Your
approach is right. A larger down payment is an investment that yields a
return that consists in part of the interest rate on the money you aren't
borrowing. If you put an additional $10,000 down, for example, you are
borrowing $10,000 less and you save the interest that you would have paid
on it. But there may be other savings as well that make the return higher
than the interest rate on the loan.

First, most borrowers pay points or other loan fees expressed as a percent of the loan amount. If you
borrow $10,000 less, you save not only the interest but the upfront fees
on the $10,000. If you are paying 3 points on your fixed-rate mortgage,
for example, and your time horizon is 7 years, the rate of return on the
increase in down payment is 8.08% rather than 7.50%. Fees of fixed dollar
amount don't affect the return because they aren't reduced when the loan
amount is reduced.

A second possibility is that the
larger down payment reduces or eliminates mortgage insurance, which must
be purchased when the down payment is less than 20% of property value. In
such event, the return on the larger down payment includes not only the
savings in interest and points but also the mortgage insurance that is
eliminated by the larger down payment.

If a $10,000 increase in down
payment increases the ratio of down payment to property value from 10% to
20%, for example, you eliminate a mortgage insurance premium of about .52%
on a fixed-rate mortgage. This would bring the return on the increase in
down payment over 7 years to 13.00%, which is what you are earning on your
other assets. The difference is that the return on investment in a down
payment has no risk to you whereas your other investments are risky. If
the returns are about the same, the down payment investment is preferable.

Still a third possibility is that
the larger down payment reduces the interest rate by bringing the loan
amount below $252,700.
Because the Federal secondary market agencies, Fannie Mae and Freddie Mac,
cannot purchase mortgages larger than $252,700, the market breaks at that
point. Interest rates on loans larger than $252,700 are 1/4 to 3/8%
higher.

If you are purchasing a house for
$285,000, for example, an increase in down payment from 10% to 20% would
be $28,500, and the loan amount would drop from $256,500 to $228,000.
Assuming the rate falls from 7.5% to 7.25%, the return on the down payment
would rise to 14.95%. The rate reduction of .25% results in an increase in
the return on the additional down payment of almost 2% because the rate
reduction applies to the entire loan while the benefit is credited to the
increase in the down payment.

The numbers I quoted above all
come from a new calculator on my web site that calculates the rate of
return earned on amounts invested in a larger down payment. The calculator
is easy to use, even if you don't understand everything you just read. You
just tell the calculator the down payment increase you want to test, along
with the other obvious pieces of information that it needs, such as the
term, and it does the rest. To use the calculator, click on Rate
of Return From Investing in a Larger Down Payment .

It took me about a minute to do
these three passes at your problem, but I'm familiar with the calculator
so it might take you 2 minutes. If you give the calculator your tax
bracket, it will also calculate the return after taxes. But if you want to
make rate of return comparisons with other assets, you must remember to
convert the returns on the other assets to an after-tax basis as well. You
do that by multiplying the before-tax return by 1 minus your tax rate. If
you are in the 28% tax bracket, for example, a before-tax return of 10%
becomes 7.20% after tax.

Copyright Jack Guttentag 2002