Roth Conversion Math Fail

by Joe 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.


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