There has been some discussion on the Bogleheads forum in the past couple of months about how Required Minimum Distributions (RMDs) affect the "should I do a traditional to Roth conversion?" analysis.
There are similarities to the "Roth vs. Traditional when contributing the maximum allowed" calculations: see ~row 150 in the 'Misc. calcs' tab of the
case study spreadsheet (CSS). That is, calculating the Roth result is straightforward, but tax drag affects the traditional side when RMDs are invested in a taxable account.
As with the "contributing the max" situation, one gets a future Break-Even Tax Rate (BETR) that measures when the traditional+RMD result equals the Roth result. If the actual tax rate on traditional withdrawals is
- above the BETR, Roth would have been better.
- below the BETR, traditional would have been better.
Unfortunately it seems the RMD situation, unlike "contributing the max", does not lend itself to a simple formula for BETR. So I'm considering adding a tab to the CSS for the RMD situation.
Having a worked example for comparison is always good, and the table that is Figure 3 on p. 8 of Michael Kitces'
https://www.kitces.com/wp-content/uploads/2014/11/Kitces-Report-May-2009.pdf seems just the thing. It uses the "current" RMD table instead of the "new" table that will take effect for 2022 (see
Current Vs. New Uniform Lifetime Table RMD), and assumes RMDs start at age 70 instead of 72, but those differences are irrelevant for our purpose here.
The Kitces article says the results come from "a generic 60% equities and 40% fixed portfolio that is rebalanced annually and has 40% turnover, where stocks earn a 3% dividend and 7%
growth (10% total return) and the fixed portfolio earns 5%, and where qualified dividends and capital gains are taxed at 15% and ordinary income/interest is taxed at 25%."
Growth within the traditional and Roth accounts is then a straightforward 60% * (3%/yr + 7%/yr) + 40% * 5%/yr = 8%/yr.
By inspection of the table, the Roth conversion (if done) and RMDs (if the Roth conversion is not done) are assumed to occur at the start of the year.
Calculating the Roth IRA column is easy enough: the $81K at the end of the first year for the Roth comes from $100K * (1 - 25%) = $75K * 1.08 = $81K. Subsequent Roth amounts are simply the result of compounding at 8%/yr.
Calculating the "IRA (EOY)" (EOY = End Of Year) column is only a little more complicated: first the RMD amount is subtracted and then 8%/yr growth is applied. E.g., ($100000 - $100000/27.4) * 1.08 = $104058, then ($104058 - $104058/26.5) * 1.08 = $108142, etc.
On to the taxable account. The RMDs used in the spreadsheet are identical to those shown in the table.
For age 70:
a) starting amount = 100000/27.4 * (1 - 25%) = $2737
b) stocks = $2737 * 60% = $1642
c) bonds = $2737 * 40% = $1095
d) after-tax dividends = $1642 * 3% * (1 - 15%) = $42
e) after-tax interest = $1095 * 5% * (1 - 25%) = $41
f) total capital gain = $1642 * 7% = $115
g) tax on realized capital gain (based on the "40% turnover" assumption) = $115 * 40% * 15% = $7
h) unrealized capital gain, not taxed for "Taxable Account (EOY)" purposes = $115 * (1 - 40%) = $69
i) Taxable Account (EOY) = a + d + e + f - g = $2737 + $42 + $41 + $115 - $7 = $2928
j) Taxable after-tax Net Worth = $2928 - "unrealized capital gain" * 15% = $2928 - $69 * 15% = $2918
k) After-Tax Net Worth (EOY) = "IRA (EOY)" * (1 - 25%) + "Taxable after-tax Net Worth" = $104058 * 0.75 + $2918 = $80962
To calculate BETR, replace the 25% in calculation 'k' with BETR, set that calculation equal to the Roth IRA amount, and solve for BETR. In other words,
"IRA (EOY)" * (1 - BETR) + "Taxable after-tax Net Worth" = "Roth IRA"
BETR = 1 - ("Roth IRA" - "Taxable after-tax Net Worth") / "IRA (EOY)"
BETR = 1 - ($81000 - $2918) / $104058 = 24.96%
Thus everything matches Kitces' table to the dollar, and the BETRs match to the hundreth of a percent. So far so good, and with a spreadsheet one can copy the formulas for subsequent years - but things start to deviate between "Figure 3" and what I have, so I hope other eyes can see better and explain....
Again, there is a perfect match for the traditional and Roth IRA numbers. Only the taxable account differs.
For the taxable account start of year, the current year after-tax RMD amount is added to the previous "Taxable Account (EOY)" value, and that amount is split into the stock and bond amounts as above.
For the "Taxable after-tax Net Worth" calculation ('j' above), the unrealized capital gain is the cumulative total of those amounts for the current and all previous years.
The table below shows the differences by age, calculated as "Kitces table minus spreadsheet". The "Adjusted BETR" comes from using the table's [After-Tax Net Worth (EOY) minus "IRA (EOY)" * (1 - 25%)] to get a "Taxable after-tax Net Worth" (rearranging calculation 'k' above) and then using that in the BETR calculation.
Taxable After-tax
Account Net worth Adjusted
Age (EOY) (EOY) BETR BETR
70 $0 $0 0.00% 0.00%
71 -$4 $0 0.00% 0.00%
72 -$16 $0 0.02% 0.00%
73 -$38 -$2 0.06% 0.00%
74 -$74 -$4 0.11% 0.00%
75 -$126 -$8 0.19% -0.01%
76 -$198 -$17 0.31% -0.01%
78 -$418 -$50 0.68% -0.04%
80 -$767 -$115 1.32% -0.08%
82 -$1287 -$232 2.35% -0.16%
84 -$2034 -$424 3.96% -0.28%
86 -$3073 -$724 6.41% -0.48%
88 -$4485 -$1173 10.12% -0.78%
90 -$6368 -$1822 15.72% -1.23%
92 -$8844 -$2739 24.21% -1.94%
94 -$12054 -$4006 37.27% -3.06%
In short, I may have misinterpreted some assumption, or mistyped some equation, and looking longer at it won't remove the blind spot.
Anyone interested enough to weigh in on which result - if either - appears correct to you?