Castles in the Sand generates a rate of return of 12% on its investments and maintains a plowback ratio of. 40. Its earnings this year will be $3 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 of the plowback ratio is reduced to. 30. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Price $ P/E ratio

(a) $34.61; 11.54

(b) $32.81; 10.94

Explanation:

(a) Stock Price = D : (Ke - G)

Where,

D is dividend next year,

Ke is required rate of return on equity

G is growth rate

Growth rate = ROE * plow-back ratio

= 0.12 * 0.40

= 0.048 or 4.8%

Dividend = Current EPS * (1 - plow back ratio)

= $3 * 0.6

= $1.8

Stock Price:

= $1.8 : (0.10 - 0.048)

= $34.61

P/E Ratio = Stock Price : EPS

= $34.61 : $3

= 11.54

(b) New growth rate = 0.12 * 0.30

= 0.036 or 3.6%

Dividend = Current EPS * (1 - plow back ratio)

= $3 * 0.7

= $2.1

Stock Price = $2.1 : (0.10 - 0.036)

= $32.81

P/E Ratio = Stock Price : EPS

= $32.81 : $3

= 10.94