Question

Problem 7-37 P/E Ratios (LO2, 4) Castles in the Sand generates a rate of return of 20% on its investments and maintains a plowback ratio of 0.30. Its earnings this year will be $5 per share. Investors expect a rate of return of 15% 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 0.20. (Do not round Intermediate calculations. Round your answers to 2 decimal places.) Price P/E ratio

Answer 1

Solution :

It is given that the rate of return on investment is 20% and plowback or retention ratio is 0.30

Sustainable growth rate = 20% * 0.3 = 6%

EPS = $ 5

Dividend payout ratio = 1-plowback = 1-0.3 = 0.7

D1 = EPS * dividend payout ratio = $5 * 0.7 = $3.5

Part A )

Using Gordon dividend model

Share price = D1/ ( cost of equity - g) = 3.5 / (0.15-0.06) = $38.89

P/E = Price / EPS = $38.89/5 = 7.78

Part B )

When plowback ratio is 0.2 then g = 20% * 0.2 = 4%

Share price = 3.5 / ( 0.15 - 0.04) = 3.5 / 0.11 = $31.82

P/E = $31.82 / $5 = 6.36