Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I. Value 4. The Value of Common Stocks © The McGraw−Hill Companies, 2003 CHAPTER FOUR 58 THE VALUE OF COMMON STOCKS Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I. Value 4. The Value of Common Stocks © The McGraw−Hill Companies, 2003 WE SHOULD WARN you that being a financial expert has its occupational hazards. One is being cor- nered at cocktail parties by people who are eager to explain their system for making creamy profits by investing in common stocks. Fortunately, these bores go into temporary hibernation whenever the market goes down. We may exaggerate the perils of the trade. The point is that there is no easy way to ensure su- perior investment performance. Later in the book we will show that changes in security prices are fundamentally unpredictable and that this result is a natural consequence of well-functioning cap- ital markets. Therefore, in this chapter, when we propose to 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 in the newspaper? 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 pub- lic by selling off shares to other investors. You and your advisers need to estimate the price at which those shares can be sold. Or suppose that Establishment Industries is proposing to sell its concate- nator division to another company. It needs to figure out the market value of this division. There is also another, deeper reason why managers need to understand how shares are valued. We have stated that a firm which acts in its shareholders’ interest should accept those investments which increase the value of their stake in the firm. But in order to do this, it is necessary to under- stand what determines the shares’ value. We start the chapter with a brief look at how shares are traded. Then we explain the basic princi- ples of share valuation. We look at the fundamental difference between growth stocks and income stocks and the significance of earnings per share and price–earnings multiples. Finally, we discuss some of the special problems managers and investors encounter when they calculate the present val- ues of entire businesses. A word of caution before we proceed. 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. 59 There are 9.9 billion shares of General Electric (GE), and at last count these shares were owned by about 2.1 million shareholders. They included 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 .000002 percent 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 additional capital, it may do so by either borrowing or sell- ing new shares to investors. Sales of new shares to raise new capital are said to oc- cur in the primary market. But most trades in GE shares take place in existing shares, which investors buy from each other. These trades do not raise new capital for the firm. This market for secondhand shares is known as the secondary market. The principal secondary marketplace for GE shares is the New York Stock Exchange 4.1 HOW COMMON STOCKS ARE TRADED Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I. Value 4. The Value of Common Stocks © The McGraw−Hill Companies, 2003 (NYSE). 1 This is the largest stock exchange in the world and trades, on an average day, 1 billion shares in some 2,900 companies. Suppose that you are the head trader for a pension fund that wishes to buy 100,000 GE shares. You contact your broker, who then relays the order to the floor of the NYSE. Trading in each stock is the responsibility of a specialist, who keeps a record of orders to buy and sell. When your order arrives, the specialist will check this record to see if an investor is prepared to sell at your price. Alternatively, the specialist may be able to get you a better deal from one of the brokers who is gath- ered around or may sell you some of his or her own stock. If no one is prepared to sell at your price, the specialist will make a note of your order and execute it as soon as possible. The NYSE is not the only stock market in the United States. For example, many stocks are traded over the counter by a network of dealers, who display the prices at which they are prepared to trade on a system of computer terminals known as NASDAQ (National Association