � C O N T I N U O US C O M P O U N D I N G A N D D IS C O U N T I N G344

CONTINUOUS COMPOUNDING AND DISCOUNTING

In Chapter 7 we dealt only with situations where interest is added at discrete intervals — annually, semiannually, monthly, and so forth. In some instances, though, it is possible to have instantaneous, or continuous, growth. In this ap- pendix, we discuss present value and future value calculations when the interest rate is compounded continuously.

CONTINUOUS COMPOUNDING

The relationship between discrete and continuous compounding is illustrated in Figure 7A-1. Panel a shows the annual compounding case, where interest is added once a year; Panel b shows the situation when compounding occurs twice a year; and Panel c shows interest being earned continuously. As the graphs show, the more frequent the compounding period, the larger the final com- pounded amount because interest is earned on interest more often.

Equation 7-9 in the chapter can be applied to any number of compounding periods per year:

More frequent compounding: FVn � (7-9)PVa1 � iNomm b mn

.

Continuous Compounding A situation in which interest is added continuously rather than at discrete points in time.

7A

F I G U R E 7 A - 1 Annual, Semiannual, and Continuous Compounding: Future Value with i � 25%

Dollars

Interest Earned

a. Annual Compounding

4

3

2

1

0 1 2 3 4 5

$3.0518

Years

Dollars

Interest Earned

b. Semiannual Compounding

4

3

2

1

0 1 2 3 4 5

$3.2473

Years

Dollars

Interest Earned

c. Continuous Compounding

4

3

2

1

0 1 2 3 4 5

$3.4903

Years

345A P P E N D I X 7 A � C O N T I N U O US C O M P O U N D I N G A N D D IS C O U N T I N G

To illustrate, let PV � $100, i � 10%, and n � 5. At various compounding pe- riods per year, we obtain the following future values at the end of five years:

We could keep going, compounding every hour, every minute, every second, and so on. At the limit, we could compound every instant, or continuously. The equation for continuous compounding is

FVn � PV(e in). (7A-1)

Here e is the value 2.7183 . . . . If $100 is invested for five years at 10 percent compounded continuously, then FV5 is calculated as follows:

1

Continuous: FV5 � $100[e 0.10(5)] � $100(2.7183 . . .)0.5

� $164.87.

CONTINUOUS DISCOUNTING

Equation 7A-1 can be transformed into Equation 7A-2 and used to determine present values under continuous discounting:

(7A-2)

Thus, if $1,649 is due in 10 years, and if the appropriate continuous discount rate, i, is 5 percent, then the present value of this future payment is

PV � $1,649

(2.7183 . . .)0.5 �

$1,649 1.649

� $1,000.

PV � FVn ein

� FVn(e �in).

Daily: FV5 � $100a1 � 0.10365 b 365(5)

� $164.86.

Monthly: FV5 � $100a1 � 0.1012 b 12(5)

� $100(1.0083)60 � $164.53.

Semiannual: FV5 � $100a1 � 0.102 b 2(5)

� $100(1.05)10 � $162.89.

Annual: FV5 � $100a1 � 0.101 b 1(5)

� $100(1.10)5 � $161.05.

1 Calculators with exponential functions can be used to evaluate Equation 7A-1. For example, with an HP-10B you would type .5, then press the ex key to get 1.6487, and then multiply by $100 to get $164.87.

SOURCE: Courtesy of Ford Motor Company

CHAPTER B o nd s a nd T he i r Va l ua t i o n8

48

Most analysts agreed that these bonds had limited

default risk. At the time, Ford held $24 billion in cash

and had earned a record $2.5 billion during the second

quarter of 1999. However, the auto industry faces some

inherent risks. When all the risk factors were balanced,

the issues all received a single-A rating. Much to the

relief of the jittery bond market, the Ford issue was well

uring the summer of 1999 the future course of

interest rates was highly uncertain. Continued

strength in the economy and growing fears of

inflation had caused interest rates to rise, and many

analysts were concerned that this trend would continue.

However, others were forecasting declining rates — they

saw no threat from inflation and were more concerned

about the economy running out of gas. Because of this

uncertainty, bond investors tended to wait on the sidelines

for some definitive economic news. At the same time,

companies tended to postpone bond issues out of fear that

nervous investors would be unwilling to purchase them.

This is exactly the situation in which Ford Motor

found itself in June 1999, when it decided to put a

large debt issue on hold. However, after just three

weeks, Ford sensed a shift in the investment climate,

and it announced plans for an $8.6 billion bond issue.

As shown in the following table, the Ford issue set a

new record, surpassing an $8 billion AT&T issue that had

taken place a few months earlier.

Ford’s $8.6 billion issue actually consisted of four

separate bonds. Ford Credit, a subsidiary that provides

customer financing, borrowed $1.0 billion dollars at a

two-year floating rate and another $1.8 billion at a

three-year floating rate. Ford Motor itself borrowed $4

billion as five-year fixed-rate debt and another $1.8

billion at a 32-year fixed rate.

