1. A company’s equity is $4 million and the volatility of the
equity is 60% The risk-free rate is 2%, the debt face value is $8 million and time to debt maturity is 1 year. Find the implied firm value and the recovery rate using the KMV approach.

14.Consider the defaultable bonds of two companies. Firm 1 hasV1= 200,F1= 150, T1= 1, σ1= 0.25,

and, firm 2 has V2 = 300, F2 = 200, T2 = 1.5, σ2 = 0.20. Let the riskless rate be 5%, and the correlation
between the two firms’ asset values is 0.2. Neither firm pays any dividends. Find the spread of each
bond, and find the VaR(5%) for a 1-day horizon for a portfolio that has face value of F1 of Firm 1’s
bonds, and face value of F2 of Firm 2’s bonds, maturing at the two dates specified. Use the options
approach and assume that the returns on each firm’s assets is normally distributed with mean zero.

15. Use the transition matrix in the excel sheet “tmatrix.xls” to find the probability of a BBB bond having
a BBB or higher rating in three years.

16. Consider a 5-year bond that pays a coupon of $4 at the end of each year, and a principal of $100 at
the end of 5 years. Let its current rating be BB, and the spot rate (rate for borrowing between current
year and next year) be 5.4%. Using the forward rates for BB bonds and the transition matrix in the
excel sheet “tmatrix.xls”, find the current bond price, the standard deviation of the bond value one
year from now, and the VaR(5%) range for a 1-year horizon.