A developer is oering 450,000 fully amortising loans for their properties at 1.8 percent interest for 25

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Question:

A developer is oering 450,000 fully amortising loans for their properties at 1.8 percent interest for 25 years. The current market rate for 25-year fully amortising loans is 2.25 percent. The properties would normally sell for 500,000 each without any special financing.

(a) At what price should the developer sell the properties to earn, in eect, the market rate of interest on the loan? Assume that the buyer would have the loan for the entire term of 25 years.

(b) How would your answer to part (a) change if the property is resold after 10 years and the loan repaid?

(c) Suppose you bought the property together with below-market financing. However, after 5 years you notice that market rates have fallen, and you could obtain a new mortgage at 1.5 percent interest. The developer charges 1 percent (of the outstanding loan amount) as early repayment fee, and the booking fee of the new mortgage is 1,000. Suppose that you expect to live in the property indefinitely, and you expect to earn a 2-percent yield on your extra investment. Would you switch to the new mortgage?

(d) Suppose that the developer sold 10 properties with special financing. After 1 year the developer decides to sell the mortgages to Secondary Mortgage Purchasing Company (SMPC). By that time the market interest rate has risen to 2.4 percent. Assuming no early repayment, how much will SMPC be willing to pay for the 10 mortgages?

(e) Suppose that instead of selling the mortgages to SMPC, the developer issues a 24-year maturity mortgage-backed bond. The annual coupon is 3 percent. Calculate the par value of the bond such that the value of the mortgage-backed bond in year 1 is the same as the market value of the mortgages computed in (d). Assume that bond market investors require a 2.7 percent annual return.