9.21
Constant growth: You own shares of Old World DVD Company stock and are interested in selling them. With so many people downloading these days, sales, profits, and dividends at Old World have been declining 6 percent per year. The firm just paid a dividend of $1.15 per share. The required rate of return for a stock this risky is 15 percent. If dividends are expected to decline at 6 percent per year, what is a share of the stock worth today?
LO 4
Solution: R = 15%;
P0 = =
9.22
D0 = $1.15; g = -6%
D (1+g) D1 = 0 R− g R−g $1.15 (1 − 0.06) 0.15 − ( 0.06) −
= $5.15
Nonconstant growth: You own a company that competes with Old World DVD Company (in the previous problem). Instead of selling DVDs, however, your company sells music downloads from a web site. Things are going well now, but you know that it is only a matter of time before someone comes up with a better way to distribute music. Your company just paid a $1.50 per share dividend and you expect to increase the dividend 10 percent next year. However, you then expect your dividend growth rate to begin going down – to 5 percent the following year, 2 percent the next year, and to -3 percent per year thereafter. Based upon these estimates, what is the value of a share of your company’s stock? Assume that the required rate of return is 12 percent.
LO 4
Solution: g1 = 10%, g2 = 5%, g3 =2%, D1 = $1.50 × 1.1 = $1.65, $1.7672,
g = -3%,
D0 = $1.50
R = 12%
D2 = $1.65 × 1.05 = $1.7325, D3 = $1.7325 ×1.02 =
D4 = $1.7672 × 0.97 = $1.7142.
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