Regular 401k: Undeniable Math it’s Better Than The Roth
Updated on June 22nd, 2020
Retirement planning does not come easy for most people and there are a plethora of choices to make in the process. This article focuses on the two account types for the Individual Retirement Account (IRA) and 401(k) (or more simply the 401k), and how you should make your choice by focusing on the after-tax value. Your options are to either choose a Roth 401k (Roth IRA), where contributions are after-tax, or choose a standard 401k (standard IRA), where contributions are pre-tax. In retirement, the Roth accounts pay no taxes on distributions, while the standard accounts pay ordinary income taxes. The Roth variation has only existed since 1997.
For a quick recap, the 401k is handled through your employer and for 2020 has a contribution limit of $19,500. With an IRA, you open an account at a retail brokerage such as Vanguard or Schwab and can contribute up to $6,000 for 2020. There are income limits that apply to IRAs that you need to be aware of. Some people open a rollover IRA where the funds are transferred from a 401k plan through a previous employer to either consolidate accounts or expand their investment options.
Should You Choose the Roth 401k or the Standard 401k?
Almost all the personal finance gurus out there favor the Roth and tout the benefits of having tax-free income in retirement after decades of compounding. But there is nothing magical about paying taxes upfront that somehow leads to more money in the future. I go against the herd and explain why most people should pick the traditional type based on the concept of tax arbitrage.
You Either Pay Taxes Now, or Pay Taxes Later.
Mathematically, if the tax rate is the same in the contribution period and the withdrawal period, the value of both account types will be exactly the same from the commutative property of multiplication:
Why The Traditional 401k is Superior
Tax arbitrage. You contribute during your peak earning years taking a deduction at a high tax rate and take distributions during retirement paying a lower tax rate.
Of course there are some assumptions for being able to exploit that tax arbitrage. If you are still working while taking distributions during ‘retirement,’ your regular working income will push up your marginal tax rate reducing any benefit. But the whole point of a retirement account is to replace working income by not actually working and that is actually the goal of most people.
How It Works
If you wonder why your tax rate will be lower during retirement, it’s because when you contribute to a traditional retirement account during your working years, the deduction is applied against your highest marginal tax bracket, but when you take a distribution during retirement, your money is spread out over several lower tax brackets, each bucket being filled with a higher tax rate along the way, creating a lower average (effective) tax rate.
The valuation formulas then become:
Since Retire_Avg_Rate <= Marginal_Rate, mathematically it is proved that the value of the traditional account will be greater than or equal to the Roth account type. The worst case scenario is that the accounts have the same after-tax value if you are in the lowest tax bracket in both the working and retirement periods. The only way the Roth could have more after-tax value is if your average retirement tax rate is higher than your working years, such as if future tax rates increase, which is what a lot of people are concerned about. I address this possibility in a section below, but first an example illustrating the numbers.
Example With Median Earning Family
Let’s say you are a median working family in America earning $55,000 annually. Most financial advisors will advise that you aim to have enough funds in retirement to withdraw 80% of your working year salary. But to make it a fair comparison, let’s say you did well with your saving and investing and have enough to withdraw exactly 100% of your working salary every year, the whole $55,000 enchilada. Tax brackets are adjusted by inflation so you can ignore the effects of inflation here. The math also works if think of it as only two years right next to each other: your last working year and your first year of retirement.
At $55,000, your marginal federal tax bracket will be 12% today (after factoring in the standard deduction), which means every $10,000 yearly contribution to a traditional 401k will save you $1,200 in taxes today right off the top. Five and a half years of contributions is $6,600 in taxes you didn’t have to pay right now, but would have to pay immediately with a Roth.
When you retire and you are not working, you will start living off your standard 401k and those distributions will be classified as ordinary income. A portion of that money will be tax free due to the standard deduction, then a portion will be subject to the lowest tax bracket, and the next portion will apply to the next highest tax bracket and so on. The key point to recognize is that the taxes you will pay in the future will have an average rate lower than the marginal rate you saved it at.
The table below shows that you first subtract the standard deduction of $24,000 per family (halve everything for singles). That leaves $31,000 of taxable income. Then with 2020 tax rates, the first $19,750 will be taxed at 10% and then next $11,250 will be taxed at 12%, creating an average tax rate of 6.05%. The tax of $3,325 to pay is about half the amount required to pay immediately with a Roth. You saved nearly 50% by choosing a traditional, standard retirement account!
When will there be no advantage of a traditional account over a Roth? If you are a low income earner and only make income in the lowest tax bracket. If your family earns $43,750 or less ($21,875 for singles), the economic value of a Roth and a traditional account is the same, since all the money is taxed in the lowest tax bracket in both periods and no tax arbitrage is possible.
If your income will increase in the future, you can contribute to a Roth 401k now until you are pushed into a higher tax bracket later and start contributing to a traditional 401k then to reap those benefits.
