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 will the bondholders pay for this debt?

Question

Quizplus · Accepted Answer

The expected value of the firm at the end of one year is the average of the two possible values, which is $(110 + 180) / 2 = $145. The bondholders will receive the lesser of the face value of the bond or the value of the firm. Since the face value of the bond is $110, and one of the firm's possible values is below the face value, the expected payout to bondholders is $(110 + 110) / 2 = $110. Discounting this at the cost of capital (10%) gives the price they would pay: $110 / (1 + 0.10) = $100.

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