Valuing Stocks PDF

CH APTE R Valuing Stocks 9 ON JANUARY 16, 2006, FOOTWEAR AND APPAREL MAKER KENNETH NOTATION Cole Product...

CH APTE R Valuing Stocks 9 ON JANUARY 16, 2006, FOOTWEAR AND APPAREL MAKER KENNETH NOTATION Cole Productions, Inc., announced that its president, Paul Blum, had resigned Pt  stock price at the to pursue “other opportunities.” The price of the company’s stock had already end of year t dropped more than 16% over the prior two years, and the firm was in the midst rE equity cost of capital of a major undertaking to restructure its brand. News that its president, who had N terminal date or been with the company for more than 15 years, was now resigning was taken as forecast horizon a bad sign by many investors. The next day, Kenneth Cole’s stock price dropped by more than 6% on the New York Stock Exchange to $26.75, with over 300,000 g expected dividend growth rate shares traded, more than twice its average daily volume. How might an investor decide whether to buy or sell a stock such as Kenneth Cole at this price? Why Div t  dividends paid in would the stock suddenly be worth 6% less on the announcement of this news? year t What actions can Kenneth Cole’s managers take to increase the stock price? EPS t  earnings per share To answer these questions, we turn to the Law of One Price, which implies on date t that the price of a security should equal the present value of the expected cash PV present value flows an investor will receive from owning it. In this chapter, we apply this idea to EBIT earnings before stocks. Thus, to value a stock, we need to know the expected cash flows an investor interest and taxes will receive and the appropriate cost of capital with which to discount those cash FCFt free cash flow flows. Both of these quantities can be challenging to estimate, and many of the on date t details needed to do so will be developed throughout the remainder of the text. In this chapter, we will begin our study of stock valuation by identifying the relevant V t  enterprise value on date t cash flows and developing the main tools that practitioners use to evaluate them. Our analysis begins with a consideration of the dividends and capital gains τ c corporate tax rate received by investors who hold the stock for different periods, from which we de- rwacc  weighted average velop the dividend-discount model of stock valuation. Next, we apply Chapter 8’s cost of capital tools to value stocks based on the free cash flows generated by the firm. Having g FCF  expected free cash developed these stock valuation methods based on discounted cash flows, we flow growth rate then relate them to the practice of using valuation multiples based on comparable EBITDA earnings before firms. We conclude the chapter by discussing the role of competition in determin- interest, taxes, ing the information contained in stock prices, as well as its implications for inves- depreciation, and tors and corporate managers. amortization 313 M09_BERK6318_06_GE_C09.indd 313 26/04/23 6:20 PM  314 Chapter 9 Valuing Stocks 9.1 The Dividend-Discount Model The Law of One Price implies that to value any security, we must determine the expected cash flows an investor will receive from owning it. Thus, we begin our analysis of stock valuation by considering the cash flows for an investor with a one-year investment horizon. We then consider the perspective of investors with longer investment horizons. We show that if investors have the same beliefs, their valuation of the stock will not depend on their investment horizon. Using this result, we then derive the first method to value a stock: the dividend-discount model. A One-Year Investor There are two potential sources of cash flows from owning a stock. First, the firm might pay out cash to its shareholders in the form of a dividend. Second, the investor might gen- erate cash by choosing to sell the shares at some future date. The total amount received in dividends and from selling the stock will depend on the investor’s investment horizon. Let’s begin by considering the perspective of a one-year investor. When an investor buys a stock, she will pay the current market price for a share, P0. While she continues to hold the stock, she will be entitled to any dividends the stock pays. Let Div 1 be the total dividends paid per share of the stock during the year. At the end of the year, the investor will sell her share at the new market price, P1. Assuming for simplicity that all dividends are paid at the end of the year, we have the following timeline for this investment: 0 1 2P0 Div1 1 P1 Of course, the future dividend payment and stock price in the timeline above are not known with certainty; rather, these values are based on the investor’s expectations at the time the stock is purchased. Given these expectations, the investor will be willing to buy the stock at today’s price as long as the NPV of the transaction is not negative—that is, as long as the current price does not exceed the present value of the expected future dividend and sale price. Because these cash flows are risky, we cannot compute their present value using the risk-free interest rate. Instead, we must discount them based on the equity cost of capital, rE , for the stock, which is the expected return of other investments available in the market with equivalent risk to the firm’s shares. Doing so leads to the following condi- tion under which an investor would be willing to buy the stock: Div 1 + P1 P0 ≤ 1 + rE Similarly, for an investor to be willing to sell the stock, she must receive at least as much today as the present value she would receive if she waited to sell next year: Div 1 + P1 P0 ≥ 1 + rE But because for every buyer of the stock there must be a seller, both equations must hold, and therefore the stock price should satisfy Div 1 + P1 P0 = (9.1) 1 + rE M09_BERK6318_06_GE_C09.indd 314 26/04/23 6:20 PM  9.1 The Dividend-Discount Model 315 In other words, as we discovered in Chapter 3, in a competitive market, buying or selling a share of stock must be a zero-NPV investment opportunity. Dividend Yields, Capital Gains, and Total Returns We can reinterpret Eq. 9.1 if we multiply by ( 1 + rE ), divide by P0 , and subtract 1 from both sides: Total Return Div 1 + P1 Div 1 P1 − P0 rE = −1 = + P0 P0 P  0   (9.2) Dividend Yield Capital Gain Rate The first term on the right side of Eq. 9.2 is the stock’s dividend yield, which is the expected annual dividend of the stock divided by its current price. The dividend yield is the percentage return the investor expects to earn from the dividend paid by the stock. The second term on the right side of Eq. 9.2 reflects the capital gain the investor will earn on the stock, which is the difference between the expected sale price and purchase price for the stock, P1 − P0. We divide the capital gain by the current stock price to express the capital gain as a percentage return, called the capital gain rate. The sum of the dividend yield and the capital gain rate is