McQ wrote: ↑Sun Aug 01, 2021 5:27 pm
In hopes of advancing the discussion of how to model Roth conversion outcomes, allow me to introduce McQuarrie’s rule:
Sooner or later, in any such discussion, a poster will introduce a simple 2-period game “for clarity,” in which the conversion occurs in period 1 and a total distribution occurs in period 2.
Outcomes will be summarized with reference to the commutative property of multiplication. The poster will cite this property as conclusive proof that if tax rates are the same in period 1 and period 2, then the Roth conversion must be a wash (or exactly breakeven); whereas if future tax rates are higher, the conversion was the right decision and must produce a better after-tax outcome. End of story.
The OP, who introduced the question of how to model outcomes over time, will protest that the example is too simple and does not clarify things at all. The 2-period poster will respond along the lines of “what part of simple arithmetic did I not understand?” The ensuing dialogue, if it occurs, will satisfy no one, until finally a third party will opine that there are too many future unknowns, just convert up until it feels right.
To advance the discussion, let me suggest that Woodspinner is attempting to model an n-period game, n > 2 (and mostly, > 20). Since he is attempting to model real world results under the US system of taxation, as it is today and as it will become, Woodspinner must model a very particular kind of n-period game. Properties:
1. n can never be known until the game is over
2. Fractional distributions from the TDA of 1/k occur in each of the n periods, and each such distribution is subject to the then prevailing rate of tax
3. The fraction 1/k is set by rule (aka, the RMD schedule), and initial fractions are very small, k about 27; however, fractions are progressive, growing each year up until a limit of k = 2
Once the problem is conceptualized in these terms, the commutative property of multiplication becomes irrelevant, because the no-conversion and the conversion scenarios are not exposed to tax at the same time or over the same n of periods.
A simple n=3 example may help. Appreciation is 10% in each period; all accounts are invested in the same asset; tax is always 24% ordinary, 15% capital gains and dividends.
n=1: Either a conversion of $100,000 is made, and tax at 24% is deducted, creating an initial Roth balance of $76,000; or no conversion occurs, leaving $100,000 in the TDA
n=2: if no conversion, there is now $110,000 in the TDA just before an RMD is taken. That (age 72) RMD will be $4029; tax of $967 is due. The remaining $3062 is invested in a taxable account. End year TDA balance after RMD is $105,971. End year taxable account balance is $3062. The Roth has appreciated to $83,600.
n=3: The TDA grows to $116 568 before the RMD, which at age 73 is $4415; tax of $1060 is due. The remaining $3356 is added to the taxable account. In the meantime, last year’s addition has appreciated by 8.5% after tax. The total and after-tax value of the taxable account is now $6678. The pretax end year TDA balance after RMD is $112,152. The Roth has appreciated to $91,960.
The game ends and after-tax values are computed. The TDA provides $85,236 after tax; with the taxable account, the no-conversion scenario has produced $91,914 of after-tax wealth.
Conclusion: Roth wins. Its $91,960 balance is $46 greater.
Even though tax rates were constant.
In this three period game, the Roth “winnings” are paltry, giving a 2 year ROI on the $24,000 tax debit equal to an annualized 0.10%. But after 20 years, the advantage of the Roth will have compounded further, into something quite reasonable. In fact, after a dozen years the Roth advantage will be able to withstand a decline in future tax rates of several percentage points, as when a converter converts themselves out of the 24% bracket into the 22% bracket. After forty years, the Roth advantage may handle a decline of ten points in tax rate.
Finally, the greater the number of periods the game lasts, the greater the Roth advantage. It is compounding at a flat 10% after tax; everything else is compounding at a slower rate. Meantime, as k shrinks and shrinks, more and more of the TDA is lost to tax. Eventually, the Roth balance will exceed even the pretax values of the TDA plus the taxable account.