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Chapter 9

Chapter 9. Valuing Shares. 9.1 Share Basics. Ordinary share: a share of ownership in the corporation, which gives its owner rights to vote on the election of directors, mergers or other major events.

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Chapter 9

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  1. Chapter 9 Valuing Shares

  2. 9.1 Share Basics • Ordinary share: a share of ownership in the corporation, which gives its owner rights to vote on the election of directors, mergers or other major events. • As an ownership claim, ordinary shares carry the right to share in the profits of the corporation through dividend payments. • Dividends: periodic payments, usually in the form of cash, that are made to shareholders as a partial return on their investment in the corporation. • Shareholders are paid dividends in proportion to the amount of shares they own. 2

  3. 9.2 The Dividend-Discount Model • A one-year investor • Two potential sources of cash flows from shares: • The firm might pay out cash to its shareholders in the form of a dividend. • The investor might generate cash by selling the shares at some future date. • Future dividend payments and share price are unknown. • Investors will be willing to pay a price up to that point that the investment has a zero NPV—at which the current share price equals the PV of the expected future dividend and sale price. 3

  4. 9.2 The Dividend-Discount Model • A one-year investor (cont’d) • As the expected cash flows are risky, we cannot discount them with the risk-free interest rate, but need to use the cost of capital for the firm’s equity. • Equity cost of capital rE: the expected return of other investments available in the market with equivalent risk to the firm’s share. • P0: the price of the share at the beginning of the period • P1: the price of the share at the end of the period • Div1: the expected dividend during the period 4

  5. 9.2 The Dividend-Discount Model • A one-year investor (cont’d) • Share Price = PV(future cash flows) • Share Price = PV(Dividends + Capital Gains) Po = (Dividends + P1 – Po ) (1+rE)

  6. 9.2 The Dividend-Discount Model • The expected total return of a share should equal its equity cost of capital—it should equal the expected return of other investments available in the market with equivalent risk. Total return: FORMULA! (Eq. 9.2) 6

  7. 9.2 The Dividend-Discount Model • Dividend yield: the expected annual dividend of the share divided by its current price. • Capital gain:the amount the investor will earn on the share - difference between the expected sale price and the original purchase price for an asset. • Total return: thesum of the dividend yield and the capital gain rate - the expected return the investor will earn for a one-year investment in the share. 7

  8. Example 9.1 Share Prices and Returns (pp.267-8) Problem: • Suppose you expect Coca Cola to pay an annual dividend of $0.56 per share in the coming year and to trade $45.50 per share at the end of the year. • If investments with equivalent risk to Coca Cola shares have an expected return of 6.80%, what is the most you would pay today for Coca Cola shares? • What dividend yield and capital gain rate would you expect at this price? 8

  9. Example 9.1 Share Prices and Returns (pp.267-8) Solution: Plan: • We can use Eq. 9.1to solve for the beginning price we would pay now (P0) given our expectations about dividends (Div1=0.56) and future price (P1=$45.50) and the return we need to expect to earn to be willing to invest (rE=6.8%). • We can then use Eq. 9.2to calculate the dividend yield and capital gain. FORMULA! (Eq. 9.1) 9

  10. Example 9.1 Share Prices and Returns (pp.267-8) Execute: 10

  11. Example 9.1 Share Prices and Returns (pp.267-8) Evaluate: • At a price of ,Coca Cola expected total return is which is equal to its equity cost of capital. • This amount is the most we would be willing to pay for the share. If we paid more, our expected return would be less than 6.8%and we would rather invest elsewhere. • If current share prices are less than this amount, it would be a positive NPV investment. • If current share price exceeds this amount, selling it would produce a positive NPV and the share price would quickly fall. 11

  12. 9.2 The Dividend-Discount Model • A multi-year investor • We now extend the intuition we developed for the 1-year investor’s return to a multi-year investor. • Eq. 9.1 depends upon the expected share price in one year, P1 • But suppose we planned to hold the shares for two years. Then, we would receive dividends in both year 1 and year 2 before selling the shares, as shown in the following timeline: 12

