Investment Operations

Investment Operations

PART ONE: INTRODUCTION IN INVESTMENT OPERATIONS PART TWO: INVESTMENT RETURNS & VALUATIONS

PART TWO: INVESTMENT RISK-RETURN ANALYSIS

Investment Operations Course Syllabus

CONTENTS IN BRIEF

COURSE SYLLABUS

PART ONE: INTRODUCTION IN INVESTMENT OPERATIONS Chapter 1: Financial System & Financial Markets Investment by Bodie, Kane, Marcus Investment Operation by Cuevas, Estrella, Morimonte Chapter 2: Financial Instruments Investment by Bodie, Kane, Marcus Chapter 3: Financial Statement Analysis: An Introduction Financial Statement Analysis – Volume 3 of 2008 CFA® Level 1 Curriculum PART TWO: INVESTMENT RETURNS & VALUATIONS Chapter 4: The Time Value of Money Quantitative Methods for Investment Analysis by DeFusco et al Chapter 5: Discounted Cash Flow Applications Quantitative Methods for Investment Analysis by DeFusco et al Chapter 6: Bonds and Their Valuation Fundamentals of Financial Management 10th Edition by Brigham & Houston Chapter 7: Stocks and Their Valuation Fundamentals of Financial Management 10th Edition by Brigham & Houston PART TWO: INVESTMENT RISK-RETURN ANALYSIS & PORTFOLIO MANAGEMENT Chapter 8: How Corporations Issue Securities Fundamentals of Corporate Finance 3rd Edition by Brealy, Myers, Marcus Chapter 9: Introduction to Risk, Return, and the Opportunity Cost of Capital Fundamentals of Corporate Finance 3rd Edition by Brealy, Myers, Marcus Chapter 10: Risk, Return, and Capital Budgeting Fundamentals of Corporate Finance 3rd Edition by Brealy, Myers, Marcus Chapter 11: Asset Allocation Decision & An Introduction to Portfolio Management Investment Analysis & Portfolio Management by Reilly & Brown

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PART ONE: Introduction in Investment Operations

Chapter 1: Financial System & Financial Markets Investment by Bodie, Kane, Marcus Investment Operation by Cuevas, Estrella, Morimonte Chapter 2: Financial Instruments Investment by Bodie, Kane, Marcus Chapter 3: Financial Statement Analysis: An Introduction

Financial Statement Analysis – Volume 3 of CFA® Level 1 Curriculum

Investment Operations Chapter 1 – Financial Systems & Financial Markets

FINANCIAL SYSTEM & FINANCIAL MARKETS

CHAPTER ONE

FINANCIAL SYSTEM

Is a set of laws, rules and physical structures and procedures that govern and facilitate all kinds of financial transactions in an economy.

Its objective is to provide efficiency & liquidity that leads to a well functioning economy.

FINANCIAL MARKETS

The essential economic function of Financial Market is to channel funds from lenders(savers) to borrowers(spenders) as the figure shows below:

Households

Enterprises

Governments

Households

Enterprises

Governments

Foreigners

Funds FINANCIAL

MARKET Funds

Foreigners

Obviously the players in the financial market are the providers & users of fund (households, institutions, governments, and foreigners) and the Financial Intermediaries.

Financial Intermediaries – can be define as any institutions that its main functions is to collect financial resources (funds) from the lenders and at the same time to provide needed financial resources (funds) to borrowers. Simply, it channels funds from lenders to borrowers.

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Common Groupings of Financial Intermediaries:

Deposit Accepting Institutions - universal banks, savings banks, commercial banks, thrift banks, etch.

Contractual Savings Institutions - these are life insurance companies, non-life insurance companies, provident fund companies & other allied businesses

Investment Intermediaries - such as closed-end and open-end mutual funds and investment banks.

Financial Intermediaries

Objectives of lenders & borrowers:

Lenders(savers) – the main objective is to acquire returns from the funds such as interest, funds appreciation, dividends, and any cash flows that accompany its investment that it can be use for future purchases like a source of fund for retirement.

Borrowers(savers) – to acquire funds that can be used for capital expansion (institutions), personal purchases (households), projects & developments (government).

STRUCTURE OF THE FINANCIAL MARKETS

The structure of the financial market can be categorized as follows:

1. Debt & Equity Markets

2. Primary & Secondary Markets

3. Money & Capital Markets

REGULATION OF THE FINANCIAL SYSTEM

Government regulates financial markets for three reasons:

1. Financial information availability

2. To provide liquidity and efficiency in the market

3. To ensure soundness of monetary policy

Philippines Government Regulatory Bodies

Bangko Sentral ng Pilipinas (BSP) is an independent government instrumentality whose mission is to provide liquidity, stability, & reliability of the domestic financial system by implementing rules and regulations that will govern the system, It directly supervise bank and non-bank/quasi-bank financial institutions.

Securities and Exchange Commission (SEC) regulates the issue and sale of privately issued securities. It also controls and regulates the organized exchange or the PSE (Philippine Stock Exchange).

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Insurance Commission controls and regulate life and non-life insurance companies ensuring that the insuring public is amply protected from fraud and other possible illegal activities of these companies.

INVESTMENT DEFINED

Investment is the current commitment of dollars for a period in order to derive future payments that will compensate investor.

The one that deter its current consumption and put its fund in any investment securities is expecting to be compensated for the ff:

1. Time the funds are committed

2. Compensation for expected inflation

3. Uncertainty of the future payments

Note that there are to types of individuals; one that spend less than its current income and the one that spend more than its current income.

The one that save the excess fund for future return greater than its current value (present value) is the lender in the investment setting.

And the one that finds fund to compensate the excess consumption is the one that represent the borrower in the investment setting.

REAL ASSETS VERSUS FINANCIAL ASSETS

Real Assets is a productive function of the economy that represents the 5 factors of productions. The 5 factors of productions are:

1. Land

2. Capital

3. Human Resources

4. Entrepreneurship

You can think of a Real Assets as the representation on the Balance Sheet of a particular company where you can see such asset accounts as Cash, Inventories, Property Plant & Equipment, and Land that are commonly present in the Current & Long-Term Assets in the Balance Sheet.

Financial Assets on the other hand represents as claims on the earnings of a company such as bonds, preferred stocks, and common stocks. It did not represent the 5 factors of production like the chair that you are using in the class or the elevator that you are using rather it represent as a source of generating your chair or the elevator in the building.

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Figure below shows further how the Financial Assets interacts to Real Assets in a corporate setting.

Real Assets-Financial Assets Interactions

Investors

Claims (dividends,

interest, etch)

Company

Products Real Assets

(land, capital, HR, Entrepreneurship)

Consumers

Funds (stoks, bonds,

etch)

Revenues

Financial Assets Real Assets

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Investment Operations Chapter 2 – Financial Instruments

FINANCIAL INSTRUMENTS

CHAPTER TWO

This chapter covers a range of financial securities and the markets in which they trade. Our goal is to introduce you to the features of various security types. This foundation will be necessary to understand the more analytic material that follows in Business 5 – Investment Operation Subject. Bare in mind that when we say financial market, we traditionally segment it into money market and capital market. As an overview and to facilitate you on the discussion on this chapter please refer to the flow chart below.

Financial Market Segments

FINANCIAL MARKET

MONEY MARKETS

Include short-term, marketable, liquid,

low-risk debt securities

Longer-Term Bond (Fixed Income)

Markets

Equity Markets Derivative Markets

CAPITAL MARKETS

Include longer-term and riskier securities

THE MONEY MARKET

The money market is a subsector of the fixed-income market. It consist of very short-term debt securities that usually are highly marketable.

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Treasury Bills

Or T-Bills or just bills for short, are the most marketable of all money market instrument.

T-Bills represent the simplest form of borrowing: The government raises money by selling bills to the public.

On the other hand, investors buy the bills at a discount from the stated maturity value. At the bill’s maturity, the holder receives from the government a payment equal to the face value of the bill.

The difference between the purchase price and ultimate maturity value constitutes the investor’s earnings.

Certificate of Deposit

A certificate of deposit, or CD, is a time deposit with a bank.

Time deposits may not be withdrawn on demand. The bank pays interest and principal to the depositor only at the end of the fixed term of the CD.

CD’s issued in denominations greater than in certain amount are called Negotiable CDs that is, they can be sold to another investor if the owner needs to cash in the certificate before its maturity date.

CDs are treated as bank deposits by the Federal Deposit Insurance Corporation in the US and same treatment here in the Philippines.

Commercial Paper

Large, well-known companies often issue their own short-term unsecured debt notes rather than borrow directly from banks. These notes are called commercial paper.

Many firm issues Commercial Paper intending to roll it over at maturity, that is, issue new paper to obtain the funds necessary to retire the old paper.

Bankers’ Acceptances

Bankers’ acceptances are essentially guarantees by a bank that a loan will be repaid. They are created as part of commercial transactions, especially international trade. As an example, consider an importer who agrees to pay for goods shipped to him by an exporter, 45 days after the goods are shipped. The importer goes to his bank and gets a letter of credit stating that the bank will guarantee the payment, say $1 million. This letter must be sent to the bank of the exporter before the exporter will actually ship the goods. When the exporter delivers the shipping documents to her bank, she will receive the present value of the $1 million, discounted because the payment will not be made for 45 days.

The final step in the creation of a bankers acceptance is that the exporter’s bank presents the evidence of shipment to the issuing bank (the importer’s bank) which then "accepts" the evidence of shipment. It is this accepted promise to pay $1 million in 45 days that is the bankers acceptance.

The credit risk of a bankers acceptance is the risk that the importer (the initial borrower of the funds) and the accepting bank will both fail to make the promised payment.

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Repurchase Agreements

A repurchase (repo) agreement is an arrangement by which an institution sells a security with a commitment to buy it back at a later date at a specified (higher) price. The repurchase price is greater than the selling price and accounts for the interest charged by the buyer, who is, in effect, lending funds to the seller.

Federal Funds

Just as most of us maintain deposits at banks, banks maintain deposits of their own at a Federal Reserve bank.

Funds in the bank’s reserve account are called federal funds, or fed funds.

In the federal funds market, banks with excess funds lend to those with a shortage. These loans, which are usually overnight transactions, are arranged at a rate of interest called the federal funds rate.

The fed funds rate is simply the rate of interest on very short-term loans among financial institutions.

Brokers’ Calls

Individual who buy stocks on margin borrow part of the funds to pay for the stocks from their broker. The broker in turn may barrow the funds from a bank, agreeing to repay the bank immediately (on call) if the bank request it. The rate paid on such loans is about 1% higher than the rate on short-term T-Bills.

London Interbank Offered Rate (LIBOR)

The LIBOR is the rate at which large banks in London are willing to lend money among themselves.

This rate, which is quoted on dollar-denominated loans, has become the premier short-term interest rate quoted in the European money market, and it serves as a reference rate for a wide range of transactions.

For example, a corporation might borrow at a floating rate equal to LIBOR plus 2%.

Yields on Money Market Instruments

Although most money market securities are of low risk, they are not risk-free.

The securities of the money market do promise yields greater than those on default-free T-Bills, at least in part because of greater relative riskiness.

In addition, many investors require more liquidity; thus they will accept lower yields on securities such as T-Bills that can be quickly and cheaply sold for cash.

THE BOND MARKETS

The bond market is composed of longer-term borrowing or debt instruments than those that trade in the money market. This market includes Treasury notes and bonds, corporate bonds, municipal bonds, mortgage secu rities, and federal agency debt.

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Treasury Notes and Bonds

The US government borrows funds in large part by selling Treasury Notes and Treasury Bonds.

T-Note maturities range up to 10 years, whereas bonds are issued with maturities ranging from 10 to 30 years.

The only major distinction between T-notes and T-bonds is that T-bonds may be callable during a given period, usually the last 5 years of the bond’s life.

The call provision gives the treasury the right to repurchase the bond at par value.

Although notes and bonds are sold in denominations of $1000 par value, the prices are quoted as a percentage of par value. Thus the bid price of 107.7813 should be interpreted as 107.7813% of par, or $1,077.813, for the $1,000 par value security.

Sample excerpt of listing of Treasury issues in the Wall Street Journal

Where: Rate the coupon rate CHS represents changes in price from the previous day trading.

+1 denotes 1/32 increase in price ASK YLD Yealt to Maturity on the ask price. Bid broker’s buying price Asked broker’s selling price

Federal Agency Debt

Some government agencies issue their own securities to finance their activities.

These agencies usually are formed to channel credit to a particular sector of the economy that Congress believes might not receive adequate credit through normal private sources.

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The major mortgage-related agencies are the fallowing:

1. Federal Home Loan Bank (FHLB)

2. Federal National Mortgage Association (FNMA or Fannie Mae)

3. Government National Mortgage Association (GNMA or Ginnie Mae)

4. Federal Home Loan Mortgage Corporation (FHLMC or Freddie Mac)

Some of these agencies are government owned, and therefore can be viewed as branches of the US government. Thus their debt is fully free of default. Ginnie Mae is an example of government-owned agency.

Other agencies, such as the farm credit agencies, the FHLB, Fannie Mae, and Freddie Mac, are merely federally sponsored.

Although the debt of federally sponsored agencies is not explicitly insured by the federal government, it is widely assumed that the government would step in with assistance if an agency neared default.

Thus these securities are considered extremely safe assets, and their yield spread above Treasury securities is usually small.

International Bonds (Eurobonds)

Eurobonds is a bond denominated in a currency other than that of the country in which it is issued. For example, a dollar-denominated bond sold in Philippines would be called a Eurodollar bond.

Similarly, investors might speak of Euroyen bonds, yen-denominated bonds sold outside Japan.

It is best to think of them simply as international bonds.

Municipal Bonds

Municipal Bonds are issued by state and local governments.

They are similar to Treasury and corporate bonds except that their interest income is exempt from federal income taxation. The interest income also is exempt from state and local taxation in the issuing state.

There are basically Two types of municipal bonds:

1. General Obligation Bonds – which are backed by the “full faith and credit” (i.e., the taxing power) of the issuer.

2. Revenue Bonds – which are issued to finance particular projects and are backed either by the revenues from that project or by the particular municipal agency operating the project.

Obviously, revenue bonds are riskier in terms of default than general obligation bonds.

The key feature of municipal bonds is their tax-exempt status. Because investors pay neither federal nor state taxes on the interest proceeds, they are willing to accept lower yields on these securities.

An investor choosing between taxable and tax-exempt bonds must compare after-tax interest rate on each bond.

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An exact comparison requires a computation of after-tax interest rate that explicitly accounts for taxes on income and realized capital gains.

The simpler rule of thumb are:

o If the After-Tax Interest Rate of a taxable bond is greater than the interest on municipal bond, invest on the taxable bond.

o If the After-Tax Interest Return of a taxable bond is lesser than the interest on municipal bond, invest on the municipal bond.

One way to compare bonds is to determine the interest rate on taxable bonds that would be necessary to provide an after-tax return equal to that of municipals. The interest rate that you determine is called After-Tax Interest Rate.

Another way is to determine interest rate of a municipal bond if it is taxable called Equivalent Taxable Interest Rate.

Thus the formula are the following:

After-Tax Interest Rate or rm = r (1 – t)

Equivalent Taxable Interest Rate or r = (1 )

mrt−

Where:

r = Equivalent Taxable Interest Rate

rm = After-Tax Interest Rate

t = tax rate

Example:

Assume a corporate bond yields 6.25%, and an investor who purchases the bond has a marginal tax rate of 28%. The after-tax yield for this investor would be: 6.25% × (1 − 28%) = 4.50%

Also, the yield of a tax-exempt security can be converted to a equivalent taxable interest rate, for comparison to taxable securities, which is calculated as: Taxable-equivalent yield = tax-free yield / (1 − marginal tax rate) Assume for the same investor, he is considering purchasing a municipal issue that has a yield of 4.25%. The taxable equivalent yield would be: 4.25% / (1 − 28%) = 5.90%

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Corporate Bonds

Corporate bonds are the means by which private firms borrow money directly from the public.

These bonds are similar in structure to Treasury issues – they typically pay semiannual coupons over their lives and return the face value to the bondholder at maturity.

They differ most importantly from Treasury bonds in degree of risk. Default risk is real consideration in the purchase of corporate bonds.

Categories of corporate bonds are the following:

1. Secured Bonds – which have specific collateral backing them in the event of firm bankruptcy.

2. Debentures – or unsecured bonds, which have no collateral.

3. Subordinated debentures – which have a lower-priority claim to the firm’s assets in the event of bankruptcy.

Sample excerpt from listing of corporate bonds

ATT – Company’s ticker number, shorthand for the company’s name

7¾ - Coupon Rate 07 – Maturity date 7.6 – Current Yield to Maturity (CurYld.) 12 – number of bonds issued (Vol.) 101¼ - current market price (Close) - ¼ - price changes from previous trading (NET CHG)

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Mortgages and Mortgage-Backed Securities

A mortgage is a loan that is collateralized with a specific piece of real property, either residential or commercial. The borrower must make a series of mortgage payments over the life of the loan, and the lender has the right to foreclose or lay claim against the real estate in the event of loan default.

A conventional mortgage is the most common residential mortgage. It is based on the creditworthiness of the borrower and is collateralized by the residential real estate that it is used to purchase. If a borrowers credit quality is questionable or is lacking sufficient down-payment, the mortgage lender may require mortgage insurance to guarantee the loan.

A fixed rate, level payment, fully amortized mortgage loan requires equal payments (usually monthly) over the life of the mortgage. Each of these payments consists of an interest component and a principal component.

To illustrate, consider a 30-year, $500,000 mortgage with a mortgage rate of 12% and monthly payments of $5,143.06 (N = 360, I/Y = 1 (12/12), PV = -500,000, FV = 0; CPT�PMT = 5,143.06). Although the monthly payment is constant, the interest and principal component are constantly changing. The portion of the payment that represents interest ($5,000) goes toward the reduction of interest, and the remaining ($143.06) goes toward the reduction of principal balance. The ending principal balance in period one ($499,856.94) is also the beginning principal balance in period two ($499,856.94).

Mortgage-Backed Security is either an ownership claim in a pool of mortgages or an obligation that is secured by such a pool. These claims represent securitization of mortgage loans. Mortgage lenders originate loans and then sell packages of these loans in the secondary market.

Specially, they sell their claim to cash inflows from the mortgages as those loans are paid off. The mortgages originator continues to service the loan, collecting principal and interest payments, and passes these payments along to the purchaser of the mortgage. For this reason, these mortgage-backed securities are called pass-throughs.

The success of mortgage-backed pass-throughs has encouraged introduction of pass-through securities backed by other assets.

Although pass-through securities often guarantee payment of interest and principal, they do not guarantee the rate of return. Holders of mortgage pass-throughs therefore can be severely disappointed in their returns in years when interest rates drop significantly.

This is because homeowners usually have an option to repay, or pay ahead of schedule, the remaining principal outstanding on their mortgages.

Mortgage-Backed Security Structure:

Mortgage 1

Mortgage 2

Mortgage 3 Investor 3

Investor 4

Investor 1

Investor 2 Mortgae-Backed Security (Pool of Mortgage Loans)

Mortgage 4

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EQUITY SECURITIES

Common Stock as Ownership Shares

Common Stock – also known as equity securities or equities, represent ownership shares in a corporation.

Each share of common stock entitles its owner to one vote on any matters of corporate governance that are put to a vote at the corporation’s annual meeting and to a share in the financial benefits of ownership.

A corporation sometimes issues two classes of common stock, one bearing the right to vote, the other not. Because of its restricted rights, the nonvoting stock might sell for a lower price.

The common stock of most large corporation can be bought or sold freely on one or more stock exchanges. A corporation whose stock is not publicly traded is said to be closely held.

Characteristics of Common Stock

The two most important characteristics of common stock as an investment:

1. Residual Claim

2. Limited Liability

Residual Claim – means that stockholders are the last in line of all those who have a claim on the assets and income of the corporation.

Limited Liability – means that the most shareholders can lose in the event of failure of the corporation is their original investment.

Unlike owners of unincorporated business, whose creditors can lay claim to the personal assets of the owner (house, car, furniture), corporate shareholders may at worst have worthless stock.

They are not personally liable for the firm’s obligations.

Stock Market Listings

The New York Stock Exchange (NYSE) is one of several markets in which investors may buy or sell shares of stock. In the Philippines it is the Philippine Stock Exchange (PSE) where you can also buy & sell shares of stock.

The dividend yield on the stock is like the current yield on a bond. Both look at the current income as a percentage of the price.

The P/E ration, or price-to-earnings ratio, is the ratio of the current stock price to last year’s earnings per share. The P/E ratio tells us how much stock purchases must pay per dollar of earnings that the firm generates.

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Sample excerpt from listing of corporate stock

DIV – Annual dividend yield (dividend/price) VOL 100s – number of 100 shares traded CLOSE – Current market price NET CHG – stock price changes in dollars

Preferred Stock

Preferred stock has features similar to both equity and debt.

Like a bond, it promises to pay to its holder a fixed amount of income each year. In this sense preferred stock is similar to an infinite-maturity bond, that is, a perpetuity.

It also resembles a bond in that it does not convey voting power regarding the management of the firm.

Preferred stock is an equity investment, however. The firm retains discretion to make the dividend payments to the preferred stockholder; it has no contractual obligation to pay those dividends. Instead, preferred dividends are usually cumulative; that is, unpaid dividends cumulate and must be paid in full before any dividends may be paid to holders of common stock.

Preferred stock also differs from bonds in terms of its tax treatment for the firm. Because preferred stock payments are treated as dividends rather than interest, they are not tax-deductible expenses for the firm.

Preferred stocks therefore make desirable fixed income investment for some corporations.

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STOCK AND BOND MARKET INDEXES

Stock Market Indexes

Stock market index series are used to measure the performance of markets, as a benchmarks to evaluate portfolio performance, and as a proxy for the overall market in academic studies.

Stock market indexes provides guidance concerning the performance of the overall market.

Most of widely used stock market index in financial markets are:

1. Dow Jones Averages

− The Dow Jones Industrial Average (DJIA) of 30 large, “blue-chip” corporations has been computed since 1896.

− Originally, the DJIA was calculated as the simple average of the stocks included in the index. Thus, if there were 30 stocks in the index, one would add up the prices of the 30 stocks and divide by 30.

− The percentage change in the DJIA would then be the percentage change in the average price of the 30 shares.

− This procedure means that the percentage change in the DJIA measures the return (excluding dividends) on a portfolio that invests one share in each of the 30 stocks in the index.

− Because the Dow measures the return (excluding dividends) on a portfolio that holds one share of each stock, it is called a price-weighted average.

− Price-weighted index: To find this, simply take the average value of the share prices of the stocks. For example, assume that you have three stocks as of December 31 with share prices of $10, $20, and $60, respectively. The price-weighted index would equal 30, or (10 + 20 + 60) / 3. Assume that as of January 31, you have three stocks with share prices of $20, $15, and $40, respectively. The price-weighted index would equal 25. The one-month percentage return is -16.7% (i.e., [(25/30) − 1] × 100).

− The amount of money invested in each company represented in the portfolio is proportional to that company’s share price.

2. Standard & Poor’s (S&P) Indexes

− The Standard & Poor’s Composite 500 (S&P 500) stock index represents an improvement over the Dow Jones Averages in two ways.

− First, it is a more broadly based index of 500 firms.

− Second, it is a market-value-weighted index.

− Market-Value-weighted index: Assume you have a December 31 total market value of $80,000 and a January 31 total market value of $95,000. The beginning base value is 100. The new index value formula = (current market value / base value) × (beginning index value). So, [(95,000 / 80,000)](100) = 118.75. Thus, the value-weighted percentage return is 18.75% [i.e., (118.75 / 100) − 1] × 100).

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− The S&P 500 in computed by calculating the total market value of the 500 firms in the index and the total market value of those firms on the previous day trading.

− The percentage increase in the total market value from one day to the next represents the increase in the index.

− The rate of return of the index equals the rate of return that would be earned by an investor holding a portfolio of all 500 firms in the index in proportion to their market values, except that the index does not reflect cash dividends paid by those firms.

− Investors today can purchase shares in mutual funds that hold shares in proportion to their representation in the S&P 500 or other index. These index funds yield a return equal to that of the index and so provide a low-cost passive investment strategy for equity investors.

3. Other U.S. Market-Value Indexes

− The New York Stock Exchange publishes a market-value-weighted composite index of all NYSE-listed stocks, in addition to subindexes for industrial, utility, transportation, and financial stocks.

− The National Association of Securities Dealers publishes an index of 4,000 over-the-counter (OTC) firms traded on the Nasdaq Market.

− The ultimate U.S. equity index so far computed is the Wilshire 5000 index of the market value of all NYSE and American Stock Exchange (Amex) stocks plus actively traded Nasdaq stocks. Despite its name, the index actually includes about 7,000 stocks.

4. Foreign and International Stock Market Indexes

− Development in financial markets worldwide includes the construction of indexes for these markets.

− Among these are the Nikkei (Japan), FTSE (UK; pronounced “fotsie”), DAX (Germany), Hang Seng (Hong Kong), and TSX (Canada).

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Performance of stock indexes

Bonds Market Indicators

Just as stock market indexes provide guidance concerning the performance of the overall stock market, several bond market indicators measure the performance of various categories of bonds.

The three most well-known groups of indexes are those of Merrill Lynch, Lehman Brothers, and Salomon Smith Barney (or Citigroup).

The major problem with these is that true rates of return on many bonds are difficult to compute because the infrequency with which the bonds trade reliable up-to-date prices difficult to obtain.

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DERIVATIVE MARKETS

One of the most significant developments in financial markets in recent years has been the growth of futures, options, and related derivatives market. A derivative is a security that derives its value from the value or return of another asset or security.

These instrument provide pay-offs that depend on the values of other assets such as commodity prices, bond and stock prices, or market index values. For this reason these instruments sometimes are called derivative assets, or contingent claims. Their values derive from or are contingent on the values of other assets.

Exchange-traded derivatives

Contracts with standard terms, features.

Traded on organized facility or exchange (futures or options exchange).

Backed by a clearinghouse.

Over-the-counter derivatives

A dealer market with no central location.

Often used for custom instruments such as forwards and swaps.

Largely unregulated markets

Each contract is with a counterparty.

May expose the owner of a derivative to default risk (when the counterparty does not honor their commitment).

Forward commitments are contractually binding commitments to engage in a transaction at a date in the future. These are agreements between two parties in which the buyer agrees to buy from the seller the underlying at a future date at a price which is specified at the start. Each party must either complete the transaction, or engage in an offsetting transaction.

Forward commitments can be written on equities, indexes, bonds, physical assets, or interest rates.

A contingent claim is a claim (to a payoff) that depends on a particular event. Options are contingent claims that depend on a stock price at some future date, rather than forward commitments. While forwards, futures, and swaps have payments that are made based on a price or rate outcome whether the movement is up or down, contingent claims only require a payment if a certain threshold price is broken (e.g., if the price is above X or the rate is below Y). It takes two options to replicate a future or forward.

Forward contract

Terms & conditions, specifics regarding delivery, are all specified in advance.

These contracts are customized.

Forward market is largely unregulated, and is private.

There is default risk.

Contracts are designed to be held to expiration.

Futures contract

Variation of a forward contract.

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This is a public, standardized transaction.

Trades on a futures exchange.

Futures exchange guarantees performance, which removes default risk.

Rather than being designed to be held to expiration, offsetting transactions near expiration are the norm.

Swap

Variation of a forward contract.

Series of forward contracts. An agreement between two parties to exchange a series of future cash flows.

Private transactions, largely unregulated.

The criticism of derivatives is that they are "too risky," especially to investors with limited knowledge of sometimes complex instruments. Because of the high leverage involved in derivatives payoffs, they are sometimes likened to gambling.

The benefits of derivatives markets are that they:

Provide price information.

Allow risk to be managed and shifted among market participants.

Reduce transactions costs.

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PART TWO: Investment Returns & Valuations

Chapter 4: The Time Value of Money Quantitative Methods for Investment Analysis by DeFusco et al Chapter 5: Discounted Cash Flow Applications Quantitative Methods for Investment Analysis by DeFusco et al Chapter 6: Bonds and Their Valuation Fundamentals of Financial Management 10th Edition by Brigham et al Chapter 7: Stocks and Their Valuation

Fundamentals of Financial Management 10th Edition by Brighamet et al















































149

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During the summer of 1999 the future course of interest rates was highly uncertain.Continued strength in the economy and growing fears of inflation had led to interestrate increases, and many analysts were concerned that this trend would continue.However, others were forecasting declining rates—they saw no threat from inflation,and they were more concerned about the economy running out of gas. Because ofthis uncertainty, bond investors tended to wait on the sidelines for some definitiveeconomic news. At the same time, companies were postponing bond issues out offear that nervous investors would be unwilling to purchase them.

One example of all this was Ford Motor, which in June 1999 decided to put alarge bond issue on hold. However, after just three weeks, Ford sensed a shift in theinvestment climate, and it announced plans to sell $8.6 billion of new bonds. Asshown in the following table, the Ford issue set a record, surpassing an $8 billionAT&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 2-year floating rate and another $1.8 billion at a 3-year floating rate. Ford Motor itselfborrowed $4 billion as 5-year fixed-rate debt and another $1.8 billion at a 32-yearfixed rate.

Most analysts agreed that these bonds had limited default risk. Ford held $24billion in cash, and it had earned a record $2.5 billion during the second quarter of1999. However, the auto industry faces some inherent risks. When all the risk factorswere balanced, the issues all received a single-A rating. Much to the relief of the jitterybond market, the Ford issue was well 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 appetitefor large bond issues with strong credit ratings. Larger issues are more liquid thansmaller ones, and liquidity is particularly important to bond investors when the direc-tion of the overall market is highly uncertain.

Anticipating even more demand, Ford is planning to regularly issue large blocksof debt in the global market. Seeing Ford’s success, less than one month later Wal-Mart entered the list of top ten U.S. corporate bond financings with a new $5 billionissue. Other large companies have subsequently followed suit.

Source: From Gregory Zuckerman, “Ford’s Record Issue May Drive Imitators,” The Wall Street Journal, July 12,1999, C1. Copyright © 1999 Dow Jones & Co., Inc. Reprinted by permission of Dow Jones & Co., Inc. via Copy-right Clearance Center.

Bonds and Their Valuation

145

4

If you skim through The Wall Street Journal, you will see references to a wide varietyof bonds. This variety may seem confusing, but in actuality just a few characteristicsdistinguish the various types of bonds.

While bonds are often viewed as relatively safe investments, one can certainly losemoney on them. Indeed, “riskless” long-term U.S. Treasury bonds declined by morethan 20 percent during 1994, and “safe” Mexican government bonds declined by 25percent on one day, December 27, 1994. More recently, investors in Russian bondssuffered massive losses when Russia defaulted. In each of these cases, investors whohad regarded bonds as being riskless, or at least fairly safe, learned a sad lesson. Note,though, that it is possible to rack up impressive gains in the bond market. High-quality corporate bonds in 1995 provided a total return of nearly 21 percent, and in1997, U.S. Treasury bonds returned 14.3 percent.

In this chapter, we will discuss the types of bonds companies and governmentagencies issue, the terms that are contained in bond contracts, the types of risks towhich both bond investors and issuers are exposed, and procedures for determiningthe values of and rates of return on bonds.

Who Issues Bonds?

A bond is a long-term contract under which a borrower agrees to make paymentsof interest and principal, on specific dates, to the holders of the bond. For exam-ple, on January 3, 2003, MicroDrive Inc. borrowed $50 million by issuing $50 mil-lion of bonds. For convenience, we assume that MicroDrive sold 50,000 individualbonds for $1,000 each. Actually, it could have sold one $50 million bond, 10 bondswith a $5 million face value, or any other combination that totals to $50 million.In any event, MicroDrive received the $50 million, and in exchange it promised tomake annual interest payments and to repay the $50 million on a specified matu-rity date.

Investors have many choices when investing in bonds, but bonds are classified intofour main types: Treasury, corporate, municipal, and foreign. Each type differs withrespect to expected return and degree of risk.

150 CHAPTER 4 Bonds and Their Valuation

Top Ten U.S. Corporate Bond Financings as of July 1999

Amount (BillionsIssuer Date of Dollars)

Ford July 9, 1999 $8.60AT&T March 23, 1999 8.00RJR Holdings May 12, 1989 6.11WorldCom August 6, 1998 6.10Sprint November 10, 1998 5.00Assoc. Corp. of N. America October 27, 1998 4.80Norfolk Southern May 14, 1997 4.30US West January 16, 1997 4.10Conoco April 15, 1999 4.00Charter Communications March 12, 1999 3.58

Source: From Thomson Financial Securities Data, Credit Suisse First Boston as reported in The Wall Street Journal, July12, 1999, C1. Copyright © 1999 Dow Jones & Co., Inc. Reprinted by permission of Dow Jones & Co., Inc. via CopyrightClearance Center.

The textbook’s web sitecontains an Excel file thatwill guide you through thechapter’s calculations. Thefile for this chapter is Ch 04Tool Kit.xls, and we encour-age you to open the file andfollow along as you read thechapter.

146 Bonds and Their Valuation

Treasury bonds, sometimes referred to as government bonds, are issued by theU.S. federal government.1 It is reasonable to assume that the federal government willmake 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 Trea-sury bonds, corporate bonds are exposed to default risk—if the issuing company getsinto 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 issu-ing company’s characteristics and the terms of the specific bond. Default risk often isreferred to as “credit risk,” and, as we saw in Chapter 1, the larger the default or creditrisk, the higher the interest rate the issuer must pay.

Municipal bonds, or “munis,” are issued by state and local governments. Likecorporate bonds, munis have default risk. However, munis offer one major advantageover all other bonds: As we will explain in Chapter 9, the interest earned on most municipal bonds is exempt from federal taxes and also from state taxes if the holder isa resident of the issuing state. Consequently, municipal bonds carry interest rates thatare considerably lower than those on corporate bonds with the same default risk.

Foreign bonds are issued by foreign governments or foreign corporations. For-eign corporate bonds are, of course, exposed to default risk, and so are some foreigngovernment bonds. An additional risk exists if the bonds are denominated in a cur-rency other than that of the investor’s home currency. For example, if a U.S. investorpurchases a corporate bond denominated in Japanese yen and the yen subsequentlyfalls relative to the dollar, then the investor will lose money, even if the company doesnot default on its bonds.

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?

Key Characteristics of Bonds

Although all bonds have some common characteristics, they do not always have thesame contractual features. For example, most corporate bonds have provisions for earlyrepayment (call features), but these provisions can be quite different for different bonds.Differences in contractual provisions, and in the underlying strength of the companiesbacking the bonds, lead to major differences in bonds’ risks, prices, and expected re-turns. 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 gener-ally assume a par value of $1,000, although any multiple of $1,000 (for example,$5,000) can be used. The par value generally represents the amount of money the firmborrows and promises to repay on the maturity date.

Key Characteristics of Bonds 151

1The U.S. Treasury actually issues three types of securities: “bills,” “notes,” and “bonds.” A bond makes anequal payment every six months until it matures, at which time it makes an additional lump sum payment.If the maturity at the time of issue is less than 10 years, it is called a note rather than a bond. A T-bill has amaturity of 52 weeks or less at the time of issue, and it makes no payments at all until it matures. Thus, billsare sold initially at a discount to their face, or maturity, value.

Bonds and Their Valuation 147

Coupon Interest Rate

MicroDrive’s bonds require the company to pay a fixed number of dollars of interesteach year (or, more typically, each six months). When this coupon payment, as it iscalled, is divided by the par value, the result is the coupon interest rate. For example,MicroDrive’s bonds have a $1,000 par value, and they pay $100 in interest each year.The bond’s coupon interest is $100, so its coupon interest rate is $100/$1,000 � 10percent. The $100 is the yearly “rent” on the $1,000 loan. This payment, which isfixed at the time the bond is issued, remains in force during the life of the bond.2 Typ-ically, at the time a bond is issued its coupon payment is set at a level that will enablethe bond to be issued at or near its par value.

In some cases, a bond’s coupon payment will vary over time. For these floatingrate bonds, the coupon rate is set for, say, the initial six-month period, after which itis adjusted every six months based on some market rate. Some corporate issues are tiedto the Treasury bond rate, while other issues are tied to other rates, such as LIBOR.Many additional provisions can be included in floating rate issues. For example, someare 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 risinginterest rates, since the interest paid on such bonds increases whenever market ratesrise. This causes the market value of the debt to be stabilized, and it also provides insti-tutional 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 floating rate loans thatthey have made rises at the same time their deposit costs are rising. The savings and loanindustry was virtually destroyed as a result of their practice of making fixed rate mort-gage loans but borrowing on floating rate terms. If you are earning 6 percent but paying10 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 withoutcommitting themselves to paying a historically high interest rate for the entire life ofthe loan.

Some bonds pay no coupons at all, but are offered at a substantial discount belowtheir par values and hence provide capital appreciation rather than interest income.These securities are called zero coupon bonds (“zeros”). Other bonds pay somecoupon interest, but not enough to be issued at par. In general, any bond originally of-fered at a price significantly below its par value is called an original issue discount(OID) bond. Corporations first used zeros in a major way in 1981. In recent years IBM,Alcoa, JCPenney, ITT, Cities Service, GMAC, Lockheed Martin, and even the U.S.Treasury have used zeros to raise billions of dollars.

Maturity Date

Bonds generally have a specified maturity date on which the par value must be repaid.MicroDrive’s bonds, which were issued on January 3, 2003, will mature on January 3,2018; thus, they had a 15-year maturity at the time they were issued. Most bonds haveoriginal maturities (the maturity at the time the bond is issued) ranging from 10 to


2At one time, bonds literally had a number of small (1/2- by 2-inch), dated coupons attached to them, andon each interest payment date the owner would clip off the coupon for that date and either cash it at his orher 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 withonly 5 coupons. Today, new bonds must be registered—no physical coupons are involved, and interest checksare mailed automatically to the registered owners of the bonds. Even so, people continue to use the termscoupon and coupon interest rate when discussing bonds.

An excellent site for infor-mation on many types ofbonds is Bonds Online,which can be found athttp://www.bondsonline.com. The site has a greatdeal of information aboutcorporates, municipals, trea-suries, and bond funds. It in-cludes free bond searches,through which the userspecifies the attributes de-sired in a bond and then thesearch returns the publiclytraded bonds meeting thecriteria. The site also in-cludes a downloadablebond calculator and an ex-cellent glossary of bond ter-minology.


40 years, but any maturity is legally permissible.3 Of course, the effective maturity ofa bond declines each year after it has been issued. Thus, MicroDrive’s bonds had a 15-year original maturity, but in 2004, a year later, they will have a 14-year maturity, andso on.

Provisions to Call or Redeem Bonds

Most corporate bonds contain a call provision, which gives the issuing corporationthe right to call the bonds for redemption.4 The call provision generally states that thecompany must pay the bondholders an amount greater than the par value if they arecalled. The additional sum, which is termed a call premium, is often set equal to oneyear’s interest if the bonds are called during the first year, and the premium declines ata constant rate of INT/N each year thereafter, where INT � annual interest and N �original maturity in years. For example, the call premium on a $1,000 par value, 10-year, 10 percent bond would generally be $100 if it were called during the first year,$90 during the second year (calculated by reducing the $100, or 10 percent, premiumby one-tenth), and so on. However, bonds are often not callable until several years(generally 5 to 10) after they were issued. This is known as a deferred call, and thebonds are said to have call protection.

Suppose a company sold bonds when interest rates were relatively high. Providedthe issue is callable, the company could sell a new issue of low-yielding securities if andwhen interest rates drop. It could then use the proceeds of the new issue to retire thehigh-rate issue and thus reduce its interest expense. This process is called a refundingoperation.

A call provision is valuable to the firm but potentially detrimental to investors. Ifinterest rates go up, the company will not call the bond, and the investor will be stuckwith the original coupon rate on the bond, even though interest rates in the economyhave risen sharply. However, if interest rates fall, the company will call the bond andpay off investors, who then must reinvest the proceeds at the current market interestrate, which is lower than the rate they were getting on the original bond. In otherwords, the investor loses when interest rates go up, but doesn’t reap the gains whenrates fall. To induce an investor to take this type of risk, a new issue of callable bondsmust provide a higher interest rate than an otherwise similar issue of noncallablebonds. For example, on August 30, 1997, Pacific Timber Company issued bondsyielding 9.5 percent; these bonds were callable immediately. On the same day, North-west Milling Company sold an issue with similar risk and maturity that yielded 9.2percent, but these bonds were noncallable for ten years. Investors were willing to ac-cept a 0.3 percent lower interest rate on Northwest’s bonds for the assurance that the9.2 percent interest rate would be earned for at least ten years. Pacific, on the otherhand, had to incur a 0.3 percent higher annual interest rate to obtain the option ofcalling the bonds in the event of a subsequent decline in rates.

Bonds that are redeemable at par at the holder’s option protect investors againsta rise in interest rates. If rates rise, the price of a fixed-rate bond declines. However, ifholders have the option of turning their bonds in and having them redeemed at par,they are protected against rising rates. Examples of such debt include Transamerica’s$50 million issue of 25-year, 81⁄2 percent bonds. The bonds are not callable by thecompany, but holders can turn them in for redemption at par five years after the date

Key Characteristics of Bonds 153

3In July 1993, Walt Disney Co., attempting to lock in a low interest rate, issued the first 100-year bonds tobe sold by any borrower in modern times. Soon after, Coca-Cola became the second company to stretch themeaning of “long-term bond” by selling $150 million of 100-year bonds.4A majority of municipal bonds also contain call provisions. Although the U.S. Treasury no longer issuescallable bonds, some past Treasury issues were callable.


of issue. If interest rates have risen, holders will turn in the bonds and reinvest the pro-ceeds at a higher rate. This feature enabled Transamerica to sell the bonds with an 81⁄2percent coupon at a time when other similarly rated bonds had yields of 9 percent.

In late 1988, the corporate bond markets were sent into turmoil by the leveragedbuyout of RJR Nabisco. RJR’s bonds dropped in value by 20 percent within days of theLBO announcement, and the prices of many other corporate bonds also plunged, be-cause investors feared that a boom in LBOs would load up many companies with ex-cessive debt, leading to lower bond ratings and declining bond prices. All this led to aresurgence of concern about event risk, which is the risk that some sudden event, suchas an LBO, will occur and increase the credit risk of the company, hence lowering thefirm’s bond rating and the value of its outstanding bonds. Investors’ concern overevent risk meant that those firms deemed most likely to face events that could harmbondholders had to pay dearly to raise new debt capital, if they could raise it at all. Inan attempt to control debt costs, a new type of protective covenant was devised tominimize event risk. This covenant, called a super poison put, enables a bondholder toturn in, or “put” a bond back to the issuer at par in the event of a takeover, merger, ormajor recapitalization.

Poison puts had actually been around since 1986, when the leveraged buyout trendtook off. However, the earlier puts proved to be almost worthless because they allowedinvestors to “put” their bonds back to the issuer at par value only in the event of an un-friendly takeover. But because almost all takeovers are eventually approved by the targetfirm’s board, mergers that started as hostile generally ended as friendly. Also, the earlierpoison puts failed to protect investors from voluntary recapitalizations, in which a com-pany sells a big issue of bonds to pay a big, one-time dividend to stockholders or to buyback its own stock. The “super” poison puts that were used following the RJR buyoutannouncement protected against both of these actions. This is a good illustration ofhow quickly the financial community reacts to changes in the marketplace.

Sinking Funds

Some bonds also include a sinking fund provision that facilitates the orderly retire-ment of the bond issue. On rare occasions the firm may be required to deposit moneywith a trustee, which invests the funds and then uses the accumulated sum to retire thebonds when they mature. Usually, though, the sinking fund is used to buy back a cer-tain percentage of the issue each year. A failure to meet the sinking fund requirementcauses the bond to be thrown into default, which may force the company into bank-ruptcy. Obviously, a sinking fund can constitute a significant cash drain on the firm.

In most cases, the firm is given the right to handle the sinking fund in either of two ways:

1. The company can call in for redemption (at par value) a certain percentage of thebonds each year; for example, it might be able to call 5 percent of the total originalamount of the issue at a price of $1,000 per bond. The bonds are numbered serially,and those called for redemption are determined by a lottery administered by thetrustee.

2. The company may buy the required number of bonds on the open market.

The firm will choose the least-cost method. If interest rates have risen, causing bondprices to fall, it will buy bonds in the open market at a discount; if interest rates havefallen, it will call the bonds. Note that a call for sinking fund purposes is quite differentfrom a refunding call as discussed above. A sinking fund call typically requires no callpremium, but only a small percentage of the issue is normally callable in any one year.5


5Some sinking funds require the issuer to pay a call premium.


