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

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

Solutions

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 1 year ago

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