called the total return of the stock. The total return is the expected return that the investor will earn for a one-year investment in the stock. Thus, Eq. 9.2 states that the stock’s total return should equal the equity cost of capital. In other words, the expected total return of the stock should equal the expected return of other investments available in the market with equivalent risk. EXAMPLE 9.1 Stock Prices and Returns Problem Suppose you expect Walgreens Boots Alliance (a drugstore chain) to pay dividends of $1.80 per share and trade for $50 per share at the end of the year. If investments with equiva- lent risk to Walgreen’s stock have an expected return of 8.5%, what is the most you would pay today for Walgreen’s stock? What dividend yield and capital gain rate would you expect at this price? Solution Using Eq. 9.1, we have Div 1 + P1 1.80 + 50.00 P0 = = = $47.74 1 + rE 1.085 At this price, Walgreen’s dividend yield is Div 1 P0 = 1.80 47.74 = 3.77%. The expected c­ apital gain is $50.00 − $47.74 = $2.26 per share, for a capital gain rate of 2.26 47.74 = 4.73%. There- fore, at this price, Walgreen’s expected total return is 3.77% + 4.73% = 8.5%, which is equal to its equity cost of capital. M09_BERK6318_06_GE_C09.indd 315 26/04/23 6:20 PM  316 Chapter 9 Valuing Stocks The Mechanics of a Short Sale If a stock’s expected total return is below that of other When you short sell a stock, first you receive the current investments with comparable risk, investors who own share price. Then, while your short position remains open, the stock will choose to sell it and invest elsewhere. But you must pay any dividends made. Finally, you must pay the what if you don’t own the stock—can you profit in this future stock price to close your position. These cash flows situation? are exactly the reverse of those from buying a stock. The answer is yes, by short selling the stock. To short Because the cash flows are reversed, if you short sell sell a stock, you must contact your broker, who will try to a stock, rather than receiving its return, you must pay its borrow the stock from someone who currently owns it.* return to the person you borrowed the stock from. But if Suppose John Doe holds the stock in a brokerage account. this return is less than you expect to earn by investing your Your broker can lend you shares from his account so that money in an alternative investment with equivalent risk, the you can sell them in the market at the current stock price. strategy has a positive NPV and is attractive.† (We will dis- Of course, at some point you must close the short sale cuss such strategies further in Chapter 11.) by buying the shares in the market and returning them to In practice, short sales typically reflect a desire of some Doe’s account. In the meantime, so that John Doe is not investors to bet against the stock. For example, in July 2008, made worse off by lending his shares to you, you must pay Washington Mutual stood on the verge of bankruptcy as a him any dividends the stock pays.** result of its exposure to subprime mortgages. Even though The following table compares the cash flows from buy- its stock price had fallen by more than 90% in the prior ing with those from short selling a stock: year, many investors apparently felt the stock was still not ­attractive—the short interest (number of shares sold short) Date 0 Date t Date 1 in Washington Mutual exceeded 500 million, representing Cash flows from − P0 + Div t + P1 more than 50% of Washington Mutual’s outstanding shares. buying a stock In the end the short-sellers were right. In September Cash flows from + P0 − Div t − P1 2008 Washington Mutual filed for bankruptcy in what is short selling a stock still the largest bank failure in U.S. history. The Cash Flows John Doe’s John Doe’s John Doe’s John Doe’s John Doe’s Associated with a Account Account Account Account Account Short Sale P0 is the initial price of the stock, P1 is the price of the stock when the short sale is closed, and Divt are Share Share dividends paid by the sold Broker borrows a Dividend Broker buys a share purchased stock at any date t in stock $ share and sells it Paid and returns it $ in stock between 0 and 1. market market $ $ $ 1P 0 2Div t 2P 1 * Selling a stock without first locating a share to borrow is known as a naked short sale, and is prohibited by the SEC. ** In practice, John Doe need not know you borrowed his shares. He continues to receive dividends, and if he needs the shares, the broker will replace them either by (1) borrowing shares from someone else or (2) forcing the short-seller to close his position and buy the shares in the market. † Typically, the broker will charge a fee for finding the shares to borrow, and require the short-seller to deposit collateral guaranteeing the short-seller’s ability to buy the stock later. Generally, these costs of shorting are small, but can be large in circumstances where the demand from short-sellers is high relative to the total supply of the stock. Note also that if the stock price suddenly rises, short-sellers who want to limit their losses need to buy the stock to close their position. This scenario, called a “short squeeze,” can drive the stock price still higher. See the interview on page 344 for further discussion of the important role of (and the challenges faced by) short-sellers. M09_BERK6318_06_GE_C09.indd 316 26/04/23 6:20 PM  9.1 The Dividend-Discount Model 317 The result in Eq. 9.2 is what we should expect: The firm must pay its shareholders a return commensurate with the return they can earn elsewhere while taking the same risk. If the stock offered a higher return than other securities with the same risk, investors would sell those other investments and buy the stock instead. This activity would drive up the stock’s current price, lowering its dividend yield and capital gain rate until Eq. 9.2 holds true. If the stock offered a lower expected return, investors would sell the stock and drive down its current price until Eq. 9.2 was again satisfied. A Multiyear Investor Equation 9.1 depends upon the expected stock price in one year, P1. But suppose we planned to hold the stock for two years. Then we would receive dividends in both year 1 and year 2 before selling the stock, as shown in the following timeline: 0 1 2 2P0 Div1 Div2 1 P2 Setting the stock price equal to the present value of the future cash flows in this case implies1 Div 1 Div 2 + P2 P0 = + (9.3) 1 + rE ( 1 + rE ) 2 Equations 9.1 and 9.3 are different: As a two-year investor we care about the dividend and stock price in year 2, but these terms do not appear in Eq. 9.1. Does this difference imply that a two-year investor will value the stock differently than a one-year investor? The answer to this question is no. While a one-year investor does not care about the dividend and stock price in year 2 directly, she will care about them indirectly because they will affect the price for which she can sell the stock at the end of year 1. For example, sup- pose