Castles in the Sand generates a rate of return of 15% on its investments and mai
ID: 2722316 • Letter: C
Question
Castles in the Sand generates a rate of return of 15% on its investments and maintains a plowback ratio of .40. Its earnings this year will be $3 per share. Investors expect a 12% rate of return on the stock.
Find the price and P/E ratio of the firm. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Find the price and P/E ratio of the firm if the plowback ratio is reduced to .30. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Castles in the Sand generates a rate of return of 15% on its investments and maintains a plowback ratio of .40. Its earnings this year will be $3 per share. Investors expect a 12% rate of return on the stock.
Explanation / Answer
a. The growth rate is given by g = ROE * b where
ROE = 15% = 0.15 and b = plowback = 0.4
hence g = 0.15*0.4 = 0.06 = 6%
According to DCF Price P0 = D0*(1+g)/(Ke-g)
where D0 = dividend = 3*(1-0.4) = 1.8
g = 0.06
Ke = 0.12
P0 = 1.8*1.06/(0.12-0.06) = 31.80
Price = $ 31.80
The price to earnings ratio = 31.80/3 = 10.6
b. When plow back is 0.3:
The growth rate is given by g = ROE * b where
ROE = 15% = 0.15 and b = plowback = 0.3
hence g = 0.15*0.3 = 0.045 = 4.5%
According to DCF Price P0 = D0*(1+g)/(Ke-g)
where D0 = dividend = 3*(1-0.3) = 2.1
g = 0.045
Ke = 0.12
P0 = 2.1*1.045/(0.12-0.045) = 29.26
Price = $ 29.26
The price to earnings ratio = 29.26/3 = 9.75
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