of Securities Dealers Automated Quotations Sys- tem). If you like the price that you see on the NASDAQ screen, you simply call the dealer and strike a bargain. The prices at which stocks trade are summarized in the daily press. Here, for ex- ample, is how The Wall Street Journal recorded the day’s trading in GE on July 2, 2001: 60 PART I Value 1 GE shares are also traded on a number of overseas exchanges. YTD 52 Weeks Vol Net % Chg Hi Lo Stock (SYM) Div Yld % PE 100s Last Chg ϩ4.7 60.50 36.42 General Electric (GE) .64 1.3 38 215287 50.20 ϩ1.45 You can see that on this day investors traded a total of 215,287 ϫ 100 ϭ 21,528,700 shares of GE stock. By the close of the day the stock traded at $50.20 a share, up $1.45 from the day before. The stock had increased by 4.7 percent from the start of 2001. Since there were about 9.9 billion shares of GE outstanding, investors were placing a total value on the stock of $497 billion. Buying stocks is a risky occupation. Over the previous year, GE stock traded as high as $60.50, but at one point dropped to $36.42. An unfortunate investor who bought at the 52-week high and sold at the low would have lost 40 percent of his or her investment. Of course, you don’t come across such people at cocktail par- ties; they either keep quiet or aren’t invited. The Wall Street Journal also provides three other facts about GE’s stock. GE pays an annual dividend of $.64 a share, the dividend yield on the stock is 1.3 percent, and the ratio of the stock price to earnings (P/E ratio) is 38. We will explain shortly why investors pay attention to these figures. 4.2 HOW COMMON STOCKS ARE VALUED Think back to the last chapter, where we described how to value future cash flows. The discounted-cash-flow (DCF) formula for the present value of a stock is just the same as it is for the present value of any other asset. We just discount the cash flows Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I. Value 4. The Value of Common Stocks © The McGraw−Hill Companies, 2003 by the return that can be earned in the capital market on securities of comparable risk. Shareholders receive cash from the company in the form of a stream of divi- dends. So PV(stock) ϭ PV(expected future dividends) At first sight this statement may seem surprising. When investors buy stocks, they usually expect to receive a dividend, but they also hope to make a capital gain. Why does our formula for present value say nothing about capital gains? As we now explain, there is no inconsistency. Today’s Price The cash payoff to owners of common stocks comes in two forms: (1) cash divi- dends and (2) capital gains or losses. Suppose that the current price of a share is P 0 , that the expected price at the end of a year is P 1 , and that the expected divi- dend per share is DIV 1 . The rate of return that investors expect from this share over the next year is defined as the expected dividend per share DIV 1 plus the ex- pected price appreciation per share P 1 Ϫ P 0 , all divided by the price at the start of the year P 0: This expected return is often called the market capitalization rate. Suppose Fledgling Electronics stock is selling for $100 a share (P 0 ϭ 100). In- vestors expect a $5 cash dividend over the next year (DIV 1 ϭ 5). They also expect the stock to sell for $110 a year hence (P 1 ϭ 110). Then the expected return to the stockholders is 15 percent: On the other hand, if you are given investors’ forecasts of dividend and price and the expected return offered by other equally risky stocks, you can predict to- day’s price: For Fledgling Electronics DIV 1 ϭ 5 and P 1 ϭ 110. If r, the expected return on se- curities in the same risk class as Fledgling, is 15 percent, then today’s price should be $100: How do we know that $100 is the right price? Because no other price could sur- vive in competitive capital markets. What if P 0 were above $100? Then Fledgling stock would offer an expected rate of return that was lower than other securities of equivalent risk. Investors would shift their capital to the other securities and in the process would force down the price of Fledgling stock. If P 0 were less than $100, the process would reverse. Fledgling’s stock would offer