Although sinking funds are designed to protect bondholders by ensuring that an is-sue is retired in an orderly fashion, you should recognize that sinking funds can work tothe detriment of bondholders. For example, suppose the bond carries a 10 percent inter-est rate, but yields on similar bonds have fallen to 7.5 percent. A sinking fund call at parwould require an investor to give up a bond that pays $100 of interest and then to rein-vest in a bond that pays only $75 per year. This obviously harms those bondholderswhose bonds are called. On balance, however, bonds that have a sinking fund are re-garded as being safer than those without such a provision, so at the time they are issuedsinking fund bonds have lower coupon rates than otherwise similar bonds without sink-ing funds.

Other Features

Several other types of bonds are used sufficiently often to warrant mention. First,convertible bonds are bonds that are convertible into shares of common stock, at afixed price, at the option of the bondholder. Convertibles have a lower coupon ratethan nonconvertible debt, but they offer investors a chance for capital gains in ex-change for the lower coupon rate. Bonds issued with warrants are similar to convert-ibles. Warrants are options that permit the holder to buy stock for a stated price,thereby providing a capital gain if the price of the stock rises. Bonds that are issuedwith warrants, like convertibles, carry lower coupon rates than straight bonds.

Another type of bond is an income bond, which pays interest only if the interest isearned. These securities cannot bankrupt a company, but from an investor’s standpointthey are riskier than “regular” bonds. Yet another bond is the indexed, or purchasingpower, bond, which first became popular in Brazil, Israel, and a few other countriesplagued by high inflation rates. The interest rate paid on these bonds is based on an in-flation index such as the consumer price index, so the interest paid rises automaticallywhen the inflation rate rises, thus protecting the bondholders against inflation. In Janu-ary 1997, the U.S. Treasury began issuing indexed bonds, and they currently pay a ratethat is roughly 1 to 4 percent plus the rate of inflation during the past year.

Define floating rate bonds and zero coupon bonds.

What problem was solved by the introduction of long-term floating rate debt,and how is the rate on such bonds determined?

Why is a call provision advantageous to a bond issuer? When will the issuer initi-ate a refunding call? Why?

What are the two ways a sinking fund can be handled? Which method will bechosen by the firm if interest rates have risen? If interest rates have fallen?

Are securities that provide for a sinking fund regarded as being riskier thanthose without this type of provision? Explain.

What is the difference between a call for sinking fund purposes and a re-funding call?

Define convertible bonds, bonds with warrants, income bonds, and indexedbonds.

Why do bonds with warrants and convertible bonds have lower coupons thansimilarly rated bonds that do not have these features?

Bond Valuation

The value of any financial asset—a stock, a bond, a lease, or even a physical asset suchas an apartment building or a piece of machinery—is simply the present value of thecash flows the asset is expected to produce.

Bond Valuation 155


The cash flows from a specific bond depend on its contractual features as describedabove. For a standard coupon-bearing bond such as the one issued by MicroDrive, thecash flows consist of interest payments during the 15-year life of the bond, plus theamount borrowed (generally the $1,000 par value) when the bond matures. In the caseof a floating rate bond, the interest payments vary over time. In the case of a zerocoupon bond, there are no interest payments, only the face amount when the bond ma-tures. For a “regular” bond with a fixed coupon rate, here is the situation:

0 rd% 1 2 3 N. . .Bond’s Value INT INT INT INT

M

Here

rd � the bond’s market rate of interest � 10%. This is the discount rate that isused to calculate the present value of the bond’s cash flows. Note that rd isnot the coupon interest rate, and it is equal to the coupon rate only if (as inthis case) the bond is selling at par. Generally, most coupon bonds are is-sued at par, which implies that the coupon rate is set at rd. Thereafter, in-terest rates as measured by rd will fluctuate, but the coupon rate is fixed, sord will equal the coupon rate only by chance. We used the term “i” or “I” todesignate the interest rate in Chapter 2 because those terms are used on fi-nancial calculators, but “r,” with the subscript “d” to designate the rate on adebt security, is normally used in finance.6

N � the number of years before the bond matures � 15. Note that N declineseach year after the bond was issued, so a bond that had a maturity of 15years when it was issued (original maturity � 15) will have N � 14 afterone year, N � 13 after two years, and so on. Note also that at this point weassume that the bond pays interest once a year, or annually, so N is mea-sured in years. Later on, we will deal with semiannual payment bonds,which pay interest each six months.

INT � dollars of interest paid each year � Coupon rate � Par value �0.10($1,000) � $100. In calculator terminology, INT � PMT � 100. If thebond had been a semiannual payment bond, the payment would have been$50 each six months. The payment would be zero if MicroDrive had issuedzero coupon bonds, and it would vary if the bond was a “floater.”

M � the par, or maturity, value of the bond � $1,000. This amount must be paidoff at maturity.

We can now redraw the time line to show the numerical values for all variables exceptthe bond’s value:

0 10% 1 2 3 15. . .Bond’s Value 100 100 100 100

1,0001,100

The following general equation, written in several forms, can be solved to find thevalue of any bond:


6The appropriate interest rate on debt securities was discussed in Chapter 1. The bond’s risk, liquidity, andyears to maturity, as well as supply and demand conditions in the capital markets, all influence the interestrate on bonds.


(4-1)

Inserting values for our particular bond, we have

Note that the cash flows consist of an annuity of N years plus a lump sum payment atthe end of Year N, and this fact is reflected in Equation 4-1. Further, Equation 4-1 canbe solved by the three procedures discussed in Chapter 2: (1) numerically, (2) with a fi-nancial calculator, and (3) with a spreadsheet.

NUMERICAL SOLUTION:

Simply discount each cash flow back to the present and sum these PVs to find thebond’s value; see Figure 4-1 for an example. This procedure is not very efficient, espe-cially if the bond has many years to maturity. Alternatively, you could use the formula

� $100(PVIFA10%,15) � $1,000(PVIF10%,15).

� $100 ° 1 �

1(1.1)15

0.1¢

�$1,000(1.1)15

VB � a15

t�1

$100(1.10)t �

$1,000(1.10)15

� INT(PVIFArd,N) � M(PVIFrd,N).

� INT° 1 �

1(1 � rd)N

rd

¢�

M(1 � rd)N

� aN

t�1

INT(1 � rd)t �

M(1 � rd)N

Bond’s value � VB �INT

(1 � rd)1 �INT

(1 � rd)2 � . . . �INT

(1 � rd)N �M

(1 � rd)N

Bond Valuation 157

FIGURE 4-1 Time Line for MicroDrive Inc.’s Bonds, 10% Interest Rate

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Payments 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 � 1,000

90.9182.6475.1368.3062.0956.4551.3246.6542.4138.5535.0531.8628.9726.3323.94

239.39� 1,000.00 where rd � 10%.

PresentValue

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in the third row of Equation 4-1 with a simple or scientific calculator, although thiswould still be somewhat cumbersome.

FINANCIAL CALCULATOR SOLUTION

In Chapter 2, we worked problems where only four of the five time value of money(TVM) keys were used. However, all five keys are used with bonds. Here is the setup:

Inputs: 15 10 100 1000

Output: � �1,000

Simply input N � 15, I � rd � 10, INT � PMT � 100, M � FV � 1000, and thenpress the PV key to find the value of the bond, $1,000. Since the PV is an outflow tothe investor, it is shown with a negative sign. The calculator is programmed to solveEquation 4-1: It finds the PV of an annuity of $100 per year for 15 years, discountedat 10 percent, then it finds the PV of the $1,000 maturity payment, and then it addsthese two PVs to find the value of the bond. Notice that even though the time line inFigure 4-1 shows a total of $1,100 at Year 15, you should not enter FV � 1100! Whenyou entered N � 15 and PMT � 100, you told the calculator that there is a $100 pay-ment at Year 15. Thus, the FV � 1000 accounts for any extra payment at Year 15,above and beyond the $100 payment.

SPREADSHEET SOLUTION

Here we want to find the PV of the cash flows, so we would use the PV function. Putthe cursor on Cell B10, click the function wizard then Financial, PV, and OK. Thenfill in the dialog box with Rate � 0.1 or F3, Nper � 15 or Q5, Pmt � 100 or C6, FV � 1000 or Q7, and Type � 0 or leave it blank. Then, when you click OK, you willget the value of the bond, �$1,000. Like the financial calculator solution, this is neg-ative because the PMT and FV are positive.

An alternative, and in this case somewhat easier procedure given that the time linehas been created, is to use the NPV function. Click the function wizard, then Finan-


A B C D E F G H I J K L M N O P Q

1 Spreadsheet for bond value calculation

2 Going rate,

3 Coupon rate 10% or yield 10%

4

5 Time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

6 Interest Pmt 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

7 Maturity Pmt 1000

8 Total CF 100 100 100 100 100 100 100 100 100 100 100 100 100 100 1100

9

10 PV of CF 1000


Bond Valuation 159

cial, NPV, and OK. Then input Rate � 0.1 or F3 and Value 1 � C8:Q8. Then clickOK to get the answer, $1,000.

Note that by changing the interest rate in F3, we can instantly find the value of thebond at any other discount rate. Note also that Excel and other spreadsheet softwarepackages provide specialized functions for bond prices. For example, in Excel youcould use the function wizard to enter this formula:

The first two arguments in the function give the current and maturity dates. Thenext argument is the bond’s coupon rate, followed by the current market interestrate, or yield. The fifth argument, 100, is the redemption value of the bond at matu-rity, expressed as a percent of the face value. The sixth argument is the number ofpayments per year, and the last argument, 0, tells the program to use the U.S. con-vention for counting days, which is to assume 30 days per month and 360 days peryear. This function produces the value 100, which is the current price expressed as apercent of the bond’s par value, which is $1,000. Therefore, you can multiply $1,000by 100 percent to get the current price, which is $1,000. This function is essential ifa bond is being evaluated between coupon payment dates.

Changes in Bond Values over Time

At the time a coupon bond is issued, the coupon is generally set at a level that willcause the market price of the bond to equal its par value. If a lower coupon were set,investors would not be willing to pay $1,000 for the bond, while if a higher couponwere set, investors would clamor for the bond and bid its price up over $1,000. Invest-ment bankers can judge quite precisely the coupon rate that will cause a bond to sell atits $1,000 par value.

A bond that has just been issued is known as a new issue. (Investment bankers clas-sify a bond as a new issue for about one month after it has first been issued. New issuesare usually actively traded, and are called “on-the-run” bonds.) Once the bond hasbeen on the market for a while, it is classified as an outstanding bond, also called a sea-soned issue. Newly issued bonds generally sell very close to par, but the prices of sea-soned bonds vary widely from par. Except for floating rate bonds, coupon paymentsare constant, so when economic conditions change, a bond with a $100 coupon thatsold at par when it was issued will sell for more or less than $1,000 thereafter.

MicroDrive’s bonds with a 10 percent coupon rate were originally issued at par. Ifrd remained constant at 10 percent, what would the value of the bond be one year af-ter it was issued? Now the term to maturity is only 14 years—that is, N � 14. With afinancial calculator, just override N � 15 with N � 14, press the PV key, and you finda value of $1,000. If we continued, setting N � 13, N � 12, and so forth, we would seethat the value of the bond will remain at $1,000 as long as the going interest rate re-mains constant at the coupon rate, 10 percent.7

� PRICE(Date(2003,1,3),Date(2018,1,3),10%,10%,100,1,0).

7The bond prices quoted by brokers are calculated as described. However, if you bought a bond between in-terest payment dates, you would have to pay the basic price plus accrued interest. Thus, if you purchased a Mi-croDrive bond six months after it was issued, your broker would send you an invoice stating that you must pay$1,000 as the basic price of the bond plus $50 interest, representing one-half the annual interest of $100. Theseller of the bond would receive $1,050. If you bought the bond the day before its interest payment date, youwould pay $1,000 � (364/365)($100) � $1,099.73. Of course, you would receive an interest payment of $100at the end of the next day. See Self-Test Problem 1 for a detailed discussion of bond quotations between inter-est payment dates.

Throughout the chapter, we assume that bonds are being evaluated immediately after an interest pay-ment date. The more expensive financial calculators such as the HP-17B have a built-in calendar that per-mits the calculation of exact values between interest payment dates, as do spreadsheet programs.


Now suppose interest rates in the economy fell after the MicroDrive bonds wereissued, and, as a result, rd fell below the coupon rate, decreasing from 10 to 5 percent.Both the coupon interest payments and the maturity value remain constant, but now 5percent values for PVIF and PVIFA would have to be used in Equation 4-1. The valueof the bond at the end of the first year would be $1,494.93:

With a financial calculator, just change rd � I from 10 to 5, and then press the PV keyto get the answer, $1,494.93. Thus, if rd fell below the coupon rate, the bond would sellabove par, or at a premium.

The arithmetic of the bond value increase should be clear, but what is the logic be-hind it? The fact that rd has fallen to 5 percent means that if you had $1,000 to invest,you could buy new bonds like MicroDrive’s (every day some 10 to 12 companies sellnew bonds), except that these new bonds would pay $50 of interest each year ratherthan $100. Naturally, you would prefer $100 to $50, so you would be willing to paymore than $1,000 for a MicroDrive bond to obtain its higher coupons. All investorswould react similarly, and as a result, the MicroDrive bonds would be bid up in priceto $1,494.93, at which point they would provide the same rate of return to a potentialinvestor as the new bonds, 5 percent.

Assuming that interest rates remain constant at 5 percent for the next 14 years,what would happen to the value of a MicroDrive bond? It would fall gradually from$1,494.93 at present to $1,000 at maturity, when MicroDrive will redeem each bondfor $1,000. This point can be illustrated by calculating the value of the bond 1 yearlater, when it has 13 years remaining to maturity. With a financial calculator, merelyinput the values for N, I, PMT, and FV, now using N � 13, and press the PV key tofind the value of the bond, $1,469.68. Thus, the value of the bond will have fallenfrom $1,494.93 to $1,469.68, or by $25.25. If you were to calculate the value of thebond at other future dates, the price would continue to fall as the maturity date ap-proached.

Note that if you purchased the bond at a price of $1,494.93 and then sold it oneyear later with rd still at 5 percent, you would have a capital loss of $25.25, or a to-tal return of $100.00 � $25.25 � $74.75. Your percentage rate of return would con-sist of an interest yield (also called a current yield ) plus a capital gains yield, calculated asfollows:

Interest, or current, yield � $100/$1,494.93 � 0.0669 � 6.69%Capital gains yield � �$25.25/$1,494.93 � �0.0169 � �1.69%

Total rate of return, or yield � $74.75/$1,494.93 � 0.0500 � 5.00%

Had interest rates risen from 10 to 15 percent during the first year after issuerather than fallen from 10 to 5 percent, then you would enter N � 14, I � 15,PMT � 100, and FV � 1000, and then press the PV key to find the value of thebond, $713.78. In this case, the bond would sell at a discount of $286.22 below itspar value:

The total expected future return on the bond would again consist of a current yieldand a capital gains yield, but now the capital gains yield would be positive. The total

� �$286.22.Discount � Price � Par value � $713.78 � $1,000.00

� $1,494.93.� $989.86 � $505.07� $100(9.89864) � $1,000(0.50507)

VB � $100(PVIFA5%,14) � $1,000(PVIF5%,14)



return would be 15 percent. To see this, calculate the price of the bond with 13 yearsleft to maturity, assuming that interest rates remain at 15 percent. With a calculator,enter N � 13, I � 15, PMT � 100, and FV � 1000, and then press PV to obtain thebond’s value, $720.84.

Note that the capital gain for the year is the difference between the bond’s value atYear 2 (with 13 years remaining) and the bond’s value at Year 1 (with 14 years remain-ing), or $720.84 � $713.78 � $7.06. The interest yield, capital gains yield, and totalyield are calculated as follows:

Interest, or current, yield � $100/$713.78 � 0.1401 � 14.01%Capital gains yield � $7.06/$713.78 � 0.0099 � 0.99%

Total rate of return, or yield � $107.06/$713.78 � 0.1500 � 15.00%

Figure 4-2 graphs the value of the bond over time, assuming that interest rates inthe economy (1) remain constant at 10 percent, (2) fall to 5 percent and then remainconstant at that level, or (3) rise to 15 percent and remain constant at that level. Ofcourse, if interest rates do not remain constant, then the price of the bond will fluctu-ate. However, regardless of what future interest rates do, the bond’s price will ap-proach $1,000 as it nears the maturity date (barring bankruptcy, in which case thebond’s value might fall dramatically).

Bond Valuation 161

FIGURE 4-2 Time Path of the Value of a 10% Coupon, $1,000 Par ValueBond When Interest Rates Are 5%, 10%, and 15%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

M = 1,000

1,495

714

Years

MTime Path of Bond Value When rd = Coupon Rate = 10%

(Par Bond)

Bond Value($) Time Path of 10% Coupon Bond's Value When

rd Falls to 5% and Remains There(Premium Bond)

Time Path of 10% Coupon Bond's Value Whenrd Rises to 15% and Remains There

(Discount Bond)

Year rd � 5% rd � 10% rd � 15%

0 — $1,000 —1 $1,494.93 1,000 $713.78. . . .. . . .. . . .

15 1,000 1,000 1,000

Note: The curves for 5% and 15% have a slight bow.

See Ch 04 Tool Kit.xls for details.


Figure 4-2 illustrates the following key points:

1. Whenever the going rate of interest, rd, is equal to the coupon rate, a fixed-ratebond will sell at its par value. Normally, the coupon rate is set equal to the goingrate when a bond is issued, causing it to sell at par initially.

2. Interest rates do change over time, but the coupon rate remains fixed after thebond has been issued. Whenever the going rate of interest rises above the couponrate, a fixed-rate bond’s price will fall below its par value. Such a bond is called adiscount bond.

3. Whenever the going rate of interest falls below the coupon rate, a fixed-rate bond’sprice will rise above its par value. Such a bond is called a premium bond.

4. Thus, an increase in interest rates will cause the prices of outstanding bonds to fall,whereas a decrease in rates will cause bond prices to rise.

5. The market value of a bond will always approach its par value as its maturity dateapproaches, provided the firm does not go bankrupt.

These points are very important, for they show that bondholders may suffer capitallosses or make capital gains, depending on whether interest rates rise or fall after thebond was purchased. And, as we saw in Chapter 1, interest rates do indeed changeover time.

Explain, verbally, the following equation:

What is meant by the terms “new issue” and “seasoned issue”?

Explain what happens to the price of a fixed-rate bond if (1) interest rates riseabove the bond’s coupon rate or (2) interest rates fall below the bond’s couponrate.

Why do the prices of fixed-rate bonds fall if expectations for inflation rise?

What is a “discount bond”? A “premium bond”?

Bond Yields

If you examine the bond market table of The Wall Street Journal or a price sheet putout by a bond dealer, you will typically see information regarding each bond’s maturitydate, price, and coupon interest rate. You will also see the bond’s reported yield. Un-like the coupon interest rate, which is fixed, the bond’s yield varies from day to day de-pending on current market conditions. Moreover, the yield can be calculated in threedifferent ways, and three “answers” can be obtained. These different yields are de-scribed in the following sections.

Yield to Maturity

Suppose you were offered a 14-year, 10 percent annual coupon, $1,000 par valuebond at a price of $1,494.93. What rate of interest would you earn on your invest-ment if you bought the bond and held it to maturity? This rate is called the bond’syield to maturity (YTM), and it is the interest rate generally discussed by in-vestors when they talk about rates of return. The yield to maturity is generally thesame as the market rate of interest, rd, and to find it, all you need to do is solveEquation 4-1 for rd:

VB � aN

t�1

INT(1 � rd)t �

M(1 � rd)N.



You could substitute values for rd until you find a value that “works” and forces thesum of the PVs on the right side of the equal sign to equal $1,494.93. Alternatively,you could substitute values of rd into the third form of Equation 4-1 until you find avalue that works.

Finding rd � YTM by trial-and-error would be a tedious, time-consumingprocess, but as you might guess, it is easy with a financial calculator.8 Here is the setup:

Inputs: 14 �1494.93 100 1000

Output: � 5

Simply enter N � 14, PV � �1494.93, PMT � 100, and FV � 1000, and then pressthe I key. The answer, 5 percent, will then appear.

The yield to maturity is identical to the total rate of return discussed in the pre-ceding section. The yield to maturity can also be viewed as the bond’s promised rate ofreturn, which is the return that investors will receive if all the promised payments aremade. However, the yield to maturity equals the expected rate of return only if (1) theprobability of default is zero and (2) the bond cannot be called. If there is some defaultrisk, or if the bond may be called, then there is some probability that the promisedpayments to maturity will not be received, in which case the calculated yield to matu-rity will differ from the expected return.

The YTM for a bond that sells at par consists entirely of an interest yield, but if thebond sells at a price other than its par value, the YTM will consist of the interest yieldplus a positive or negative capital gains yield. Note also that a bond’s yield to maturitychanges whenever interest rates in the economy change, and this is almost daily. Onewho purchases a bond and holds it until it matures will receive the YTM that existedon the purchase date, but the bond’s calculated YTM will change frequently betweenthe purchase date and the maturity date.

Yield to Call

If you purchased a bond that was callable and the company called it, you would nothave the option of holding the bond until it matured. Therefore, the yield to maturity would not be earned. For example, if MicroDrive’s 10 percent coupon bondswere callable, and if interest rates fell from 10 percent to 5 percent, then the companycould call in the 10 percent bonds, replace them with 5 percent bonds, and save $100 � $50 � $50 interest per bond per year. This would be beneficial to the com-pany, but not to its bondholders.

If current interest rates are well below an outstanding bond’s coupon rate, then acallable bond is likely to be called, and investors will estimate its expected rate of re-turn as the yield to call (YTC) rather than as the yield to maturity. To calculate theYTC, solve this equation for rd:

(4-2)Price of bond � aN

t�1

INT(1 � rd)t �

Call price

(1 � rd)N.

VB � $1,494.93 �$100

(1 � rd)1 � � � � �$100

(1 � rd)14 �$1,000

(1 � rd)14.

Bond Yields 163

8You could also find the YTM with a spreadsheet. In Excel, you would use the RATE function for this bond,inputting Nper � 14, Pmt � 100, Pv � �1494.93, Fv � 1000, 0 for Type, and leave Guess blank.


Here N is the number of years until the company can call the bond; call price is theprice the company must pay in order to call the bond (it is often set equal to the parvalue plus one year’s interest); and rd is the YTC.

To illustrate, suppose MicroDrive’s bonds had a provision that permitted thecompany, if it desired, to call the bonds 10 years after the issue date at a price of$1,100. Suppose further that interest rates had fallen, and one year after issuancethe going interest rate had declined, causing the price of the bonds to rise to$1,494.93. Here is the time line and the setup for finding the bond’s YTC with afinancial calculator:

0 YTC� ? 1 2� �

8 9

�1,494.93 100 100 100 1001,100

9 �1494.93 100 1100

4.21 � YTC

The YTC is 4.21 percent—this is the return you would earn if you bought the bond ata price of $1,494.93 and it was called nine years from today. (The bond could not becalled until 10 years after issuance, and one year has gone by, so there are nine yearsleft until the first call date.)

Do you think MicroDrive will call the bonds when they become callable?MicroDrive’s action would depend on what the going interest rate is when the bondsbecome callable. If the going rate remains at rd � 5%, then MicroDrive could save 10% � 5% � 5%, or $50 per bond per year, by calling them and replacing the 10 per-cent bonds with a new 5 percent issue. There would be costs to the company to refundthe issue, but the interest savings would probably be worth the cost, so MicroDrivewould probably refund the bonds. Therefore, you would probably earn YTC � 4.21%rather than YTM � 5% if you bought the bonds under the indicated conditions.

In the balance of this chapter, we assume that bonds are not callable unless other-wise noted, but some of the end-of-chapter problems deal with yield to call.

Current Yield

If you examine brokerage house reports on bonds, you will often see reference to abond’s current yield. The current yield is the annual interest payment divided by thebond’s current price. For example, if MicroDrive’s bonds with a 10 percent couponwere currently selling at $985, the bond’s current yield would be 10.15 percent($100/$985).

Unlike the yield to maturity, the current yield does not represent the rate of returnthat investors should expect on the bond. The current yield provides information re-garding the amount of cash income that a bond will generate in a given year, but sinceit does not take account of capital gains or losses that will be realized if the bond isheld until maturity (or call), it does not provide an accurate measure of the bond’s to-tal expected return.

The fact that the current yield does not provide an accurate measure of a bond’stotal return can be illustrated with a zero coupon bond. Since zeros pay no annual in-come, they always have a current yield of zero. This indicates that the bond will notprovide any cash interest income, but since the bond will appreciate in value overtime, its total rate of return clearly exceeds zero.



Explain the difference between the yield to maturity and the yield to call.

How does a bond’s current yield differ from its total return?

Could the current yield exceed the total return?

Bonds with Semiannual Coupons

Although some bonds pay interest annually, the vast majority actually pay interestsemiannually. To evaluate semiannual payment bonds, we must modify the valuationmodel (Equation 4-1) as follows:

1. Divide the annual coupon interest payment by 2 to determine the dollars of inter-est paid each six months.

2. Multiply the years to maturity, N, by 2 to determine the number of semiannual pe-riods.

3. Divide the nominal (quoted) interest rate, rd, by 2 to determine the periodic (semi-annual) interest rate.

By making these changes, we obtain the following equation for finding the value ofa bond that pays interest semiannually:

(4-1a)

To illustrate, assume now that MicroDrive’s bonds pay $50 interest each six monthsrather than $100 at the end of each year. Thus, each interest payment is only half aslarge, but there are twice as many of them. The coupon rate is thus “10 percent, semi-annual payments.” This is the nominal, or quoted, rate.9

VB � a2N

t�1

INT/2(1 � rd/2)t �

M(1 � rd/2)2N

Bonds with Semiannual Coupons 165

Drinking Your Coupons

In 1996 Chateau Teyssier, an English vineyard, was lookingfor some cash to purchase some additional vines and to mod-ernize its production facilities. Their solution? With the as-sistance of a leading underwriter, Matrix Securities, the vine-yard issued 375 bonds, each costing 2,650 British pounds.The issue raised nearly 1 million pounds, or roughly $1.5million.

What makes these bonds interesting is that, instead ofgetting paid with something boring like money, these bonds paid their investors back with wine. Each June until2002, when the bond matured, investors received their

“coupons.” Between 1997 and 2001, each bond provided sixcases of the vineyard’s rose or claret. Starting in 1998 andcontinuing through maturity in 2002, investors also receivedfour cases of its prestigious Saint Emilion Grand Cru. Then,in 2002, they got their money back.

The bonds were not without risk. The vineyard’s owner,Jonathan Malthus, acknowledges that the quality of thewine, “is at the mercy of the gods.”Source: Steven Irvine, “My Wine Is My Bond, and I Drink My Coupons,”Euromoney, July 1996, 7. Reprinted by permission.

9In this situation, the nominal coupon rate of “10 percent, semiannually,” is the rate that bond dealers, cor-porate treasurers, and investors generally would discuss. Of course, the effective annual rate would be higherthan 10 percent at the time the bond was issued:

Note also that 10 percent with annual payments is different than 10 percent with semiannual payments.Thus, we have assumed a change in effective rates in this section from the situation in the preceding section,where we assumed 10 percent with annual payments.

EAR � EFF% � a1 �rNom

mbm

�1 � a1 �0.10

2b2

�1 � (1.05)2 �1 � 10.25%.


When the going (nominal) rate of interest is 5 percent with semiannual com-pounding, the value of this 15-year bond is found as follows:

Inputs: 30 2.5 50 1000

Output: � �1,523.26

Enter N � 30, r � I � 2.5, PMT � 50, FV � 1000, and then press the PV key to ob-tain the bond’s value, $1,523.26. The value with semiannual interest payments isslightly larger than $1,518.98, the value when interest is paid annually. This highervalue occurs because interest payments are received somewhat faster under semian-nual compounding.

Describe how the annual bond valuation formula is changed to evaluate semian-nual coupon bonds. Then, write out the revised formula.

Assessing the Risk of a Bond

Interest Rate Risk

As we saw in Chapter 1, interest rates go up and down over time, and an increase ininterest rates leads to a decline in the value of outstanding bonds. This risk of a de-cline in bond values due to rising interest rates is called interest rate risk. To illus-trate, suppose you bought some 10 percent MicroDrive bonds at a price of $1,000,and interest rates in the following year rose to 15 percent. As we saw earlier, the priceof the bonds would fall to $713.78, so you would have a loss of $286.22 per bond.10

Interest rates can and do rise, and rising rates cause a loss of value for bondholders.Thus, people or firms who invest in bonds are exposed to risk from changing inter-est rates.

One’s exposure to interest rate risk is higher on bonds with long maturities thanon those maturing in the near future.11 This point can be demonstrated by showinghow the value of a 1-year bond with a 10 percent annual coupon fluctuates withchanges in rd, and then comparing these changes with those on a 14-year bond ascalculated previously. The 1-year bond’s values at different interest rates are shownbelow:


10You would have an accounting (and tax) loss only if you sold the bond; if you held it to maturity, you wouldnot have such a loss. However, even if you did not sell, you would still have suffered a real economic loss in anopportunity cost sense because you would have lost the opportunity to invest at 15 percent and would be stuckwith a 10 percent bond in a 15 percent market. In an economic sense, “paper losses” are just as bad as real-ized accounting losses.11Actually, a bond’s maturity and coupon rate both affect interest rate risk. Low coupons mean that most ofthe bond’s return will come from repayment of principal, whereas on a high coupon bond with the same ma-turity, more of the cash flows will come in during the early years due to the relatively large coupon pay-ments. A measurement called “duration,” which finds the average number of years the bond’s PV of cashflows remain outstanding, has been developed to combine maturity and coupons. A zero coupon bond,which has no interest payments and whose payments all come at maturity, has a duration equal to the bond’smaturity. Coupon bonds all have durations that are shorter than maturity, and the higher the coupon rate,the shorter the duration. Bonds with longer duration are exposed to more interest rate risk.


Value at rd � 5%:

Inputs: 1 5 100 1000

Output: �1,047.62 � 1-year bond’svalue at rd � 5%.

Value at rd � 10%:

Inputs: 1 10 100 1000

Output: �1,000.00 � 1-year bond’svalue at rd � 10%.

Value at rd � 15%:

Inputs: 1 15 100 1000

Output: �956.52 � 1-year bond’svalue at rd � 15%.

You would obtain the first value with a financial calculator by entering N � 1, I � 5,PMT � 100, and FV � 1000, and then pressing PV to get $1,047.62. With everythingstill in your calculator, enter I � 10 to override the old I � 5, and press PV to find thebond’s value at rd � I � 10; it is $1,000. Then enter I � 15 and press the PV key to find the last bond value, $956.52.

The values of the 1-year and 14-year bonds at several current market interest rates are summarized and plotted in Figure 4-3. Note how much more sensitive theprice of the 14-year bond is to changes in interest rates. At a 10 percent interest rate, both the 14-year and the 1-year bonds are valued at $1,000. When rates rise to 15 percent, the 14-year bond falls to $713.78, but the 1-year bond only falls to $956.52.

For bonds with similar coupons, this differential sensitivity to changes in interest rates al-ways holds true—the longer the maturity of the bond, the more its price changes in response toa given change in interest rates. Thus, even if the risk of default on two bonds is exactlythe same, the one with the longer maturity is exposed to more risk from a rise ininterest rates.12

The logical explanation for this difference in interest rate risk is simple. Supposeyou bought a 14-year bond that yielded 10 percent, or $100 a year. Now suppose

Assessing the Risk of a Bond 167

12If a 10-year bond were plotted in Figure 4-3, its curve would lie between those of the 14-year bond andthe 1-year bond. The curve of a 1-month bond would be almost horizontal, indicating that its price wouldchange very little in response to an interest rate change, but a 100-year bond (or a perpetuity) would have avery steep slope. Also, zero coupon bond prices are quite sensitive to interest rate changes, and the longerthe maturity of the zero, the greater its price sensitivity. Therefore, 30-year zero coupon bonds have a hugeamount of interest rate risk.


interest rates on comparable-risk bonds rose to 15 percent. You would be stuck withonly $100 of interest for the next 14 years. On the other hand, had you bought a 1-year bond, you would have a low return for only 1 year. At the end of the year, youwould get your $1,000 back, and you could then reinvest it and receive 15 percent, or$150 per year, for the next 13 years. Thus, interest rate risk reflects the length of timeone is committed to a given investment.

As we just saw, the prices of long-term bonds are more sensitive to changes in in-terest rates than are short-term bonds. To induce an investor to take this extra risk,long-term bonds must have a higher expected rate of return than short-term bonds.This additional return is the maturity risk premium (MRP), which we discussed inChapter 1. Therefore, one might expect to see higher yields on long-term than onshort-term bonds. Does this actually happen? Generally, the answer is yes. Recallfrom Chapter 1 that the yield curve usually is upward sloping, which is consistent withthe idea that longer maturity bonds must have a higher expected rate of return tocompensate for their higher risk.


FIGURE 4-3 Value of Long- and Short-Term 10% Annual Coupon Bonds at Different Market Interest Rates

Value of

Current Market 1-Year 14-YearInterest Rate, rd Bond Bond

5% $1,047.62 $1,494.9310 1,000.00 1,000.0015 956.52 713.7820 916.67 538.9425 880.00 426.39

Note: Bond values were calculated using a financial calculator assuming annual, or once-a-year, compounding.

500

1,000

1,500

2,000

5 10 15 20 250

Bond Value($)

14-Year Bond

1-Year Bond

Interest Rate, r (%)

d

See Ch 04 Tool Kit.xlsfor details.


Reinvestment Rate Risk

As we saw in the preceding section, an increase in interest rates will hurt bondholdersbecause it will lead to a decline in the value of a bond portfolio. But can a decrease in in-terest rates also hurt bondholders? The answer is yes, because if interest rates fall, abondholder will probably suffer a reduction in his or her income. For example, con-sider a retiree who has a portfolio of bonds and lives off the income they produce. Thebonds, on average, have a coupon rate of 10 percent. Now suppose interest rates de-cline to 5 percent. Many of the bonds will be called, and as calls occur, the bondholderwill have to replace 10 percent bonds with 5 percent bonds. Even bonds that arenot callable will mature, and when they do, they will have to be replaced with lower-yielding bonds. Thus, our retiree will suffer a reduction of income.

The risk of an income decline due to a drop in interest rates is called reinvest-ment rate risk, and its importance has been demonstrated to all bondholders in re-cent years as a result of the sharp drop in rates since the mid-1980s. Reinvestment raterisk is obviously high on callable bonds. It is also high on short maturity bonds, be-cause the shorter the maturity of a bond, the fewer the years when the relatively highold interest rate will be earned, and the sooner the funds will have to be reinvested atthe new low rate. Thus, retirees whose primary holdings are short-term securities,such as bank CDs and short-term bonds, are hurt badly by a decline in rates, but hold-ers of long-term bonds continue to enjoy their old high rates.

Comparing Interest Rate and Reinvestment Rate Risk

Note that interest rate risk relates to the value of the bonds in a portfolio, while rein-vestment rate risk relates to the income the portfolio produces. If you hold long-termbonds, you will face interest rate risk, that is, the value of your bonds will decline if interest rates rise, but you will not face much reinvestment rate risk, so your incomewill be stable. On the other hand, if you hold short-term bonds, you will not be ex-posed to much interest rate risk, so the value of your portfolio will be stable, but youwill be exposed to reinvestment rate risk, and your income will fluctuate with changesin interest rates.

We see, then, that no fixed-rate bond can be considered totally riskless—even mostTreasury bonds are exposed to both interest rate and reinvestment rate risk.13 One canminimize interest rate risk by holding short-term bonds, or one can minimize rein-vestment rate risk by holding long-term bonds, but the actions that lower one type ofrisk increase the other. Bond portfolio managers try to balance these two risks, butsome risk generally remains in any bond.

Differentiate between interest rate risk and reinvestment rate risk.

To which type of risk are holders of long-term bonds more exposed? Short-termbondholders?

Default Risk

Another important risk associated with bonds is default risk. If the issuer defaults, in-vestors receive less than the promised return on the bond. Therefore, investors needto assess a bond’s default risk before making a purchase. Recall from Chapter 1 that

Default Risk 169

13Note, though, that indexed Treasury bonds are essentially riskless, but they pay a relatively low real rate.Also, risks have not disappeared—they are simply transferred from bondholders to taxpayers.


the quoted interest rate includes a default risk premium—the greater the default risk,the higher the bond’s yield to maturity. The default risk on Treasury securities is zero,but default risk can be substantial for corporate and municipal bonds.

Suppose two bonds have the same promised cash flows, coupon rate, maturity, li-quidity, and inflation exposure, but one bond has more default risk than the other. In-vestors will naturally pay less for the bond with the greater chance of default. As a result, bonds with higher default risk will have higher interest rates: rd � r* � IP �DRP � LP � MRP.

If its default risk changes, this will affect the price of a bond. For example, if thedefault risk of the MicroDrive bonds increases, the bonds’ price will fall and the yieldto maturity (YTM � rd) will increase.

In this section we consider some issues related to default risk. First, we show thatcorporations can influence the default risk of their bonds by changing the type ofbonds they issue. Second we discuss bond ratings, which are used to measure defaultrisk. Third, we describe the “junk bond market,” which is the market for bonds with arelatively high probability of default. Finally, we consider bankruptcy and reorganiza-tion, which affect how much an investor will recover if a default occurs.

Bond Contract Provisions That Influence Default Risk

Default risk is affected by both the financial strength of the issuer and the terms of thebond contract, especially whether collateral has been pledged to secure the bond. Sev-eral types of contract provisions are discussed below.

Bond Indentures An indenture is a legal document that spells out the rights ofboth bondholders and the issuing corporation, and a trustee is an official (usually abank) who represents the bondholders and makes sure the terms of the indenture arecarried out. The indenture may be several hundred pages in length, and it will in-clude restrictive covenants that cover such points as the conditions under whichthe issuer can pay off the bonds prior to maturity, the levels at which certain of the issuer’s ratios must be maintained if the company is to issue additional debt, andrestrictions against the payment of dividends unless earnings meet certain specifi-cations.

The trustee is responsible for monitoring the covenants and for taking appropriateaction if a violation does occur. What constitutes “appropriate action” varies with thecircumstances. It might be that to insist on immediate compliance would result inbankruptcy and possibly large losses on the bonds. In such a case, the trustee mightdecide that the bondholders would be better served by giving the company a chance towork out its problems and thus avoid forcing it into bankruptcy.

The Securities and Exchange Commission (1) approves indentures and (2) makessure that all indenture provisions are met before allowing a company to sell new secu-rities to the public. Also, it should be noted that the indentures of many larger corpo-rations were actually written in the 1930s or 1940s, and that many issues of new bondssold since then were covered by the same indenture. The interest rates on the bonds,and perhaps also the maturities, vary depending on market conditions at the time ofeach issue, but bondholders’ protection as spelled out in the indenture is the same forall bonds of the same type. A firm will have different indentures for each of the majortypes of bonds it issues. For example, one indenture will cover its first mortgagebonds, another its debentures, and a third its convertible bonds.

Mortgage Bonds Under a mortgage bond, the corporation pledges certain assetsas security for the bond. To illustrate, in 2002 Billingham Corporation needed $10



million to build a major regional distribution center. Bonds in the amount of $4million, secured by a first mortgage on the property, were issued. (The remaining $6million was financed with equity capital.) If Billingham defaults on the bonds, thebondholders can foreclose on the property and sell it to satisfy their claims.

If Billingham chose to, it could issue second mortgage bonds secured by the same $10million of assets. In the event of liquidation, the holders of these second mortgagebonds would have a claim against the property, but only after the first mortgage bond-holders had been paid off in full. Thus, second mortgages are sometimes called juniormortgages, because they are junior in priority to the claims of senior mortgages, or firstmortgage bonds.

All mortgage bonds are subject to an indenture. The indentures of many majorcorporations were written 20, 30, 40, or more years ago. These indentures are gener-ally “open ended,” meaning that new bonds can be issued from time to time under thesame indenture. However, the amount of new bonds that can be issued is virtually al-ways limited to a specified percentage of the firm’s total “bondable property,” whichgenerally includes all land, plant, and equipment.

For example, in the past Savannah Electric Company had provisions in its bond in-denture that allowed it to issue first mortgage bonds totaling up to 60 percent of itsfixed assets. If its fixed assets totaled $1 billion, and if it had $500 million of first mort-gage bonds outstanding, it could, by the property test, issue another $100 million ofbonds (60% of $1 billion � $600 million).

At times, Savannah Electric was unable to issue any new first mortgage bonds be-cause of another indenture provision: its interest coverage ratio (pre-interest incomedivided by interest expense) was below 2.5, the minimum coverage that it must have inorder to sell new bonds. Thus, although Savannah Electric passed the property test, itfailed the coverage test, so it could not issue any more first mortgage bonds. SavannahElectric then had to finance with junior bonds. Because first mortgage bonds carriedlower interest rates, this restriction was costly.

Savannah Electric’s neighbor, Georgia Power Company, had more flexibility un-der its indenture—its interest coverage requirement was only 2.0. In hearings beforethe Georgia Public Service Commission, it was suggested that Savannah Electricshould change its indenture coverage to 2.0 so that it could issue more first mortgagebonds. However, this was simply not possible—the holders of the outstanding bondswould have to approve the change, and they would not vote for a change that wouldseriously weaken their position.

Debentures A debenture is an unsecured bond, and as such it provides no lienagainst specific property as security for the obligation. Debenture holders are, there-fore, general creditors whose claims are protected by property not otherwise pledged.In practice, the use of debentures depends both on the nature of the firm’s assets andon its general credit strength. Extremely strong companies often use debentures; theysimply do not need to put up property as security for their debt. Debentures are alsoissued by weak companies that have already pledged most of their assets as collateralfor mortgage loans. In this latter case, the debentures are quite risky, and they willbear a high interest rate.

Subordinated Debentures The term subordinate means “below,” or “inferior to,”and, in the event of bankruptcy, subordinated debt has claims on assets only after se-nior debt has been paid off. Subordinated debentures may be subordinated either todesignated notes payable (usually bank loans) or to all other debt. In the event of li-quidation or reorganization, holders of subordinated debentures cannot be paid untilall senior debt, as named in the debentures’ indenture, has been paid.

Default Risk 171


Development Bonds Some companies may be in a position to benefit from the saleof either development bonds or pollution control bonds. State and local govern-ments may set up both industrial development agencies and pollution control agencies.These agencies are allowed, under certain circumstances, to sell tax-exempt bonds,then to make the proceeds available to corporations for specific uses deemed (by Con-gress) to be in the public interest. Thus, an industrial development agency in Floridamight sell bonds to provide funds for a paper company to build a plant in the FloridaPanhandle, where unemployment is high. Similarly, a Detroit pollution controlagency might sell bonds to provide Ford with funds to be used to purchase pollutioncontrol equipment. In both cases, the income from the bonds would be tax exempt tothe holders, so the bonds would sell at relatively low interest rates. Note, however,that these bonds are guaranteed by the corporation that will use the funds, not by agovernmental unit, so their rating reflects the credit strength of the corporation usingthe funds.

Municipal Bond Insurance Municipalities can have their bonds insured, whichmeans that an insurance company guarantees to pay the coupon and principal pay-ments should the issuer default. This reduces risk to investors, who will thus accepta lower coupon rate for an insured bond vis-à-vis an uninsured one. Even thoughthe municipality must pay a fee to get its bonds insured, its savings due to the lowercoupon rate often makes insurance cost-effective. Keep in mind that the insurers areprivate companies, and the value added by the insurance depends on the creditwor-thiness of the insurer. However, the larger ones are strong companies, and their ownratings are AAA. Therefore, the bonds they insure are also rated AAA, regardless ofthe credit strength of the municipal issuer. Bond ratings are discussed in the nextsection.

Bond Ratings

Since the early 1900s, bonds have been assigned quality ratings that reflect their prob-ability of going into default. The three major rating agencies are Moody’s InvestorsService (Moody’s), Standard & Poor’s Corporation (S&P), and Fitch Investors Ser-vice. Moody’s and S&P’s rating designations are shown in Table 4-1.14 The triple- anddouble-A bonds are extremely safe. Single-A and triple-B bonds are also strongenough to be called investment grade bonds, and they are the lowest-rated bondsthat many banks and other institutional investors are permitted by law to hold. Double-B and lower bonds are speculative, or junk bonds. These bonds have a


TABLE 4-1 Moody’s and S&P Bond Ratings

Investment Grade Junk Bonds

Moody’s Aaa Aa A Baa Ba B Caa CS&P AAA AA A BBB BB B CCC D

Note: Both Moody’s and S&P use “modifiers” for bonds rated below triple-A. S&P uses a plus and minus system;thus, A� designates the strongest A-rated bonds and A� the weakest. Moody’s uses a 1, 2, or 3 designation, with1 denoting the strongest and 3 the weakest; thus, within the double-A category, Aa1 is the best, Aa2 is average,and Aa3 is the weakest.

14In the discussion to follow, reference to the S&P code is intended to imply the Moody’s and Fitch’s codesas well. Thus, triple-B bonds mean both BBB and Baa bonds; double-B bonds mean both BB and Ba bonds;and so on.


