Question
Consider a firm that has issued zero coupon debt. It only has one type of debt outstanding. The face value of the debt is F. The market value of the firm's assets is 100 (= A(0)). The volatility of the rate of return on the firm's assets is 20%. The instantaneous risk free rate of interest is 3%.
Part A
If the maturity of the debt is one year, what is the probability of default, the distance to default and market value of debt?
How does leverage affect the distance to default?
When you increase the face value of debt, how does this affect the probability of default and the market value of debt?
Part B
Plot your results, with the distance to default on the x-axis and the probability of default on the y-axis (vertical axis).
How could you use this graph to predict the probability of default on a commercial basis?
Part C
If the firm had short term debt of 40 and long term debt of 80, what is the probability of default? Please provide a justification for your answer.
(Hint: the firm has two types of debt outstanding. If you want to use the Merton model, how would represent the total amount of debt. Try different combinations.) Justify your recommendation.