the investor sells the stock to another one-year investor with the same beliefs. The new investor will expect to receive the dividend and stock price at the end of year 2, so he will be willing to pay Div 2 + P2 P1 = 1 + rE for the stock. Substituting this expression for P1 into Eq. 9.1, we get the same result as shown in Eq. 9.3: P 1   Div 1 + P1 Div 1 1  Div 2 + P2  P0 = = + 1 + rE 1 + rE 1 + rE  1 + rE  Div 1 Div 2 + P2 = + 1 + rE (1 + rE ) 2 1 By using the same equity cost of capital for both periods, we are assuming that the equity cost of capital does not depend on the term of the cash flows. Otherwise, we would need to adjust for the term structure of the equity cost of capital (as we did with the yield curve for risk-free cash flows in Chapter 5). This step would complicate the analysis but would not change the results. M09_BERK6318_06_GE_C09.indd 317 26/04/23 6:20 PM  318 Chapter 9 Valuing Stocks Thus, the formula for the stock price for a two-year investor is the same as the one for a sequence of two one-year investors. The Dividend-Discount Model Equation We can continue this process for any number of years by replacing the final stock price with the value that the next holder of the stock would be willing to pay. Doing so leads to the general dividend-discount model for the stock price, where the horizon N is arbitrary: Dividend -Discount Model Div 1 Div 2 Div N PN (9.4) P0 = + +  + + 1 + rE ( 1 + rE ) 2 ( 1 + rE ) N ( 1 + rE ) N Equation 9.4 applies to a single N-year investor, who will collect dividends for N years and then sell the stock, or to a series of investors who hold the stock for shorter periods and then resell it. Note that Eq. 9.4 holds for any horizon N. Thus, all investors (with the same beliefs) will attach the same value to the stock, independent of their investment horizons. How long they intend to hold the stock and whether they collect their return in the form of dividends or capital gains is irrelevant. For the special case in which the firm eventually pays dividends and is never acquired, it is possible to hold the shares forever. Consequently, we can let N go to infinity in Eq. 9.4 and write it as follows: ∞ Div 1 Div 2 Div 3 Div P0 = + 1 + rE ( 1 + rE ) 2 + ( 1 + rE ) 3 +  = ∑ ( 1 + r n )n (9.5) n =1 E That is, the price of the stock is equal to the present value of the expected future dividends it will pay. CONCEPT CHECK 1. How do you calculate the total return of a stock? 2. What discount rate do you use to discount the future cash flows of a stock? 3. Why will a short-term and long-term investor with the same beliefs be willing to pay the same price for a stock? 9.2 Applying the Dividend-Discount Model Equation 9.5 expresses the value of the stock in terms of the expected future dividends the firm will pay. Of course, estimating these dividends—especially for the distant future—is difficult. A common approximation is to assume that in the long run, dividends will grow at a constant rate. In this section, we will consider the implications of this assumption for stock prices and explore the tradeoff between dividends and growth. Constant Dividend Growth The simplest forecast for the firm’s future dividends states that they will grow at a constant rate, g, forever. That case yields the following timeline for the cash flows for an investor who buys the stock today and holds it: 0 1 2 3... 2P0 Div1 Div1(1 1 g) Div1(1 1 g) 2 M09_BERK6318_06_GE_C09.indd 318 26/04/23 6:20 PM  9.2 Applying the Dividend-Discount Model 319 Because the expected dividends are a constant growth perpetuity, we can use Eq. 4.11 to calculate their present value. We then obtain the following simple formula for the stock price:2 Constant Dividend Growth Model Div 1 (9. 6) P0 = rE − g According to the constant dividend growth model, the value of the firm depends on the dividend level for the coming year, divided by the equity cost of capital adjusted by the expected growth rate of dividends. EXAMPLE 9.2 Valuing a Firm with Constant Dividend Growth Problem Consolidated Edison, Inc. (Con Edison), is a regulated utility company that services the New York City area. Suppose Con Edison plans to pay $3.40 per share in dividends in the coming year. If its equity cost of capital is 6% and dividends are expected to grow by 2% per year in the future, estimate the value of Con Edison’s stock. Solution If dividends are expected to grow perpetually at a rate of 2% per year, we can use Eq. 9.6 to calculate the price of a share of Con Edison stock: Div 1 $3.40 P0 = = = $85 rE − g 0.06 − 0.02 For another interpretation of Eq. 9.6, note that we can rearrange it as follows: Div 1 rE = + g (9.7) P0 Comparing Eq. 9.7 with Eq. 9.2, we see that g equals the expected capital gain rate. In other words, with constant expected dividend growth, the expected growth rate of the share price matches the growth rate of dividends. Dividends Versus Investment and Growth In Eq. 9.6, the firm’s share price increases with the current dividend level, Div 1, and the expected growth rate, g. To maximize its share price, a firm would like to increase both these quantities. Often, however, the firm faces a tradeoff: Increasing growth may require investment, and money spent on investment cannot be used to pay dividends. We can use the constant dividend growth model to gain insight into this tradeoff. 2 As we discussed in Chapter 4, this formula requires that g < rE. Otherwise, the present value of the growing perpetuity is infinite. The implication here is that it is impossible for a stock’s dividends to grow at a rate g > rE forever. If the growth rate exceeds rE , it must be temporary, and the constant growth model does not apply. M09_BERK6318_06_GE_C09.indd 319 26/04/23 6:20 PM  320 Chapter 9 Valuing Stocks John Burr Williams’s Theory of Investment Value The first formal derivation of the dividend-discount model Williams’s book was not widely appreciated in its day— appeared in the Theory of Investment Value, written by John indeed, legend has it there was a lively debate at Harvard Burr Williams in 1938. The book was an important land- over whether it was acceptable as his Ph.D. dissertation. But mark in the history of corporate finance, because Williams Williams went on to become a very successful investor, and demonstrated for the first time that corporate finance relied by the time he died in 1989, the importance of the math- on certain principles that could be derived using formal ana- ematical method in corporate finance was indisputable, and lytical methods. As Williams wrote in the preface: the discoveries that resulted from this “new” tool had fun- The truth is that the mathematical method is a new tool of great damentally changed its practice. Today, Williams is regarded power whose use promises to lead to notable advances in Invest- as the founder of fundamental analysis, and his book pio- ment Analysis. Always it has been the rule in the history of neered the use of pro forma modeling of financial statements science that the invention of new tools is the key to new discoveries, and cash flows for valuation purposes, as well as many other and we may expect the same rule to hold true in this branch of ideas now central to modern finance (see Chapter 14 for Economics as well. ­further contributions). A Simple Model of Growth. What determines the rate of growth of a firm’s dividends? If we define a firm’s dividend payout rate as the fraction of its earnings that the firm pays as dividends each year, then we can write the firm’s dividend per share at date t as follows: Earnings t Div t = × Dividend Payout Rate t (9.8) Shares Outstanding t  EPS t That is, the dividend each year is the firm’s earnings per share (EPS) multiplied by its dividend payout rate. Thus the firm can increase its dividend in three ways: 1. It can increase its earnings (net income). 