A firm can be worth $60 million or $120 million with equal probability. The debt of the firm consists of a zero-coupon bond with a $100 million face that matures in one year. Assume risk neutrality and a cost of capital of 8%.
-Refer to the information above. What is the value of this firm's equity?

Question

Quizplus · Accepted Answer

The value of the firm's equity can be calculated by first determining the expected value of the firm and then subtracting the present value of the debt. The expected value of the firm is the average of its two possible values, which is ($60 million + $120 million) / 2 = $90 million. The present value of the debt, given a cost of capital of 8%, is $100 million / (1 + 0.08) = $92.59 million. However, since the debt exceeds the lower value of the firm ($60 million), the debt's value in the case of the lower firm value is capped at that lower value, making the calculation for the expected debt payoff more nuanced. To accurately calculate the equity value, consider the outcomes:1. If the firm is worth $120 million, the debt holders will be paid $100 million, leaving $20 million for equity.2. If the firm is worth $60 million, it's all taken by the debt holders, leaving $0 for equity.The expected equity value is thus (0.5 * $20 million + 0.5 * $0) = $10 million. Discounting this back at the 8% cost of capital gives the present value of the equity: $10 million / (1 + 0.08) = $9.26 million, which rounds to $9.3 million.

A Firm Can Be Worth $60 Million or $120 Million