Athens First S&L originated a pool containing 75 ten-year fully amortizing fixed interest rate mortgages with an average balance of $100,000 each. All mortgages in the pool carry an interest rate of 12% and have annual payments.

1. Athens First S&L would now like to sell the pool to FNMA. Assuming a constant annual prepayment rate of 10% (for simplicity assume that prepayments are based on the pool balance at the end of the preceding year and begin at the end of year 1, except in the final year where the prepayments should be zero since all remaining principal will be paid in the final years scheduled principal),[1] what is the price that Athens First S&L could obtain if market interest rates are 11%?

[1] In an earlier section of the course, when market rates were below the contract rate, the value of the mortgage was approximately the RMB (rather than the PV of remaining payments at the market rate) because there was a high likelihood of prepayment. Here, however, we are formally modelling prepayment for the entire pool. Thus, when market rates are below the contract rates in the pool, the value of the pool is not simply the total of the RMBs.

2. Instead of selling the pool of mortgages, Athens First S&L decides to securitize the mortgages by issuing 100 pass-through securities. The mortgage servicing fee will be 50 basis points, and there is no guarantee fee. The current market rate of return is 10.5% (Assume the same 10% prepayment rate as in question 1; again, there will be no prepayment in the final year).

1. 1. How much will Athens First S&L obtain for this offering of MPTs?
2. 2. What will each purchaser pay for an individual MPT security?
   3. What is the IRR to the MPT investor assuming that the loans prepay as planned?
   4. What is the investors realized return if the actual prepayment rate is 5%?
   5. What is the investors realized return if the actual prepayment rate is 15%?