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It seems to me that Roth contributions to a 401(k) or a Roth IRA could be extremely tax-advantaged over pre-tax 401(k) or traditional IRA contributions, but at the same time, I have trouble believing that analysis.


Here is my analysis:

Assumptions: Let's assume that the marginal income tax brackets and rates never change in the future. And let's assume that my income never changes either, at least before I retire. Today, my annual income is such that my overall tax rate is 25%.

Scenario 1: I contribute $1,000 pre-tax to a 401(k). Assuming it grows at 5% annually, after 25 years I now have about 3.386 times what I originally had, or $3,386. I then retire and start withdrawing the money just fast enough to match my pre-retirement annual income, until it is all gone.

By my understanding, pre-tax contributions to a 401(k) or IRA and the earnings on them are taxed on withdrawal at the ordinary income tax rates. So in this scenario, I have $3,386 in taxable income from my 401(k).

Since I withdrew my 401(k) money at the same rate as my pre-retirement income, the overall tax rate I face while I withdraw that money is still 25%. So I pay about $847 in taxes.

Scenario 2: I make a $1,000 Roth contribution to a 401(k). Since I can't deduct Roth contributions from my taxable income, I separately pay $250 tax on the income I contributed.

The money grows at the same rate as in Scenario 1, and I also retire after 25 years with $3,386 in the account. And like in Scenario 1, I withdraw the money just fast enough to match my pre-retirement income, until it is all gone.

Earnings on Roth contributions are not taxed ever. So, my $1,000 Roth contribution is taxable income on which I've already paid tax, but the $2,386 in earnings over 25 years is not taxable income. This means my total tax burden is $250.

Conclusion: In Scenario 1, my total tax burden is $847, while in Scenario 2, it is $250. That is $597 less, or over 70% less tax.


So based on this back-of-the-envelope analysis, it seems that I would save a lot of money in tax payments by favoring Roth contributions over pre-tax contributions. And yet it feels like Roth contributions would be orders of magnitude more popular than they are if that were really true for most people. Hence the question:

Have I gotten the math wrong in my analysis, or are there other things I am missing (such as in my assumptions)?

  • 1
    Others have said this in paragraphs, but here it is in one sentence: You should be comparing putting $1250 in the traditional vs $1000 in the roth. – TTT Feb 26 '16 at 17:49
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    That's 20%. A marginal 25% rate offer the choice of $1333 or $1000 – JoeTaxpayer Feb 26 '16 at 21:03
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I think the math is wrong.

Note that in Scenario #1, you are only out of pocket $1000, while in Scenario #2, you are out of pocket $1250; the contribution and the tax you paid with respect to it.

A better concept than tax rate is "Retention Rate". This is the fraction of your money that the Feds let you keep. And Growth Factor is the how much the investment grows.

So In Scenario #1, you multiply $1000 by the investment Growth Factor and then by the retirement Retention Rate.

And in Scenario #2, you multiply the same $1000 by the current Retention Rate and then by the Growth Factor.

Since in your approximation, the two GFs are the same, there is no saving...

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Keep in mind, there are too many variables to address in a single post. I could (and might) write a full book on the topic.

One simple way to comprehend your perceived observation. In the 25% bracket, you have $1000 of income and two choices. Net out $750, and deposit to Roth, or deposit the full $1000 to the traditional IRA or 401(k). Sufficient time passes for the investment to grow 10 fold. For what it's worth, 8% at 30 years will do that.

The Roth is now worth $7500 tax free. The traditional 401(k) is worth $10000 but subject to tax. At 25%, we're at the same $7500.

For those looking to invest more than a gross $18,000, the Roth flavor is an effective $24,000, as post tax, this is $18,000. I wrote a bit more on this in the whimsically titled The Density of Your IRA. This is really a top 10%er issue, as it takes quite a bit of income for the $23,000 combined IRA and 401(k) limits to be a problem.

In my writing, the larger case to be made is for taking advantage of the tax rate difference between the time of deposit and withdrawal. A look at the 2016 tax rates is in order.