What if Taxes Increase?
Many people are worried about the national debt and assume that taxes will be higher in the future, even though tax rates have been declining for decades. It’s impossible to know what congress has in store for future generations, but the best assumption for people with 8-12 years to go until retirement is to assume that rates will be about the same, since presidential cycles are the primary cause for adjustments.
But we can play with this assumption: What if the tax rates were to double during your retirement years?
There are two parts to the tax brackets, the rates and how wide the bracket is, but assume the width of the brackets don’t change. If the width of the brackets increases, it just means more money is taxed at lower rates and since we are trying to challenge the traditional account type, we won’t make the comparison any easier.
Would you have been much better off with a Roth account in this scenario? No, not really. The after-tax value is almost the same (an extra $50 a year in taxes paid with the Traditional).
It’s a pretty strong result that the rates of the tax brackets could double after you’ve already saved your money and the traditional account still holds it weight against the Roth.
Additional Factors that Favor the Traditional 401(k)
State tax is another consideration in the analysis. Some states, like Pennsylvania, tax your contributions regardless of account type, but don’t tax distributions during retirement. Most other states, like Massachusetts, treat contributions and withdrawals the same way the federal tax code does. If you live in a state that follows the federal method and plan on retiring to a state with lower or no state income taxes, this strongly favors the traditional retirement account since you’ll be saving both the marginal federal rate and the state rate on top of it.
To illustrate the complete picture, say your family earns $55,000, makes 20 years of contributions of $5,000, invested in index funds and earns 7% a year. Your state tax is 5% but you will move to Florida in retirement. At the end of the 20 years, the after-tax value of the traditional account will have 13% more than the Roth or taxable account. The taxable account and Roth have the same after-tax value here because the capital gains tax for families who earn under $80,000 a year is 0% in 2020, a very nice perk.
For a higher income family where the 22% tax bracket applies, and a 15% capital gains tax rate applies with a $10,000 yearly contribution, the Roth is worth 12% more than the taxable account, after-tax, and the traditional account is worth 20% more than the Roth, after-tax. That’s a full $60,000 more! Again, the value of the traditional retirement account is hard to beat.
My goal here is only to compare the after-tax economic value of the different account types. Roth accounts do have some other advantages, such as a lack of required minimum distributions (RMDs), being able to withdrawal contributions for specific purposes without penalty, and income that doesn’t count towards Medicare Plan B payments, but these are largely minor benefits that don’t skew the analysis away from the big expense which is the tax you actually pay. See the comments for a lively discussion of RMDs, Medicare Plan B and Social Security analysis thrown in – my conclusion is the same.
Roth accounts also technically let you stuff more after-tax value into the account since you pay the taxes from funds outside of the account and part of your traditional contribution is earmarked for the federal government later on, but that still doesn’t change the fact that you are substituting a high tax for a low tax.
A lot of people have trouble understanding this concept as if the money you pay immediately doesn’t count. For the traditional 401k, you can look at it as the federal government loaning you tax money to invest for decades of tax deferred compounding.
Either 401(k) Type Is Better Than None At All
If you have any long term savings at all and you make enough income to pay over 0% in capital gains, you should use a tax advantaged account because Uncle Sam takes a cut on both ends, first when you earn it, and second when you grow it it, if you don’t.
But the conclusion is to first maximize your traditional 401k’s and IRA’s before considering Roth 401k’s and IRA’s if you are making more than $21,875 as a single or $43,750 as a family as of 2020.
Only after you have maximized traditional accounts should you consider the Roth variants to capitalize on the tax arbitrage that leads to a higher balance of assets. If you are a high income earner and are above the traditional IRA income limits, first maximize your traditional 401k and then maximize your Roth IRA account. And if you are above the income limit for the Roth IRA account, consider a backdoor Roth conversion by first contributing after-tax money to a traditional IRA and then immediately converting it to a Roth.
Use the free tool from Blooom to analyze your 401k and IRA accounts to see if you should make any changes to your fund allocation or if there are hidden fees you should be aware of.
As long as you never cash out early, you’ll be on your way to a satisfying retirement and you’ve done your best to maximize your after-tax retirement account value by skipping the Roth 401(k).
In the end, this is just a guideline to get you thinking about this tax arbitrage concept and not to blindly accept the conventional ‘wisdom’ that is constantly nudging you into a Roth 401(k) everywhere on the web. In the comments we have continued the discussion for high income earners mixed with Social Security, Medicare Plan B and RMDs in retirement.
For an investment that defers taxes like a retirement account (and eliminates tax upon death), continue reading about Master Limited Partnerships (MLP).
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Just found your site and subscribed. Very interested in Preferred instead of bonds in my retirement income portfolio. I’m a 72 year old Pitt MBA and share your bent for analysis! However, I think your analysis of 401K vs ROTH leaves out two very salient factors for retirees.
