Wiki: Backdoor Roth IRA (conversion formula)

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celia
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Wiki: Backdoor Roth IRA (conversion formula)

Post by celia » Sat Dec 08, 2018 7:40 am

In another thread, the OP had a question that referenced the Backdoor Roth IRA wiki page. I think there is something wrong with the formula shown there but first want comments from others.

C = Amount to Convert to Roth

B = Balances of all pre-tax IRAs

TF = The percentage of the amount you're computing this would be tax-free

TF = 100 * [ C / (C + B)]
If you convert over multiple years with some non-deductible contributions remaining from a previous year Roth conversion, that appears to not be reflected in this formula. I think the formula should be:
ND = Amount of Non-Deductible dollars in all the non-Roth IRAs, including contributions made for the year
SB = Sum of the Balances of all the non-Roth IRAs at year-end, including the amount converted
TF = The percentage of the amount you're computing that would be tax-free

TF = 100 * ND/SB
What do others say? (Feel free to confirm my math, but that doesn't change my claim that the formula is wrong.)


For example, assume you contributed $5,000 non-deductible to a new tIRA and already had a pre-tax $15,000 IRA and converted $4,000 in the first year. To keep this example simple, suppose there are no more contributions in the following years and no growth. You want to convert half of the remaining IRAs in the second year and the rest in the third year. So $8,000 is projected to be converted in the second and third year.

A. Using the current formula gives:
first year:
TF = 100 * [ C / (C + B)]
TF = 100 * [4,000 / (4,000 + 15,000)] = 21% = $842 of the $4,000 conversion leaving $3,158 to be taxed

That leaves behind $16,000 in the IRAs, of which $4,158 (5,000-842) is basis (non-deductible dollars) and 11,842 is pre-tax.

second year:
TF = 100 * [ C / (C + B)]
TF = 100 * [8,000 / (8,000 + 11,842)] = 40% = $3,225 of the $8,000 conversion leaving $4,775 to be taxed

That leaves behind $8,000 in the IRAs, of which $933 (4,158-3,225) is basis (non-deductible dollars) and $7,067 is pre-tax.

third year:
TF = 100 * [ C / (C + B)]
TF = 100 * [8,000 / (8,000 +7,067)] = 53% = $4,247 of the $8,000 conversion leaving $3,753 to be taxed

But something's wrong since we converted and had untaxed amounts over the three years of $842 + 3,225 + 4,247 = $8,314 when our original basis was only $5,000.


B. Using the "new" formula gives:
first year:
TF = 100 * ND/SB
TF = 100 * 5,000 / 20,000 = 25% = $1,000 of the $4,000 conversion was tax-free leaving $3,000 to be taxed

That leaves behind $16,000 in the IRAs, of which $4,000 (5,000-1,000) is basis (non-deductible dollars) and $12,000 is pre-tax.

second year:
TF = 100 * ND/SB
TF = 100 * 4,000/16,000 = 25% = $2,000 of the $8,000 conversion was tax-free leaving $6,000 to be taxed.

That leaves behind $8,000 in the IRAs, of which $2,000 (4,000-2,000) is basis (non-deductible dollars) and $6,000 is pre-tax.

third year:
TF = 100 * ND/SB
TF = 100 * 2,000/8,000 = 25% = $2,000 of the $8,000 conversion was tax-free leaving $6,000 to be taxed.

In this case, the untaxed amount over the three years is $1,000 + $2,000 + $2,000 = $5,000 which equals the total basis.


The first sentence of the wiki page also references a "nondeductible traditional IRA". There is no such thing. The contribution is deductible or nondeductible, not the IRA. (The term is also implied in the section titled "Mechanics".)

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Re: Wiki: Backdoor Roth IRA (conversion formula)

Post by kaneohe » Sat Dec 08, 2018 9:25 am

Celia...........nice catch. Perhaps consider some minor rewording:

ND = Amount of Non-Deductible dollars in all the non-Roth IRAs at start of year, plus contributions made for the year
SB = Sum of the Balances of all the non-Roth IRAs at year-end, plus the amount converted

Valuation of amounts implies at a specified time so that time should be given. The word "included" is a bit confusing since balances at the specified times do not include the contribution for the yr or the amount converted.....so change to "plus"

The way I like to think about these conversions..........if I add antifreeze (non-deductible) to water (deductible) so that the mixture is 25%, when I remove an amount to convert, that mixture will always be 25% (assuming no more antifreeze added) which is what your new formula shows.