a higher rate of return than comparable securities. In that case, investors would rush to buy, forcing the price up to $100. P 0 ϭ 5 ϩ 110 1.15 ϭ $100 Price ϭ P 0 ϭ DIV 1 ϩ P 1 1 ϩ r r ϭ 5 ϩ 110 Ϫ 100 100 ϭ .15, or 15% Expected return ϭ r ϭ DIV 1 ϩ P 1 Ϫ P 0 P 0 CHAPTER 4 The Value of Common Stocks 61 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I. Value 4. The Value of Common Stocks © The McGraw−Hill Companies, 2003 The general conclusion is that at each point in time all securities in an equivalent risk class are priced to offer the same expected return. This is a condition for equilibrium in well-functioning capital markets. It is also common sense. But What Determines Next Year’s Price? We have managed to explain today’s stock price P 0 in terms of the dividend DIV 1 and the expected price next year P 1 . Future stock prices are not easy things to fore- cast directly. But think about what determines next year’s price. If our price for- mula holds now, it ought to hold then as well: That is, a year from now investors will be looking out at dividends in year 2 and price at the end of year 2. Thus we can forecast P 1 by forecasting DIV 2 and P 2 , and we can express P 0 in terms of DIV 1 , DIV 2 , and P 2: Take Fledgling Electronics. A plausible explanation why investors expect its stock price to rise by the end of the first year is that they expect higher dividends and still more capital gains in the second. For example, suppose that they are look- ing today for dividends of $5.50 in year 2 and a subsequent price of $121. That would imply a price at the end of year 1 of Today’s price can then be computed either from our original formula or from our expanded formula We have succeeded in relating today’s price to the forecasted dividends for two years (DIV 1 and DIV 2 ) plus the forecasted price at the end of the second year (P 2 ). You will probably not be surprised to learn that we could go on to replace P 2 by (DIV 3 ϩ P 3 )/(1 ϩ r) and relate today’s price to the forecasted dividends for three years (DIV 1 , DIV 2 , and DIV 3 ) plus the forecasted price at the end of the third year (P 3 ). In fact we can look as far out into the future as we like, removing P’s as we go. Let us call this final period H. This gives us a general stock price formula: The expression simply means the sum of the discounted dividends from year 1 to year H. a H tϭ1 ϭ a H tϭ1 DIV t 11 ϩ r2 t ϩ P H 11 ϩ r2 H P 0 ϭ DIV 1 1 ϩ r ϩ DIV 2 11 ϩ r2 2 ϩ … ϩ DIV H ϩ P H 11 ϩ r2 H P 0 ϭ DIV 1 1 ϩ r ϩ DIV 2 ϩ P 2 11 ϩ r2 2 ϭ 5.00 1.15 ϩ 5.50 ϩ 121 11.152 2 ϭ $100 P 0 ϭ DIV 1 ϩ P 1 1 ϩ r ϭ 5.00 ϩ 110 1.15 ϭ $100 P 1 ϭ 5.50 ϩ 121 1.15 ϭ $110 P 0 ϭ 1 1 ϩ r 1DIV 1 ϩ P 1 2ϭ 1 1 ϩ r aDIV 1 ϩ DIV 2 ϩ P 2 1 ϩ r bϭ DIV 1 1 ϩ r ϩ DIV 2 ϩ P 2 11 ϩ r2 2 P 1 ϭ DIV 2 ϩ P 2 1 ϩ r 62 PART I Value Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I. Value 4. The Value of Common Stocks © The McGraw−Hill Companies, 2003 Table 4.1 continues the Fledgling Electronics example for various time horizons, assuming that the dividends are expected to increase at a steady 10 percent com- pound rate. The expected price P t increases at the same rate each year. Each line in the table represents an application of our general formula for a different value of H. Figure 4.1 provides a graphical representation of the table. Each column shows the present value of the dividends up to the time horizon and the present value of the price at the horizon. As the horizon recedes, the dividend stream accounts for an increasing proportion of present value, but the total present value of dividends plus terminal price always equals $100. CHAPTER 4 The Value of Common Stocks 63 Expected Future Values Present Values Horizon Cumulative Future Period (H) Dividend (DIV t ) Price (P t ) Dividends Price Total 0 — 100 — — 100 1 5.00 110 4.35 95.65 100 2 5.50 121 8.51 91.49 100 3 6.05 133.10 12.48 87.52 100 4 6.66 146.41 16.29 83.71 100 10 11.79 259.37 35.89 64.11 100 20 30.58 672.75 58.89 41.11 100 50 533.59 11,739.09 89.17 10.83 100 100 62,639.15 1,378,061.23 98.83 1.17 100 TABLE 4.1 Applying the stock valuation formula to fledgling electronics. Assumptions: 1. Dividends increase at 10 percent per year, compounded. 