1. 7 - 1 CHAPTER 7 Stocks and Their Valuation Features of common stock Determining common stock values Efficient markets Preferred stock

2. 7 - 2 Expected Dividends as the Basis for Stock Values Stock Value = PV of Dividends In our discussion of bonds, we found the value of a bond as the present value of interest payments over the life of the bond plus the present value of the bond’s maturity (or par) value:

3. 7 - 3 where you expect to hold the stock for a finite period and then sell it. What will be the value of P 0 in this case? To see this, recognize that for any individual investor, the expected cash flows consist of expected dividends plus the expected sale price of the stock. the sale price the current investor receives will depend on the dividends some future investor expects. Expected cash flows must be based on expected future dividends What about the more typical case? ˆ

4. 7 - 4 The stock whose dividends are expected to grow forever at a constant rate, g. What is a constant growth stock? If g is constant, then: For a constant growth stock,

5. 7 - 5 $ 0.25 Years (t) 0 Dollar Amount of Each Dividend PV of Each Dividend

6. 7 - 6 What happens if g > r s ? If r s < g, get negative stock price, which is nonsense. We can’t use model unless : 1.g  r s and 2.g is expected to be constant forever. Because g must be a long-term growth rate, it cannot be  r s.

7. 7 - 7 Assume beta = 1.2, r RF = 7%, and RP M = 5%. What is the required rate of return on the firm’s stock? r s = r RF + (RP M )b Firm = 7% + (5%) (1.2) = 13%. Use the SML to calculate r s :

8. 7 - 8 D 0 was $2.00 and g is a constant 6%. Find the expected dividends for the next 3 years, and their PVs. r s = 13%. 01 2.2472 2 2.3820 3 g=6% 4 1.8761 1.7599 1.6508 D 0 =2.00 13% 2.12

9. 7 - 9 What’s the stock’s market value? D 0 = 2.00, r s = 13%, g = 6%.

10. 7 - 10 What’s the stock’s market value? D 0 = 2.00, r s = 13%, g = 6%. Constant growth model: = = $30.29. 0.13 - 0.06 $2.12 0.07

11. 7 - 11 What is the stock’s market value one year from now, P 1 ? ^

12. 7 - 12 What is the stock’s market value one year from now, P 1 ? D 1 will have been paid, so expected dividends are D 2, D 3, D 4 and so on. Thus, ^

13. 7 - 13 Find the expected dividend yield and capital gains yield during the first year.

14. 7 - 14 Find the expected dividend yield and capital gains yield during the first year. Dividend yield = = = 7.0%. $2.12 $30.29 D1D1 P0P0 CG Yield = = P 1 - P 0 ^ P0P0 $32.10 - $30.29 $30.29 = 6.0%.

15. 7 - 15 Find the total return during the first year. Total return = Dividend yield + Capital gains yield. Total return = 7% + 6% = 13%. Total return = 13% = r s. For constant growth stock: Capital gains yield = 6% = g.

16. 7 - 16 Rearrange model to rate of return form: Then, r s = $2.12/$30.29 + 0.06 = 0.07 + 0.06 = 13%. ^ = r RF + (RP M )b Firm

17. 7 - 17 What would P 0 be if g = 0? The dividend stream would be a perpetuity. 2.00 0123 r s =13% P 0 = = = $15.38. PMT r $2.00 0.13 ^

18. 7 - 18 Can no longer use constant growth model. However, growth becomes constant after 3 years. Valuing Stocks That Have a Nonconstant Growth Rate If we have supernormal growth of 30% for 3 years, then a long-run constant g = 6%, what is P0? r is still 13%. ^

19. 7 - 19 Nonconstant growth followed by constant growth: 0 2.3009 2.6470 3.0453 46.1135 1234 r s =13% 54.1067 = P 0 g = 30% g = 6% D 0 = 2.00 2.603.38 4.394 4.6576 ^

20. 7 - 20 What is the expected dividend yield and capital gains yield at t = 0? At t = 4? Dividend yield = = = 4.8%. $2.60 $54.11 D1D1 P0P0 CG Yield = 13.0% - 4.8% = 8.2%. At t = 0: (More…) During nonconstant growth, dividend yield and capital gains yield are not constant. If current growth is greater than g, current capital gains yield is greater than g.

