1. 9 - 1 Copyright © 2002 by Harcourt, Inc.All rights reserved. Stocks and Their Valuation (Ref: Brigham, E.F., and J.F. Houston. 2001. Fundamentals of Financial Management, 9th Ed, Harcourt College Publishers, Ch. 9) Features of common stock Determining common stock values Efficient markets Preferred stock

2. 9 - 2 Copyright © 2002 by Harcourt, Inc.All rights reserved. Represents ownership. Ownership implies control. Stockholders elect directors. Directors elect management. Management’s goal: Maximize the stock price. Facts about Common Stock

3. 9 - 3 Copyright © 2002 by Harcourt, Inc.All rights reserved. Social/Ethical Question Should management be equally concerned about employees, customers, suppliers, and “the public,” or just the stockholders? In an enterprise economy, management should work for stockholders subject to constraints (environmental, fair hiring, etc.) and competition.

4. 9 - 4 Copyright © 2002 by Harcourt, Inc.All rights reserved. A firm “goes public” through an IPO when the stock is first offered to the public. When is a stock sale an initial public offering (IPO)?

5. 9 - 5 Copyright © 2002 by Harcourt, Inc.All rights reserved. IssuerProceeds from sale AT&T Wireless$9.03 billion Infineon Technologies$2.72 billion Metropolitan Life Ins. Co.$2.50 billion TyCom$2.88 billion Genuity$1.91 billion Biggest IPOs of 2000 in the USA

6. 9 - 6 Copyright © 2002 by Harcourt, Inc.All rights reserved. Average Initial Returns on IPOs in Various Countries Malaysia 100% 75% 50% 25% Brazil Portugal Japan Sweden United States Canada

7. 9 - 7 Copyright © 2002 by Harcourt, Inc.All rights reserved. 1. Dividend growth model: - Constant Growth (Gordon) Model - Supernormal (Non-constant) Growth Stock - Erratic Growth Stock 2. Free cash flow method 3. Using the multiples of comparable firms Different Approaches for Valuing Common Stock

8. 9 - 8 Copyright © 2002 by Harcourt, Inc.All rights reserved. When to use the models? Constant growth model: most appropriate for mature companies w stable history of growth, and stable future dividends. Free cash flow method: good for the large number of companies that don’t pay a dividend, or for whom it is hard to forecast dividends.

9. 9 - 9 Copyright © 2002 by Harcourt, Inc.All rights reserved. Definitions of Terms D t = Dividend the stockholder expects to receive at the end of Year t. D 0 is the most recent dividend, which has already been paid; D 1 is the first dividend expected, and will be paid at the end of this year; D 2 is the dividend expected at the end of two years, and so forth. D 1 represents the first cash flow a new purchaser of the stock will receive. Note that D 0, the dividend that has been paid, is known with certainty. But all future dividends are expected values, so the estimate of D t may differ among investors. P 0 = Actual market price of the stock today

10. 9 - 10 Copyright © 2002 by Harcourt, Inc.All rights reserved. P 0 = Expected price of the stock at the end of Year t (pronounced “P hat t”). P 0 is the intrinsic, or theoretical, value of the stock today as seen by the particular investor doing the analysis; P 1 is the price expected at the end of one year; and so on. Note that P 0 is the intrinsic value of the stock today based on a particular investor’s estimate of the stock’s expected dividend stream and the riskiness of that stream. Hence, whereas the market price P 0 is fixed and is identical for all investors, P 0 could differ among investors depending on how optimistic they are about the company. The caret, or “hat” is used to indicate that P t is an estimated value. cont…

11. 9 - 11 Copyright © 2002 by Harcourt, Inc.All rights reserved. cont… P 0, the individual investor’s estimate of the intrinsic value today, could be above or below P 0, the current stock price, but an investor would buy the stock only if his/her estimate of P 0 were equal or greater than P 0. Since they are many investors in the market, there can be many values for P 0. However, we can think of an “average” or “marginal” investors whose actions actually determine the market price. For these marginal investors, P 0 must = P 0 ; otherwise a disequilibrium would exist, and buying and selling in the market would change P 0, until P 0 = P 0 for the marginal investor.

12. 9 - 12 Copyright © 2002 by Harcourt, Inc.All rights reserved. Market Price, P 0 = the price at which the stock sell in the market Intrinsic Value, P 0 = the value of an asset that, in the mind of a particular investor, is justified by the facts; P 0 may be different from the asset’s current market price. Growth Rate, g = The expected rate of growth in dividends per share.

