“In your columns on repaying mortgage loans, you skip over a detail that I have often wondered about … I don’t think that saving 6 percent interest on a mortgage is quite the same as earning 6 percent on other investments because mortgage interest is deductible … I get further confused by the possibility that the income taxes due on other investments may be deferred if they are in a 401K or other tax-deferred retirement account….”

In numerous articles, I have argued that mortgage repayment should be viewed as an investment with a yield equal to the mortgage rate — and that this yield should be compared to those available on other low-risk investments. The “low-risk” qualifier is important, because mortgage repayment has zero risk to the borrower.

You are right that in making such comparisons, account should be taken of possible different tax treatment. Mortgage interest is always deductible on first mortgages up to $1 million, but other investments can be subject to different tax rules. Four different situations are worth distinguishing.

The Alternative Investment is Fully Taxable: In this case, the before-tax rate on the mortgage, say 6 percent, can be compared to the before-tax yield on the other investment. If it is a corporate bond yielding 5 percent before tax, the mortgage repayment is the better investment.

We could also make this comparison after tax, but the result will be the same. The after-tax return is equal to R x (1 – T) where R is the before-tax return and T is the tax rate. If the borrower is in the 40 percent tax bracket, the after-tax return on mortgage repayment is 6 percent x (1 – .4), or 3.6 percent, and the after-tax return on the bond is 3 percent. Whether measured before or after tax, mortgage repayment is the better investment.

The Alternative Investment is Tax Exempt: In this case, you must make the comparison after tax for them to be comparable. If the alternative investment is a 4 percent tax-exempt bond, for example, the 4 percent after-tax return beats the 3.6 percent after-tax return on mortgage repayment.

The Alternative Investment is Taxable But the Tax Payment is Deferred: This is the most difficult situation to analyze, and it requires an assumption regarding when the taxes will be paid on the alternative investment. The longer the deferment, the lower the effective tax rate — the tax rate adjusted for the deferment.

The best way to compare investment in mortgage repayment with investment in a tax-deferred fund is to compare future values at the end of the period when the taxes are due on the tax-deferred investment. You need a financial calculator, but it is pretty simple.

For example, lets compare investing $100,000 in repayment of a 6 percent mortgage with investing it in a fund that pays 5 percent before tax, and taxes are deferred for 10 years. For the mortgage, we enter 10 years for the period, 3.6 percent for the after-tax return, $100,000 as the present value, and we obtain a future value of $142,429.

For the alternative investment, we do the same except we enter 5 percent as the return, and we get a future value of $162,889. However, taxes are now due on the $62,889 of interest, which reduces the future value to $137,734. The mortgage repayment does a little better.

For readers who are calculator-challenged, here is a quick and dirty shortcut. If your tax rate is about .4, multiply it by the following numbers for tax-deferred investments lasting for the specified number of years: For five years, .95; 10 years, .89; 15 years, .84; 20 years, .78; and 25 years, .72. If your tax rate is closer to .2, use the following adjustment factors: .98, .95, .91, .88 and .85.

Using the previous example, multiply the tax rate of .4 by .89 to get an effective tax rate of .356. Multiplying the before-tax return of 5 percent by (1 – .356), you get an after-tax return of 3.22 percent.

The Alternative Investment Shields Current Income: This is the easiest case. An alternative investment that shields current income is going to be the best possible investment for anyone who pays income taxes. It will beat mortgage repayment hands down. The amount of income that can be shielded is always restricted by law, but those not using this privilege to the maximum are guilty of financial self-abuse.

The writer is professor of finance emeritus at the Wharton School of the University of Pennsylvania. Comments and questions can be left at www.mtgprofessor.com.

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