2. It can increase its dividend payout rate. 3. It can decrease its shares outstanding. Let’s suppose for now that the firm does not issue new shares (or buy back its existing shares), so that the number of shares outstanding is fixed, and explore the potential trade- off between options 1 and 2. A firm can do one of two things with its earnings: It can pay them out to investors, or it can retain and reinvest them. By investing more today, a firm can increase its future earnings and dividends. For simplicity, let’s assume that if no investment is made, the firm does not grow, so the current level of earnings generated by the firm remains constant. If all increases in future earnings result exclusively from new investment made with retained earnings, then Change in Earnings = New Investment × Return on New Investment (9.9) New investment equals earnings multiplied by the firm’s retention rate, the fraction of current earnings that the firm retains: New Investment = Earnings × Retention Rate (9.10) Substituting Eq. 9.10 into Eq. 9.9 and dividing by earnings gives an expression for the growth rate of earnings: M09_BERK6318_06_GE_C09.indd 320 26/04/23 6:20 PM  9.2 Applying the Dividend-Discount Model 321 Change in Earnings Earnings Growth Rate = Earnings = Retention Rate × Return on New Investment (9.11) If the firm chooses to keep its dividend payout rate constant, then the growth in dividends will equal growth of earnings: g = Retention Rate × Return on New Investment (9.12) This growth rate is sometimes referred to as the firm’s sustainable growth rate, the rate at which it can grow using only retained earnings. Profitable Growth. Equation 9.12 shows that a firm can increase its growth rate by retaining more of its earnings. However, if the firm retains more earnings, it will be able to pay out less of those earnings and, according to Eq. 9.8, will have to reduce its dividend. If a firm wants to increase its share price, should it cut its dividend and invest more, or should it cut investment and increase its dividend? Not surprisingly, the answer will depend on the profitability of the firm’s investments. Let’s consider an example. EXAMPLE 9.3 Cutting Dividends for Profitable Growth Problem Crane Sporting Goods expects to have earnings per share of $6 in the coming year. Rather than reinvest these earnings and grow, the firm plans to pay out all of its earnings as a dividend. With these expectations of no growth, Crane’s current share price is $60. Suppose Crane could cut its dividend payout rate to 75% for the foreseeable future and use the retained earnings to open new stores. The return on its investment in these stores is expected to be 12%. Assuming its equity cost of capital is unchanged, what effect would this new policy have on Crane’s stock price? Solution First, let’s estimate Crane’s equity cost of capital. Currently, Crane plans to pay a dividend equal to its earnings of $6 per share. Given a share price of $60, Crane’s dividend yield is $6 $60 = 10%. With no expected growth ( g = 0), we can use Eq. 9.7 to estimate rE : Div 1 rE = + g = 10% + 0% = 10% P0 In other words, to justify Crane’s stock price under its current policy, the expected return of other stocks in the market with equivalent risk must be 10%. Next, we consider the consequences of the new policy. If Crane reduces its divi- dend payout rate to 75%, then from Eq. 9.8 its dividend this coming year will fall to Div 1 = EPS 1 × 75% = $6 × 75% = $4.50. At the same time, because the firm will now retain 25% of its earnings to invest in new stores, from Eq. 9.12 its growth rate will increase to g = Retention Rate × Return on New Investment = 25% × 12% = 3% Assuming Crane can continue to grow at this rate, we can compute its share price under the new policy using the constant dividend growth model of Eq. 9.6: Div 1 $4.50 P0 = = = $64.29 rE − g 0.10 − 0.03 Thus, Crane’s share price should rise from $60 to $64.29 if it cuts its dividend to invest in projects that offer a return (12%) greater than their cost of capital (which we assume remains 10%). These projects are positive NPV, and so by taking them Crane has created value for its shareholders. M09_BERK6318_06_GE_C09.indd 321 26/04/23 6:20 PM  322 Chapter 9 Valuing Stocks In Example 9.3, cutting the firm’s dividend in favor of growth raised the firm’s stock price. But this is not always the case, as the next example demonstrates. EXAMPLE 9.4 Unprofitable Growth Problem Suppose Crane Sporting Goods decides to cut its dividend payout rate to 75% to invest in new stores, as in Example 9.3. But now suppose that the return on these new investments is 8%, rather than 12%. Given its expected earnings per share this year of $6 and its equity cost of capi- tal of 10%, what will happen to Crane’s current share price in this case? Solution Just as in Example 9.3, Crane’s dividend will fall to $6 × 75% = $4.50. Its growth rate under the new policy, given the lower return on new investment, will now be g = 25% × 8% = 2%. The new share price is therefore Div 1 $4.50 P0 = = = $56.25 rE − g 0.10 − 0.02 Thus, even though Crane will grow under the new policy, the new investments have negative NPV. Crane’s share price will fall if it cuts its dividend to make new investments with a return of only 8% when its investors can earn 10% on other investments with comparable risk. Comparing Example 9.3 with Example 9.4, we see that the effect of cutting the firm’s dividend to grow crucially depends on the return on new investment. In Example 9.3, the return on new investment of 12% exceeds the firm’s equity cost of capital of 10%, so the investment has a positive NPV. In Example 9.4, the return on new investment is only 8%, so the new investment has a negative NPV (even though it will lead to earnings growth). Thus, cutting the firm’s dividend to increase investment will raise the stock price if, and only if, the new investments have a positive NPV. Changing Growth Rates Successful young firms often have very high initial earnings growth rates. During this pe- riod of high growth, firms often retain 100% of their earnings to exploit profitable invest- ment opportunities. As they mature, their