13. 9 - 13 Copyright © 2002 by Harcourt, Inc.All rights reserved. g = expected growth rate in dividends as predicted by a marginal investor. If dividends are expected to grow at a constant rate, g is also equal to the expected rate of growth in earnings and in the stock’s price. Different investors may use different g’s to evaluate a firm’s stock, but the market price, P 0, is set on the basis of the g estimated by marginal investors.

14. 9 - 14 Copyright © 2002 by Harcourt, Inc.All rights reserved. Required Rate of Return, k s = The minimum rate of return on a common stock that a stockholder considers acceptable. k s = minimum acceptable, or required, rate of return on the stock, considering both its riskiness and the returns available on other investments. Again, this term generally relates to marginal investors. The determinants of k s include the real rate of return, expected inflation, and risk.

15. 9 - 15 Copyright © 2002 by Harcourt, Inc.All rights reserved. Expected Rate of Return, k s = The rate of return on a common stock that a stockholder expects to receive in the future. k s = Expected rate of return that an investor who buys the stock expects to receive in the future. Ks (pronounced “k hat s”) could be above or below k s, but one would buy the stock only if k s were equal or greater than k s.

16. 9 - 16 Copyright © 2002 by Harcourt, Inc.All rights reserved. Actual, Realized Rate of Return, k s = The rate of return on a common stock actually received by stockholders in some past period. Ks may be greater, or less than, and/or k s. k s = actual, or realized, after-the fact rate of return (pronounce “k bar s”). You may expect to obtain a return of k s = 15% if you buy Exxon today, but if the market goes down, you may end up next year with an actual realized return that is much lower, perhaps even negative.

17. 9 - 17 Copyright © 2002 by Harcourt, Inc.All rights reserved. Dividend Yield = The expected dividend divided by the current price of a share of stock. D 1 /P 0 = Expected dividend yield on the stock during the coming year. If the stock is expected to pay a dividend of D 1 = $1 during the next 12 months, and its current price is P 0 = $10, then the expected dividend yield is $1/$10 = 0.10 = 10%

18. 9 - 18 Copyright © 2002 by Harcourt, Inc.All rights reserved. Capital Gains Yield = The capital gain during a given year divided by the beginning price. (P 1 -P 0 )/P 0 = Expected capital gains yield on the stock during the coming year. If the stock sells for $10 today, and if it is expected to rise to $10.50 at the end of one year, the expected capital gain is P 1 - P 0 = $0.50. Expected capital gain yield = $0.50/$10 = 5%

19. 9 - 19 Copyright © 2002 by Harcourt, Inc.All rights reserved. Expected Total Return = The sum of the dividend yield and the expected capital gains yield. Expected total return = k s = Expected dividend yield (D 1 /P 0 ) + expected capital gains yield (P 1 -P 0 )/P 0. In our example, the expected total return is 10% + 5% = 15%

20. 9 - 20 Copyright © 2002 by Harcourt, Inc.All rights reserved. A stock whose dividends are expected to grow forever at a constant rate, g. Stock Value = PV of Dividends What is a constant growth stock?.

21. 9 - 21 Copyright © 2002 by Harcourt, Inc.All rights reserved. For a Constant Growth Stock D 1 = D 0 (1 + g) 1 D 2 = D 0 (1 + g) 2 = D 1 (1+g) 1 D t = D 0 (1 + g) t P 0 = = If g is constant, then: D 0 (1 + g) k s – g D 1 k s – g ^

22. 9 - 22 Copyright © 2002 by Harcourt, Inc.All rights reserved. $ 0.25 Years (t) 0

23. 9 - 23 Copyright © 2002 by Harcourt, Inc.All rights reserved. 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. = requires k s > g D 1 k s – g

24. 9 - 24 Copyright © 2002 by Harcourt, Inc.All rights reserved. Assume beta = 1.2, k RF = 7%, and k M = 12%. What is the required rate of return (k s ) on the firm’s stock? k s = k RF + (k M – k RF ) β Firm = 7% + (12% – 7%) (1.2) = 13% Use the SML to calculate k s :

25. 9 - 25 Copyright © 2002 by Harcourt, Inc.All rights reserved. D 0 was $2.00 and g is a constant 6%. Find the expected dividends for the next 3 years, and their PVs (k s = 13%) 01 2.247 2 2.382 3 g = 6% $1.8761 $1.7599 D 0 = 2.00 $1.6509 13% 2.12

26. 9 - 26 Copyright © 2002 by Harcourt, Inc.All rights reserved. = What’s the stock’s market value? D 0 = 2.00, k s = 13%, g = 6% Constant growth model: P 0 = = D1D1 k s – g 0.13 – 0.06 $2.12 0.07 $30.29

