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What is the present value of a $15 million pool of 30-year mortgages with an 10.5...

What is the present value of a $15 million pool of 30-year mortgages with an 10.5 percent per year monthly mortgage coupon if market rates are 7 percent? The GNMA guarantee fee is 7 basis points and the FI servicing fee is 43 basis points.

a. Assume that the GNMA pass-through is fully amortized.
b. Assume that the GNMA pass-through is only half amortized. Market rates are still 7 percent. If there is a lump sum payment at the maturity of the GNMA pass-through that equals 60 percent of the mortgage pool's face value, find the present value of the pass-through.

PLEASE PROVIDE EXCEL FORMULA SPELLED OUT TO ANSWER THESE PROBLEMS. SPECIFICALLY QUESTION B. I'm having trouble understanding how to get the answer properly I understand how to get answer A.

Solutions

Expert Solution

formula for PV of annuity:-

P = $15 million;

n = 12*30 = 360;

i = The GNMA monthly coupon rate = 10.5 - (0.07 + 0.43)

= 10.5 ‑ 0.5 = 10% P.A. = 10/12 = 0.8333% = .0083

R (monthly payments) = ?

a). Assuming GNMA is fully amortized

  1. Calculating the monthly payments:

15,000,000 = R*[{1-(1.00833)-360}/0.0083]

R = 15,000,000 / 113.989

=> R = $131591.4

  1. Calculating PV @ 7% market rate using monthly payments (R) calculated above:-

R = 131591.4; n = 360;

i = 7/12 = 0.5833% PA => 0.0058

P=?

P = 131591.4 * [{1-(1.00583)-360}/0.00583]

=> $19787172.4

b) The GNMA pass-through is only half amortized., assume there is a lump sum payment at the maturity of the GNMA pass-through that equals 60% of the mortgage pool's face value

  1. If there is a 50 percent amortization, the monthly payments are:-

15,000,000 = R*[{1-(1.00833)-360}/0.0083] + 7,500,000 / (1.00833)360

15,000,000 = R * 113.989 +378524

R = 14621476/113.989

R= $128270.94

  1. Calculating PV @ 7% market rate using monthly payments (R) calculated above:-

R = 128270.94; n = 360;

i = 7/12 = 0.5833% PA => 0.0058

P=?

P = 131591.4 * [{1-(1.00583)-360}/0.00583] + 9,000,000 / (1.00833)360

=> 131591.4 * 150.3683 + 454228.75

=> 19787175.11 + 454228.75

P = $20241403.86


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