Question

What is the present value of a $20 million pool of 15-year mortgages with an 8.5 percent per year monthly mortgage coupon if market rates are 5 percent? The GNMA guarantee fee is 5 basis points and the FI servicing fee is 45 basis points.

a.	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.)

Present value

$

b.

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 40 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.)

Present value

$

Answer 1

Part (a)

There is a monthly coupon. Thus the period is 1 month.

We can calculate the monthly payment using PMT function. Inputs are:

Interest rate = Mortgage coupon rate - The GNMA guarantee fee - the FI servicing fee = 8.5% - 5 basis points - 45 basis points

1 basis points = 1% / 100 = 0.01%

Hence, interest rate = = 8.5% - 5 basis points - 45 basis points = 8.5% - 0.05% - 0.45% = 8.00%

Interest Rate per month = 8%/12 = 0.006666667

Period = nos. of months in 15 years = 12 x 15 = 180

PV = Current value of pool = - $ 20 mn

Hence, payment per month = PMT(Rate, Period, PV, FV) = PMT (0.00666667, 180, -20000000, 0) = $ 191,130.42

Market rate = 5%

Hence, yield per month = y = 5% / 12 = 0.004167

Hence, the present value = PV of annuity = PMT / y x [1 - (1 + y)^-n] = 191,130.42 / 0.004167 x [1 - (1 + 0.004167)^-180] = $  24,169,443.25

Hence, please enter your answer as: 24,169,443

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Part (b)

Hence, payment per month = PMT(Rate, Period, PV, FV) = PMT (0.00666667, 180, -20000000, 40% x 20000000) = $168,011.58

Market rate = 5%

Hence, yield per month = y = 5% / 12 = 0.004167

Hence, the present value = PV of annuity + PV of maturity amount= PMT / y x [1 - (1 + y)^-n] + 40% x 20,000,000 x (1 + y)^-n = $168,011.58 / 0.004167 x [1 - (1 + 0.004167)^-180] + 40% x 20,000,000 x (1 + 0.004167)^-180 = $ 25,030,770.81

Hence, please enter your answer as: 25,030,771