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The price of a stock is equal to the present value of all future dividends. The intuition behind this insight is
that the cash payoff to owners of the stock is equal to cash dividends plus capital gains or losses. Thus, the
expected return that an investor expects from a investing in a stock over a set period of time is equal to: (14) Expected return on stock r dividend capital gain
investment Div1 P1 P0
P0 Where Divt and Pt denote the dividend and stock price in year t, respectively. Isolating the current stock
price P0 in the expected return formula yields: (15) Div1 P1
1 r P0 The question then becomes "What determines next years stock price P1?". By changing the subscripts next
year's price is equal to the discounted value of the sum of dividends and expected price in year 2: Div2 P2
1 r P
1 Inserting this into the formula for the current stock price P0 yields: Div1 P1
1 r P0 1 Div1 P1 1 § Div1 Div 2 P2 ·
¸
¨
1 r
1 r ©
1 r ¹ Div1 Div 2 P2
1 r
(1 r ) 2 By recursive substitution the current stock price is equal to the sum of the present value of all...
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 Spring '12
 

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