Default Risk 173

significant probability of going into default. A later section discusses junk bonds inmore detail.

Bond Rating Criteria Bond ratings are based on both qualitative and quantitativefactors, some of which are listed below:

1. Various ratios, including the debt ratio, the times-interest-earned ratio, and theEBITDA coverage ratio. The better the ratios, the higher the rating.15

2. Mortgage provisions: Is the bond secured by a mortgage? If it is, and if the prop-erty has a high value in relation to the amount of bonded debt, the bond’s rating isenhanced.

3. Subordination provisions: Is the bond subordinated to other debt? If so, it will berated at least one notch below the rating it would have if it were not subordinated.Conversely, a bond with other debt subordinated to it will have a somewhathigher rating.

4. Guarantee provisions: Some bonds are guaranteed by other firms. If a weak com-pany’s debt is guaranteed by a strong company (usually the weak company’s par-ent), the bond will be given the strong company’s rating.

5. Sinking fund: Does the bond have a sinking fund to ensure systematic repayment?This feature is a plus factor to the rating agencies.

6. Maturity: Other things the same, a bond with a shorter maturity will be judgedless risky than a longer-term bond, and this will be reflected in the ratings.

7. Stability: Are the issuer’s sales and earnings stable?8. Regulation: Is the issuer regulated, and could an adverse regulatory climate cause

the company’s economic position to decline? Regulation is especially importantfor utilities and telephone companies.

9. Antitrust: Are any antitrust actions pending against the firm that could erode itsposition?

10. Overseas operations: What percentage of the firm’s sales, assets, and profits arefrom overseas operations, and what is the political climate in the host countries?

11. Environmental factors: Is the firm likely to face heavy expenditures for pollutioncontrol equipment?

12. Product liability: Are the firm’s products safe? The tobacco companies today areunder pressure, and so are their bond ratings.

13. Pension liabilities: Does the firm have unfunded pension liabilities that could posea future problem?

14. Labor unrest: Are there potential labor problems on the horizon that couldweaken the firm’s position? As this is written, a number of airlines face this prob-lem, and it has caused their ratings to be lowered.

15. Accounting policies: If a firm uses relatively conservative accounting policies, itsreported earnings will be of “higher quality” than if it uses less conservative pro-cedures. Thus, conservative accounting policies are a plus factor in bond ratings.

Representatives of the rating agencies have consistently stated that no precise formulais used to set a firm’s rating; all the factors listed, plus others, are taken into account,but not in a mathematically precise manner. Nevertheless, as we see in Table 4-2,there is a strong correlation between bond ratings and many of the ratios described inChapter 10. Not surprisingly, companies with lower debt ratios, higher cash flow todebt, higher returns on capital, higher EBITDA interest coverage ratios, and EBITinterest coverage ratios typically have higher bond ratings.

15See Chapter 10 for an explanation of these and other ratios.



Importance of Bond Ratings Bond ratings are important both to firms and toinvestors. First, because a bond’s rating is an indicator of its default risk, the rating has adirect, measurable influence on the bond’s interest rate and the firm’s cost of debt. Sec-ond, most bonds are purchased by institutional investors rather than individuals, andmany institutions are restricted to investment-grade securities. Thus, if a firm’s bondsfall below BBB, it will have a difficult time selling new bonds because many potentialpurchasers will not be allowed to buy them. In addition, the covenants may stipulatethat the interest rate is automatically increased if the rating falls below a specified level.

As a result of their higher risk and more restricted market, lower-grade bonds havehigher required rates of return, rd, than high-grade bonds. Figure 4-4 illustrates thispoint. In each of the years shown on the graph, U.S. government bonds have had thelowest yields, AAAs have been next, and BBB bonds have had the highest yields. Thefigure also shows that the gaps between yields on the three types of bonds vary overtime, indicating that the cost differentials, or risk premiums, fluctuate from year toyear. This point is highlighted in Figure 4-5, which gives the yields on the three typesof bonds and the risk premiums for AAA and BBB bonds in June 1963 and August2001.16 Note first that the risk-free rate, or vertical axis intercept, rose 1.5 percentagepoints from 1963 to 2001, primarily reflecting the increase in realized and anticipatedinflation. Second, the slope of the line has increased since 1963, indicating an increasein investors’ risk aversion. Thus, the penalty for having a low credit rating varies overtime. Occasionally, as in 1963, the penalty is quite small, but at other times it is large.These slope differences reflect investors’ aversion to risk.

TABLE 4-2 Bond Rating Criteria; Three-Year (1998–2000) Median Financial Ratios for Different Bond Rating Classifications

Ratiosa AAA AA A BBB BB B CCC

EBIT interest coverage (EBIT/Interest) 21.4� 10.1� 6.1� 3.7� 2.1� 0.8� 0.1�

EBITDA interest coverage (EBITDA/Interest) 26.5 12.9 9.1 5.8 3.4 1.8 1.3Funds from operations/Total debt 84.2 25.2 15.0 8.5 2.6 (3.2) (12.9)Free operating cash flow/Total debt 128.8 55.4 43.2 30.8 18.8 7.8 1.6Return on capital 34.9 21.7 19.4 13.6 11.6 6.6 1.0Operating income/Sales 27.0 22.1 18.6 15.4 15.9 11.9 11.9Long-term debt/Long-term capital 13.3 28.2 33.9 42.5 57.2 69.7 68.8Total debt/Total capital 22.9 37.7 42.5 48.2 62.6 74.8 87.7

Note:aSee the Source for a detailed definition of the ratios.

Source: Reprinted with permission of Standard & Poor’s, A Division of The McGraw-Hill Companies.http://www.standardandpoors.com/ResourceCenter/RatingsCriteria/CorporateFinance/2001CorporateRatingsCriteria.html.

16The term risk premium ought to reflect only the difference in expected (and required) returns between twosecurities that results from differences in their risk. However, the differences between yields to maturity ondifferent types of bonds consist of (1) a true risk premium; (2) a liquidity premium, which reflects the factthat U.S. Treasury bonds are more readily marketable than most corporate bonds; (3) a call premium, be-cause most Treasury bonds are not callable whereas corporate bonds are; and (4) an expected loss differen-tial, which reflects the probability of loss on the corporate bonds. As an example of the last point, supposethe yield to maturity on a BBB bond was 8.0 percent versus 5.5 percent on government bonds, but there wasa 5 percent probability of total default loss on the corporate bond. In this case, the expected return on theBBB bond would be 0.95(8.0%) � 0.05(0%) � 7.6%, and the risk premium would be 2.1 percent, not thefull 2.5 percentage points difference in “promised” yields to maturity. Because of all these points, the riskpremiums given in Figure 4-5 overstate somewhat the true (but unmeasurable) theoretical risk premiums.


Default Risk 175

FIGURE 4-4 Yields on Selected Long-Term Bonds, 1960–2001

Source: Federal Reserve Board, Historical Chart Book, 1983, and Federal Reserve Bulletin: http://www.federalreserve.gov/releases.

16

14

12

10

8

6

4

2

16

14

12

10

8

6

4

2

1960 1965 1970 1975 1980 1985 1990

U.S. Government

Wide Spread

Corporate BBB

Corporate AAA

Narrow Spread

Percent

1995 2000

Changes in Ratings Changes in a firm’s bond rating affect both its ability to borrowlong-term capital and the cost of that capital. Rating agencies review outstandingbonds on a periodic basis, occasionally upgrading or downgrading a bond as a result ofits issuer’s changed circumstances. For example, in October 2001, Standard & Poor’sreported that it had raised the rating on King Pharmaceuticals Inc. to BB� from BBdue to the “continued success of King Pharmaceuticals’ lead product, the cardiovascu-lar drug Altace, as well as the company’s increasing sales diversity, growing financial



flexibility, and improved financial profile.”17 However, S&P also reported that XeroxCorporation’s senior unsecured debt had been downgraded from a BBB� to a BB�due to expectations of lower operating income in 2001 and 2002.

Junk BondsPrior to the 1980s, fixed-income investors such as pension funds and insurance com-panies were generally unwilling to buy risky bonds, so it was almost impossible forrisky companies to raise capital in the public bond markets. Then, in the late 1970s,Michael Milken of the investment banking firm Drexel Burnham Lambert, relying onhistorical studies that showed that risky bonds yielded more than enough to compen-sate for their risk, began to convince institutional investors of the merits of purchasingrisky debt. Thus was born the “junk bond,” a high-risk, high-yield bond issued to fi-nance a leveraged buyout, a merger, or a troubled company.18 For example, Public

FIGURE 4-5 Relationship between Bond Ratings and Bond Yields, 1963 and 2001

Long-Term Risk PremiumsGovernment

Bonds AAA Corporate BBB Corporate(Default-Free) Bonds Bonds AAA BBB

(1) (2) (3) (4) � (2) � (1) (5) � (3) � (1)

June 1963 4.0% 4.2% 4.8% 0.2% 0.8%August 2001 5.5 7.0 8.0 1.5 2.5

RPAAA � risk premium on AAA bonds.RPBBB � risk premium on BBB bonds.

Source: Federal Reserve Bulletin, December 1963, and Federal Reserve Statistical Release, Selected Interest Rates, Historical Data, August, 2001:http://www.federalreserve.gov/releases.

AAA BBBU.S.TreasuryBonds

Bond Ratings

Rate of Return(%)

1963

4.0

6.0

5.0

7.0

8.0

RPBBB = 2.5%RPAAA = 1.5%

2001

RPAAA = 0.2%

RPBBB = 0.8%

9.0

17See the Standard & Poor’s web site for this and other changes in ratings: http://www.standardandpoors.com/RatingsActions/RatingsNews/CorporateFinance/index.html.18Another type of junk bond is one that was highly rated when it was issued but whose rating has fallen be-cause the issuing corporation has fallen on hard times. Such bonds are called “fallen angels.”


Default Risk 177

Santa Fe Bonds Finally Mature after 114 Years

In 1995, Santa Fe Pacific Company made the final paymenton some outstanding bonds that were originally issued in1881! While the bonds were paid off in full, their history hasbeen anything but routine.

Since the bonds were issued in 1881, investors have seenSanta Fe go through two bankruptcy reorganizations, twodepressions, several recessions, two world wars, and the col-lapse of the gold standard. Through it all, the company re-mained intact, although ironically it did agree to be acquiredby Burlington Northern just prior to the bonds’ maturity.

When the bonds were issued in 1881, they had a 6 per-cent coupon. After a promising start, competition in the rail-road business, along with the Depression of 1893, dealt acrippling one-two punch to the company’s fortunes. Aftertwo bankruptcy reorganizations—and two new managementteams—the company got back on its feet, and in 1895 it re-placed the original bonds with new 100-year bonds. Thenew bonds, sanctioned by the Bankruptcy Court, matured in1995 and carried a 4 percent coupon. However, they alsohad a wrinkle that was in effect until 1900—the companycould skip the coupon payment if, in management’s opinion,earnings were not sufficiently high to service the debt. After1900, the company could no longer just ignore the coupon,

but it did have the option of deferring the payments if man-agement deemed deferral necessary. In the late 1890s, SantaFe did skip the interest, and the bonds sold at an all-time lowof $285 (28.5% of par) in 1896. The bonds reached a peak in1946, when they sold for $1,312.50 in the strong, low inter-est rate economy after World War II.

Interestingly, the bonds’ principal payment was originallypegged to the price of gold, meaning that the principal re-ceived at maturity would increase if the price of gold in-creased. This type of contract was declared invalid in 1933by President Roosevelt and Congress, and the decision wasupheld by the Supreme Court in a 5–4 vote. If just oneSupreme Court justice had gone the other way, then, due toan increase in the price of gold, the bonds would have beenworth $18,626 rather than $1,000 when they matured in1995!

In many ways, the saga of the Santa Fe bonds is a testa-ment to the stability of the U.S. financial system. On theother hand, it illustrates the many types of risks that in-vestors face when they purchase long-term bonds. Investorsin the 100-year bonds issued by Disney and Coca-Cola,among others, should perhaps take note.

Service of New Hampshire financed construction of its troubled Seabrook nuclearplant with junk bonds, and junk bonds were used by Ted Turner to finance the devel-opment of CNN and Turner Broadcasting. In junk bond deals, the debt ratio is gen-erally extremely high, so the bondholders must bear as much risk as stockholders nor-mally would. The bonds’ yields reflect this fact—a promised return of 25 percent perannum was required to sell some Public Service of New Hampshire bonds.

The emergence of junk bonds as an important type of debt is another example ofhow the investment banking industry adjusts to and facilitates new developments incapital markets. In the 1980s, mergers and takeovers increased dramatically. Peoplelike T. Boone Pickens and Henry Kravis thought that certain old-line, establishedcompanies were run inefficiently and were financed too conservatively, and theywanted to take these companies over and restructure them. Michael Milken and hisstaff at Drexel Burnham Lambert began an active campaign to persuade certain insti-tutions (often S&Ls) to purchase high-yield bonds. Milken developed expertise inputting together deals that were attractive to the institutions yet feasible in the sensethat projected cash flows were sufficient to meet the required interest payments. Thefact that interest on the bonds was tax deductible, combined with the much higherdebt ratios of the restructured firms, also increased after-tax cash flows and helpedmake the deals feasible.

The development of junk bond financing has done much to reshape the U.S. fi-nancial scene. The existence of these securities contributed to the loss of indepen-dence of Gulf Oil and hundreds of other companies, and it led to major shake-ups insuch companies as CBS, Union Carbide, and USX (formerly U.S. Steel). It also caused



Drexel Burnham Lambert to leap from essentially nowhere in the 1970s to becomethe most profitable investment banking firm during the 1980s.

The phenomenal growth of the junk bond market was impressive, but controver-sial. In 1989, Drexel Burnham Lambert was forced into bankruptcy, and “junk bondking” Michael Milken, who had earned $500 million two years earlier, was sent to jail.Those events led to the collapse of the junk bond market in the early 1990s. Sincethen, however, the junk bond market has rebounded, and junk bonds are here to stayas an important form of corporate financing.

Bankruptcy and Reorganization

During recessions, bankruptcies normally rise, and recent recessions are no exception.The 1991–1992 casualties included Pan Am, Carter Hawley Hale Stores, ContinentalAirlines, R. H. Macy & Company, Zale Corporation, and McCrory Corporation. Therecession beginning in 2001 has already claimed Kmart and Enron, and there willlikely be more bankruptcies in 2002 if the economy continues to decline. Because ofits importance, a brief discussion of bankruptcy is warranted.

When a business becomes insolvent, it does not have enough cash to meet its inter-est and principal payments. A decision must then be made whether to dissolve the firmthrough liquidation or to permit it to reorganize and thus stay alive. These issues are ad-dressed in Chapters 7 and 11 of the federal bankruptcy statutes, and the final decisionis made by a federal bankruptcy court judge.

The decision to force a firm to liquidate versus permit it to reorganize depends onwhether the value of the reorganized firm is likely to be greater than the value of thefirm’s assets if they are sold off piecemeal. In a reorganization, the firm’s creditors ne-gotiate with management on the terms of a potential reorganization. The reorgani-zation plan may call for a restructuring of the firm’s debt, in which case the interestrate may be reduced, the term to maturity lengthened, or some of the debt may beexchanged for equity. The point of the restructuring is to reduce the financial chargesto a level that the firm’s cash flows can support. Of course, the common stockholdersalso have to give up something—they often see their position diluted as a result of ad-ditional shares being given to debtholders in exchange for accepting a reducedamount of debt principal and interest. In fact, the original common stockholders of-ten end up with nothing. A trustee may be appointed by the court to oversee the re-organization, but generally the existing management is allowed to retain control.

Liquidation occurs if the company is deemed to be too far gone to be saved—if itis worth more dead than alive. If the bankruptcy court orders a liquidation, assets aresold off and the cash obtained is distributed as specified in Chapter 7 of the Bank-ruptcy Act. Here is the priority of claims:

1. Secured creditors are entitled to the proceeds from the sale of the specific prop-erty that was used to support their loans.

2. The trustee’s costs of administering and operating the bankrupt firm are next in line.3. Expenses incurred after bankruptcy was filed come next.4. Wages due workers, up to a limit of $2,000 per worker, follow.5. Claims for unpaid contributions to employee benefit plans are next. This amount,

together with wages, cannot exceed $2,000 per worker.6. Unsecured claims for customer deposits up to $900 per customer are sixth in line.7. Federal, state, and local taxes due come next.8. Unfunded pension plan liabilities are next although some limitations exist.9. General unsecured creditors are ninth on the list.

10. Preferred stockholders come next, up to the par value of their stock.11. Common stockholders are finally paid, if anything is left, which is rare.


The key points for you to know are (1) the federal bankruptcy statutes govern bothreorganization and liquidation, (2) bankruptcies occur frequently, and (3) a priority of the specified claims must be followed when distributing the assets of a liquidated firm.

Differentiate between mortgage bonds and debentures.

Name the major rating agencies, and list some factors that affect bond ratings.

Why are bond ratings important both to firms and to investors?

For what purposes have junk bonds typically been used?

Differentiate between a Chapter 7 liquidation and a Chapter 11 reorganization.When would each be used?

List the priority of claims for the distribution of a liquidated firm’s assets.

Bond Markets

Corporate bonds are traded primarily in the over-the-counter market. Most bonds areowned by and traded among the large financial institutions (for example, life insurancecompanies, mutual funds, and pension funds, all of which deal in very large blocks ofsecurities), and it is relatively easy for the over-the-counter bond dealers to arrangethe transfer of large blocks of bonds among the relatively few holders of the bonds. Itwould be much more difficult to conduct similar operations in the stock market, withits literally millions of large and small stockholders, so a higher percentage of stocktrades occur on the exchanges.

Information on bond trades in the over-the-counter market is not published, but arepresentative group of bonds is listed and traded on the bond division of the NYSEand is reported on the bond market page of The Wall Street Journal. Bond data are alsoavailable on the Internet, at sites such as http://www.bondsonline. Figure 4-6 reportsdata for selected bonds of BellSouth Corporation. Note that BellSouth actually hadmore than ten bond issues outstanding, but Figure 4-6 reports data for only ten bonds.

The bonds of BellSouth and other companies can have various denominations, butfor convenience we generally think of each bond as having a par value of $1,000—this ishow much per bond the company borrowed and how much it must someday repay.However, since other denominations are possible, for trading and reporting purposesbonds are quoted as percentages of par. Looking at the fifth bond listed in the data inFigure 4-6, we see that the bond is of the series that pays a 7 percent coupon, or0.07($1,000) � $70.00 of interest per year. The BellSouth bonds, and most others, payinterest semiannually, so all rates are nominal, not EAR rates. This bond matures andmust be repaid on October 1, 2025; it is not shown in the figure, but this bond was is-sued in 1995, so it had a 30-year original maturity. The price shown in the last column isexpressed as a percentage of par, 106.00 percent, which translates to $1,060.00. Thisbond has a yield to maturity of 6.501 percent. The bond is not callable, but several oth-ers in Figure 4-6 are callable. Note that the eighth bond in Figure 4-6 has a yield to callof only 3.523 percent compared with its yield to maturity of 7.270 percent, indicatingthat investors expect BellSouth to call the bond prior to maturity.

Coupon rates are generally set at levels that reflect the “going rate of interest” onthe day a bond is issued. If the rates were set lower, investors simply would not buy thebonds at the $1,000 par value, so the company could not borrow the money it needed.Thus, bonds generally sell at their par values on the day they are issued, but theirprices fluctuate thereafter as interest rates change.

Bond Markets 179


As shown in Figure 4-7, the BellSouth bonds initially sold at par, but then fell be-low par in 1996 when interest rates rose. The price rose above par in 1997 and 1998when interest rates fell, but the price fell again in 1999 and 2000 after increases in in-terest rates. It rose again in 2001 when interest rates fell. The dashed line in Figure 4-7


FIGURE 4-6 Selected Bond Market Data

FIGURE 4-7 BellSouth 7%, 30-Year Bond: Market Value as Interest Rates Change

Note: The line from 2001 to 2025 appears linear, but it actually has a slight downward curve.

1995 2020 20252015201020052000

Bond Value

1,200

1,100

0

900

1,000

Years

Bond's Projected Priceif Interest Rates RemainConstant from 2001 to 2025

Actual Price of the7% Coupon Bond

($)

S&P Bond Issue Coupon Yield to Yield to Rating Name Rate Maturity Datea Maturity Callb Pricec

A� BellSouth 6.375 6/15/2004 3.616 NC 106.843A� BellSouth 7.000 2/1/2005 4.323 NC 108.031A� BellSouth 5.875 1/15/2009 5.242 NC 103.750A� BellSouth 7.750 2/15/2010 5.478 NC 114.962A� BellSouth 7.000 10/1/2025 6.501 NC 106.000A� BellSouth 6.375 6/1/2028 6.453 NC 99.000A� BellSouth 7.875 2/15/2030 6.581 NC 116.495A� BellSouth 7.875 08-01-2032C 7.270 3.523 107.375A� BellSouth 7.500 06-15-2033C 7.014 6.290 106.125A� BellSouth 7.625 05-15-2035C 7.169 6.705 105.750

Notes: aC denotes a callable bond.bNC indicates the bond is not callable.cThe price is reported as a percentage of par.

Source: 10/25/01, http://www.bondsonline.com. At the top of the web page, select the icon for Bond Search,then select the button for Corporate. When the bond-search dialog box appears, type in BellSouth for Issue andclick the Find Bonds button. Reprinted by permission.


shows the projected price of the bonds, in the unlikely event that interest rates remainconstant from 2001 to 2025. Looking at the actual and projected price history of thesebonds, we see (1) the inverse relationship between interest rates and bond values and(2) the fact that bond values approach their par values as their maturity date ap-proaches.

Why do most bond trades occur in the over-the-counter market?

If a bond issue is to be sold at par, how will its coupon rate be determined?

Summary

This chapter described the different types of bonds governments and corporations is-sue, explained how bond prices are established, and discussed how investors estimatethe rates of return they can expect to earn. We also discussed the various types of risksthat investors face when they buy bonds.

It is important to remember that when an investor purchases a company’s bonds,that investor is providing the company with capital. Therefore, when a firm issuesbonds, the return that investors receive represents the cost of debt financing for the issuingcompany. This point is emphasized in Chapter 6, where the ideas developed in thischapter are used to help determine a company’s overall cost of capital, which is a basiccomponent in the capital budgeting process.

The key concepts covered are summarized below.

� A bond is a long-term promissory note issued by a business or governmental unit.The issuer receives money in exchange for promising to make interest paymentsand to repay the principal on a specified future date.

� Some recent innovations in long-term financing include zero coupon bonds,which pay no annual interest but that are issued at a discount; floating rate debt,whose interest payments fluctuate with changes in the general level of interestrates; and junk bonds, which are high-risk, high-yield instruments issued by firmsthat use a great deal of financial leverage.

� A call provision gives the issuing corporation the right to redeem the bonds priorto maturity under specified terms, usually at a price greater than the maturity value(the difference is a call premium). A firm will typically call a bond if interest ratesfall substantially below the coupon rate.

� A redeemable bond gives the investor the right to sell the bond back to the issu-ing company at a previously specified price. This is a useful feature (for investors)if interest rates rise or if the company engages in unanticipated risky activities.

� A sinking fund is a provision that requires the corporation to retire a portion ofthe bond issue each year. The purpose of the sinking fund is to provide for the or-derly retirement of the issue. A sinking fund typically requires no call premium.

� The value of a bond is found as the present value of an annuity (the interest pay-ments) plus the present value of a lump sum (the principal). The bond is evaluatedat the appropriate periodic interest rate over the number of periods for whichinterest payments are made.

� The equation used to find the value of an annual coupon bond is:

An adjustment to the formula must be made if the bond pays interest semi-annually: divide INT and rd by 2, and multiply N by 2.

VB � aN

t�1

INT(1 � rd)t �

M(1 � rd)N.

Summary 181


� The return earned on a bond held to maturity is defined as the bond’s yield tomaturity (YTM). If the bond can be redeemed before maturity, it is callable, and thereturn investors receive if it is called is defined as the yield to call (YTC). The YTCis found as the present value of the interest payments received while the bond is out-standing plus the present value of the call price (the par value plus a call premium).

� The longer the maturity of a bond, the more its price will change in response to agiven change in interest rates; this is called interest rate risk. However, bondswith short maturities expose investors to high reinvestment rate risk, which isthe risk that income from a bond portfolio will decline because cash flows receivedfrom bonds will be rolled over at lower interest rates.

� Corporate and municipal bonds have default risk. If an issuer defaults, investorsreceive less than the promised return on the bond. Therefore, investors shouldevaluate a bond’s default risk before making a purchase.

� There are many different types of bonds with different sets of features. These in-clude convertible bonds, bonds with warrants, income bonds, purchasingpower (indexed) bonds, mortgage bonds, debentures, subordinated deben-tures, junk bonds, development bonds, and insured municipal bonds. The re-turn required on each type of bond is determined by the bond’s riskiness.

� Bonds are assigned ratings that reflect the probability of their going into default.The highest rating is AAA, and they go down to D. The higher a bond’s rating, thelower its risk and therefore its interest rate.

Questions

Define each of the following terms:a. Bond; Treasury bond; corporate bond; municipal bond; foreign bondb. Par value; maturity date; coupon payment; coupon interest ratec. Floating rate bond; zero coupon bond; original issue discount bond (OID)d. Call provision; redeemable bond; sinking funde. Convertible bond; warrant; income bond; indexed, or purchasing power, bondf. Premium bond; discount bondg. Current yield (on a bond); yield to maturity (YTM); yield to call (YTC)h. Reinvestment risk; interest rate risk; default riski. Indentures; mortgage bond; debenture; subordinated debenturej. Development bond; municipal bond insurance; junk bond; investment-grade bond

“The values of outstanding bonds change whenever the going rate of interest changes. In gen-eral, short-term interest rates are more volatile than long-term interest rates. Therefore, short-term bond prices are more sensitive to interest rate changes than are long-term bond prices.” Isthis statement true or false? Explain.

The rate of return you would get if you bought a bond and held it to its maturity date is called thebond’s yield to maturity. If interest rates in the economy rise after a bond has been issued, what willhappen to the bond’s price and to its YTM? Does the length of time to maturity affect the extent towhich a given change in interest rates will affect the bond’s price?

If you buy a callable bond and interest rates decline, will the value of your bond rise by as muchas it would have risen if the bond had not been callable? Explain.

A sinking fund can be set up in one of two ways:(1) The corporation makes annual payments to the trustee, who invests the proceeds in secu-

rities (frequently government bonds) and uses the accumulated total to retire the bond is-sue at maturity.

(2) The trustee uses the annual payments to retire a portion of the issue each year, either call-ing a given percentage of the issue by a lottery and paying a specified price per bond or buy-ing bonds on the open market, whichever is cheaper.

Discuss the advantages and disadvantages of each procedure from the viewpoint of both thefirm and its bondholders.

4–5

4–4

4–3

4–2

4–1



Self-Test Problems (Solutions Appear in Appendix A)

The Pennington Corporation issued a new series of bonds on January 1, 1979. The bonds weresold at par ($1,000), have a 12 percent coupon, and mature in 30 years, on December 31, 2008.Coupon payments are made semiannually (on June 30 and December 31).a. What was the YTM of Pennington’s bonds on January 1, 1979?b. What was the price of the bond on January 1, 1984, 5 years later, assuming that the level of

interest rates had fallen to 10 percent?c. Find the current yield and capital gains yield on the bond on January 1, 1984, given the price

as determined in part b.d. On July 1, 2002, Pennington’s bonds sold for $916.42. What was the YTM at that date?e. What were the current yield and capital gains yield on July 1, 2002?f. Now, assume that you purchased an outstanding Pennington bond on March 1, 2002, when

the going rate of interest was 15.5 percent. How large a check must you have written to com-plete the transaction? This is a hard question! (Hint: PVIFA7.75%,13 � 8.0136 andPVIF7.75%,13 � 0.3789.)

The Vancouver Development Company has just sold a $100 million, 10-year, 12 percent bondissue. A sinking fund will retire the issue over its life. Sinking fund payments are of equalamounts and will be made semiannually, and the proceeds will be used to retire bonds as the pay-ments are made. Bonds can be called at par for sinking fund purposes, or the funds paid into thesinking fund can be used to buy bonds in the open market.a. How large must each semiannual sinking fund payment be?b. What will happen, under the conditions of the problem thus far, to the company’s debt ser-

vice requirements per year for this issue over time?c. Now suppose Vancouver Development set up its sinking fund so that equal annual amounts,

payable at the end of each year, are paid into a sinking fund trust held by a bank, with the pro-ceeds being used to buy government bonds that pay 9 percent interest. The payments, plusaccumulated interest, must total $100 million at the end of 10 years, and the proceeds will beused to retire the bonds at that time. How large must the annual sinking fund payment benow?

d. What are the annual cash requirements for covering bond service costs under the trusteeshiparrangement described in part c? (Note: Interest must be paid on Vancouver’s outstandingbonds but not on bonds that have been retired.)

e. What would have to happen to interest rates to cause the company to buy bonds on the openmarket rather than call them under the original sinking fund plan?

Problems

Callaghan Motors’ bonds have 10 years remaining to maturity. Interest is paid annually, thebonds have a $1,000 par value, and the coupon interest rate is 8 percent. The bonds have a yieldto maturity of 9 percent. What is the current market price of these bonds?

Wilson Wonders’ bonds have 12 years remaining to maturity. Interest is paid annually, thebonds have a $1,000 par value, and the coupon interest rate is 10 percent. The bonds sell at aprice of $850. What is their yield to maturity?

Thatcher Corporation’s bonds will mature in 10 years. The bonds have a face value of $1,000 andan 8 percent coupon rate, paid semiannually. The price of the bonds is $1,100. The bonds arecallable in 5 years at a call price of $1,050. What is the yield to maturity? What is the yield to call?

Heath Foods’ bonds have 7 years remaining to maturity. The bonds have a face value of $1,000and a yield to maturity of 8 percent. They pay interest annually and have a 9 percent couponrate. What is their current yield?

Nungesser Corporation has issued bonds that have a 9 percent coupon rate, payable semiannu-ally. The bonds mature in 8 years, have a face value of $1,000, and a yield to maturity of 8.5 per-cent. What is the price of the bonds?

4–5BOND VALUATION; FINANCIAL

CALCULATOR NEEDED

4–4CURRENT YIELD

4–3YIELD TO MATURITY AND CALL;

FINANCIAL CALCULATORNEEDED

4–2YIELD TO MATURITY; FINANCIAL

CALCULATOR NEEDED

4–1BOND VALUATION

ST–2SINKING FUND

ST–1BOND VALUATION

Problems 183


The Garraty Company has two bond issues outstanding. Both bonds pay $100 annual interestplus $1,000 at maturity. Bond L has a maturity of 15 years, and Bond S a maturity of 1 year.a. What will be the value of each of these bonds when the going rate of interest is (1) 5 percent,

(2) 8 percent, and (3) 12 percent? Assume that there is only one more interest payment to bemade on Bond S.

b. Why does the longer-term (15-year) bond fluctuate more when interest rates change thandoes the shorter-term bond (1-year)?

The Heymann Company’s bonds have 4 years remaining to maturity. Interest is paid annually;the bonds have a $1,000 par value; and the coupon interest rate is 9 percent.a. What is the yield to maturity at a current market price of (1) $829 or (2) $1,104?b. Would you pay $829 for one of these bonds if you thought that the appropriate rate of in-

terest was 12 percent—that is, if rd � 12%? Explain your answer.

Six years ago, The Singleton Company sold a 20-year bond issue with a 14 percent annual couponrate and a 9 percent call premium. Today, Singleton called the bonds. The bonds originally weresold at their face value of $1,000. Compute the realized rate of return for investors who purchasedthe bonds when they were issued and who surrender them today in exchange for the call price.

A 10-year, 12 percent semiannual coupon bond, with a par value of $1,000, may be called in 4years at a call price of $1,060. The bond sells for $1,100. (Assume that the bond has just beenissued.)a. What is the bond’s yield to maturity?b. What is the bond’s current yield?c. What is the bond’s capital gain or loss yield?d. What is the bond’s yield to call?

You just purchased a bond which matures in 5 years. The bond has a face value of $1,000, andhas an 8 percent annual coupon. The bond has a current yield of 8.21 percent. What is thebond’s yield to maturity?

A bond which matures in 7 years sells for $1,020. The bond has a face value of $1,000 and ayield to maturity of 10.5883 percent. The bond pays coupons semiannually. What is the bond’scurrent yield?

Lloyd Corporation’s 14 percent coupon rate, semiannual payment, $1,000 par value bonds,which mature in 30 years, are callable 5 years from now at a price of $1,050. The bonds sell at aprice of $1,353.54, and the yield curve is flat. Assuming that interest rates in the economy areexpected to remain at their current level, what is the best estimate of Lloyd’s nominal interestrate on new bonds?

Suppose Ford Motor Company sold an issue of bonds with a 10-year maturity, a $1,000 parvalue, a 10 percent coupon rate, and semiannual interest payments.a. Two years after the bonds were issued, the going rate of interest on bonds such as these fell

to 6 percent. At what price would the bonds sell?b. Suppose that, 2 years after the initial offering, the going interest rate had risen to 12 percent.

At what price would the bonds sell?c. Suppose that the conditions in part a existed—that is, interest rates fell to 6 percent 2 years

after the issue date. Suppose further that the interest rate remained at 6 percent for the next 8 years. What would happen to the price of the Ford Motor Company bonds overtime?

A bond trader purchased each of the following bonds at a yield to maturity of 8 percent. Imme-diately after she purchased the bonds, interest rates fell to 7 percent. What is the percentagechange in the price of each bond after the decline in interest rates? Fill in the following table:

Price @ 8% Price @ 7% Percentage Change

10-year, 10% annual coupon10-year zero5-year zero30-year zero$100 perpetuity

4–14INTEREST RATE SENSITIVITY;

FINANCIAL CALCULATORNEEDED

4–13BOND VALUATION

4–12NOMINAL INTEREST RATE

4–11CURRENT YIELD; FINANCIAL

CALCULATOR NEEDED

4–10YIELD TO MATURITY; FINANCIAL

CALCULATOR NEEDED

4–9BOND YIELDS; FINANCIAL

CALCULATOR NEEDED

4–8YIELD TO CALL

4–7YIELD TO MATURITY

4–6BOND VALUATION



An investor has two bonds in his portfolio. Each bond matures in 4 years, has a face value of$1,000, and has a yield to maturity equal to 9.6 percent. One bond, Bond C, pays an annualcoupon of 10 percent, the other bond, Bond Z, is a zero coupon bond.a. Assuming that the yield to maturity of each bond remains at 9.6 percent over the next 4

years, what will be the price of each of the bonds at the following time periods? Fill in thefollowing table:

t Price of Bond C Price of Bond Z

01234

b. Plot the time path of the prices for each of the two bonds.

Spreadsheet Problem

Start with the partial model in the file Ch 04 P16 Build a Model.xls from the textbook’s website. Rework Problem 4-9. After completing parts a through d, answer the following relatedquestions.e. How would the price of the bond be affected by changing interest rates? (Hint: Conduct a

sensitivity analysis of price to changes in the yield to maturity, which is also the going mar-ket interest rate for the bond. Assume that the bond will be called if and only if the going rateof interest falls below the coupon rate. That is an oversimplification, but assume it anyway forpurposes of this problem.)

f. Now assume that the date is 10/25/2002. Assume further that our 12 percent, 10-year bondwas issued on 7/1/2002, is callable on 7/1/2006 at $1,060, will mature on 6/30/2012, pays in-terest semiannually (January 1 and July 1), and sells for $1,100. Use your spreadsheet to find(1) the bond’s yield to maturity and (2) its yield to call.

4–16BUILD A MODEL:

BOND VALUATION

4–15BOND VALUATION; FINANCIAL

CALCULATOR NEEDED

Spreadsheet Problem 185

Robert Balik and Carol Kiefer are vice-presidents of Mutual of Chicago Insurance Companyand codirectors of the company’s pension fund management division. A major new client, theCalifornia League of Cities, has requested that Mutual of Chicago present an investment semi-nar to the mayors of the represented cities, and Balik and Kiefer, who will make the actual pre-sentation, have asked you to help them by answering the following questions. Because the WaltDisney Company operates in one of the league’s cities, you are to work Disney into the presen-tation.a. What are the key features of a bond?b. What are call provisions and sinking fund provisions? Do these provisions make bonds

more or less risky?c. How is the value of any asset whose value is based on expected future cash flows determined?d. How is the value of a bond determined? What is the value of a 10-year, $1,000 par value

bond with a 10 percent annual coupon if its required rate of return is 10 percent?e. (1) What would be the value of the bond described in part d if, just after it had been issued,

the expected inflation rate rose by 3 percentage points, causing investors to require a 13percent return? Would we now have a discount or a premium bond? (If you do not havea financial calculator, PVIF13%,10 � 0.2946; PVIFA13%,10 � 5.4262.)

(2) What would happen to the bond’s value if inflation fell, and rd declined to 7 percent?Would we now have a premium or a discount bond?

(3) What would happen to the value of the 10-year bond over time if the required rate ofreturn remained at 13 percent, or if it remained at 7 percent? (Hint: With a financialcalculator, enter PMT, I, FV, and N, and then change (override) N to see what happensto the PV as the bond approaches maturity.)

See Ch 04 Show.ppt andCh 04 Mini Case.xls.



Selected Additional References and Cases

Many investment textbooks cover bond valuation models in depthand detail. Some of the better ones are listed in the Chapter 3references.

For some recent works on valuation, seeBey, Roger P., and J. Markham Collins, “The Relationship

between Before- and After-Tax Yields on Financial As-sets,” The Financial Review, August 1988, 313–343.

Taylor, Richard W., “The Valuation of Semiannual BondsBetween Interest Payment Dates,” The Financial Review,August 1988, 365–368.

Tse, K. S. Maurice, and Mark A. White, “The Valuation ofSemiannual Bonds between Interest Payment Dates: ACorrection,” Financial Review, November 1990, 659–662.

The following cases in the Cases in Financial Management series cover many of the valuation concepts contained in Chapter 4.Case 3, “Peachtree Securities, Inc. (B);” Case 43, “Swan

Davis;” Case 49, “Beatrice Peabody;” and Case 56,“Laura Henderson.”

f. (1) What is the yield to maturity on a 10-year, 9 percent, annual coupon, $1,000 par valuebond that sells for $887.00? That sells for $1,134.20? What does the fact that a bondsells at a discount or at a premium tell you about the relationship between rd and thebond’s coupon rate?

(2) What are the total return, the current yield, and the capital gains yield for the discountbond? (Assume the bond is held to maturity and the company does not default on thebond.)

g. What is interest rate (or price) risk? Which bond has more interest rate risk, an annual pay-ment 1-year bond or a 10-year bond? Why?

h. What is reinvestment rate risk? Which has more reinvestment rate risk, a 1-year bond or a10-year bond?

i. How does the equation for valuing a bond change if semiannual payments are made? Findthe value of a 10-year, semiannual payment, 10 percent coupon bond if nominal rd � 13%.(Hint: PVIF6.5%,20 � 0.2838 and PVIFA6.5%,20 � 11.0185.)

j. Suppose you could buy, for $1,000, either a 10 percent, 10-year, annual payment bond or a10 percent, 10-year, semiannual payment bond. They are equally risky. Which would youprefer? If $1,000 is the proper price for the semiannual bond, what is the equilibrium pricefor the annual payment bond?

k. Suppose a 10-year, 10 percent, semiannual coupon bond with a par value of $1,000 is cur-rently selling for $1,135.90, producing a nominal yield to maturity of 8 percent. However,the bond can be called after 5 years for a price of $1,050.(1) What is the bond’s nominal yield to call (YTC)?(2) If you bought this bond, do you think you would be more likely to earn the YTM or the

YTC? Why?l. Disney’s bonds were issued with a yield to maturity of 7.5 percent. Does the yield to matu-

rity represent the promised or expected return on the bond?m. Disney’s bonds were rated AA� by S&P. Would you consider these bonds investment grade

or junk bonds?n. What factors determine a company’s bond rating?o. If this firm were to default on the bonds, would the company be immediately liquidated?

Would the bondholders be assured of receiving all of their promised payments?


187

5

From slightly less than 4000 in early 1995, the Dow surged to 11723 in early 2000. Toput this remarkable 7723-point rise in perspective, consider that the Dow first reached1000 in 1965, then took another 22 years to hit 2000, then four more years to reach3000, and another four to get to 4000 (in 1995). Then, in just over five years, itreached 11723. Thus, in those five years investors made almost twice as much in thestock market as they made in the previous 70 years!

That bull market made it possible for many people to take early retirement, buyexpensive homes, and afford large expenditures such as college tuition. Encouragedby this performance, more and more investors flocked to the market, and today morethan 79 million Americans own stock. Moreover, a rising stock market made it easierand cheaper for corporations to raise equity capital, which facilitated economicgrowth.

However, some observers were concerned that many investors did not realizejust how risky the stock market can be. There was no guarantee that the market wouldcontinue to rise, and even in bull markets some stocks crash and burn. Indeed, severaltimes during 2001 the market fell to below 10000 and surged above 11000. In fact,the market fell all the way to 8236 in the days following the September 11, 2001, ter-rorist attacks.

Note too that while all boats may rise with the tide, the same does not hold forthe stock market—regardless of the trend, some individual stocks make huge gainswhile others suffer substantial losses. For example, in 2001, Lowe’s stock rose morethan 108 percent, but during this same period Enron lost nearly 100 percent of itsvalue.

While it is difficult to predict prices, we are not completely in the dark when itcomes to valuing stocks. After studying this chapter, you should have a reasonablygood understanding of the factors that influence stock prices. With that knowledge—and a little luck—you may be able to find the next Lowe’s and avoid future Enrons.

Stocks and Their Valuation

183

5

In Chapter 4 we examined bonds. We now turn to common and preferred stock, be-ginning with some important background material that helps establish a frameworkfor valuing these securities.

While it is generally easy to predict the cash flows received from bonds, forecast-ing the cash flows on common stocks is much more difficult. However, two fairlystraightforward models can be used to help estimate the “true,” or intrinsic, value of acommon stock: (1) the dividend growth model, which we describe in this chapter, and(2) the total corporate value model, which we explain in Chapter 12.

The concepts and models developed here will also be used when we estimate thecost of capital in Chapter 6. In subsequent chapters, we demonstrate how the cost ofcapital is used to help make many important decisions, especially the decision to investor not invest in new assets. Consequently, it is critically important that you understandthe basics of stock valuation.

Legal Rights and Privileges of Common Stockholders

The common stockholders are the owners of a corporation, and as such they have cer-tain rights and privileges as discussed in this section.

Control of the Firm

Its common stockholders have the right to elect a firm’s directors, who, in turn, electthe officers who manage the business. In a small firm, the largest stockholder typicallyassumes the positions of president and chairperson of the board of directors. In alarge, publicly owned firm, the managers typically have some stock, but their personalholdings are generally insufficient to give them voting control. Thus, the manage-ments of most publicly owned firms can be removed by the stockholders if the man-agement team is not effective.

State and federal laws stipulate how stockholder control is to be exercised. First,corporations must hold an election of directors periodically, usually once a year, withthe vote taken at the annual meeting. Frequently, one-third of the directors are electedeach year for a three-year term. Each share of stock has one vote; thus, the owner of1,000 shares has 1,000 votes for each director.1 Stockholders can appear at the annualmeeting and vote in person, but typically they transfer their right to vote to a secondparty by means of a proxy. Management always solicits stockholders’ proxies and usu-ally gets them. However, if earnings are poor and stockholders are dissatisfied, an out-side group may solicit the proxies in an effort to overthrow management and take con-trol of the business. This is known as a proxy fight. Proxy fights are discussed in detailin Chapter 12.

The Preemptive Right

Common stockholders often have the right, called the preemptive right, to purchaseany additional shares sold by the firm. In some states, the preemptive right is auto-matically included in every corporate charter; in others, it is necessary to insert itspecifically into the charter.

188 CHAPTER 5 Stocks and Their Valuation

The textbook’s web sitecontains an Excel file thatwill guide you through thechapter’s calculations. Thefile for this chapter is Ch 05Tool Kit.xls, and we encour-age you to open the file andfollow along as you read thechapter.

1In the situation described, a 1,000-share stockholder could cast 1,000 votes for each of three directors ifthere were three contested seats on the board. An alternative procedure that may be prescribed in the cor-porate charter calls for cumulative voting. Here the 1,000-share stockholder would get 3,000 votes if therewere three vacancies, and he or she could cast all of them for one director. Cumulative voting helps smallgroups to get representation on the board.

