A firm can be worth $110 or $180 with equal probability. The firm's debt consists of a zero-coupon bond with a face value of $110 that matures at the end of one year. Assume risk neutrality and a cost of capital of 10%.
-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 considering the expected payoff to equity holders and discounting it back at the firm's cost of capital. The expected payoff to equity holders is the expected value of the firm minus the debt obligation, if the firm's value exceeds the debt obligation, and zero otherwise. Given the firm can be worth $110 or $180 with equal probability:1. If the firm is worth $110, the equity holders get nothing because all value goes to debt holders.2. If the firm is worth $180, the equity holders get $70 ($180 - $110).The expected payoff to equity holders is thus 0.5 * $0 + 0.5 * $70 = $35. To find the present value of this expected payoff, we discount it back at the cost of capital, which is 10%. $$ \text{Present Value} = \frac{\$35}{(1 + 0.10)} = \$31.82 $$Therefore, the value of the firm's equity is $31.82.

A Firm Can Be Worth $110 or $180 with Equal