You should think of this as a selection
between two investments. One investment is securities. The other is a "less
mortgage" investment. By making a larger down payment you are borrowing
less, and the amount you are borrowing is being paid off over a shorter period.
When you compare investments, you should
select the one that provides the highest yield, after adjusting for differences
in their risk and liquidity. (Liquidity is how easy it is to convert the
investment back into cash). Whoever sells you a security will be able to tell
you the yield, and usually they can provide information on risk and liquidity as
well. Many investors do their own research on securities, and sources of
information are readily available.
Measuring the yield on the "less
mortgage" investment is more of a challenge. Many people have difficulty
with the concept. They are accustomed to thinking that an investment involves
paying money today and receiving a return flow of money in the future, which is
what happens when you purchase a security.
But a decision not to borrow is the same
thing. The money you give up today is the money you would have had if you had
borrowed. And the return flow in the future consists of the larger payments you
avoid by not borrowing. It also includes the smaller debt you would have if you
terminate the loan anytime prior to term.
In your case, the amount invested is the
$100,000 you don’t borrow, which is the down payment. The return on that
investment has two parts. First, the monthly payment is $548 lower for 15 years.
The lower payment is due to the smaller loan amount and the lower interest rate,
which are only partly offset by the shorter term. Second, at the end of 15
years, you save $152,219, which is the amount you would have owed at that point
had you taken the 30-year loan.
The yield on the "less mortgage"
investment over 15 years is 8.33%, and it is risk free. Since there are no
risk-free investments around that generate this kind of return, I would vote for
that option.
I calculated the yield with a spreadsheet
program that handles all differences between the larger and smaller mortgage.
This includes points and other upfront charges, which must be taken account of
in an accurate yield measurement. It also shows the yield over every possible
time horizon.
For example, if both mortgages have an
upfront charge of 2 points (2% of the loan), the yield would increase from 8.33%
to 8.54% over 15 years, and from 8.61% to 9.08% over 5 years.
The "less mortgage" investment may
have less liquidity than marketable securities, since you can’t sell a piece
of your house as you can sell some of your securities. With the significant
equity in your house, however, getting a home equity loan at favorable terms is
very easy. Differences in liquidity would not change my selection.
Readers who want to use the spreadsheet to
analyze their own unique situation can get it by clicking on Invest
in Less Mortgage.
Copyright Jack Guttentag 2007