In: Finance
Castles in the Sand generates a rate of return of 20% on its investments and maintains a plowback ratio of .30. Its earnings this year will be $4 per share. Investors expect a 12% rate of return on the stock.
a. Find the price and P/E ratio of the firm. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
b. Find the price and P/E ratio of the firm if the plowback ratio is reduced to .20. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
a. The price is computed as shown below:
= Dividend / (required rate of return - growth rate)
growth rate is computed as follows:
= rate of return generates x plowback ratio
= 0.20 x 0.30
= 6% or 0.06
Dividend is computed as follows:
= Earnings per share x ( 1 - plowback ratio)
= $ 4 x (1 - 0.30)
= $ 2.80
So, the price will be as follows:
= $ 2.80 / ( 0.12 - 0.06)
= $ 46.67 Approximately
So, the PE ratio will be:
= $ 46.6666667 / EPS
= $ 46.6666667 / $ 4
= 11.67 times Approximately
b. The price is computed as shown below:
= Dividend / (required rate of return - growth rate)
growth rate is computed as follows:
= rate of return generates x plowback ratio
= 0.20 x 0.20
= 4% or 0.04
Dividend is computed as follows:
= Earnings per share x ( 1 - plowback ratio)
= $ 4 x (1 - 0.20)
= $ 3.20
So, the price will be as follows:
= $ 3.20 / ( 0.12 - 0.04)
= $ 40
So, the PE ratio will be:
= $ 40 / EPS
= $ 40 / $ 4
= 10 times
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