“I am buying a house for $180,000, which I could payfor by selling assets, but everybody tells me to leave my assets alone and takeout a mortgage. Their advice makes me nervous because it is always based ongeneralities, such as ‘you want the mortgage as a tax shelter’ or ‘you shouldleave your investments alone.’ They don’t know anything about my tax status ormy investments. Is there a better way to make this decision?”
There is a better way. Use a spreadsheet called “Future Net Worth,”which can be downloaded from my Web site.
The spreadsheet allows you to measure your future net worthon the assumption that you pay all cash, then measure it again on theassumption that you take a mortgage, and see where you end up in each case. Thespreadsheet calculates your net worth year by year in both cases. I willillustrate the process, using my own assumptions, which will be simplified tomake the explanation easier to follow.
I assume you are purchasing a house for $180,000 and yournest egg also amounts to $180,000. You can use the nest egg to pay for the house,or you can leave it untouched and borrow the $180,000. (Of course, thespreadsheet also allows any combination in between, such as making a 20 percentdown payment from the nest egg and borrowing the balance.) The loan would be a30-year fixed-rate mortgage at 6 percent with a monthly payment of $1,079. Iassume that you have $1,500 of income on top of that available for investment.
Hence, if you take the mortgage, you have $180,000 plus$1,500 a month to invest. If you pay all cash, you have no lump sum to invest,but you do have $2,579 available every month, which is the $1,500 plus themortgage payment of $1,079 you wouldn’t be making. I assume you are in the 28percent tax bracket, which provides tax savings on the mortgage interest, and atax payment on the investment income.
The most important determinant of the outcome is the assumedrate of return on investment compared to the mortgage rate. For example, if youearn 6 percent on your investments, matching the rate you pay on the mortgage,your net wealth after 15 years is $831,602 if you borrow the $180,000, and$831,599 if you pay all cash. If the rates are the same, future wealth will bethe same — the trivial difference I found is a rounding error.
These numbers understate the actual wealth you would havebecause I have assumed zero property appreciation. Since the future value ofthe house will be the same regardless of how you finance the purchase,appreciation has no bearing on which mode of financing is better.
Now let’s assume that you can earn 9 percent on yourinvestments. This is a reasonable assumption if you invest in a diversifiedportfolio of common stock. It is an appropriate assumption if you are youngenough to have a long time horizon, and can maintain an equable disposition inthe face of short-run fluctuations in your wealth. On this assumption, yourwealth after 15 years would be approximately $1.05 million if you borrowcompared with $961,556 if you pay all cash.
Rule number one is simple: If the rate of return on yourinvestments exceeds the mortgage rate, borrowing leaves you better off thanpaying all cash.
Now let’s assume that you earn only 4 percent on yourinvestment. This is a reasonable assumption if you have an extremelyconservative investment policy, a relatively short time horizon, or both. Youhave guessed correctly that you will do better paying all cash in thissituation. After 15 years, your wealth would be $759,824, compared with$716,727 if you borrow.
But, there is an important proviso. My calculation assumesthat if you pay all cash for the house, you invest (at 4 percent) the $1,079per month you would have paid on the mortgage. If you spend it instead, yourwealth after 15 years will be only $517,211, or much less than if you hadborrowed, despite the fact that the borrowing rate exceeds the investment rate.The mortgage forces you to save whereas the all-cash strategy doesn’t.
Rule number two includes the proviso: If the rate of returnon your investments is less than the mortgage rate, paying all cash leaves youbetter off than borrowing, provided you save an amount every month equal to themortgage payment that you would have had following a mortgage strategy.
The writer is professor of finance emeritus at theWharton School of the University of Pennsylvania. Comments and questions can beleft at www.mtgprofessor.com.
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Copyright 2007 Jack Guttentag