Part 1 Value
36. Prices and spot interest rates Look one more time at Table 3.5
a. Suppose you knew the bond prices but not the spot interest rates. Explain how you would calculate the spot rates. (Hint: You have four unknown spot rates, so you need four
equations.)
b. Suppose that you could buy bond C in large quantities at $1,040 rather than at its
equilibrium price of $1,076.20. Show how you could make a zillion dollars without taking on any risk.
● ● ● ● ●
FINANCE ON THE WEB
The websites of The Wall Street Journal (www.wsj.com) and the Financial Times (www.ft.com) are wonderful sources of market data. You should become familiar with them.
1. Use www.wsj.com to answer the following questions:
a. Find the prices of coupon strips. Use these prices to plot the term structure. If the
expectations theory is correct, what is the expected one-year interest rate three years hence?
b. Find a three- or four-year bond and construct a package of coupon and principal strips that provides the same cash flows. The law of one price predicts that the cost of the package should be very close to that of the bond. Is it?
c. Find a long-term Treasury bond with a low coupon and calculate its duration. Now find another bond with a similar maturity and a higher coupon. Which has the longer duration?
d. Look up the yields on 10-year nominal Treasury bonds and on TIPS. If you are confident that inflation will average 2% a year, which bond will provide the higher real return?
2. Bond transactions are reported on FINRA’s TRACE service, which was the source of the data for Table 3.6. Use the Advanced Search facility in TRACE to find bond prices for Johnson &
Johnson (JNJ), Walmart (WMT), Disney (DIS), SunTrust Banks (STI), and U.S. Steel (X). If possible, exclude callable issues that the company can buy back. Have the bond ratings changed? What has happened to the yields of these companies’ bonds? (You will find that bonds issued by the same company may have very different yields, so you will need to use your best judgment to answer this second question.)
___________
1Bonds used to come with coupons attached, which had to be clipped off and presented to the issuer to obtain the interest payments. This is still the case with bearer bonds, where the only evidence of indebtedness is the bond itself. In many parts of the world bearer bonds are still issued and are popular with investors who would rather remain anonymous. The alternative is registered bonds, where the identity of the bond’s owner is recorded and the coupon payments are sent automatically. OATs are registered bonds.
2You could also value a four-year annuity of €5.00 plus a final payment of €105.00.
3The frequency of interest payments varies from country to country. For example, most euro bonds pay interest annually, while most bonds in the UK, Canada, and Japan pay interest semiannually.
4The quoted bond price is known as the flat (or clean) price. The price that the bond buyer actually pays (sometimes called the full or dirty price) is equal to the flat price plus the interest that the seller has already earned on the bond since the last interest payment. The precise method for calculating this accrued interest varies from one type of bond to another. Always use the flat price to calculate the
yield.
5From this point forward, we will just say “bonds,” and not distinguish notes from bonds unless we are referring to a specific security. Note also that bonds with long maturities end up with short maturities when they approach the final payment date. Thus you will encounter 30-year bonds trading 20 years later at the same prices as new 10-year notes (assuming equal coupons).
6In other words, the derivative of the bond price with respect to a change in yield to maturity is dPV/dy = – duration/(1 + y) = – modified duration.
7If you look back at Figure 3.2, you will see that the plot of price against yield is not a straight line.
This means that modified duration is a good predictor of the effect of interest rate changes only for small moves in interest rates.
8For simplicity, we assumed that the two Treasury bonds paid annual coupons. Calculating Macaulay duration for a bond with semiannual coupons is no different except that there are twice as many cash flows. To calculate modified duration with semiannual coupons you need to divide Macaulay duration by the yield every six months.
9We exaggerate Ms. Kraft’s profits. There are always costs to financial transactions, though they may be very small. For example, Ms. Kraft could use her investment in the one-year strip as security for the bank loan, but the bank would need to charge more than 7% on the loan to cover its costs.
10The extra return for lending for one more year is termed the forward rate of interest. In our example the forward rate is 9.0%. In Ms. Kraft’s arbitrage example, the forward interest rate was negative. In real life, forward interest rates can’t be negative. At the lowest they are zero.
11Indexed bonds were not completely unknown in the United States before 1997. For example, in 1780 American Revolutionary soldiers were compensated with indexed bonds that paid the value of “five bushels of corn, 68 pounds and four-seventh parts of a pound of beef, ten pounds of sheep’s wool, and sixteen pounds of sole leather.”
12The reverse happens if there is deflation. In this case the coupon payment and principal amount are adjusted downward. However, the U.S. government guarantees that when the bond matures it will not pay less than its original nominal face value.
13The yield on short-term TIPs was negative. You were actually losing in real terms.
14Some of this saving is done indirectly. For example, if you hold 100 shares of IBM stock, and IBM retains and reinvests earnings of $1.00 a share, IBM is saving $100 on your behalf. The government may also oblige you to save by raising taxes to invest in roads, hospitals, etc.
