9 - 1 Copyright © 2002 by Harcourt, Inc.All rights reserved. CHAPTER 9 Stocks and Their Valuation Features of common stock Determining common stock values Efficient markets Preferred stock

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

9 - 3 Copyright © 2002 by Harcourt, Inc.All rights reserved. Dividend growth model Free cash flow method Using the multiples of comparable firms Different Approaches for Valuing Common Stock

9 - 4 Copyright © 2002 by Harcourt, Inc.All rights reserved. One whose dividends are expected to grow forever at a constant rate, g. Stock Value = PV of Dividends What is a constant growth stock?.

9 - 5 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 t = D t (1 + g) t P 0 = =. If g is constant, then: D 0 (1 + g) k s – g D 1 k s – g ^

9 - 6 Copyright © 2002 by Harcourt, Inc.All rights reserved. $ 0.25 Years (t) 0

9 - 7 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

9 - 8 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 on the firm’s stock? k s = k RF + (k M – k RF )b Firm = 7% + (12% – 7%) (1.2) = 13%. Use the SML to calculate k s :

9 - 9 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% g = 6% D 0 = % 2.12

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 $ $30.29.

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. Thus, 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 ^ = $ P 1 = P 0 (1.06) = $32.10.

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 $ %. $32.10 – $30.29 $30.29 = 6.0%.

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

Copyright © 2002 by Harcourt, Inc.All rights reserved. P 0 = = = $ What would P 0 be if g = 0? The dividend stream would be a perpetuity %... ^ PMT k $ ^

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 is still 13%. ^

Copyright © 2002 by Harcourt, Inc.All rights reserved. Nonconstant growth followed by constant growth: k s = 13% = P 0 g = 30% g = 6% D 0 = ... $66.54P    0... ^

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 = = 4.81%. Cap. gain 0 = 13.00% – 4.81% = 8.19%. $2.60 $54.11

Copyright © 2002 by Harcourt, Inc.All rights reserved. During nonconstant growth, 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 = 13%; so D/P = 13% – 6% = 7%.

Copyright © 2002 by Harcourt, Inc.All rights reserved Suppose g = 0 for t = 1 to 3, and then g is a constant 6%. What is P 0 ? k s =13% g = 0% g = 6%  P  ^...

Copyright © 2002 by Harcourt, Inc.All rights reserved. t = 3: Now have constant growth with g = capital gains yield = 6% and D/P = 7%. $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%. CGY = 13% – 7.78% = 5.22%.

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 =  =   $2.00(0.94) $ – (-0.06) 0.19 = = = $9.89. – – +

Copyright © 2002 by Harcourt, Inc.All rights reserved. What is the annual 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.

Copyright © 2002 by Harcourt, Inc.All rights reserved. Free Cash Flow Method 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.

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 ^

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 (More...)

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)

Copyright © 2002 by Harcourt, Inc.All rights reserved 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% k = 10% g = 6% *TV 3 represents the terminal value of the firm, at t = = = *TV 3

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 = $ – $40 = $ million. Price per share = Value of equity/# of shares = $376.94/10 = $37.69.

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

Copyright © 2002 by Harcourt, Inc.All rights reserved. What is market equilibrium? k s = D 1 /P 0 + g = k s = k RF + (k M – k RF )b. ^ 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:

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

Copyright © 2002 by Harcourt, Inc.All rights reserved. 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

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

Copyright © 2002 by Harcourt, Inc.All rights reserved. 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.

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.

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.

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.

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:

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.

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