Another Approach to Roth IRA Conversions

I recently read two misleading items on Roth IRAs in back issues of the JofA: a tax brief, “Risky Roth IRAs” (Dec.98, page 123), and a letter, “More about the Elusive Roth IRA Advantage” (Jan.00, page 102). The first does not correctly state the total future value of the contributory Roth because it omits the principal amount. There is also a subtle methodological flaw in both items: The fundamental distinction between tax-sheltered growth vs. taxable growth was ignored in computing opportunity costs.

When a Roth IRA (either contributory or a conversion) is selected over a traditional IRA, a potential future tax bill generated by the traditional IRA can be preemptively paid using nonsheltered assets. Typically, these nonsheltered assets, if not otherwise paid as taxes, would remain invested in a taxable account. Thus the opportunity cost of the prepayment should be computed using the anticipated rate of return on taxable assets, which is, of course, almost invariably lower than the rate of return on sheltered assets (because of capital gains taxes). Thus, no comparative analysis of Roth vs. traditional IRAs that ignores capital gains taxes, and that uses a single interest rate to compute all present and future values, can be satisfactory.

For example, if the 10% rate of return used in “Risky Roth IRAs” is assumed to be the return on taxable assets, and long-term capital gains taxes are 20%, then the equivalent sheltered rate of return must be

10% .80 = 12.5%

At 12.5% growth, the projected future value of the Roth IRA after 25 years will be twice as large as the value claimed in the tax brief. Consequently, contrary to the conclusions drawn from that example (where income tax rates are the same before and after retirement), the Roth is superior to the traditional IRA.

The letter cited above also seems to assume that one interest rate alone can be used to analyze both Roth and traditional IRAs.

I find it disheartening that the same fundamental mistake of ignoring taxation could be repeated in the JofA. I hope the editors will be alert to its appearance in the future.

Ricardo Diaz
Professor of Mathematics
University of Northern Colorado
Greeley, Colorado