Question

Bluechips Inc. generates a rate of return of 18 percent on its investments and maintains a retention ratio of 0.40. Its earnings this year will be $3 per share. The required rate of return is 14 percent. a) Find the price and P/E ratio of the firm. b) What happens to the P/E ratio if the retention ratio is increased to 0.55? Why? c) Show that if the retention ratio equals zero, the earnings-price ratio, E/P, falls to the expected rate of return on the stock.

Answer 1

Answer a
Price per share = [EPS x (1-retention ratio)] / Required rate of return
Price per share = [$3 x (1-0.40)] / 0.14
Price per share = $12.86
P/E ratio = Price per share / EPS
P/E ratio of the firm = $12.86 / $3
P/E ratio of the firm = 4.29
Answer b
Calculation of P/E ratio if the retention ratio is increased to 0.55
Price per share = [EPS x (1-retention ratio)] / Required rate of return
Price per share = [$3 x (1-0.55)] / 0.14
Price per share = $9.64
P/E ratio = Price per share / EPS
P/E ratio of the firm = $9.64 / $3
P/E ratio of the firm = 3.21
If retention ratio is increased to 0.55 , then P/E ratio falls to 3.21 due to fall in price per share.
Answer c
If the retention ratio equals zero, the earnings-price ratio, E/P, falls to the expected rate of return on the stock.
Price per share = [EPS x (1-retention ratio)] / Required rate of return
Price per share = [$3 x (1-0)] / 0.14
Price per share = $21.43
Earnings-price ratio = EPS / Price per share
Earnings-price ratio = $3 / $21.43
Earnings-price ratio = 14% which is equal to the expected rate of return on the stock.