Polar Express Corporation has just reported a net income of $400,000.It has 250,000 common shares outstanding with a book value of $2 million.The firm always maintain a retention ratio of 25%.What is the firm's price-earnings ratio if its required return is 10%?

Question

Quizplus · Accepted Answer

1. First, we need to calculate the earnings per share (EPS):
EPS = net income / number of common shares outstanding
EPS = $400,000 / 250,000 = $1.60

2. Then, we need to calculate the dividends per share (DPS), which is equal to the retention ratio times the EPS:
DPS = retention ratio x EPS
DPS = 0.25 x $1.60 = $0.40

3. The dividend payout ratio (DPR) is equal to the dividends per share divided by the earnings per share:
DPR = DPS / EPS
DPR = $0.40 / $1.60 = 0.25

4. The earnings retention ratio (ERR) is equal to 1 minus the dividend payout ratio:
ERR = 1 - DPR
ERR = 1 - 0.25 = 0.75

5. The growth rate (g) is equal to the earnings retention ratio times the return on equity (ROE):
g = ERR x ROE
g = 0.75 x 0.10 = 0.075

6. Finally, we can calculate the price-earnings (P/E) ratio using the Gordon growth model:
P/E ratio = (dividend per share / (required return - growth rate))
P/E ratio = ($0.40 / (0.10 - 0.075))
P/E ratio = ($0.40 / 0.025)
P/E ratio = 16

However, since the P/E ratio is the market price per share divided by the earnings per share, and we were not given any information about the market price per share, we cannot calculate the exact P/E ratio. Instead, we can only compare the calculated P/E ratio using the Gordon growth model to the answer choices given. The closest answer choice to our calculated P/E ratio is C) 15. Therefore, C) 15 is the best answer choice.

Polar Express Corporation Has Just Reported a Net Income of $400,000.It