184 Stocks and Their Valuation

The preemptive right enables current stockholders to maintain control and preventsa transfer of wealth from current stockholders to new stockholders. If it were not for thissafeguard, the management of a corporation could issue a large number of additionalshares and purchase these shares itself. Management could thereby seize control of thecorporation and steal value from the current stockholders. For example, suppose 1,000shares of common stock, each with a price of $100, were outstanding, making the totalmarket value of the firm $100,000. If an additional 1,000 shares were sold at $50 a share,or for $50,000, this would raise the total market value to $150,000. When total marketvalue is divided by new total shares outstanding, a value of $75 a share is obtained. Theold stockholders thus lose $25 per share, and the new stockholders have an instant profitof $25 per share. Thus, selling common stock at a price below the market value woulddilute its price and transfer wealth from the present stockholders to those who were al-lowed to purchase the new shares. The preemptive right prevents such occurrences.

What is a proxy fight?

What are the two primary reasons for the existence of the preemptive right?

Types of Common Stock

Although most firms have only one type of common stock, in some instances classi-fied stock is used to meet the special needs of the company. Generally, when specialclassifications are used, one type is designated Class A, another Class B, and so on.Small, new companies seeking funds from outside sources frequently use differenttypes of common stock. For example, when Genetic Concepts went public recently, itsClass A stock was sold to the public and paid a dividend, but this stock had no votingrights for five years. Its Class B stock, which was retained by the organizers of thecompany, had full voting rights for five years, but the legal terms stated that dividendscould not be paid on the Class B stock until the company had established its earningpower by building up retained earnings to a designated level. The use of classifiedstock thus enabled the public to take a position in a conservatively financed growthcompany without sacrificing income, while the founders retained absolute controlduring the crucial early stages of the firm’s development. At the same time, outside in-vestors were protected against excessive withdrawals of funds by the original owners.As is often the case in such situations, the Class B stock was called founders’ shares.

Note that “Class A,” “Class B,” and so on, have no standard meanings. Most firmshave no classified shares, but a firm that does could designate its Class B shares asfounders’ shares and its Class A shares as those sold to the public, while another couldreverse these designations. Still other firms could use stock classifications for entirelydifferent purposes. For example, when General Motors acquired Hughes Aircraft for$5 billion, it paid in part with a new Class H common, GMH, which had limited vot-ing rights and whose dividends were tied to Hughes’s performance as a GM subsidiary.The reasons for the new stock were reported to be (1) that GM wanted to limit votingprivileges on the new classified stock because of management’s concern about a possi-ble takeover and (2) that Hughes employees wanted to be rewarded more directly onHughes’s own performance than would have been possible through regular GM stock.

GM’s deal posed a problem for the NYSE, which had a rule against listing a com-pany’s common stock if the company had any nonvoting common stock outstanding.GM made it clear that it was willing to delist if the NYSE did not change its rules. TheNYSE concluded that such arrangements as GM had made were logical and werelikely to be made by other companies in the future, so it changed its rules to accom-modate GM. In reality, though, the NYSE had little choice. In recent years, the

Types of Common Stock 189

Stocks and Their Valuation 185

Nasdaq market has proven that it can provide a deep, liquid market for commonstocks, and the defection of GM would have hurt the NYSE much more than GM.

As these examples illustrate, the right to vote is often a distinguishing characteris-tic between different classes of stock. Suppose two classes of stock differ in but one re-spect: One class has voting rights but the other does not. As you would expect, thestock with voting rights would be more valuable. In the United States, which has a le-gal system with fairly strong protection for minority stockholders (that is, noncontrol-ling stockholders), voting stock typically sells at a price 4 to 6 percent above that ofotherwise similar nonvoting stock. Thus, if a stock with no voting rights sold for $50,then one with voting rights would probably sell for $52 to $53. In those countries withlegal systems that provide less protection for minority stockholders, the right to voteis far more valuable. For example, voting stock on average sells for 45 percent morethan nonvoting stock in Israel, and for 82 percent more in Italy.

As we noted above, General Motors created its Class H common stock as a partof its acquisition of Hughes Aircraft. This type of stock, with dividends tied to a par-ticular part of a company, is called tracking stock. It also is called target stock. Al-though GM used its tracking stock in an acquisition, other companies are attemptingto use such stock to increase shareholder value. For example, in 1995 US West hadseveral business areas with very different growth prospects, ranging from slow-growth local telephone services to high-growth cellular, cable television, and direc-tory services. US West felt that investors were unable to correctly value its high-growth lines of business, since cash flows from slow-growth and high-growthbusinesses were mingled. To separate the cash flows and to allow separate valuations,the company issued tracking stocks. Other companies in the telephone industry, suchas Sprint, have also issued tracking stock. Similarly, Georgia-Pacific Corp. issuedtracking stock for its timber business, and USX Corp. has tracking stocks for its oil,natural gas, and steel divisions. Despite this trend, many analysts are skeptical as towhether tracking stock increases a company’s total market value. Companies still re-port consolidated financial statements for the entire company, and they have consid-erable leeway in allocating costs and reporting the financial results for the various di-visions, even those with tracking stock. Thus, a tracking stock is not the same as thestock of an independent, stand-alone company.

What are some reasons a company might use classified stock?

The Market for Common Stock

Some companies are so small that their common stocks are not actively traded; theyare owned by only a few people, usually the companies’ managers. Such firms are saidto be privately owned, or closely held, corporations, and their stock is called closelyheld stock. In contrast, the stocks of most larger companies are owned by a large num-ber of investors, most of whom are not active in management. Such companies arecalled publicly owned corporations, and their stock is called publicly held stock.

As we saw in Chapter 1, the stocks of smaller publicly owned firms are not listedon a physical location exchange or Nasdaq; they trade in the over-the-counter (OTC)market, and the companies and their stocks are said to be unlisted. However, largerpublicly owned companies generally apply for listing on a formal exchange, and theyand their stocks are said to be listed. Many companies are first listed on Nasdaq or ona regional exchange, such as the Pacific Coast or Midwest exchanges. Once they be-come large enough to be listed on the “Big Board,” many, but by no means all, choose



to move to the NYSE. One of the largest companies in the world in terms of marketvalue, Microsoft, trades on the Nasdaq market, as do most other high-tech firms.

A recent study found that institutional investors owned more than 60 percent of allpublicly held common stocks. Included are pension plans, mutual funds, foreign in-vestors, insurance companies, and brokerage firms. These institutions buy and sell rel-atively actively, so they account for about 75 percent of all transactions. Thus, institu-tional investors have a heavy influence on the prices of individual stocks.

Types of Stock Market Transactions

We can classify stock market transactions into three distinct types:

1. Trading in the outstanding shares of established, publicly owned companies: the secondarymarket. MicroDrive Inc., a company we analyze throughout the book, has 50 mil-lion shares of stock outstanding. If the owner of 100 shares sells his or her stock,the trade is said to have occurred in the secondary market. Thus, the market foroutstanding shares, or used shares, is the secondary market. The company receivesno new money when sales occur in this market.

2. Additional shares sold by established, publicly owned companies: the primary market. IfMicroDrive decides to sell (or issue) an additional 1 million shares to raise new eq-uity capital, this transaction is said to occur in the primary market.2

3. Initial public offerings by privately held firms: the IPO market. Several years ago, theCoors Brewing Company, which was owned by the Coors family at the time, de-cided to sell some stock to raise capital needed for a major expansion program.3

This type of transaction is called going public—whenever stock in a closely heldcorporation is offered to the public for the first time, the company is said to be go-ing public. The market for stock that is just being offered to the public is called theinitial public offering (IPO) market.

IPOs have received a lot of attention in recent years, primarily because a num-ber of “hot” issues have realized spectacular gains—often in the first few minutes oftrading. Consider the IPO of Boston Rotisserie Chicken, which has since been re-named Boston Market and acquired by McDonald’s. The company’s underwriter,Merrill Lynch, set an offering price of $20 a share. However, because of intensedemand for the issue, the stock’s price rose 75 percent within the first two hours oftrading. By the end of the first day, the stock price had risen by 143 percent, and thecompany’s end-of-the-day market value was $800 million—which was particularlystartling, given that it had recently reported a $5 million loss on only $8.3 millionof sales. More recently, shares of the trendy restaurant chain Planet Hollywoodrose nearly 50 percent in its first day of trading, and when Netscape first hit themarket, its stock’s price hit $70 a share versus an offering price of only $28 a share.4

Table 5-1 lists the best performing and the worst performing IPOs of 2001, andit shows how they performed from their offering dates through year-end 2001. As

The Market for Common Stock 191

2MicroDrive has 60 million shares authorized but only 50 million outstanding; thus, it has 10 million au-thorized but unissued shares. If it had no authorized but unissued shares, management could increase theauthorized shares by obtaining stockholders’ approval, which would generally be granted without any argu-ments.3The stock Coors offered to the public was designated Class B, and it was nonvoting. The Coors family re-tained the founders’ shares, called Class A stock, which carried full voting privileges. The company waslarge enough to obtain an NYSE listing, but at that time the Exchange had a requirement that listed com-mon stocks must have full voting rights, which precluded Coors from obtaining an NYSE listing.4If someone bought Boston Chicken or Planet Hollywood at the initial offering price and sold the sharesshortly thereafter, he or she would have done well. A long-term holder would have fared less well—bothcompanies later went bankrupt. Netscape was in serious trouble, but it was sold to AOL in 1998.

Note that http://finance.yahoo.com provides aneasy way to find stocksmeeting specified criteria.Under the section on StockResearch, select StockScreener. To find the largestcompanies in terms of mar-ket value, for example, goto the pull-down menu forMarket Cap and choose aMinimum of $100 billion.Then click the Find Stocksbutton at the bottom, and itwill return a list of all com-panies with market capital-izations greater than $100billion.


the table shows, not all IPOs are as well received as were Netscape and BostonChicken. Moreover, even if you are able to identify a “hot” issue, it is often difficultto purchase shares in the initial offering. These deals are generally oversubscribed,which means that the demand for shares at the offering price exceeds the number ofshares issued. In such instances, investment bankers favor large institutional in-vestors (who are their best customers), and small investors find it hard, if not im-possible, to get in on the ground floor. They can buy the stock in the after-market,but evidence suggests that if you do not get in on the ground floor, the average IPOunderperforms the overall market over the longer run.5

Before you conclude that it isn’t fair to let only the best customers have thestock in an initial offering, think about what it takes to become a best customer.Best customers are usually investors who have done lots of business in the past withthe investment banking firm’s brokerage department. In other words, they havepaid large sums as commissions in the past, and they are expected to continue do-ing so in the future. As is so often true, there is no free lunch—most of the in-vestors who get in on the ground floor of an IPO have in fact paid for this privilege.

Finally, it is important to recognize that firms can go public without raising anyadditional capital. For example, Ford Motor Company was once owned exclusivelyby the Ford family. When Henry Ford died, he left a substantial part of his stock tothe Ford Foundation. Ford Motor went public when the Foundation later soldsome of its stock to the general public, even though the company raised no capitalin the transaction.

Differentiate between a closely held corporation and a publicly owned corpora-tion.

Differentiate between a listed stock and an unlisted stock.

Differentiate between primary and secondary markets.

What is an IPO?


5See Jay R. Ritter, “The Long-Run Performance of Initial Public Offerings,” Journal of Finance, March1991, Vol. 46, No. 1, 3–27.

Martha Bodyslams WWF

During the week of October 18, 1999, both Martha StewartLiving Omnimedia Inc. and the World Wrestling Federa-tion (WWF) went public in IPOs. This created a lot of pub-lic interest, and it led to media reports comparing the twocompanies. Both deals attracted strong investor demand,and both were well received. In its first day of trading,WWF’s stock closed above $25, an increase of nearly 49 per-cent above its $17 offering price. Martha Stewart did evenbetter—it closed a little above $37, which was 105 percentabove its $18 offering price. This performance led CBSMarketWatch reporter Steve Gelsi to write an online reportentitled, “Martha Bodyslams the WWF!”

Both stocks generated a lot of interest, but when the hypedied down, astute investors recognized that both stocks haverisk. Indeed, one month later, WWF had declined to justabove $21, while Martha Stewart had fallen to $28 a share.Many analysts believe that over the long term WWF mayhave both more upside potential and less risk. However,Martha Stewart has a devoted set of investors, so despite allthe uncertainty, the one certainty is that this battle is farfrom over.

Source: Steve Gelsi, “Martha Bodyslams the WWF,” http://cbs.marketwatch.com, October 19, 1999.


Common Stock Valuation

Common stock represents an ownership interest in a corporation, but to the typicalinvestor a share of common stock is simply a piece of paper characterized by twofeatures:

1. It entitles its owner to dividends, but only if the company has earnings out of whichdividends can be paid, and only if management chooses to pay dividends ratherthan retaining and reinvesting all the earnings. Whereas a bond contains a promiseto pay interest, common stock provides no such promise—if you own a stock, youmay expect a dividend, but your expectations may not in fact be met. To illustrate,Long Island Lighting Company (LILCO) had paid dividends on its common stockfor more than 50 years, and people expected those dividends to continue. However,when the company encountered severe problems a few years ago, it stopped payingdividends. Note, though, that LILCO continued to pay interest on its bonds; if ithad not, then it would have been declared bankrupt, and the bondholders couldpotentially have taken over the company.

2. Stock can be sold at some future date, hopefully at a price greater than the purchaseprice. If the stock is actually sold at a price above its purchase price, the investor

Common Stock Valuation 193

TABLE 5-1 Initial Public Stock Offerings in 2001

% Change from OfferU.S.

Issue Offer Proceeds in 1st Day’s throughIssuer (Business) Date Price (millions) Trading Dec. 31

The Best Performers

Verisity 3/21/01 $ 7.00 $ 26.8 �14.3% �170.7%Magma Design Automation 11/19/01 13.00 63.1 �46.1 �129.2Monolithic System Technology 6/27/01 10.00 50.0 �12.2 �108.0Williams Energy Partners 2/5/01 21.50 98.9 �11.6 �91.2Nassda 12/12/01 11.00 55.0 �40.5 �85.6Accenture 7/18/01 14.50 1,900.2 �4.6 �83.1PDF Solutions 7/26/01 12.00 62.1 �26.3 �77.9Willis Group Holdings 6/11/01 13.50 310.5 �23.0 �73.3Select Medical 4/4/01 9.50 98.3 �6.6 �71.3Odyssey Healthcare 10/30/01 15.00 62.1 �15.0 �68.3

The Worst Performers

Briazz 5/2/01 $ 8.00 $ 16.0 �0.4% �88.9%ATP Oil & Gas 2/5/01 14.00 84.0 0.0 �79.9Investors Capital Holdings 2/8/01 8.00 8.0 �6.1 �64.9Align Technology 1/25/01 13.00 149.5 �33.2 �64.6Torch Offshore 6/7/01 16.00 80.0 �0.4 �62.8Enterraa 1/10/01 4.50 5.2 �4.2 �60.4Tellium 5/17/01 15.00 155.3 �39.5 �57.5Smith & Wollensky Restaurant 5/22/01 8.50 45.0 �8.6 �55.3General Maritime 6/12/01 18.00 144.0 �6.9 �47.2GMX Resources 3/15/01 8.00 10.0 0.0 �46.9

aWent public as Westlinks and changed name later

Source: Kate Kelly, “For IPOs, Market Conditions Go from Decent to Downright Inhospitable,” The Wall Street Journal, January 2, 2002, R8. Copyright ©2001 Dow Jones & Co., Inc. Reprinted by permission of Dow Jones & Co. via Copyright Clearance Center.


will receive a capital gain. Generally, at the time people buy common stocks, theydo expect to receive capital gains; otherwise, they would not purchase the stocks.However, after the fact, one can end up with capital losses rather than capital gains.LILCO’s stock price dropped from $17.50 to $3.75 in one year, so the expected cap-ital gain on that stock turned out to be a huge actual capital loss.

Definitions of Terms Used in Stock Valuation Models

Common stocks provide an expected future cash flow stream, and a stock’s value isfound in the same manner as the values of other financial assets—namely, as the pres-ent value of the expected future cash flow stream. The expected cash flows consist oftwo elements: (1) the dividends expected in each year and (2) the price investors expectto receive when they sell the stock. The expected final stock price includes the returnof the original investment plus an expected capital gain.

We saw in Chapter 1 that managers seek to maximize the values of their firms’stocks. A manager’s actions affect both the stream of income to investors and the riskiness of that stream. Therefore, managers need to know how alternative actionsare likely to affect stock prices. At this point we develop some models to help showhow the value of a share of stock is determined. We begin by defining the followingterms:

Dt � dividend the stockholder expects to receive at the end ofYear t. D0 is the most recent dividend, which has alreadybeen paid; D1 is the first dividend expected, and it will bepaid at the end of this year; D2 is the dividend expected atthe end of two years; and so forth. D1 represents the firstcash flow a new purchaser of the stock will receive. Notethat D0, the dividend that has just been paid, is known withcertainty. However, all future dividends are expected val-ues, so the estimate of Dt may differ among investors.6

P0 � actual market price of the stock today.P̂t � expected price of the stock at the end of each Year t (pro-

nounced “P hat t”). P̂0 is the intrinsic, or fundamental,value of the stock today as seen by the particular investordoing the analysis; ̂P1 is the price expected at the end of oneyear; and so on. Note that P̂0 is the intrinsic value of thestock today based on a particular investor’s estimate of thestock’s expected dividend stream and the riskiness of thatstream. Hence, whereas the market price P0 is fixed and isidentical for all investors, P̂0 could differ among investorsdepending on how optimistic they are regarding the com-pany. The caret, or “hat,” is used to indicate that ̂Pt is an es-timated value. P̂0, the individual investor’s estimate of theintrinsic value today, could be above or below P0, the cur-rent stock price, but an investor would buy the stock only ifhis or her estimate of P̂0 were equal to or greater than P0.


6Stocks generally pay dividends quarterly, so theoretically we should evaluate them on a quarterly basis.However, in stock valuation, most analysts work on an annual basis because the data generally are not pre-cise enough to warrant refinement to a quarterly model. For additional information on the quarterly model,see Charles M. Linke and J. Kenton Zumwalt, “Estimation Biases in Discounted Cash Flow Analysis ofEquity Capital Cost in Rate Regulation,” Financial Management, Autumn 1984, 15–21.


Since there are many investors in the market, there canbe many values for P̂0. However, we can think of a group of“average,” or “marginal,” investors whose actions actuallydetermine the market price. For these marginal investors,P0 must equal P̂0; otherwise, a disequilibrium would exist,and buying and selling in the market would change P0 untilP0 �P̂0 for the marginal investor.

g � expected growth rate in dividends as predicted by a mar-ginal investor. If dividends are expected to grow at a con-stant rate, g is also equal to the expected rate of growth inearnings and in the stock’s price. Different investors mayuse different g’s to evaluate a firm’s stock, but the marketprice, P0, is set on the basis of the g estimated by marginalinvestors.

rs � minimum acceptable, or required, rate of return on thestock, considering both its riskiness and the returns avail-able on other investments. Again, this term generally re-lates to marginal investors. The determinants of rs includethe real rate of return, expected inflation, and risk, as dis-cussed in Chapter 3.

r̂s � expected rate of return that an investor who buys thestock expects to receive in the future. r̂s (pronounced “rhat s”) could be above or below rs, but one would buy thestock only if r̂s were equal to or greater than rs.

r̄s � actual, or realized, after-the-fact rate of return, pro-nounced “r bar s.” You may expect to obtain a return ofr̂s � 15 percent if you buy Exxon Mobil today, but if themarket goes down, you may end up next year with anactual realized return that is much lower, perhaps evennegative.

D1/P0 � expected dividend yield during the coming year. If thestock is expected to pay a dividend of D1 � $1 during thenext 12 months, and if its current price is P0 � $10, thenthe expected dividend yield is $1/$10 � 0.10 � 10%.

� expected capital gains yield during the coming year. Ifthe stock sells for $10 today, and if it is expected to rise to$10.50 at the end of one year, then the expected capitalgain is P̂1 � P0 � $10.50 � $10.00 � $0.50, and theexpected capital gains yield is $0.50/$10 � 0.05 � 5%.

Expected total return � r̂s � expected dividend yield (D1/P0) plus expected capitalgains yield [(P̂1 � P0)/P0]. In our example, the expectedtotal return � r̂s � 10% � 5% � 15%.

Expected Dividends as the Basis for Stock Values

In our discussion of bonds, we found the value of a bond as the present value of inter-est payments over the life of the bond plus the present value of the bond’s maturity (orpar) value:

VB �INT

(1 � rd)1 �INT

(1 � rd)2 � � � � �INT

(1 � rd)N �M

(1 � rd)N.

P̂1 � P0

P0

Common Stock Valuation 195


Stock prices are likewise determined as the present value of a stream of cash flows, andthe basic stock valuation equation is similar to the bond valuation equation. What arethe cash flows that corporations provide to their stockholders? First, think of yourself asan investor who buys a stock with the intention of holding it (in your family) forever. Inthis case, all that you (and your heirs) will receive is a stream of dividends, and the valueof the stock today is calculated as the present value of an infinite stream of dividends:

(5-1)

What about the more typical case, where you expect to hold the stock for a finite period and then sell it—what will be the value of P̂0 in this case? Unless the company islikely to be liquidated or sold and thus to disappear, the value of the stock is again deter-mined by Equation 5-1. To see this, recognize that for any individual investor, the ex-pected cash flows consist of expected dividends plus the expected sale price of the stock.However, the sale price the current investor receives will depend on the dividends somefuture investor expects. Therefore, for all present and future investors in total, expectedcash flows must be based on expected future dividends. Put another way, unless a firm isliquidated or sold to another concern, the cash flows it provides to its stockholders willconsist only of a stream of dividends; therefore, the value of a share of its stock must beestablished as the present value of that expected dividend stream.

The general validity of Equation 5-1 can also be confirmed by asking the follow-ing question: Suppose I buy a stock and expect to hold it for one year. I will receivedividends during the year plus the value P̂1 when I sell out at the end of the year. Butwhat will determine the value of P̂1? The answer is that it will be determined as thepresent value of the dividends expected during Year 2 plus the stock price at the end ofthat year, which, in turn, will be determined as the present value of another set of fu-ture dividends and an even more distant stock price. This process can be continued adinfinitum, and the ultimate result is Equation 5-1.7

Explain the following statement: “Whereas a bond contains a promise to pay in-terest, a share of common stock typically provides an expectation of, but nopromise of, dividends plus capital gains.”

What are the two parts of most stocks’ expected total return?

How does one calculate the capital gains yield and the dividend yield of a stock?

Constant Growth Stocks

Equation 5-1 is a generalized stock valuation model in the sense that the time patternof Dt can be anything: Dt can be rising, falling, fluctuating randomly, or it can even bezero for several years, and Equation 5-1 will still hold. With a computer spreadsheet

� a�

t�1

Dt

(1 � rs)t.

�D1

(1 � rs)1 �

D2

(1 � rs)2 � � � � �

D�

(1 � rs)�

Value of stock � P̂0 � PV of expected future dividends


7We should note that investors periodically lose sight of the long-run nature of stocks as investments andforget that in order to sell a stock at a profit, one must find a buyer who will pay the higher price. If you an-alyze a stock’s value in accordance with Equation 5-1, conclude that the stock’s market price exceeds a rea-sonable value, and then buy the stock anyway, then you would be following the “bigger fool” theory of investment—you think that you may be a fool to buy the stock at its excessive price, but you also think thatwhen you get ready to sell it, you can find someone who is an even bigger fool. The bigger fool theory waswidely followed in the spring of 2000, just before the Nasdaq market lost more than one-third of its value.


we can easily use this equation to find a stock’s intrinsic value for any pattern of divi-dends. In practice, the hard part is getting an accurate forecast of the future dividends.However, in many cases, the stream of dividends is expected to grow at a constant rate.If this is the case, Equation 5-1 may be rewritten as follows:8

(5-2)

The last term of Equation 5-2 is called the constant growth model, or the Gordonmodel after Myron J. Gordon, who did much to develop and popularize it.

Note that a necessary condition for the derivation of Equation 5-2 is that rs begreater than g. Look back at the second form of Equation 5-2. If g is larger than rs,then (1 � g)t/(1 � rs)

t must always be greater than one. In this case, the second line ofEquation 5-2 is the sum of an infinite number of terms, with each term being a num-ber larger than one. Therefore, if the constant g were greater than rs, the resultingstock price would be infinite! Since no company is worth an infinite price, it is impos-sible to have a constant growth rate that is greater than rs. So, if you try to use the con-stant growth model in a situation where g is greater than rs, you will violate laws of economicsand mathematics, and your results will be both wrong and meaningless.

Illustration of a Constant Growth Stock

Assume that MicroDrive just paid a dividend of $1.15 (that is, D0 � $1.15). Its stockhas a required rate of return, rs, of 13.4 percent, and investors expect the dividend togrow at a constant 8 percent rate in the future. The estimated dividend one year hencewould be D1 � $1.15(1.08) � $1.24; D2 would be $1.34; and the estimated dividendfive years hence would be $1.69:

Dt � D0(1 � g)t � $1.15(1.08)5 � $1.69.

We could use this procedure to estimate each future dividend, and then use Equation5-1 to determine the current stock value, P̂0. In other words, we could find each ex-pected future dividend, calculate its present value, and then sum all the present valuesto find the intrinsic value of the stock.

Such a process would be time consuming, but we can take a short cut—just insertthe illustrative data into Equation 5-2 to find the stock’s intrinsic value, $23:

.

The concept underlying the valuation process for a constant growth stock isgraphed in Figure 5-1. Dividends are growing at the rate g � 8%, but because rs �g, the present value of each future dividend is declining. For example, the dividendin Year 1 is D1 � D0(1 � g)1 � $1.15(1.08) � $1.242. However, the present value ofthis dividend, discounted at 13.4 percent, is PV(D1) � $1.242/(1.134)1 � $1.095.

P̂0 �$1.15(1.08)

0.134 � 0.08�

$1.2420.054

� $23.00

�D0(1 � g)

rs � g�

D1

rs � g.

� D0a�

t�1

(1 � g)t

(1 � rs)t

P̂0 �D0(1 � g)1

(1 � rs)1 �

D0(1 � g)2

(1 � rs)2 � � � � �

D0(1 � g)�

(1 � rs)�

Constant Growth Stocks 197

8The last term in Equation 5-2 is derived in the Extensions to Chapter 5 of Eugene F. Brigham and Phillip R. Daves, Intermediate Financial Management, 7th ed. (Fort Worth, TX: Harcourt College Publish-ers, 2002). In essence, Equation 5-2 is the sum of a geometric progression, and the final result is the solution value of the progression.


The dividend expected in Year 2 grows to $1.242(1.08) � $1.341, but the presentvalue of this dividend falls to $1.043. Continuing, D3 � $1.449 and PV(D3) �$0.993, and so on. Thus, the expected dividends are growing, but the present valueof each successive dividend is declining, because the dividend growth rate (8%) isless than the rate used for discounting the dividends to the present (13.4%).

If we summed the present values of each future dividend, this summation wouldbe the value of the stock, P̂0. When g is a constant, this summation is equal toD1/(rs � g), as shown in Equation 5-2. Therefore, if we extended the lower step func-tion curve in Figure 5-1 on out to infinity and added up the present values of eachfuture dividend, the summation would be identical to the value given by Equation5-2, $23.00.

Although Equation 5-2 assumes that dividends grow to infinity, most of the value isbased on dividends during a relatively short time period. In our example, 70 percent ofthe value is attributed to the first 25 years, 91 percent to the first 50 years, and 99.4 per-cent to the first 100 years. So, companies don’t have to live forever for the Gordongrowth model to be used.

Dividend and Earnings Growth

Growth in dividends occurs primarily as a result of growth in earnings per share (EPS).Earnings growth, in turn, results from a number of factors, including (1) inflation, (2)the amount of earnings the company retains and reinvests, and (3) the rate of return thecompany earns on its equity (ROE). Regarding inflation, if output (in units) is stable,but both sales prices and input costs rise at the inflation rate, then EPS will also grow at


Dividend($)

1.15PV D = 1.10

0 5 10 15 20

PV of Each Dividend =D (1 + g)

(1 + r )

= Area under PV Curve= $23.00

Dollar Amount of Each Dividend= D (1 + g)

t

t

1

0

t0

s

Years

tPV DP = ∑

8

t = 1

ˆ0

FIGURE 5-1 Present Values of Dividends of a Constant Growth Stockwhere D0 � $1.15, g � 8%, rs � 13.4%


the inflation rate. Even without inflation, EPS will also grow as a result of the reinvest-ment, or plowback, of earnings. If the firm’s earnings are not all paid out as dividends(that is, if some fraction of earnings is retained), the dollars of investment behind eachshare will rise over time, which should lead to growth in earnings and dividends.

Even though a stock’s value is derived from expected dividends, this does not nec-essarily mean that corporations can increase their stock prices by simply raising thecurrent dividend. Shareholders care about all dividends, both current and thoseexpected in the future. Moreover, there is a trade-off between current dividends andfuture dividends. Companies that pay high current dividends necessarily retain andreinvest less of their earnings in the business, and that reduces future earnings and div-idends. So, the issue is this: Do shareholders prefer higher current dividends at the costof lower future dividends, the reverse, or are stockholders indifferent? There is no sim-ple answer to this question. Shareholders prefer to have the company retain earnings,hence pay less current dividends, if it has highly profitable investment opportunities,but they want the company to pay earnings out if investment opportunities are poor.Taxes also play a role—since dividends and capital gains are taxed differently, dividendpolicy affects investors’ taxes. We will consider dividend policy in detail in Chapter 14.

Do Stock Prices Reflect Long-Term or Short-Term Events?

Managers often complain that the stock market is shortsighted, and that it cares onlyabout next quarter’s performance. Let’s use the constant growth model to test this as-sertion. MicroDrive’s most recent dividend was $1.15, and it is expected to grow at arate of 8 percent per year. Since we know the growth rate, we can forecast the divi-dends for each of the next five years and then find their present values:

Recall that MicroDrive’s stock price is $23.00. Therefore, only $5.00, or 22 percent,of the $23.00 stock price is attributable to short-term cash flows. This means thatMicroDrive’s managers will have a bigger effect on the stock price if they work toincrease long-term cash flows rather than focus on short-term flows. This situationholds for most companies. Indeed, a number of professors and consulting firms haveused actual company data to show that more than 80 percent of a typical company’sstock price is due to cash flows expected more than five years in the future.

This brings up an interesting question. If most of a stock’s value is due to long-term cash flows, why do managers and analysts pay so much attention to quarterlyearnings? Part of the answer lies in the information conveyed by short-term earnings.For example, if actual quarterly earnings are lower than expected, not because of fun-damental problems but only because a company has increased its R&D expenditures,studies have shown that the stock price probably won’t decline and may actually in-crease. This makes sense, because R&D should increase future cash flows. On theother hand, if quarterly earnings are lower than expected because customers don’t likethe company’s new products, then this new information will have negative implica-tions for future values of g, the long-term growth rate. As we show later in thischapter, even small changes in g can lead to large changes in stock prices. Therefore,

� $5.00. � 1.095 � 1.043 � 0.993 � 0.946 � 0.901

�$1.242(1.134)1 �

$1.341(1.134)2 �

$1.449(1.134)3 �

$1.565(1.134)4 �

$1.690(1.134)5

�$1.15(1.08)1

(1.134)1 �$1.15(1.08)2

(1.134)2 �$1.15(1.08)3

(1.134)3 �$1.15(1.08)4

(1.134)4 �$1.15(1.08)5

(1.134)5

PV �D0(1 � g)1

(1 � rs)1 �

D0(1 � g)2

(1 � rs)2 �

D0(1 � g)3

(1 � rs)3 �

D0(1 � g)4

(1 � rs)4 �

D0(1 � g)5

(1 � rs)5

Constant Growth Stocks 199


while the quarterly earnings themselves might not be very important, the informationthey convey about future prospects can be terribly important.

Another reason many managers focus on short-term earnings is that some firmspay managerial bonuses on the basis of current earnings rather than stock prices(which reflect future earnings). For these managers, the concern with quarterly earn-ings is not due to their effect on stock prices—it’s due to their effect on bonuses.9

When Can the Constant Growth Model Be Used?

The constant growth model is often appropriate for mature companies with a stablehistory of growth. Expected growth rates vary somewhat among companies, but divi-dend growth for most mature firms is generally expected to continue in the future atabout the same rate as nominal gross domestic product (real GDP plus inflation). Onthis basis, one might expect the dividends of an average, or “normal,” company togrow at a rate of 5 to 8 percent a year.

Note too that Equation 5-2 is sufficiently general to handle the case of a zerogrowth stock, where the dividend is expected to remain constant over time. If g � 0,Equation 5-2 reduces to Equation 5-3:

(5-3)

This is essentially the same equation as the one we developed in Chapter 2 for a per-petuity, and it is simply the dividend divided by the discount rate.

Write out and explain the valuation formula for a constant growth stock.

Explain how the formula for a zero growth stock is related to that for a constantgrowth stock.

Are stock prices affected more by long-term or short-term events?

Expected Rate of Return on a Constant Growth Stock

We can solve Equation 5-2 for rs, again using the hat to indicate that we are dealingwith an expected rate of return:10

(5-4)

Thus, if you buy a stock for a price P0 � $23, and if you expect the stock to pay adividend D1 � $1.242 one year from now and to grow at a constant rate g � 8% in thefuture, then your expected rate of return will be 13.4 percent:

r̂s �$1.242

$23� 8% � 5.4% � 8% � 13.4%.

g.�D1

P0�r̂s

Expected rate Expected Expected growthof return � dividend � rate, or capital

yield gains yield

P̂0 �Drs

.


9Many apparent puzzles in finance can be explained either by managerial compensation systems or by pecu-liar features of the Tax Code. So, if you can’t explain a firm’s behavior in terms of economic logic, look tobonuses or taxes as possible explanations.10The rs value in Equation 5-2 is a required rate of return, but when we transform to obtain Equation 5-4, we are finding an expected rate of return. Obviously, the transformation requires that rs � r̂s. This equal-ity holds if the stock market is in equilibrium, a condition that will be discussed later in the chapter.


In this form, we see that r̂s is the expected total return and that it consists of an ex-pected dividend yield, D1/P0 � 5.4%, plus an expected growth rate or capital gains yield,g � 8%.

Suppose this analysis had been conducted on January 1, 2003, so P0 � $23 is theJanuary 1, 2003, stock price, and D1 � $1.242 is the dividend expected at the end of2003. What is the expected stock price at the end of 2003? We would again applyEquation 5-2, but this time we would use the year-end dividend, D2 � D1 (1 � g) �$1.242(1.08) � $1.3414:

Now, note that $24.84 is 8 percent larger than P0, the $23 price on January 1, 2003:

$23(1.08) � $24.84.

Thus, we would expect to make a capital gain of $24.84 � $23.00 � $1.84 during2003, which would provide a capital gains yield of 8 percent:

We could extend the analysis on out, and in each future year the expected capital gainsyield would always equal g, the expected dividend growth rate.

Continuing, the dividend yield in 2004 could be estimated as follows:

The dividend yield for 2005 could also be calculated, and again it would be 5.4 per-cent. Thus, for a constant growth stock, the following conditions must hold:

1. The dividend is expected to grow forever at a constant rate, g.2. The stock price is expected to grow at this same rate.3. The expected dividend yield is a constant.4. The expected capital gains yield is also a constant, and it is equal to g.5. The expected total rate of return, r̂s, is equal to the expected dividend yield plus the

expected growth rate: r̂s � dividend yield � g.

The term expected should be clarified—it means expected in a probabilistic sense, asthe “statistically expected” outcome. Thus, if we say the growth rate is expected to re-main constant at 8 percent, we mean that the best prediction for the growth rate inany future year is 8 percent, not that we literally expect the growth rate to be exactly 8percent in each future year. In this sense, the constant growth assumption is a reason-able one for many large, mature companies.

What conditions must hold if a stock is to be evaluated using the constantgrowth model?

What does the term “expected” mean when we say expected growth rate?

Valuing Stocks That Have a Nonconstant Growth Rate

For many companies, it is inappropriate to assume that dividends will grow at a con-stant rate. Firms typically go through life cycles. During the early part of their lives,their growth is much faster than that of the economy as a whole; then they match the

Dividend yield2003 �D2004

P̂12/31/03

�$1.3414$24.84

� 0.054 � 5.4%.

Capital gains yield2003 � Capital gain

Beginning price �

$1.84$23.00

� 0.08 � 8%.

P̂12/31/03 �D2004

rs � g�

$1.34140.134 � 0.08

� $24.84.

Valuing Stocks That Have a Nonconstant Growth Rate 201

The popular Motley Foolweb site http://www.fool.com/school/introductiontovaluation.htm provides a good de-scription of some of thebenefits and drawbacks of afew of the more commonlyused valuation procedures.


economy’s growth; and finally their growth is slower than that of the economy.11

Automobile manufacturers in the 1920s, computer software firms such as Microsoft inthe 1990s, and Internet firms such as AOL in the 2000s are examples of firms in theearly part of the cycle; these firms are called supernormal, or nonconstant, growthfirms. Figure 5-2 illustrates nonconstant growth and also compares it with normalgrowth, zero growth, and negative growth.12

In the figure, the dividends of the supernormal growth firm are expected togrow at a 30 percent rate for three years, after which the growth rate is expectedto fall to 8 percent, the assumed average for the economy. The value of this firm,like any other, is the present value of its expected future dividends as determinedby Equation 5-1. When Dt is growing at a constant rate, we simplified Equation5-1 to P̂0 � D1/(rs � g). In the supernormal case, however, the expected growthrate is not a constant—it declines at the end of the period of supernormalgrowth.


11The concept of life cycles could be broadened to product cycle, which would include both small startupcompanies and large companies like Procter & Gamble, which periodically introduce new products thatgive sales and earnings a boost. We should also mention business cycles, which alternately depress and boostsales and profits. The growth rate just after a major new product has been introduced, or just after a firmemerges from the depths of a recession, is likely to be much higher than the “expected long-run averagegrowth rate,” which is the proper number for a DCF analysis.12A negative growth rate indicates a declining company. A mining company whose profits are falling be-cause of a declining ore body is an example. Someone buying such a company would expect its earnings, andconsequently its dividends and stock price, to decline each year, and this would lead to capital losses ratherthan capital gains. Obviously, a declining company’s stock price will be relatively low, and its dividend yieldmust be high enough to offset the expected capital loss and still produce a competitive total return. Studentssometimes argue that they would never be willing to buy a stock whose price was expected to decline. How-ever, if the annual dividends are large enough to more than offset the falling stock price, the stock could stillprovide a good return.

FIGURE 5-2 Illustrative Dividend Growth Rates

Dividend($)

1.15

Declining Growth, –8%

Zero Growth, 0%

Normal Growth, 8%

Normal Growth, 8%

End of SupernormalGrowth Period

Supernormal Growth, 30%

0 1 2 3 4 5

Years


Because Equation 5-2 requires a constant growth rate, we obviously cannot use itto value stocks that have nonconstant growth. However, assuming that a companycurrently enjoying supernormal growth will eventually slow down and become a con-stant growth stock, we can combine Equations 5-1 and 5-2 to form a new formula,Equation 5-5, for valuing it. First, we assume that the dividend will grow at a noncon-stant rate (generally a relatively high rate) for N periods, after which it will grow at aconstant rate, g. N is often called the terminal date, or horizon date.

We can use the constant growth formula, Equation 5-2, to determine what thestock’s horizon, or terminal, value will be N periods from today:

(5-2a)

The stock’s intrinsic value today, P̂0, is the present value of the dividends during thenonconstant growth period plus the present value of the horizon value:

(5-5)

To implement Equation 5-5, we go through the following three steps:

1. Find the PV of the dividends during the period of nonconstant growth.2. Find the price of the stock at the end of the nonconstant growth period, at which

point it has become a constant growth stock, and discount this price back to thepresent.

3. Add these two components to find the intrinsic value of the stock, P̂0.

Figure 5-3 can be used to illustrate the process for valuing nonconstant growth stocks.Here we assume the following five facts exist:

rs � stockholders’ required rate of return � 13.4%. This rate is used to discountthe cash flows.

N � years of supernormal growth � 3.gs � rate of growth in both earnings and dividends during the supernormal

growth period � 30%. This rate is shown directly on the time line. Note:The growth rate during the supernormal growth period could vary fromyear to year. Also, there could be several different supernormal growthperiods, e.g., 30% for three years, then 20% for three years, and then aconstant 8%.)

gn � rate of normal, constant growth after the supernormal period � 8%. Thisrate is also shown on the time line, between Periods 3 and 4.

D0 � last dividend the company paid � $1.15.

PV of horizonvalue, P̂N:

[(DN�1)/(rs � g)]

(1 � rs)N.

PV of dividends during thenonconstant growth period

t � 1, � � � N.

P̂N

(1 � rs)N.P̂0 �

D1

(1 � rs)1 �

D2

(1 � rs)2 � � � � �

DN

(1 � rs)N �

PV of dividends during theconstant growth period

t � N � 1, � � � �.

PV of dividends during thenonconstant growth period

t � 1, � � � N.

P̂0 �D1

(1 � rs)1 �

D2

(1 � rs)2 � � � � �

DN

(1 � rs)N �

DN�1

(1 � rs)N�1 � � � � �

D�

(1 � rs)�.

Horizon value � P̂N �DN�1

rs � g�

DN(1 � g)rs � g

Valuing Stocks That Have a Nonconstant Growth Rate 203


0 gs � 30% 1 30% 2 30% 3 gn � 8% 4

D1 � 1.4950 D2 � 1.9435 D3 � 2.5266 D4 � 2.7287

1.3183 13.4%

1.5113 13.4% P̂3 � 50.531036.3838 13.4% 53.0576

39.2134 � $39.21 � P̂0


The valuation process as diagrammed in Figure 5-3 is explained in the steps set forthbelow the time line. The value of the supernormal growth stock is calculated to be$39.21.

Explain how one would find the value of a supernormal growth stock.

Explain what is meant by “horizon (terminal) date” and “horizon (terminal) value.”

Market Multiple Analysis

Another method of stock valuation is market multiple analysis, which applies amarket-determined multiple to net income, earnings per share, sales, book value, or,for businesses such as cable TV or cellular telephone systems, the number of sub-scribers. While the discounted dividend method applies valuation concepts in a pre-cise manner, focusing on expected cash flows, market multiple analysis is more judg-mental. To illustrate the concept, suppose that a company’s forecasted earnings per

FIGURE 5-3 Process for Finding the Value of a Supernormal Growth Stock

Notes to Figure 5-3:Step 1. Calculate the dividends expected at the end of each year during the supernormal growth period. Calculate

the first dividend, D1 � D0(1 � gs) � $1.15(1.30) � $1.4950. Here gs is the growth rate during the three-year supernormal growth period, 30 percent. Show the $1.4950 on the time line as the cash flow at Time 1.Then, calculate D2 � D1(1 � gs) � $1.4950(1.30) � $1.9435, and then D3 � D2(1 � gs) � $1.9435(1.30) �$2.5266. Show these values on the time line as the cash flows at Time 2 and Time 3. Note that D0 is usedonly to calculate D1.

Step 2. The price of the stock is the PV of dividends from Time 1 to infinity, so in theory we could project each fu-ture dividend, with the normal growth rate, gn � 8%, used to calculate D4 and subsequent dividends. How-ever, we know that after D3 has been paid, which is at Time 3, the stock becomes a constant growth stock.Therefore, we can use the constant growth formula to find P̂3, which is the PV of the dividends from Time 4to infinity as evaluated at Time 3.

First, we determine D4 � $2.5266(1.08) � $2.7287 for use in the formula, and then we calculate P̂3 asfollows:

We show this $50.5310 on the time line as a second cash flow at Time 3. The $50.5310 is a Time 3 cashflow in the sense that the owner of the stock could sell it for $50.5310 at Time 3 and also in the sense that$50.5310 is the present value of the dividend cash flows from Time 4 to infinity. Note that the total cashflow at Time 3 consists of the sum of D3 � P̂3 � $2.5266 � $50.5310 � $53.0576.

Step 3. Now that the cash flows have been placed on the time line, we can discount each cash flow at the requiredrate of return, rs � 13.4%. We could discount each flow by dividing by (1.134)t, where t � 1 for Time 1, t � 2 for Time 2, and t � 3 for Time 3. This produces the PVs shown to the left below the time line, and thesum of the PVs is the value of the supernormal growth stock, $39.21.

With a financial calculator, you can find the PV of the cash flows as shown on the time line with the cash flow (CFLO) register of your calculator. Enter 0 for CF0 because you get no cash flow at Time 0, CF1 � 1.495, CF2 � 1.9435, and CF3 � 2.5266 � 50.531 � 53.0576. Then enter I � 13.4, and press theNPV key to find the value of the stock, $39.21.

P̂3 �D4

rs � gn�

$2.72870.134 � 0.08

� $50.5310.

↑

↑

↑


share is $7.70 in 2003. The average price per share to earnings per share (P/E) ratiofor similar publicly traded companies is 12.

To estimate the company’s stock value using the market P/E multiple approach,simply multiply its $7.70 earnings per share by the market multiple of 12 to obtain thevalue of $7.70(12) � $92.40. This is its estimated stock price per share.

