Final answer:
To calculate the firm's P/E ratio when the payout rate is 50 percent, divide the market price per share by the earnings per share.
Step-by-step explanation:
The P/E ratio, or price-to-earnings ratio, is a financial metric used to evaluate a company's valuation. It is calculated by dividing the market price per share by the earnings per share (EPS). The payout ratio, on the other hand, measures the percentage of earnings that a company distributes as dividends to its shareholders.
To calculate the P/E ratio, you need to know the earnings per share (EPS). If the payout rate is 50 percent, it means that half of the earnings are paid out as dividends. Therefore, the remaining half, which represents the retained earnings, is what contributes to the EPS. This means that the EPS is 50 percent of the total earnings per share.
So, if you know the firm's earnings per share, you can calculate the P/E ratio by dividing the market price per share by the earnings per share. Let's say the earnings per share is $2. In this case, the P/E ratio would be calculated as follows:
P/E ratio = Market price per share / Earnings per share
P/E ratio = Market price per share / (0.5 x total earnings per share)
Let's assume the market price per share is $100. Using the given information:
P/E ratio = $100 / (0.5 x $2) = $100 / $1 = 100
Therefore, the firm's P/E ratio would be 100.