## Wednesday, August 27, 2014

### What is more important house price or mortgage interest rate?

The cost of 0.125 percentage points

A recent CNBC article suggests that mortgage interest rates are a more important determinant of the home purchase decision than house prices.

A quote from the article:

"It never ceases to amaze me how hung up mortgage borrowers can be on rate," said Matthew Graham of Mortgage News Daily. "In fact, a lot of times we have to remind them that the .125 percent difference in rate only amounts to X dollars and they're surprised."

The issue of a 0.125 percent difference in rates is a red herring that is not applicable for many real world situations because often differences among options are much larger than 0.125.

Rate differentials due to FICO score problems are much larger than 0.125.

When rates fall the ability to refinance is crucial.   A marginal borrower that gets a slightly higher rate may pay much more over the life of the loan because of her inability to refinance.

The rate difference across mortgage types is huge right now.   A borrower capable of using a 7/23 ARM or a 15-year FRM might have an interest rate more than 1 full percentage point lower than the 30-year FRM.

Still it is worth analyzing the lifetime loan costs attributable to a 0.125 percentage point difference in interest rates.

There are two components to the lifetime cost differential stemming from the 0.125 percentage points.   The first component involves the lower monthly mortgage payment.   The second component involves differences in the rate at which the mortgage is paid down.

The total value of the cost savings from the lower mortgage interest rate also depends on the length of time the person holds the mortgage.

Questions:   What is the difference between a 0.125 percentage point difference in mortgage rates on mortgage payment and the pay down of the mortgage balance over a 5, 10, 15, 20, 25 and 30 year period for a 30-year mortgage with 4.0% interest rate and a 4.125% interest rate?  What is the future value of both the lower mortgage payment and the faster equity build up under the two interest rate assumptions?

Assume a \$500,000 mortgage.

Calculations:

The monthly mortgage payment on the 4.0% loan and the 4.125% loan are calculated directly from the PMT function.  The difference summarized below is \$36 per month.

 Rate 0.04 0.04125 0.00125 Period 360 360 0 PV 500000 500000 0 FV 0 0 0 TYPE 0 0 0 Mortgage Payment -\$2,387 -\$2,423 -\$36

The mortgage balance reduces faster at the lower interest rate.  However, by definition after 30 years both 30-year FRMs have a \$0 balance.

The mortgage balance reduction calculation is obtained by plugging rate, number of payments, payment amount, PV of the loan and loan type into the payment function.   PMT is calculated above and other parameters are given in the problem.

 Impact of the 0.125 percentage points on loan balances Loan Balance After 5 Years -\$452,238 -\$453,144 -\$907 Loan Balance After 10 Years -\$393,920 -\$395,576 -\$1,656 Loan Balance After 15 Years -\$322,714 -\$324,846 -\$2,132 Loan Balance After 20 Years -\$235,772 -\$237,946 -\$2,174 Loan Balance After 25 Years -\$129,616 -\$131,178 -\$1,562 Loan Balance After 30 Years \$0 \$0 \$0

The loan balance impact is not large for this 30-year FRM problem.  It is a bit over \$2,000 for a borrower who holds the property for 15 years.

\$36 per month does not sound like much but the mortgage is for 30 years.   The future value of the monthly payment differential also includes interest.

 FV of Mortgage Payment Differential Years FV @ 4% FV @ 4.125% 5 \$2,398 \$2,406 10 \$5,326 \$5,362 15 \$8,902 \$8,993 20 \$13,267 \$13,455 25 \$18,597 \$18,937 30 \$25,105 \$25,672

Most people hold their mortgage for around 7 years so for the typical mortgage holder we are talking about \$4,000 on a \$500,000 loan.

However, the person who holds the mortgage for 30 full years will pay around \$26,000 more on the loan because of the 0.125 percentage points.

Concluding Thoughts:  Is the 0.125 percentage point the actual excess interest rate on your loan.  If so, the penalty is small.   However, you may be able to save far more than 0.125 percentage points by waiting a bit and reducing your FICO prior to purchasing your house.

As I said above, the CNBC quote is a bit of a red herring.  Rates are more important than depicted by this problem because the spread among alternatives can be very large and issues like the ability to refinance are also important.

Related Issue:  One of the issues where rates matter a lot involves the mortgage term decision.   The term structure of mortgage rates remains fairly steep in that the 30-year FRM remains substantially higher than the 15-year FRM.  A 15-year FRM (even at a lower interest rate) entails higher payments but the 15-year FRM is still probably for most of us the best investment out there.

I wrote this post on the mortgage term decision in 2013 but the term structure is still steep and this post is still relevant today.