  13. 9.2 The Dividend-Discount Model • Setting the share price equal to the present value of the future cash flows: • As a two-year investor, we care about the dividend and share price in year 2. (Eq. 9.3) FORMULA! 13

  14. 9.2 The Dividend-Discount Model • Dividend-discount model • This equation applies to a N-year investor. • The share price is equal to the present value of all of the expected future dividends it will pay. Dividend–discount model: (Eq. 9.4) (Eq. 9.5) FORMULA! 14

  15. 9.3 Estimating Dividends in the Dividend-Discount Model • Constant dividend growth model • A constantly used approximation is to assume that dividends will grow at a constant rate, g, forever. • The value of the firm depends on the dividend level of next year, divided by the equity cost of capital adjusted by the growth rate. Constant dividend growth model: (Eq. 9.6) FORMULA! 15

  16. Example 9.2 Valuing a Firm with Constant Dividend Growth (p.270) Problem: • Greta’s Garbos is a waste collection company. • Suppose Greta’s Garbos plans to pay $2.30per share in dividends in the coming year. • If its equity cost of capital is 7% and dividends are expected to grow by 2% per year in the future, estimate the value of Greta’s Garbos’ shares. 16

  17. Example 9.2 Valuing a Firm with Constant Dividend Growth (p.270) Plan: • Because the dividends are expected to grow perpetually at a constant rate, we can use Eq. 9.6to value Greta’s Garbos. • The next dividend (Div1) is expected to be $2.30, the growth rate (g) is 2%and the equity cost of capital (rE) is7%. Execute: 17

  18. Example 9.2 Valuing a Firm with Constant Dividend Growth (p.270) Evaluate: • You would be willing to pay 20 times this year’s dividend of $2.30 to own Greta’s Garbos shares because you are buying a claim to this year’s dividend and to an infinite growing series of future dividends. 18

  19. 9.3 Estimating Dividends in the Dividend-Discount Model • Dividend versus investment and growth • Often firms face a trade-off—increasing growth may require investment, and money spent on investment cannot be used to pay dividends. • What determines the rate of growth of a firm’s dividend? • We can define a firm’s dividend payout rate as the fraction of earnings that the firm pays as dividends each year: 19

  20. 9.3 Estimating Dividends in the Dividend-Discount Model • Dividend payout rate • The firm’s dividend each year is equal to the firm’s earnings per share (EPS) multiplied by its dividend payout rate. • The firm can, increase its dividend in three ways: • It can increase its earnings (net income). • It can increase its dividend payout rate. • It can decrease its number of shares outstanding. FORMULA! (Eq. 9.8) 20

  21. 9.3 Estimating Dividends in the Dividend-Discount Model • Retention rate • New investment equals the firm’s earnings multiplied by its retention rate, or the fraction of current earnings that the firm retains: Retention Rate = 1 – Dividend Payout Rate FORMULA! 21

  22. 9.3 Estimating Dividends in the Dividend-Discount Model • A simple model of growth • A firm can do two things with its earnings—it can pay them out to investors, or it can retain and invest them. • If all increases in future earnings result exclusively from new investment made with retained earnings, then: (Eq. 9.9) 22

  23. 9.3 Estimating Dividends in the Dividend-Discount Model • The equation shows that a firm can increase its growth by retaining more of its earnings, but will have to reduce its dividends. FORMULA! 23

  24. Example 9.3 Cutting Dividends for Profitable Growth (pp.272-3) Problem: • Crane Sporting Goods expects to have earnings per share of $6in 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. 24

  25. Example 9.3 Cutting Dividends for Profitable Growth (pp.272-3) Problem (cont'd): • 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 investment in these stores is expected to be 12%. • If we assume that the risk of these new investments is the same as the risk of its existing investments, then the firm’s equity cost of capital is unchanged. • What effect would this new policy have on Crane’s share price? 25

  26. Example 9.3 Cutting Dividends for Profitable Growth (pp.272-3) Solution: Plan: • We need to calculate Crane’s equity cost of capital and determine its dividend and growth rate under the new policy. • Because we know that Crane currently has a growth rate of 0 (g = 0), a dividend of $6and a price of$60, we can use Eq. 9.6to estimate rE. • Next, the new dividend will simply be 75%of the old dividend of $6. • Finally, given a retention rate of 25%and a return on new investment of 12%, we can calculate the new growth rate (g) and calculate the price of Crane’s shares if it institutes the new policy. 26