21. 7 - 21 What is the expected dividend yield and capital gains yield at t = 0? At t = 4? At t = 4: (More…) After t = 3, g = constant = 6% so At the t = 4 capital gains yield = 6%. Because r s = 13%, At the t = 4 dividend yield = 13% - 6% = 7%.

22. 7 - 22 During nonconstant growth, dividend yield and capital gains yield are not constant. If current growth is greater than g, current capital gains yield is greater than g. After t = 3, g = constant = 6%, so the t t = 4 capital gains gains yield = 6%. Because r s = 13%, the t = 4 dividend yield = 13% - 6% = 7%.

23. 7 - 23 The current stock price is $54.11. The PV of dividends beyond year 3 is $46.11 (P 3 discounted back to t = 0). The percentage of stock price due to “long-term” dividends is: Is the stock price based on short-term growth? ^ = 85.2%. $46.11 $54.11

24. 7 - 24 If most of a stock’s value is due to long- term cash flows, why do so many managers focus on quarterly earnings? Sometimes changes in quarterly earnings are a signal of future changes in cash flows. This would affect the current stock price. Sometimes managers have bonuses tied to quarterly earnings.

25. 7 - 25 Suppose g = 0 for t = 1 to 3, and then g is a constant 6%. What is P 0 ? 0 1.7699 1.5663 1.3861 20.9895 1234 r s =13% 25.7118 g = 0% g = 6% 2.00 2.00 2.00 2.12 2.12.  P 3 007 30.2857  ^...

26. 7 - 26 What is dividend yield and capital gains yield at t = 0 and at t = 3? t = 0: D1D1 P0P0 CGY = 13.0% - 7.8% = 5.2%.  2.00 $25.72 7.8%. t = 3: Now have constant growth with g = capital gains yield = 6% and dividend yield = 7%.

27. 7 - 27 If g = -6%, would anyone buy the stock? If so, at what price? Firm still has earnings and still pays dividends, so P 0 > 0: ^ = = = $9.89. $2.00(0.94) 0.13 - (-0.06) $1.88 0.19

28. 7 - 28 What are the annual dividend and capital gains yield? Capital gains yield = g = -6.0%. Dividend yield= 13.0% - (-6.0%) = 19.0%. Both yields are constant over time, with the high dividend yield (19%) offsetting the negative capital gains yield.

29. 7 - 29 Analysts often use the P/E multiple (the price per share divided by the earnings per share) or the P/CF multiple (price per share divided by cash flow per share, which is the earnings per share plus the dividends per share) to value stocks. Example: Estimate the average P/E ratio of comparable firms. This is the P/E multiple. Multiply this average P/E ratio by the expected earnings of the company to estimate its stock price. Using the Stock Price Multiples to Estimate Stock Price

30. 7 - 30 Price/Earnings Ratio The price/earnings (P/E) ratio shows how much investors are willing to pay per dollar of reported profits. P/E ratios are higher for firms with strong growth prospects, other things held constant, but they are lower for riskier firms

31. 7 - 31 Price/Cash Flow Ratio In some industries, stock price is tied more closely to cash flow rather than net income. Consequently, investors often look at the price/cash flow ratio:

32. 7 - 32 Calculate and appraise the P/E, P/CF, and M/B ratios. Price = $12.17. EPS = = = $1.01. P/E = = = 12x. NI Shares out. $253.6 250 Price per share EPS $12.17 $1.01

33. 7 - 33 P/E: How much investors will pay for $1 of earnings. High is good. M/B: How much paid for $1 of book value. Higher is good. P/E and M/B are high if ROE is high, risk is low. 2005E 2004 2003 Ind. P/E12.0x-6.3x9.7x14.2x P/CF8.2x27.5x8.0x7.6x M/B1.5x1.1x1.3x2.9x

