This
post calculated the yield on a 30year fixed rate mortgage with points. The mortgage is held for 30 years. The calculation is made with the PMT, IRR
and EFFECT functions.
Question: Consider a 30year $500,000
fixed rate mortgage with a 6.0 % APR. What is the yield on the
loan if the lender charges 0 points, 1 point, or 2
points? Assume the loan is held for all thirty years.
Analysis: The yield on a loan with no
points is simply the APR. The reader can confirm this in the
following manner.
First, find the monthly payment for the loan
(=PMT(0.06/12,360,500000)= ($2,997.75))
Second, find the IRR of a series of cash flows starting at time 0
with a $500,000 disbursement followed by 360 monthly payments of $2967.75.
Observe the IRR is 6.0 % the same as the APR with no points.
This is the nominal rate.
The effective rate accounts for the fact that there are 12 payments in
the year.
EFFECT(0.06,12)=6.168%
When there are points the net disbursement at time 0 is the loan
balance minus the dollar value of the points. The dollar value
of points on a $500,000 loan is $5,000 when points are 1.0 percent and $10,000
when points are 2 percent. Net disbursements at time 0 are
$495,000 at 1 point and $490,000 at 2 points.
To get the yield take the IRR of the series of cash flows where
disbursement is made at time 0 and the monthly mortgage payment is made for 360
consecutive months. The results are presented below.
Yield
on a 30year FRM with 6.0 Percent Annual Mortgage
Rate
by Level of points


Points

0

1

2

IRR

6.000%

6.094%

6.189%

EFFECTIVE
RATE

6.168%

6.267%

6.368%

The IRR gives us the annual percentage rate. Again, use the
EFFECT function to get the yield after accounting for the 12 payments per
years.
The next post will examine yield of mortgage when there are points
and when prepayment occurs.
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