2. Capitalization rate is 15 percent. 10050201043210 0 50 100 Present value, dollars Horizon period PV (dividends for 100 years) PV (price at year 100) FIGURE 4.1 As your horizon recedes, the present value of the future price (shaded area) declines but the present value of the stream of dividends (unshaded area) increases. The total present value (future price and dividends) remains the same. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I. Value 4. The Value of Common Stocks © The McGraw−Hill Companies, 2003 How far out could we look? In principle the horizon period H could be infinitely distant. Common stocks do not expire of old age. Barring such corporate hazards as bankruptcy or acquisition, they are immortal. As H approaches infinity, the pres- ent value of the terminal price ought to approach zero, as it does in the final col- umn of Figure 4.1. We can, therefore, forget about the terminal price entirely and express today’s price as the present value of a perpetual stream of cash dividends. This is usually written as where ϱ indicates infinity. This discounted-cash-flow (DCF) formula for the present value of a stock is just the same as it is for the present value of any other asset. We just discount the cash flows—in this case the dividend stream—by the return that can be earned in the capital market on securities of comparable risk. Some find the DCF formula im- plausible because it seems to ignore capital gains. But we know that the formula was derived from the assumption that price in any period is determined by ex- pected dividends and capital gains over the next period. Notice that it is not correct to say that the value of a share is equal to the sum of the discounted stream of earnings per share. Earnings are generally larger than dividends because part of those earnings is reinvested in new plant, equipment, and working capital. Discounting earnings would recognize the rewards of that in- vestment (a higher future dividend) but not the sacrifice (a lower dividend today). The correct formulation states that share value is equal to the discounted stream of dividends per share. P 0 ϭ a ∞ tϭ1 DIV t 11 ϩ r2 t 64 PART I Value 4.3 A SIMPLE WAY TO ESTIMATE THE CAPITALIZATION RATE In Chapter 3 we encountered some simplified versions of the basic present value formula. Let us see whether they offer any insights into stock values. Suppose, for example, that we forecast a constant growth rate for a company’s dividends. This does not preclude year-to-year deviations from the trend: It means only that expected dividends grow at a constant rate. Such an investment would be just another example of the growing perpetuity that we helped our fickle phi- lanthropist to evaluate in the last chapter. To find its present value we must di- vide the annual cash payment by the difference between the discount rate and the growth rate: Remember that we can use this formula only when g, the anticipated growth rate, is less than r, the discount rate. As g approaches r, the stock price becomes infinite. Obviously r must be greater than g if growth really is perpetual. Our growing perpetuity formula explains P 0 in terms of next year’s expected dividend DIV 1 , the projected growth trend g, and the expected rate of return on other securities of comparable risk r. Alternatively, the formula can be used to ob- tain an estimate of r from DIV 1 , P 0 , and g: P 0 ϭ DIV 1 r Ϫ g Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I. Value 4. The Value of Common Stocks © The McGraw−Hill Companies, 2003 The market capitalization rate equals the dividend yield (DIV 1 /P 0 ) plus the ex- pected rate of growth in dividends (g). These two formulas are much easier to work with than the general statement that “price equals the present value of expected future dividends.” 2 Here is a prac- tical example. Using the DCF Model to Set Gas and Electricity Prices The prices charged by local electric and gas utilities are regulated by state com- missions. The regulators try to keep consumer prices down but are supposed to al- low the utilities to earn a fair rate of return. But what is fair? It is usually interpreted as r, the market capitalization rate for the firm’s common stock. That is, the fair rate of return on equity for a public utility ought to be the rate offered by securities that have the same risk as the utility’s common stock. 