6

Using round numbers, let's assume I have $5,000 (pre-tax) to invest annually in an account that earns 10% per year.

In a Roth IRA scenario, this $5,000 would be reduced to $3,750 if we assume a (nice and round) 25% tax rate. For the Traditional IRA, the full $5,000 would be invested.

Now, if we fast forward 40 years, the Roth IRA account will hold roughly $1.6M whereas the traditional IRA will hold closer to $2.2M. This makes sense, as the Traditional IRA account had a larger basis on which to grow annually. However, if we assume that the $2.2M is taxed as the same 25% rate that the Roth money was taxed going in, then we end up with the same $1.6M that is present in the Roth account.

That being the case, is the sole advantage of the Roth account that you 'lock in' your tax rate? In other words, is a Roth IRA play simply a hedge against higher income taxes in the future? Or is there something I'm missing in my analysis?

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    All the answers naively assume that what the government is promising regarding the Roth is going to hold true once they reach retirement. To say those people are naive is generous. Keep in mind that Roth is relatively new meaning there are relatively few retirees who have any substantial savings in Roth accounts. Given what we know about the scruples of our congress-people, who honestly believes that in 20 or so years when many people have large Roth savings that the government is going to sit back and let all that money go untaxed? They'll certainly backdoor a tax on that money. – Dunk Apr 5 '17 at 21:21
  • @Dunk That is why I personally have mine split 50/50 Traditional/Roth. – Aaron D. Marasco Apr 5 '17 at 21:42
  • I looked into switching to Roth when it started, but considering I still had about 40 years til retirement, I didn't trust congress back then to keep their promise of being tax free at withdrawal. That's when I was naive and generally had a good opinion of congress (or maybe they really were better back then). Anyways, now that I know what money grubbing scum we have for elected officials, I have absolutely no faith in their promises. Thus, I am extremely happy I didn't make the switch in 97 because I don't think there's even 0.1% chance they'll let people go tax free. – Dunk Apr 5 '17 at 21:51
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    I have more faith that the tax-free promise will still hold by the time I retire than I do that Congress won't raise my marginal tax rate to 50% by then. I think the uproar would be higher at the former, as that is a clear backtrack on a promise or contractual agreement, than at the latter, which is "merely" an "adjustment" or "redistribution of wealth". At any rate, I'm split (diversified) also. – shoover Apr 5 '17 at 22:10
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    @Dunk Ex post facto laws are explicitly unconstitutional. They could eliminate the benefit for future contributions, but they can't legally change the rules on money that was already put in Roth IRAs - it would never pass a court test. – EJoshuaS Apr 6 '17 at 3:57
15

Your math is correct. As you point out, because of the commutative property of multiplication, Roth and traditional IRAs offer the same terminal wealth if your tax rate is the same when you pull it out as when you put it in. Roth does lock in your tax rate as of today as you point out, which is why it frequently does not maximize wealth (most of us have a higher tax bracket when we are saving than when we are withdrawing from savings).

There are a few other potential considerations/advantages of a Roth:

  1. Roth and traditional IRAs have the same maximum contribution amount. This means the effective amount you can contribute to a Roth is higher ($5,500 after tax instead of before). If this constraint is binding for you and you don't expect your tax rate to change, Roth is better.

  2. Roth IRAs allow you to withdraw your contributed money (not the gains) at any time without any tax or penalty whatsoever. This can be an advantage to some who would like to use it for something like a down payment instead of keeping it all the way to retirement. In this sense the Roth is more flexible.

  3. As your income becomes high, the deductibility of traditional IRA contributions goes to zero if you have a 401(k) at work (you can still contribute but can't deduct contributions). At high incomes you also may be disallowed from contributing to a Roth, but because of the backdoor Roth loophole you can make Roth contributions at any income level and preserve the full Roth tax advantage.

Which type of account is better for any given person is a complex problem with several unknowns (like future tax rates). However, because tax rates are generally higher when earning money, for most people who can contribute to them, traditional IRAs maximize your tax savings and therefore wealth.

