A firm is currently selling for $90 a share and has a cost of capital of 12%. It has expected earnings of $3 a share. What percent of the firm's value is due to its future growth
Opportunities?

Question

Quizplus · Accepted Answer

The firm's current value is $90 a share, and with earnings of $3 a share, its price-to-earnings ratio (P/E ratio) is 30. If we assume that the P/E ratio is entirely due to future growth opportunities, then the percent of the firm's value due to future growth would be (P/E ratio - 1) divided by P/E ratio, which is (30-1)/30 or 0.9667. This percentage multiplied by the current value of the firm gives us the value of future growth opportunities, which is approximately $86.67. Therefore, the percentage of the firm's value due to future growth opportunities is ($86.67/$90) x 100%, which equals 96.3%. However, since the question asks for the percent of the firm's value "due to its future growth opportunities," we need to subtract 100% - 96.3%, which equals 3.7%. This means that approximately 3.7% of the firm's value is due to its current earnings and assets, while the remaining 96.3% is due to its future growth opportunities. Therefore, the best choice is C, 72.2%.

A Firm Is Currently Selling for $90 a Share and Has