Of course in the real world, account amounts generally do not remain constant since there can be appreciation/depreciation so the F8606 works better there than the assumptions here.
Last edited by kaneohe on Sat Dec 08, 2018 12:21 pm, edited 1 time in total.

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Re: Wiki: Backdoor Roth IRA (conversion formula)

Post by LadyGeek » Sat Dec 08, 2018 9:54 am

This thread is now in the Personal Finance (Not Investing) forum (Roth IRA).

(The thread was formerly in the Local Chapters and Bogleheads Community forum, which includes the wiki as a community effort. The discussion is more appropriate here.)
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Re: Wiki: Backdoor Roth IRA (conversion formula)

Post by Alan S. » Sat Dec 08, 2018 12:29 pm

The wiki article apparently attempts to simplify the Form 8606 mechanics. However, this might be a challenging pursuit when the illustrated formula only works in very limited situations. Celia has exposed at least one of those situations.

A more frequent transaction is a ND contribution converted along with limited gains on that contribution. Since the wiki formula does not include a specific dollar basis, it would fail to show that the gains in such a conversion would be taxable.

Yet another situation where simple formulas would not work is when there is also a non converted distribution (Form 8606 line 7) in addition to the conversion and the other distribution receives a share of basis depending on the relative amounts of the conversion and the other distribution.

Since Form 8606 is tricky, most people do not understand it, and many in the IRS do not understand it either, simplification is a noble endeavor but would come with a bunch of footnotes and qualifications limiting it's use. However, the current wiki can certainly be improved.

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Re: Wiki: Backdoor Roth IRA (conversion formula)

Post by celia » Sat Dec 08, 2018 3:11 pm

This is one of the wiki pages I put on my "To-Do" list a long time ago. It needs a major overhaul, which I was planning on doing, so keep the comments coming.

Another big problem is that there is no such thing as a "Backdoor Roth IRA" (which impacts all the wiki pages that link to that page--I will let someone else find and fix those). The "Backdoor Roth" is a process, not an IRA. To emphasize that, I was going to give the primary example of a non-deductible contribution going into the same IRA as deductible contributions. However, I also want to warn readers not to "contaminate" a Rollover IRA, since if they may want to roll that money back to a 401K in the future, some 401K custodians will not accept rollovers that have been co-mingled with direct-contribution IRAs. (Is there a better term for that?) Alan S., can you confirm this last concept?
LadyGeek wrote: This thread...
This is just to get the admin's attention that the title of the page needs to be changed as well as links to it. Or maybe we can leave the page there, but empty, and auto-forward to the correct page as forum pages will then have broken links.

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Re: Wiki: Backdoor Roth IRA (conversion formula)

Post by FiveK » Sat Dec 08, 2018 3:25 pm

celia wrote:
Sat Dec 08, 2018 7:40 am
In another thread, the OP had a question that referenced the Backdoor Roth IRA wiki page. I think there is something wrong with the formula shown there but first want comments from others.
C = Amount to Convert to Roth

B = Balances of all pre-tax IRAs

TF = The percentage of the amount you're computing this would be tax-free

TF = 100 * [ C / (C + B)]
Using the word "traditional" instead of "pre-tax" and adding "at the end of the tax year" for the definition of "B" would make the wiki correct, and be consistent with form 8606's line 6 "value of all your traditional, SEP, and SIMPLE IRAs as of December 31."

For example,
Image

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Re: Wiki: Backdoor Roth IRA (conversion formula)

Post by celia » Sat Dec 08, 2018 4:34 pm

FiveK wrote:
Sat Dec 08, 2018 3:25 pm
Using the word "traditional" instead of "pre-tax" and adding "at the end of the tax year" for the definition of "B" would make the wiki correct, and be consistent with form 8606's line 6 "value of all your traditional, SEP, and SIMPLE IRAs as of December 31."
FiveK, That would fix the denominator, but not the numerator. The problem still is with "C" (the numerator). That should not be "the amount converted", but "the amount of basis" (pre-tax) in both the remainder and the amount withdrawn. Note that the IRS worksheet doesn't reference the "amount converted".
25% of ANY AMOUNT converted in the first year would be tax-free, so the amount converted is irrelevant to the equation.