Edit: Note that traditional IRA contributions also reduce your AGI, which is used to compute eligibility for other tax advantages, like the child care tax credit and earned income credit. AGI is also often used for state income tax calculation. In retirement, traditional IRA distributions may or may not be state taxable, depending on your state and circumstances.

  • "traditional IRAs maximize your tax savings" did you mean Roth IRAs? If you can contribute the max (or at least the same amount) either way, Roth has a tax benefit since the gains are tax-free. – D Stanley Apr 5 '17 at 19:23
  • @DStanley No, I did not. X*(1+R)^t*(1-tax) = X*(1-tax)*(1+R)^t. Roth and traditional have the same effect on terminal wealth if the tax rate is the same. Roth just shifts the tax burden from the future to now as the OP correctly points out. – farnsy Apr 5 '17 at 19:25
  • So how does a traditional IRA maximize your tax savings? You pay more tax in the future, but can contribute more now if you use a traditional IRA. If you contribute the same amount now, the tax savings of a roth can be significant (the (1-t) factor on the right side of your equation goes away. – D Stanley Apr 5 '17 at 19:28
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    "As your income becomes high, the deductibility of traditional IRA contributions goes to zero" Only if you are covered by an employer retirement plan during the year (e.g. if you have contributed to a 401(k) during the year). Otherwise, deductibility of Traditional IRA contributions is not affected by income. – user102008 Apr 5 '17 at 20:18
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    "In principle at these incomes you are also disallowed from contributing to a Roth" - well, not quite. For a single filer covered by an employer retirement plan, the traditional IRA deduction phaseout starts at $61,000, while the Roth IRA contribution phaseout starts at $117,000. So, disregarding backdoor, there's a rather wide $56,000 MAGI range where you can make Roth contributions but can't deduct tIRA contributions. – senshin Apr 5 '17 at 20:46
2

Couple points:

1) Since the Roth is after tax, you can effectively contribute more than you could with the Traditional IRA before hitting the limits. So in your example, if you had extra money you wanted to invest in an IRA, you could invest up to $1,750 more into the Roth but only $500 more into the Traditional (current limits are $5,500 per year for single filers under 50). Your example assumes that you have exactly $3,750 in spare money looking for an IRA home.

2) The contributions (but not earnings) can be withdrawn from the Roth at any time, penalty and tax free.

3) The tax rate "lock-in" can be significant, especially early on when you are at a relatively low tax bracket, say 15%, but expect to be higher at retirement.

4) Traditional IRAs and 401(k) are taxed as ordinary income, so you go through the tax brackets. Even if the marginal rate is 25%, the effective rate may be lower. If you have a Roth, conceivably you could reduce the amount you need to withdrawal from the Trad IRA/401(k) to reduce the effective tax rate on those (of course subject to minimum distributions and all that). This is more an argument to have a mix of pre- and post-tax retirement accounts than strictly a pro-Roth reason.

  • "Traditional IRAs and 401(k) are taxed as ordinary income, so you go through the tax brackets." I think that's more of an advantage of Traditional over Roth. – user102008 Apr 5 '17 at 20:21
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    @user102008 it's an argument to diversify and not rely exclusively on the Roth or Traditional. For example, withdraw from Traditional through the 15% bracket, and withdraw from the Roth for any additional needs will be better off than do either one exclusively (if you can deduct the Traditional at >15% when contributing) – pwcnorthrop Apr 5 '17 at 20:28
  • All else equal, Traditional wins if your tax rate while contributing is greater than at retirement. Roth wins if the tax rates during contribution is less than at withdrawals. You want to make your contributions and withdrawals to maximize both "wins". – pwcnorthrop Apr 5 '17 at 20:40
2

This analysis misses the opportunities the Roth IRA presents to those with special access. It assumes that all money grows at the same rate, with investments at regular intervals. These assumptions hold for normal workers, but not for the privileged.

Suppose, for example, that in a single year you have limited access to a security that is an acorn you know will grow into a mighty oak; for this example, this security will grow 1000x over some short period of time. For simplicity, assume both the value of acorns you can buy and the the maximum IRA contribution in this year is $5K.

