A reader writes in, asking:

“I am planning to do a smallish conversion each year before I turn 72. I am 66.

Now though, I recall hearing a CFP say that it is important also to do a ‘breakeven analysis’ before converting money from a traditional to a Roth IRA. He has found that, for most of his clients, the breakeven point is too distant for a conversion to provide a meaningful benefit. Clients would have to be in their 90s.

If you have room in your blog, please touch on what a “breakeven analysis” is in the context of a Roth conversion and how to do it.”

This is a common misconception — one that is common even among financial professionals, unfortunately.

In most cases, breakeven analysis simply is not applicable to a Roth conversion decision. (There is one specific exception, discussed below.) For a Roth conversion decision, the length of time in question usually does not matter at all.

The reason has to do with the commutative property of multiplication. That’s the rule from grade school math that tells us that A x B x C is the same as C x B x A. The order in which we multiply figures is irrelevant — we get the same answer every time.

When you pay taxes on a distribution from a tax-deferred account, it’s a multiplication function. For example, if you take a distribution and you have a 20% total marginal tax rate, you’d be multiplying the amount by 0.8 in order to see how much is left after taxes. And the same is true for a Roth conversion, if you pay the tax from the IRA.

Imagine that you are considering doing a $50,000 conversion. And imagine that you have a 20% tax rate right now. If you convert it, you’re left with $40,000 in a Roth IRA. And the Roth IRA can now grow tax-free, which means your after-tax value can be represented as:

- $50,000 x 0.8 x Year-1 return x Year-2 return x [any additional years of returns]

(Note that in the above, a 7% return would mean multiplying by 1.07. A negative 5% return would mean multiplying by 0.95.)

Or, you can keep the money in a traditional IRA, let it grow, and pay tax later. If we assume that you would also have a 20% tax rate later, then your after-tax value can be represented as:

- $50,000 x Year-1 return x Year-2 return x [any additional years of returns] x 0.8

And the key point here is that those are the same thing. It doesn’t matter whether the returns are good or bad. Nor does it matter how many years of returns there are in between. It’s a textbook case of the commutative property of multiplication.

Breakeven analysis is predicated on the concept that you’re paying some cost up front, which is bad, and that you have to wait for some period of time before paying that cost is “worth it.” But with Roth conversion analysis, if you don’t pay the cost now, you have to pay it later (i.e., the cost cannot be completely avoided). And because the figures in question are all multiplication, it’s no worse to pay it sooner rather than later. (And in fact paying it sooner is often advantageous, because waiting until later to pay the tax often means the distributions themselves are larger — because the account has grown — which can itself increase the *rate* of tax. And again, the rate of tax is what we care about.)

Some smarty-pants might say, “but you’re forgetting time value of money! Time value of money tells us that it’s better to pay the cost later.” Nope. Not in this case. If the cost were a fixed *dollar* amount, that would be true. (Because then what we’re doing is subtraction. And once you mix subtraction in with a bunch of multiplication, the order becomes important.) Paying $10,000 today is worse than paying $10,000 several years from now.

But the tax on a distribution from a retirement account is not a fixed dollar amount. It’s a percentage. Paying 20% now vs. 20% later really does not matter. (Again, see our two bullet point options above. They’re the same.)

The Roth conversion question is generally just about whether you can pay a lower percentage now than you would pay later. If so, a Roth conversion *is* advantageous. And that would be true even if you planned to take the money out of the account next year (assuming, that is, that you’re at least age 59.5, so we don’t have to worry about the Roth conversion 5-year rule).

Again, we can just try the math for ourselves to demonstrate. Imagine it’s again a $50,000 amount you’re considering converting. And imagine that you have a 15% marginal tax rate this year, and a 25% tax rate next year.

If you do a Roth conversion, the after-tax amount is: $50,000 x 0.85 x the return over the next year.

And if you don’t do a Roth conversion (and instead take the money out of the account next year) the after-tax amount is: $50,000 x return over the next year x 0.75.

No matter what you plug in for the return, the first option is better. No need for the money to be in the account for a given length of time. (Again this is assuming that you’re at least age 59.5. Otherwise we have the Roth conversion 5-year rule to consider.)

### When Breakeven Analysis Does Apply to Roth Conversions

As noted above, if the tax rate you would pay on a conversion is lower than the tax rate you would pay when the money comes out of the account later, a Roth conversion is advantageous. But there’s one case in which it can make sense to do a Roth conversion even when your current marginal tax rate is *slightly* higher than the marginal tax rate you expect to face later. Specifically, that can occur if you aren’t paying the tax out of the IRA but rather paying the tax out of assets you have in a taxable account.

And that’s when a breakeven analysis could apply. Because in that case, we’re no longer multiplying the IRA assets by a given figure, to represent the tax paid on the conversion. Instead, the *entire* amount taken out of the traditional IRA is going into the Roth IRA. And you’re paying the tax from somewhere else. (Effectively, you’re using taxable assets to “buy more” Roth IRA space.) And whether it makes sense to do that depends on a whole bunch of things, one of which *is* the length of time that the money will stay in the Roth (i.e., how long do you get to benefit from the tax-free growth that the assets will now experience, because they’re no longer in a taxable account). Other factors that are relevant in such a situation include:

- What rate of return you anticipate earning on the assets,
- What rate of tax you would have to pay on that return (and when you would have to pay it), if the assets stayed in a taxable account,
- What (if any) tax cost is incurred as a result of selling the taxable assets in question now in order to use that money to pay the tax on the conversion.

But if I’m being honest, I would be reluctant to recommend a conversion to anybody if they’re paying a higher rate of tax on the conversion than they expect to face in the future, even if a breakeven sort of analysis showed that it might ultimately be advantageous. In most cases, I think it’s best to simply compare the tax rates, and if the current marginal tax rate is lower than the anticipated future marginal tax rate, a conversion is advantageous. And if you’re paying the tax out of taxable assets, then, great, it’s a little bit *more* advantageous.