  27. Example 9.3 Cutting Dividends for Profitable Growth (pp.272-3) Execute: 27

  28. Example 9.3 Cutting Dividends for Profitable Growth (pp.272-3) Execute (cont’d): 28

  29. Example 9.3 Cutting Dividends for Profitable Growth (pp.272-3) Evaluate: • Crane’s share price should rise from $60 to$64.29 if the company cuts its dividend in order to increase its investment and growth, implying that the investment has positive NPV. • By using its earnings to invest in projects that offer a rate of return (12%) greater than its equity cost of capital (10%), Crane has created value for its shareholders. 29

  30. 9.3 Estimating Dividends in the Dividend-Discount Model • Changing growth rates • Successful young firms have very high initial growth rates and often retain 100% of their earnings to exploit investment opportunities. • As they mature, growth slows, earnings exceed their investment needs and they begin to pay dividends. • We cannot use the constant dividend model to value such a firm for two reasons: • These firms often pay no dividends when they are young. • Their growth rate continues to change over time until they mature. 30

  31. 9.3 Estimating Dividends in the Dividend-Discount Model • Limitations of the DDM • Uncertainty is associated with forecasting a firm’s future dividends. • Let’s consider an example, where a firm pays annual dividends of $0.72. • With an equity cost of capital of 11% and expected dividend growth of 8%, the DDM implies a share price of: • With a 10% growth rate, however, this estimate would rise to $72per share; with a 5% growth rate it would fall to $12per share (Figure 9.2). 31

  32. Figure 9.2 Share Prices for Different Expected Growth Rates 32

  33. 9.4 Total Payout and Free Cash Flow Valuation Models • Discounted free cash flow model • The discounted free cash flow model determines the total value of the firm to all investors - equity holders and debt holders. • The enterprise value is equivalent to owning the unlevered business. It can be interpreted as the net cost of acquiring the firm’s equity, taking its cash and paying off all debt. Enterprise value(V0)= Market value of equity + Debt – Cash (Eq. 9.16) FORMULA! 33

  34. 9.4 Total Payout and Free Cash Flow Valuation Models • Discounted free cash flow model (cont’d) • Measures the cash generated by the firm before any payments to debt and equity holders are considered Enterprise Value (V0)= PV (Future free cash flow of firm) • Given the enterprise value, V0,we can estimate the share price by using Eq. 9.16 to solve for the value of equity and then divide by the total number of shares outstanding. Market Value of Equity = V0 – Debt0 + Cash0 (Eq. 9.18) FORMULA! (Eq. 9.19) 34

  35. 9.4 Total Payout and Free Cash Flow Valuation Models • Implementing the model • A key difference between the discounted free cash flow model and the dividend discount model is the discount rate. • Previously, we used the firm’s equity cost of capital, rE, because we were discounting the cash flow to equity holders. • Here, we are discounting the free cash flow that will be paid to both debt and equity holders, thus, we use the firm’s weighted average cost of capital (WACC)—it is the cost of capital that reflects the overall risk of the business, rWACC, and is the expected return that a firm needs to pay to investors. 35

  36. 9.4 Total Payout and Free Cash Flow Valuation Models • Free cash flow (FCF) measures the cash generated by the firm before any payments to debt or equity holders are considered • We can forecast the firm’s free cash flow up to some horizon and add a terminal (continuation) value of the enterprise • Often we estimate the terminal value(Vn) by assuming a constant long-run growth rate g FCF for free cash flows beyond year n (Eq. 9.17) (Eq. 9.20) (Eq. 9.21) FORMULA! 36

  37. Problem: JBH’s free cash flows over the next 5 years are estimated as follows After then, the free cash flows are expected to grow at the industry average of 4% per year. The weighted average cost of capital of JBH is 10%, while JBH has $30 million in cash and $90 million in debt and 107.25 million shares outstanding Estimate the value of JBH shares in 2009 using the free cash flow method. Example 9.8 Valuation Using free cash flow (pp.281) 37

