# It is dangerous to rely on rules of thumb for calculating how long you need to hold a mortgage to make it worthwhile to pay points in exchange for a lower rate. The proper way is to calculate a break-even period that takes account of all costs and benefits, including tax savings and interest opportunity costs.

The Break-Even Period For Paying Points on a Mortgage
October 30, 1999, Revised August 29, 2007, April 10, 2011

"Re your column on 'How Much Is a 1/4 Percent Rate Reduction Worth?', as a mortgage broker of 20-years standing, I want to add a simple explanation that I always give to my clients. On a \$200,000 loan, a 1/4% lower rate reduces the monthly payment by about \$33 a month whereas 1.5 points amounts to \$3,000. Dividing 3,000 by 33 you get 91 months you have to wait to break evenâ€¦Most people see the light and opt out of doing it."

Sometimes the light can blind.

## Break-Even Periods For Paying Points Based on Rules of Thumb Can Be Far Off the Mark

The broker quoted above is referring to a case where a borrower who had previously agreed to pay 6.75% on a 30-year fixed-rate mortgage, was offered 6.50% for an additional 1.5 points. The broker divided the additional \$3,000 in points by the \$33 saving in the monthly payment from the lower rate to determine a breakeven period of 91 months. What's wrong with that?

Plenty! First, it ignores differences in the loan balance in the two cases. The lower rate mortgage amortizes faster -- the borrower owes less after any period. On a \$200,000 loan, for example, the borrower with a 6.50% loan owes \$178,807 after 91 months where the borrower with the 6.75% loan owes \$179,611.

Second, the back-of-the-envelope method ignores the time value of money. Money paid today is worth more than money paid in the future. The \$3,000 discount paid upfront, for example, would have earned about \$2,000 in interest if it had been invested at 7% rather than being paid out as part of the mortgage transaction.

Third, the broker's approach ignore taxes, which affect the answer because points and interest are treated differently by the tax code. On a home purchase transaction, points are fully deductible in the year the loan is made whereas interest payments are deductible in future years as they are paid.

## Proper Calculation of the Break-Even Period For Paying Points

The breakeven period is the period over which the cost to the borrower would end up the same whether the borrower took the high points/low rate mortgage or the low points/high rate mortgage. To calculate it properly, the cost must includes points, monthly payments, the lost interest earnings on both the points and the monthly payments using the borrower's investment rate, less tax savings and less the reduction in the loan balance.

Charles Freedenberg and I have developed rate/point calculators that take account of all the factors that affect the break-even period. It is very simple to use. Just indicate whether the transaction is a house purchase or a refinancing, and enter the loan amount, term, income tax bracket and reinvestment rate. For FRMs, the calculator is The Break-Even Period for Paying Points on Fixed-Rate Mortgages. The comparable version for ARMs is The Break-Even Period for Paying Points on Adjustable-Rate Mortgages.

The income tax bracket is the rate you pay on the last dollar of income you earn, sometimes referred to as the "marginal tax rate". If you pay taxes but don't have a clue, enter "28"; any error will be small.

The reinvestment rate is important. To get the lower rate, you pay higher points, and the money used to pay those points could be invested. Similarly, to get lower points you pay a higher rate, and the money used to make the larger monthly payments could be invested. If your spare money is held in a money market fund on which you earn 2% or 3%, you should use that figure. If you own a stock portfolio that returns 15%, you will want to use a higher reinvestment rate, although probably not 15% because that return is far from a sure thing.

When you click on the "Compute" button, you will get the break-even period calculated before and after-taxes. In both cases, the calculator shows you the costs on both loans over the period to break-even. The costs consist of the sum of the monthly payments, the points, and the interest on the payments and points, less the increase in equity from loan repayments.

In the after-tax case, tax savings are deducted from the mortgage payments and the points, and interest is calculated on the net figures.

The total cost of the two loans will seldom be exactly the same to the penny over the break-even period. The breakeven month is the month when the total cost of the low interest rate loan flips from being above that of the high interest rate loan to being below.