Question

Castles in the Sand generates a rate of return of 15% on its investments and maintains a plowback ratio of 0.20. Its earnings this year will be $6 per share. Investors expect a rate of return of 10% 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.) b. Find the price and P/E ratio of the firm if the plowback ratio is reduced to 0.10. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

a.first let us find out growth rate

growth rate = rate of return on investment * plow back ratio

=>15%*0.20

=>3%.

now,

current year dividend = earnings * (1- plowback ratio)

=>$6*(1-0.20)

=>$4.80.

now,

as per gordon growth model.

price = dividend / (required return - growth rate)

=>$4.80 / (0.10-0.03)

=>$68.57

PE ratio = price per share / earning per share

=>$68.57 / 6

=>11.43 times

b.if plowback ratio is 0.10.

growth rate = 15%*0.10

=>1.5%.

dividend = $6*(1-0.10)

=>$5.40.

price = $5.40 / (0.10-0.015)

=>$63.53

PE ratio = $63.53/ 6

=>10.59 times.