  38. Plan: In order to calculate the enterprise value of JBH we need the terminal value for JBH at the end of the given projections. Given an expected constant growth rate (4%) for JBH after 2015, we can use eq 9.21 to calculate a terminal enterprise value. The present value of the free cash flows during years 2010-2015 and the terminal value will be the total enterprise value for JBH. Using that value, we can subtract the debt, add the cash and divide by the number of shares outstanding to calculate the price per share. Example 9.8 Valuation Using free cash flow (pp.281) 38

  39. Execute: Example 9.8 Valuation Using free cash flow (pp.281) 39

  40. Example 9.8 Valuation Using free cash flow (pp.281) Evaluate: • The valuation principal tells us that the present value of all future cash flows generated by JBH plus the value of the cash held by the firm today must equal the total value today of all the claims, both debt and equity, on those cash flows and cash. • Using that principal we calculate the total value of all of JBH’s claims and then subtract the debt portion to value the equity.

  41. 9.5 Valuation Based on Comparable Firms • Method of comparables:estimates the value of the firm based on the value of other comparable firms or investments that we expect will generate very similar cash flows in the future. • Valuation multiples:ratio of the value to some measure of the firm’s scale. • Trailing earnings:earnings over the prior 12 months. • Forward earnings:expected earnings over the coming 12 months. • Trailing P/E:the resulting ratio from trailing earnings. • Forward P/E:the resulting ratio from forward earnings. 41

  42. Example 9.9 Valuation Using the Price–Earnings Ratio (pp.284-5) Problem: • Suppose electronics retailer Great Spark has earnings per share of $1.38. • If the average P/E of comparable retail shares is 21.3, estimate a value for Great Spark’s shares using the P/E as a valuation multiple. • What are the assumptions underlying this estimate? 42

  43. Example 9.9 Valuation Using the Price–Earnings Ratio (pp.284-5) Solution: Plan: • We estimate a share price for Great Spark by multiplying its EPS by the P/E of comparable firms. Execute: P0 = $1.38 x 21.3 = $29.39 • This estimate assumes that Great Spark will have similar future risk, payout rates and growth rates to comparable firms in the industry. 43

  44. Example 9.9 Valuation Using the Price–Earnings Ratio (pp.284-5) Evaluate: • Although valuation multiples are simple to use, they rely on some very strong assumptions about the similarity of the comparable firms to the firm you are valuing. • It is important to consider these assumptions are likely to be reasonable—and thus to hold—in each case. 44

  45. 9.5 Valuation Based on Comparable Firms • Limitations of multiples • Firms are not identical, so usefulness of a valuation multiple will depend on the nature of the differences. • Furthermore, multiples only provide information about value of the firm relative to other firms in the comparison set. • Table 9.1lists several valuation multiples for selected firms in the retail industry as of October 2009. • Data shows that the retail industry has a lot of dispersion for all of the multiples, which most likely reflects differences in expected growth rates and risks (therefore, cost of capital). 45

  46. Table 9.1 Share Prices and Multiples for Selected Firms in the Retail Sector 46

  47. 9.5 Valuation Based on Comparable Firms • Share valuation techniques—the final word • No single technique provides a final answer regarding a share’s true value. • Practitioners use a combination of these approaches. • Confidence comes from consistent results from a variety of these methods. 47

  48. 9.6 Information, Competition and Share Prices • Information in share prices • Investors trade until they reach a consensus regarding the value of the shares, which aggregate the information and views of many different investors. • A valuation model is best applied to tell us something about the firm’s future cash flows or cost of capital, based on its current share price. • Only if we have some superior information that other investors lack regarding the firm’s cash flows and cost of capital would it make sense to second-guess the stock price. 48

  49. Figure 9.5 The Valuation Triad 49

  50. Example 9.10 Using the Information in Share Prices (p.289) Problem: • Suppose Tecnor Industries will pay a dividend this year of $5 per share. • Its equity cost of capital is 10%, and you expect its dividend to grow at a rate of approximately 4% per year, though you are somewhat unsure of the precise growth rate. • If shares are currently trading at $76.92, how would you update your beliefs about its dividend growth rate? 50

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