After the short acorn growth period, the after tax values are:

  • IRA $5M * (1 - .25 [income tax, illustrative only]) = $3.75M
  • Roth IRA $5M

There is a minor difference in the amount of money you need to buy the acorns (pre v. post tax), but this is negligible relative to the amount of cash you can assume you have on hand to have special access.

The Atlantic provides an acorn example from private equity (not used with a Roth) and this Washington Post article describes someone with non-publicly traded startup stocks and a Roth.

  • I suspect Mitt Romney used these strategies to pad his IRA. Even at the limit and 401(k) rollover, hundreds of millions of dollars could only have come as you suggested. – JoeTaxpayer Apr 5 '17 at 22:13
  • This is an interesting comment. Ultimately, though, it's a restatement of the fact that Roth IRAs have a higher effective maximum contribution. Your example is one in which the maximum contribution effect completely dominates the marginal tax rate effect. – farnsy Apr 7 '17 at 14:32
2

Time to look at a tax table.

A retired couple hits the top of the 15% bracket with an income of $96,700. (I include just the standard deduction and exemptions.) The tax on this gross sum is $10,452.50 for an 'average' rate of 10.8%.

This is what 2 answers here seem to miss, and the 3rd touches, but doesn't keep going.

The tax, paid or avoided, upon deposit, is one's marginal rate. But, at retirement, the withdrawals first go through the zero bracket (i.e. the STD deduction and exemptions), then 10%, then 15%.

The Roth benefit is maximized

  • Use the Roth to deposit when in the 10 or 15% bracket
  • Use Roth conversions to 'top off' the 15% bracket when able to do so
  • Using a more sophisticated method of multiple account/asset conversions and annual recharacterizations to magnify the value of converted funds.

In the end, to choose between Traditional or Roth, one would have to have far more details regarding the person's financial situation. The right choice is rarely 100% known except in hindsight.

1

In a Roth IRA scenario, this $5,000 would be reduced to $3,750 if we assume a (nice and round) 25% tax rate. For the Traditional IRA, the full $5,000 would be invested.

No, that's not how it works. Taxes aren't removed from your Roth account. You'll have $5,000 invested either way. The difference is that you'll have a tax deduction if you invest in a traditional IRA, but not a Roth. So you'll "save" $1,250 in taxes up front if you invest in a traditional IRA versus a Roth.

The flip side is when you withdraw the money. Since you've already paid tax on the Roth investment, and it grows tax free, you'll pay no tax when you withdraw it. But you'll pay tax on the investment and the gains when you withdraw from a traditional IRA. Using your numbers, you'd pay tax on $2.2MM from the traditional IRA, but NO TAX on $2.2MM from the Roth. At that point, you've saved over $500,000 in taxes.

Now if you invested the tax savings from the traditional IRA and it earned the same amount, then yes, you'd end up in the same place in the end, provided you have the same marginal tax rate. But I suspect that most don't invest that savings, and if you withdraw significant amount, you'll likely move into higher tax brackets.

In your example, suppose you only had $3,750 of "discretionary" income that you could put toward retirement. You could put $5,000 in a traditional IRA (since you'll get a $1,250 tax deduction), or $3,750 in a Roth. Then your math works out the same. If you invest the same amount in either, though, the math on the Roth is a no-brainer.

