## Monday, July 8, 2019

### Mortgage Yields with Points

This post calculated the yield on a 30-year 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 30-year \$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 30-year 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.