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 will the bondholders pay for this debt?

Question

Quizplus · Accepted Answer

The expected value of the firm is ($60 million + $120 million)/2 = $90 million. 
The present value of the zero-coupon bond is $100 million / (1 + 0.08) = $92.6 million. 
In the event that the firm is worth $60 million, the bondholders will receive $60 million and will repay $92.6 million, resulting in a loss of $32.6 million. 
In the event that the firm is worth $120 million, the bondholders will receive $120 million and will repay $92.6 million, resulting in a gain of $27.4 million. 
The expected value of the bond is -0.5($32.6 million) + 0.5($27.4 million) = -$2.6 million. 
Therefore, the bondholders will pay less than the face value of $100 million to compensate for the negative expected value. 
The only answer choice that is less than $100 million is C, $74.1 million.

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