How do RMDs affect Roth conversion choices?

[MDM]

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.

Code: [Select]

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?

[seattlecyclone]

I'm not going to wade through the math. You tend to be pretty good at that stuff.

What I will suggest is to consider something at a bit higher level. In the absence of RMDs you'd likely want to withdraw the amount you intend to spend and no more. The RMDs are designed to force you to draw down your account over your remaining life expectancy, so the main reason you'd concern yourself with RMDs is if you have more money in your IRA than you intend to spend in your lifetime.

For that reason I think the analysis really should look at the differences in tax treatment after death as well. You'll likely be passing your IRA on to your adult children who are perhaps themselves in their peak earning years, and handing them a large tax-deferred inheritance that they need to distribute over 10 years might land them in a higher tax bracket than you'd experience even with aggressive Roth conversions during your life. Conversely, handing them a large Roth inheritance allows them to let the money continue compounding tax-free for a decade if they have no immediate use for it.

[MDM]

For that reason I think the analysis really should look at the differences in tax treatment after death as well.

Yes, completely agree that's where this needs to go. 

Just trying to get the first steps correct for now.

Thought I was well on the way when the first year matched the Kitces article, but then things diverged in the subsequent years, so...?

The presence or absence of a basis step-up for inheritance would make a big difference for the that situation....

[MDM]

OK, I think I (at least somewhat better) understand Kitces' assumption: he calculated the BETR assuming that rate applied to all years after the first.  That gives a different answer than assuming the first year's tax rate applied until withdrawal. 

Neither approach is more correct than the other in general.

I'll clean up the spreadsheet I've been using, add cell comments, etc., and post a link.  Then people can find errors. ;)

At least I don't expect there will be major errors, as this one gives results very close to Kitces, using what I think were his assumptions. 

Of course, one can make some assumptions that favor Roth conversions and others than do not favor Roth conversions.  Seems there are some reasonable situations that favor Roth conversion, even if the inheritor will have a much lower tax rate than the original owner.  More details to come.

[MDM]

For anyone interested, https://docs.google.com/spreadsheets/d/1TmiOk5AlnGzsxZO7mjFeVwaOrh0J98Vi/edit?usp=sharing is a spreadsheet that allows some "what if...?" tests showing how RMDs affect Roth conversion choices.

There can be a benefit to the Roth side of the scales if paying taxes out of cash on hand when making Roth contributions or doing Roth conversions, as this gets money out of taxable and into a Roth account.

It stands to reason, then, that there is a detriment to moving money out of a tax-advantaged account and into a taxable account, which is what RMDs force.  The question is, how much detriment?  As with most traditional vs. Roth questions, the answer starts with "it depends...." 

All the input cells have notes with some details on what the cell is for.  The non-input cells are protected from changes, but there is no password if anyone wants to download and modify those cells.  Should anyone use it and have questions, I'll be happy to answer.

Some built-in assumptions:
- Any Roth conversion and RMDs for the original owner are assumed to occur at the start of the year
- RMDs for the heir are taken at the end of the year

The spreadsheet 'Model' tab is loaded with the following scenario, but these inputs are adjustable:
- Roth conversion (or not) at age 71.  Tax paid from conversion funds.  The IRA owner is subject to 32% marginal ordinary income tax, holds a 60/40 stock/bond asset allocation.  See the spreadsheet inputs for more details.
- Original owner dies at age 85.  Heir gets a basis step-up.
- Heir pays a 22% marginal rate on ordinary income, and 15% on dividends and capital gains.  Heir holds a 100/0 stock/bond asset allocation.  See the spreadsheet inputs for more details.

Some observations:
- If the original owner had lived to age 94, it would have been slightly better to do the Roth conversion even if the heir had been a tax-exempt charity.
- With the default scenario, not converting is slightly better for the heir if the heir would use the inheritance within two years.  If the heir would let the money grow for the full 10 years, an age 71 conversion by the original owner would give the heir more spendable after-tax income after the 10 years.