Note that measures other than net income can be used in the market multiple ap-proach. For example, another commonly used measure is earnings before interest, taxes,depreciation, and amortization (EBITDA). The EBITDA multiple is the total value of acompany (the market value of equity plus debt) divided by EBITDA. This multiple isbased on total value, since EBITDA measures the entire firm’s performance. There-fore, it is called an entity multiple. The EBITDA market multiple is the averageEBITDA multiple for similar publicly traded companies. Multiplying a company’sEBITDA by the market multiple gives an estimate of the company’s total value. Tofind the company’s estimated stock price per share, subtract debt from total value, andthen divide by the number of shares of stock.

As noted above, in some businesses such as cable TV and cellular telephone, animportant element in the valuation process is the number of customers a company has.For example, telephone companies have been paying about $2,000 per customer whenacquiring cellular operators. Managed care companies such as HMOs have appliedsimilar logic in acquisitions, basing their valuations on the number of people insured.Some Internet companies have been valued by the number of “eyeballs,” which is thenumber of hits on the site.

What is market multiple analysis?

What is an entity multiple?

Stock Market Equilibrium

Recall that ri, the required return on Stock i, can be found using the Security MarketLine (SML) equation as it was developed in our discussion of the Capital Asset Pric-ing Model (CAPM) back in Chapter 3:

ri � rRF � (rM � rRF)bi.

If the risk-free rate of return is 8 percent, the required return on an average stock is 12percent, and Stock i has a beta of 2, then the marginal investor will require a return of16 percent on Stock i:

ri � 8% � (12% � 8%) 2.0� 16%

This 16 percent required return is shown as the point on the SML in Figure 5-4associated with beta � 2.0.

The marginal investor will want to buy Stock i if its expected rate of return ismore than 16 percent, will want to sell it if the expected rate of return is less than 16percent, and will be indifferent, hence will hold but not buy or sell, if the expected rateof return is exactly 16 percent. Now suppose the investor’s portfolio contains Stock i,and he or she analyzes the stock’s prospects and concludes that its earnings, dividends,and price can be expected to grow at a constant rate of 5 percent per year. The last div-idend was D0 � $2.8571, so the next expected dividend is

D1 � $2.8571(1.05) � $3.

Our marginal investor observes that the present price of the stock, P0, is $30. Shouldhe or she purchase more of Stock i, sell the stock, or maintain the present position?

Stock Market Equilibrium 205


The investor can calculate Stock i’s expected rate of return as follows:

r̂i � �DP0

1� � g � �

$$330

� � 5% � 15%.

This value is plotted on Figure 5-4 as Point i, which is below the SML. Because theexpected rate of return is less than the required return, this marginal investor wouldwant to sell the stock, as would most other holders. However, few people would wantto buy at the $30 price, so the present owners would be unable to find buyers unlessthey cut the price of the stock. Thus, the price would decline, and this decline wouldcontinue until the price reached $27.27, at which point the stock would be inequilibrium, defined as the price at which the expected rate of return, 16 percent, isequal to the required rate of return:

r̂i � �$2

$73.27� � 5% � 11% � 5% � 16% � ri.

Had the stock initially sold for less than $27.27, say, at $25, events would havebeen reversed. Investors would have wanted to buy the stock because its expected rateof return would have exceeded its required rate of return, and buy orders would havedriven the stock’s price up to $27.27.

To summarize, in equilibrium two related conditions must hold:

1. A stock’s expected rate of return as seen by the marginal investor must equal its re-quired rate of return: r̂i � ri.

2. The actual market price of the stock must equal its intrinsic value as estimated bythe marginal investor: P0 � P̂0.

Of course, some individual investors may believe that r̂i � r and P̂0 � P0, hencethey would invest most of their funds in the stock, while other investors may havean opposite view and would sell all of their shares. However, it is the marginalinvestor who establishes the actual market price, and for this investor, we musthave r̂i � ri and P0 � P̂0. If these conditions do not hold, trading will occur untilthey do.


FIGURE 5-4 Expected and Required Returns on Stock i

Rate of Return(%)

r = 16r = 15

r = 12

r = 8RF

M

i

i

0 1.0 2.0 Risk, bi

SML: ri = rRF + (rM– rRF) bi

>

i



Changes in Equilibrium Stock Prices

Stock prices are not constant—they undergo violent changes at times. For exam-ple, on September 17, 2001, the first day of trading after the terrorist attacks of Septem-ber 11, the Dow Jones average dropped 685 points. This was the largest decline ever inthe Dow, but not the largest percentage loss, which was �22.6 percent on October 19,1987. The Dow has also had some spectacular increases. In fact, its fifth largest increasewas 368 points on September 24, 2001, shortly after its largest-ever decline. The Dow’slargest increase ever was 499 points on April 16, 2000, and its largest percentage gain of15.4 percent occurred on March 15, 1933. At the risk of understatement, the stock mar-ket is volatile!

To see how such changes can occur, assume that Stock i is in equilibrium, selling ata price of $27.27. If all expectations were exactly met, during the next year the pricewould gradually rise to $28.63, or by 5 percent. However, many different events couldoccur to cause a change in the equilibrium price. To illustrate, consider again the set ofinputs used to develop Stock i’s price of $27.27, along with a new set of assumed inputvariables:

13A price change of this magnitude is by no means rare. The prices of many stocks double or halve during ayear. For example, Ciena, a phone equipment maker, fell by 76.1 percent in 1998 but increased by 183 per-cent in 2000. 14It should be obvious by now that actual realized rates of return are not necessarily equal to expected and re-quired returns. Thus, an investor might have expected to receive a return of 15 percent if he or she had boughtCiena stock, but after the fact, the realized return was far above 15 percent in 2000 and was far below in 1998.

Variable Value

Original New

Risk-free rate, rRF 8% 7%Market risk premium, rM � rRF 4% 3%Stock i’s beta coefficient, bi 2.0 1.0Stock i’s expected growth rate, gi 5% 6%D0 $2.8571 $2.8571Price of Stock i $27.27 ?

Now give yourself a test: How would the change in each variable, by itself, affect theprice, and what is your guess as to the new stock price?

Every change, taken alone, would lead to an increase in the price. The first threechanges all lower ri, which declines from 16 to 10 percent:

Original ri � 8% � 4%(2.0) � 16%.New ri � 7% � 3%(1.0) � 10%.

Using these values, together with the new g value, we find that P̂0 rises from $27.27 to$75.71.13

At the new price, the expected and required rates of return are equal:14

r̂i �$3.0285$75.71

� 6% � 10% � ri.

New P̂0 �$2.8571(1.06)0.10 � 0.06

�$3.0285

0.04� $75.71.

Original P̂0 �$2.8571(1.05)0.16 � 0.05

�$3

0.11� $27.27.



As this example illustrates, even small changes in the size or riskiness of expectedfuture dividends can cause large changes in stock prices. What might cause investorsto change their expectations about future dividends? It could be new informationabout the company, such as preliminary results for an R&D program, initial sales of anew product, or the discovery of harmful side effects from the use of an existing prod-uct. Or, new information that will affect many companies could arrive, such as a tight-ening of interest rates by the Federal Reserve. Given the existence of computers andtelecommunications networks, new information hits the market on an almost contin-uous basis, and it causes frequent and sometimes large changes in stock prices. Inother words, ready availability of information causes stock prices to be volatile!

If a stock’s price is stable, that probably means that little new information is arriving.But if you think it’s risky to invest in a volatile stock, imagine how risky it would be to in-vest in a stock that rarely released new information about its sales or operations. It maybe bad to see your stock’s price jump around, but it would be a lot worse to see a stablequoted price most of the time but then to see huge moves on the rare days when new in-formation was released. Fortunately, in our economy timely information is readilyavailable, and evidence suggests that stocks, especially those of large companies, adjustrapidly to new information. Consequently, equilibrium ordinarily exists for any givenstock, and required and expected returns are generally equal. Stock prices certainlychange, sometimes violently and rapidly, but this simply reflects changing conditionsand expectations. There are, of course, times when a stock appears to react for severalmonths to favorable or unfavorable developments. However, this does not signify along adjustment period; rather, it simply indicates that as more new pieces of informa-tion about the situation become available, the market adjusts to them. The ability of themarket to adjust to new information is discussed in the next section.

The Efficient Markets Hypothesis

A body of theory called the Efficient Markets Hypothesis (EMH) holds (1) thatstocks are always in equilibrium and (2) that it is impossible for an investor to consis-tently “beat the market.” Essentially, those who believe in the EMH note that there are100,000 or so full-time, highly trained, professional analysts and traders operating inthe market, while there are fewer than 3,000 major stocks. Therefore, if each analystfollowed 30 stocks (which is about right, as analysts tend to specialize in the stocks in aspecific industry), there would on average be 1,000 analysts following each stock. Fur-ther, these analysts work for organizations such as Citibank, Merrill Lynch, PrudentialInsurance, and the like, which have billions of dollars available with which to take ad-vantage of bargains. In addition, as a result of SEC disclosure requirements and elec-tronic information networks, as new information about a stock becomes available, these1,000 analysts generally receive and evaluate it at about the same time. Therefore, theprice of a stock will adjust almost immediately to any new development.

Levels of Market Efficiency

If markets are efficient, stock prices will rapidly reflect all available information. Thisraises an important question: What types of information are available and, therefore,incorporated into stock prices? Financial theorists have discussed three forms, or lev-els, of market efficiency.

Weak-Form Efficiency The weak form of the EMH states that all information con-tained in past price movements is fully reflected in current market prices. If this weretrue, then information about recent trends in stock prices would be of no use inselecting stocks—the fact that a stock has risen for the past three days, for example,


would give us no useful clues as to what it will do today or tomorrow. People who be-lieve that weak-form efficiency exists also believe that “tape watchers” and “chartists”are wasting their time.15

For example, after studying the past history of the stock market, a chartist might“discover” the following pattern: If a stock falls three consecutive days, its price typicallyrises 10 percent the following day. The technician would then conclude that investorscould make money by purchasing a stock whose price has fallen three consecutive days.

But if this pattern truly existed, wouldn’t other investors also discover it, and if so,why would anyone be willing to sell a stock after it had fallen three consecutive days ifhe or she knows its price is expected to increase by 10 percent the next day? In otherwords, if a stock is selling at $40 per share after falling three consecutive days, whywould investors sell the stock if they expected it to rise to $44 per share one day later?Those who believe in weak-form efficiency argue that if the stock was really likely torise to $44 tomorrow, its price today would actually rise to somewhere near $44 imme-diately, thereby eliminating the trading opportunity. Consequently, weak-form effi-ciency implies that any information that comes from past stock prices is rapidly incorporated into the current stock price.

Semistrong-Form Efficiency The semistrong form of the EMH states that currentmarket prices reflect all publicly available information. Therefore, if semistrong-formefficiency exists, it would do no good to pore over annual reports or other published databecause market prices would have adjusted to any good or bad news contained in suchreports back when the news came out. With semistrong-form efficiency, investorsshould expect to earn the returns predicted by the SML, but they should not expect to doany better unless they have either good luck or information that is not publicly available.However, insiders (for example, the presidents of companies) who have informationthat is not publicly available can earn consistently abnormal returns (returns higher thanthose predicted by the SML) even under semistrong-form efficiency.

Another implication of semistrong-form efficiency is that whenever information isreleased to the public, stock prices will respond only if the information is different fromwhat had been expected. If, for example, a company announces a 30 percent increase inearnings, and if that increase is about what analysts had been expecting, the announce-ment should have little or no effect on the company’s stock price. On the other hand,the stock price would probably fall if analysts had expected earnings to increase by morethan 30 percent, but it probably would rise if they had expected a smaller increase.

Strong-Form Efficiency The strong form of the EMH states that current marketprices reflect all pertinent information, whether publicly available or privately held. Ifthis form holds, even insiders would find it impossible to earn consistently abnormalreturns in the stock market.16

Implications of Market Efficiency

What bearing does the EMH have on financial decisions? Since stock prices do seemto reflect public information, most stocks appear to be fairly valued. This does not


15Tape watchers are people who watch the NYSE tape, while chartists plot past patterns of stock pricemovements. Both are called “technical analysts,” and both believe that they can tell if something is happen-ing to the stock that will cause its price to move up or down in the near future.16Several cases of illegal insider trading have made the headlines. These cases involved employees of severalmajor investment banking houses and even an employee of the SEC. In the most famous case, Ivan Boeskyadmitted to making $50 million by purchasing the stock of firms he knew were about to merge. He went tojail, and he had to pay a large fine, but he helped disprove the strong-form EMH.



mean that new developments could not cause a stock’s price to soar or to plummet, butit does mean that stocks in general are neither overvalued nor undervalued—they arefairly priced and in equilibrium. However, there are certainly cases in which corporateinsiders have information not known to outsiders.

If the EMH is correct, it is a waste of time for most of us to analyze stocks by look-ing for those that are undervalued. If stock prices already reflect all publicly availableinformation, and hence are fairly priced, one can “beat the market” consistently onlyby luck, and it is difficult, if not impossible, for anyone to consistently outperform themarket averages. Empirical tests have shown that the EMH is, in its weak and semi-strong forms, valid. However, people such as corporate officers, who have insideinformation, can do better than the averages, and individuals and organizations that areespecially good at digging out information on small, new companies also seem to doconsistently well. Also, some investors may be able to analyze and react more quicklythan others to releases of new information, and these investors may have an advantageover others. However, the buy-sell actions of those investors quickly bring marketprices into equilibrium. Therefore, it is generally safe to assume that r̂i � r, that P̂0 �P0, and that stocks plot on the SML.17

For a stock to be in equilibrium, what two conditions must hold?

What is the Efficient Markets Hypothesis (EMH)?

What are the differences among the three forms of the EMH: (1) weak form, (2)semistrong form, and (3) strong form?

What are the implications of the EMH for financial decisions?

Actual Stock Prices and Returns

Our discussion thus far has focused on expected stock prices and expected rates of return.Anyone who has ever invested in the stock market knows that there can be, and theregenerally are, large differences between expected and realized prices and returns.

Figure 5-5 shows how the market value of a portfolio of stocks has moved in recentyears, and Figure 5-6 shows how total realized returns on the portfolio have varied fromyear to year. The market trend has been strongly up, but it has gone up in some yearsand down in others, and the stocks of individual companies have likewise gone up and

17Market efficiency also has important implications for managerial decisions, especially those pertaining tocommon stock issues, stock repurchases, and tender offers. Stocks appear to be fairly valued, so decisionsbased on the premise that a stock is undervalued or overvalued must be approached with caution. However,managers do have better information about their own companies than outsiders, and this information canlegally be used to the companies’ (but not the managers’) advantage.

We should also note that some Wall Street pros have consistently beaten the market over many years,which is inconsistent with the EMH. An interesting article in the April 3, 1995, issue of Fortune (Terence P. Paré, “Yes, You Can Beat the Market”) argued strongly against the EMH. Paré suggested that each stockhas a fundamental value, but when good or bad news about it is announced, most investors fail to interpretthat news correctly. As a result, stocks are generally priced above or below their long-term values.

Think of a graph with stock price on the vertical axis and years on the horizontal axis. A stock’s fundamen-tal value might be moving up steadily over time as it retains and reinvests earnings. However, its actual pricemight fluctuate about the intrinsic value line, overreacting to good or bad news and indicating departuresfrom equilibrium. Successful value investors, according to the article, use fundamental analysis to identifystocks’ intrinsic values, and then they buy stocks that are undervalued and sell those that are overvalued.

Paré’s argument implies that the market is systematically out of equilibrium and that investors can act onthis knowledge to beat the market. That position may turn out to be correct, but it may also be that thesuperior performance Paré noted simply demonstrates that some people are better at obtaining and inter-preting information than others, or have just had a run of good luck.


Actual Stock Prices and Returns 211

down.18 We know from theory that expected returns, as estimated by a marginal investor, are always positive, but in some years, as Figure 5-6 shows, actual returns arenegative. Of course, even in bad years some individual companies do well, so “the nameof the game” in security analysis is to pick the winners. Financial managers attempt totake actions that will put their companies into the winners’ column, but they don’t

18If we constructed graphs like Figures 5-5 and 5-6 for individual stocks rather than for a large portfolio, fargreater variability would be shown. Also, if we constructed a graph like Figure 5-6 for bonds, it would havethe same general shape, but the bars would be smaller, indicating that gains and losses on bonds are gener-ally smaller than those on stocks. Above-average bond returns occur in years when interest rates decline,and losses occur when interest rates rise sharply.

FIGURE 5-5 S&P 500 Index, 1967–2001

Source: Data taken from various issues of The Wall Street Journal, “Stock Market Data Bank” section.

500

400

300

200

100

01967 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000

Years

700

600

800

1,000

900

1,200

1,400

1,500

1,300

1,100


always succeed. In subsequent chapters, we will examine the actions that managers cantake to increase the odds of their firms doing relatively well in the marketplace.

Investing in International Stocks

As noted in Chapter 3, the U.S. stock market amounts to only about 40 percent of theworld stock market, and this is prompting many U.S. investors to hold at least someforeign stocks. Analysts have long touted the benefits of investing overseas, arguing thatforeign stocks both improve diversification and provide good growth opportunities.For example, after the U.S. stock market rose an average of 17.5 percent a year duringthe 1980s, many analysts thought that the U.S. market in the 1990s was due for a cor-rection, and they suggested that investors should increase their holdings of foreignstocks. To the surprise of many, however, U.S. stocks outperformed foreign stocks inthe 1990s—they gained about 15 percent a year versus only 3 percent for foreign stocks.

Figure 5-7 shows how stocks in different countries performed in 2001. The num-ber on the left indicates how stocks in each country performed in terms of its local cur-rency, while the right numbers show how the country’s stocks performed in terms of theU.S. dollar. For example, in 2001 Swiss stocks fell by 22.02 percent, but the Swiss Francfell by about 7.24 percent versus the U.S. dollar. Therefore, if U.S. investors hadbought Swiss stocks, they would have lost 22.02 percent in Swiss Franc terms, but thoseSwiss Francs would have bought 7.24 percent fewer U.S. dollars, so the effective returnwould have been �29.26 percent. So, the results of foreign investments depend in parton what happens to the exchange rate. Indeed, when you invest overseas, you are mak-ing two bets: (1) that foreign stocks will increase in their local markets and (2) that thecurrencies in which you will be paid will rise relative to the dollar.

Although U.S. stocks have outperformed foreign stocks in recent years, this by nomeans suggests that investors should avoid foreign stocks. Foreign investments stillimprove diversification, and it is inevitable that there will be years when foreign stocksoutperform domestic stocks. When this occurs, U.S. investors will be glad they putsome of their money in overseas markets.


FIGURE 5-6 S&P 500 Index, Total Returns: Dividend Yield � Capital Gain or Loss, 1967–2001

Source: Data taken from various issues of The Wall Street Journal.

Percent

1991 1994 199719881985198219791976197319701967

40

30

20

10

0

–10

–20

–302000

Years


Actual Sto

ck Prices and R

eturns213

FIGURE 5-7 2001 Performance of the Dow Jones Global Stock Indexes

Source: “World Markets Stumble, Leaving Investors Cautious,” The Wall Street Journal, January 2, 2002, R21. ©2002 Dow Jones & Company, Inc. Reprinted by permission of Dow Jones & Co.via Copyright Clearance Center.



Stock Market Reporting

Up until a couple of years ago, the best source of stock quotations was the businesssection of a daily newspaper, such as The Wall Street Journal. One problem with news-papers, however, is that they are only printed once a day. Now it is possible to getquotes all during the day from a wide variety of Internet sources.19 One of the best isYahoo!, and Figure 5-8 shows a detailed quote for Abbott Labs. As the first row of thequote shows, Abbott Labs is traded on the New York Stock Exchange under the sym-bol ABT. The first row also provides links to additional information. The second rowstarts with the price of the last trade. For Abbott Labs, this was 4:03 P.M. on October31, 2001, at a price of $52.98. Note that the price is reported in decimals rather thanfractions, reflecting a recent change in trading conventions. The second row also re-ports the closing price from the previous day ($53.78) and the change from the previ-ous closing price to the current price. For Abbott Labs, the price fell by $0.80, whichwas a 1.49 percent decline. The trading volume during the day was 3,478,100 shares ofstock. In other words, almost 3.5 million shares of Abbott Labs’ stock changed hands.Immediately below the daily volume is the average daily volume for the past threemonths. For Abbott Labs, this was 3.1 million shares, which means that trading onOctober 31 was a little heavier than usual.

The last item in the second row shows that Abbott Labs is scheduled to pay a div-idend on November 15. As shown on the last row, the annual dividend is $0.84 pershare, so the quarterly dividend payment will be $0.21 per share. The third rowshows an ex-dividend date of October 11, meaning that the owner of the stock as ofOctober 10 will receive the dividend, no matter who owns the stock on November15. In other words, the stock trades without the dividend as of October 11. The last

19Most free sources actually provide quotes that are delayed by 15 minutes.

FIGURE 5-8 Stock Quote for Abbott Labs, October 31, 2001

Source: Stock quote for Abbott Labs, 10/31/01. Reprinted by permission. For an update of this quote, go to the web site http://finance.yahoo.com.Enter the ticker symbol for Abbott Labs, ABT, select Detailed from the pull-down menu, and then click the Get button.

ABBOTT LABS (NYSE:ABT)- More Info: News, Profile, Research, Insider, Options, Msgs - Trade: Choose Brokerage

BidN/A

Volume3,478,100

PrevCls

53.78

Earn/Shr1.08

MktCap

82.195B

Div/Shr0.84

P/E49.80

Yield1.56

AskN/A

Ex-DivOct 11

Avg Vol3,149,409

Open53.50

Change-0.80 (-1.49%)

52-week Range42.0000 -56.2500

Day's Range52.98 - 53.99

Last Trade4:03PM · 52.98

DivDate

Nov 15

Small: [1d | 5d | 1y | none]Big: [1d | 5d | 3m | 6m | 1y | 2y | 5y | max]


row also reports a dividend yield of 1.56 percent, which is the dividend divided by thestock price.

The third row reports the range of prices for the day and the first trade of the day,called the open price. Thus, Abbott Labs opened the day at $53.50, traded as low as$52.98 and as high as $53.99, and finally closed at $52.98, its low for the day. If AbbottLabs had been listed on Nasdaq, the most recent bid and ask quotes from dealerswould have been shown. Because Abbott Labs trades on the NYSE, this data is notavailable.

The bottom row shows the price range of Abbott Labs’ stock during the past year,which was from $42.00 to $56.25. The chart to the right shows the daily prices forthe past year, and the links below the chart allow a web user to pick different intervalsfor data in the chart. The bottom row also reports the earnings per share, based onthe earnings in the past 12 months. The ratio of the price per share to the earningsper share, the P/E ratio, is shown on the bottom row. For Abbott Labs, this is 49.80.The total market value of all its stock is called Mkt Cap, and it is $82.195 billion.

If a stock is not in equilibrium, explain how financial markets adjust to bring itinto equilibrium.

Explain why expected, required, and realized returns are often different.

What are the key benefits of adding foreign stocks to a portfolio?

When a U.S. investor purchases foreign stocks, what two things is he or she hop-ing will happen?

Actual Stock Prices and Returns 215

A Nation of Traders

A recent story in Fortune profiled the dramatic revolution inthe way investors trade stocks. Just a few years ago, the vastmajority of investors bought and sold stocks by calling a full-service broker. The typical broker would execute orders,maintain records, assist with stock selection, and provideguidance regarding long-run asset allocations. These ser-vices came at a price—when investors bought stocks, thecommissions were often well in excess of $100 a trade.

While the full-service broker is far from dead, many areon the ropes. Now large and small investors have online ac-cess to the same type of company and market informationthat brokers provide, and they can trade stocks online at lessthan $10 a trade.

These technological changes, combined with the eupho-ria surrounding the long-running bull market, have encour-aged more and more investors to become actively involvedin managing their own investments. They tune in regularlyto CNBC, and they keep their computer screens “at theready” to trade on any new information that hits the market.

Online trading is by no means relegated to just a few investors—it now represents a significant percentage of alltrades that occur. The Fortune article pointed out, for exam-ple, that in 1989 only 28 percent of households owned stock,

while 10 years later this percentage had risen to 48 percent.Moreover, in 1999 there were 150 Internet brokerage firmsversus only 5 three years earlier. Virtually nonexistent threeyears ago, today the percentage of stocks traded online is ap-proximately 12.5 percent, and that number is expected torise to nearly 30 percent in the next two or three years.

Changing technology is encouraging more and more in-vestors to take control of their own finances. While thistrend has lowered traditional brokers’ incomes, it has re-duced transaction costs, increased information, and empow-ered investors. Of course, concerns have been raised aboutwhether individual investors fully understand the risks in-volved, and whether they have sound strategies in place forlong-run investing once the current bull market ends.

Good or bad, most observers believe that online tradingis here to stay. However, there will surely be a continuing,but changing, need for professional advisors and stockbro-kers to work with the many investors who need guidance orwho tire of the grind of keeping track of their positions.

Source: Andy Serwer, Christine Y. Chen, and Angel Key, “A Nation ofTraders,” Fortune (1999), 116–120. Copyright © 1999 Time Inc. All rights re-served. Reprinted by permission.



Preferred Stock

Preferred stock is a hybrid—it is similar to bonds in some respects and to commonstock in others. The hybrid nature of preferred stock becomes apparent when we tryto classify it in relation to bonds and common stock. Like bonds, preferred stock has apar value and a fixed amount of dividends that must be paid before dividends can bepaid on the common stock. However, if the preferred dividend is not earned, thedirectors can omit (or “pass”) it without throwing the company into bankruptcy. So,although preferred stock has a fixed payment like bonds, a failure to make this pay-ment will not lead to bankruptcy.

As noted above, a preferred stock entitles its owners to regular, fixed dividend pay-ments. If the payments last forever, the issue is a perpetuity whose value, Vp, is foundas follows:

(5-6)

Vp is the value of the preferred stock, Dp is the preferred dividend, and rp is the re-quired rate of return. MicroDrive has preferred stock outstanding that pays a dividendof $10 per year. If the required rate of return on this preferred stock is 10 percent,then its value is $100, found by solving Equation 5-6 as follows:

If we know the current price of a preferred stock and its dividend, we can solve for therate of return as follows:

(5-6a)

Some preferred stocks have a stated maturity date, say, 50 years. If MicroDrive’spreferred matured in 50 years, paid a $10 annual dividend, and had a required returnof 8 percent, then we could find its price as follows: Enter N � 50, I � 8, PMT � 10,and FV � 100. Then press PV to find the price, Vp � $124.47. If rp � I � 10%,change I � 8 to I � 10, and find P � Vp � PV � $100. If you know the price of a shareof preferred stock, you can solve for I to find the expected rate of return, r̂p.

Most preferred stocks pay dividends quarterly. This is true for MicroDrive, so wecould find the effective rate of return on its preferred stock (perpetual or maturing) asfollows:

If an investor wanted to compare the returns on MicroDrive’s bonds and its preferredstock, it would be best to convert the nominal rates on each security to effective ratesand then compare these “equivalent annual rates.”

Explain the following statement: “Preferred stock is a hybrid security.”

Is the equation used to value preferred stock more like the one used to evaluatea perpetual bond or the one used for common stock?

EFF% � EARp � a1 �rNom

mbm

� 1 � a1 �0.10

4b4

� 1 � 10.38%.

rp �Dp

Vp.

Vp �$10.00

0.10� $100.00.

Vp �Dp

rp.


Summary

Corporate decisions should be analyzed in terms of how alternative courses of actionare likely to affect a firm’s value. However, it is necessary to know how stock prices areestablished before attempting to measure how a given decision will affect a specificfirm’s value. This chapter showed how stock values are determined, and also how in-vestors go about estimating the rates of return they expect to earn. The key conceptscovered are listed below.

� A proxy is a document that gives one person the power to act for another, typicallythe power to vote shares of common stock. A proxy fight occurs when an outsidegroup solicits stockholders’ proxies in an effort to vote a new management teaminto office.

� A takeover occurs when a person or group succeeds in ousting a firm’s manage-ment and takes control of the company.

� Stockholders often have the right to purchase any additional shares sold by thefirm. This right, called the preemptive right, protects the control of the presentstockholders and prevents dilution of their value.

� Although most firms have only one type of common stock, in some instances clas-sified stock is used to meet the special needs of the company. One type isfounders’ shares. This is stock owned by the firm’s founders that carries sole vot-ing rights but restricted dividends for a specified number of years.

� A closely held corporation is one that is owned by a few individuals who are typ-ically associated with the firm’s management.

� A publicly owned corporation is one that is owned by a relatively large numberof individuals who are not actively involved in its management.

� Whenever stock in a closely held corporation is offered to the public for the firsttime, the company is said to be going public. The market for stock that is just be-ing offered to the public is called the initial public offering (IPO) market.

� The value of a share of stock is calculated as the present value of the stream ofdividends the stock is expected to provide in the future.

� The equation used to find the value of a constant growth stock is:

� The expected total rate of return from a stock consists of an expected dividendyield plus an expected capital gains yield. For a constant growth firm, both the ex-pected dividend yield and the expected capital gains yield are constant.

� The equation for r̂s, the expected rate of return on a constant growth stock,can be expressed as follows:

� A zero growth stock is one whose future dividends are not expected to grow atall, while a supernormal growth stock is one whose earnings and dividends areexpected to grow much faster than the economy as a whole over some specifiedtime period and then to grow at the “normal” rate.

� To find the present value of a supernormal growth stock, (1) find the dividendsexpected during the supernormal growth period, (2) find the price of the stock atthe end of the supernormal growth period, (3) discount the dividends and the pro-jected price back to the present, and (4) sum these PVs to find the current value ofthe stock, P̂0.

r̂s �D1

P0� g.

P̂0 �D1

rs � g.

Summary 217



� The horizon (terminal) date is the date when individual dividend forecasts are nolonger made because the dividend growth rate is assumed to be constant.

� The horizon (terminal) value is the value at the horizon date of all future divi-dends after that date.

� The marginal investor is a representative investor whose actions reflect the be-liefs of those people who are currently trading a stock. It is the marginal investorwho determines a stock’s price.

� Equilibrium is the condition under which the expected return on a security asseen by the marginal investor is just equal to its required return, r̂ � r. Also, thestock’s intrinsic value must be equal to its market price, P̂0 � P0, and the marketprice is stable.

� The Efficient Markets Hypothesis (EMH) holds (1) that stocks are always inequilibrium and (2) that it is impossible for an investor who does not have insideinformation to consistently “beat the market.” Therefore, according to the EMH,stocks are always fairly valued (P̂0 � P0), the required return on a stock is equal toits expected return (r � r̂), and all stocks’ expected returns plot on the SML.

� Differences can and do exist between expected and realized returns in the stockand bond markets—only for short-term, risk-free assets are expected and actual(or realized) returns equal.

� When U.S. investors purchase foreign stocks, they hope (1) that stock prices willincrease in the local market and (2) that the foreign currencies will rise relative tothe U.S. dollar.

� Preferred stock is a hybrid security having some characteristics of debt and someof equity.

� Most preferred stocks are perpetuities, and the value of a share of perpetualpreferred stock is found as the dividend divided by the required rate of return:

� Maturing preferred stock is evaluated with a formula that is identical in form tothe bond value formula.

Questions

Define each of the following terms:a. Proxy; proxy fight; takeover; preemptive right; classified stock; founders’ sharesb. Closely held corporation; publicly owned corporationc. Secondary market; primary market; going public; initial public offering (IPO)d. Intrinsic value (P̂0); market price (P0)e. Required rate of return, rs; expected rate of return, r̂s; actual, or realized, rate of return, f. Capital gains yield; dividend yield; expected total returng. Normal, or constant, growth; supernormal, or nonconstant, growth; zero growth stockh. Equilibrium; Efficient Markets Hypothesis (EMH); three forms of EMHi. Preferred stock

Two investors are evaluating AT&T’s stock for possible purchase. They agree on the expectedvalue of D1 and also on the expected future dividend growth rate. Further, they agree on theriskiness of the stock. However, one investor normally holds stocks for 2 years, while the othernormally holds stocks for 10 years. On the basis of the type of analysis done in this chapter, theyshould both be willing to pay the same price for AT&T’s stock. True or false? Explain.

A bond that pays interest forever and has no maturity date is a perpetual bond. In what respectis a perpetual bond similar to a no-growth common stock, and to a share of preferred stock?

5–3

5–2

rs

5–1

Vp �Dp

rp.


Problems 219

Self-Test Problems (Solutions Appear in Appendix A)

Ewald Company’s current stock price is $36, and its last dividend was $2.40. In view of Ewald’sstrong financial position and its consequent low risk, its required rate of return is only 12 per-cent. If dividends are expected to grow at a constant rate, g, in the future, and if rs is expected toremain at 12 percent, what is Ewald’s expected stock price 5 years from now?

Snyder Computer Chips Inc. is experiencing a period of rapid growth. Earnings and dividendsare expected to grow at a rate of 15 percent during the next 2 years, at 13 percent in the thirdyear, and at a constant rate of 6 percent thereafter. Snyder’s last dividend was $1.15, and the re-quired rate of return on the stock is 12 percent.a. Calculate the value of the stock today.b. Calculate P̂1 and P̂2.c. Calculate the dividend yield and capital gains yield for Years 1, 2, and 3.

Problems

Warr Corporation just paid a dividend of $1.50 a share (i.e., D0 � $1.50). The dividend is ex-pected to grow 5 percent a year for the next 3 years, and then 10 percent a year thereafter. Whatis the expected dividend per share for each of the next 5 years?

Thomas Brothers is expected to pay a $0.50 per share dividend at the end of the year (i.e., D1 �$0.50). The dividend is expected to grow at a constant rate of 7 percent a year. The requiredrate of return on the stock, rs, is 15 percent. What is the value per share of the company’s stock?

Harrison Clothiers’ stock currently sells for $20 a share. The stock just paid a dividend of $1.00a share (i.e., D0 � $1.00). The dividend is expected to grow at a constant rate of 10 percent ayear. What stock price is expected 1 year from now? What is the required rate of return on thecompany’s stock?

Fee Founders has preferred stock outstanding which pays a dividend of $5 at the end of each year.The preferred stock sells for $60 a share. What is the preferred stock’s required rate of return?

A company currently pays a dividend of $2 per share, D0 � 2. It is estimated that the company’sdividend will grow at a rate of 20 percent per year for the next 2 years, then the dividend willgrow at a constant rate of 7 percent thereafter. The company’s stock has a beta equal to 1.2, therisk-free rate is 7.5 percent, and the market risk premium is 4 percent. What would you esti-mate is the stock’s current price?

A stock is trading at $80 per share. The stock is expected to have a year-end dividend of $4 pershare (D1 � 4), which is expected to grow at some constant rate g throughout time. The stock’srequired rate of return is 14 percent. If you are an analyst who believes in efficient markets, whatwould be your forecast of g?

You are considering an investment in the common stock of Keller Corp. The stock is expectedto pay a dividend of $2 a share at the end of the year (D1 � $2.00). The stock has a beta equal to0.9. The risk-free rate is 5.6 percent, and the market risk premium is 6 percent. The stock’s div-idend is expected to grow at some constant rate g. The stock currently sells for $25 a share. As-suming the market is in equilibrium, what does the market believe will be the stock price at theend of 3 years? (That is, what is P̂3?)

What will be the nominal rate of return on a preferred stock with a $100 par value, a stated dividend of 8 percent of par, and a current market price of (a) $60, (b) $80, (c) $100, and (d) $140?

Martell Mining Company’s ore reserves are being depleted, so its sales are falling. Also, its pit isgetting deeper each year, so its costs are rising. As a result, the company’s earnings and divi-dends are declining at the constant rate of 5 percent per year. If D0 � $5 and rs � 15%, what isthe value of Martell Mining’s stock?

5–9DECLINING GROWTH STOCK

VALUATION

5–8PREFERRED STOCK RATE

OF RETURN

5–7CONSTANT GROWTH

VALUATION

5–6CONSTANT GROWTH RATE, G

5–5SUPERNORMAL GROWTH

VALUATION

5–4PREFERRED STOCK VALUATION


VALUATION


VALUATION

5–1DPS CALCULATION

ST–2SUPERNORMAL GROWTH

STOCK VALUATION

ST–1CONSTANT GROWTH

STOCK VALUATION



The beta coefficient for Stock C is bC � 0.4, whereas that for Stock D is bD � �0.5. (Stock D’sbeta is negative, indicating that its rate of return rises whenever returns on most other stocksfall. There are very few negative beta stocks, although collection agency stocks are sometimescited as an example.)a. If the risk-free rate is 9 percent and the expected rate of return on an average stock is 13 per-

cent, what are the required rates of return on Stocks C and D?b. For Stock C, suppose the current price, P0, is $25; the next expected dividend, D1, is $1.50;

and the stock’s expected constant growth rate is 4 percent. Is the stock in equilibrium? Ex-plain, and describe what will happen if the stock is not in equilibrium.

Assume that the average firm in your company’s industry is expected to grow at a constant rate of6 percent and its dividend yield is 7 percent. Your company is about as risky as the average firmin the industry, but it has just successfully completed some R&D work that leads you to expectthat its earnings and dividends will grow at a rate of 50 percent [D1 � D0(1 � g) � D0(1.50)] thisyear and 25 percent the following year, after which growth should match the 6 percent industryaverage rate. The last dividend paid (D0) was $1. What is the value per share of your firm’s stock?

Microtech Corporation is expanding rapidly, and it currently needs to retain all of its earnings,hence it does not pay any dividends. However, investors expect Microtech to begin paying divi-dends, with the first dividend of $1.00 coming 3 years from today. The dividend should growrapidly—at a rate of 50 percent per year—during Years 4 and 5. After Year 5, the companyshould grow at a constant rate of 8 percent per year. If the required return on the stock is 15 per-cent, what is the value of the stock today?

Ezzell Corporation issued preferred stock with a stated dividend of 10 percent of par. Preferredstock of this type currently yields 8 percent, and the par value is $100. Assume dividends arepaid annually.a. What is the value of Ezzell’s preferred stock?b. Suppose interest rate levels rise to the point where the preferred stock now yields 12 percent.

What would be the value of Ezzell’s preferred stock?

Your broker offers to sell you some shares of Bahnsen & Co. common stock that paid a dividendof $2 yesterday. You expect the dividend to grow at the rate of 5 percent per year for the next 3years, and, if you buy the stock, you plan to hold it for 3 years and then sell it.a. Find the expected dividend for each of the next 3 years; that is, calculate D1, D2, and D3.

Note that D0 � $2.b. Given that the appropriate discount rate is 12 percent and that the first of these dividend

payments will occur 1 year from now, find the present value of the dividend stream; that is,calculate the PV of D1, D2, and D3, and then sum these PVs.

c. You expect the price of the stock 3 years from now to be $34.73; that is, you expect P̂3 toequal $34.73. Discounted at a 12 percent rate, what is the present value of this expected fu-ture stock price? In other words, calculate the PV of $34.73.

d. If you plan to buy the stock, hold it for 3 years, and then sell it for $34.73, what is the mostyou should pay for it?

e. Use Equation 5-2 to calculate the present value of this stock. Assume that g � 5%, and it isconstant.

f. Is the value of this stock dependent upon how long you plan to hold it? In other words, ifyour planned holding period were 2 years or 5 years rather than 3 years, would this affect thevalue of the stock today, P̂0?

You buy a share of The Ludwig Corporation stock for $21.40. You expect it to pay dividends of$1.07, $1.1449, and $1.2250 in Years 1, 2, and 3, respectively, and you expect to sell it at a priceof $26.22 at the end of 3 years.a. Calculate the growth rate in dividends.b. Calculate the expected dividend yield.c. Assuming that the calculated growth rate is expected to continue, you can add the dividend

yield to the expected growth rate to get the expected total rate of return. What is this stock’sexpected total rate of return?

5–15RETURN ON COMMON STOCK


STOCK VALUATION

5–13PREFERRED STOCK VALUATION


STOCK VALUATION


STOCK VALUATION

5–10RATES OF RETURN AND EQUILIBRIUM


Investors require a 15 percent rate of return on Levine Company’s stock (rs � 15%).a. What will be Levine’s stock value if the previous dividend was D0 � $2 and if investors ex-

pect dividends to grow at a constant compound annual rate of (1) �5 percent, (2) 0 percent,(3) 5 percent, and (4) 10 percent?

b. Using data from part a, what is the Gordon (constant growth) model value for Levine’s stockif the required rate of return is 15 percent and the expected growth rate is (1) 15 percent or(2) 20 percent? Are these reasonable results? Explain.

c. Is it reasonable to expect that a constant growth stock would have g � rs?

Wayne-Martin Electric Inc. (WME) has just developed a solar panel capable of generating200 percent more electricity than any solar panel currently on the market. As a result, WMEis expected to experience a 15 percent annual growth rate for the next 5 years. By the end of5 years, other firms will have developed comparable technology, and WME’s growth rate willslow to 5 percent per year indefinitely. Stockholders require a return of 12 percent onWME’s stock. The most recent annual dividend (D0), which was paid yesterday, was $1.75per share.a. Calculate WME’s expected dividends for t � 1, t � 2, t � 3, t � 4, and t � 5.b. Calculate the value of the stock today, P̂0. Proceed by finding the present value of the divi-

dends expected at t � 1, t � 2, t � 3, t � 4, and t � 5 plus the present value of the stock pricewhich should exist at t � 5, P̂5. The P̂5 stock price can be found by using the constant growthequation. Notice that to find P̂5, you use the dividend expected at t � 6, which is 5 percentgreater than the t � 5 dividend.

c. Calculate the expected dividend yield, D1/P0, the capital gains yield expected during thefirst year, and the expected total return (dividend yield plus capital gains yield) duringthe first year. (Assume that P̂0 � P0, and recognize that the capital gains yield is equal to thetotal return minus the dividend yield.) Also calculate these same three yields for t � 5 (e.g., D6/P5).

Taussig Technologies Corporation (TTC) has been growing at a rate of 20 percent per year inrecent years. This same growth rate is expected to last for another 2 years.a. If D0 � $1.60, rs � 10%, and gn � 6%, what is TTC’s stock worth today? What are its ex-

pected dividend yield and capital gains yield at this time?b. Now assume that TTC’s period of supernormal growth is to last another 5 years rather than

2 years. How would this affect its price, dividend yield, and capital gains yield? Answer inwords only.

c. What will be TTC’s dividend yield and capital gains yield once its period of supernormalgrowth ends? (Hint: These values will be the same regardless of whether you examine thecase of 2 or 5 years of supernormal growth; the calculations are very easy.)

d. Of what interest to investors is the changing relationship between dividend yield and capitalgains yield over time?

The risk-free rate of return, rRF, is 11 percent; the required rate of return on the market, rM, is14 percent; and Upton Company’s stock has a beta coefficient of 1.5.a. If the dividend expected during the coming year, D1, is $2.25, and if g � a constant 5%, at

what price should Upton’s stock sell?b. Now, suppose the Federal Reserve Board increases the money supply, causing the risk-free

rate to drop to 9 percent and rM to fall to 12 percent. What would this do to the price of thestock?

c. In addition to the change in part b, suppose investors’ risk aversion declines; this fact, com-bined with the decline in rRF, causes rM to fall to 11 percent. At what price would Upton’s stocksell?

d. Now, suppose Upton has a change in management. The new group institutes policies thatincrease the expected constant growth rate to 6 percent. Also, the new management stabi-lizes sales and profits, and thus causes the beta coefficient to decline from 1.5 to 1.3. Assumethat rRF and rM are equal to the values in part c. After all these changes, what is Upton’s newequilibrium price? (Note: D1 goes to $2.27.)

5–19EQUILIBRIUM STOCK PRICE


STOCK VALUATION


STOCK VALUATION


STOCK VALUATION

Problems 221



Robert Balik and Carol Kiefer are senior vice-presidents of the Mutual of Chicago InsuranceCompany. They are co-directors of the company’s pension fund management division, withBalik having responsibility for fixed income securities (primarily bonds) and Kiefer beingresponsible for equity investments. A major new client, the California League of Cities, hasrequested that Mutual of Chicago present an investment seminar to the mayors of the repre-sented cities, and Balik and Kiefer, who will make the actual presentation, have asked you tohelp them.