34. 7 - 34 The entity value (V) is: the market value of equity (# shares of stock multiplied by the price per share) plus the value of debt. Pick a measure, such as EBITDA, Sales, Customers, Eyeballs, etc. Calculate the average entity ratio for a sample of comparable firms. For example, V/EBITDA V/Customers Using Entity Multiples

35. 7 - 35 Find the entity value of the firm in question. For example, Multiply the firm’s sales by the V/Sales multiple. Multiply the firm’s # of customers by the V/Customers ratio The result is the total value of the firm. Subtract the firm’s debt to get the total value of equity. Divide by the number of shares to get the price per share. Using Entity Multiples (Continued)

36. 7 - 36 It is often hard to find comparable firms. The average ratio for the sample of comparable firms often has a wide range. For example, the average P/E ratio might be 20, but the range could be from 10 to 50. How do you know whether your firm should be compared to the low, average, or high performers? Problems with Market Multiple Methods

37. 7 - 37 Why are stock prices volatile? r s = r RF + (RP M )b i could change. Inflation expectations Risk aversion Company risk g could change. ^

38. 7 - 38 Stock value vs. changes in r s and g D 1 = $2, r s = 10%, and g = 5%: P 0 = D 1 / (r s -g) = $2 / (0.10 - 0.05) = $40. What if r s or g change? ggg r s 4%5%6% 9%40.0050.0066.67 10%33.3340.0050.00 11%28.5733.3340.00

39. 7 - 39 Are volatile stock prices consistent with rational pricing? Small changes in expected g and r s cause large changes in stock prices. As new information arrives, investors continually update their estimates of g and r s. If stock prices aren’t volatile, then this means there isn’t a good flow of information.

40. 7 - 40 What is market equilibrium? ^ In equilibrium, stock prices are stable. There is no general tendency for people to buy versus to sell. The expected price, P, must equal the actual price, P. In other words, the fundamental value must be the same as the price. (More…)

41. 7 - 41 In equilibrium, expected returns must equal required returns: r s = D 1 /P 0 + g = r s = r RF + (r M - r RF )b. ^

42. 7 - 42 How is equilibrium established? If r s = + g > r s, then P 0 is “too low.” If the price is lower than the fundamental value, then the stock is a “bargain.” Buy orders will exceed sell orders, the price will be bid up, and D 1 /P 0 falls until D 1 /P 0 + g = r s = r s. ^ ^ D1P0D1P0 ^

43. 7 - 43 Why do stock prices change? r i = r RF + (r M - r RF )b i could change. Inflation expectations Risk aversion Company risk g could change. ^

44. 7 - 44 What’s the Efficient Market Hypothesis (EMH)? Securities are normally in equilibrium and are “fairly priced.” One cannot “beat the market” except through good luck or inside information. (More…)

45. 7 - 45 1.Weak-form EMH: Can’t profit by looking at past trends. A recent decline is no reason to think stocks will go up (or down) in the future. Evidence supports weak-form EMH, but “technical analysis” is still used.

46. 7 - 46 2.Semistrong-form EMH: All publicly available information is reflected in stock prices, so it doesn’t pay to pore over annual reports looking for undervalued stocks. Largely true.

47. 7 - 47 3.Strong-form EMH: All information, even inside information, is embedded in stock prices. Not true--insiders can gain by trading on the basis of insider information, but that’s illegal.

48. 7 - 48 Markets are generally efficient because: 1.100,000 or so trained analysts--MBAs, CFAs, and PhDs--work for firms like Fidelity, Merrill, Morgan, and Prudential. 2.These analysts have similar access to data and megabucks to invest. 3.Thus, news is reflected in P 0 almost instantaneously.

49. 7 - 49 Preferred Stock Hybrid security. Similar to bonds in that preferred stockholders receive a fixed dividend which must be paid before dividends can be paid on common stock. However, unlike bonds, preferred stock dividends can be omitted without fear of pushing the firm into bankruptcy.

50. 7 - 50 What’s the expected return on preferred stock with V ps = $50 and annual dividend = $5?