F O R D ’ S B O N D IS S U E S E TS A N E W R E C O R D

FORD MOTOR COMPANY

$

D

349

Top Ten U.S. Corporate Bond Financings as of July 1999

AMOUNT (BILLIONS

ISSUER DATE OF DOLLARS)

Ford July 9, 1999 $8.60 AT&T March 23, 1999 8.00 RJR Holdings May 12, 1989 6.11 WorldCom August 6, 1998 6.10 Sprint November 10, 1998 5.00 Assoc. Corp. of N. America October 27, 1998 4.80 Norfolk Southern May 14, 1997 4.30 US West January 16, 1997 4.10 Conoco April 15, 1999 4.00 Charter Communications March 12, 1999 3.58

SOURCE: Thomson Financial Securities Data, Credit Suisse First Boston as reported in The Wall Street Journal, July 12, 1999, C1.

C H A P T E R 8 � B O N D S A N D T H E I R VA L UAT IO N350

Bonds are one of the most important types of securities. If you skim through The

Wall Street Journal, you will see references to a wide variety of these securities.

This variety may seem confusing, but in actuality just a few characteristics dis-

tinguish the various types of bonds.

While bonds are often viewed as relatively safe investments, one can certainly

lose money on them. Indeed, “riskless” long-term U.S. Treasury bonds have de-

clined in value three of the last seven years. Note, though, that it is also possi-

ble to rack up impressive gains in the bond market. Long-term government bonds

provided a total return of nearly 16 percent in 1997 and more than 30 percent in

1995.

In this chapter, we will discuss the types of bonds companies and government

agencies issue, the terms that are contained in bond contracts, the types of risks

to which both bond investors and issuers are exposed, and procedures for deter-

mining the values of and rates of return on bonds. �

bonds outstanding will decrease, forcing many Treasury

investors into the corporate bond market, where they

will look for investment-grade issues by companies such

as Ford.

Already anticipating this demand, Ford is planning

to regularly issue large blocks of debt in the global

market. Seeing Ford’s success, less than one month

after the Ford issue, Wal-Mart entered the list of top

ten U.S. corporate bond financings with a new $5

billion issue. Other large companies have subsequently

followed suit. �

SOURCE: Gregory Zuckerman, “Ford’s Record Issue May Drive Imitators,” The Wall Street Journal, July 12, 1999, C1.

received. Dave Cosper, Ford Credit’s Treasurer, said

“There was a lot of excitement, and demand exceeded

our expectations.”

The response to the Ford offering revealed that

investors had a strong appetite for large bond issues

with strong credit ratings. Larger issues are more liquid

than smaller ones, and liquidity is particularly important

to bond investors when the direction of the overall

market is highly uncertain.

Interestingly, large investment-grade issues by well-

known companies such as Ford are also helping to fill

the vacuum created by the reduction in Treasury debt.

The Federal government is forecasting future budget

surpluses, and it plans to use a portion of the surplus to

reduce its outstanding debt. As this occurs, Treasury

351

W H O I S S U E S B O N D S ?

A bond is a long-term contract under which a borrower agrees to make pay- ments of interest and principal, on specific dates, to the holders of the bond. For example, on January 3, 2002, Allied Food Products borrowed $50 million by issuing $50 million of bonds. For convenience, we assume that Allied sold 50,000 individual bonds for $1,000 each. Actually, it could have sold one $50 million bond, 10 bonds with a $5 million face value, or any other combination that totals to $50 million. In any event, Allied received the $50 million, and in exchange it promised to make annual interest payments and to repay the $50 million on a specified maturity date.

Investors have many choices when investing in bonds, but bonds are classi- fied into four main types: Treasury, corporate, municipal, and foreign. Each type differs with respect to expected return and degree of risk.

Treasury bonds, sometimes referred to as government bonds, are issued by the federal government.1 It is reasonable to assume that the federal government will make good on its promised payments, so these bonds have no default risk. However, Treasury bond prices decline when interest rates rise, so they are not free of all risks.

Corporate bonds, as the name implies, are issued by corporations. Unlike Treasury bonds, corporate bonds are exposed to default risk — if the issuing company gets into trouble, it may be unable to make the promised interest and principal payments. Different corporate bonds have different levels of default risk, depending on the issuing company’s characteristics and on the terms of the specific bond. Default risk is often referred to as “credit risk,” and, as we saw in Chapter 5, the larger the default or credit risk, the higher the interest rate the issuer must pay.

Municipal bonds, or “munis,” are issued by state and local governments. Like corporate bonds, munis have default risk. However, munis offer one major advantage over all other bonds: As we discussed in Chapter 2, the interest earned on most municipal bonds is exempt from federal taxes and also from state taxes if the holder is a resident of the issuing state. Consequently, munic- ipal bonds carry interest rates that are considerably lower than those on corpo- rate bonds with the same default risk.