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Let's stick with 25% while working. Now, at retirement, but before social security, as that's another story, the couple has $20,600 in standard deduction and exemption, and both the 10 and 15% brackets to enjoy.

Ignoring any other deductions, potential credits, etc, let's look at a gross $80,000 withdrawal.

https://turbotax.intuit.com/tax-tools/calculators/taxcaster/

The numbers happen to work out to an average 10%, with the couple being in a marginal 15% bracket. A full 25% or $20,000 tax would be the break-even to the "same bracket in/out" analysis, so this produces a $12,000 benefit.

This issue is often treated as if there were 2 points in time, the deposit, and the withdrawal. For most people, that may be the case. Keep in mind, current law allows a conversion to Roth any time in between. This gives an opportunity to make a deposit while in the 25% bracket, and convert in any year the marginal rate drops back to 15% for whatever reason.

Last - I can't ignore the Social Security problem. Simply put, when half of your Social Security benefits plus other income exceed $25,000 ($32,000 if married filing joint) your benefits start to become taxable, until 85% of your benefits are fully taxed. This issue is worthy of multiple posts by itself. It's not a deal killer, just another point to consider. A very high income earner might be beyond these levels already, in which case the point is moot. A low income earner, not impacted at all. It's those who are in the range to navigate this that would benefit to take advantage of the scenario I presented above and spend down pre-tax accounts, while planning to use the Roths when Social Security starts. This should make it clear - it's not all or none. Those retiring with $2M in 100% pretax, or $1.5M 100% in Roth have both missed the chance to have the optimal mix.

  • Another point to consider - probability of tax rates changing in the future (at the time of retirement). – alexandroid Dec 15 '17 at 7:13
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Fundamentally, there are two differences between traditional and Roth:

1) With traditional you pay the tax rate that's in effect when you draw it out, with Roth you pay the tax rate when you put it in. Assuming the same tax rate this is a wash.

2) As a Roth contains after-tax money this lets you put more in than you could with a traditional. This is only a benefit if you are in a financial position to put more in, though. If you can't come fairly close to maxing your contribution this gains you nothing.

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    #2 is a pretty huge benefit if you are able to take advantage – Oliver Oberdorf Feb 26 '16 at 3:25
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The first problem with your analysis is that you are not comparing equivalent contributions. The deductible Traditional IRA contribution is in terms of pre-tax money, whereas the Roth IRA contribution is in terms of post-tax money. A certain nominal amount of pre-tax money is equivalent to a smaller nominal amount of post-tax money, because taxes are taken out of it.

For a fair comparison, you need to start with the same amount of pre-tax money being taken out of your wages. If you start with $1000 being taken out of your pre-tax wages, the deductible Traditional IRA contribution will be $1000, but your Roth IRA contribution will be $750, because 25% of it went to paying taxes. If you go through the calculation, you will see that after you withdraw it (and 25% taxes are paid in the Traditional case), you will be left with the exact same amount of money in your hand at the end in both cases.

Even though you see that you end up with the same amount of money, you may still be confused because you paid different nominal amounts in taxes. That's the second problem with your analysis -- you are comparing the nominal amounts of taxes paid at different times. You are missing the time value of money. Would you rather pay $1000 of taxes today or $1001 of taxes in 10 years? Of course you would rather the latter, even though it is a higher nominal amount. A given amount of money now has the same value to you now as a bigger amount of money later. If I invest a given amount of money now, and it grows in to a bigger amount of money later, then that bigger amount of money later has the same value as the original contribution now.

So the 25% tax on the contribution now is equivalent to the 25% tax on the total value later, even though the latter is a much bigger nominal amount. Another way to think about it is that you could have taken that 25% tax you paid now, and instead invest it, let it grow, and pay that result (which will still be 25% of the total later) in taxes later. You get to keep the remaining 75% of your investment either way. You are simply investing on behalf of the government the part of the money you would have paid them, and paying them the result of investing that portion of the money later.

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