ABC Bank originates a pool of containing 100 15-year fixed-rate mortgages with loan amount of $100,000 each. All mortgages in the pool carry a rate of 6% with annual payments. Suppose that the servicing fee is 0.5%. ABC Bank would like to sell the pool to investors via Mortgage Pass Through (MPT) security. Suppose that 100,000 shares will be issued and the market interest rate is 5.5%.

Questions

1. [3 points] Assume that there are no prepayment and no default, how much an investor would like to pay for each share of the MPT security?
2. [3 points] What is the price of each share of the MPT if there are a constant annual prepayment rate of 10% and no default?
3. [3 points] What is the price of each share of the MPT if there are a constant annual default rate of 10% (assuming the recovering rate is 50%) and no prepayment?
4. [1 points] Please briefly discuss your findings.