You acquire a debt security that is a claim on a mortgage pool (e.g., a Ginnie Mae pass-through...

Question

You acquire a debt security that is a claim on a mortgage pool (e.g., a Ginnie Mae pass-through security). The mortgages pay 9 percent and have an expected life of 20 years. Currently, interest rates are 9 percent, so the cost of the investment is its par value of $100,000.
a) What are the expected annual payments from the investment?
b) If interest rates decline to 7 percent, what is the current value of the mortgage pool based on the assumption that the loans will be retired over 20 years?
c) If interest rates decline to 7 percent and you expect homeowners to refinance after four years by repaying the loan, what is the current value of the mortgages? (To answer this question, you must determine the amount owed at the end of four years.)
d) Why do your valuations differ?
e) You acquire the security for the price determined in part (c) but homeowners do not refinance, so the payments occur over 20 years. What is the annual return on your investment? Did you earn your expected return?

Robert · Accepted Answer

The formula to calculate the amount of yearly installments is 
 
 
1
1 1
n
n
r r
A P
r


 
  
Here, we have 
A= amount of yearly installment 
P= principal 
r= rate of interest 
n= number of years 
we have the following information: 
P=$100,000 
n=20 years 
i=9% 
(a) 
The yearly installment amount is  
 
 
1
1 1
n
n
r r
A P
r


 
 
By substituting the values, we have 
 
 
 
 
20
20
1
1 1
0.09 1 0.09
100000
1 0.09 1
$10,954.67
n
n
r r
A P
r


 

 
 

  
The yearly installment amount for the new mortgage is $10,954.67 
(b) 
If the interest rate declines to 7%, the present value of the mortgage for 20 years is  
   1 1 1
n
i n
i
C F
PV
i i
 
  
   
   
Here,

You acquire a debt security that is a claim on a mortgage pool (e.g., a Ginnie Mae pass-through security). The mortgages pay 9 percent and have an expected life of 20 years. Currently, interest rates...

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