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Finance Reading Notes-Exam 2 - FINA 3330

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Finance Reading Notes – Ch 2, 8-14 Chapter 8 – Stock Valuation Share of common stock much harder to price than a bond because o Not even the promised cash flows are known in advance o Life of investment is essentially forever (no maturity for common stock) o No way to easily observe the rate of return that the market requires P 0 = (D 1 +P 1 )/(1+R) o R is required return in the market o P 0 is the current price of the stock and P 1 is the price in one period Given the price in two periods, and finding from that the price in one period you use: P 0 = [D 1 /(1+R) 1 ] + [D 2 /(1+R) 2 ] + [P 2 /(1+R) 2 ] Price of stock today is essentially equal the PV of all future dividends Three cases in which we can come up with a value for stock o The dividend has a zero growth rate o The dividend grows at a constant rate o Dividend grows at a constant rate after some length of time Dividend with zero growth rate o D 1 = D 2 = D 3 = D = constant o Stock can be viewed as an ordinary perpetuity b/c the cash flow is the same every period so per-share value is: P 0 = D/R Constant growth o Growth rate g is constant o D 0 is the dividend just paid, so the next dividend is D 1 o D 1 = D 0 x (1+g) o D 2 = D 0 x (1+g) 2 o Growing perpetuity: an asset with cash flows that grow at a constant rate forever o As long as the g is less than r (discount rate) then the present value of a constant growth series of cash flows is: P 0 = D 1 /(R-g) OR [D x (1+g)]/(R-g) (called the dividend growth model ) o At any point in time we can get the price of a stock (as of time t) by the equation: P = D (t+1) /(R-g) OR [D t x (1+g)]/(R-g) o GORDON GROWTH MODEL ON PAGE 239 o If the constant growth rate, g, is larger than the discount rate, r, then the stock price is indefinitely large (same if g and r are equal b/c the PV of the dividends keeps getting bigger) Nonconstant growth o Allow for “supernormal” growth rates over some finite length of time o The dividends start growing at a constant rate sometime in the future o To see what the stock is worth today you need to find what will be the worth when dividends are paid, then calculate PV of that future price Example: price in four years will be P = [D 4 x (1+g)]/(R-g) OR D 5 /(R-g) discounting that value back four years at 20%, P 0 = \$5/1.20 4 = \$2.41 o Also can happen that the dividends are not 0 before constant growth, in this case it helps to draw a timeline and notice when constant growth starts o Find the PV of the amount of the “perpetuity” (where constant growth occurs) and the PV of the dividends w/out constant growth individually and add them together Two-stage growth

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o The dividend will grow at a rate of g 1 for t years and then grow at a rate of g 2 forever after o (1) PV of growing annuity (g 1 can be greater than r) and (2) PV of stock price once second stage begins (in second stage, g 1 must be less than R) o P t = D t+1 /(R-g 2 ) = [D 0 x (1+g 1 ) t x (1+g 2 )]/(R-g 2 ) Total return, R, has 2 components o D 1 /P 0 is called dividend yield o Growth rate, g, is called capital gains yield
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