Question

Upsilon's assets have a current market value of $240. Its debt has a face value of $130, and it matures in one year. Assume a risk-free rate of interest is 5%. Suppose that the standard deviation of the return on Upsilon's assets is 50%.

Calculate the probability that the company will default.

Answer 1

Given about Upsilon's assets,

Market value of assets V = $240

debt D = $130

risk free rate r = 5%

Time T = 1 years

standard deviation sd = 50%

So, default probability is calculated using Black-Scholes-Merton formula:

first calculating d1 = (ln(V/D) + ((r + sd^2)*T)/(sd*T^(1/2)) = (ln(240/130) + ((0.05 + 0.5^2)*1))/0.5 = 1.8262

Now, d2 = d1 - sd*t^(0.5) = 1.8262 - 0.5 = 1.3262

So, probability that company will default is N(-d2) = N(-1.3262)

Using Z table to calculate N(-1.3262), we get N(-1.3262) = 0.0924 or 9.24%

So, Probability that the company will default is 9.24%