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October 30, 1999
"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 even�Most
people see the light and opt out of doing it."
This
mortgage broker is incorrectly calculating a number that may be of
critical importance to a borrower's decision. Unfortunately, such
back-of-the-envelope methods of answering complex questions are typical of
what a borrower runs into when shopping for a mortgage through traditional
channels.
The broker 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.
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.
Pulling all these factors together
to calculate a correct breakeven period is not rocket science, but you
can't do it in your head or with a standard calculator. I would guess that
not one loan officer in a hundred has access to the technology needed to
do this calculation.
But the good news
is that Charles Freedenberg and I have developed a rate/point calculator
that takes 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. Just click here. 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 4% or 5%, 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 never be exactly the same 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.
Copyright Jack Guttentag
2002
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