Roth tax-deferred savings vehicles (IRAs and 401Ks) are frequently touted as superior to traditional IRA or 401K savings for young savers, sometimes for the wrong reasons. Both types of vehicles offer tax advantages for retirement saving. Roth contributions are taxed immediately, but they grow tax-free and are completely tax-free at withdrawal. Traditional IRA and 401k contributions (“traditionals”) are tax-deductible, but the contributions and growth are taxed at withdrawal. The key determinant of which type of plan contribution is best at a given time is the tax rate faced today relative to the years of withdrawal. Based on this consideration, the Roth is better (for today’s contribution) if today’s tax rate is lower. If today’s tax rate is higher than during the withdrawal period, the traditional plan is more advantageous.

Comparing the two types of saving vehicles must be done on a basis that is equivalent in terms of post-tax, post-contribution income. For example, suppose an individual with a current annual income of $50,000 desires to set aside 6% of their income in their employer’s Roth 401k. The individual’s marginal tax rate is 15% federal plus 5% state. Therefore, they must part with pre-tax income of $3,750 to generate a net $3,000 plan contribution (ignoring the FICA tax). The individual has a “disposable” income after taxes and saving of $50,000 – $10,000 (taxes) – $3,000 = $37,000. Instead, if the individual contributed $3,750 to a traditional 401k, their disposable income would be exactly the same. (The contribution is tax deductible, but the extra tax savings from the 401k deduction is invested in the plan.) This equivalence in terms of the current disposable income is crucial, because the extra contribution in the traditional plan made possible by the immediate tax deduction serves to offset the Roth’s later tax advantage. Megan McArdle, for whom I have tremendous respect, overlooks this point in a piece about Roths here. Moreover, the number of years of untaxed growth in a Roth does not matter if the traditional vehicle grows as well, contrary to one popular explanation of the Roth’s advantages.

Some Easy Math: The conclusions stated above can be deduced easily from basic equations for future value (FV – for the time of the last contribution) in the presence of proportional taxes:

Net FV(Roth) = Gross Monthly Contrib x FVfactor x (1 – tax rate @ contrib)

Gross FV(Trad) = Gross Monthly Contrib x FVfactor

Net FV(Trad) = Gross Monthly Contrib x FVfactor x (1 – tax rate @ w/drawal)

where FVfactor is a function of the return on savings (naturally assumed to be common to the plans) and the number of months of contributions. Obviously, the two plans are equivalent if the two tax rates are equal. While these equations assume that the plan values are compared at the time of the last contribution, the results are robust to longer or differing patterns of withdrawals, as long as the same gross returns are available to both plans (this statement ignores certain rules for mandatory distributions, discussed later).

Comparing Future Outcomes: The table below shows comparisons of Roth and traditional contributions under various scenarios (click on the “?” icon to view the table). The withdrawals in these examples are structured as fixed monthly payouts (annuities) over 30 years. Returns during “retirement” (4%) are assumed to be lower than during the years of contributions (7%). The two vehicles yield the same ultimate level of benefits if the tax rates are the same during the years of contribution and withdrawal (the first “panel” of four rows in the table). If the current tax rate is lower, the traditional vehicle benefits more from the immediate tax deduction than the Roth gains later via non-taxable withdrawals (the second and third panels). The opposite is true if the current tax rate is higher than during the years of withdrawal (the fourth panel). The rightmost column of the table shows the aggregate value of the government’s tax revenue on a time-valued basis, carried forward (traditional) or discounted (Roth) to the date at which contributions end. It should come as no surprise that the difference in the net value of the two vehicles to the saver is equal to the difference in the government’s take (but of opposite sign). If you expect your tax rate to be lower in retirement, you lose and the government wins if you elect to be taxed early on retirement saving, i.e., the Roth.

Likely Tax Rates? What tax rate assumptions are realistic for most savers? First, current marginal federal and state tax rates should be applied to gross Roth contributions. However, a strong argument can be made that tax rates during the period of withdrawal (traditional) should be lower than during the years of contribution. There are three resaons for this:

1) Retirement incomes tend to be lower than during working years for most savers, which often implies a lower tax bracket.

2) Just as importantly, withdrawals from accumulated savings may not represent marginal income, because they are often taxed across multiple brackets because they represent a substantial portion of retirement income. An average tax rate may be more appropriate for calculating the net benefit of withdrawals from a traditional plan. To some extent, this depends upon how social security benefits are taxed, since those benefits may represent “base income” for purposes of calculating an average tax rate applicable to plan withdrawals. Regardless, it can be argued that taxable withdrawals should be assessed at lower tax rates than taxable contributions.

3)   Finally, many retirees choose to spend their post-working years in states with lower or no state income taxes, such as Florida and Texas. This would imply an even greater advantage for traditional plans over Roths.

Despite these considerations, there are many young savers laboring in cubicles who are cheerfully anticipating much higher earning years ahead, even for those distant years of retirement from the corner office. For this group, it is possible that contributions to a Roth make sense, but probably not beyond a certain point in their careers, when their marginal tax rate rises above the likely tax rate they will face in retirement. By then, the Roth option will be foreclosed if their incomes exceed the Roth limits on earnings eligibility. Still, the Roth is probably less likely to pan out as the best choice for most workers currently above the 25% federal tax bracket and many at or below it.

Other Roth Advantages: There may be other potential advantages of Roth savings over traditional tax-deferred plans. One is that Roths give the saver more flexibility over the timing of withdrawals simply because the withdrawals are not taxed as ordinary income. (Early Roth withdrawals are subject to the 10% penalty tax (before age 59½, with exceptions.)) Perhaps more importantly, by taking the tax hit immediately on Roth contributions, with no tax liability on future earnings, a Roth has a more certain tax impact than a traditional plan. It may be comforting to think that one’s tax rate is likely to be low in retirement, but who can say how high tax rates will be in the future, given the sorry state of government finances? Then again, the federal government could one day elect to violate its pledge not to tax Roth withdrawals, or it could even impose a wealth tax with broad applicability to all Roth and traditional plan balances. Death and taxes may be certain, but the integrity of government is not.

Finally, there are no mandatory Roth distributions at any age. This flexibility may be useful to some retirees, since complete deferral of taes beyond age 70½ is impossible on traditional plan assets. In terms of estate planning, the final accumulation of assets in a Roth can be passed along to heirs income tax-free. Therefore, an inherited Roth will have more value than a traditional plan if the heirs are in relatively high tax brackets. This argument is often used in favor of Roth conversions from traditional plans, even for individuals of advanced age. Extending the logic, even if traditional plans had no mandatory distributions, Roths would have an estate planning advantage beyond age 70½ if the heirs are in higher tax brackets than their benefactor. In any case, the traditional option is foreclosed for this purpose, given the mandatory distribution requirement on traditional tax-deferred savings.