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 $5 per share. Investors expect a 12% rate of return on the stock. a. Find the price and P/E ratio of the firm.

b. Find the price and P/E ratio of the firm if the plowback ratio is reduced to 0.20.

a. Earnings per share = $5

Expected dividend per share (D1) = 70% x $5 = $3.50

Current market price (Po) = D1/Ke - g

Current market price (Po) = $3.50/0.12-0.06

Po = $3.50/0.06

Po = $58.33

Growth rate (g) = b x r

= 0.3 x 0.2

= 0.06

Price-earnings (P/E) ratio = market price per share/Earnings per share

= 58.33/5

= 11.67

b. Earnings per share = $5

D1 = 80% x $5 = $4

Po = D1/Ke - g

Po = $4/0.12-0.04

Po = $50

g = b x r

g = 0.2 x 0.2

g = 0.04

P/E ratio = $50/$5

P/E ratio = 10

Explanation:

In this question, there is need to determine the growth rate, which is a function of return on investment and plowback ratio. Then, we will calculate the current market price as shown above. Finally, the current market price is divided by earnings per share in order to obtain the P/E ratio.