To illustrate the common stock valuation process, Balik and Kiefer have asked you to ana-lyze the Bon Temps Company, an employment agency that supplies word processor operatorsand computer programmers to businesses with temporarily heavy workloads. You are to answerthe following questions.a. Describe briefly the legal rights and privileges of common stockholders.b. (1) Write out a formula that can be used to value any stock, regardless of its dividend pat-

tern.(2) What is a constant growth stock? How are constant growth stocks valued?(3) What happens if a company has a constant g which exceeds its rs? Will many stocks have

expected g � rs in the short run (i.e., for the next few years)? In the long run (i.e., for-ever)?

c. Assume that Bon Temps has a beta coefficient of 1.2, that the risk-free rate (the yield on T-bonds) is 7 percent, and that the market risk premium is 5 percent. What is the requiredrate of return on the firm’s stock?

d. Assume that Bon Temps is a constant growth company whose last dividend (D0, which waspaid yesterday) was $2.00 and whose dividend is expected to grow indefinitely at a 6 percentrate.(1) What is the firm’s expected dividend stream over the next 3 years?(2) What is the firm’s current stock price?(3) What is the stock’s expected value 1 year from now?(4) What are the expected dividend yield, the capital gains yield, and the total return during

the first year?e. Now assume that the stock is currently selling at $30.29. What is the expected rate of return

on the stock?f. What would the stock price be if its dividends were expected to have zero growth?g. Now assume that Bon Temps is expected to experience supernormal growth of 30 percent

for the next 3 years, then to return to its long-run constant growth rate of 6 percent. Whatis the stock’s value under these conditions? What is its expected dividend yield and capitalgains yield in Year 1? In Year 4?

h. Is the stock price based more on long-term or short-term expectations? Answer this by find-ing the percentage of Bon Temps’ current stock price based on dividends expected morethan 3 years in the future.

i. Suppose Bon Temps is expected to experience zero growth during the first 3 years and then to resume its steady-state growth of 6 percent in the fourth year. What is the stock’svalue now? What is its expected dividend yield and its capital gains yield in Year 1? In Year 4?

j. Finally, assume that Bon Temps’ earnings and dividends are expected to decline by a con-stant 6 percent per year, that is, g � �6%. Why would anyone be willing to buy such astock, and at what price should it sell? What would be the dividend yield and capital gainsyield in each year?

See Ch 05 Show.ppt andCh 05 Mini Case.xls.

Spreadsheet Problem

Start with the partial model in the file Ch 05 P20 Build a Model.xls from the textbook’sweb site. Rework Problem 5-18, parts a, b, and c, using a spreadsheet model. For part b,calculate the price, dividend yield, and capital gains yield as called for in the problem.

5–20BUILD A MODEL:

SUPERNORMAL GROWTH ANDCORPORATE VALUATION


Selected Additional References and Cases 223

Selected Additional References and Cases

Many investment textbooks cover stock valuation models in depth,and some are listed in the Chapter 3 references.

For some recent works on valuation, seeBey, Roger P., and J. Markham Collins, “The Relationship

between Before- and After-Tax Yields on Financial As-sets,” The Financial Review, August 1988, 313–343.

Brooks, Robert, and Billy Helms, “An N-Stage, FractionalPeriod, Quarterly Dividend Discount Model,” FinancialReview, November 1990, 651–657.

Copeland, Tom, Tim Koller, and Jack Murrin, Valuation:Measuring and Managing the Value of Companies, 3rd ed.(New York: John Wiley & Sons, Inc., 2000).

The following cases in the Cases in Financial Management se-ries cover many of the valuation concepts contained in this chapter:Case 3, “Peachtree Securities, Inc. (B)”; Case 43, “Swan-

Davis”; Case 49, Beatrice Peabody”; and Case 101,“TECO Energy.”

k. What is market multiple analysis?l. Why do stock prices change? Suppose the expected D1 is $2, the growth rate is 5 percent,

and rs is 10 percent. Using the constant growth model, what is the price? What is the impacton stock price if g is 4 percent or 6 percent? If rs is 9 percent or 11 percent?

m. What does market equilibrium mean?n. If equilibrium does not exist, how will it be established?o. What is the Efficient Markets Hypothesis, what are its three forms, and what are its impli-

cations?p. Bon Temps recently issued preferred stock. It pays an annual dividend of $5, and the issue

price was $50 per share. What is the expected return to an investor on this preferredstock?


PART THREE: Investment Risk-Return Analysis & Portfolio Management

Chapter 8: How Corporations Issue Securities Fundamentals of Corporate Finance 3rd Edition by Brealy, Myers, Marcus Chapter 9: Introduction to Risk, Return, and the Opportunity Cost of Capital Fundamentals of Corporate Finance 3rd Edition by Brealy, Myers, Marcus Chapter 10: Risk, Return, and Capital Budgeting Fundamentals of Corporate Finance 3rd Edition by Brealy, Myers, Marcus Chapter 11: Asset Allocation Decision & An Introduction to Portfolio Management

Investment Analysis & Portfolio Management by Reilly & Brown

517

HOW CORPORATIONSISSUE SECURITIES

Venture Capital

The Initial Public OfferingArranging a Public Issue

The UnderwritersWho Are the Underwriters?

General Cash Offers by Public CompaniesGeneral Cash Offers and Shelf Registration

Costs of the General Cash Offer

Market Reaction to Stock Issues

The Private Placement

Summary

Appendix: Hotch Pot’s New Issue Prospectus

Planet Hollywood shares are offered to investors.IPOs often provide stellar first-day returns, but their long-term performance tends to be weak.Reuters/Ethan Miller/Archive Photos

518

ill Gates and Paul Allen founded Microsoft in 1975, when both

were around 20 years old. Eleven years later Microsoft shares were sold

to the public for $21 a share and immediately zoomed to $35. The largest

shareholder was Bill Gates, whose shares in Microsoft then were worth

$350 million.

In 1976 two college dropouts, Steve Jobs and Steve Wozniak, sold their most valu-

able possessions, a van and a couple of calculators, and used the cash to start manufac-

turing computers in a garage. In 1980, when Apple Computer went public, the shares

were offered to investors at $22 and jumped to $36. At that point, the shares owned by

the company’s two founders were worth $414 million.

In 1994 Marc Andreesen, a 24-year-old from the University of Illinois, joined with

an investor, James Clark, to found Netscape Communications. Just over a year later

Netscape stock was offered to the public at $28 a share and immediately leapt to $71.

At this price James Clark’s shares were worth $566 million, while Marc Andreesen’s

shares were worth $245 million.

Such stories illustrate that the most important asset of a new firm may be a good

idea. But that is not all you need. To take an idea from the drawing board to a prototype

and through to large-scale production requires ever greater amounts of capital.

To get a new company off the ground, entrepreneurs may rely on their own savings

and personal bank loans. But this is unlikely to be sufficient to build a successful en-

terprise. Venture capital firms specialize in providing new equity capital to help firms

over the awkward adolescent period before they are large enough to “go public.” In the

first part of this material we will explain how venture capital firms do this.

If the firm continues to be successful, there is likely to come a time when it needs to

tap a wider source of capital. At this point it will make its first public issue of common

stock. This is known as an initial public offering, or IPO. In the second section of the

material we will describe what is involved in an IPO.

A company’s initial public offering is seldom its last. Earlier we saw that internally

generated cash is not usually sufficient to satisfy the firm’s needs. Established compa-

nies make up the deficit by issuing more equity or debt. The remainder of this material

looks at this process.

After studying this material you should be able to

� Understand how venture capital firms design successful deals.

� Understand how firms make initial public offerings and the costs of such offerings.

� Know what is involved when established firms make a general cash offer or a pri-

vate placement of securities.

� Explain the role of the underwriter in an issue of securities.

B

How Corporations Issue Securities 519

Venture CapitalYou have taken a big step. With a couple of friends, you have formed a corporation toopen a number of fast-food outlets, offering innovative combinations of national dishessuch as sushi with sauerkraut, curry Bolognese, and chow mein with Yorkshire pudding.Breaking into the fast-food business costs money, but, after pooling your savings andborrowing to the hilt from the bank, you have raised $100,000 and purchased 1 millionshares in the new company. At this zero-stage investment, your company’s assets are$100,000 plus the idea for your new product.

That $100,000 is enough to get the business off the ground, but if the idea takes off,you will need more capital to pay for new restaurants. You therefore decide to look foran investor who is prepared to back an untried company in return for part of the prof-its. Equity capital in young businesses is known as venture capital and it is providedby specialist venture capital firms, wealthy individuals, and investment institutions suchas pension funds.

Most entrepreneurs are able to spin a plausible yarn about their company. But it is ashard to convince a venture capitalist to invest in your business as it is to get a first novelpublished. Your first step is to prepare a business plan. This describes your product, thepotential market, the production method, and the resources—time, money, employees,plant, and equipment—needed for success. It helps if you can point to the fact that youare prepared to put your money where your mouth is. By staking all your savings in thecompany, you signal your faith in the business.

The venture capital company knows that the success of a new business depends onthe effort its managers put in. Therefore, it will try to structure any deal so that you havea strong incentive to work hard. For example, if you agree to accept a modest salary(and look forward instead to increasing the value of your investment in the company’sstock), the venture capital company knows you will be committed to working hard.However, if you insist on a watertight employment contract and a fat salary, you won’tfind it easy to raise venture capital.

You are unlikely to persuade a venture capitalist to give you as much money as youneed all at once. Rather, the firm will probably give you enough to reach the next majorcheckpoint. Suppose you can convince the venture capital company to buy 1 millionnew shares for $.50 each. This will give it one-half ownership of the firm: it owns 1 mil-lion shares and you and your friends also own 1 million shares. Because the venturecapitalist is paying $500,000 for a claim to half your firm, it is placing a $1 millionvalue on the business. After this first-stage financing, your company’s balance sheetlooks like this:

FIRST-STAGE MARKET-VALUE BALANCE SHEET(figures in millions)

Assets Liabilities and Shareholders’ Equity

Cash from new equity $ .5 New equity from venture capital $ .5Other assets .5 Your original equity .5Value $1.0 Value $1.0

� Self-Test 1 Why might the venture capital company prefer to put up only part of the funds up-front? Would this affect the amount of effort put in by you, the entrepreneur? Is your

VENTURE CAPITALMoney invested to finance anew firm.

520 SECTION FIVE

willingness to accept only part of the venture capital that will eventually be needed agood signal of the likely success of the venture?

Suppose that 2 years later your business has grown to the point at which it needs afurther injection of equity. This second-stage financing might involve the issue of a fur-ther 1 million shares at $1 each. Some of these shares might be bought by the originalbackers and some by other venture capital firms. The balance sheet after the new fi-nancing would then be as follows:

SECOND-STAGE MARKET-VALUE BALANCE SHEET(figures in millions)

Assets Liabilities and Shareholders’ Equity

Cash from new equity $1.0 New equity from second-stage financing $1.0Other assets 2.0 Equity from first stage 1.0

Your original equity 1.0Value $3.0 Value $3.0

Notice that the value of the initial 1 million shares owned by you and your friendshas now been marked up to $1 million. Does this begin to sound like a money machine?It was so only because you have made a success of the business and new investors areprepared to pay $1 to buy a share in the business. When you started out, it wasn’t clearthat sushi and sauerkraut would catch on. If it hadn’t caught on, the venture capital firmcould have refused to put up more funds.

You are not yet in a position to cash in on your investment, but your gain is real. Thesecond-stage investors have paid $1 million for a one-third share in the company. (Thereare now 3 million shares outstanding, and the second-stage investors hold 1 millionshares.) Therefore, at least these impartial observers—who are willing to back up theiropinions with a large investment—must have decided that the company was worth atleast $3 million. Your one-third share is therefore also worth $1 million.

For every 10 first-stage venture capital investments, only two or three may surviveas successful, self-sufficient businesses, and only one may pay off big. From these sta-tistics come two rules of success in venture capital investment. First, don’t shy awayfrom uncertainty; accept a low probability of success. But don’t buy into a business un-less you can see the chance of a big, public company in a profitable market. There’s nosense taking a big risk unless the reward is big if you win. Second, cut your losses; iden-tify losers early, and, if you can’t fix the problem—by replacing management, for ex-ample—don’t throw good money after bad.

The same advice holds for any backer of a risky startup business—after all, only afraction of new businesses are funded by card-carrying venture capitalists. Some start-ups are funded directly by managers or by their friends and families. Some grow usingbank loans and reinvested earnings. But if your startup combines high risk, sophisti-cated technology, and substantial investment, you will probably try to find venture-capital financing.

The Initial Public OfferingVery few new businesses make it big, but those that do can be very profitable. For ex-ample, an investor who provided $1,000 of first-stage financing for Intel would by mid-2000 have reaped $43 million. So venture capitalists keep sane by reminding them-


selves of the success stories1—those who got in on the ground floor of firms like Inteland Federal Express and Lotus Development Corporation.2 If a startup is successful, thefirm may need to raise a considerable amount of capital to gear up its production ca-pacity. At this point, it needs more capital than can comfortably be provided by a smallnumber of individuals or venture capitalists. The firm decides to sell shares to the pub-lic to raise the necessary funds.

An IPO is called a primary offering when new shares are sold to raise additional cashfor the company. It is a secondary offering when the company’s founders and the ven-ture capitalist cash in on some of their gains by selling shares. A secondary offer there-fore is no more than a sale of shares from the early investors in the firm to new in-vestors, and the cash raised in a secondary offer does not flow to the company. Ofcourse, IPOs can be and commonly are both primary and secondary: the firm raises newcash at the same time that some of the already-existing shares in the firm are sold to thepublic. Some of the biggest secondary offerings have involved governments selling offstock in nationalized enterprises. For example, the Japanese government raised $12.6billion by selling its stock in Nippon Telegraph and Telephone and the British govern-ment took in $9 billion from its sale of British Gas. The world’s largest IPO took placein 1999 when the Italian government raised $19.3 billion from the sale of shares in thestate-owned electricity company, Enel.

ARRANGING A PUBLIC ISSUE

Once a firm decides to go public, the first task is to select the underwriters.

A small IPO may have only one underwriter, but larger issues usually require a syn-dicate of underwriters who buy the issue and resell it. For example, the initial public of-fering by Microsoft involved a total of 114 underwriters.

In the typical underwriting arrangement, called a firm commitment, the underwritersbuy the securities from the firm and then resell them to the public. The underwriters re-ceive payment in the form of a spread—that is, they are allowed to sell the shares at aslightly higher price than they paid for them. But the underwriters also accept the riskthat they won’t be able to sell the stock at the agreed offering price. If that happens, theywill be stuck with unsold shares and must get the best price they can for them. In themore risky cases, the underwriter may not be willing to enter into a firm commitmentand handles the issue on a best efforts basis. In this case the underwriter agrees to sellas much of the issue as possible but does not guarantee the sale of the entire issue.

Underwriters are investment banking firms that act as financial midwives to anew issue. Usually they play a triple role—first providing the company withprocedural and financial advice, then buying the stock, and finally reselling itto the public.

A firm is said to go public when it sells its first issue of shares in a generaloffering to investors. This first sale of stock is called an initial public offering,or IPO.

INITIAL PUBLICOFFERING (IPO) Firstoffering of stock to thegeneral public.

UNDERWRITER Firmthat buys an issue ofsecurities from a companyand resells it to the public.

SPREAD Differencebetween public offer priceand price paid byunderwriter.

522 SECTION FIVE

Before any stock can be sold to the public, the company must register the stock withthe Securities and Exchange Commission (SEC). This involves preparation of a detailedand sometimes cumbersome registration statement, which contains information aboutthe proposed financing and the firm’s history, existing business, and plans for the fu-ture. The SEC does not evaluate the wisdom of an investment in the firm but it doescheck the registration statement for accuracy and completeness. The firm must alsocomply with the “blue-sky” laws of each state, so named because they seek to protectthe public against firms that fraudulently promise the blue sky to investors.3

The first part of the registration statement is distributed to the public in the form ofa preliminary prospectus. One function of the prospectus is to warn investors about therisks involved in any investment in the firm. Some investors have joked that if they readprospectuses carefully, they would never dare buy any new issue. The appendix to thismaterial is a possible prospectus for your fast-food business.

The company and its underwriters also need to set the issue price. To gauge howmuch the stock is worth, they may undertake discounted cash-flow calculations likethose described earlier. They also look at the price-earnings ratios of the shares of thefirm’s principal competitors.

Before settling on the issue price, the underwriters may arrange a “roadshow,” whichgives the underwriters and the company’s management an opportunity to talk to poten-tial investors. These investors may then offer their reaction to the issue, suggest whatthey think is a fair price, and indicate how much stock they would be prepared to buy.This allows the underwriters to build up a book of likely orders. Although investors arenot bound by their indications, they know that if they want to remain in the underwrit-ers’ good books, they must be careful not to renege on their expressions of interest.

The managers of the firm are eager to secure the highest possible price for theirstock, but the underwriters are likely to be cautious because they will be left with anyunsold stock if they overestimate investor demand. As a result, underwriters typicallytry to underprice the initial public offering. Underpricing, they argue, is needed totempt investors to buy stock and to reduce the cost of marketing the issue to customers.

It is common to see the stock price increase substantially from the issue price in thedays following an issue. Such immediate price jumps indicate the amount by which theshares were underpriced compared to what investors were willing to pay for them. Astudy by Ibbotson, Sindelar, and Ritter of approximately 9,000 new issues from 1960 to1987 found average underpricing of 16 percent.4 Sometimes new issues are dramati-cally underpriced. In November 1998, for example, 3.1 million shares in theglobe.com

Underpricing represents a cost to the existing owners since the new investorsare allowed to buy shares in the firm at a favorable price. The cost ofunderpricing may be very large.

3 Sometimes states go beyond blue-sky laws in their efforts to protect their residents. In 1980 when AppleComputer Inc. made its first public issue, the Massachusetts state government decided the offering was toorisky for its residents and therefore banned the sale of the shares to investors in the state. The state relentedlater, after the issue was out and the price had risen. Massachusetts investors obviously did not appreciate this“protection.”4 R. G. Ibbotson, J. L. Sindelar, and J. R. Ritter, “Initial Public Offerings,” Journal of Applied Corporate Fi-nance 1 (Summer 1988), pp. 37–45. Note, however, that initial underpricing does not mean that IPOs are su-perior long-run investments. In fact, IPO returns over the first 3 years of trading have been less than a con-trol sample of matching firms. See J. R. Ritter, “The Long-Run Performance of Initial Public Offerings,”Journal of Finance 46 (March 1991), pp. 3–27.

PROSPECTUS Formalsummary that providesinformation on an issue ofsecurities.

UNDERPRICINGIssuing securities at anoffering price set below thetrue value of the security.

Project Analysis 523

were sold in an IPO at a price of $9 a share. In the first day of trading 15.6 millionshares changed hands and the price at one point touched $97. Unfortunately, the bo-nanza did not last. Within a year the stock price had fallen by over two-thirds from itsfirst-day peak. The nearby box reports on the phenomenal performance of Internet IPOsin the late 1990s.

� EXAMPLE 1 Underpricing of IPOs

Suppose an IPO is a secondary issue, and the firm’s founders sell part of their holdingto investors. Clearly, if the shares are sold for less than their true worth, the founderswill suffer an opportunity loss.

But what if the IPO is a primary issue that raises new cash for the company? Do thefounders care whether the shares are sold for less than their market value? The follow-ing example illustrates that they do care.

Suppose Cosmos.com has 2 million shares outstanding and now offers a further 1million shares to investors at $50. On the first day of trading the share price jumps to$80, so that the shares that the company sold for $50 million are now worth $80 mil-lion. The total market capitalization of the company is 3 million × $80 = $240 million.

The value of the founders’ shares is equal to the total value of the company less thevalue of the shares that have been sold to the public—in other words, $240 – $80 = $160million. The founders might justifiably rejoice at their good fortune. However, if thecompany had issued shares at a higher price, it would have needed to sell fewer sharesto raise the $50 million that it needs, and the founders would have retained a largershare of the company. For example, suppose that the outside investors, who put up $50million, received shares that were worth only $50 million. In that case the value of thefounders’ shares would be $240 –$50 = $190 million.

The effect of selling shares below their true value is to transfer $30 million of valuefrom the founders to the investors who buy the new shares.

Unfortunately, underpricing does not mean that anyone can become wealthy by buy-ing stock in IPOs. If an issue is underpriced, everybody will want to buy it and the un-derwriters will not have enough stock to go around. You are therefore likely to get onlya small share of these hot issues. If it is overpriced, other investors are unlikely to wantit and the underwriter will be only too delighted to sell it to you. This phenomenon isknown as the winner’s curse.5 It implies that, unless you can spot which issues are un-derpriced, you are likely to receive a small proportion of the cheap issues and a largeproportion of the expensive ones. Since the dice are loaded against uninformed in-vestors, they will play the game only if there is substantial underpricing on average.

� EXAMPLE 2 Underpricing of IPOs and Investor Returns

Suppose that an investor will earn an immediate 10 percent return on underpriced IPOsand lose 5 percent on overpriced IPOs. But because of high demand, you may get only

5 The highest bidder in an auction is the participant who places the highest value on the auctioned object.Therefore, it is likely that the winning bidder has an overly optimistic assessment of true value. Winning theauction suggests that you have overpaid for the object—this is the winner’s curse. In the case of IPOs, yourability to “win” an allotment of shares may signal that the stock is overpriced.

SEE BOX

FINANCE IN ACTION

half the shares you bid for when the issue is underpriced. Suppose you bid for $1,000 ofshares in two issues, one overpriced and the other underpriced. You are awarded the full$1,000 of the overpriced issue, but only $500 worth of shares in the underpriced issue.The net gain on your two investments is (.10 × $500) – (.05 × $1,000) = 0. Your net profitis zero, despite the fact that on average, IPOs are underpriced. You have suffered thewinner’s curse: you “win” a larger allotment of shares when they are overpriced.

� Self-Test 2 What is the percentage profit earned by an investor who can identify the underpricedissues in Example 2? Who are such investors likely to be?

The costs of a new issue are termed flotation costs. Underpricing is not the onlyflotation cost. In fact, when people talk about the cost of a new issue, they often thinkonly of the direct costs of the issue. For example, preparation of the registration state-ment and prospectus involves management, legal counsel, and accountants, as well asunderwriters and their advisers. There is also the underwriting spread. (Remember, un-derwriters make their profit by selling the issue at a higher price than they paid for it.)

Table 5.10 summarizes the costs of going public. The table includes the underwrit-ing spread and administrative costs as well as the cost of underpricing, as measured bythe initial return on the stock. For a small IPO of no more than $10 million, the under-

524

Internet Shares: Loopy.com?

The tiny images are like demented postage stampscoming jerkily to life; the sound is prone to break up and at times could be coming from a bathroom plughole.Welcome to the Internet live broadcasting experience.However, despite offering audio-visual quality that would have been unacceptable in the pioneering daysof television, a small, loss-making company calledBroadcast.com broke all previous records when it madeits Wall Street debut on July 17th.

Shares in the Dallas-based company were offered at$18 and reached as high as $74 before closing at$62.75— a gain of nearly 250% on the day after a feed-ing frenzy in which 6.5m shares changed hands. Afterthe dust had settled, Broadcast.com was establishedas a $1 billion company, and its two 30-somethingfounders, Mark Cuban and Todd Wagner, were worthnearly $500m between them.

In its three years of existence, Broadcast.com, for-merly known as AudioNet, has lost nearly $13m, and itsoffer document frankly told potential investors that ithad absolutely no idea when it might start to makemoney. So has Wall Street finally taken leave of itssenses?

The value being placed on Broadcast.com is not ob-viously loopier than a number of other gravity-defyingInternet stocks, particularly the currently fashionable“ portals” — gateways to the Web— such as Yahoo! andAmerica Online. Yahoo!, the Internet’s leading contentaggregator, has nearly doubled in value since June. Onthe back of revenue estimates of around $165m, it hasa market value of $8.7 billion.

Mark Hardie, an analyst with the high-tech con-sultancy Forrester Research, does not believe, in anycase, that the enthusiasm for Broadcast.com has beenoverdone. He says: “ There are no entrenched players inthis space. The ‘old’ media are aware that the intelli-gence to exploit the Internet lies outside their organiza-tions and are standing back waiting to see what hap-pens. Broadcast.com is well-positioned to be a serviceintermediary for those companies and for other contentowners.” Persuaded?

Source: © 1998 The Economist Newspaper Group, Inc. Reprintedwith permission. Further reproduction prohibited. www.economist.com.

FLOTATION COSTSThe costs incurred when afirm issues new securities tothe public.


writing spread and administrative costs are likely to absorb 15 to 20 percent of the pro-ceeds from the issue. For the very largest IPOs, these direct costs may amount to only5 percent of the proceeds.

� EXAMPLE 3 Costs of an IPO

When the investment bank Goldman Sachs went public in 1999, the sale was partly aprimary issue (the company sold new shares to raise cash) and partly a secondary one(two large existing shareholders cashed in some of their shares). The underwriters ac-quired a total of 69 million Goldman Sachs shares for $50.75 each and sold them to thepublic at an offering price of $53.6 The underwriters’ spread was therefore $53 – $50.75= $2.25. The firm and its shareholders also paid a total of $9.2 million in legal fees andother costs. By the end of the first day’s trading Goldman’s stock price had risen to $70.

Here are the direct costs of the Goldman Sachs issue:

Direct Expenses

Underwriting spread 69 million × $2.25 = $155.25 millionOther expenses 9.2Total direct expenses $164.45 million

The total amount of money raised by the issue was 69 million × $53 = $3,657 million.Of this sum 4.5 percent was absorbed by direct expenses (that is, 164.45/3,657 = .045).

In addition to these direct costs, there was underpricing. The market valued eachshare of Goldman Sachs at $70, so the cost of underpricing was 69 million × ($70 –

TABLE 5.10Average expenses of 1,767initial public offerings,1990–1994a

Value of Issue Direct Average First-Day Total(millions of dollars) Costs, %b Return, %b Costs, %c

2–9.99 16.96 16.36 25.1610–19.99 11.63 9.65 18.1520–39.99 9.70 12.48 18.1840–59.99 8.72 13.65 17.9560–79.99 8.20 11.31 16.3580–99.99 7.91 8.91 14.14

100–199.99 7.06 7.16 12.78200–499.99 6.53 5.70 11.10500 and up 5.72 7.53 10.36All issues 11.00 12.05 18.69

a The table includes only issues where there was a firm underwriting commitment.b Direct costs (i.e., underwriting spread plus administrative costs) and average initial return are expressed asa percentage of the issue price.c Total costs (i.e., direct costs plus underpricing) are expressed as a percentage of the market price of theshare.Source: J. R. Ritter et al., “The Costs of Raising Capital,” Journal of Financial Research 19, No. 1, Spring1996. Reprinted by permission.

6 No prizes for guessing which investment bank acted as lead underwriter.

526 SECTION FIVE

$53) = $1,173 million, resulting in total costs of $164.45 + $1,173 = $1,337.45 million.Therefore, while the total market value of the issued shares was 69 million × $70 =$4,830 million, direct costs and the costs of underpricing absorbed nearly 28 percent ofthe market value of the shares.

� Self-Test 3 Suppose that the underwriters acquired Goldman Sachs shares for $60 and sold them tothe public at an offering price of $64. If all other features of the offer were unchanged(and investors still valued the stock at $70 a share), what would have been the directcosts of the issue and the costs of underpricing? What would have been the total costsas a proportion of the market value of the shares?

The UnderwritersWe have described underwriters as playing a triple role—providing advice, buying anew issue from the company, and reselling it to investors. Underwriters don’t just helpthe company to make its initial public offering; they are called in whenever a companywishes to raise cash by selling securities to the public.

Underwriting is not always fun. On October 15, 1987, the British government final-ized arrangements to sell its holding of British Petroleum (BP) shares at £3.30 a share.This huge issue involving more than $12 billion was underwritten by an internationalgroup of underwriters and simultaneously marketed in a number of countries. Four daysafter the underwriting arrangement was finalized, the October stock market crash oc-curred and stock prices nose-dived. The underwriters appealed to the British govern-ment to cancel the issue but the government hardened its heart and pointed out that theunderwriters knew the risks when they agreed to handle the sale.7 By the closing dateof the offer, the price of BP stock had fallen to £2.96 and the underwriters had lost morethan $1 billion.

WHO ARE THE UNDERWRITERS?

Since underwriters play such a crucial role in new issues, we should look at who theyare. Several thousand investment banks, security dealers, and brokers are at least spo-

Most companies raise capital only occasionally, but underwriters are in thebusiness all the time. Established underwriters are careful of their reputationand will not handle a new issue unless they believe the facts have beenpresented fairly to investors. Thus, in addition to handling the sale of an issue, the underwriters in effect give it their seal of approval. This impliedendorsement may be worth quite a bit to a company that is coming to themarket for the first time.

7 The government’s only concession was to put a floor on the underwriters’ losses by giving them the optionto resell their stock to the government at £2.80 a share. The BP offering is described and analyzed in C. Mus-carella and M. Vetsuypens, “The British Petroleum Stock Offering: An Application of Option Pricing,” Jour-nal of Applied Corporate Finance 1 (1989), pp. 74–80.


radically involved in underwriting. However, the market for the larger issues is domi-nated by the major investment banking firms, which specialize in underwriting new is-sues, dealing in securities, and arranging mergers. These firms enjoy great prestige, ex-perience, and financial muscle. Table 5.11 lists some of the largest firms, ranked bytotal volume of issues in 1998. Merrill Lynch, the winner, raised a total of $304 billion.Of course, only a small proportion of these issues was for companies that were comingto the market for the first time.

Earlier we pointed out that instead of issuing bonds in the United States, many cor-porations issue international bonds in London, which are then sold to investors outsidethe United States. In addition, new equity issues by large multinational companies areincreasingly marketed to investors throughout the world. Since these securities are soldin a number of countries, many of the major international banks are involved in under-writing the issues. For example, look at Table 5.12 which shows the names of the prin-cipal underwriters of international issues in 1998.

TABLE 5.12Top underwriters ofinternational issues ofsecurities, 1998 (figures inbillions)

Underwriter Value of Issues

Warburg Dillon Read $ 63.6Merrill Lynch 52.3Morgan Stanley Dean Witter 43.6Goldman Sachs 42.5ABN AMRO 41.5Deutsche Bank 39.0Paribas 38.7J. P. Morgan 36.0Barclays Capital 31.1Credit Suisse First Boston 25.7All underwriters $665.5

Source: Securities Data Co.

TABLE 5.11Top underwriters of U.S. debtand equity, 1998 (figures inbillions)

Underwriter Value of Issues

Merrill Lynch $ 304Salomon Smith Barney 225Morgan Stanley Dean Witter 203Goldman Sachs 192Lehman Brothers 147Credit Suisse First Boston 127J. P. Morgan 89Bear Stearns 83Chase Manhattan 71Donaldson Lufkin & Jenrette 61All underwriters $1,820

Source: Securities Data Co.

528 SECTION FIVE

General Cash Offers by Public CompaniesAfter the initial public offering a successful firm will continue to grow and from timeto time it will need to raise more money by issuing stock or bonds. An issue of addi-tional stock by a company whose stock already is publicly traded is called a seasonedoffering. Any issue of securities needs to be formally approved by the firm’s board ofdirectors. If a stock issue requires an increase in the company’s authorized capital, italso needs the consent of the stockholders.

Public companies can issue securities either by making a general cash offer to in-vestors at large or by making a rights issue, which is limited to existing shareholders.In the latter case, the company offers the shareholders the opportunity, or right, to buymore shares at an “attractive” price. For example, if the current stock price is $100, thecompany might offer investors an additional share at $50 for each share they hold. Sup-pose that before the issue an investor has one share worth $100 and $50 in the bank. Ifthe investor takes up the offer of a new share, that $50 of cash is transferred from theinvestor’s bank account to the company’s. The investor now has two shares that are aclaim on the original assets worth $100 and on the $50 cash that the company hasraised. So the two shares are worth a total of $150, or $75 each.

� EXAMPLE 4 Rights Issues

Easy Writer Word Processing Company has 1 million shares outstanding, selling at $20a share. To finance the development of a new software package, it plans a rights issue,allowing one new share to be purchased for each 10 shares currently held. The purchaseprice will be $10 a share. How many shares will be issued? How much money will beraised? What will be the stock price after the rights issue?

The firm will issue one new share for every 10 old ones, or 100,000 shares. Soshares outstanding will rise to 1.1 million. The firm will raise $10 × 100,000 = $1 mil-lion. Therefore, the total value of the firm will increase from $20 million to $21 mil-lion, and the stock price will fall to $21 million/1.1 million shares = $19.09 per share.

In some countries the rights issue is the most common or only method for issuingstock, but in the United States rights issues are now very rare. We therefore will con-centrate on the mechanics of the general cash offer.

GENERAL CASH OFFERS AND SHELFREGISTRATION

When a public company makes a general cash offer of debt or equity, it essentially fol-lows the same procedure used when it first went public. This means that it must firstregister the issue with the SEC and draw up a prospectus.8 Before settling on the issueprice, the underwriters will usually contact potential investors and build up a book of

SEASONED OFFERINGSale of securities by a firmthat is already publiclytraded.

RIGHTS ISSUE Issue ofsecurities offered only tocurrent stockholders.

GENERAL CASH OFFERSale of securities open to allinvestors by an already-public company.

8 The procedure is similar when a company makes an international issue of bonds or equity, but as long asthese issues are not sold publicly in the United States, they do not need to be registered with the SEC.


likely orders. The company will then sell the issue to the underwriters, and they in turnwill offer the securities to the public.

Companies do not need to prepare a separate registration statement every time theyissue new securities. Instead, they are allowed to file a single registration statement cov-ering financing plans for up to 2 years into the future. The actual issues can then be soldto the public with scant additional paperwork, whenever the firm needs cash or thinksit can issue securities at an attractive price. This is called shelf registration—the regis-tration is put “on the shelf,” to be taken down, dusted off, and used as needed.

Think of how you might use shelf registration when you are a financial manager.Suppose that your company is likely to need up to $200 million of new long-term debtover the next year or so. It can file a registration statement for that amount. It now hasapproval to issue up to $200 million of debt, but it isn’t obliged to issue any. Nor is itrequired to work through any particular underwriters—the registration statement mayname the underwriters the firm thinks it may work with, but others can be substitutedlater.

Now you can sit back and issue debt as needed, in bits and pieces if you like. Sup-pose Merrill Lynch comes across an insurance company with $10 million ready to in-vest in corporate bonds, priced to yield, say, 7.3 percent. If you think that’s a good deal,you say “OK” and the deal is done, subject to only a little additional paperwork. Mer-rill Lynch then resells the bonds to the insurance company, hoping for a higher pricethan it paid for them.

Here is another possible deal. Suppose you think you see a window of opportunityin which interest rates are “temporarily low.” You invite bids for $100 million of bonds.Some bids may come from large investment bankers acting alone, others from ad hocsyndicates. But that’s not your problem; if the price is right, you just take the best dealoffered.

Thus shelf registration gives firms several different things that they did not have pre-viously:

1. Securities can be issued in dribs and drabs without incurring excessive costs.2. Securities can be issued on short notice.3. Security issues can be timed to take advantage of “market conditions” (although any

financial manager who can reliably identify favorable market conditions could makea lot more money by quitting and becoming a bond or stock trader instead).

4. The issuing firm can make sure that underwriters compete for its business.

Not all companies eligible for shelf registration actually use it for all their public is-sues. Sometimes they believe they can get a better deal by making one large issuethrough traditional channels, especially when the security to be issued has some unusualfeature or when the firm believes it needs the investment banker’s counsel or stamp ofapproval on the issue. Thus shelf registration is less often used for issues of commonstock than for garden-variety corporate bonds.

COSTS OF THE GENERAL CASH OFFER

Whenever a firm makes a cash offer, it incurs substantial administrative costs. Also, thefirm needs to compensate the underwriters by selling them securities below the pricethat they expect to receive from investors. Figure 5.7 shows the average underwritingspread and administrative costs for several types of security issues in the United States.9

SHELF REGISTRATIONA procedure that allows firmsto file one registrationstatement for several issuesof the same security.

9 These figures do not capture all administrative costs. For example, they do not include management timespent on the issue.

530 SECTION FIVE

The figure clearly shows the economies of scale in issuing securities. Costs may ab-sorb 15 percent of a $1 million seasoned equity issue but less than 4 percent of a $500million issue. This occurs because a large part of the issue cost is fixed.

Figure 5.7 shows that issue costs are higher for equity than for debt securities—thecosts for both types of securities, however, show the same economies of scale. Issuecosts are higher for equity than for debt because administrative costs are somewhathigher, and also because underwriting stock is riskier than underwriting bonds. The un-derwriters demand additional compensation for the greater risk they take in buying andreselling equity.

� Self-Test 4 Use Figure 5.7 to compare the costs of 10 issues of $15 million of stock in a seasonedoffering versus one issue of $150 million.

MARKET REACTION TO STOCK ISSUES

Because stock issues usually throw a sizable number of new shares onto the market, itis widely believed that they must temporarily depress the stock price. If the proposedissue is very large, this price pressure may, it is thought, be so severe as to make it al-most impossible to raise money.

This belief in price pressure implies that a new issue depresses the stock price tem-porarily below its true value. However, that view doesn’t appear to fit very well with thenotion of market efficiency. If the stock price falls solely because of increased supply,

FIGURE 5.7Total direct costs as a percentage of gross proceeds. The total direct costs for initialpublic offerings (IPOs), seasoned equity offerings (SEOs), convertible bonds, andstraight bonds are composed of underwriter spreads and other direct expenses.

Proceeds ($ millions)

Tota

l dir

ect

cost

s (%

)

20

15

10

5

02– 9.99 10– 19.99 20– 39.99 40– 59.99 60– 79.99

IPOs

80– 99.99 100– 199.99 200– 499.99 500– up

SEOs

Convertibles

Bonds

Source: Immoo Lee, Scott Lochhead, Jay Ritter, and Quanshui Zhao, “The Costs of Raising Capital,” Journal of Financial Research 19 (Spring1996), pp. 59–74. Copyright © 1996. Reprinted by permission.


then that stock would offer a higher return than comparable stocks and investors wouldbe attracted to it as ants to a picnic.

Economists who have studied new issues of common stock have generally found thatthe announcement of the issue does result in a decline in the stock price. For industrialissues in the United States this decline amounts to about 3 percent.10 While this may notsound overwhelming, such a price drop can be a large fraction of the money raised. Sup-pose that a company with a market value of equity of $5 billion announces its intentionto issue $500 million of additional equity and thereby causes the stock price to drop by3 percent. The loss in value is .03 × $5 billion, or $150 million. That’s 30 percent of theamount of money raised (.30 × $500 million = $150 million).

What’s going on here? Is the price of the stock simply depressed by the prospect ofthe additional supply? Possibly, but here is an alternative explanation.

Suppose managers (who have better information about the firm than outside in-vestors) know that their stock is undervalued. If the company sells new stock at this lowprice, it will give the new shareholders a good deal at the expense of the old share-holders. In these circumstances managers might be prepared to forgo the new invest-ment rather than sell shares at too low a price.

If managers know that the stock is overvalued, the position is reversed. If the com-pany sells new shares at the high price, it will help its existing shareholders at the ex-pense of the new ones. Managers might be prepared to issue stock even if the new cashwere just put in the bank.

Of course investors are not stupid. They can predict that managers are more likely toissue stock when they think it is overvalued and therefore they mark the price of thestock down accordingly.

The Private PlacementWhenever a company makes a public offering, it must register the issue with the SEC. It could avoid this costly process by selling the issue privately. There are no hard-and-fast definitions of a private placement, but the SEC has insisted that the securityshould be sold to no more than a dozen or so knowledgeable investors.

The tendency for stock prices to decline at the time of an issue may havenothing to do with increased supply. Instead, the stock issue may simply be asignal that well-informed managers believe the market has overpriced thestock.11

10 See, for example, P. Asquith and D. W. Mullins, “Equity Issues and Offering Dilution,” Journal of Finan-cial Economics 15 (January–February 1986), pp. 61–90; R. W. Masulis and A. N. Korwar, “Seasoned EquityOfferings: An Empirical Investigation,” Journal of Financial Economics 15 (January–February 1986), pp.91–118; W. H. Mikkelson and M. M. Partch, “Valuation Effects of Security Offerings and the IssuanceProcess,” Journal of Financial Economics 15 (January–February 1986), pp. 31–60. There appears to be asmaller price decline for utility issues. Also Marsh observed a smaller decline for rights issues in the UnitedKingdom; see P. R. Marsh, “Equity Rights Issues and the Efficiency of the UK Stock Market,” Journal of Fi-nance 34 (September 1979), pp. 839–862.11 This explanation was developed in S. C. Myers and N. S. Majluf, “Corporate Financing and Investment De-cisions When Firms Have Information that Investors Do Not Have,” Journal of Financial Economics 13(1984), pp. 187–222.

PRIVATE PLACEMENTSale of securities to a limitednumber of investors withouta public offering.

532 SECTION FIVE

One disadvantage of a private placement is that the investor cannot easily resell thesecurity. This is less important to institutions such as life insurance companies, whichinvest huge sums of money in corporate debt for the long haul. However, in 1990 theSEC relaxed its restrictions on who could buy unregistered issues. Under the new rule,Rule 144a, large financial institutions can trade unregistered securities among them-selves.

As you would expect, it costs less to arrange a private placement than to make a pub-lic issue. That might not be so important for the very large issues where costs are lesssignificant, but it is a particular advantage for companies making smaller issues.

Another advantage of the private placement is that the debt contract can be custom-tailored for firms with special problems or opportunities. Also, if the firm wishes laterto change the terms of the debt, it is much simpler to do this with a private placementwhere only a few investors are involved.

Therefore, it is not surprising that private placements occupy a particular niche in thecorporate debt market, namely, loans to small and medium-sized firms. These are thefirms that face the highest costs in public issues, that require the most detailed investi-gation, and that may require specialized, flexible loan arrangements.

We do not mean that large, safe, and conventional firms should rule out privateplacements. Enormous amounts of capital are sometimes raised by this method. For ex-ample, AT&T once borrowed $500 million in a single private placement. Nevertheless,the advantages of private placement—avoiding registration costs and establishing a di-rect relationship with the lender—are generally more important to smaller firms.

Of course these advantages are not free. Lenders in private placements have to becompensated for the risks they face and for the costs of research and negotiation. Theyalso have to be compensated for holding an asset that is not easily resold. All these fac-tors are rolled into the interest rate paid by the firm. It is difficult to generalize aboutthe differences in interest rates between private placements and public issues, but a typ-ical yield differential is on the order of half a percentage point.

SummaryHow do venture capital firms design successful deals?

Infant companies raise venture capital to carry them through to the point at which they canmake their first public issue of stock. More established publicly traded companies can issueadditional securities in a general cash offer.

Financing choices should be designed to avoid conflicts of interest. This is especiallyimportant in the case of a young company that is raising venture capital. If both managersand investors have an important equity stake in the company, they are likely to pull in thesame direction. The willingness to take that stake also signals management’s confidence inthe new company’s future. Therefore, most deals require that the entrepreneur maintain largestakes in the firm. In addition, most venture financing is done in stages that keep the firmon a short leash, and force it to prove at several crucial points that it is worthy of additionalinvestment.

How do firms make initial public offerings and what are the costs of such offerings?

The initial public offering is the first sale of shares in a general offering to investors. Thesale of the securities is usually managed by an underwriting firm which buys the sharesfrom the company and resells them to the public. The underwriter helps to prepare aprospectus, which describes the company and its prospects. The costs of an IPO include

311

INTRODUCTION TO RISK,RETURN, AND THEOPPORTUNITY COST OFCAPITAL

Rates of Return: A Review

Seventy-Three Years ofCapital Market HistoryMarket Indexes

The Historical Record

Using Historical Evidence to EstimateToday’s Cost of Capital

Measuring RiskVariance and Standard Deviation

A Note on Calculating Variance

Measuring the Variation in StockReturns

Risk and DiversificationDiversification

Asset versus Portfolio Risk

Market Risk versus Unique Risk

Thinking about RiskMessage 1: Some Risks Look Big andDangerous but Really Are Diversifiable

Message 2: Market Risks Are Macro Risks

Message 3: Risk Can Be Measured

Summary

More generally, though, investors will want to spread their investments across many securities.© The New Yorker Collection 1957 Richard Decker from cartoonbank.com. All Rights Reserved.

e have thus far skirted the issue of project risk; now it is time to confront

it head-on. We can no longer be satisfied with vague statements like

“The opportunity cost of capital depends on the risk of the project.” We

need to know how to measure risk and we need to understand the relationship

between risk and the cost of capital.

Think for a moment what the cost of capital for a project means. It is the rate of re-

turn that shareholders could expect to earn if they invested in equally risky securities.

So one way to estimate the cost of capital is to find securities that have the same risk as

the project and then estimate the expected rate of return on these securities.

We start our analysis by looking at the rates of return earned in the past from differ-

ent investments, concentrating on the extra return that investors have received for in-

vesting in risky rather than safe securities. We then show how to measure the risk of a

portfolio by calculating its standard deviation and we look again at past history to find

out how risky it is to invest in the stock market.

Finally, we explore the concept of diversification. Most investors do not put all their

eggs into one basket—they diversify. Thus investors are not concerned with the risk of

each security in isolation; instead they are concerned with how much it contributes to

the risk of a diversified portfolio. We therefore need to distinguish between the risk that

can be eliminated by diversification and the risk that cannot be eliminated.


� Estimate the opportunity cost of capital for an “average-risk” project.