3 Small variations in estimates of this return can have a substantial effect on the prices charged to the customers and on the firm’s profits. So both utilities and reg- ulators devote considerable resources to estimating r. They call r the cost of equity capital. Utilities are mature, stable companies which ought to offer tailor-made cases for application of the constant-growth DCF formula. 4 Suppose you wished to estimate the cost of equity for Pinnacle West Corp. in May 2001, when its stock was selling for about $49 per share. Dividend payments for the next year were expected to be $1.60 a share. Thus it was a simple matter to calculate the first half of the DCF formula: The hard part was estimating g, the expected rate of dividend growth. One op- tion was to consult the views of security analysts who study the prospects for each company. Analysts are rarely prepared to stick their necks out by forecasting divi- dends to kingdom come, but they often forecast growth rates over the next five years, and these estimates may provide an indication of the expected long-run growth path. In the case of Pinnacle West, analysts in 2001 were forecasting an Dividend yield ϭ DIV 1 P 0 ϭ 1.60 49 ϭ .033, or 3.3% r ϭ DIV 1 P 0 ϩ g CHAPTER 4 The Value of Common Stocks 65 2 These formulas were first developed in 1938 by Williams and were rediscovered by Gordon and Shapiro. See J. B. Williams, The Theory of Investment Value (Cambridge, Mass.: Harvard University Press, 1938); and M. J. Gordon and E. Shapiro, “Capital Equipment Analysis: The Required Rate of Profit,” Management Science 3 (October 1956), pp. 102–110. 3 This is the accepted interpretation of the U.S. Supreme Court’s directive in 1944 that “the returns to the equity owner [of a regulated business] should be commensurate with returns on investments in other enterprises having corresponding risks.” Federal Power Commission v. Hope Natural Gas Company, 302 U.S. 591 at 603. 4 There are many exceptions to this statement. For example, Pacific Gas & Electric (PG&E), which serves northern California, used to be a mature, stable company until the California energy crisis of 2000 sent wholesale electric prices sky-high. PG&E was not allowed to pass these price increases on to retail cus- tomers. The company lost more than $3.5 billion in 2000 and was forced to declare bankruptcy in 2001. PG&E is no longer a suitable subject for the constant-growth DCF formula. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I. Value 4. The Value of Common Stocks © The McGraw−Hill Companies, 2003 annual growth of 6.6 percent. 5 This, together with the dividend yield, gave an esti- mate of the cost of equity capital: An alternative approach to estimating long-run growth starts with the payout ratio, the ratio of dividends to earnings per share (EPS). For Pinnacle, this was fore- casted at 43 percent. In other words, each year the company was plowing back into the business about 57 percent of earnings per share: Also, Pinnacle’s ratio of earnings per share to book equity per share was about 11 percent. This is its return on equity, or ROE: If Pinnacle earns 11 percent of book equity and reinvests 57 percent of that, then book equity will increase by .57 ϫ .11 ϭ .063, or 6.3 percent. Earnings and divi- dends per share will also increase by 6.3 percent: Dividend growth rate ϭ g ϭ plowback ratio ϫ ROE ϭ .57 ϫ .11 ϭ .063 That gives a second estimate of the market capitalization rate: Although this estimate of the market capitalization rate for Pinnacle stock seems reasonable enough, there are obvious dangers in analyzing any single firm’s stock with the constant-growth DCF formula. First, the underlying assumption of regu- lar future growth is at best an approximation. Second, even if it is an acceptable ap- proximation, errors inevitably creep into the estimate of g. Thus our two methods for calculating the cost of equity give similar answers. That was a lucky chance; dif- ferent methods can sometimes give very different answers. Remember, Pinnacle’s cost of equity is not its