1. The following quantities for a company are given:
V0 = 100,
σ = 40%,
LR = 60%
T = 1 ár
r = ln(1 + 5%).
Use the Merton model to answer the following questions
1. What is the total debt of the company, F?
2. What is the expected asset value a year from now, VT?
3. Given that the company will default a year from now, what is the expected recovery
rate?
4. What is the price of a hedge against the company default?
2. A bank lends company $ 100m to buy $ 150m of shares in American Airlines (AMR). The company
pays the difference between the acquisition price and the loan that the bank provides. It is the only
purpose of the company involved in the AMR transaction to own the shares and it has no other assets.
The loan is a bullet loan for two years and risk free rates are 5%.
What interest rate should the bank charge the company according to the Merton model?
3. Premium on a CDS is 60bp per year with semiannual payments (twice a year). The notional amount of
the contract is $ 300 mn and insurance is paid in cash. Default occurs after 4 years and two months and
at that time the value of the underlying bond is estimated to be 40% of the notional. Show cashflow an
their timing as they look from the seller of the CDS Agreement.