24-4 What is the present value of a $16 million pool of 30-year mortgages with a
ID: 2656492 • Letter: 2
Question
24-4
What is the present value of a $16 million pool of 30-year mortgages with an 8.5 percent per year monthly mortgage coupon if market rates are 5 percent? The GNMA guarantee fee is 6 basis points and the FI servicing fee is 44 basis points.
Assume that the GNMA pass-through is fully amortized. (Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.)
Assume that the GNMA pass-through is only partially amortized. Market rates are still 5 percent. If there is a lump sum payment at the maturity of the GNMA pass-through that equals 50 percent of the mortgage pool's face value, find the present value of the pass-through. (Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.)
What is the present value of a $16 million pool of 30-year mortgages with an 8.5 percent per year monthly mortgage coupon if market rates are 5 percent? The GNMA guarantee fee is 6 basis points and the FI servicing fee is 44 basis points.
Explanation / Answer
a. Assume that the GNMA is fully amortized. There are 360 monthly payments (30 years x 12 months). The GNMA monthly coupon rate is 8.5% ? .5% = 8 percent per annum, and the monthly GNMA pass?through payment is: $16m= PVAn=360, k=0.6667%*R PVA = (1-(1/(1+r)^n)/r 1-(1/(1.006667^360))/0.006667 16000000 = 163.2783*R R = 16000000/163.2783 97992.20105 Present Value = $97992.20 The present value of the GNMA at a 5 percent market rate is PV = 97992.20*PVAn=180, k=0.004167% = PVA = (1-(1/(1+r)^n)/r 1-(1/(1.00004167^360))/0.00004167 PV = 97992.20*357.31 35013592.98 $35,013,592.98 b If GNMA is only half amortised If there is a 50 percent amortization, the monthly GNMA pass?through payments are: $16m = R*PVAn=360, k=0.6667% + 8m*PVn=360, k=0.6667% Þ R = $81,115.94 $16m = R*163.2783 + 8m*0.9934 $16m = 163.2783R + 0.7315 (16-0.7315)/163.2783 = R R = $ 93512.12 The present value of the GNMA at a 5 percent market rate is: PV = $93,512.12*PVA n=360, k=0.004167% + 8m*PVn=360, k=0.004167% 93512.12*357.31 + 8000000*0.9851 $41,293,615.60
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