Foreign bonds are issued by foreign governments or foreign corporations. Foreign corporate bonds are, of course, exposed to default risk, and so are some foreign government bonds. An additional risk exists if the bonds are denomi- nated in a currency other than that of the investor’s home currency. For exam- ple, if you purchase corporate bonds denominated in Japanese yen, you will lose money — even if the company does not default on its bonds — if the Japanese yen falls relative to the dollar.

W H O I S S U E S B O N D S ?

Bond A long-term debt instrument.

1 The U.S. Treasury actually calls its debt issues “bills,” “notes,” or “bonds.” T-bills generally have maturities of 1 year or less at the time of issue, notes generally have original maturities of 2 to 7 years, and bond maturities extend out to 30 years. There are technical differences between bills, notes, and bonds, but they are not important for our purposes, so we generally call all Treasury securities “bonds.” Note too that a 30-year T-bond at the time of issue becomes a 1-year bond 29 years later.

Treasury Bonds Bonds issued by the federal government, sometimes referred to as government bonds.

Corporate Bonds Bonds issued by corporations.

Municipal Bonds Bonds issued by state and local governments.

Foreign Bonds Bonds issued by either foreign governments or foreign corporations.

C H A P T E R 8 � B O N D S A N D T H E I R VA L UAT IO N352

K E Y C H A R AC T E R I S T I C S O F B O N D S

Although all bonds have some common characteristics, they do not always have the same contractual features. For example, most corporate bonds have provisions for early repayment (call features), but these provisions can be quite different for different bonds. Differences in contractual provisions, and in the underlying strength of the companies backing the bonds, lead to major differ- ences in bonds’ risks, prices, and expected returns. To understand bonds, it is important that you understand the following terms.

PAR VALUE

The par value is the stated face value of the bond; for illustrative purposes we generally assume a par value of $1,000, although any multiple of $1,000 (for ex- ample, $5,000) can be used. The par value generally represents the amount of money the firm borrows and promises to repay on the maturity date.

COUPON INTEREST RATE

Allied’s bonds require the company to pay a fixed number of dollars of interest each year (or, more typically, each six months). When this coupon payment, as it is called, is divided by the par value, the result is the coupon interest rate. For example, Allied’s bonds have a $1,000 par value, and they pay $100 in in- terest each year. The bond’s coupon interest is $100, so its coupon interest rate is $100/$1,000 � 10 percent. The $100 is the yearly “rent” on the $1,000 loan. This payment, which is fixed at the time the bond is issued, remains in force during the life of the bond.2 Typically, at the time a bond is issued, its coupon payment is set at a level that will enable the bond to be issued at or near its par

Par Value The face value of a bond.

Coupon Payment The specified number of dollars of interest paid each period, generally each six months.

Coupon Interest Rate The stated annual interest rate on a bond.

2 Incidentally, some time ago bonds literally had a number of small (1/2- by 2-inch), dated coupons attached to them, and on each interest payment date, the owner would clip off the coupon for that date and either cash it at his or her bank or mail it to the company’s paying agent, who would then mail back a check for the interest. A 30-year, semiannual bond would start with 60 coupons, whereas a 5-year annual payment bond would start with only 5 coupons. Today, new bonds must be registered — no physical coupons are involved, and interest checks are mailed automatically to the registered owners of the bonds. Even so, people continue to use the terms coupon and coupon in- terest rate when discussing registered bonds.

SELF-TEST QUESTIONS

What is a bond?

What are the four main types of bonds?

Why are U.S. Treasury bonds not riskless?

To what types of risk are investors of foreign bonds exposed?

An excellent site for information on many types of bonds is Bonds Online, which can be found at http://www.

bondsonline.com. The site has a great deal of information about corporates, municipals, treasuries, and bond funds. It includes free bond searches, through which the user specifies the attributes desired in a bond and then the search returns the publicly traded bonds meeting the criteria. The site also includes a downloadable bond calculator and an excellent glossary of bond terminology.

353

value. Consequently, most of our examples and problems throughout this text will focus on bonds with fixed coupon rates.

In some cases, however, a bond’s coupon payment will vary over time. These floating rate bonds work as follows. The coupon rate is set for, say, the initial six-month period, after which it is adjusted every six months based on some market rate. Some corporate issues are tied to the Treasury bond rate, while other issues are tied to other rates. Many additional provisions can be included in floating rate issues. For example, some are convertible to fixed rate debt, whereas others have upper and lower limits (“caps” and “floors”) on how high or low the rate can go.

Floating rate debt is popular with investors who are worried about the risk of rising interest rates, since the interest paid increases whenever market rates rise. This causes the market value of the debt to be stabilized, and it also provides in- stitutional buyers such as banks with income that is better geared to their own obligations. Banks’ deposit costs rise with interest rates, so the income on float- ing rate loans that they have made rises at the same time their deposit costs are rising. The savings and loan industry was virtually destroyed as a result of their practice of making fixed rate mortgage loans but borrowing on floating rate terms. If you are earning 6 percent but paying 10 percent — which they were — you soon go bankrupt — which they did.

Moreover, floating rate debt appeals to corporations that want to issue long- term debt without committing themselves to paying an historically high interest rate for the entire life of the loan.