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 levered equity holders?

Question

Quizplus · Accepted Answer

The expected payoff to the levered equity holders is the sum of the expected value of the firm and the expected value of the bond minus the initial investment.

Expected value of the firm = (0.25 x $50 million) + (0.25 x $80 million) + (0.25 x $120 million) + (0.25 x $150 million) = $100 million

Expected value of the bond = $100 million

Therefore, the expected payoff to the levered equity holders = ($100 million + $100 million) x (1 - 0.06) - $100 million x (1 - 0.12) = $17.5 million.

A Firm Is Equally Likely to Be Worth $50 Million