1. 8 - 1 Lecture Ten Cost of Capital From Issuing Stocks or Stocks and Their Valuation Determining common stock values Efficient markets Preferred stock

2. 8 - 2 One whose dividends are expected to grow forever at a constant rate, g. Stock Value = PV of Dividends What is a constant growth stock?

3. 8 - 3 For a constant growth stock, If g is constant, then:

4. 8 - 4 $ 0.25 Years (t) 0

5. 8 - 5 What happens if g > k s ? If k s < g, get negative stock price, which is nonsense. We can’t use model unless (1) k s > g and (2) g is expected to be constant forever. See slide #8-8.

6. 8 - 6 Assume beta = 1.2, k RF = 6%, and k M = 11%. What is the required rate of return on the firm’s stock? k s = k RF + (k M - k RF )b Firm = 6% + (11% - 6%) (1.2) = 12%. Also, this is the cost of capital to the firm from issuing common Stk. Use the SML to calculate k s :

7. 8 - 7 D 0 was $0.25 and g is a constant 6%. Find the expected dividends for the next 3 years, and their PVs. k s = 12%. 01 0.2809 2 0.2978 3 g=6% 4 0.2366 0.2239 0.2120 D 0 =0.25 12% 0.265

8. 8 - 8 What’s the stock’s market value? D 0 = 0.25, k s = 12%, g = 6%. Constant growth model:

9. 8 - 9 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, Could also find P 1 as follows: ^ ^ ^

10. 8 - 10 Find the expected dividend yield, capital gains yield, and total return during the first year.

11. 8 - 11 Rearrange model to rate of return form: Then, k s = $0.265/$4.42 + 0.06 = 0.06 + 0.06 = 12%. Again, this is the cost of raising funds from the sale of common stock. ^

12. 8 - 12 What would P 0 be if g = 0? The dividend stream would be a perpetuity. 0.25 0123 12%... ^

13. 8 - 13 If we have supernormal growth of 30% for 3 yrs, then a long-run constant g = 10%, what is P 0 ? k is still 12%. Can no longer use constant growth model. However, growth becomes constant after 3 years. ^

14. 8 - 14 Nonconstant growth followed by constant growth: 0 0.2902 0.3368 0.3910 21.5029 1234 k s =12% 22.52 = P 0 g = 30% g = 10% D 0 = 0.250.32500.4225 0.5493 0.6042 ... $30.P 3 06042 12010 21    0... ^

15. 8 - 15 What is the expected dividend yield and capital gains yield at t = 0? At t = 4?

16. 8 - 16 During nonconstant growth, D/P and capital gains yield are not constant, and capital gains yield is less than g. After t = 3, g = constant = 10% = capital gains yield; k = 12%; so D/P = 12% - 10% = 2%.

17. 8 - 17 Suppose g = 0 for t = 1 to 3, and then g is a constant 11%. What is P 0 ? 0 0.2232 0.1993 0.1779 19.7519 1234 k s =12% 20.3523 g = 0% g = 11% 0.25 0.25 0.25 0.2775..  P 3 02775 001 27.75.  ^...

18. 8 - 18 What is D/P and capital gains yield at t = 0 and at t = 3? t = 0: D1D1 P0P0 CGY   25 35 123%. 12%123%1077%. $0. $20.... t = 3: Now have constant growth with g = capital gains yield = 11% and D/P = 1%.

19. 8 - 19 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:

20. 8 - 20 What is the annual D/P and capital gains yield? Capital gains yield = g = -6.0%, Dividend yield= 12.0% - (-6.0%) = 18%. D/P and cap. gains yield are constant, with high dividend yield (18%) offsetting negative capital gains yield.

21. 8 - 21 What is market equilibrium? In equilibrium, stock prices are stable. There is no general tendency for people to buy versus to sell. In equilibrium, expected returns must equal required returns: k s = D 1 /P 0 + g = k s = k RF + (k M - k RF )b. ^

22. 8 - 22 How is equilibrium established? If k s = + g > k s, then P 0 is “too low” (a bargain). Buy orders > sell orders; P 0 bid up; D 1 /P 0 falls until D 1 /P 0 + g = k s = k s. ^ ^ D1P0D1P0

23. 8 - 23 Why do stock prices change? 1. k i could change: k i = k RF + (k M - k RF )b i k RF = k* + IP 2. g could change due to economic or firm situation. ^

24. 8 - 24 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 better information.

25. 8 - 25 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.

26. 8 - 26 2.Semistrong-form EMH: All publicly available information is reflected in stock prices, so doesn’t pay to pore over annual reports looking for undervalued stocks. Largely true, but superior analysts can still profit by finding and using new information.

27. 8 - 27 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.

28. 8 - 28 Markets are generally efficient because: 1.15,000 or so trained analysts; MBAs, CFAs, Technical PhDs. 2.Work for firms like Merrill, Morgan, Prudential, which have much money. 3.Have similar access to data. 4.Thus, news is reflected in P 0 almost instantaneously.

29. 8 - 29 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 interest payments on bonds, companies can omit dividend payments on preferred stock without fear of pushing the firm into bankruptcy.

30. 8 - 30 What’s the expected return of preferred stock with V ps = $50 and annual dividend = $5?