15We assume that investors save more as interest rates rise. It doesn’t have to be that way. Suppose that 20 years hence you will need $50,000 in today’s dollars for your children’s college tuition. How much will you have to set aside today to cover this obligation? The answer is the present value of a real expenditure of $50,000 after 20 years, or 50,000/(1 + real interest rate)20. The higher the real interest rate, the lower the present value and the less you have to set aside.
16Corporate bonds are also less liquid than Treasuries: they are more difficult and expensive to trade, particularly in large quantities or on short notice. Many investors value liquidity and will demand a higher interest rate on a less liquid bond. Lack of liquidity accounts for some of the spread between yields on corporate and Treasury bonds.
17Occasionally, defaults have been a case of “won’t pay” rather than “can’t pay.” For example, in 2008 Ecuador’s president announced that his country would disavow $3.9 billion of “illegal” debts
contracted by earlier regimes. In dealing with international lenders, he said, “We are up against real monsters.”
W
Part 1 Value
The Value of Common Stocks
e should warn you that being a financial expert has its occupational hazards. One is being cornered at cocktail parties by people who are eager to explain their system for making creamy profits by investing in common stocks. One of the few good things about a financial crisis is that these bores tend to disappear, at least temporarily.
We may exaggerate the perils of the trade. The point is that there is no easy way to ensure superior investment performance. Later in the book we show that in well-functioning capital markets it is impossible to predict changes in security prices. Therefore, in this chapter, when we use the concept of present value to price common stocks, we are not promising you a key to investment success; we simply believe that the idea can help you to understand why some investments are priced higher than others.
Why should you care? If you want to know the value of a firm’s stock, why can’t you look up the stock price on the Internet? Unfortunately, that is not always possible. For example, you may be the founder of a successful business. You currently own all the shares but are thinking of going public by selling off shares to other investors. You and your advisers need to estimate the price at which those shares can be sold.
There is also another, deeper reason why managers need to understand how shares are valued. If a firm acts in its shareholders’ interest, it should accept those investments that increase the value of their stake in the firm. But in order to do this, it is necessary to understand what determines the shares’ value.
We begin with a look at how stocks are traded. Then we explain the basic principles of share valuation and the use of discounted-cash-flow (DCF) models to estimate expected rates of return.
Later in the chapter we show how DCF models can be used to value entire businesses rather than individual shares.
We will also explain the fundamental difference between growth and income stocks. A growth stock doesn’t just grow; its future investments are also expected to earn rates of return that are higher than the cost of capital. It’s the combination of growth and superior returns that generates high price–earnings ratios for growth stocks.
Still another warning: Everybody knows that common stocks are risky and that some are more risky than others. Therefore, investors will not commit funds to stocks unless the expected rates of return are commensurate with the risks. But we say next to nothing in this chapter about the linkages between risk and expected return. A more careful treatment of risk starts in Chapter 7.
4-1 How Common Stocks Are Traded
General Electric (GE) has about 10.6 billion shares outstanding. Shareholders include large pension funds and insurance companies that each own several million shares, as well as individuals who own a handful of shares. If you owned one GE share, you would own .00000001% of the company and have a claim on the same tiny fraction of GE’s profits. Of course, the more shares you own, the larger your
“share” of the company.
If GE wishes to raise new capital, it can do so either by borrowing or by selling new shares to investors. Sales of shares to raise new capital are said to occur in the primary market. But most trades in GE take place on the stock exchange, where investors buy and sell existing GE shares. Stock exchanges are really markets for secondhand shares, but they prefer to describe themselves as secondary markets, which sounds more important.
The two principal U.S. stock exchanges are the New York Stock Exchange and Nasdaq. Both compete vigorously for business and just as vigorously tout the advantages of their trading systems.
The volume of business that they handle is immense. For example, on an average day the NYSE trades around 2 billion shares in some 2,300 companies.
BEYOND THE PAGE
● ● ● ● ●
Major world stock exchanges
brealey.mhhe.com/c04
In addition to the NYSE and Nasdaq, there are computer networks called electronic communication networks (ECNs) that connect traders with each other. Large U.S. companies may also arrange for their shares to be traded on foreign exchanges, such as the London exchange or the Euronext exchange in Paris. At the same time many foreign companies are listed on the U.S. exchanges. For example, the NYSE trades shares in Sony, Royal Dutch Shell, Canadian Pacific, Tata Motors, Deutsche Bank, Brasil Telecom, China Eastern Airlines, and 500 other companies.
Suppose that Ms. Jones, a longtime GE shareholder, no longer wishes to hold her shares in the company. She can sell them via the NYSE to Mr. Brown, who wants to increase his stake in the firm.
The transaction merely transfers partial ownership of the firm from one investor to another. No new shares are created, and GE will neither care nor know that the trade has taken place.
Ms. Jones and Mr. Brown do not trade the GE shares themselves. Instead, their orders must go through a brokerage firm. Ms. Jones, who is anxious to sell, might give her broker a market order to sell stock at the best available price. On the other hand, Mr. Brown might state a price limit at which he is willing to buy GE stock. If his limit order cannot be executed immediately, it is recorded in the exchange’s limit order book until it can be executed.
