Assume that a firm's earnings are expected to be $4 million next year and that this number is expected to grow by 10% a year indefinitely. If the appropriate cost of capital is 12%, what is
This firm's P/E ratio?

Question

Quizplus · Accepted Answer

The formula for calculating the P/E ratio is P/E = Price per share/Earnings per share. First, we need to calculate the expected earnings per share (EPS) for the next year. EPS = Earnings/Number of shares. Since the number of shares has not been provided, assume that it is 1 million shares to simplify the calculation. EPS = $4 million/1 million shares = $4 per share.

To calculate the price per share, we can use the Gordon growth model: Price per share = (Next year's EPS/Discount rate - Growth rate). 
Price per share = ($4.40/0.12-0.10) = $44. 
Therefore, the P/E ratio = $44/$4 = 11.

However, we need to adjust the P/E ratio for any expected changes in market conditions, risk, or future growth prospects. A P/E ratio of 50 represents an extremely high valuation, so it is unlikely that the market would assign such a high multiple to this firm. A P/E ratio of 20-45 is more realistic, considering the expected growth rate and cost of capital. Therefore, the best answer is C, a P/E ratio of 50, since it is the closest choice to the calculated ratio, but it should be interpreted with caution.

Assume That a Firm's Earnings Are Expected to Be $4