Yield on a Mortgage with
Points
Post uses PMT and IRR
Question: Consider a 30year 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.
Find the monthly payment for
the loan (=PMT(0.06/12,360,500000)= ($2,997.75))
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.
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 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. The effective rate accounts for monthly payments as described in a previous post. The effective rate was obtained with the EFFECT function.
Go here for a discussion of the EFFECT function.
http://www.dailymathproblem.com/2017/08/theeffectfunction.html
Go here for a discussion of the EFFECT function.
http://www.dailymathproblem.com/2017/08/theeffectfunction.html
Other exercises involving points:
How do yields of 15year FRM
loans vary with points?
What are the yields of a
30year mortgage when the home buyer moves or refinances and repays the loan
after 5 years? What are yields when
repayment occurs after 7 years?
(THIS IS MY NEXT
PROBLEM. WILL PUT LINK TO THIS PROBLEM
HERE SOON.)
Authors Note: I am continuing creating posts
solving financial problems with Excel functions. Go to the page below for the current list of
problems.
Come back to this page
frequently because I am adding lots of new questions.
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