personal property. In well- functioning capital markets investors capitalize the dividends of all securities in Pinnacle’s risk class at exactly the same rate. But any estimate of r for a single common stock is “noisy” and subject to error. Good practice does not put too much weight on single-company cost-of-equity estimates. It collects samples of similar companies, estimates r for each, and takes an average. The average gives a more reliable benchmark for decision making. Table 4.2 shows DCF cost-of-equity estimates for Pinnacle West and 10 other electric utilities in May 2001. These utilities are all stable, mature companies for which the constant-growth DCF formula ought to work. Notice the variation in the cost-of-equity estimates. Some of the variation may reflect differences in the risk, but some is just noise. The average estimate is 10.7 percent. r ϭ DIV 1 P 0 ϩ g ϭ .033 ϩ .063 ϭ .096, or 9.6% Return on equity ϭ ROE ϭ EPS book equity per share ϭ .11 Plowback ratio ϭ 1 Ϫ payout ratio ϭ 1 Ϫ DIV EPS ϭ 1 Ϫ .43 ϭ .57 r ϭ DIV 1 P 0 ϩ g ϭ .033 ϩ .066 ϭ .099, or 9.9% 66 PART I Value 5 In this calculation we’re assuming that earnings and dividends are forecasted to grow forever at the same rate g. We’ll show how to relax this assumption later in this chapter. The growth rate was based on the average earnings growth forecasted by Value Line and IBES. IBES compiles and averages fore- casts made by security analysts. Value Line publishes its own analysts’ forecasts Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I. Value 4. The Value of Common Stocks © The McGraw−Hill Companies, 2003 Figure 4.2 shows DCF costs of equity estimated at six-month intervals for a sam- ple of electric utilities over a seven-year period. The burgundy line indicates the median cost-of-equity estimates, which seem to lie about 3 percentage points above the 10-year Treasury bond yield. The dots show the scatter of individual es- timates. Again, most of this scatter is probably noise. Some Warnings about Constant-Growth Formulas The simple constant-growth DCF formula is an extremely useful rule of thumb, but no more than that. Naive trust in the formula has led many financial analysts to silly conclusions. We have stressed the difficulty of estimating r by analysis of one stock only. Try to use a large sample of equivalent-risk securities. Even that may not work, but at least it gives the analyst a fighting chance, because the inevitable errors in estimat- ing r for a single security tend to balance out across a broad sample. In addition, resist the temptation to apply the formula to firms having high cur- rent rates of growth. Such growth can rarely be sustained indefinitely, but the constant-growth DCF formula assumes it can. This erroneous assumption leads to an overestimate of r. Consider Growth-Tech, Inc., a firm with DIV 1 ϭ $.50 and P 0 ϭ $50. The firm has plowed back 80 percent of earnings and has had a return on equity (ROE) of 25 per- cent. This means that in the past Dividend growth rate ϭ plowback ratio ϫ ROE ϭ .80 ϫ .25 ϭ .20 The temptation is to assume that the future long-term growth rate g also equals .20. This would imply r ϭ .50 50.00 ϩ .20 ϭ .21 CHAPTER 4 The Value of Common Stocks 67 Stock Price, Dividend, Dividend Yield, Growth Cost of Equity, P 0 DIV 1 DIV 1 /P 0 Rate, gr؍ DIV 1 /P 0 ؉ g American Corp. $41.71 $2.64 6.3% 3.8% 10.1% CH Energy Corp. 43.85 2.20 5.0 2.0 7.0 CLECO Corp. 46.00 .92 2.0 8.8 10.8 DPL, Inc. 30.27 1.03 3.4 9.6 13.0 Hawaiian Electric 36.69 2.54 6.9 2.6 9.5 Idacorp 39.42 1.97 5.0 5.7 10.7 Pinnacle West 49.16 1.60 3.3 6.6 9.9 Potomac Electric 22.00 1.75 8.0 5.7 13.7 Puget Energy 23.49 1.93 8.2 4.8 13.0 TECO Energy 31.38 1.44 4.6 7.7 12.3 UIL Holdings 48.21 2.93 6.1 1.9 8.0 Average 10.7% TABLE 4.2 DCF cost-of-equity estimates for electric utilities in 2001. Source: The Brattle Group, Inc. [...]... pershare dividends Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value © The McGraw−Hill Companies, 2003 4 The Value of Common Stocks CHAPTER 4 The Value of Common Stocks 20 04 Cash flow Depreciation Pretax profits Tax Aftertax profits Dividends Retained profits 2005 2006 2007 2008 2009 2010 10 .47 2 .40 8.08 2.83 5.25 2.00 3.25 11.87 3.10 8.77 3.07 5.70 2.00 3.70 7. 