"I have been advised
not to borrow more than 80% of the value of my property so that I won�t
have to purchase mortgage insurance. The insurance premiums I have been
shown, however, only amount to about � of 1% of the loan balance per
year, which seems like small potatoes. Am I wrong?"

Is a 4-ounce potato
"small?" Anyone can weigh a potato, but judgments of
"small" and "large" are in the eyes of the eater. It
is similar with mortgage insurance.

Since measuring the cost of
mortgage insurance is more difficult than weighing a potato, I�ll show
you how to do it. But the measurement is just step one. Step two is
deciding what it means for you, which you have to do for yourself. But to
help in that, I am also going to show you how to convert the mortgage
insurance decision into an investment decision, with which more people are
familiar.

Lets take a concrete example.
Assume I can obtain a 15-year fixed rate mortgage at 7.5% and zero points
to purchase a $100,000 house. Without mortgage insurance, I could borrow
up to $80,000 (80% of property value), whereas with mortgage insurance I
could borrow up to $95,000 (95% of property value). The insurance premium
on the $95,000 loan is .79% of the balance per year for the first 10
years, after which it drops to .20%.

The best approach to
measuring the cost of the insurance premium is to view the loan of $95,000
as consisting of 2 loans: one for $80,000 which has an interest cost of
7.5% consisting solely of the interest rate; and one for $15,000 the cost
of which includes both the interest rate and the insurance premium. The
interest cost on the $15,000 loan turns out to be 12.7% if you stay in
your house for up to 10 years, declining slowly after that to 12% if you
stay a full 15 years.

Since the insurance premium
is only .79%, how can the cost of the $15,000 loan be 5.2% higher than the
cost of the $80,000 loan? The reason is that while you are borrowing an
additional $15,000, you pay the premium on the entire $95,000.

The cost calculation above
assumes that you take a fixed-rate mortgage with a loan-to-value ratio of
95%, and pay mortgage insurance for 10 years. Change the assumptions and
you change the cost. For example:

On 85% and 90% loans, the
cost is 13.4% and 12.5%, respectively. While the insurance premiums
are smaller, the incremental loans are also smaller.

On smaller loans within
the same mortgage insurance premium bracket, the cost is higher. For
example, the cost of insurance on a 91% fixed-rate loan, which has the
same premium as a 95% loan, is 14.3%.

Adjustable rate mortgages
have higher insurance premiums, and therefore higher costs, than
fixed-rate mortgages.

Mortgage insurance costs can
be reduced if you manage to get the insurance removed early. For example,
if the insurance on a 95% fixed-rate mortgage is removed in 5 years but
you stay with the mortgage for 10, the cost falls to 10.8%. However, if
you move in 5 years and pay off the mortgage, there is no saving.

Here is a handy rule-of-thumb
for estimating the interest cost on the incremental loan made possible by
mortgage insurance, assuming the loan runs 10 years. Divide the total loan
by the incremental loan and multiply the result by the annual insurance
premium, e.g.,95,000 divided by 15,000 equals 6.33 which multiplied by
.79% equals 5%. Adding that to the interest rate gives an estimated cost
of 12.5% on the incremental $15,000 loan.

Is an increase in interest
cost of 5 percentage points on the incremental loan "small
potatoes"? The best way to answer this question is to view the choice
between the smaller loan without insurance and the larger loan with
insurance as an investment decision. Taking the smaller loan means
investing $15,000 in a larger down payment that provides a risk free
return of 12.5%. Is this an attractive investment?

Not if you don�t have the
$15,000. Even if you have it, you would be locking it up for an indefinite
period, although you might borrow against it using a home equity loan. Or
you may not be impressed with a 12.5% return if you can earn more than
that in your business, or are paying more on credit card loans. On the
other hand, if you have a bond portfolio earning 7%, you might well want
to liquidate it to invest in the larger down payment.

In short, a 12.5% cost on an
incremental loan made possible by mortgage insurance is like a 4-ounce
potato. It will be "small" to some and "large" to
others.

Copyright Jack
Guttentag
2002

Jack Guttentag is Professor of Finance Emeritus at the Wharton School of the University of Pennsylvania. Visit the Mortgage Professor's web site for more answers to commonly asked questions.

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