Castles in the Sand generates a rate of return of 16% on its investments and mai

Question

Castles in the Sand generates a rate of return of 16% on its investments and maintains a plowback ratio of .60. Its earnings this year will be $5 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.) Price $ P/E ratio b. Find the price and P/E ratio of the firm if the plowback ratio is reduced to .50. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Price $ P/E ratio

Explanation / Answer

Return generated =16%

Plowback Ratio =0.60

Earnings Per Share =$5

a.) Earnings Growth = ROE x Plowback = 0.16 x 0.60 = 0.096

Using Gordon Growth Model,

Price = EPS x (1+g) / (r-g) = 5 x (1+0.096) / (0.12 -0.096) = 5 x 1.096 / 0.024 =$228.33

Trailing P/E = 228.33/5 =45.67

Forward P/E = 228.33/(5x1.096) = 41.67

b.) New Plowback Ratio =0.50

New Growth Rate = 0.50 x 0.16 =0.08

Using Gordon Growth Model,

Price = EPS x (1+g) / (r-g) = 5 x (1+0.08) / (0.12 -0.08) = 5 x 1.08 / 0.04 =$135

Trailing P/E = 135/5 =27

Forward P/E = 135/(5x1.08) = 25

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