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    If I have $5,000 to invest, before taxes have been considered, then in effect investing that $5,000 in a Roth does 'remove' the $1,250 from the account. This is because I must pay taxes on that $5,000 before investing it. Either way, I think we're saying the same thing in different ways. – wesanyer Apr 5 '17 at 19:03
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    No, you're saying that you'll have $3,750 in your Roth which is incorrect. If you invest $5,000 in a traditional IRA you'll get a $1,250 deduction from your taxes. If you're under-withholding and need the $1,250 to pay taxes (and therefore can only invest $3,750 in a Roth) then you'll be in the same place. You don't "pay tax" when you invest it; you pay tax when you file. – D Stanley Apr 5 '17 at 19:07
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    Ok, I'm still a bit confused. But I can see that you think I'm saying "If I put $5,000 in a roth account it will shrink to $3,750". That's not what I'm saying. I'm saying if I have $5,000 of 'discretionary' income (as you put it), I can pay taxes on them and put $3,750 in a roth, or not pay taxes and put all $5,000 in an ira. It amounts to the same thing you're saying: you're "$1,250 in tax savings" is the same as my "$1,250 in taxes". I think... – wesanyer Apr 5 '17 at 19:56
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    @wesanyer Yes I agree with that. Although I would word it as "I have $3,750 in discretionary income, but can invest $5,000 in a traditional IRA since I'll also get a $1,250 tax deduction". Mathematically it works the same, but from a different angle. You don't pay the tax immediately, but when you file. – D Stanley Apr 5 '17 at 19:58
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    @wesanyer Or alternately "I can invest $3,750 and save $1,250 to pay my taxes". – D Stanley Apr 5 '17 at 20:08
0

There's a serious mistake in your analysis: granted, in the traditional IRA, you avoid paying taxes on the $5000 now, but you're now stuck paying taxes on $2.2 million dollars when you withdraw it later. Obviously, you'll end up paying massively more than $1250 in taxes on this in the end.

As other people have pointed out, if you can afford to cut the $1250 elsewhere in your budget, you could still end up with the $2.2M. However, let's say just for argument that you don't; the question then becomes if you're better off taking the tax hit on the $5,000 now or the $2.2 million later.

It also really matters how much money you'll be withdrawing when you retire as well as how you'll be doing the withdraws. Personally, my goal is to be able to withdraw as much per year as my highest salary while working, so clearly the Roth IRA is a good deal for me.

An important consideration here is that most people believe that their expenses will go down when they retire, but the majority of retirees in some surveys have indicated that their expenses either stayed approximately the same or actually increased.

Also, quick reality check: would the fact that you know you'd be saving $1250 on your taxes by contributing to the IRA actually cause you to contribute an extra $1250 to your retirement? Even if you personally would, I highly doubt that most people, with the exception of people who post on this site :), actually think that way (especially given how little most people actually save for retirement).

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    You meant $1250, right? – JoeTaxpayer Apr 7 '17 at 14:09
  • Aside from the possible tax number typo, this is an excellent point. Health care expenses alone typically increase dramatically in retirement. Having tax-free access to that Roth money would pay off when you need that heart surgery or nursing home stay. – Ogre Psalm33 Apr 7 '17 at 14:17
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    Your first few paragraphs appear to ignore the time-value of money. At an appropriate discount rate, the millions of dollars you mention in the future have a present value exactly equal to the $5000 today. Ultimately your argument hinges on your last paragraph: people make larger effective contributions to their Roth because they don't understand that an after tax dollar saved is more than a before tax dollar saved. I don't agree that people are that irrational overall, but it would depend on the person. – farnsy Apr 7 '17 at 14:38
-1

Fast Forward 40 - 45 years, you're 70.5. You must take out ~5% from your Traditional IRA. If that was a Roth, you take out as much as you need (within reason) when you need it with zero tax consequences. I don't know (and don't care) whether they'll change the Roth tax exclusion in 40 years. It's almost guaranteed that the rate on the Roth will be less than the regular income status of a Traditional IRA. Most likely we'll have a value added tax (sales tax) then. Possibly even a Wealth Tax. The former doesn't care where the money comes from (source neutral) the latter means you loose more (probably) of that 2.2 MM than the 1.7. Finally, if you're planning on 10%/yr over 40 yrs, good luck! But that's crazy wild speculation and you're likely to be disappointed. If you're that good at picking winners, then why stop at 10%? Money makes money. Your rate of return should increase as your net worth increases. So, you should be able to pick better opportunities with 2.2 million than with a paltry 1.65 MM.

  • The RMD at 70.5 is less than 4%, $80,292 on that 2.2M for an average rate of less than 10%, although I'd suggest taking out the full $96,700 I mention in my answer. – JoeTaxpayer Apr 5 '17 at 23:56

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