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Unformatted text preview: Stocks and Their Valuation CHAPTER 9 Stoc ks and The ir Val uat ion Val uat ion Ma rket Equ ilibrium and Efficient Ma rkets FIN 340 3  Bus iness Finan ce Bas ics Common Stock: Terminology Voting rights Preemptive rights Classified stock Initial public offering (IPO) Par value Dividends Stock splits Control Stock represents ownership Ownership implies control Stockholders elect directors Directors hire management Management’s goal: Maximize the stock price Common Stock Symbols D t = Expected dividend at period t P = Current price P t = Expected price at period t g = Expected growth rate BR = Sustainable growth rate B = Retention rate = (1  DPR) R = Return on equity ^ Common Stock Symbols r S = Required rate of return r S = Expected rate of return r S = Actual rate of return = Expected dividend yield = Expected capital gains yield ^ D 1 P P 1P P ^ __ Stock Valuation Assume that you plan to buy a share of stock today. You expect to hold this stock for 1 year, receive a dividend payment at the end of the year, then immediately sell the stock in the market. How much should you pay for the stock today? Stock Valuation P = [D 1 + P 1 ] But, what is the value of P 1 P 1 = [D 2 + P 2 ] 1 1+r S 1 ^ 1 1+r S 1 ^ ^ ^ ________ ________ Stock Valuation P = [D 1 ] + [D 2 + P 2 ] P = [D 1 ] + [D 2 ] + ... + [D ∞ + P ∞ ] 1 1+r S 1 1 1+r S 2 ^ 1 1+r S 1 1 1+r S 2 1 1+r S ∞ ^ ________ ________ ________ ________ ________ Stock Valuation 0 1 2 ∞ P = D 1 D 2 D ∞ Assume present value of P ∞ will be zero: r S P = + + … + D 1 D 2 D ∞ (1+r S ) 1 (1+r S ) 2 (1+r S ) ∞ Stock Valuation Our only problem now is to determine the dividend in each period and the correct discount rate (investor’s required rate of return) to use. Discount Rate Assume that this stock has a beta of 1.25, the riskfree rate is 5%, and the expected return on the market is 13%. We can use the CAPM to then determine r S as follows: r S = .05 + [.13 .05][1.25] = 15% Dividends Assume that the firm just paid a dividend of $1.50 (you won’t get this). Future dividends will depend on growth rate assumptions: Zero (or no) growth Constant growth Nonconstant growth Zero Growth P = Σ [D t ] Assume D t = D for all t, since g = 0 P = [D] Σ = ∞ t =1 1 (1+r S ) t D r S 1 (1+r S ) t ∞ t =1 __________ ___________ Zero Growth At a zero growth rate, the dividend will be the same in each period (this is a valid assumption for preferred stock, which pays a constant dividend forever). The price will be: P = [$1.50] / [.15] = $10.00 Constant Growth Assume: D t = D (1+g) t P = Σ D (1+g) t P = = ∞ t =1 1 (1+r S ) t D (1+g) D 1 r S  g r S g __________ Constant Growth One measure of longrun sustainable growth is given by the formula: g = BR Assume : B = Retention rate = 50% R = ROE = 20% g = (.50)(.20) = 10% Constant Growth...
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 Spring '06
 Tapley
 Finance, Net Present Value, Valuation

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