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April 22, 2002
"We are turning 50 and soon will be
selling our house to buy another. We have no savings aside from the equity in
our current house, which is approximately $180,000. We plan to work for another
15 years, during which time we will have available about $1500 a month for
mortgage repayment or investment. Should we use the $180,000 to pay cash for our
next home, or should we take out a mortgage and invest that money?"
Many couples at your stage of life face this
type of decision. There is no one answer that is right for everyone, but there
is one right way to assess the decision.
Assuming that your objective is to be worth
as much as possible when you retire in 15 years, you have two options to
compare. Under the mortgage option, you purchase your house with a new mortgage
that I assume is $144,000 -- 80% of the $ 180,000 sale price � at 7% for 15
years. In this case, you are free to invest $144,000 as you see fit. The amount
available for investment monthly, however, is only $206, which is the difference
between the $1500 you have available and the monthly mortgage payment of $1294.
Under the all-cash option, you use all of the
$180,000 realized from the sale of your current house to pay for the new one.
You thus have no investment funds at the outset. But you have no mortgage
payment, either, so all of your monthly discretionary income of $1500 can be
invested.
To help analyze this decision, I have
developed a spreadsheet that is available by clicking on Spreadsheet.
The spreadsheet measures your net worth year-by-year, taking into account tax
savings on the mortgage and tax payments on the investments. You make two passes
with the spreadsheet, one assuming all-cash, the other assuming a mortgage, and
compare the net worth in the two cases after 180 months -- or any shorter
period, if you think you might be moving out earlier.
In the all-cash case, your financial net
worth is simply the value of your monthly investments plus accumulated interest
net of taxes. I assumed you could earn 3% on your investments, which is 2.16%
after taxes if you are in the 28% tax bracket. In 15 years, your $1500 a month
will accumulate to $318,537.
In the mortgage case, you can invest $144,000
plus $206 a month plus tax savings on the mortgage. After taxes, these
accumulate over 15 years to $199,043, $43,679 and $30,701, respectively. (If you
stopped short of 15 years, you would have to deduct the mortgage balance from
this, but at 15 years the balance is zero.) The total is $273,423, or $45,114
less than in the all-cash case.
While the spreadsheet includes the value of
your house in net worth, I omitted it above because it is the same whether you
borrow or pay all cash.
While there are many factors affecting the
results, as you will see if you try the spreadsheet, the most critical variable
is the interest rate you can earn on your investments, relative to the mortgage
rate. If the investment rate is below the mortgage rate, as it would be for most
borrowers, your future net worth is higher when you purchase the house for
all-cash.
Few borrowers can find safe investments that
yield a return as high as the rate they have to pay on a mortgage. An exception
might be borrowers with businesses of their own in which they can earn a higher
return.
But there is a very important proviso to the
conclusion that most borrowers would do better buying for all-cash. To end up
ahead using the all-cash option, you must invest the $1294 that you would
otherwise have used to repay your mortgage. This requires discipline. If the
all-cash option is viewed as an opportunity to spend the money that otherwise
would have been used to repay the mortgage, choosing the all-cash option will
leave you with a lower net worth down the road.
Copyright Jack Guttentag 2002
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