� Calculate the standard deviation of returns for individual common stocks or for a

stock portfolio.

� Understand why diversification reduces risk.

� Distinguish between unique risk, which can be diversified away, and market risk,

which cannot.

312

W

Rates of Return: A ReviewWhen investors buy a stock or a bond, their return comes in two forms: (1) a dividendor interest payment, and (2) a capital gain or a capital loss. For example, suppose youwere lucky enough to buy the stock of General Electric at the beginning of 1999 whenits price was about $102 a share. By the end of the year the value of that investment hadappreciated to $155, giving a capital gain of $155 – $102 = $53. In addition, in 1999General Electric paid a dividend of $1.46 a share.

The percentage return on your investment was therefore

Percentage return =capital gain + dividend

initial share price

=$53 + $1.46

= 0.534, or 53.4%$102

Introduction to Risk, Return, and the Opportunity Cost of Capital 313

The percentage return can also be expressed as the sum of the dividend yield and per-centage capital gain. The dividend yield is the dividend expressed as a percentage ofthe stock price at the beginning of the year:

Dividend yield =dividend

initial share price

=$1.46

= .014, or 1.4%$102

Similarly, the percentage capital gain is

Percentage capital gain =capital gain

initial share price

=$53

= 0.520, or 52.0%$102

Thus the total return is the sum of 1.4% + 52.0% = 53.4%.Remember we made a distinction between the nominal rate of return and the real rate

of return. The nominal return measures how much more money you will have at the endof the year if you invest today. The return that we just calculated for General Electricstock is therefore a nominal return. The real rate of return tells you how much more youwill be able to buy with your money at the end of the year. To convert from a nominalto a real rate of return, we use the following relationship:

1 + real rate of return =1 + nominal rate of return

1 + inflation rate

In 1999 inflation was only 2.7 percent. So we calculate the real rate of return on Gen-eral Electric stock as follows:

1 + real rate of return =1.534

= 1.4941.027

Therefore, the real rate of return equals .494, or 49.4 percent. Fortunately inflation in1999 was low; the real return was only slightly less than the nominal return.

� Self-Test 1 Suppose you buy a bond for $1,020 with a 15-year maturity paying an annual couponof $80. A year later interest rates have dropped and the bond’s price has increased to$1,050. What are your nominal and real rates of return? Assume the inflation rate is 4percent.

Seventy-Three Years of Capital Market HistoryWhen you invest in a stock, you can’t be sure that your return is going to be as high asthat of General Electric in 1999. But by looking at the history of security returns, youcan get some idea of the return that investors might reasonably expect from investmentsin different types of securities and of the risks that they face. Let us look, therefore, atthe risks and returns that investors have experienced in the past.

314 SECTION THREE

MARKET INDEXES

Investors can choose from an enormous number of different securities. Currently, about3,100 common stocks trade on the New York Stock Exchange, about 1,000 are tradedon the American Stock Exchange and regional exchanges, and more than 5,000 aretraded by a network of dealers linked by computer terminals and telephones.1

Financial analysts can’t track every stock, so they rely on market indexes to sum-marize the return on different classes of securities. The best-known stock market indexin the United States is the Dow Jones Industrial Average, generally known as the Dow.The Dow tracks the performance of a portfolio that holds one share in each of 30 largefirms. For example, suppose that the Dow starts the day at a value of 9,000 and thenrises by 90 points to a new value of 9,090. Investors who own one share in each of the30 companies make a capital gain of 90/9,000 = .01, or 1 percent.2

The Dow Jones Industrial Average was first computed in 1896. Most people are usedto it and expect to hear it on the 6 o’clock news. However, it is far from the best meas-ure of the performance of the stock market. First, with only 30 large industrial stocks,it is not representative of the performance of stocks generally. Second, investors don’tusually hold an equal number of shares in each company. For example, in 1999 therewere 3.3 billion shares in General Electric and only 1.1 billion in Du Pont. So on aver-age investors did not hold the same number of shares in the two firms. Instead, they heldthree times as many shares in General Electric as in Du Pont. It doesn’t make sense,therefore, to look at an index that measures the performance of a portfolio with an equalnumber of shares in the two firms.

The Standard & Poor’s Composite Index, better known as the S&P 500, includesthe stocks of 500 major companies and is therefore a more comprehensive index thanthe Dow. Also, it measures the performance of a portfolio that holds shares in each firmin proportion to the number of shares that have been issued to investors. For example,the S&P portfolio would hold three times as many shares in General Electric as DuPont. Thus the S&P 500 shows the average performance of investors in the 500 firms.

Only a small proportion of the 9,000 or so publicly traded companies are representedin the S&P 500. However, these firms are among the largest in the country and they ac-count for roughly 70 percent of the stocks traded. Therefore, success for professionalinvestors usually means “beating the S&P.”

Some stock market indexes, such as the Wilshire 5000, include an even larger num-ber of stocks, while others focus on special groups of stocks such as the stocks of smallcompanies. There are also stock market indexes for other countries, such as the NikkeiIndex for Tokyo and the Financial Times (FT) Index for London. Morgan Stanley Cap-ital International (MSCI) even computes a world stock market index. The FinancialTimes Company and Standard & Poor’s have combined to produce their own worldindex.

THE HISTORICAL RECORD

The historical returns of stock or bond market indexes can give us an idea of the typi-cal performance of different investments. One popular source of such information is an

1 This network of traders comprises the over-the-counter market. The computer network and price quotationsystem is called the NASDAQ system. NASDAQ stands for the National Association of Security Dealers Au-tomated Quotation system.2 Stock market indexes record the market value of the portfolio. To calculate the total return on the portfoliowe would also need to add in any dividends that are paid.

STANDARD & POOR’SCOMPOSITE INDEXIndex of the investmentperformance of a portfolio of500 large stocks. Also calledthe S&P 500.

MARKET INDEXMeasure of the investmentperformance of the overallmarket.

DOW JONESINDUSTRIAL AVERAGEIndex of the investmentperformance of a portfolio of30 “blue-chip” stocks.


ongoing study by Ibbotson Associates which reports the performance of several portfo-lios of securities since 1926. These include

1. A portfolio of 3-month loans issued each week by the U.S. government. These loansare known as Treasury bills.

2. A portfolio of long-term Treasury bonds issued by the U.S. government and matur-ing in about 20 years.

3. A portfolio of stocks of the 500 large firms that make up the Standard & Poor’sComposite Index.

These portfolios are not equally risky. Treasury bills are about as safe an investment asyou can make. Because they are issued by the U.S. government, you can be sure thatyou will get your money back. Their short-term maturity means that their prices are rel-atively stable. In fact, investors who wish to lend money for 3 months can achieve a cer-tain payoff by buying 3-month Treasury bills. Of course, they can’t be sure what thatmoney will buy; there is still some uncertainty about inflation.

Long-term Treasury bonds are also certain to be repaid when they mature, but theprices of these bonds fluctuate more as interest rates vary. When interest rates fall, thevalue of long-term bonds rises; when rates rise, the value of the bonds falls.

Common stocks are the riskiest of the three groups of securities. When you invest incommon stocks, there is no promise that you will get your money back. As a part-ownerof the corporation, you receive whatever is left over after the bonds and any other debtshave been repaid.

Figure 3.13 illustrates the investment performance of stocks, bonds, and bills since1926. The figure shows how much one dollar invested at the start of 1926 would havegrown to by the end of 1998 assuming that all dividend or interest income had beenreinvested in the portfolio.

You can see that the performance of the portfolios fits our intuitive risk ranking.Common stocks were the riskiest investment but they also offered the greatest gains.One dollar invested in 1926 in a portfolio of the S&P 500 stocks would have grown to

FIGURE 3.13The value to which a $1investment in 1926 wouldhave grown by the end of1998.

Ind

ex

’25 ’29 ’33 ’37 ’41 ’45 ’49 ’53 ’57

Year-end

’61 ’65 ’69 ’73 ’77 ’81 ’85

$2,350.89

$44.18

$14.94

’89 ’93 ’98

Long-term Treasury bonds

Treasury bills

Common stocks (S&P 500)

10,000.0

1,000.0

100.0

10.0

1.0

0.1

Source: Stocks, Bonds, Bills and Inflation® 1999 Yearbook, ©1999 Ibbotson Associates, Inc. Based oncopyrighted works by Ibbotson and Sinquefield. All Rights Reserved. Used with permission.

316 SECTION THREE

$2,351 by 1998. At the other end of the spectrum, an investment of $1 in a Treasury billwould have accumulated to only $14.94.

Ibbotson Associates has calculated rates of return for each of these portfolios foreach year from 1926 to 1998. These rates of return are comparable to the figure that wecalculated for General Electric. In other words, they include (1) dividends or interestand (2) any capital gains or losses. The averages of the 73 rates of return are shown inTable 3.9.

The safest investment, Treasury bills, had the lowest rates of return—they averaged3.8 percent a year. Long-term government bonds gave slightly higher returns than Trea-sury bills. This difference is called the maturity premium. Common stocks were in aclass by themselves. Investors who accepted the risk of common stocks received on av-erage an extra return of just under 9.4 percent a year over the return on Treasury bills.This compensation for taking on the risk of common stock ownership is known as themarket risk premium:

Rate of return=

interest rate on+

market riskon common stocks Treasury bills premium

You may ask why we look back over such a long period to measure average rates ofreturn. The reason is that annual rates of return for common stocks fluctuate so muchthat averages taken over short periods are extremely unreliable. In some years investorsin common stocks had a disagreeable shock and received a substantially lower returnthan they expected. In other years they had a pleasant surprise and received a higher-than-expected return. By averaging the returns across both the rough years and thesmooth, we should get a fair idea of the typical return that investors might justifiablyexpect.

While common stocks have offered the highest average returns, they have also beenriskier investments. Figure 3.14 shows the 73 annual rates of return for the three port-folios. The fluctuations in year-to-year returns on common stocks are remarkably wide.There were two years (1933 and 1954) when investors earned a return of more than 50percent. However, Figure 3.14 shows that you can also lose money by investing in thestock market. The most dramatic case was the stock market crash of 1929–1932.Shortly after President Coolidge joyfully observed that stocks were “cheap at currentprices,” stocks rapidly became even cheaper. By July 1932 the Dow Jones Industrial Av-erage had fallen in a series of slides by 89 percent.

Another major market crash, that of Monday, October 19, 1987, does not show up inFigure 3.14. On that day stock prices fell by 23 percent, their largest one-day fall in his-tory. However, Black Monday came after a prolonged rise in stock prices, so that over

The historical record shows that investors have received a risk premium forholding risky assets. Average returns on high-risk assets are higher than thoseon low-risk assets.

TABLE 3.9Average rates of return onTreasury bills, governmentbonds, and common stocks,1926–1998 (figures inpercent per year)

Portfolio Average Annual Average Risk Premium Rate of Return (Extra Return versus Treasury Bills)

Treasury bills 3.8Treasury bonds 5.7 1.9Common stocks 13.2 9.4

MATURITY PREMIUMExtra average return frominvesting in long- versusshort-term Treasurysecurities.

RISK PREMIUMExpected return in excess ofrisk-free return ascompensation for risk.


1987 as a whole investors in common stocks earned a return of 5.2 percent. This wasnot a terrible return, but many investors who rode the 1987 roller coaster feel that it isnot a year they would care to repeat.

� Self-Test 2 Here are the average rates of return for the postwar period 1950–1998:

Stocks 14.7%Treasury bonds 6.4Treasury bills 5.2

What were the risk premium on stocks and the maturity premium on Treasury bonds forthis period?

USING HISTORICAL EVIDENCE TO ESTIMATETODAY’S COST OF CAPITAL

Later we will, show how firms calculate the present value of a new project by dis-counting the expected cash flows by the opportunity cost of capital. The opportunitycost of capital is the return that the firm’s shareholders are giving up by investing in theproject rather than in comparable risk alternatives.

Measuring the cost of capital is easy if the project is a sure thing. Since sharehold-ers can obtain a sure-fire payoff by investing in a U.S. Treasury bill, the firm should in-vest in a risk-free project only if it can at least match the rate of interest on such a loan.If the project is risky—and most projects are—then the firm needs to at least match thereturn that shareholders could expect to earn if they invested in securities of similar risk.It is not easy to put a precise figure on this, but our skim through history provides anidea of the average return an investor might expect to earn from an investment in riskycommon stocks.

FIGURE 3.14Rates of return, 1926–1998.

Rat

e o

f re

turn

(%)

StocksT-bondsT-bills

50%

30%

10%

�10%

�30%

�50%’26 ’30 ’34 ’38 ’42 ’46 ’50 ’54 ’58

Year

’62 ’66 ’70 ’74 ’78 ’82 ’86 ’90 ’94 ’98

Source: Stocks, Bonds, Bills and Inflation® 1999 Yearbook, © 1999 Ibbotson Associates, Inc. Based oncopyrighted works by Ibbotson and Sinquefield. All Rights Reserved. Used with permission.

318 SECTION THREE

Suppose there is an investment project which you know—don’t ask how—has thesame risk as an investment in the portfolio of stocks in Standard & Poor’s CompositeIndex. We will say that it has the same degree of risk as the market portfolio of com-mon stocks.3

Instead of investing in the project, your shareholders could invest directly in thismarket portfolio of common stocks. Therefore, the opportunity cost of capital for yourproject is the return that the shareholders could expect to earn on the market portfolio.This is what they are giving up by investing money in your project.

The problem of estimating the project cost of capital boils down to estimating thecurrently expected rate of return on the market portfolio. One way to estimate the ex-pected market return is to assume that the future will be like the past and that today’sinvestors expect to receive the average rates of return shown in Table 3.9. In this case,you would judge that the expected market return today is 13.2 percent, the average ofpast market returns.

Unfortunately, this is not the way to do it. Investors are not likely to demand the samereturn each year on an investment in common stocks. For example, we know that the in-terest rate on safe Treasury bills varies over time. At their peak in 1981, Treasury billsoffered a return of 14 percent, more than 10 percentage points above the 3.8 percent av-erage return on bills shown in Table 3.9.

What if you were called upon to estimate the expected return on common stocks in1981? Would you have said 13.2 percent? That doesn’t make sense. Who would investin the risky stock market for an expected return of 13.2 percent when you could get asafe 14 percent from Treasury bills?

A better procedure is to take the current interest rate on Treasury bills plus 9.4 per-cent, the average risk premium shown in Table 3.9. In 1981, when the rate on Treasurybills was 14 percent, that would have given

Expected market=

interest rate on+

normal riskreturn (1981) Treasury bills (1981) premium

= 14% + 9.4% = 23.4%

The first term on the right-hand side tells us the time value of money in 1981; the sec-ond term measures the compensation for risk.

What about today? As we write this in mid-1999, Treasury bills offer a return of only4.8 percent. This suggests that investors in common stocks are looking for a return ofjust over 14 percent:4

Expected market return (1999)

= interest rate on Treasury bills (1999) + normal risk premium

= 4.8 + 9.4 = 14.2%

The expected return on an investment provides compensation to investors both for waiting (the time value of money) and for worrying (the risk of theparticular asset).

3 This is speaking a bit loosely, because the S&P 500 does not include all stocks traded in the United States,much less in world markets.4 In practice, things might be a bit more complicated. We’ve mentioned the yield curve, the relationship be-tween bond maturity and yield. When firms consider investments in long-lived projects, they usually thinkabout risk premiums relative to long-term bonds. In this case, the risk-free rate would be taken as the currentlong-term bond yield less the average maturity premium on such bonds.


These calculations assume that there is a normal, stable risk premium on the marketportfolio, so that the expected future risk premium can be measured by the average pastrisk premium. But even with 73 years of data, we cannot estimate the market risk pre-mium exactly; moreover, we cannot be sure that investors today are demanding the samereward for risk that they were in the 1940s or 1960s. All this leaves plenty of room forargument about what the risk premium really is. Many financial managers and econo-mists believe that long-run historical returns are the best measure available and there-fore settle on a risk premium of about 9 percent. Others have a gut instinct that investorsdon’t need such a large risk premium to persuade them to hold common stocks and soshade downward their estimate of the expected future risk premium.

Measuring RiskYou now have some benchmarks. You know that the opportunity cost of capital for safeprojects must be the rate of return offered by safe Treasury bills and you know that theopportunity cost of capital for “average-risk” projects must be the expected return onthe market portfolio. But you don’t know how to estimate the cost of capital for proj-ects that do not fit these two simple cases. Before you can do this you need to under-stand more about investment risk.

The average fuse time for army hand grenades is 7.0 seconds, but that average hidesa lot of potentially relevant information. If you are in the business of throwing grenades,you need some measure of the variation around the average fuse time.5 Similarly, if youare in the business of investing in securities, you need some measure of how far the re-turns may differ from the average.

Figure 3.14 showed the year-by-year returns for several investments from 1926 to1998. Another way of presenting these data is by histograms such as Figure 3.15. Eachbar shows the number of years that the market return fell within a specific range. Forexample, you can see that in 8 of the 73 years the return on common stocks was be-tween +15 percent and +20 percent. The risk shows up in the wide spread of outcomes.In 2 years the return was between +50 percent and +55 percent but there was also 1 yearin which it was between –40 percent and –45 percent.

VARIANCE AND STANDARD DEVIATION

The third histogram in Figure 3.15 shows the variation in common stock returns. Thereturns on common stock have been more variable than returns on bonds and Treasurybills. Common stocks have been risky investments. They will almost certainly continueto be risky investments.

Investment risk depends on the dispersion or spread of possible outcomes. Some-times a picture like Figure 3.15 tells you all you need to know about (past) dispersion.But in general, pictures do not suffice. The financial manager needs a numerical meas-ure of dispersion. The standard measures are variance and standard deviation. Morevariable returns imply greater investment risk. This suggests that some measure of dis-persion will provide a reasonable measure of risk, and dispersion is precisely what ismeasured by variance and standard deviation.

Here is a very simple example showing how variance and standard deviation are

5 We can reassure you; the variation around the standard fuse time is very small.

VARIANCE Averagevalue of squared deviationsfrom mean. A measure ofvolatility.

STANDARD DEVIATIONSquare root of variance.Another measure of volatility.

320 SECTION THREE

calculated. Suppose that you are offered the chance to play the following game. Youstart by investing $100. Then two coins are flipped. For each head that comes up your starting balance will be increased by 20 percent, and for each tail that comes up yourstarting balance will be reduced by 10 percent. Clearly there are four equally likely outcomes:

FIGURE 3.15Historical returns on major asset classes, 1926–1998.

Rate of return, percent

Num

ber

of

year

s

0�10 10

Averagereturn,percent

Standarddeviation,percent

3.8 3.2

Treasury bills


Num

ber

of

year

s

0�10�20�30�40 10 20 30 40 50

13.2 20.3

Common stocks


Num

ber

of

year

s

0�10 10 20

3.2 4.5

Inflation


Num

ber

of

year

s

0�10 10 20 30 40

5.7 9.2

Treasury bonds

0123

50454035302520151050

4567

98

05

3025201510

3540

5045

0

5

10

15

20

25

Source: Stocks, Bonds, Bills and Inflation® 1999 Yearbook, © 1999 Ibbotson Associates, Inc. Based on copyrighted works by Ibbotson andSinquefield. All Rights Reserved. Used with permission.


• Head + head: You make 20 + 20 = 40%• Head + tail: You make 20 – 10 = 10%• Tail + head: You make –10 + 20 = 10%• Tail + tail: You make –10 – 10 = –20%

There is a chance of 1 in 4, or .25, that you will make 40 percent; a chance of 2 in 4, or.5, that you will make 10 percent; and a chance of 1 in 4, or .25, that you will lose 20percent. The game’s expected return is therefore a weighted average of the possible out-comes:

Expected return = probability-weighted average of possible outcomes = (.25 × 40) + (.5 × 10) + (.25 × –20) = +10%

If you play the game a very large number of times, your average return should be 10percent.

Table 3.10 shows how to calculate the variance and standard deviation of the returnson your game. Column 1 shows the four equally likely outcomes. In column 2 we cal-culate the difference between each possible outcome and the expected outcome. You cansee that at best the return could be 30 percent higher than expected; at worst it could be30 percent lower.

These deviations in column 2 illustrate the spread of possible returns. But if we wanta measure of this spread, it is no use just averaging the deviations in column 2—the av-erage is always going to be zero. To get around this problem, we square the deviationsin column 2 before averaging them. These squared deviations are shown in column 3.The variance is the average of these squared deviations and therefore is a natural meas-ure of dispersion:

Variance = average of squared deviations around the average

=1,800

= 4504

When we squared the deviations from the expected return, we changed the units ofmeasurement from percentages to percentages squared. Our last step is to get back topercentages by taking the square root of the variance. This is the standard deviation:

Standard deviation = square root of variance

= √450 = 21%

Because standard deviation is simply the square root of variance, it too is a naturalmeasure of risk. If the outcome of the game had been certain, the standard deviationwould have been zero because there would then be no deviations from the expected

TABLE 3.10The coin-toss game;calculating variance andstandard deviation

(1) (2) (3)Percent Rate of Return Deviation from Expected Return Squared Deviation

+40 +30 900+10 0 0+10 0 0–20 –30 900

Variance = average of squared deviations = 1,800/4 = 450Standard deviation = square root of variance = √450 = 21.2, about 21%

322 SECTION THREE

outcome. The actual standard deviation is positive because we don’t know what willhappen.

Now think of a second game. It is the same as the first except that each head meansa 35 percent gain and each tail means a 25 percent loss. Again there are four equallylikely outcomes:

• Head + head: You gain 70%• Head + tail: You gain 10%• Tail + head: You gain 10%• Tail + tail: You lose 50%

For this game, the expected return is 10 percent, the same as that of the first game, butit is more risky. For example, in the first game, the worst possible outcome is a loss of20 percent, which is 30 percent worse than the expected outcome. In the second gamethe downside is a loss of 50 percent, or 60 percent below the expected return. This in-creased spread of outcomes shows up in the standard deviation, which is double that ofthe first game, 42 percent versus 21 percent. By this measure the second game is twiceas risky as the first.

A NOTE ON CALCULATING VARIANCE

When we calculated variance in Table 3.10 we recorded separately each of the four pos-sible outcomes. An alternative would have been to recognize that in two of the cases theoutcomes were the same. Thus there was a 50 percent chance of a 10 percent returnfrom the game, a 25 percent chance of a 40 percent return, and a 25 percent chance ofa –20 percent return. We can calculate variance by weighting each squared deviation bythe probability and then summing the results. Table 9.3 confirms that this method givesthe same answer.

� Self-Test 3 Calculate the variance and standard deviation of this second coin-tossing game in thesame formats as Tables 3.10 and 3.11.

MEASURING THE VARIATION IN STOCK RETURNS

When estimating the spread of possible outcomes from investing in the stock market,most financial analysts start by assuming that the spread of returns in the past is a rea-

TABLE 3.11The coin-toss game;calculating variance andstandard deviation whenthere are differentprobabilities of each outcome

(1) (2) (3) (4)Percent Rate Probability Deviation from Probability ×

of Return of Return Expected Return Squared Deviation

+40 .25 +30 .25 × 900 = 225+10 .50 0 .50 × 0 = 0–20 .25 –30 .25 × 900 = 225

Variance = sum of squared deviations weighted by probabilities = 225 + 0 + 225 = 450Standard deviation = square root of variance = √450 = 21.2, about 21%


sonable indication of what could happen in the future. Therefore, they calculate thestandard deviation of past returns. To illustrate, suppose that you were presented withthe data for stock market returns shown in Table 3.12. The average return over the 5years from 1994 to 1998 was 24.75 percent. This is just the sum of the returns over the5 years divided by 5 (123.75/5 = 24.75 percent).

Column 2 in Table 3.12 shows the difference between each year’s return and the av-erage return. For example, in 1994 the return of 1.31 percent on common stocks wasbelow the 5-year average by 23.44 percent (1.31 – 24.75 = –23.44 percent). In column3 we square these deviations from the average. The variance is then the average of thesesquared deviations:

Variance = average of squared deviations

=801.84

= 160.375

Since standard deviation is the square root of the variance,

Standard deviation = square root of variance

= √160.37 = 12.66%

It is difficult to measure the risk of securities on the basis of just five past outcomes.Therefore, Table 3.13 lists the annual standard deviations for our three portfolios of securities over the period 1926–1998. As expected, Treasury bills were the least variablesecurity, and common stocks were the most variable. Treasury bonds hold the middleground.

TABLE 3.12The average return andstandard deviation of stockmarket returns, 1994–1998

Deviation fromYear Rate of Return Average Return Squared Deviation

1994 1.31 –23.44 549.431995 37.43 12.68 160.781996 23.07 –1.68 2.821997 33.36 8.61 74.131998 28.58 3.83 14.67Total 123.75 801.84

Average rate of return = 123.75/5 = 24.75Variance = average of squared deviations = 801.84/5 = 160.37Standard deviation = square root of variance = 12.66%Source: Stocks, Bonds, Bills and Inflation 1999 Yearbook, Chicago: R. G. Ibbotson Associates, 1999.

TABLE 3.13Standard deviation of rates ofreturn, 1926–1998

Portfolio Standard Deviation, %

Treasury bills 3.2Long-term government bonds 9.2Common stocks 20.3

Source: Computed from data in Ibbotson Associates, Stocks, Bonds, Bills and Inflation 1999 Yearbook(Chicago, 1999).

324 SECTION THREE

Of course, there is no reason to believe that the market’s variability should stay thesame over many years. Indeed many people believe that in recent years the stock mar-ket has become more volatile due to irresponsible speculation by . . . (fill in here thename of your preferred guilty party). Figure 3.16 provides a chart of the volatility of theUnited States stock market for each year from 1926 to 1998.6 You can see that there areperiods of unusually high variability, but there is no long-term upward trend.

Risk and DiversificationDIVERSIFICATION

We can calculate our measures of variability equally well for individual securities andportfolios of securities. Of course, the level of variability over 73 years is less interest-ing for specific companies than for the market portfolio because it is a rare companythat faces the same business risks today as it did in 1926.

Table 3.14 presents estimated standard deviations for 10 well-known common stocksfor a recent 5-year period.7 Do these standard deviations look high to you? They should.Remember that the market portfolio’s standard deviation was about 20 percent over theentire 1926–1998 period. Of our individual stocks only Exxon had a standard deviationof less than 20 percent. Most stocks are substantially more variable than the marketportfolio; only a handful are less variable.

This raises an important question: The market portfolio is made up of individualstocks, so why isn’t its variability equal to the average variability of its components?The answer is that diversification reduces variability.

6 We converted the monthly variance to an annual variance by multiplying by 12. In other words, the varianceof annual returns is 12 times that of monthly returns. The longer you hold a security, the more risk you haveto bear.7 We pointed out earlier that five annual observations are insufficient to give a reliable estimate of variability.Therefore, these estimates are derived from 60 monthly rates of return and then the monthly variance is mul-tiplied by 12.

FIGURE 3.16Stock market volatility,1926–1998.

Ann

ualiz

ed s

tand

ard

dev

iati

on

of

mo

nthl

y re

turn

s, p

erce

nt

’26 ’30 ’340.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

’38 ’42 ’46 ’50 ’54 ’58

Year

’62 ’66 ’70 ’74 ’78 ’82 ’86 ’90 ’94 ’98

DIVERSIFICATIONStrategy designed to reducerisk by spreading theportfolio across manyinvestments.


Selling umbrellas is a risky business; you may make a killing when it rains but youare likely to lose your shirt in a heat wave. Selling ice cream is no safer; you do well inthe heat wave but business is poor in the rain. Suppose, however, that you invest in bothan umbrella shop and an ice cream shop. By diversifying your investment across the twobusinesses you make an average level of profit come rain or shine.

ASSET VERSUS PORTFOLIO RISK

The history of returns on different asset classes provides compelling evidence of arisk–return trade-off and suggests that the variability of the rates of return on each assetclass is a useful measure of risk. However, volatility of returns can be a misleadingmeasure of risk for an individual asset held as part of a portfolio. To see why, considerthe following example.

Suppose there are three equally likely outcomes, or scenarios, for the economy: a re-cession, normal growth, and a boom. An investment in an auto stock will have a rate ofreturn of –8 percent in a recession, 5 percent in a normal period, and 18 percent in aboom. Auto firms are cyclical: They do well when the economy does well. In contrast,gold firms are often said to be countercyclical, meaning that they do well when otherfirms do poorly. Suppose that stock in a gold mining firm will provide a rate of returnof 20 percent in a recession, 3 percent in a normal period, and –20 percent in a boom.These assumptions are summarized in Table 3.15.

It appears that gold is the more volatile investment. The difference in return acrossthe boom and bust scenarios is 40 percent (–20 percent in a boom versus +20 percentin a recession), compared to a spread of only 26 percent for the auto stock. In fact, wecan confirm the higher volatility by measuring the variance or standard deviation of re-turns of the two assets. The calculations are set out in Table 3.16.

Since all three scenarios are equally likely, the expected return on each stock is

Portfolio diversification works because prices of different stocks do not moveexactly together. Statisticians make the same point when they say that stockprice changes are less than perfectly correlated. Diversification works bestwhen the returns are negatively correlated, as is the case for our umbrella and ice cream businesses. When one business does well, the other does badly.Unfortunately, in practice, stocks that are negatively correlated are as rare aspecan pie in Budapest.

TABLE 3.14Standard deviations forselected common stocks, July1994–June 1999

Stock Standard Deviation, %

Biogen 46.6Compaq 46.7Delta Airlines 26.9Exxon 16.0Ford Motor Co. 24.9MCI WorldCom 34.4Merck 24.5Microsoft 34.0PepsiCo 26.5Xerox 27.3

326 SECTION THREE

simply the average of the three possible outcomes.8 For the auto stock the expected re-turn is 5 percent; for the gold stock it is 1 percent. The variance is the average of thesquared deviations from the expected return, and the standard deviation is the squareroot of the variance.

� Self-Test 4 Suppose the probabilities of the recession or boom are .30, while the probability of anormal period is .40. Would you expect the variance of returns on these two investmentsto be higher or lower? Why? Confirm by calculating the standard deviation of the autostock.

The gold mining stock offers a lower expected rate of return than the auto stock, andmore volatility—a loser on both counts, right? Would anyone be willing to hold goldmining stocks in an investment portfolio? The answer is a resounding yes.

To see why, suppose you do believe that gold is a lousy asset, and therefore hold yourentire portfolio in the auto stock. Your expected return is 5 percent and your standard

TABLE 3.16SExpected return and volatility for two stocks

Auto Stock Gold Stock

Deviation from Deviation fromRate of Expected Squared Rate of Expected Squared

Scenario Return, % Return, % Deviation Return, % Return, % Deviation

Recession –8 –13 169 +20 +19 361Normal +5 0 0 +3 +2 4Boom +18 +13 169 –20 –21 441

Expected return 1 (–8 + 5 + 18) = 5% 1 (+20 + 3 – 20) = 1%3 3

Variancea 1 (169 + 0 + 169) = 112.7 1 (361 + 4 + 441) = 268.73 3Standard deviation √112.7 = 10.6% √268.7 = 16.4%(= √variance)

a Variance = average of squared deviations from the expected value.

TABLE 3.15Rate of return assumptionsfor two stocks

Rate of Return, %

Scenario Probability Auto Stock Gold Stock

Recession 1/3 –8 +20Normal 1/3 +5 +3Boom 1/3 +18 –20

8 If the probabilities were not equal, we would need to weight each outcome by its probability in calculatingthe expected outcome and the variance.


deviation is 10.6 percent. We’ll compare that portfolio to a partially diversified one, in-vested 75 percent in autos and 25 percent in gold. For example, if you have a $10,000portfolio, you could put $7,500 in autos and $2,500 in gold.

First, we need to calculate the return on this portfolio in each scenario. The portfo-lio return is the weighted average of returns on the individual assets with weights equalto the proportion of the portfolio invested in each asset. For a portfolio formed fromonly two assets,

Portfolio rate= (fraction of portfolio

�rate of return)of return in first asset on first asset

+ (fraction of portfolio�

rate of return )in second asset on second asset

For example, autos have a weight of .75 and a rate of return of –8 percent in the reces-sion, and gold has a weight of .25 and a return of 20 percent in a recession. Therefore,the portfolio return in the recession is the following weighted average:9

Portfolio return in recession = [.75 × (–8%)] + [.25 × 20%]

= –1%

Table 3.17 expands Table 3.15 to include the portfolio of the auto stock and the goldmining stock. The expected returns and volatility measures are summarized at the bot-tom of the table. The surprising finding is this: When you shift funds from the autostock to the more volatile gold mining stock, your portfolio variability actually de-creases. In fact, the volatility of the auto-plus-gold stock portfolio is considerably lessthan the volatility of either stock separately. This is the payoff to diversification.

We can understand this more clearly by focusing on asset returns in the two extremescenarios, boom and recession. In the boom, when auto stocks do best, the poor returnon gold reduces the performance of the overall portfolio. However, when auto stocksare stalling in a recession, gold shines, providing a substantial positive return that boosts

TABLE 3.17Rates of return for two stocksand a portfolio

Rate of Return, %Portfolio

Scenario Probability Auto Stock Gold Stock Return, %a

Recession 1/3 –8 +20 –1.0%Normal 1/3 +5 +3 +4.5Boom 1/3 +18 –20 +8.5

Expected return 5% 1% 4%Variance 112.7 268.7 15.2Standard deviation 10.6% 16.4% 3.9%

a Portfolio return = (.75 × auto stock return) + (.25 × gold stock return).

9 Let’s confirm this. Suppose you invest $7,500 in autos and $2,500 in gold. If the recession hits, the rate ofreturn on autos will be –8 percent, and the value of the auto investment will fall by 8 percent to $6,900. Therate of return on gold will be 20 percent, and the value of the gold investment will rise 20 percent to $3,000.The value of the total portfolio falls from its original value of $10,000 to $6,900 + $3,000 = $9,900, which isa rate of return of –1 percent. This matches the rate of return given by the formula for the weighted average.

328 SECTION THREE

portfolio performance. The gold stock offsets the swings in the performance of the autostock, reducing the best-case return but improving the worst-case return. The inverse relationship between the returns on the two stocks means that the addition of the goldmining stock to an all-auto portfolio stabilizes returns.

A gold stock is really a negative-risk asset to an investor starting with an all-autoportfolio. Adding it to the portfolio reduces the volatility of returns. The incrementalrisk of the gold stock (that is, the change in overall risk when gold is added to the port-folio) is negative despite the fact that gold returns are highly volatile.

In general, the incremental risk of a stock depends on whether its returns tend to varywith or against the returns of the other assets in the portfolio. Incremental risk does notjust depend on a stock’s volatility. If returns do not move closely with those of the restof the portfolio, the stock will reduce the volatility of portfolio returns.

We can summarize as follows:

� EXAMPLE 1 Merck and Ford Motor

Let’s look at a more realistic example of the effect of diversification. Figure 3.17ashows the monthly returns of Merck stock from 1994 to 1999. The average monthly re-turn was 3.1 percent but you can see that there was considerable variation around thataverage. The standard deviation of monthly returns was 7.1 percent. As a rule of thumb,in roughly one-third of the months the return is likely to be more than one standard de-viation above or below the average return.10 The figure shows that the return did indeeddiffer by more than 7.1 percent from the average on about a third of the occasions.

Figure 3.17b shows the monthly returns of Ford Motor. The average monthly returnon Ford was 2.3 percent and the standard deviation was 7.2 percent, about the same asthat of Merck. Again you can see that in about a third of the cases the return differedfrom the average by more than one standard deviation.

An investment in either Merck or Ford would have been very variable. But the for-tunes of the two stocks were not perfectly related.11 There were many occasions when a

1. Investors care about the expected return and risk of their portfolio ofassets. The risk of the overall portfolio can be measured by the volatility of returns, that is, the variance or standard deviation.

2. The standard deviation of the returns of an individual security measureshow risky that security would be if held in isolation. But an investor whoholds a portfolio of securities is interested only in how each security affects the risk of the entire portfolio. The contribution of a security to the risk of the portfolio depends on how the security’s returns vary withthe investor’s other holdings. Thus a security that is risky if held inisolation may nevertheless serve to reduce the variability of the portfolio,as long as its returns vary inversely with those of the rest of the portfolio.

10 For any normal distribution, approximately one-third of the observations lie more than one standard devi-ation above or below the average. Over short intervals stock returns are roughly normally distributed.11 Statisticians calculate a correlation coefficient as a measure of how closely two series move together. IfFord’s and Merck’s stock moved in perfect lockstep, the correlation coefficient between the returns would be1.0. If their returns were completely unrelated, the correlation would be zero. The actual correlation betweenthe returns on Ford and Merck was .03. In other words, the returns were almost completely unrelated.


decline in the value of one stock was canceled by a rise in the price of the other. Be-cause the two stocks did not move in exact lockstep, there was an opportunity to reducevariability by spreading one’s investment between them. For example, Figure 3.17c

FIGURE 3.17The variability of a portfolio with equal holdings in Merck and Ford Motor wouldhave been only 70 percent of the variability of the individual stocks.

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shows the returns on a portfolio that was equally divided between the stocks. Themonthly standard deviation of this portfolio would have been only 5.1 percent—that is,about 70 percent of the variability of the individual stocks.

� Self-Test 5 An investor is currently fully invested in gold mining stocks. Which action would domore to reduce portfolio risk: diversification into silver mining stocks or into automo-tive stocks? Why?

MARKET RISK VERSUS UNIQUE RISK

Our examples illustrate that even a little diversification can provide a substantial re-duction in variability. Suppose you calculate and compare the standard deviations ofrandomly chosen one-stock portfolios, two-stock portfolios, five-stock portfolios, andso on. You can see from Figure 3.18 that diversification can cut the variability of returnsby about half. But you can get most of this benefit with relatively few stocks: the im-provement is slight when the number of stocks is increased beyond, say, 15.

Figure 3.18 also illustrates that no matter how many securities you hold, you cannoteliminate all risk. There remains the danger that the market—including your portfolio—will plummet.

The risk that can be eliminated by diversification is called unique risk. The risk thatyou can’t avoid regardless of how much you diversify is generally known as marketrisk or systematic risk.

Figure 3.19 divides risk into its two parts—unique risk and market risk. If you haveonly a single stock, unique risk is very important; but once you have a portfolio of 30or more stocks, diversification has done most of what it can to eliminate risk.

Unique risk arises because many of the perils that surround an individualcompany are peculiar to that company and perhaps its direct competitors.Market risk stems from economywide perils that threaten all businesses.Market risk explains why stocks have a tendency to move together, so thateven well-diversified portfolios are exposed to market movements.

FIGURE 3.18Diversification reduces risk(standard deviation) rapidlyat first, then more slowly.

Number of securities

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UNIQUE RISK Riskfactors affecting only thatfirm. Also called diversifiablerisk.

MARKET RISKEconomywide(macroeconomic) sources ofrisk that affect the overallstock market. Also calledsystematic risk.


Thinking about RiskHow can you tell which risks are unique and diversifiable? Where do market risks comefrom? Here are three messages to help you think clearly about risk.

MESSAGE 1: SOME RISKS LOOK BIG ANDDANGEROUS BUT REALLY ARE DIVERSIFIABLE

Managers confront risks “up close and personal.” They must make decisions about particular investments. The failure of such an investment could cost a promotion, bonus,or otherwise steady job. Yet that same investment may not seem risky to an investor whocan stand back and combine it in a diversified portfolio with many other assets or securities.

� EXAMPLE 2 Wildcat Oil Wells

You have just been promoted to director of exploration, Western Hemisphere, of MPSOil. The manager of your exploration team in far-off Costaguana has appealed for $20million extra to drill in an even steamier part of the Costaguanan jungle. The managerthinks there may be an “elephant” field worth $500 million or more hidden there. Butthe chance of finding it is at best one in ten, and yesterday MPS’s CEO sourly com-mented on the $100 million already “wasted” on Costaguanan exploration.

Is this a risky investment? For you it probably is; you may be a hero if oil is foundand a goat otherwise. But MPS drills hundreds of wells worldwide; for the company as

For a reasonably well-diversified portfolio, only market risk matters.

FIGURE 3.19Diversification eliminatesunique risk. But there is somerisk that diversificationcannot eliminate. This iscalled market risk.

Number of securities

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332 SECTION THREE

a whole, it’s the average success rate that matters. Geologic risks (is there oil or not?)should average out. The risk of a worldwide drilling program is much less than the ap-parent risk of any single wildcat well.

Back up one step, and think of the investors who buy MPS stock. The investors mayhold other oil companies too, as well as companies producing steel, computers, cloth-ing, cement, and breakfast cereal. They naturally—and realistically—assume that yoursuccesses and failures in drilling oil wells will average out with the thousands of inde-pendent bets made by the companies in their portfolio.

Therefore, the risks you face in Costaguana do not affect the rate of return they de-mand for investing in MPS Oil. Diversified investors in MPS stock will be happy if youfind that elephant field, but they probably will not notice if you fail and lose your job.In any case, they will not demand a higher average rate of return for worrying about ge-ologic risks in Costaguana.

� EXAMPLE 3 Fire Insurance

Would you be willing to write a $100,000 fire insurance policy on your neighbor’shouse? The neighbor is willing to pay you $100 for a year’s protection, and experienceshows that the chance of fire damage in a given year is substantially less than one in athousand. But if your neighbor’s house is damaged by fire, you would have to pay up.

Few of us have deep enough pockets to insure our neighbors, even if the odds of firedamage are very low. Insurance seems a risky business if you think policy by policy.But a large insurance company, which may issue a million policies, is concerned onlywith average losses, which can be predicted with excellent accuracy.

� Self-Test 6 Imagine a laboratory at IBM, late at night. One scientist speaks to another.“You’re right, Watson, I admit this experiment will consume all the rest of this year’s

budget. I don’t know what we’ll do if it fails. But if this yttrium–magnoosium alloy su-perconducts, the patents will be worth millions.”

Would this be a good or bad investment for IBM? Can’t say. But from the ultimateinvestors’ viewpoint this is not a risky investment. Explain why.

MESSAGE 2: MARKET RISKS ARE MACRO RISKS

We have seen that diversified portfolios are not exposed to the unique risks of individ-ual stocks but are exposed to the uncertain events that affect the entire securities mar-ket and the entire economy. These are macroeconomic, or “macro,” factors such aschanges in interest rates, industrial production, inflation, foreign exchange rates, andenergy costs. These factors affect most firms’ earnings and stock prices. When the rel-evant macro risks turn generally favorable, stock prices rise and investors do well; whenthe same variables go the other way, investors suffer.

You can often assess relative market risks just by thinking through exposures to thebusiness cycle and other macro variables. The following businesses have substantialmacro and market risks:


• Airlines. Because business travel falls during a recession, and individuals postponevacations and other discretionary travel, the airline industry is subject to the swingsof the business cycle. On the positive side, airline profits really take off when busi-ness is booming and personal incomes are rising.

• Machine tool manufacturers. These businesses are especially exposed to the busi-ness cycle. Manufacturing companies that have excess capacity rarely buy new ma-chine tools to expand. During recessions, excess capacity can be quite high.

Here, on the other hand, are two industries with less than average macro exposures:

• Food companies. Companies selling staples, such as breakfast cereal, flour, and dogfood, find that demand for their products is relatively stable in good times and bad.

• Electric utilities. Business demand for electric power varies somewhat across thebusiness cycle, but by much less than demand for air travel or machine tools. Also,many electric utilities’ profits are regulated. Regulation cuts off upside profit poten-tial but also gives the utilities the opportunity to increase prices when demand isslack.

� Self-Test 7 Which company of each of the following pairs would you expect to be more exposed tomacro risks?

a. A luxury Manhattan restaurant or an established Burger Queen franchise?b. A paint company that sells through small paint and hardware stores to do-it-your-

selfers, or a paint company that sells in large volumes to Ford, GM, and Chrysler?

MESSAGE 3: RISK CAN BE MEASURED

United Airlines clearly has more exposure to macro risks than food companies such asKellogg or General Mills. These are easy cases. But is IBM stock a riskier investmentthan Exxon? That’s not an easy question to reason through. We can, however, measurethe risk of IBM and Exxon by looking at how their stock prices fluctuate.

We’ve already hinted at how to do this. Remember that diversified investors are con-cerned with market risks. The movements of the stock market sum up the net effects ofall relevant macroeconomic uncertainties. If the market portfolio of all traded stocks isup in a particular month, we conclude that the net effect of macroeconomic news is pos-itive. Remember, the performance of the market is barely affected by a firm-specificevent. These cancel out across thousands of stocks in the market.

How do we measure the risk of a single stock, like IBM or Exxon? We do not lookat the stocks in isolation, because the risks that loom when you’re up close to a singlecompany are often diversifiable. Instead we measure the individual stock’s sensitivity tothe fluctuations of the overall stock market.

Remember, investors holding diversified portfolios are mostly concerned withmacroeconomic risks. They do not worry about microeconomic risks peculiarto a particular company or investment project. Micro risks wash out indiversified portfolios. Company managers may worry about both macro andmicro risks, but only the former affect the cost of capital.

