A firm has one-year zero-coupon debt with face value $7 billion. Assuming the firm value at the end of the year is normally distributed with a mean of 10 billion and a standard deviation of 2 billion, , what is the probability that the firm's assets will not be sufficient to repay the debt at the end of the year?
A) 0.14%
B) 4.44%
C) 5.39%
D) 6.68%

Question

Quizplus · Accepted Answer

The probability that the firm's assets will not be sufficient to repay the debt is the probability that the firm value is less than $7 billion. This is calculated using the cumulative distribution function (CDF) of a normal distribution. The Z-score is (7-10)/2 = -1.5. The probability corresponding to a Z-score of -1.5 is approximately 6.68%.

A Firm Has One-Year Zero-Coupon Debt with Face Value $7