Financial Markets and Institutions
Financial Markets and Institutions
6th Edition
ISBN: 9780077641825
Author: SAUNDERS
Publisher: Mcgraw-Hill Course Content Delivery
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Chapter 24, Problem 8P

a)

Summary Introduction

To determine: The present value of $10million if the GNMA is fully amortized.

a)

Expert Solution
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Explanation of Solution

In this case 180(15 years x 12 months) monthly payments are there. The coupon rate at which each month in GNMA is 8.5% ‑ 0.5% = 8 percent per year, and the monthly GNMA pass‑through payment is:

 $10Million= {[1-(1(1+coupon rate12)Number of  monthly payments)](coupon rate12)}×PMT 10Million={[1-(1(1+0.0812)180)](0.0812)}×PMT  PMT = $95,565.21

Hence, the PMT is $95,565.21

The computation of current value of GNMA at a market rate of 5% is as follows:

Present value = × PMT×{[1-(1(1+Market rate12)Number of  monthly payments)](Market rate12)}= $95,565.21× {[1-(1(1+0.0512)180)](0.0512)}= $81,115.94

b)

Summary Introduction

To compute: The present value of $10million if the GNMA is only half amortized and pass through 50% face value of mortgage pools.

b)

Expert Solution
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Explanation of Solution

While considering the GNMA is only half amortized. At the maturity of the GNMA the payment is lump sum that is same as 50 % face value of mortgage pools.

In case of amortization at which 50% the monthly payments of GNMA are:

The computation is as follows:

 $10Million=(PMT× {[1-(1(1+coupon rate12)Number of  monthly payments)](coupon rate12)}+50%10million(1+coupon rate12)Number of  monthly payments=R)R={[1-(1(1+0.0812)180)](0.0812)}5Million(1+0.0812)180=$81,115.94

The computation of current value of GNMA at a market rate of 5% is as follow:

Present value = ( R×{[1-(1(1+Market rate12)Number of  monthly payments)](Market rate12)}+50%10million(1+Market rate12)Number of  monthly payments)= $81,115.94× {[1-(1(1+0.0512)180)](0.0512)}+50%10million(1+0.0512)180=$12,623,051.35 

Hence, the present value is $12,623,051.35

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