Castles in the Sand generates a rate of return of 14% on its investments and mai

Question

Castles in the Sand generates a rate of return of 14% on its investments and maintains a plowback ratio of .30. Its earnings this year will be $4 per share. Investors expect a 10% 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.) Price $ P/E ratio 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.) Price $ P/E ratio

Explanation / Answer

first let us calculate the growth rate => rate of return * plow back ratio

=>14% * 0.30.

=>4.2%.

Price = earnings *(1+ growth rate) / (required return - growth rate)

=>$4 *(1.042) / (0.10 -0.042)

=>$4.168 / (0.058)

=>$71.86.

PE ratio = Price per share / earnings per share

=>$71.86 / $4

=>17.97....(rounded to two decimals).

2nd part

If plowback ratio is 0.20.

growth rate = 14% *0.20 =>2.80%.

now,

price = earnings *(1+ growth rate) / (required return - growth rate)

=>$4 *(1.028) / (0.10 - 0.028)

=>$4..112 / (0.072)

=>$57.11....(rounded to 2 decimals)

PE ration = Price per share / earnings per share

=>$57.11 / $4

=>14.28.....(rouded to 2 decimals).

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