A firm is equally likely to be worth $50 million, $80 million, $120 million, or $150 million. There is one bond outstanding that promises to pay $100 million at an interest rate of 6%. The appropriate cost of capital for the firm's projects is 12%.
-Refer to the information above. What is the expected payoff to the bondholders?

Question

Quizplus · Accepted Answer

The expected payoff to the bondholders is calculated by taking the average of the payoffs in each state, considering the bond's promise to pay $100 million. For the firm worth $50 million, bondholders receive $50 million (since the firm cannot pay more than its worth). For the other three states ($80 million, $120 million, and $150 million), bondholders receive the full $100 million (as the firm's value exceeds the bond's payoff). Thus, the expected payoff = (50 + 100 + 100 + 100) / 4 = 350 / 4 = $87.5 million.

A Firm Is Equally Likely to Be Worth $50 Million