When they transact on the NYSE, Brown and Jones are participating in a huge auction market in which the exchange’s designated market makers match up the orders of thousands of investors. Most major exchanges around the world, such as the Tokyo Stock Exchange, the London Stock Exchange, and the Deutsche Börse, are also auction markets, but the auctioneer in these cases is a computer.1
This means that there is no stock exchange floor to show on the evening news and no one needs to ring a bell to start trading.
Nasdaq is not an auction market. All trades on Nasdaq take place between the investor and one of a group of professional dealers who are prepared to buy and sell stock. Dealer markets are common for other financial instruments. For example, most bonds are traded in dealer markets.
Trading Results for GE
You can track trades in GE or other public corporations on the Internet. For example, if you go to finance.yahoo.com, enter the ticker symbol GE, and ask to “Get Quotes,” you will see results like the table on the next page.2
GE’s closing price on January 27, 2012, was $19.03, down $.04 or .21% from the previous day’s close. GE traded in a range of $18.92 to 19.13, and between $14.02 and $21.65 over the prior 52 weeks. Trading volume was 32,617,690 shares, well below the three-month average of 60,699,500 shares per day. GE’s market cap (shorthand for market capitalization) was $201.07 billion.
GE’s earnings per share (EPS) over the previous 12 months were $1.24 (“ttm” stands for “trailing 12 months”). The ratio of stock price to EPS (the P/E ratio) was 15.4. Notice that this P/E ratio uses past EPS. P/E ratios using forecasted EPS are generally more useful. Security analysts forecasted an increase in GE’s EPS to 1.54 per share for 2012, which gives a forward P/E of 12.4.3
GE paid a cash dividend of $.68 per share per year, so its dividend yield (the ratio of dividend to price) was 3.60%.
Buying stocks is a risky occupation. GE stock traded at over $40 in 2007. By January 2012, the unfortunate investor who bought in at $40 lost more than half of his investment. Of course, you don’t come across such people at cocktail parties; they either keep quiet or aren’t invited.
Most of the trading on the NYSE and Nasdaq is in ordinary common stocks, but other securities are traded also, including preferred shares, which we cover in Chapter 14, and warrants, which we cover in Chapter 21. Investors can also choose from hundreds of exchange-traded funds (ETFs), which are portfolios of stocks that can be bought or sold in a single trade. With a few exceptions ETFs are not actively managed. Many simply aim to track a well-known market index such as the Dow Jones
Industrial Average or the S&P 500. Others track specific industries or commodities. (We discuss ETFs more fully in Chapter 14.) You can also buy shares in closed-end mutual funds4 that invest in portfolios of securities. These include country funds, for example, the Mexico and Chile funds, that invest in portfolios of stocks in specific countries. Unlike ETFs, most closed-end funds are actively managed and seek to “beat the market.”
4-2 How Common Stocks Are Valued
Finding the value of GE stock may sound like a simple problem. Each quarter, the company publishes a balance sheet, which lists the value of the firm’s assets and liabilities. At the end of September 2011 the book value of all GE’s assets—plant and machinery, inventories of materials, cash in the bank, and so on—was $738 billion. GE’s liabilities—money that it owes the banks, taxes that are due to be paid, and the like—amounted to $613 billion. The difference between the value of the assets and the liabilities was $125 billion. This was the book value of GE’s equity.
Book value is a reassuringly definite number. Each year KPMG, one of America’s largest accounting firms, gives its opinion that GE’s financial statements present fairly in all material respects the company’s financial position, in conformity with U.S. generally accepted accounting principles (commonly called GAAP). However, the book value of GE’s assets measures only their original (or
“historical”) cost less an allowance for depreciation. This may not be a good guide to what those assets are worth today.
One can go on and on about the deficiencies of book value as a measure of market value. Book values are historical costs that do not incorporate inflation. (Countries with high or volatile inflation often require inflation-adjusted book values, however.) Book values usually exclude intangible assets such as trademarks and patents. Also accountants simply add up the book values of individual assets, and thus do not capture going-concern value. Going-concern value is created when a collection of assets is organized into a healthy operating business.
Book values can nevertheless be a useful benchmark. If a financial analyst says, “Holstein Oil sells for two times book value,” she is effectively saying that Holstein has doubled its shareholders’ past investments in the company.
Book values may also be useful clues about liquidation value. Liquidation value is what investors get when a failed company is shut down and its assets are sold off. Book values of “hard” assets like land, buildings, vehicles, and machinery can indicate possible liquidation values.
Intangible “soft” assets can be important even in liquidation, however. Eastman Kodak provides a good recent example. Kodak, which was one of the Nifty Fifty growth stocks of the 1960s, suffered a long decline and finally filed for bankruptcy in January 2012. What was its most valuable asset in bankruptcy? Its portfolio of patents, which was put up for sale. The present value of the patents was estimated, perhaps optimistically, at $3 billion.
Valuation by Comparables
When financial analysts need to value a business, they often start by identifying a sample of similar firms as potential comparables. They then examine how much investors in the comparable companies are prepared to pay per dollar of earnings or book assets. They see what the business would be worth if it traded at the comparables’ price–earnings or price-to-book-value ratios. This valuation approach is called valuation by comparables.