74 3.12 4. 62 1.62 3.00... estimates of rates of return for the stock market as a whole: S C Myers and L S Borucki: “Discounted Cash Flow Estimates of the Cost of Equity Capital—A Case Study,” Financial Markets, Institutions and Instruments, 3:9 45 (August 19 94) Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value 4 The Value of Common Stocks © The McGraw−Hill Companies, 2003 CHAPTER 4 The Value of Common... 4. 62 1.62 3.00 2.50 50 8 .40 3.17 5.23 1.83 3 .40 2.50 90 9.95 3.26 6.69 2. 34 4.35 2.50 1.85 12.67 3 .44 9.23 3.23 6.00 2.50 3.50 89 15.38 3.68 11.69 4. 09 7.60 3.00 4. 60 TA B L E 4 1 0 Forecasted profits and dividends (figures in $ millions) 2005 2006 2007 2008 2009 2010 4. 26 10.50 3. 34 3.65 4. 18 5.37 6.28 1.39 5.65 60 11.10 28 3.62 42 4. 07 93 5.11 1.57 6. 94 2.00 8.28 TA B L E 4 1 1 Forecasted investment... Growth-Tech as offering 8 percent per year dividend growth We will apply the constant-growth formula: Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value © The McGraw−Hill Companies, 2003 4 The Value of Common Stocks CHAPTER 4 The Value of Common Stocks TA B L E 4 3 Year 1 Book equity Earnings per share, EPS Return on equity, ROE Payout ratio Dividends per share, DIV Growth rate of. .. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 88 PART I I Value Value TA B L E 4 8 1999 Summary income data (figures in $ millions) Note: Reeby Sports has never paid a dividend and all the earnings have been retained in the business TA B L E 4 9 Cash flow Depreciation Pretax profits Tax Aftertax profits 2000 2001 2002 2003 5. 84 1 .45 4. 38 1.53 2.85 6 .40 1.60 4. 80 1.68 3.12 7 .41 ... discuss share repurchases in Chapter 16 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value 4 The Value of Common Stocks © The McGraw−Hill Companies, 2003 In this chapter we have used our newfound knowledge of present values to examine the market price of common stocks The value of a stock is equal to the stream of cash payments discounted at the rate of return that investors expect.. .Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 68 I Value © The McGraw−Hill Companies, 2003 4 The Value of Common Stocks PART I Value Cost of equity, percent 25 20 Median estimate 15 10 5 10-year Treasury bond yield 0 Jan 86 Jan 87 Jan 88 Jan 89 Jan 90 Jan 91 Jan 92 FIGURE 4. 2 DCF cost -of- equity estimates for a sample of 17 utilities The median estimates... (December 2, 1985), p 102 73 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 74 PART I I Value © The McGraw−Hill Companies, 2003 4 The Value of Common Stocks Value Stock Price, P0 (October 2001) EPS* Cost of Equity, r† PVGO ‫ ؍‬P0 ؊ EPS/r Income stocks: Chubb Exxon Mobil Kellogg Weyerhaeuser $77.35 42 .29 29.00 50 .45 $4. 90 2.13 1 .42 3.21 088 072 056 128 $21.67 12.71 3. 64 25.37 28 30 13 50 Growth... the problems encountered in measuring earnings and profitability in Chapter 12 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I Value 4 The Value of Common Stocks CHAPTER 4 © The McGraw−Hill Companies, 2003 The Value of Common Stocks 75 What Do Price–Earnings Ratios Mean? The price–earnings ratio is part of the everyday vocabulary of investors in the stock market People casually refer... is the amount of cash that a firm can pay out to investors after paying for Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 76 PART I I Value © The McGraw−Hill Companies, 2003 4 The Value of Common Stocks Value Year 1 Asset value Earnings Investment Free cash flow Earnings growth from previous period (%) 2 3 4 5 6 7 8 9 10 10.00 1.20 2.00 Ϫ.80 12.00 1 .44 2 .40 Ϫ.96 14. 40 1.73 2.88 Ϫ1.15 . 10.7% TABLE 4. 2 DCF cost -of- equity estimates for electric utilities in 2001. Source: The Brattle Group, Inc. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I. Value 4. The Value of. I Value Year 1 2 345 678910 Asset value 10.00 12.00 14. 40 17.28 20. 74 23 .43 26 .47 28.05 29.73 31.51 Earnings 1.20 1 .44 1.73 2.07 2 .49 2.81 3.18 3.36 3.57 3.78 Investment 2.00 2 .40 2.88 3 .46 2.69 3. 04 1.59. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition I. Value 4. The Value of Common Stocks © The McGraw−Hill Companies, 2003 CHAPTER FOUR 58 THE VALUE OF COMMON STOCKS Brealey−Meyers: