The Key to Your Success in Three Easy Steps!

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The Key to Your Success in Three Easy Steps! 1.

Review your personalized Study Plan to see where you need more work. 3.

individualized feedback where you need it.

to let students know their current progress in the course and has a detailed calendar

2 The Key to Your Success in Three Easy Steps! 1. Take a Sample Test to assess your knowledge. 2. Review your personalized Study Plan to see where you need more work. 3. Use the Study Plan exercises and step-by-step tutorials to get practice and individualized feedback where you need it. If your instructor assigns homework and tests using The Course Home page uses graphs to let students know their current progress in the course and has a detailed calendar that displays due dates and instructors can add entries. Did your textbook come with a Student Access Kit? If so, go to to register using the code. If not, you can purchase access to online at

3 Chapter 7 Stock Valuation 199 FIGURE 7.2 NKE Stock Prices for Different Expected Growth Rates Stock prices are based on the constant dividend growth model. We assume a dividend next year of $1.08 and an equity cost of capital of 10%. The expected dividend growth rate varies from 0% to 9%. Note how even a small change in the expected growth rate produces a large change in the stock price, especially at higher growth rates. $120 $100 $80 Stock Price $60 $40 $20 $0 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% Growth Rate From Eq. 7.8, forecasting dividends requires forecasting the firm s earnings, dividend payout rate, and future share count. Future earnings, however, will depend on interest expenses (which, in turn, depend on how much the firm borrows), and the firm s share count and dividend payout rate will depend on whether NKE uses a portion of its earnings to repurchase shares. Because borrowing and repurchase decisions are at management s discretion, they are more difficult to forecast reliably than other fundamental aspects of the firm s cash flows. 6 Non-Dividend-Paying Stocks Many companies do not pay dividends Apple, Amazon.com, and Google are just a few examples. How then do we value those stocks? In the next section, we discuss a small modification to the dividend-discount model to capture total payouts to shareholders, whether the payouts are dividends or not. In Chapter 10, we will discuss other valuation approaches that do not rely on payouts. Those approaches will be more meaningful once we have covered how financial managers create value within the firm through decisions about which projects to approve. So, in the next two chapters, we will cover investment decision rules and project evaluation. Concept Check 9. What are the main limitations of the dividend-discount model? 10. What pieces of information are needed to forecast dividends? 6 We discuss management s decision to borrow funds or repurchase shares in Part 6 of the text.

4 200 Part 2 Interest Rates and Valuing Cash Flows share repurchase A transaction in which a firm uses cash to buy back its own stock. total payout model A method that values shares of a firm by discounting the firm s total payouts to equity holders (that is, all the cash distributed as dividends and stock repurchases) and then dividing by the current number of shares outstanding. 7.6 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. In recent years, an increasing number of firms have replaced dividend payouts with share repurchases. In a share repurchase, 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 cash it has available to pay dividends. 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: P 0 = PV1Future Dividends per Share2 (7.14) 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 use this model, we discount the total payouts that the firm makes to shareholders, which is the total amount spent on both dividends and share repurchases (net of new share issuance). 7 This gives the total value of the firm s equity. We then divide by the current number of shares outstanding to determine the share price: Total Payout Model PV1Future Total Dividends and Net Repurchases2 P 0 = (7.15) Shares Outstanding 0 We can apply the same simplifications to the total payout method that we obtained by assuming constant growth in Section 7.3. The only change is that we discount total dividends and share repurchases and use the growth rate of earnings (rather than earnings per share) when forecasting the growth of the firm s total payouts. When the firm uses share repurchases, this method can be more reliable and easier to apply than the dividend-discount model. EXAMPLE 7.6 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 Plan Based on the equity cost of capital of 10% and an expected earnings growth rate of 7.5%, we can compute the present value of Titan s future payouts as a constant growth perpetuity. The only input missing here is Titan s total payouts this year, which we can calculate as 50% of its earnings. The present value of all of Titan s future payouts is the value of its total equity. To obtain the price of a share, we divide the total value by the number of shares outstanding (217 million). Execute Titan will have total payouts this year of 50% * +860 million = +430 million. Using the constant growth perpetuity formula, we have 7 You can think of the total payouts as the amount you would receive if you owned 100% of the firm s shares: You would receive all the dividends, plus the proceeds from selling shares back to the firm in the share repurchase.

5 Chapter 7 Stock Valuation million PV1Future Total Dividends and Repurchases2 = = billion 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: P 0 = billion = per share 217 million shares Evaluate 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% * million/217 million shares2 = per share, for a dividend yield of 1.19/79.26 = 1.50%. From Eq. 7.7, we can solve for Titan s expected growth rates of EPS, dividend, and share price: g = r E - Div 1 = = = = 8.5%. P This growth rate exceeds the 7.50% growth rate of earnings because Titan s share count will decline over time owing to its share repurchases. 8 Concept Check 11. How does the total payout model address part of the dividend-discount model s limitations? 12. How does the growth rate used in the total payout model differ from the growth rate used in the dividenddiscount model? 7.7 Putting It All Together We now return to the questions posed at the beginning of the chapter. First, how would an investor decide whether to buy or sell Nike stock? She would value the stock using her own expectations. We showed one set of expectations about dividend growth that would be consistent with the price. If her expectations were substantially different, she might conclude that the stock was over- or under-priced at $ Based on that conclusion, she would sell or buy the stock, and time would reveal whether her expectations were better than the market s. Second, how could Nike stock suddenly be worth 5% more after Nike s announcement? As investors digested the news in Nike s announcement and updated their expectations, they would have determined that the previous day s closing price was too low based on the new information about future earnings growth. Buying pressure would then drive the stock price up until the buys and sells came into balance. Third, what should Nike s managers do to raise the stock price further? The only way to raise the stock price is to make value-increasing decisions. We turn to this task in the next section of the book. As shown in the next two chapters, through capital budgeting analysis, managers can identify projects that add value to the company. By increasing the value of the company through good investment decisions, Nike s managers can increase the stock price. Chapter 10 returns to the question of stock valuation and extends the techniques developed here to incorporate the lessons of the next two chapters on project selection. 8 We can check that an 8.5% EPS growth rate is consistent with 7.5% earnings growth and Titan s repurchase plans as follows: Given an expected share price of * = next year, Titan will repurchase 20% * +860 million per share2 = 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 * 1217/2152 = or by 8.5%.

6 202 Part 2 Interest Rates and Valuing Cash Flows Here is what you should know after reading this chapter. will help you identify what you know, and where to go when you need to practice. Key Points and Equations 7.1 Stock Basics Ownership in a corporation is divided into shares of stock. These shares carry rights to share in the profits of the firm through future dividend payments. The shares also come with rights to vote to elect directors and decide on other important matters. Some firms issue preferred stock, which has preference over common stock in the payment of dividends and in liquidation, but typically carries no voting rights. 7.2 The Mechanics of Stock Trades The NYSE has a physical trading location, but many small trades execute electronically. NASDAQ is a computer network without a specific trading location. Many trades execute automatically, while larger trades must be negotiated with one or more of the stock s dealers. 7.3 The Dividend-Discount Model The Valuation Principle states that the value of a stock is equal to the present value of the dividends and future sale price the investor will receive. Because these cash flows are risky, they must be discounted at the equity cost of capital, which is the expected return of other securities available in the market with equivalent risk to the firm s equity. The total return of a stock is equal to the dividend yield plus the capital gain rate. The expected total return of a stock should equal its equity cost of capital: r E = Div 1 + P 1 P 0-1 = Div 1 (7.2) When investors have the same beliefs, the dividenddiscount model states that, for any horizon N, the stock price satisfies the following equation: P 0 = Div r E + P 0 + ()* Dividend Yield P 1 - P 0 P (')'* 0 Capital Gain Rate Div 2 Div N P N 11 + r E g r E 2 N r E 2 N (7.4) If the stock eventually pays dividends and is never acquired, the dividend-discount model implies that the stock price equals the present value of all future dividends. Terms annual meeting, p. 186 classes, p. 186 common stock, p. 184 cumulative preferred stock, p. 186 cumulative voting, p. 185 non-cumulative preferred stock, p. 186 preferred stock, p. 186 proxy, p. 186 proxy contest, p. 186 straight voting, p. 185 ticker symbol, p. 184 floor broker, p. 187 capital gain, p. 189 capital gain rate, p. 189 dividend-discount model, p. 191 dividend yield, p. 189 equity cost of capital, p. 189 total return, p. 189 Online Practice Opportunities Study Plan 7.1 Study Plan 7.2 Study Plan 7.3 Using Excel: Building a Dividend-Discount Model

7 Here is what you should know after reading this chapter. will help Chapter 7 Stock Valuation 203 you identify what you know, and where to go when you need to practice. 7.4 Estimating Dividends in the Dividend-Discount Model The constant dividend growth model assumes that dividends grow at a constant expected rate, g. In that case, g is also the expected capital gain rate, and P 0 = Div 1 r E - g (7.6) Future dividends depend on earnings, shares outstanding, and the dividend payout rate: Div t = Earnings t * Dividend Payout Rate Shares Outstanding t t ('''')''''* (7.8) EPS t If all increases in future earnings result exclusively from new investments made with retained earnings, then earnings growth can be found as: Change in Earnings Earnings Growth Rate = Earnings (7.11) = Retention Rate * Return on New Investment (where Retention Rate = 1 - Payout Rate) If the dividend payout rate and the number of shares outstanding is constant, and if earnings change only as a result of new investment from retained earnings, then the growth rate of the firm s earnings, dividends, and share price is calculated as follows: g = Retention Rate * Return on New Investment (7.12) Cutting the firm s dividend to increase investment will raise the stock price if, and only if, the new investments generate a return greater than their cost of capital. If the firm has a long-term growth rate of g after the period N + 1, then we can apply the dividend-discount model and use the constant dividend growth formula to estimate the terminal stock value P N. 7.5 Limitations of the Dividend-Discount Model The dividend-discount model is sensitive to the dividend growth rate, which is difficult to estimate accurately. The dividend-discount model is not practical for valuing the majority of stocks not paying dividends. In Chapter 10, we discuss alternative approaches. 7.6 Share Repurchases and the Total Payout Model If the firm undertakes share repurchases, it is more reliable to use the total payout model to value the firm. In this model, the value of equity equals the present value of future total dividends and repurchases. To determine the stock price, we divide the equity value by the initial number of shares outstanding of the firm: PV1Future Total Dividends and Repurchases2 P 0 = (7.15) Shares Outstanding 0 The growth rate of the firm s total payout is governed by the growth rate of earnings, not earnings per share. constant dividend growth model, p. 192 dividend payout rate, p. 193 retention rate, p. 193 share repurchase, p. 200 total payout model, p. 200 Study Plan 7.4 Study Plan 7.5 Study Plan 7.6

Chapter 6. Stock Valuation

Chapter 6. Stock Valuation Chapter 6 Stock Valuation Comprehend that stock prices depend on future dividends and dividend growth Compute stock prices using the dividend growth model Understand how growth opportunities affect stock