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2010 IRA conversion - here's a formula to help you decide
Old 10-25-2009, 08:12 AM   #1
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2010 IRA conversion - here's a formula to help you decide

What follows is a ‘special case’ analysis of a traditional->roth IRA conversion in 2010. I say ‘special case’ because I make one key assumption that may not be true for many people, namely that the taxes can be paid from either cash or current income and not by selling assets, which may incur their own tax liability.

Since I’m assuming the taxes get paid out of current income, the problem can be analyzed as a simple choice of what to do with that current income or cash – invest it in the market or ‘invest’ it by paying the conversion tax?

That previous sentence is key, if you don’t follow it you won’t follow the rest of the analysis. Let me give an example. Pretend you have 100k worth of gains in your traditional IRA. In your tax bracket, you’d owe (say) 35k on those gains if you converted in 2010. Thus, for your purposes, the question of conversion can be thought of as ‘what’s the best return I can get on that 35k? Do I invest it in the market, according to my asset allocation strategy? Or do I ‘invest ‘ it by paying taxes on that 100k of gains, the return on which will be the future income tax on that 100k (plus growth) that I don’t have to pay?’

In the following analysis I’m going to make two simplifying assumptions. First of all, I’ll assume the taxes on the conversion are due in 2010 (in actual fact they are due in equal parts in 2011 and 2012). This simplification makes the math much easier without materially changing the result. At any rate, it would be pretty straightforward to account for this later.

The other assumption is that the compound annual growth rate that I earn on my IRA is equal to the compound annual growth rate of my taxable portfolio. In other words, I’m treating them each (before taxes) as equivalent investment vehicles.

Ok, here we go. Start by defining variables.

Let X be the current taxable gain on my IRA. This is the amount on which I would owe income taxes were I to convert.

CAGR is the Compound Annual Growth Rate of my portfolio. This is the amount that I earn, pre tax, on both the taxable and IRA portions of my portfolio.

‘Ip’ is ‘Income Tax – Present’. It is my current marginal income tax rate – the rate I would owe on the converted balance.

‘Ifut’ is ‘Income Tax – Future’ It is my future marginal income tax rate – the rate I would owe on a (non-converted) IRA balance when I withdraw it in retirement.

‘Cf’ is Capital Gains Tax – Future. I is the capital gains tax rate I envision paying while in retirement.

‘Y’ is the number of years between 2010 and my retirement.

Ok, on to the analysis.

Scenario 1 – do the conversion.
The tax I pay is Ip*X. That’s my current marginal income tax rate (state plus federal) multiplied by the taxable gain on my IRA.
The ‘return’ on that use of the money is the future tax I don’t have to pay. That would be calculated as follows:
X * (1+CAGR)^Y * Ifut. That’s the current gain in my IRA, with Y years of growth applied, multiplied by my future income tax rate.

Scenario 2 I don’t do the conversion. So rather that pay the tax Ip * X, I invest it in the market. The return on that after Y years would be as follows:
(Ip* X) * (1+CAGR)^Y * (1-Cf)

So the conversion question becomes, which is the better use of that Ip*X? Do I pay the tax or invest it?

Expressed formulaically, conversion makes sense if and only if:

X * (1+CAGR)^Y * Ifut > (Ip*X) * (1+CAGR)^Y * (1-Cf)

You can see right away the result is independent of growth rate, portfolio value, or years to retirement.

Ifut > Ip * (1-Cf)

At this point it makes sense to put in your actual value for present marginal tax rate (Ip). Mine is 47.62% (really, it is! – 35% fed, 8.97% NYS, 3.65% NYC)

So putting that in the equation gives:

Ifut > 47.62* (1-Cf)


Ifut > .4762 - .4762Cf

Now I can look at a range of future income tax rates, for each I can easily calculate a capital gains tax rate above which conversion makes sense.

Say I think I’ll be in a 30% income tax bracket in retirement. That means that if capital gains tax rate is over 37%, I’m better off converting.

But if I’m only in a 20% income tax bracket upon retirement, then capital gains taxes would have to be a whopping 57% for conversion to make sense.

However if income tax rates rise such tat I’m paying 40% in retirement, then conversion makes sense as long as future capital gains rates are over 16%.

Here’s a table of numbers for my situation (in other words, using 47.62% as a present marginal tax rate)

The number on the left represents a potential future income tax rate. At that rate, the number on the right is the future capital gains tax that would be required in order for conversion to have been a good deal. (you can create your own table by making the right hand number = (Ip-Ifut)/Ip )

15% 68.5%
20% 58%
25% 47.5%
30% 37%
40% 16%
45% 5.5%
50% >0%

Now lets look at the situation for someone else, say in a 30% tax bracket.

Now the numbers look like this:

15% 50%
20% 33.3%
25% 16.7%
30% 0%

This is a much more compelling case. Given our fiscal situation and demographic problem, its easy to imagine future income tax rates at 25% or more, even for those with moderate income. If income tax rates were 25%, conversion would make sense if capital gains taxes were at or above 16.7%.

By the way, it would be relatively straightforward to extend this analysis to the general case which contemplates a tax penalty on the funds needed to pay the income tax due at conversion. It would also be easy to account for the fact that the taxes wouldn’t be due in 2010, rather they’re spread out between 2011 and 2012. I just haven’t bothered since it wouldn’t materially change my result.

Hope this helps, also I welcome any comments or corrections.
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Old 10-25-2009, 09:10 AM   #2
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Very interesting. I hope to post a Q later, but first let me check my thinking on one point:

Let X be the current taxable gain on my IRA. This is the amount on which I would owe income taxes were I to convert.

Maybe it's just semantics, or maybe I'm confused, but don't you mean to say "X = the taxable amount of the conversion"?

IIRC, the taxable amount has nothing to do with gains, it represents the % that was contributed tax free. This is probably 100% for most people, it would be less if you made non-deductible contributions to a Trad IRA at some point.

Do I have that right? Or should I have more coffee? Both?

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Old 10-25-2009, 09:51 AM   #3
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Sure, call it the taxable amount. Its 100% for most people, and either way the results are independent of that, as it neatly drops out of the equation.
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Old 10-25-2009, 11:47 AM   #4
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To add to Maurice's work, here is an article written in 2007 from the Journal of Retirement Planning. The authors propose several scenarios to consider when thinking about conversion (either full or partial).

For myself, I'm committed to partial conversions as the tax hit on a full conversion wouldn't let me sleep at night.

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