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# Roth Conversion Math

When deciding whether or not to convert a traditional IRA to a Roth IRA, many investors overlook the fact that the goal is not to minimize the amount of tax dollars paid. Rather, the goal is to maximize the ending value of the portfolio.

### What Am I Talking About?

Let’s consider a simplified example. Imagine that an investor has a choice between paying a 25% tax on her portfolio right now or in three years. And let’s say that her portfolio earns the following annual returns over those three years: +8%, +17%, +20%.

1. If she pays the tax right now, the math will look like this: Ending value = beginning value x 0.75 x 1.08 x 1.17 x 1.2.
2. If she pays the tax at the end, the math will look like this: Ending value = beginning value x 1.08 x 1.17 x 1.2 x 0.75.

Note that, due to the commutative property of multiplication, the ending portfolio value is the same in either case–even though the investor will pay more tax if she selects option #2 (because her portfolio value will be higher at the time she pays the 25% tax).

The same analysis applies for Roth conversions: The amount of tax paid doesn’t matter. What we care about is the ending portfolio value.

### Roth Conversion Scenarios

Admittedly, this is something of an oversimplification, but Roth conversions can be roughly broken down into three scenarios:

1. You plan to pay the tax on the conversion out of the IRA (rather than with money from a taxable account), and you’re over age 59.5
2. You plan to pay the tax on the conversion out of the IRA, and you’re under age 59.5, or
3. You have enough money in taxable accounts to pay the tax without having to use money from the IRA.

### Paying the Tax from the IRA

In the simplest scenario–the one in which you’re paying the tax on the conversion out of the IRA and in which you’re over age 59.5 (such that there’s no penalty for doing so)–things work out like this:

• It’s a wash if you expect your tax bracket to stay the same. The commutative property of multiplication tells us that multiplying by, say, 0.75 now as opposed to multiplying by 0.75 later makes no difference.
• It’s a good idea if you expect to be in a higher tax bracket later.
• It’s a bad idea if you expect to be in a lower tax bracket later.

In the second scenario–in which you’re under age 59.5 and paying the tax out of the IRA–things become slightly more complicated. We have to account for the 10% early withdrawal penalty. For example, if you’re in the 25% tax bracket and you convert a \$40,000 IRA and withdraw \$10,000 to pay the tax, the 10% penalty will be charged on that \$10,000.

End result: You need to expect a higher tax bracket in retirement in order for it just to be a break-even decision. (Specifically, your retirement tax bracket must be at least 1.1-times your current tax bracket for it to make sense.)

### Paying the Tax from a Taxable Account

In the third scenario–in which you’re paying the tax out of taxable funds rather than out of the IRA–things get trickier. We have to make assumptions about the after-tax rate of return that will be earned (if you choose not to convert) on the money that would otherwise have been used to pay the tax.

That said, in this last scenario, things usually (though not always) work out like this:

• If you expect your tax bracket to remain the same, there’s a benefit to converting. It’s essentially a way to use non-tax-advantaged money to increase the size of your tax-advantaged accounts.
• If you expect your tax rate to increase, converting is a good idea.
• If you expect your tax rate to decrease, converting is likely (though not necessarily) a bad idea.

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1. Don says:

This still isn’t the whole answer, since we have a graduated tax system (you just posted about this a couple of days ago). It really sort of depends where things fall against the tax bracket breaks.

For example, if you do a conversion and it happens completely in the 15% bracket, that will be worse than leaving it and withdrawing part in the 10% bracket and part in the 15% bracket.

2. That’s definitely a point that many people forget, maybe because it feels like there are so many variables to consider. In my case I went ahead and did the conversion and will be paying the taxes out of a taxable account, but I still don’t feel completely comfortable with my decision because there are a lot of things up in the air in my situation. Still, based on what I do know, it seems like the right choice.

3. Don: You’re absolutely right that this isn’t the whole answer. For example, I didn’t even touch on estate planning considerations.

Also, just to be clear, when I talk about an investor’s “retirement tax bracket” I’m referring to the rate(s) at which distributions from a tax-deferred account would be taxed–not the tax bracket that the investor is in after taking that distribution. So if an investor is in the 15% bracket right now and his distributions would occur partially in the 10% bracket and partially in the 15% bracket, his “retirement tax bracket” per the above analysis would be lower than his current bracket.

Jackie: That gets at the heart of the matter. There are a lot of things “in the air” for just about everybody’s situation. It’s hard to predict tax rates even a few years from now, much less a decade or two from now. (And then there are a whole list of other unknown variables too…)

4. I have recently been figuring out if this would be of interest to me. I am young right now (mid twenties) and thought to myself “hell yes i want to earn money which can never be taxed”

But the fact of the matter is living in CA the income tax (around 10%) is higher than most anywhere else in the country. Since i’m not 100% sure that I want to stay in CA forever it is to large of a gamble for me to assume that it’s worth me spending an extra 10% on my investment from the start (it’s like some kind of sick buy-in fee). Therefore i’ve decided to hedge my bet and I put about 2/3 of my retirement savings into my 401k and 1/3 into my RothIra.

Of course eventually i’m sure i’ll max out both but for now this is what I feel is balanced (and it sure is fun seeing pretax money grow faster).

5. Good work Mike, I thought everything was clear .

I feel like most fail to realize that while you reduce your gross estate with a Roth conversion you do not reduce the “net” estate. I like the term “transferring assets from a taxable environment to a tax free environment”. That is essentially what is happening if you pay from outside the IRA. Of course the math still needs to work but the likely-hood that it will is fairly high in most cases. It can also offer an individual significant piece of mind (what if taxes sky-rocket?). Especially considering the distributions come out of the after-tax basis first (what if you need emergency money?). Like you mentioned in your comment, there are other benefits you did not mention. A more efficient estate tax asset, suspension of RMDs, absorbing tax losses, etc…

Engin33r, if you are in your mid twenties, it is highly unlikely that contributions to a traditional account will favor those of a designated Roth account, assuming you keep the money in the account through 59 1/2. Also, if it turns out the net yield would of been higher in the traditional account, it probably won’t be by much. I understand where your head is at, but definitely consider that. Time can be the most powerful asset, and you have it.

Good stuff Mike.

6. I’d add one very overlooked issue.
What are the chances that one stay fully employed from their current age right through retirement? I don’t know, but I guess slim.
In that year of low income, that’s the time to consider the conversion.

7. Joe A. and Joe T: Thank you both for sharing your thoughts on a matter I know you both deal with frequently. 🙂

Joe T: Absolutely agree–especially in the instances in which employment has been re-secured by the end of the year such that forking over the cash for the conversion isn’t such a scary proposition.

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