1. A bank has a 5-year $10 million loan that pays annual payments of 7 percent and returns the principal at maturity. The bank can sell the loan with recourse at a price of $9 million and without recourse at a price of $8.9 million. If the probability of default (with no interest or principal being repaid) is 1.5 percent, should it sell the loan with or without recourse (assume risk neutrality)? Explain. [Note: the expected proceeds on the loan sale with recourse is the price times the probability that the loan will NOT default.]
2. Assume a bank originates a pool of short-term real estate loans worth $15 million with maturities of 5 years and with annual interest payments of 7 percent and return of principal at maturity. (These are called “balloon” loans.) If the loans are converted to pass-through securities and the bank charges 50 basis points servicing fee per year, what is the payment expected by the holders (purchasers) of the securities at the end of the first year if 10% of the mortgages are expected to be prepaid? Note: the servicing fee is based on the book value of the loans at the beginning of each year.