To make it more obvious, what if the account owner converted half of the tIRAs in the first year. Under the existing formula, the amount that is tax-free would be:
TF = 100 * [ C / (C + B)]
TF = 100 * [10,000 / (10,000 + 10,000)] = 50%
when it should be 25%.

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Re: Wiki: Backdoor Roth IRA (conversion formula)

Post by Alan S. » Sat Dec 08, 2018 5:09 pm

celia wrote:
Sat Dec 08, 2018 3:11 pm
I was going to give the primary example of a non-deductible contribution going into the same IRA as deductible contributions. However, I also want to warn readers not to "contaminate" a Rollover IRA, since if they may want to roll that money back to a 401K in the future, some 401K custodians will not accept rollovers that have been co-mingled with direct-contribution IRAs. (Is there a better term for that?) Alan S., can you confirm this last concept?

Yes, some custodians will not accept rollovers from contributory IRA accounts, although the number of such custodians is decreasing. "Contributory" IRA accounts is a better term to denote an IRA account that has received regular IRA contributions regardless of deductibility. Contributory IRAs would also include IRA accounts which received a rollover from an IRA account that itself received regular IRA contributions.

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Re: Wiki: Backdoor Roth IRA (conversion formula)

Post by LadyGeek » Sat Dec 08, 2018 5:16 pm

I have created a draft page: User:Celia/Backdoor Roth

Wiki editors can make changes there and get a consensus without affecting the "live" content.

Members who wish to update the content can post here and an editor will update the draft page for you.

(This follows Wikipedia policy - draft changes are placed under the editor's user page. When ready, the content is moved to the "live" page. All editors are welcome to edit the page.)

Update: The draft page has been renamed, see below.
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Re: Wiki: Backdoor Roth IRA (conversion formula)

Post by FiveK » Sat Dec 08, 2018 5:46 pm

celia wrote:
Sat Dec 08, 2018 4:34 pm
FiveK wrote:
Sat Dec 08, 2018 3:25 pm
Using the word "traditional" instead of "pre-tax" and adding "at the end of the tax year" for the definition of "B" would make the wiki correct, and be consistent with form 8606's line 6 "value of all your traditional, SEP, and SIMPLE IRAs as of December 31."
FiveK, That would fix the denominator, but not the numerator. The problem still is with "C" (the numerator). That should not be "the amount converted", but "the amount of basis" (pre-tax) in both the remainder and the amount withdrawn. Note that the IRS worksheet doesn't reference the "amount converted".
25% of ANY AMOUNT converted in the first year would be tax-free, so the amount converted is irrelevant to the equation.

To make it more obvious, what if the account owner converted half of the tIRAs in the first year. Under the existing formula, the amount that is tax-free would be:
TF = 100 * [ C / (C + B)]
TF = 100 * [10,000 / (10,000 + 10,000)] = 50%
when it should be 25%.
Right you are!

So other than being incorrect/misleading on both the numerator and denominator, the current wiki isn't too bad? ;)

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Re: Wiki: Backdoor Roth IRA (conversion formula)

Post by celia » Sat Dec 08, 2018 5:54 pm

FiveK wrote:
Sat Dec 08, 2018 5:46 pm
So other than being incorrect/misleading on both the numerator and denominator, the current wiki isn't too bad? ;)
LOL, I guess it depends on what "too bad" means to you. I see lots of little things that contribute to fuzzy thinking that I hope to fix.
For example, there's no such thing as a "Backdoor Roth IRA" nor a "nondeductible Traditional IRA".

We get in trouble too easily if we don't use the correct terminology!

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Re: Wiki: Backdoor Roth IRA (conversion formula)

Post by LadyGeek » Sat Dec 08, 2018 5:58 pm

I have renamed the draft page: User:Celia/Backdoor Roth

If we want to change the name of the "live" page to just "Backdoor Roth", we can do that.* Links to the old title "Backdoor Roth IRA" won't be broken.

FYI - Any wiki editor can rename (move) the page.

* Wiki editors - we just need to use a redirect from the old page to the new page. Any editor can do this, but I can take care of it after the changes have been made.
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Re: Wiki: Backdoor Roth IRA (conversion formula)

Post by celia » Sat Dec 08, 2018 6:10 pm

Thanks, LadyGeek.

There was a thread from several years ago that also commented on this wiki page. So I will also read that and make sure the concerns were taken care of. The current footnote #2 references a post in that thread that doesn't sound like an authoritative footnote source. So this is a reminder to look at that too.

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