Disclaimers:
- None of this should be interpreted to be an unqualified "Roth is better" or "traditional is better."  As always, it depends....
- At the time of this post, the spreadsheet has not been checked for errors by anyone other than the author.  It has passed several self-checking reasonableness tests, but any good tool developer knows that the original developer is not the best reviewer....

[frugalecon]

Thank you for putting this together. I have bookmarked and will come back to study. As someone who has been a W-2 employee since I was 14 (> 40 years), my tax situation has always been straightforward. Tax planning is something that will get substantially more complex in retirement, as I have income from a variety of streams that have different tax treatments. (SS, pensions, IRAs, capital gains, dividends) It is ironic that tax planning becomes much more complex right at the time one’s cognitive abilities are declining!

[MDM]

For anyone interested, https://docs.google.com/spreadsheets/d/1TmiOk5AlnGzsxZO7mjFeVwaOrh0J98Vi/edit?usp=sharing is a spreadsheet that allows some "what if...?" tests showing how RMDs affect Roth conversion choices.

Just uploaded a new version of this tool.  Link remains the same.

As noted in the spreadsheet itself:

• The original version of this tool used the following for comparison: https://www.kitces.com/wp-content/uploads/2014/11/Kitces-Report-May-2009.pdf
  Full credit to Mr. Kitces and that article for inspiring this work.
• The current version has been compared with a spreadsheet developed by Mr. McQuarrie and discussed in https://www.bogleheads.org/forum/viewtopic.php?f=10&t=358688
  Full credit to Mr. McQuarrie for his work to publicize this issue (and for developing a fine spreadsheet!)
  

Most of the changes were cosmetic, e.g., putting all the input cells up top.  Some substantive changes:
- Roth conversions and RMDs for the original owner now may be taken at the start or end of the year
- The new IRS RMD table is used

One observation: the discussion in the Bogleheads thread linked above included comments on the effect of taxing (or not) capital gains each year.  Changing the "Turnover" assumption (cell B15) from 100% (all annual capital gains are realized and thus taxed) to 0% (all annual capital gains remain unrealized and thus not taxed until withdrawn) can make a significant difference....

Disclaimers:
- None of this should be interpreted to be an unqualified "Roth is better" or "traditional is better."  As always, it depends....
- At the time of this post, this spreadsheet's results have been compared with results from another spreadsheet (see reference to Mr. McQuarrie's work above) for a limited number of scenarios.  The main comparison was the "Roth Gain" (column T in this tool) vs. "Roth surplus" (column O in the McQuarrie tool).  Those appear to match exactly - again, for the limited number of scenarios checked.

[MDM]

Version 2.01

The sausage making continues....

- Added a summary table.  Example below, with the inputs saved in this version, shows the effect of a basis step-up and lower heir's tax rate.  Again, just one example....

Code: [Select]

                              Roth Gain
Just before owner's death          $7,899
Just after inheritance                -$28,068
After 10 years                           -$862
After 10 years (if unspent)           -$862
Owner's age at which conversion wins      82
Years after inheritance for Roth to win   Never
- Added an option (RMD timing) to the heir's section and fixed a typo (thanks to Boglehead's member marcopolo for that one)
- Other miscellaneous additions.

Version 2.01: https://docs.google.com/spreadsheets/d/1TmiOk5AlnGzsxZO7mjFeVwaOrh0J98Vi/edit?usp=sharing

[MDM]

Version 2.02

Allow the heir to inherit after an extra 14 years of the original owner's life.  Thanks to Boglehead cas for that one.

Modifications and comments seem to have stopped.  May roll this sheet into the case study spreadsheet (CSS) when a new CSS version comes out.

Version 2.02: https://docs.google.com/spreadsheets/d/1TmiOk5AlnGzsxZO7mjFeVwaOrh0J98Vi/edit?usp=sharing

[aperture]

Reply to follow