27. 9 - 27 Copyright © 2002 by Harcourt, Inc.All rights reserved. D 1 will have been paid, so expected dividends are D 2, D 3, D 4 and so on. With P 0 = $30.29, D 2 =D 1 (1+g)=$2.12(1.06)=$2.247; Could also find P 1 as follows: k s – g 0.13 – 0.06 P 1 = = What is the stock’s market value one year from now, P 1 ? ^ ^ D2D2 $2.247 ^ = $32.10 P 1 = P 0 (1.06)=30.29(1.06)=$32.10

28. 9 - 28 Copyright © 2002 by Harcourt, Inc.All rights reserved. Find the expected dividend yield, capital gains yield, and total return during the first year. Dividend yld = = = Cap gains yld = = Total return = 7.0% + 6.0% = 13.0% D1D1 P0P0 P 1 – P 0 P0P0 ^ $30.29 $2.12 7.0% $32.10 – $30.29 $30.29 = 6.0%

29. 9 - 29 Copyright © 2002 by Harcourt, Inc.All rights reserved. Rearrange model to rate of return form:  P D kg D P g s 0 11 0    tok s Then, k s = $2.12/$30.29 + 0.06 = 0.07 + 0.06 = 13% ^ –

30. 9 - 30 Copyright © 2002 by Harcourt, Inc.All rights reserved. P 0 = = = $15.38 What would P 0 be if g = 0? The dividend stream would be a perpetuity. 2.00 0123 13%... ^ PMT k $2.00 0.13 ^

31. 9 - 31 Copyright © 2002 by Harcourt, Inc.All rights reserved. Can no longer use constant growth model. However, growth becomes constant after 3 years. If we have supernormal growth of 30% for 3 years, then a long-run constant g = 6%, what is P 0 ? k s is still 13%. ^

32. 9 - 32 Copyright © 2002 by Harcourt, Inc.All rights reserved. Valuing a Supernormal/Non-constant Growth Stock Supernormal/non-constant growth is that part of the firm’s life cycle in which it grows faster than the economy as a whole. Steps to Value Supernormal Growth Stock: 1.Compute the expected future cash dividends cont….

33. 9 - 33 Copyright © 2002 by Harcourt, Inc.All rights reserved. 2. Compute the stock’s price at a future point in time, using constant growth model P t = D t+1 /(r-g). (You must pick a point after the dividend growth rate has become constant) 3. Compute the PV of the expected future sale price and add that to the PV of all the expected cash dividends between now and then. ( Source: Emery, D.R., J.D. Finnerty and J.D. Stowe.1998. Principles of Financial Management. Prentice Hall, pp 172-173)

34. 9 - 34 Copyright © 2002 by Harcourt, Inc.All rights reserved. Nonconstant growth followed by constant growth: 0 2.301 2.647 3.045 46.114 1234 k s = 13% 54.107 = P 0 g = 30% g = 6%... D 0 = 2.00 2.600 3.380 4.394 4.658 ... $66.54P 3 4.658 13006    0... ^

35. 9 - 35 Copyright © 2002 by Harcourt, Inc.All rights reserved. What is the expected dividend yield and capital gains yield at t = 0? At t = 4? (Div yield 0 =Div 1 /Price) Div. yield 0 = = 4.81%. Cap. gain 0 = (k s - div yield) =13.00% – 4.81% = 8.19%. $2.60 $54.11

36. 9 - 36 Copyright © 2002 by Harcourt, Inc.All rights reserved. During nonconstant growth, dividend yield (D/P) and capital gains yield are not constant, and capital gains yield is not equal to g. After t = 3, g = constant = 6% = capital gains yield; k s = 13%; so D/P = 13% – 6% = 7%.

37. 9 - 37 Copyright © 2002 by Harcourt, Inc.All rights reserved. 25.72 Suppose g = 0% for t = 1 to 3, and then g is a constant 6%. What is P 0 ? 0 1.77 1.57 1.39 20.99 1234 k s =13% g = 0% g = 6% 2.00 2.00 2.00 2.00 2.12.  P 3 2.12 007 30.29.  ^...

38. 9 - 38 Copyright © 2002 by Harcourt, Inc.All rights reserved. t = 3: Now have constant growth with g = capital gains yield = 6% and D/P = 7%. (CGY=capital gain yield) $2.00 $25.72 What is D/P and capital gains yield at t = 0 and at t = 3? t = 0: D1D1 P0P0 = = 7.78% (D/P=div yield) CGY = 13% – 7.78% = 5.22%.

