24-4 What is the present value of a $16 million pool of 30-year mortgages with an...

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.

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 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.)

Present value

$

Expert Solution

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= PVA_{n=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*PVA_{n=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 = RPVA_{n=360, k=0.6667%} + 8mPV_{n=360, k=0.6667%} Þ R = $81,115.94
	$16m = R163.2783 + 8m0.9934
	$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 = $93,512.12PVA _{n=360, k=0.004167%} + 8mPV_{n=360, k=0.004167%}
	93512.12357.31 + 80000000.9851
	$41,293,615.60

jeff jeffy answered 2 years ago

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