growth slows to rates more typical of established companies. At that point, their earnings exceed their investment needs and they begin to pay dividends. We cannot use the constant dividend growth model to value the stock of such a firm, for several reasons. First, these firms often pay no dividends when they are young. Second, their growth rate continues to change over time until they mature. However, we can use the general form of the dividend-discount model to value such a firm by applying the constant growth model to calculate the future share price of the stock PN once the firm matures and its expected growth rate stabilizes: 0 1 2 N N11 N12 N13...... Div1 Div2 DivN DivN 11 DivN 11 DivN 11 1 PN 3(1 1 g) 3(1 1 g) 2 M09_BERK6318_06_GE_C09.indd 322 26/04/23 6:20 PM  9.2 Applying the Dividend-Discount Model 323 Specifically, if the firm is expected to grow at a long-term rate g after year N + 1, then from the constant dividend growth model: Div N + 1 PN = (9.13) rE − g We can then use this estimate of PN as a terminal (continuation) value in the dividend- discount model. Combining Eq. 9.4 with Eq. 9.13, we have Dividend-Discount Model with Constant Long-Term Growth Div 1 Div 2 Div N 1  Div N + 1  P0 = + +... + +  r − g  (9.14) 1 + rE ( 1 + rE ) 2 ( 1 + rE ) N ( 1 + rE ) N E EXAMPLE 9.5 Valuing a Firm with Two Different Growth Rates Problem Small Fry, Inc., has just invented a potato chip that looks and tastes like a french fry. Given the phenomenal market response to this product, Small Fry is reinvesting all of its earnings to expand its operations. Earnings were $2 per share this past year and are expected to grow at a rate of 20% per year until the end of year 4. At that point, other companies are likely to bring out competing products. Analysts project that at the end of year 4, Small Fry will cut investment and begin paying 60% of its earnings as dividends and its growth will slow to a long-run rate of 4%. If Small Fry’s equity cost of capital is 8%, what is the value of a share today? Solution We can use Small Fry’s projected earnings growth rate and payout rate to forecast its future earn- ings and dividends as shown in the following spreadsheet: Year 0 1 2 3 4 5 6 Earnings 1 EPS Growth Rate (versus prior year) 20% 20% 20% 20% 4% 4% 2 EPS $2.00 $2.40 $2.88 $3.46 $4.15 $4.31 $4.49 Dividends 3 Dividend Payout Rate 0% 0% 0% 60% 60% 60% 4 Dividend $ — $ — $ — $2.49 $2.59 $2.69 Starting from $2.00 in year 0, EPS grows by 20% per year until year 4, after which growth slows to 4%. Small Fry’s dividend payout rate is zero until year 4, when competition reduces its invest- ment opportunities and its payout rate rises to 60%. Multiplying EPS by the dividend payout ratio, we project Small Fry’s future dividends in line 4. From year 4 onward, Small Fry’s dividends will grow at the expected long-run rate of 4% per year. Thus, we can use the constant dividend growth model to project Small Fry’s share price at the end of year 3. Given its equity cost of capital of 8%, Div 4 $2.49 P3 = = = $62.25 rE − g 0.08 − 0.04 We then apply the dividend-discount model (Eq. 9.4) with this terminal value: Div 1 Div 2 Div 3 P3 $62.25 P0 = + + + = = $49.42 1 + rE ( 1 + rE )2 ( 1 + rE )3 ( 1 + rE )3 ( 1.08 )3 As this example illustrates, the dividend-discount model is flexible enough to handle any fore- casted pattern of dividends. M09_BERK6318_06_GE_C09.indd 323 26/04/23 6:20 PM  324 Chapter 9 Valuing Stocks Limitations of the Dividend-Discount Model The dividend-discount model values the stock based on a forecast of the future dividends paid to shareholders. But unlike a Treasury bond, where the future cash flows are known with virtual certainty, there is a large amount of uncertainty associated with any forecast of a firm’s future dividends. Let’s consider the example of Kenneth Cole Productions (KCP), mentioned in the in- troduction to this chapter. In early 2006, KCP paid annual dividends of $0.72. With an equity cost of capital of 11% and expected dividend growth of 8%, the constant dividend growth model implies a share price for KCP of Div 1 $0.72 P0 = = = $24 rE − g 0.11 − 0.08 which is reasonably close to the $26.75 share price the stock had at the time. With a 10% dividend growth rate, however, this estimate would rise to $72 per share; with a 5% divi- dend growth rate, the estimate falls to $12 per share. As we see, even small changes in the assumed dividend growth rate can lead to large changes in the estimated stock price. Furthermore, it is difficult to know which estimate of the dividend growth rate is more rea- sonable. KCP more than doubled its dividend between 2003 and 2005, but earnings remained relatively flat during that time. Consequently, this rapid rate of dividend growth was not likely to be sustained. Forecasting dividends requires forecasting the firm’s earnings, dividend payout rate, and future share count. But future earnings depend on interest expenses (which in turn depend on how much the firm borrows), and the firm’s share count and dividend payout rate depend on whether the firm uses a portion of its earnings to repurchase shares. Because borrowing and repurchase decisions are at management’s discretion, they can be difficult to forecast reliably.3 We look at two alternative methods that avoid some of these difficulties in the next section. CONCEPT CHECK 1. In what three ways can a firm increase its future dividend per share? 2. Under what circumstances can a firm increase its share price by cutting its dividend and investing more? 9.3  Total Payout and Free Cash Flow Valuation Models In this section, we outline two alternative approaches to valuing the firm’s shares that avoid some of the difficulties of the dividend-discount model. First, we consider the total payout model, which allows us to ignore the firm’s choice between dividends and share repurchases. Then, we consider the discounted free cash flow model, which focuses on the cash flows to all of the firm’s investors, both debt and equity holders, allowing us to avoid estimating the impact of the firm’s borrowing decisions on earnings. Share Repurchases and the Total Payout Model In our discussion of the dividend-discount model, we implicitly assumed that any cash paid out by the firm to shareholders takes the form of a dividend. However, in recent years, an increasing number of firms have replaced dividend payouts with share repurchases. In a 3 We discuss management’s decision to borrow funds or repurchase shares in Part 5. M09_BERK6318_06_GE_C09.indd 324 26/04/23 6:20 PM  9.3 Total Payout and Free Cash Flow Valuation Models 325 share repurchase, also called a stock buyback, the firm uses excess cash to buy back its own stock. Share repurchases have two consequences for the dividend-discount model. First, the more cash the firm uses to repurchase shares, the less it has available to pay divi- dends. Second, by repurchasing shares, the firm decreases its share count, which increases its earnings and dividends on a per-share basis. In