Prepayment Risk and Default Risk

BOA originates 100 Fully Amortizing Fixed Rate Mortgages, each has a $1,000 balance, 4% interest rate (no fees), 25-year term, and annual payments. BOA immediately issues IO and PO strips backed by the pool of these mortgages and sells them to investors who discount payoffs at 3%.

2. What is the value of this pool of mortgages, according to investors?

3. What profits does BOA make immediately? (the answer will be a few thousand dollars)

4. What would be the profits if the expected prepayment rate was 10% per year?

5. What would be the profits if instead the expected default rate was 10% per year? Assume that in case of default, BOA recovers 80% of balance (i.e. default is prepayment but you receive only 80% of the `prepaid' balance).