ART has come out with a new and improved product. As a result, the firm projects an ROE of 26%, and it will maintain a plowback ratio of 0.20. Its earnings this year will be $2.5 per share. Investors expect a 14% rate of return on the stock. What price do you expect ART shares to sell for in 4 years? A. $26.46
B. $39.69
C. $27.84
D. $30.34

27.84

Explanation:

In order to find the price(value of the stock) after 4 years, we must have the growth rate to reach that level. In this question the growth rate will be identified first by the given information.

DATA

ROE = 26%

Plow back ratio = 0.20

Dividend this year = Do = $2.5

Rate of return = 14%

Time period = 4 years

Solution

growth rate = ROE x plow back ratio

growth rate = 26% * 0.2

growth rate  = 5.2%

Dividend next year D1 = Do x (1-plowback ratio)

D1  = 2.5 x (1-0.2)  

D1 = $2

Value of stock now Po = D1/(return - growth rate)

Value of stock now Po = 2/(0.14-0.052)

Value of stock now Po  = $22.73

Value of stock in 4 years   = Po * (1+growth rate)^4

Value of stock in 4 years   = 22.73 * (1+0.052)^4

Value of stock in 4 years   = $27.84

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