39. 9 - 39 Copyright © 2002 by Harcourt, Inc.All rights reserved. What is the annual dividend yield (D/P) and capital gains yield? Capital gains yield = g = -6.0%, Dividend yield= 13.0% – (-6.0%) = 19%. D/P and cap. gains yield are constant, with high dividend yield (19%) offsetting negative capital gains yield.

40. 9 - 40 Copyright © 2002 by Harcourt, Inc.All rights reserved. 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:   P D kg D g kg ss 0 1 0 1 =  =   $2.00(0.94) $1.88 0.13 – (-0.06) 0.19 = = = $9.89. – – +

41. 9 - 41 Copyright © 2002 by Harcourt, Inc.All rights reserved. Further Example of Supernormal Growth Stock Netscape is operating in a new industry that has recently caught on with the public. Sales are growing at 80% per year. This high sales growth is expected to translate into a 25% growth rate in cash dividends for each of the next 4 years. After that, the dividend growth rate is expected to be 5% forever. Annual dividend paid yesterday is $0.75. The stock’s required return is 22%. What is Netscape’s stock’s price? (Source: Emery et al, Principles of Financial Management. 1998. pp 172-173) cont….

42. 9 - 42 Copyright © 2002 by Harcourt, Inc.All rights reserved. i) Compute the expected future cash dividends: Time 0 1 2 3 4 5 6... Div($) 0.75 0.938 1.172 1.465 1.831 1.923 2.019 … g(%) 25% 25% 25% 25% 5% 5% 5% … ii) Find the stock price at a future time, a point after which the dividend growth rate has become constant forever. That point is at year 5, thus: P 5 = D 6 /(r-g) = $2.019/(0.22-0.05) = $11.876 iii) Compute the PVs of all the future expected cash dividends found in step (i) and add to the PV of the expected future sale price (P 5 ) calculated in step (ii): P 0 = 0.938/1.22 1 + 1.172/1.22 2 + 1.465/1.22 3 + 1.831/1.22 4 + 1.923/1.22 5 + 11.876/1.22 5 = $(0.768 + 0.787 + 0.807 + 0.827 + 0.711 + 4.394) = $8.295

43. 9 - 43 Copyright © 2002 by Harcourt, Inc.All rights reserved. Valuing An Erratic-Growth Stock (EGS) Definition: An EGS is a stock which is expected to have an erratic dividend growth for some finite time, followed by a normal rate forever into the future. P 0 =D 1 /( 1+r) 1 + D 2 /(1+r) 2 +…D n /(1+r) n + {(1+g)D n )/[(1+r) n (r-g)]} (Source: Emery et al., Principles of Financial Management. 1998. pp 173-174) cont…..

44. 9 - 44 Copyright © 2002 by Harcourt, Inc.All rights reserved. Example: Novell’s dividend was $1 last year and is to be $1 for each of the next 3 years. After its projects have been developed, earnings are expected to grow at a high rate for 2 years as sales resulting from new projects are realized. The higher earnings are expected to result in 40% increase in dividends for 2 years. After these 2 extraordinary increases in dividends, the dividend growth rate is expected to be 3% per year forever. Novell’s required rate of return is 12%. What is the worth of its share today? (i) First compute the expected future dividends: Time 0 1 2 3 4 5 6 7 ….. Div($) 1.00 1.00 1.00 1.00 1.40 1.96 2.019 2.079 … Growth 0% 0% 0% 40% 40% 3% 3% 3% …. cont…

45. 9 - 45 Copyright © 2002 by Harcourt, Inc.All rights reserved. (ii) D 5 is where the growth rate in dividends is expected to become constant forever and is the earliest point that satisfies the constant-growth assumption. With D 5 =$1.96, g=3%, and r = 12%, P 0 = D 1 /( 1+r) 1 + D 2 /(1+r) 2 +…D n /(1+r) n + (1+g)D n /{(1+r) n (r-g)} P 0 = 1.00/1.12 1 + 1.00/1.12 2 + 1.00/1.12 3 +1.40/1.12 4 + 1.96/1.12 5 + (1+0.03)1.96/{(1.12) 5 (0.12-0.03)} = $17.13

46. 9 - 46 Copyright © 2002 by Harcourt, Inc.All rights reserved. Free Cash Flow Method/Total Company or Corporate Valuation Model The free cash flow method suggests that the value of the entire firm equals the present value of the firm’s free cash flows (calculated on an after-tax basis). Recall that the free cash flow in any given year can be calculated as: NOPAT – Net capital investment (NOPAT= Net operating profit after taxes)

