Castles in the Sand generates a rate of return of 10% on its investments and mai

Question

Castles in the Sand generates a rate of return of 10% on its investments and maintains a plowback ratio of .20. Its earnings this year will be $4 per share. Investors expect a 8% 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 .10. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Find the price and P/E ratio of the firm. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Explanation / Answer

a) Dividend this year, D1 = Earnings x (1 - plowback) = 4 x (1 - 20%) = $3.2

Growth rate, g = ROE x plowback = 10% x 20% = 2%

=> Price today, P0 = D1 / (r - g) = 3.2 / (8% - 2%) = $53.33

P/E = 53.33 / 4 = 13.33

b) if plowback = 10%, D1 = 3.6, g = 10% x 10% = 1%

=> Price = 3.6 / (8% - 1%) = $51.43

P/E = 51.43 / 4 = 12.86%

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