the dividend-discount model, we valued a share from the perspective of a single shareholder, discounting the dividends the shareholder will receive: P0 = PV (Future Dividends per Share) (9.15) An alternative method that may be more reliable when a firm repurchases shares is the total payout model, which values all of the firm’s equity, rather than a single share. To do so, we discount the total payouts that the firm makes to shareholders, which is the total amount spent on both dividends and share repurchases.4 Then, we divide by the current number of shares outstanding to determine the share price. Total Payout Model PV (Future Total Dividends and Repurchases) P0 = (9.16) Shares Outstanding 0 We can apply the same simplifications that we obtained by assuming constant growth in Section 9.2 to the total payout method. The only change is that we discount total dividends and share repurchases and use the growth rate of total earnings (rather than earnings per share) when forecast- ing the growth of the firm’s total payouts. This method can be more reliable and easier to apply when the firm uses share repurchases. EXAMPLE 9.6 Valuation with Share Repurchases Problem Titan Industries has 217 million shares outstanding and expects earnings at the end of this year of $860 million. Titan plans to pay out 50% of its earnings in total, paying 30% as a dividend and using 20% to repurchase shares. If Titan’s earnings are expected to grow by 7.5% per year and these payout rates remain constant, determine Titan’s share price assuming an equity cost of capital of 10%. Solution Titan will have total payouts this year of 50% × $860 million = $430 million. Based on the equity cost of capital of 10% and an expected earnings growth rate of 7.5%, the present value of Titan’s future payouts can be computed as a constant growth perpetuity: $430 million PV (Future Total Dividends and Repurchases) = = $17.2 billion 0.10 − 0.075 This present value represents the total value of Titan’s equity (i.e., its market capitalization). To compute the share price, we divide by the current number of shares outstanding: $17.2 billion P0 = = $79.26 per share 217 million shares 4 Think of the total payouts as the amount you would receive if you owned 100% of the firm’s shares: You would receive all of the dividends, plus the proceeds from selling shares back to the firm in the share repurchase. M09_BERK6318_06_GE_C09.indd 325 26/04/23 6:20 PM  326 Chapter 9 Valuing Stocks Using the total payout method, we did not need to know the firm’s split between dividends and share repurchases. To compare this method with the dividend-discount model, note that Titan will pay a dividend of 30% × $860 million ( 217 million shares ) = $1.19 per share, for a dividend yield of 1.19 79.26 = 1.50%. From Eq. 9.7, Titan’s expected EPS, dividend, and share price growth rate is g = rE − Div 1 P0 = 8.50%. These “per share” growth rates exceed the 7.5% growth rate of total earnings because Titan’s share count will decline over time due to share repurchases.5 The Discounted Free Cash Flow Model In the total payout model, we first value the firm’s equity, rather than just a single share. The discounted free cash flow model goes one step further and begins by determining the total value of the firm to all investors—both equity and debt holders. That is, we begin by estimating the firm’s enterprise value, which we defined in Chapter 2 as6 Enterprise Value = Market Value of Equity + Debt − Cash (9.17) The enterprise value is the value of the firm’s underlying business, unencumbered by debt and separate from any cash or marketable securities. We can interpret the enterprise value as the net cost of acquiring the firm’s equity, taking its cash, paying off all debt, and thus owning the unlevered business. The advantage of the discounted free cash flow model is that it allows us to value a firm without explicitly forecasting its dividends, share repur- chases, or its use of debt. Valuing the Enterprise. How can we estimate a firm’s enterprise value? To estimate the value of the firm’s equity, we computed the present value of the firm’s total payouts to equity holders. Likewise, to estimate a firm’s enterprise value, we compute the present value of the free cash flow (FCF) that the firm has available to pay all investors, both debt and eq- uity holders. We saw how to compute the free cash flow for a project in Chapter 8; we now perform the same calculation for the entire firm: Unlevered  Net  Income  Free Cash Flow = EBIT × (1 − τ c ) + Depreciation − Capital Expenditures − Increases in Net Working Capital                                   (9.18) When we are looking at the entire firm, it is natural to define the firm’s net investment as its capital expenditures in excess of depreciation: Net Investment = Capital Expenditures − Depreciation (9.19) We can loosely interpret net investment as investment intended to support the firm’s growth, above and beyond the level needed to maintain the firm’s existing capital. With that definition, we can also write the free cash flow formula as 5 The difference in the per share and total earnings growth rate results from Titan’s “repurchase yield” of (20% × $860 million/217 million shares)/($79.26/share) = 1%. Indeed, given an expected share price of $79.26 × 1.085 = $86.00 next year, Titan will repurchase 20% × $860 million ÷ ($86 per share) = 2 million shares next year. With the decline in the number of shares from 217 million to 215 million, EPS grows by a factor of 1.075 × (217/215) = 1.085 or 8.5%. 6 To be precise, by cash we are referring to the firm’s cash in excess of its working capital needs, which is the amount of cash it has invested at a competitive market interest rate. M09_BERK6318_06_GE_C09.indd 326 26/04/23 6:20 PM  9.3 Total Payout and Free Cash Flow Valuation Models 327 Free Cash Flow = EBIT × ( 1 − τ c ) − Net Investment − Increases in Net Working Capital (9.20) Free cash flow measures the cash generated by the firm before any payments to debt or equity holders are considered. Thus, just as we determine the value of a project by calculating the NPV of the project’s free cash flow, we estimate a firm’s current enterprise value V 0 by computing the present value of the firm’s free cash flow: Discounted Free Cash Flow Model V 0 = PV (Future Free Cash Flow of Firm) (9.21) Given the enterprise value, we can estimate the share price by using Eq. 9.17 to solve for the value of equity and then divide by the total number of shares outstanding: V 0 + Cash 0 − Debt 0 P0 = (9.22) Shares Outstanding 0 Intuitively, the difference between the discounted free cash flow model and the dividend- discount model is that in the dividend-discount model, the firm’s cash and debt are included indirectly through the effect of interest income and expenses on earnings. In the discounted free cash flow model, we ignore interest income and expenses (free cash flow is based on EBIT ), but then adjust for cash and debt directly in Eq. 9.22. Implementing