334 SECTION THREE

SummaryHow can one estimate the opportunity cost of capital for an “average-risk” project?

Over the past 73 years the return on the Standard & Poor’s Composite Index of commonstocks has averaged almost 9.4 percent a year higher than the return on safe Treasury bills.This is the risk premium that investors have received for taking on the risk of investing instocks. Long-term bonds have offered a higher return than Treasury bills but less than stocks.

If the risk premium in the past is a guide to the future, we can estimate the expectedreturn on the market today by adding that 9.4 percent expected risk premium to today’sinterest rate on Treasury bills. This would be the opportunity cost of capital for an average-risk project, that is, one with the same risk as a typical share of common stock.

How is the standard deviation of returns for individual common stocks or for astock portfolio calculated?

The spread of outcomes on different investments is commonly measured by the variance orstandard deviation of the possible outcomes. The variance is the average of the squareddeviations around the average outcome, and the standard deviation is the square root of thevariance. The standard deviation of the returns on a market portfolio of common stocks hasaveraged about 20 percent a year.

Why does diversification reduce risk?

The standard deviation of returns is generally higher on individual stocks than it is on themarket. Because individual stocks do not move in exact lockstep, much of their risk can bediversified away. By spreading your portfolio across many investments you smooth out therisk of your overall position. The risk that can be eliminated through diversification isknown as unique risk.

What is the difference between unique risk, which can be diversified away, andmarket risk, which cannot?

Even if you hold a well-diversified portfolio, you will not eliminate all risk. You will still beexposed to macroeconomic changes that affect most stocks and the overall stock market.These macro risks combine to create market risk—that is, the risk that the market as awhole will slump.

Stocks are not all equally risky. But what do we mean by a “high-risk stock”? We don’tmean a stock that is risky if held in isolation; we mean a stock that makes an above-averagecontribution to the risk of a diversified portfolio. In other words, investors don’t need toworry much about the risk that they can diversify away; they do need to worry about risk thatcan’t be diversified. This depends on the stock’s sensitivity to macroeconomic conditions.

www.financialengines.com Some good introductory material on risk, return, and inflationwww.stern.nyu.edu/~adamodar/ This New York University site contains some historical data on

market risk and return

market indexDow Jones Industrial AverageStandard & Poor’s Composite Indexmaturity premium

risk premiumvariancestandard deviation

diversificationunique riskmarket risk

Related WebLinks

Key Terms

407

RISK, RETURN, ANDCAPITAL BUDGETING

Measuring Market RiskMeasuring Beta

Betas for MCI WorldCom and Exxon

Portfolio Betas

Risk and ReturnWhy the CAPM Works

The Security Market Line

How Well Does the CAPM Work?

Using the CAPM to Estimate Expected Returns

Capital Budgeting and Project RiskCompany versus Project Risk

Determinants of Project Risk

Don’t Add Fudge Factors to Discount Rates

Summary

Professor William F. Sharpe receiving the Nobel Prize in Economics.The prize was for Sharpe’s development of the capital asset pricing model. This model showshow risk should be measured and provides a formula relating risk to the opportunity cost ofcapital.Leif Jansson/Pica Pressfoto

arlier we began to come to grips with the topic of risk. We made the dis-

tinction between unique risk and macro, or market, risk. Unique risk

arises from events that affect only the individual firm or its immediate

competitors; it can be eliminated by diversification. But regardless of how

much you diversify, you cannot avoid the macroeconomic events that create market risk.

This is why investors do not require a higher rate of return to compensate for unique

risk but do need a higher return to persuade them to take on market risk.

How can you measure the market risk of a security or a project? We will see that

market risk is usually measured by the sensitivity of the investment’s returns to fluctu-

ations in the market. We will also see that the risk premium investors demand should be

proportional to this sensitivity. This relationship between risk and return is a useful way

to estimate the return that investors expect from investing in common stocks.

Finally, we will distinguish between the risk of the company’s securities and the risk

of an individual project. We will also consider what managers should do when the risk

of the project is different from that of the company’s existing business.


� Measure and interpret the market risk, or beta, of a security.

� Relate the market risk of a security to the rate of return that investors demand.

� Calculate the opportunity cost of capital for a project.

408

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Measuring Market RiskChanges in interest rates, government spending, monetary policy, oil prices, foreign ex-change rates, and other macroeconomic events affect almost all companies and the re-turns on almost all stocks. We can therefore assess the impact of “macro” news bytracking the rate of return on a market portfolio of all securities. If the market is up ona particular day, then the net impact of macroeconomic changes must be positive. Weknow the performance of the market reflects only macro events, because firm-specificevents—that is, unique risks—average out when we look at the combined performanceof thousands of companies and securities.

In principle the market portfolio should contain all assets in the world economy—not just stocks, but bonds, foreign securities, real estate, and so on. In practice, however,financial analysts make do with indexes of the stock market, usually the Standard &Poor’s Composite Index (the S&P 500).1

Our task here is to define and measure the risk of individual common stocks. Youcan probably see where we are headed. Risk depends on exposure to macroeconomicevents and can be measured as the sensitivity of a stock’s returns to fluctuations in re-turns on the market portfolio. This sensitivity is called the stock’s beta. Beta is oftenwritten as the Greek letter β.

1 We discussed the most popular stock market indexes in Section 9.2.

MARKET PORTFOLIOPortfolio of all assets in theeconomy. In practice a broadstock market index, such asthe Standard & Poor’sComposite, is used torepresent the market.

BETA Sensitivity of astock’s return to the returnon the market portfolio.

Risk, Return, and Capital Budgeting 409

MEASURING BETA

Earlier we looked at the variability of individual securities. Compaq had the higheststandard deviation and Exxon the lowest. If you had held Compaq on its own, your re-turns would have varied almost three times as much as if you had held Exxon. But wiseinvestors don’t put all their eggs in just one basket: they reduce their risk by diversifi-cation. An investor with a diversified portfolio will be interested in the effect each stockhas on the risk of the entire portfolio.

Diversification can eliminate the risk that is unique to individual stocks, but not therisk that the market as a whole may decline, carrying your stocks with it.

Some stocks are less affected than others by market fluctuations. Investment man-agers talk about “defensive” and “aggressive” stocks. Defensive stocks are not very sen-sitive to market fluctuations. In contrast, aggressive stocks amplify any market move-ments. If the market goes up, it is good to be in aggressive stocks; if it goes down, it isbetter to be in defensive stocks (and better still to have your money in the bank).

Now we’ll show you how betas are measured.

� EXAMPLE 1 Measuring Beta for Turbot-Charged Seafoods

Suppose we look back at the trading history of Turbot-Charged Seafoods and pick out6 months when the return on the market portfolio was plus or minus 1 percent.

Month Market Return, % Turbot-Charged Seafood’s Return, %

1 +1 + .82 +1 + 1.8 } Average = .8%3 +1 – .24 –1 – 1.85 –1 + .2 } Average = –.8%6 –1 – .8

Look at Figure 4.7, where these observations are plotted. We’ve drawn a line throughthe average performance of Turbot when the market is up or down by 1 percent. Theslope of this line is Turbot’s beta. You can see right away that the beta is .8, because onaverage Turbot stock gains or loses .8 percent when the market is up or down by 1 per-cent. Notice that a 2-percentage-point difference in the market return (–1 to +1) gener-ates on average a 1.6-percentage-point difference for Turbot shareholders (–.8 to +.8).The ratio, 1.6/2 = .8, is beta.

In 4 months, Turbot’s returns lie above or below the line in Figure 4.7. The distancefrom the line shows the response of Turbot’s stock returns to news or events that affectedTurbot but did not affect the overall market. For example, in Month 2, investors in Turbot stock benefited from good macroeconomic news (the market was up 1 percent)and also from some favorable news specific to Turbot. The market rise gave a boost of .8 percent to Turbot stock (beta of .8 times the 1 percent market return). Then

Aggressive stocks have high betas, betas greater than 1.0, meaning that theirreturns tend to respond more than one-for-one to changes in the return of theoverall market. The betas of defensive stocks are less than 1.0. The returns ofthese stocks vary less than one-for-one with market returns. The average betaof all stocks is—no surprises here—1.0 exactly.

410 SECTION FOUR

firm-specific news gave Turbot stockholders an extra 1 percent return, for a total returnthat month of 1.8 percent.

Of course diversification can get rid of the unique risks. That’s why wise investors,who don’t put all their eggs in one basket, will look to Turbot’s less-than-average betaand call its stock “defensive.”

� Self-Test 1 Here are 6 months’ returns to stockholders in the Anchovy Queen restaurant chain:

Month Market Return, % Anchovy Queen Return, %

1 +1 +2.02 +1 + 03 +1 +1.04 –1 – 1.05 –1 + 06 –1 – 2.0

Draw a figure like Figure 4.7 and check the slope of the fitted line. What is AnchovyQueen’s beta?

Real life doesn’t serve up numbers quite as convenient as those in our examples sofar. However, the procedure for measuring real companies’ betas is exactly the same:

1. Observe rates of return, usually monthly, for the stock and the market.2. Plot the observations as in Figure 4.7.3. Fit a line showing the average return to the stock at different market returns.

Beta is the slope of the fitted line.

As this example illustrates, we can break down common stock returns into two parts: the part explained by market returns and the firm’s beta, and thepart due to news that is specific to the firm. Fluctuations in the first partreflect market risk; fluctuations in the second part reflect unique risk.

FIGURE 4.7This figure is a plot of thedata presented in the tablefrom Example 1. Each pointshows the performance ofTurbot-Charged Seafoodsstock when the overall marketis either up or down by 1percent. On average, Turbot-Charged moves in the samedirection as the market, butnot as far. Therefore, Turbot-Charged’s beta is less than1.0. We can measure beta bythe slope of a line fitted tothe points in the figure. Inthis case it is .8.

Turbot-Charged return,percent

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This may sound like a lot of work but in practice computers do it for you. Here aretwo real examples.

BETAS FOR MCI WORLDCOM AND EXXON

Each point in Figure 4.8a shows the return on MCI WorldCom stock and the return onthe market index in a different month. For example, the circled point shows that in themonth of May 1997 MCI stock price rose by 23 percent, whereas the market index roseby 5.9 percent. Notice that more often than not MCI outperformed the market when theindex rose and underperformed the market when the index fell. Thus MCI was a rela-tively aggressive, high-beta stock.

We have drawn a line of best fit through the points in the figure.2 The slope of this

FIGURE 4.8(a) Each point in this figureshows the returns on MCIcommon stock and theoverall market in a particularmonth. Sixty months areplotted in all. MCI’s beta isthe slope of the line fitted tothese points. MCI has arelatively high beta of 1.3.(b) In this plot of 60 months’returns for Exxon and theoverall market the slope ofthe fitted line is much lessthan MCI’s beta in (a). Exxonhas a relatively low beta of.61.

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412 SECTION FOUR

line is 1.3. For each extra 1 percent rise in the market MCI stock price moved on aver-age an extra 1.3 percent. For each extra 1 percent fall in the market, MCI stock pricefell an extra 1.3 percent. Thus MCI’s beta was 1.3.

Of course, MCI’s stock returns are not perfectly related to market returns. The com-pany was also subject to unique risk, which shows up in the scatter of points around theline. Sometimes MCI flew south while the market went north, or vice versa.

Figure 4.8b shows a similar plot of the monthly returns for Exxon. In contrast toMCI, Exxon was a defensive, low-beta stock. It was not highly sensitive to marketmovements, usually lagging when the market rose and yet doing better (or less badly)when the market fell. The slope of the line of best fit shows that on average an extra 1percent change in the index resulted in an extra .61 percent change in the price of Exxonstock. Thus Exxon’s beta was .61.

You may find it interesting to look at Table 4.9, which shows how past marketmovements have affected several well-known stocks. Exxon had the lowest beta: itsstock return was .61 times as sensitive as the average stock to market movements. Mi-crosoft was at the other extreme: its return was 1.33 times as sensitive as the averagestock to market movements.

PORTFOLIO BETAS

Diversification decreases variability from unique risk but not from market risk. Thebeta of a portfolio is just an average of the betas of the securities in the portfolio,weighted by the investment in each security. For example, a portfolio comprised of onlytwo stocks would have a beta as follows:

Thus a portfolio invested 50-50 in MCI and Exxon would have a beta of (.5 × 1.3) + (.5× .61) = .95.

A well-diversified portfolio of stocks all with betas of 1.3, like MCI, would still havea portfolio beta of 1.3. However, most of the individual stocks’ unique risk would be di-versified away. The market risk would remain, and such a portfolio would end up 1.3

Beta of portfolio = (fraction of portfolio in first stock × beta of first stock) + (fraction of portfolio in second stock × beta of

second stock)

TABLE 4.9Betas for selected commonstocks, July 1994–June 1999

Stock Beta

Biogen 1.07Compaq 1.14Delta Airlines .85Exxon .61Ford Motor Co. .97MCI WorldCom 1.30Merck .92Microsoft 1.33PepsiCo 1.33Xerox 1.20

Note: Betas are calculated from 5 years of monthly returns.


times as variable as the market. For example, if the market has an annual standard de-viation of 20 percent (about the historical average reported earlier), a fully diversifiedportfolio with beta of 1.3 has a standard deviation of 1.3 × 20 = 26 percent.

Portfolios with betas between 0 and 1.0 tend to move in the same direction as themarket but not as far. A well-diversified portfolio of low-beta stocks like Exxon, allwith betas of .61, has almost no unique risk and is relatively unaffected by marketmovements. Such a portfolio is .61 times as variable as the market.

Of course, on average stocks have a beta of 1.0. A well-diversified portfolio includ-ing all kinds of stocks, with an average beta of 1, has the same variability as the mar-ket index.

� Self-Test 2 Say you invested an equal amount in each of the stocks shown in Table 4.9. Calculatethe beta of your portfolio.

� EXAMPLE 2 How Risky Are Mutual Funds?

You don’t have to be wealthy to own a diversified portfolio. You can buy shares in oneof the more than 6,000 mutual funds in the United States.

Investors buy shares of the funds, and the funds use the money to buy portfolios ofsecurities. The returns on the portfolios are passed back to the funds’ owners in pro-portion to their shareholdings. Therefore, the funds act like investment cooperatives, offering even the smallest investors diversification and professional management at low cost.

Let’s look at the betas of two mutual funds that invest in stocks. Figure 4.9a plots themonthly returns of Vanguard’s Windsor II mutual fund and of the S&P index from July1994 to June 1999. You can see that the stocks in the Windsor II fund had nearly aver-age sensitivity to market changes: they had on average a beta of .87.

If the Windsor II fund had no unique risk, its portfolio would have been .87 times asvariable as the market portfolio. But the fund had not diversified away quite all theunique risk; there is still some scatter about the line in Figure 4.9a. As a result, the vari-ability of the fund was somewhat more than .87 times that of the market.

Figure 4.9b shows the same sort of plot for Vanguard’s Index Trust 500 Portfolio mu-tual fund. Notice that this fund has a beta of 1.0 and only a tiny residual of unique risk—the fitted line fits almost exactly because an index fund is designed to track the marketas closely as possible. The managers of the fund do not attempt to pick good stocks butjust work to achieve full diversification at very low cost. (The Vanguard index fundtakes investments of as little as $3,000 and manages the fund for an annual fee of lessthan .20 percent of the fund’s assets.) The index fund is fully diversified. Investors inthis fund buy the market as a whole and don’t have to worry at all about unique risk.

� Self-Test 3 Suppose you could achieve full diversification in a portfolio constructed from stockswith an average beta of .5. If the standard deviation of the market is 20 percent per year,what is the standard deviation of the portfolio return?

414 SECTION FOUR

Risk and ReturnEarlier we looked at past returns on selected investments. The least risky investmentwas U.S. Treasury bills. Since the return on Treasury bills is fixed, it is unaffected bywhat happens to the market. Thus the beta of Treasury bills is zero. The most risky in-vestment that we considered was the market portfolio of common stocks. This has av-erage market risk: its beta is 1.0.

Wise investors don’t run risks just for fun. They are playing with real money andtherefore require a higher return from the market portfolio than from Treasury bills. Thedifference between the return on the market and the interest rate on bills is termed themarket risk premium. Over the past 73 years the average market risk premium hasbeen just over 9 percent a year. Of course, there is plenty of scope for argument as towhether the past 73 years constitute a typical period, but we will just assume here that9 percent is the normal risk premium, that is, the additional return that an investor couldreasonably expect from investing in the stock market rather than Treasury bills.

FIGURE 4.9(a) The slope of the fitted lineshows that investors in theWindsor II mutual fund boremarket risk slightly belowthat of the S&P 500portfolio. Windsor II’s betawas .87. This was the averagebeta of the individualcommon stocks held by thefund. They also bore someunique risk, however; notethe scatter of Windsor II’sreturns above and below thefitted line.(b) The Vanguard 500Portfolio is a fully diversifiedindex fund designed to trackthe performance of themarket. Note the fund’s beta(1.0) and the absence ofunique risk. The fund’sreturns lie almost preciselyon the fitted line relating itsreturns to those of the S&P500 portfolio.

�20

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MARKET RISKPREMIUM Risk premiumof market portfolio.Difference between marketreturn and return on risk-freeTreasury bills.


In Figure 4.10a we plotted the risk and expected return from Treasury bills and themarket portfolio. You can see that Treasury bills have a beta of zero and a risk-free re-turn; we’ll assume that return is 5 percent. The market portfolio has a beta of 1.0 andan assumed expected return of 14 percent.3

Now, given these two benchmarks, what expected rate of return should an investorrequire from a stock or portfolio with a beta of .5? Halfway between, of course. Thus in Figure 4.10b we drew a straight line through the Treasury bill return and the expectedmarket return and marked with an X the expected return for a beta of .5, that is, 9.5 percent. This includes a risk premium of 4.5 percent above the Treasury bill return of 5percent.

You can calculate this return as follows: start with the difference between the ex-pected market return rm and the Treasury bill rate rf. This is the expected market riskpremium.

FIGURE 4.10(a) Here we begin the plot ofexpected rate of returnagainst beta. The firstbenchmarks are Treasurybills (beta = 0) and themarket portfolio (beta = 1.0).We assume a Treasury billrate of 5 percent and amarket return of 14 percent.The market risk premium is14 – 5 = 9 percent.(b) A portfolio split evenlybetween Treasury bills andthe market will have beta =.5 and an expected return of9.5 percent (point X). Aportfolio invested 80 percentin the market and 20 percentin Treasury bills has beta =.8 and an expected rate ofreturn of 12.2 percent (pointY). Note that the expectedrate of return on anyportfolio mixing Treasurybills and the market lies on astraight line. The riskpremium is proportional tothe portfolio beta.

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Treasury bills

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14

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3 On past evidence the risk premium on the market is 9 percent. With a 5 percent Treasury bill rate, the ex-pected market return would be 5 + 9 = 14 percent.

416 SECTION FOUR

Market risk premium = rm – rf = 14% – 5% = 9%

Beta measures risk relative to the market. Therefore, the expected risk premium onany asset equals beta times the market risk premium:

Risk premium on any asset = r – rf = β(rm – rf)

With a beta of .5 and a market risk premium of 9 percent,

Risk premium = β(rm – rf) = .5 × 9 = 4.5%

The total expected rate of return is the sum of the risk-free rate and the risk premium:

Expected return = risk-free rate + risk premium

r = rf + β(rm – rf)

= 5% + 4.5% = 9.5%

You could have calculated the expected rate of return in one step from this formula:

Expected return = r = rf + β(rm – rf)

= 5% + (.5 × 9%) = 9.5%

This formula states the basic risk–return relationship called the capital asset pricingmodel, or CAPM. The CAPM has a simple interpretation:

Note that the expected rate of return on an asset with β = 1 is just the market return.With a risk-free rate of 5 percent and market risk premium of 9 percent,


= 5% + (1 × 9%) = 14%

� Self-Test 4 What are the risk premium and expected rate of return on a stock with β = 1.5? Assumea Treasury bill rate of 6 percent and a market risk premium of 9 percent.

WHY THE CAPM WORKS

The CAPM assumes that the stock market is dominated by well-diversified investorswho are concerned only with market risk. That makes sense in a stock market wheretrading is dominated by large institutions and even small fry can diversify at very lowcost.

� EXAMPLE 3 How Would You Invest $1 Million?

Have you ever daydreamed about receiving a $1 million check, no strings attached, froman unknown benefactor? Let’s daydream about how you would invest it.

We have two good candidates: Treasury bills, which offer an absolutely safe return,and the market portfolio (possibly via the Vanguard index fund discussed earlier in this

The expected rates of return demanded by investors depend on two things:(1) compensation for the time value of money (the risk-free rate rf), and (2) arisk premium, which depends on beta and the market risk premium.

CAPITAL ASSETPRICING MODEL(CAPM) Theory of therelationship between risk andreturn which states that theexpected risk premium onany security equals its betatimes the market riskpremium.


material). The market has generated superior returns on average, but those returns havefluctuated a lot. (Look back to Figure 3.15.) So your investment policy is going to de-pend on your tolerance for risk.

If you’re a cautious soul, you may invest only part of your money in the market port-folio and lend the remainder to the government by buying Treasury bills. Suppose thatyou invest 80 percent of your money in the market portfolio and lend out the other 20percent to the government by buying U.S. Treasury bills. Then the beta of your portfo-lio will be a mixture of the beta of the market (βmarket = 1.0) and the beta of the T-bills(βT-bills = 0):

Beta of portfolio = (proportion × beta of ) + (proportion × beta of )in market market in T-bills T-bills

β = (.8 × βmarket) + (.2 × βT-bills)

= (.8 × 1.0) + (.2 × 0) = .80

The fraction of funds that you invest in the market also affects your return. If you in-vest your entire million in the market portfolio, you earn the full market risk premium.But if you invest only 80 percent of your money in the market, you earn only 80 per-cent of the risk premium.

Expectedrisk premium = (proportion in × risk premium ) + ( proportion in × market risk)on portfolio

T-bills on T-bills market premium

= (.2 × 0) + (.8 × expected market risk premium)

= .8 × expected market risk premium

= .8 × 9 = 7.2%

The expected return on your portfolio is equal to the risk-free interest rate plus theexpected risk premium:

Expected portfolio return = rportfolio = 5 + 7.2 = 12.2%

In Figure 4.10b we show the beta and expected return on this portfolio by the letter Y.

THE SECURITY MARKET LINE

Example 3 illustrates a general point: by investing some proportion of your money inthe market portfolio and lending (or borrowing)4 the balance, you can obtain any com-bination of risk and expected return along the sloping line in Figure 4.11. This line isgenerally known as the security market line.

4 Notice that the security market line extends above the market return at β = 1. How would you generate aportfolio with, say, β = 2? It’s easy, but it’s risky. Suppose you borrow $1 million and invest the loan plus $1million in the market portfolio. That gives you $2 million invested and a $1 million liability. Your portfolionow has a beta of 2.0:

Beta of portfolio = (proportion in market × beta of market) + (proportion in loan × beta of loan)β = (2 × βmarket) + (–1 × βloan)

= (2 × 1.0) + (–1 × 0) = 2

Notice that the proportion in the loan is negative because you are borrowing, not lending money.By the way, borrowing from a bank or stockbroker would not be difficult or unduly expensive as long as

you put up your $2 million stock portfolio as security for the loan.Can you calculate the risk premium and the expected rate of return on this borrow-and-invest strategy?

SECURITY MARKETLINE Relationshipbetween expected return andbeta.

418 SECTION FOUR

� Self-Test 5 How would you construct a portfolio with a beta of .25? What is the expected return tothis strategy? Assume Treasury bills yield 6 percent and the market risk premium is 9percent.

Look back to Figure 4.10b, which asserts that an individual common stock with β =.5 must offer a 9.5 percent expected rate of return when Treasury bills yield 5 percentand the market risk premium is 9 percent. You can now see why this has to be so. If thatstock offered a lower rate of return, nobody would buy even a little of it—they could get9.5 percent just by investing 50-50 in Treasury bills and the market. And if nobody wantsto hold the stock, its price has to drop. A lower price means a better buy for investors,that is, a higher rate of return. The price will fall until the stock’s expected rate of returnis pushed up to 9.5 percent. At that price and expected return the CAPM holds.

If, on the other hand, our stock offered more than 9.5 percent, diversified investorswould want to buy more of it. That would push the price up and the expected returndown to the levels predicted by the CAPM.

This reasoning holds for stocks with any beta. That’s why the CAPM makes sense,and why the expected risk premium on an investment should be proportional to its beta.

� Self-Test 6 Suppose you invest $400,000 in Treasury bills and $600,000 in the market portfolio.What is the return on your portfolio if bills yield 6 percent and the expected return onthe market is 15 percent? What does the return on this portfolio imply for the expectedreturn on individual stocks with betas of .6?

The security market line describes the expected returns and risks frominvesting different fractions of your funds in the market. It also sets astandard for other investments. Investors will be willing to hold otherinvestments only if they offer equally good prospects. Thus the required riskpremium for any investment is given by the security market line:

Risk premium on investment = beta × expected market risk premium

FIGURE 4.11The security market lineshows how expected rate ofreturn depends on beta.According to the capitalasset pricing model, expectedrates of return for allsecurities and all portfolioslie on this line.

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Security market line

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HOW WELL DOES THE CAPM WORK?

The basic idea behind the capital asset pricing model is that investors expect a rewardfor both waiting and worrying. The greater the worry, the greater the expected return.If you invest in a risk-free Treasury bill, you just receive the rate of interest. That’s thereward for waiting. When you invest in risky stocks, you can expect an extra return orrisk premium for worrying. The capital asset pricing model states that this risk premiumis equal to the stock’s beta times the market risk premium. Therefore,

Expected return on stock = risk-free interest rate + (beta × market risk premium)


How well does the CAPM work in practice? Do the returns on stocks with betas of.5 on average lie halfway between the return on the market portfolio and the interest rateon Treasury bills? Unfortunately, the evidence is conflicting. Let’s look back to the ac-tual returns earned by investors in low-beta stocks and in high-beta stocks.

Imagine that in 1931 ten investors gathered in a Wall Street bar to discuss their port-folios. Each agreed to follow a different strategy. Investor 1 opted to buy each year the10 percent of New York Stock Exchange stocks with the lowest betas; investor 2 chosethe 10 percent with the next-lowest betas; and so on, up to investor 10, who agreed tobuy the stocks with the highest betas. They also agreed that they would return 60 yearslater to compare results, and so they parted with much cordiality and good wishes.

In 1991 the same 10 investors, now much older and wealthier, met again in the samebar. Figure 4.12 shows how they fared. Investor 1’s portfolio turned out to be much lessrisky than the market; its beta was only .49. However, investor 1 also realized the low-est return, 9 percent above the risk-free rate of interest. At the other extreme, the betaof investor 10’s portfolio was 1.52, about three times that of investor 1’s portfolio. Butinvestor 10 was rewarded with the highest return, averaging 17 percent above the inter-est rate. So over this 60-year period returns did indeed increase with beta.

As you can see from Figure 4.12, the market portfolio over the same 60-year periodprovides an average return of 14 percent above the interest rate5 and (of course) had a

FIGURE 4.12The capital asset pricingmodel states that theexpected risk premium fromany investment should lie onthe security market line. Thedots show the actual averagerisk premiums from portfolioswith different betas. Thehigh-beta portfoliosgenerated higher averagereturns, just as predicted bythe CAPM. But the high-betaportfolios plotted below thesecurity market line, and fourof the five low-beta portfoliosplotted above. A line fitted tothe 10 portfolio returnswould be flatter than themarket line.

30

25

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Investor 1

Market portfolio

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Source: F. Black, “Beta and Return,” Journal of Portfolio Management 20:8–18 (Fall 1993). © 1993. Usedby permission of Institutional Investor, Inc.

5 In Figure 4.12 the stocks in the “market portfolio” are weighted equally. Since the stocks of small firms haveprovided higher average returns than those of large firms, the risk premium on an equally weighted index ishigher than on a value-weighted index. This is one reason for the difference between the 14 percent marketrisk premium in Figure 4.2 and the 9.4 percent premium reported in Table 3.9.

420 SECTION FOUR

beta of 1.0. The CAPM predicts that the risk premium should lie on the upward-sloping security market line in Figure 4.12. Since the market provided a risk premiumof 14 percent, investor 1’s portfolio, with a beta of .49, should have provided a risk pre-mium of a shade under 7 percent and investor 10’s portfolio, with a beta of 1.52, shouldhave given a premium of a shade over 21 percent. You can see that while high-betastocks performed better than low-beta stocks, the difference was not as great as theCAPM predicts.

Figure 4.12 provides broad support for the CAPM, though it suggests that the linerelating return to beta has been too flat. But recent years have been less kind to theCAPM. For example, if the 10 friends had invested their cash in 1966 rather than 1931,there would have been very little relation between their portfolio returns and beta. Doesthis imply that there has been a fundamental change in the relation between risk and re-turn in the last 30 years or did high-beta stocks just happen to perform worse duringthese years than investors expected? It is hard to be sure.

There is little doubt that the CAPM is too simple to capture everything that is goingon in the stock market. For example, it appears that stocks of small companies or stockswith low price-earnings ratios have offered higher rates of return than the CAPM pre-dicts. This has prompted headlines like “Is Beta Dead?” in the business press.6 It is notthe first time that beta has been declared dead, but the CAPM is still being used. Onlystrong theories can have more than one funeral.

The CAPM is not the only model of risk and return. It has several brothers and sis-ters as well as second cousins. However, the CAPM captures in a simple way two fun-damental ideas. First, almost everyone agrees that investors require some extra returnfor taking on risk. Second, investors appear to be concerned principally with the mar-ket risk that they cannot eliminate by diversification. That is why financial managersrely on the capital asset pricing model as a good rule of thumb.

USING THE CAPM TO ESTIMATE EXPECTED RETURNS

To calculate the returns that investors are expecting from particular stocks, we needthree numbers—the risk-free interest rate, the expected market risk premium, and beta.In mid-1999, the interest rate on Treasury bills was about 4.8 percent. Assume that themarket risk premium is about 9 percent. Finally, look back to Table 4.9, where we gaveyou betas of several stocks. Table 4.10 puts these numbers together to give an estimateof the expected return from each stock. Let’s take Exxon as an example:

Expected return on Exxon = risk-free interest rate + (beta × expected market )risk premium

r = 4.8% + (.61 × 9%)

= 10.3%

You can also use the capital asset pricing model to find the discount rate for a newcapital investment. For example, suppose you are asked to analyze a proposal by Merckto expand its operations. At what rate should you discount the forecast cash flows? Ac-cording to Table 4.10 investors are looking for a return of 13.1 percent from investmentswith the risk of Merck stock. That is the opportunity cost of capital for Merck’s expan-sion project.

In practice, choosing a discount rate is seldom this easy. (After all, you can’t expect

6 A. Wallace, “Is Beta Dead?” Institutional Investor 14 (July 1980), pp. 22–30.


to become a captain of finance simply by plugging numbers into a formula.) For ex-ample, you must learn how to estimate the return demanded by the company’s investorswhen the company has issued both equity and debt securities.7 We will come to such re-finements later.

� EXAMPLE 4 Comparing Project Returns and the Opportunity Cost of Capital

You have forecast the cash flows on a project and calculated that its internal rate of re-turn is 15.0 percent. Suppose that Treasury bills offer a return of 5 percent and the ex-pected market risk premium is 9 percent. Should you go ahead with the project?

To answer this question you need to figure out the opportunity cost of capital r. Thisdepends on the project’s beta. For example, if the project is a sure thing, the beta is zeroand the cost of capital equals the interest rate on Treasury bills:

r = 5 + (0 × 9) = 5%

If your project offers a return of 15.0 percent when the cost of capital is 5 percent, youshould obviously go ahead.8

Sure-fire projects rarely occur outside finance texts. So let’s think about the cost ofcapital if the project has the same risk as the market portfolio. In this case beta is 1.0and the cost of capital is the expected return on the market:

r = 5 + (1.0 × 9) = 14%

The project appears less attractive than before but still worth doing.But what if the project has even higher risk? Suppose, for example, that it has a beta

of 1.5. What is the cost of capital in this case? To find the answer, we plug a beta of 1.5into our formula for r:

7 We could ignore this complication in the case of Merck, because Merck is financed almost entirely by com-mon stock. Therefore, the risk of its assets equals the risk of its stock. But most companies issue a mix of debtand common stock.8 Earlier we described some special cases where you should prefer projects that offer a lower internal rate ofreturn than the cost of capital. We assume here that your project is a “normal” one, and that you prefer highIRRs to low ones.

TABLE 4.10Expected rates of return Stock Expected Return, %

Biogen 14.4Compaq 15.1Delta Airlines 12.5Exxon 10.3Ford Motor Co. 13.5MCI WorldCom 16.5Merck 13.1Microsoft 16.8PepsiCo 16.8Xerox 15.6

Note: Expected return = r = rf + β(rm – rf) = 4.8% + (β × 9%).

422 SECTION FOUR

r = 5 + (1.5 × 9) = 18.5%

A project this risky would need a return of at least 18.5 percent to justify going ahead.The 15 percent project should be rejected.

This rejection occurs because, as Figure 4.13 shows, the project’s expected rate of re-turn plots below the security market line. The project offers a lower return than investorscan get elsewhere, so it is a negative-NPV investment.

� Self-Test 7 Suppose that Merck’s expansion project is forecast to produce cash flows of $50 mil-lion a year for each of 10 years. What is its present value? Use data from Table 4.10.What would the present value be if the beta of the investment were .7?

Capital Budgeting and Project RiskCOMPANY VERSUS PROJECT RISK

Long before the development of modern theories linking risk and return, smart finan-cial managers adjusted for risk in capital budgeting. They realized intuitively that, otherthings equal, risky projects are less desirable than safe ones and must provide higherrates of return.

Many companies estimate the rate of return required by investors in their securitiesand use this company cost of capital to discount the cash flows on all new projects.

The security market line provides a standard for project acceptance. If theproject’s return lies above the security market line, then the return is higherthan investors could expect to get by investing their funds in the capitalmarket and therefore is an attractive investment opportunity.

FIGURE 4.13The expected return of thisproject is less than theexpected return one couldearn on stock marketinvestments with the samemarket risk (beta). Therefore,the project’s expectedreturn–risk combination liesbelow the security marketline, and the project shouldbe rejected.

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COMPANY COST OFCAPITAL Expected rateof return demanded byinvestors in a company,determined by the averagerisk of the company’s assetsand operations.


Since investors require a higher rate of return from a risky company, risky firms willhave a higher company cost of capital and will set a higher discount rate for their newinvestment opportunities. For example, we showed in Table 4.9 that on past evidenceMerck has a beta of .92 and the corresponding expected rate of return (see Table 4.10)is about 13 percent. According to the company cost of capital rule, Merck should use a13 percent cost of capital to calculate project NPVs.

This is a step in the right direction, but we must take care when the firm has issuedsecurities other than equity. Moreover, this approach can get a firm in trouble if its newprojects do not have the same risk as its existing business. Merck’s beta reflects in-vestors’ estimate of the risk of the pharmaceutical business and its company cost of cap-ital is the return that investors require for taking on this risk. If Merck is considering anexpansion of its regular business, it makes sense to discount the forecast cash flows bythe company cost of capital. But suppose that Merck is wondering whether to branchout into production of computer hardware. Its beta tells us nothing about the projectcost of capital. That depends on the risk of the hardware business and the return thatshareholders require from investing in such a business.

The nearby box discusses how companies decide on the discount rate. It notes, forexample, that Siemens, a German industrial giant, uses 16 different discount rates, de-pending on the riskiness of each line of its business.

� Self-Test 8 The company cost of capital for Merck is about 13 percent (see Table 4.10); for Com-paq Computer it is about 15 percent. What would be the more reasonable discount ratefor Merck to use for its proposed computer hardware division? Why?

DETERMINANTS OF PROJECT RISK

We have seen that the company cost of capital is the correct discount rate for projectsthat have the same risk as the company’s existing business, but not for those projectsthat are safer or riskier than the company’s average. How do we know whether a proj-ect is unusually risky? Estimating project risk is never going to be an exact science, buthere are two things to bear in mind.

First, we saw earlier that operating leverage increases the risk of a project. When alarge fraction of your costs is fixed, any change in revenues can have a dramatic effecton earnings. Therefore, projects that involve high fixed costs tend to have higher betas.

Second, many people intuitively associate risk with the variability of earnings. Butmuch of this variability reflects diversifiable risk. Lone prospectors in search of goldlook forward to extremely uncertain future earnings, but whether they strike it rich isnot likely to depend on the performance of the rest of the economy. These investmentshave a high standard deviation but a low beta.

The project cost of capital depends on the use to which that capital is put.Therefore, it depends on the risk of the project and not on the risk of thecompany. If a company invests in a low-risk project, it should discount thecash flows at a correspondingly low cost of capital. If it invests in a high-riskproject, those cash flows should be discounted at a high cost of capital.

PROJECT COST OFCAPITAL Minimumacceptable expected rate ofreturn on a project given itsrisk.

SEE BOX

FINANCE IN ACTION

DON’T ADD FUDGE FACTORS TO DISCOUNT RATES

Risk to an investor arises because an investment adds to the spread of possible portfo-lio returns. To a diversified investor, risk is predominantly market risk. But in everydayusage risk simply means “bad outcome.” People think of the “risks” of a project as thethings that can go wrong. For example,

• A geologist looking for oil worries about the risk of a dry hole.• A pharmaceutical manufacturer worries about the risk that a new drug which re-

verses balding may not be approved by the Food and Drug Administration.• The owner of a hotel in a politically unstable part of the world worries about the po-

litical risk of expropriation.

What matters is the strength of the relationship between the firm’s earningsand the aggregate earnings of all firms. Thus cyclical businesses, whoserevenues and earnings are strongly dependent on the state of the economy,tend to have high betas and a high cost of capital. By contrast, businesses thatproduce essentials, such as food, beer, and cosmetics, are less affected by thestate of the economy. They tend to have low betas and a low cost of capital.

424

How High a Hurdle?It did raise some eyebrows at first. Two months ago,when Aegon, a Dutch life insurer known for taking careof its shareholders, bought Transamerica, a San Fran-cisco– based insurer, Aegon said it was expecting a re-turn of only 9% from the deal, well below the 11% “ hur-dle rate” it once proclaimed as its benchmark. Had thisdarling of the stock market betrayed its devoted in-vestors for the sake of an eye-catching deal?

Not at all. Years of falling interest rates and rising eq-uity valuations have shrunk the cost of capital for firmssuch as Aegon. So companies that regularly adjust thehurdle rates they use to evaluate potential investmentprojects and acquisitions are not cheating their share-holders. Far from it: they are doing their investors aservice. Unfortunately, such firms are rare in Europe. “ Idon’t know many companies at all who lowered theirhurdle rates in line with interest rates, so they’re all un-derinvesting,” says Greg Milano, a partner at SternStewart, a consultancy that helps companies estimatetheir cost of capital.

This has a huge impact on corporate strategy. Com-panies generally make their investment decisions bydiscounting the net cash flows a project is estimated togenerate to their present value. If the net present value

is positive, the project should make shareholders betteroff.

Generally speaking, says Paul Gibbs, an analyst atJ.P. Morgan, an American bank, finance directors inAmerica often review their hurdle rates; in continentalEurope they do so sometimes, and in Britain, rarely. Asa result, the Confederation of British Industry, a big-business lobby, worries about underinvestment, and of-ficials at the Bank of England grumble about firms’ re-luctance to lower hurdles. This reluctance seemssurprising, since companies with high hurdle rates willtend to lose out in bidding for business assets or firms.The hurdle rate should reflect not only interest rates butalso the riskiness of each individual project. For in-stance, Siemens, a German industrial giant, last yearstarted assigning a different hurdle rate to each of its 16businesses, ranging from household appliances tomedical equipment and semiconductors. The hurdlerates— from 8% to 11%— are based on the volatility ofshares in rival companies in the relevant industry, andare under constant review.

Source: “How High a Hurdle?” The Economist, May 8, 1999, p. 82.© 1999 The Economist Newspaper Group, Inc. Reprinted with per-mission. Further reproduction prohibited. www.economist.com.


Managers sometimes add fudge factors to discount rates to account for worries such as these.

This sort of adjustment makes us nervous. First, the bad outcomes we cited appearto reflect diversifiable risks which would not affect the expected rate of return de-manded by investors. Second, the need for an adjustment in the discount rate usuallyarises because managers fail to give bad outcomes their due weight in cash-flow fore-casts. They then try to offset that mistake by adding a fudge factor to the discount rate.For example, if a manager is worried about the possibility of a bad outcome such as adry hole in oil exploration, he or she may reduce the value of the project by using ahigher discount rate. This approach is unsound, however. Instead, the possibility of thedry hole should be included in the calculation of the expected cash flows to be derivedfrom the well. Suppose that there is a 50 percent chance of a dry hole and a 50 percentchance that the well will produce oil worth $20 million. Then the expected cash flow isnot $20 million but (.5 × 0) + (.5 × 20) = $10 million. You should discount the $10 mil-lion expected cash flow at the opportunity cost of capital: it does not make sense to dis-count the $20 million using a fudged discount rate.

SummaryHow can you measure and interpret the market risk, or beta, of a security?

The contribution of a security to the risk of a diversified portfolio depends on its marketrisk. But not all securities are equally affected by fluctuations in the market. The sensitivityof a stock to market movement is known as beta. Stocks with a beta greater than 1.0 areparticularly sensitive to market fluctuations. Those with a beta of less than 1.0 are not sosensitive to such movements. The average beta of all stocks is 1.0.

What is the relationship between the market risk of a security and the rate of re-turn that investors demand of that security?

The extra return that investors require for taking risk is known as the risk premium. Themarket risk premium—that is, the risk premium on the market portfolio—averagedalmost 9.4 percent between 1926 and 1998. The capital asset pricing model states that theexpected risk premium of an investment should be proportional to both its beta and themarket risk premium. The expected rate of return from any investment is equal to the risk-free interest rate plus the risk premium, so the CAPM boils down to


The security market line is the graphical representation of the CAPM equation. Thesecurity market line relates the expected return investors demand of a security to the beta.

How can a manager calculate the opportunity cost of capital for a project?

The opportunity cost of capital is the return that investors give up by investing in the projectrather than in securities of equivalent risk. Financial managers use the capital asset pricing

Expected cash-flow forecasts should already reflect the probabilities of allpossible outcomes, good and bad. If the cash-flow forecasts are preparedproperly, the discount rate should reflect only the market risk of the project.It should not have to be fudged to offset errors or biases in the cash-flowforecast.

426 SECTION FOUR

model to estimate the opportunity cost of capital. The company cost of capital is theexpected rate of return demanded by investors in a company, determined by the average riskof the company’s assets and operations.

The opportunity cost of capital depends on the use to which the capital is put. Therefore,required rates of return are determined by the risk of the project, not by the risk of thefirm’s existing business. The project cost of capital is the minimum acceptable expectedrate of return on a project given its risk.

Your cash-flow forecasts should already factor in the chances of pleasant and unpleasantsurprises. Potential bad outcomes should be reflected in the discount rate only to the extentthat they affect beta.

www.stanford.edu/~wfsharpe/ws/wksheets.htm William Sharpe’s site contains “portfolio opti-mizers,” spreadsheets that can be used to construct efficiently diversified portfolios

www.riskmetrics.com RiskMetrics® Group maintains this site, which uses modern portfoliotheory to help manage risk; some of the content at this site, including educational and demon-stration materials, is free.

www.riskview.com A nice site with historical risk and return data as well as software to manageand measure portfolio risk

www.finance.yahoo.com You can find stock betas as well as other risk measures and companyprofiles here

1. Risk and Return. True or false? Explain or qualify as necessary.

a. Investors demand higher expected rates of return on stocks with more variable rates ofreturn.

b. The capital asset pricing model predicts that a security with a beta of zero will providean expected return of zero.

c. An investor who puts $10,000 in Treasury bills and $20,000 in the market portfolio willhave a portfolio beta of 2.0.

d. Investors demand higher expected rates of return from stocks with returns that are highlyexposed to macroeconomic changes.

e. Investors demand higher expected rates of return from stocks with returns that are verysensitive to fluctuations in the stock market.

2. Diversifiable Risk. In light of what you’ve learned about market versus diversifiable(unique) risks, explain why an insurance company has no problem in selling life insuranceto individuals but is reluctant to issue policies insuring against flood damage to residents ofcoastal areas. Why don’t the insurance companies simply charge coastal residents a premiumthat reflects the actuarial probability of damage from hurricanes and other storms?

3. Unique vs. Market Risk. Figure 4.14 plots monthly rates of return from 1993 to 1999 forthe Snake Oil mutual fund. Was this fund well-diversified? Explain.

4. Risk and Return. Suppose that the risk premium on stocks and other securities did in fact

market portfoliobetamarket risk premiumcapital asset pricing model (CAPM)

security market linecompany cost of capitalproject cost of capital

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