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Unformatted text preview: What is the value of a stock with The stock value is found from: P = D t 1 + r ( ) t t = 1 T " + D T + 1 r # g c $ % & ' ( ) 1 + r ( ) # T P is the stock price at time t = 0 D t is the expected dividend at time t = D t1 (1 + g i ) r is the required rate of return g i is the initial growth rate g c is the rate of constant growth The first step is to calculate all of the D t values, and then substitute them into the above equation to get the stock value. a. A Dividend at time zero of $1.25, a required rate of return of 14%, and expected growth of 12% for 5 years followed by a constant growth rate of 4%? D 1 = ($1.25)(1 + .12) = $1.400 D 4 = ($1.25)(1 + .12) 4 = $1.967 D 2 = ($1.25)(1 + .12) 2 = $1.568 D 5 = ($1.25)(1 + .12) 5 = $2.203 D 3 = ($1.25)(1 + .12) 3 = $1.756 D 6 = ($1.25)(1 + .12) 6 = $2.467 P = (1.400)/(1 + .14) + (1.568)/(1 + .14) 2 + (1.756)/(1 + .14) 3 + (1.967)/(1 + .14) 4 + (2.203)/(1 + .14) 5 + [ 2.467/(.14 .04) ](1 + 0.14)5 P = 1.228 + 1.207 + 1.185 + 1.165 + 1.144 + 12.814 P = $18.74 b. A Dividend at time zero of $2.50, a required rate of return of 18%, and expected growth of 15% for 7 years followed by a constant growth rate of 2%? D 1 = ($2.50)(1 + .15) = $2.875 D 5 = ($2.50)(1 + .15) 5 = $5.028 D 2 = ($2.50)(1 + .15) 2 = $3.306 D 6 = ($2.50)(1 + .15) 6 = $5.783 D 3 = ($2.50)(1 + .15) 3 = $3.802 D 7 = ($2.50)(1 + .15) 7 = $6.650 D 4 = ($2.50)(1 + .15) 4 = $4.373 D 8 = ($2.50)(1 + .15) 8 = $7.648 P = (2.875)/(1 + .18) + (3.306)/(1.18) 2 + (3.802)/(1.18) 3 + (4.373)/(1.18) 4 + (5.028)/(1.18) 5 + (5.783)/(1.18) 6 + (6.650)/(1.18) 7 + [ 7.648/(.18 .02) ](1 + 0.18)7 P = 2.436 + 2.374 + 2.314 + 2.255 + 2.198 + 2.142 + 2.088 + 15.005 P = $30.81 c. A Dividend at time zero of $5, a required rate of return of 28%, and expected growth c....
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 Spring '11
 Houston
 Corporate Finance

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