the Model. A key difference between the discounted free cash flow model and the earlier models we have considered is the discount rate. In previous calculations we used the firm’s equity cost of capital, rE , because we were discounting the cash flows to equity holders. Here we are discounting the free cash flow that will be paid to both debt and equity holders. Thus, we should use the firm’s weighted average cost of capital (WACC), denoted by rwacc , which is the average cost of capital the firm must pay to all of its investors, both debt and equity holders. If the firm has no debt, then rwacc = rE. But when a firm has debt, rwacc is an average of the firm’s debt and eq- uity cost of capital. In that case, because debt is generally less risky than equity, rwacc is generally less than rE. We can also interpret the WACC as reflecting the average risk of all of the firm’s investments. We’ll develop methods to calculate the WACC explicitly in Parts 4 and 5. Given the firm’s weighted average cost of capital, we implement the discounted free cash flow model in much the same way as we did the dividend-discount model. That is, we fore- cast the firm’s free cash flow up to some horizon, together with a terminal (continuation) value of the enterprise: FCF1 FCF2 FCFN + V N V0 = + +  + (9.23) 1 + rwacc ( 1 + rwacc ) 2 ( 1 + rwacc ) N Often, the terminal value is estimated by assuming a constant long-run growth rate g FCF for free cash flows beyond year N, so that FCFN + 1  1 + g FCF  VN = = × FCFN (9.24) rwacc − g FCF  rwacc − g FCF  The long-run growth rate g FCF is typically based on the expected long-run growth rate of the firm’s revenues. M09_BERK6318_06_GE_C09.indd 327 26/04/23 6:20 PM  328 Chapter 9 Valuing Stocks EXAMPLE 9.7 Valuing Kenneth Cole Using Free Cash Flow Problem Kenneth Cole (KCP) had sales of $518 million in 2005. Suppose you expect its sales to grow at a 9% rate in 2006, but that this growth rate will slow by 1% per year to a long-run growth rate for the apparel industry of 4% by 2011. Based on KCP’s past profitability and investment needs, you expect EBIT to be 9% of sales, increases in net working capital requirements to be 10% of any increase in sales, and net investment (capital expenditures in excess of depreciation) to be 8% of any increase in sales. If KCP has $100 million in cash, $3 million in debt, 21 million shares out- standing, a tax rate of 37%, and a weighted average cost of capital of 11%, what is your estimate of the value of KCP’s stock in early 2006? Solution Using Eq. 9.20, we can estimate KCP’s future free cash flow based on the estimates above as follows: Year 2005 2006 2007 2008 2009 2010 2011 FCF Forecast ($ millions) 1 Sales 518.0 564.6 609.8 652.5 691.6 726.2 755.3 2 Growth versus Prior Year 9.0% 8.0% 7.0% 6.0% 5.0% 4.0% 3 EBIT (9% of sales) 50.8 54.9 58.7 62.2 65.4 68.0 4 Less: Income Tax (37% EBIT) (18.8) (20.3) (21.7) (23.0) (24.2) (25.1) 5 Less: Net Investment (8% DSales) (3.7) (3.6) (3.4) (3.1) (2.8) (2.3) 6 Less: Inc. in NWC (10% DSales) (4.7) (4.5) (4.3) (3.9) (3.5) (2.9) 7 Free Cash Flow 23.6 26.4 29.3 32.2 35.0 37.6 Because we expect KCP’s free cash flow to grow at a constant rate after 2011, we can use Eq. 9.24 to compute a terminal enterprise value:  1 + g FCF  1.04 V 2011 =  × FCF2011 =   × 37.6 = $558.6 million  rwacc − g FCF   0.11 − 0.04  From Eq. 9.23, KCP’s current enterprise value is the present value of its free cash flows plus the terminal enterprise value: 23.6 26.4 29.3 32.2 35.0 37.6 + 558.6 V0 = + + + + + = $424.8 million 1.11 1.112 1.113 1.114 1.115 1.116 We can now estimate the value of a share of KCP’s stock using Eq. 9.22: 424.8 + 100 − 3 P0 = = $24.85 21 Connection to Capital Budgeting. There is an important connection between the dis- counted free cash flow model and the NPV rule for capital budgeting that we developed in Chapter 8. Because the firm’s free cash flow is equal to the sum of the free cash flows from the firm’s current and future investments, we can interpret the firm’s enterprise value as the total NPV that the firm will earn from continuing its existing projects and initiating new ones. Hence, the NPV of any individual project represents its contribution to the firm’s enterprise value. To maximize the firm’s share price, we should accept projects that have a positive NPV. Recall also from Chapter 8 that many forecasts and estimates were necessary to estimate the free cash flows of a project. The same is true for the firm: We must forecast future sales, operating expenses, taxes, capital requirements, and other factors. On the one hand, estimating free cash flow in this way gives us flexibility to incorporate many specific details about the M09_BERK6318_06_GE_C09.indd 328 26/04/23 6:20 PM  9.3 Total Payout and Free Cash Flow Valuation Models 329 future prospects of the firm. On the other hand, some uncertainty inevitably surrounds each assumption. It is therefore important to conduct a sensitivity analysis, as we described in Chapter 8, to translate this uncertainty into a range of potential values for the stock. EXAMPLE 9.8 Sensitivity Analysis for Stock Valuation Problem In Example 9.7, KCP’s revenue growth rate was assumed to be 9% in 2006, slowing to a long- term growth rate of 4%. How would your estimate of the stock’s value change if you expected revenue growth of 4% from 2006 on? How would it change if in addition you expected EBIT to be 7% of sales, rather than 9%? Solution With 4% revenue growth and a 9% EBIT margin, KCP will have 2006 revenues of 518 × 1.04 = $538.7 million, and EBIT of 9% ( 538.7 ) = $48.5 million. Given the increase in sales of 538.7 − 518.0 = $20.7 million, we expect net investment of 8% ( 20.7 ) = $1.7 million and additional net working capital of 10% ( 20.7 ) = $2.1 million. Thus, KCP’s expected FCF in 2006 is FCF06 = 48.5 (1 −.37) − 1.7 − 2.1 = $26.8 million Because growth is expected to remain constant at 4%, we can estimate KCP’s enterprise value as a growing perpetuity: V 0 = $26.8 ( 0.11 − 0.04 ) = $383 million for an initial share value of P0 = ( 383 + 100 − 3 ) 21 = $22.86. Thus, comparing this result with that of Example 9.7, we see that a higher initial revenue growth of 9% versus 4% contributes about $2 to the value of KCP’s stock. If, in addition, we expect KCP’s EBIT margin to be only 7%, our FCF estimate would decline to FCF06 = (.07 × 538.7 ) ( 1 −.37 ) − 1.7 − 2.1 = $20.0 million for an enterprise value of V 0 = $20 ( 0.11 − 0.04 ) = $286 million and a share value of P0 = ( 286 + 100 − 3 ) 21 = $18.24. Thus, we can see that maintaining an EBIT margin of 9% versus 7% contributes more than $4.50 to KCP’s stock value in this scenario. Figure 9.1 summarizes the different valuation methods we have discussed thus far. The value of the stock is determined by the present value of its future dividends. We can esti- mate the total market capitalization of the firm’s equity from the present value of the firm’s total payouts, which includes dividends and share repurchases. Finally, the present value of the firm’s free cash flow, which is the cash the firm has available to make payments to equity or debt holders, determines the firm’s enterprise value. FIGURE 9.1 A Comparison of Discounted Cash Flow Models of Stock Valuation By computing the pres- Present Value of … At the … Determines the... ent value of the firm’s Dividend Payments Equity cost of capital Stock Price dividends, total payouts or free cash flows, we can Total Payouts (All dividends and repurchases) Equity cost of capital Equity Value estimate the value of the stock, the total value of the Free Cash Flow firm’s equity, or the firm’s (Cash available to pay all security holders) Weighted average cost of capital Enterprise Value enterprise value. M09_BERK6318_06_GE_C09.indd 329 26/04/23 6:20 PM  330 Chapter 9 Valuing Stocks CONCEPT CHECK 1. How does the growth rate used in the total payout model differ from the growth rate used in the dividend-discount model? 