# Roth Conversion Math Fail

by on October 17, 2012

When writing on such an important and misunderstood topic such as IRAs and Conversions to Roth, I believe that authors need to spell out very clearly what they mean. If the reader misunderstands the intent of an article due to some ambiguous writing, the author may just as well have gotten his facts wrong. In an article I’ll share with you today, I’m not 100% sure of the author’s intent, I only know the right way to do the math, and that I tried to help clarify his discussion.

The article How To Convert A Non-Deductible IRA Into A Roth IRA recently appeared at Investopedia. It started with some great info, introducing the idea of the Roth IRA, Traditional IRA, and Tradition IRA with post tax money. But then this section had me wondering:

John Doe, a 30% taxpayer, has a Traditional IRA worth \$200,000 on Dec. 31, 2012, of which \$100,000 is non-deductible contributions. Doe wants to convert \$100,000 of this IRA to Roth. Because Doe has \$100,000 of non-deductible contributions in this Traditional IRA, you would think that he could convert the \$100,000 of non-deductible contributions tax-free. Unfortunately, the IRS has a special formula that must be followed if you own an IRA with normal contributions.

Here’s how it works:
Tax-free Percentage = Total Non-deductible Contributions divided by
(Sum of year-end value of all IRA accounts + Conversion Amount) = \$100,000/(\$200,000 + \$100,000) = \$100,000/\$300,000

Tax-Free amount of Conversion = 33.3% (or \$33,333)
Therefore, if John converts \$100,000 to the Roth, he will have \$33,333 (\$100,000 x 33.3%) that is not-taxed and \$66,667 (\$100,000 x 66.7%) that will be taxed at his 30% tax rate.

Now, I’ll ignore the fact that there is no 30% bracket. Not all states recognize the Traditional IRA pre-tax status, so when I talk IRAs, it’s usually from a federal-only tax perspective. Let’s move on. The author states Doe wants to convert \$100K of an IRA worth \$200K. \$100K is post-tax (“non-deducted”) money. Absent any further growth, this conversion takes place in 2013, as the author is looking back at Dec 31, 2012 in hindsight. On Dec 31, 2013, he has \$100K in a Roth and \$100K in the Traditional IRA. The amount that he owes tax on is \$50K, as half his IRA is attributed to post-tax deposits. I’ll even agree his equation was correct but the numbers are \$100K/(\$100K+\$100K) or \$100K/\$200K so the tax free conversion is 50%. The author has added the converted amount to all IRA balances which includes the converted amount in the new Roth.

Unfortunately, when I tried to kindly point this out, the author rejected my clarification, and held firm. “The IRS and JK Lasser’s Tax Guide use the specific formula that’s mentioned above.” Well, right, that equation is correct, but the Traditional IRA ended the year with \$100K, not \$200K. It would stand to reason that if preconversion, your IRA is half post tax, half the conversion will be taxed at your marginal rate.

Mistakes happen. I’ve caught professionals with simple typos that change the meaning of articles. More often than not, they’ll correct their article and jot me a note thanking me for my obsession. I’m not insulted when they don’t but am a bit dismayed that such an error remain uncorrected and a search for advice on the topic will lead a reader to an incorrect calculation. Unfortunately, no one else has commented to point out the error. The punchline remains – do your research when it comes to any financial decisions you make. Better to spend a bit more time and find two or three sources that confirm your understanding than to go with the first explanation you find, as there’s a chance it may be wrong.

{ 6 comments… read them below or add one }

Lou October 17, 2012 at 5:12 pm

Thanks for showing this math! I now understand the right way as well as a simple mistake to avoid. Nice work.

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Adam October 20, 2012 at 1:58 am

Joe, you are absolutely correct. Additionally he didn’t bother to address the earnings/returns from that nondeductible traditional IRA.

For example.

If john has 1 traditional IRAs(one deductible and one nondeductible) worth 150k. 50k is deductible contributions, 25k is interest earned on the 50k deductible contributions, 50k is nondeductible contributions, 25k is interest earned on the nondeductible contributions. Say John want’s to convert the nondeductible portion of his traditional IRA. on the contributions (50k), 50% would be taxable (nondeductible contributions)/(nondeductible contributions + deductible contributions). On the earnings (25k) all of it would be taxable. So John would have 50k * 50% + 25k = 50k of taxable conversion 25k of nontaxable conversion. in this instance 75% of his nondeductible conversion would be taxable. However if he had no capital gains and equal amounts as in the investopedia article, he would have 50% taxable.

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joe October 20, 2012 at 8:18 am

Adam, the simplest way to look at this is to track non-deducted deposits. Pretax deposits, and growth on either pre or post-tax deposits are all subject to tax either during a conversion or ultimate withdrawal.

The author went off course by adding the Roth account value twice. The equation he used was fine, just misapplied.
As you know, but for the sake of my readers, non-deducted contributions are tracked for each deposit via form 8606 along with your tax return.

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Dave Bucher February 21, 2013 at 9:54 am

I have a quick question about specifically what is meant by “Sum of year end value of all IRA Accounts”.

Tax-free Percentage = Total Non-deductible Contributions divided by
(Sum of year-end value of all IRA accounts + Conversion Amount)

I have an SEP-IRA and a Roth (both 100% pre-tax). I am considering setting up a traditional IRA this year so that I can make additional contributions beyond what I can do with SEP or Roth, then converting to Roth IRA.

If I set up a new Traditional IRA and contribute post-tax, do the balances in the SEP and Roth accounts still get factored into the calculation of taxable %? I would think that since I’m converting from an account that is 100% post-tax, that 0% would be taxable.

One other note, I do also have a rollover acct which is also 100% pre-tax if that factors into the equation.

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joe March 11, 2013 at 9:33 am

Dave – The Roth, by definition, is post tax, I think you meant a SEP-IRA and a Traditional IRA?

When converting, you must add all your IRAs. You exclude Roth accounts, and you exclude Inherited IRAs if you have one. The remaining IRAs are added up and the tax is calculated on the percent that was pretax money.

The rollover IRA is part of this equation as well. I agree, it feels like since you are depositing the pretax money into a new account, you should be ok. But this is not the case. IRA stands for individual retirement arrangement, not ‘account.’ So, the ‘arrangement’ comprises all the accounts as discussed.

I hope that helps you, Dave!

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Dave Bucher March 11, 2013 at 9:52 am

Yeah, sounds like there is no “back door” to Roth if you are self employed then since SEP-IRA counts against you. Would have to use 401K rather than SEP-IRA which has its own issues.

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