One hundred identical mortgages are pooled together into a pass-through security. Each mortgage has a $150,000 principal, a fixed annual interest rate of 8 percent (paid monthly), and is fully amortized over a term of 30 years.
-What is the present value of the mortgage pass-through if, immediately after origination, interest rates increase to 8.25 percent per annum?
A)$15,000,000.
B)$14,650,591.
C)$14,000,000.
D)$15,115,493.
E)$15,267,549.

Question

Quizplus · Accepted Answer

First, we need to calculate the monthly payment on each mortgage using the formula:

PMT = (P*r/12) / (1 - (1+r/12)^(-n*12))

where:
P = principal = $150,000
r = annual interest rate = 8% / 12 = 0.006667
n = term in years = 30
PMT = $1,099.27

Next, we need to calculate the total monthly cash flow from the pool of mortgages, which is simply the sum of the monthly payments:

Total cash flow = $1,099.27 * 100 = $109,927

To calculate the present value of the pass-through security, we need to discount the future cash flows using the current interest rate (8%). We could use the PV formula in Excel, but since the cash flows are constant, we can also use the annuity formula:

PV = PMT * ((1 - (1 + r/12)^(-n*12)) / (r/12))

where:
r = 8% / 12 = 0.006667
n = 30

PV = $109,927 * ((1 - (1 + 0.006667)^(-30*12)) / (0.006667)) = $14,650,591

Finally, we need to adjust for the increase in interest rates. To do this, we can use the PV formula again, but with the new interest rate (8.25%):

PV (new) = $109,927 * ((1 - (1 + 0.006875)^(-30*12)) / (0.006875)) = $14,228,049

Therefore, the present value of the mortgage pass-through security decreases to $14,228,049. The best choice is B.

One Hundred Identical Mortgages Are Pooled Together into a Pass-Through