2. What is the enterprise value of the firm? 3. How can you estimate a firm’s stock price based on its projected free cash flows? 9.4 Valuation Based on Comparable Firms Thus far, we have valued a firm or its stock by considering the expected future cash flows it will provide to its owner. The Law of One Price then tells us that its value is the present value of its future cash flows, because the present value is the amount we would need to invest elsewhere in the market to replicate the cash flows with the same risk. Another application of the Law of One Price is the method of comparables. In the method of comparables (or “comps”), rather than value the firm’s cash flows directly, we estimate the value of the firm based on the value of other, comparable firms or invest- ments that we expect will generate very similar cash flows in the future. For example, con- sider the case of a new firm that is identical to an existing publicly traded company. If these firms will generate identical cash flows, the Law of One Price implies that we can use the value of the existing company to determine the value of the new firm. Of course, identical companies do not exist. Although they may be similar in many respects, even two firms in the same industry selling the same types of products are likely to be of a different size or scale. In this section, we consider ways to adjust for scale dif- ferences to use comparables to value firms with similar business, and then discuss the strengths and weaknesses of this approach. Valuation Multiples We can adjust for differences in scale between firms by expressing their value in terms of a valuation multiple, which is a ratio of the value to some measure of the firm’s scale. As an analogy, consider valuing an office building. A natural measure to consider would be the price per square foot for other buildings recently sold in the area. Multiplying the size of the office building under consideration by the average price per square foot would typically provide a reasonable estimate of the building’s value. We can apply this same idea to stocks, replacing square footage with some more appropriate measure of the firm’s scale. The Price-Earnings Ratio. The most common valuation multiple is the price-earnings (P/E) ratio, which we introduced in Chapter 2. A firm’s P/E ratio is equal to the share price divided by its earnings per share. The intuition behind its use is that when you buy a stock, you are in a sense buying the rights to the firm’s future earnings. Because differences in the scale of firms’ earnings are likely to persist, you should be willing to pay propor- tionally more for a stock with higher current earnings. Thus, we can estimate the value of a firm’s share by multiplying its current earnings per share by the average P/E ratio of comparable firms. To interpret the P/E multiple, consider the stock price formula we derived in Eq. 9.6 for the case of constant dividend growth: P0 = Div 1 ( rE − g ). If we divide both sides of this equation by EPS 1 , we have the following formula: P0 Div 1 EPS 1 Dividend Payout Rate Forward P E = = = (9.25) EPS 1 rE − g rE − g M09_BERK6318_06_GE_C09.indd 330 26/04/23 6:20 PM  9.4 Valuation Based on Comparable Firms 331 Equation 9.25 provides a formula for the firm’s forward P/E, which is the P/E multiple computed based on its forward earnings (expected earnings over the next twelve months). We can also compute a firm’s trailing P/E ratio using trailing earnings (earnings over the prior 12 months).7 For valuation purposes, the forward P/E is generally preferred, as we are most concerned about future earnings.8 Equation 9.25 implies that if two stocks have the same payout and EPS growth rates, as well as equivalent risk (and therefore the same equity cost of capital), then they should have the same P/E. It also shows that firms and industries with high growth rates, and that gen- erate cash well in excess of their investment needs so that they can maintain high payout rates, should have high P/E multiples. EXAMPLE 9.9 Valuation Using the Price-Earnings Ratio Problem Johnson Outdoors is a maker of fishing, camping, and diving gear with current earnings per share of $5.55. If the average P/E of comparable recreational products firms is 11.0, estimate a value for Johnson Outdoors using the P/E as a valuation multiple. What are the assumptions underlying this estimate? Solution We estimate a share price for Johnson Outdoors by multiplying its EPS by the P/E of comparable firms. Thus, P0 = $5.55 × 11.0 = $61.05. This estimate assumes that Johnson Outdoors will have similar future risk, payout rates, and growth rates to comparable firms in the industry. Enterprise Value Multiples. It is also common practice to use valuation multiples based on the firm’s enterprise value. As we discussed in Section 9.3, because it represents the total value of the firm’s underlying business rather than just the value of equity, using the enterprise value is advantageous if we want to compare firms with different amounts of leverage. Because the enterprise value represents the entire value of the firm before the firm pays its debt, to form an appropriate multiple, we divide it by a measure of earnings or cash flows before interest payments are made. Common multiples to consider are enterprise value to EBIT, EBITDA (earnings before interest, taxes, depreciation, and amortization), and free cash flow. However, because capital expenditures can vary substantially from pe- riod to period (e.g., a firm may need to add capacity and build a new plant one year, but then not need to expand further for many years), most practitioners rely on enterprise value to EBITDA multiples. From Eq. 9.24, if expected free cash flow growth is constant, then V0 FCF1 EBITDA1 = (9.26) EBITDA1 rwacc − g FCF As with the P/E multiple, this multiple is higher for firms with high growth rates and low capital requirements (so that free cash flow is high in proportion to EBITDA). 7 Assuming EPS grows at rate g 0 between date 0 and 1, Trailing P/E = P0 /EPS 0 = (