47. 9 - 47 Copyright © 2002 by Harcourt, Inc.All rights reserved. The Corporate Valuation Model (Text,pg 306) Market Value=V company = PV of expected future Free cash flows of company = FCF1/(1+r)1 +FCF2/(1+r)2+…FCFn/(1+r)n FCF = (EBIT(1-T) + Dep + Amort) - (Cap Exp + Change in NOWC); or FCF= NOPAT – New Investment in Operating Cap

48. 9 - 48 Copyright © 2002 by Harcourt, Inc.All rights reserved. Once the value of the firm is estimated, an estimate of the stock price can be found as follows: MV of common stock (market capitalization) = MV of firm – MV of debt and preferred stock. P = MV of common stock/# of shares. Using the Free Cash Flow Method ^

49. 9 - 49 Copyright © 2002 by Harcourt, Inc.All rights reserved. Free cash flow method is often preferred to the dividend growth model -- particularly for the large number of companies that don’t pay a dividend, or for whom it is hard to forecast dividends. Issues Regarding the Free Cash Flow Method Cont..

50. 9 - 50 Copyright © 2002 by Harcourt, Inc.All rights reserved. Similar to the dividend growth model, the free cash flow method generally assumes that at some point in time, the growth rate in free cash flow will become constant. Terminal value represents the value of the firm at the point in which growth becomes constant. FCF Method Issues (continued)

51. 9 - 51 Copyright © 2002 by Harcourt, Inc.All rights reserved. $416.942 FCF estimates for the next 3 years are -$5, $10, and $20 million, after which the FCF is expected to grow at 6%. The overall firm cost of capital is 10%. (r-g = 0.10-0.06 = 0.04) 0 -4.545 8.264 15.026 398.197 1234 k = 10% g = 6% -5 10 2021.20 21.20 0.04... *TV 3 represents the terminal value of the firm, at t = 3 $530 = = *TV 3

52. 9 - 52 Copyright © 2002 by Harcourt, Inc.All rights reserved. If the firm has $40 million in debt and has 10 million shares of stock, what is the price per share? Value of equity = Total value – Value of debt = $416.94 – $40 = $376.94 million Price per share = Value of equity/# of shares = $376.94/10 = $37.69

53. 9 - 53 Copyright © 2002 by Harcourt, Inc.All rights reserved. Analysts often use the following multiples to value stocks: P/E P/CF P/Sales P/Customer Example: Based on comparable firms, estimate the appropriate P/E. Multiply this by expected earnings to back out an estimate of the stock price. Using the Multiples of Comparable Firms to Estimate Stock Price

54. 9 - 54 Copyright © 2002 by Harcourt, Inc.All rights reserved. What is market equilibrium?(Text,pg310-312) k s = (D 1 /P 0 ) + g = k s = k RF + (k M – k RF )β firm ^ 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:

55. 9 - 55 Copyright © 2002 by Harcourt, Inc.All rights reserved. Expected returns are obtained by estimating dividends and expected capital gains (which can be found using any of the three common stock valuation approaches). ^ K s = (D 1/ P 0 ) + g Required returns are obtained from the CAPM: k s = k RF + (k M – k RF )βfirm

56. 9 - 56 Copyright © 2002 by Harcourt, Inc.All rights reserved. How is equilibrium established? If k s = + g > k s (CAPM) 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

57. 9 - 57 Copyright © 2002 by Harcourt, Inc.All rights reserved. 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. P 0 =. ^ D 1 k i – g

58. 9 - 58 Copyright © 2002 by Harcourt, Inc.All rights reserved. What’s the Efficient Market Hypothesis (EMH)? EMH: Securities are normally in equilibrium and are “fairly priced.” One cannot “beat the market” except through good luck or better information.

59. 9 - 59 Copyright © 2002 by Harcourt, Inc.All rights reserved. 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.

60. 9 - 60 Copyright © 2002 by Harcourt, Inc.All rights reserved. 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.

61. 9 - 61 Copyright © 2002 by Harcourt, Inc.All rights reserved. 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.

62. 9 - 62 Copyright © 2002 by Harcourt, Inc.All rights reserved. 1.15,000 or so trained analysts; MBAs, CFAs, Technical PhDs. 2.Work for firms like Merrill, Morgan, Prudential, which have a lot of money. 3.Have similar access to data. 4.Thus, news is reflected in P 0 almost instantaneously. Markets are generally efficient because:

63. 9 - 63 Copyright © 2002 by Harcourt, Inc.All rights reserved. Preferred Stock Hybrid security. Similar to bonds in that preferred stockholders receive a fixed dividend that 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.

64. 9 - 64 Copyright © 2002 by Harcourt, Inc.All rights reserved. What’s the expected return of preferred stock with V p = $50 and annual dividend = $5?