1. Taxation of Social Security benefits, the Provisional Income formula. Say our SS income is $63,900. Take 1/2 of that figure and add other income, say $50,000 from ROTH or IRA. The ROTH is ignored and Provisional Income is less than $32,000 so no tax is owed on the SS or the ROTH income! In the case of the IRA, 85% of the SS is taxable and 100% of the IRA is taxable (less the standard deduction). Huge difference!
2. IRMMA determines how much you pay for your Medicare Part B. Consider a single person with income of $87,000 pays 144.60 per month. Adding $50,000 of ROTH has no effect. Adding $50,000 of IRA RMD add a surcharge of 231.40 per month or an additional charge of $2776.80 per year.
There may be other effects like NIIT taxes and Medicare .009 surcharges, but I am not sure.
I have found that there are many aspects of retirement that are very obscure until you become old enough to pay attention, at which point it is costly to change.
Looking forward to learning from you as I intend to convert a significant amount of my IRA mutual funds into Preferreds in my ROTH. I will leave enough in the IRA to do our tithing and charitable giving via QCDs.
I hope this sparks an ongoing conversation!
I always thought that Pitt was coolest campus with the Cathedral of Learning. Very unique.
Two things on Social Security:
1) The income figures I was using in my examples has the implicit assumption that it consists of all income sources. The average $55,000 earner probably won’t actually have a large enough 401(k) balance by retirement to pull out $55,000 every year in retirement when the average account balance in one’s 60s is less than a few hundred thousand (source).
But say the retiree has $1,000,000 by retirement and employs the oft cited 4% rule; $40,000 a year will come from the taxable retirement accounts. With the average benefit of social security being $16,272 a year (source), and assuming someone making an average $55,000 a year would get approximately that, that would put someone right back to the $56k range. Then we are right back to the tax arbitrage comparison point of earning the same amount in both periods.
Two things that it are hard to forecast:
1. What one’s Social Security benefit will be when one has 30 years of work remaining.
2. How much one’s 401(k) balance will be at retirement.
2) You are safe at your age with the social security benefits you are currently receiving, but for us youngins, social security might not make up a significant portion of our retirement income. The trust is scheduled to run out of funds by 2035 (source), at which point payouts will only be 75% of what they are supposed to be. Congress will probably increase taxes and lower benefits to prevent this from happening, but both of these events are not great for people of my age. If I could opt out of social security and never have to pay the 7% again, I certainly would.
As for medicare Part B, I did look at this but when I looked at the table (source), a single person making $87,000 or less ($ 174,000 married) will pay $144.60 a month anyway. It’s only when your income is above that do the surcharges start kicking in. At the next level up to $109,000 for a single and $218,000 for a married couple, it’s an extra $689 a year. Or like you said it you are earning an extra $50,000 a year on top of the minimum threshold ($137,000/$272,000) it’s an extra $2,776 a year, or about 2% of the income. High income readers should consider if that surcharge will cost them more than they are saving.
And I agree that there are other variables like the the ACA surcharge for net investment income over $200,000. The moral of the story is that high income earners have more to worry about with the potential gotchas and should fine tune any analysis to their own personal situation. Luckily most readers won’t have to worry about these issues.
And you are exactly right that most people should think about these obscure issues now instead of making an arbitrary decision that might cost them in the future. I hope this page and comments will do exactly that.
To your final comment, if you have stocks or highly appreciated mutual funds outside of retirement accounts, you should look into donating those shares without first selling them. You’ll be able to avoid paying taxes on them and the donation will amount to more. Probably can’t do that same tactic from IRA funds, but a tax advisor might have some special tricks up their sleeve.
Thanks for the thoughtful reply.
Perfect explanation, thank you
Liked the math analysis – could tell you have a solid math background. However, I think Roth works out better for higher earners. If one is 30 years old & maxing out their 401K till they retire (let’s say another 30 years), they would end up with ~5 mil (assuming an 8% yoy increase). The RMD for such a portfolio would be almost 200K a year on retirement (& increases with age). Wouldn’t Roth be flat out a better case for such high earners?
^Assuming you roll over your ROth 401K to a Roth IRA to prevent RMD, i.e
Hi Ayush,
Thanks for the comment. I love putting some numbers to the story line. So, with your assumptions, the account balance 30 years later will be about $2.5 million. There are these cool little calculators I am using in this comment for illustration (source).
Ultimately the answer really depends on what tax bracket (+state tax) the high income earner is in now versus later. Even if the RMD is $200,000 a year, the effective federal tax rate is only 15% (if married) today. The marginal tax rate for the same income is 24%, so there is still about 6% of arbitrage if the state tax in both periods is the same (source).
That 24% rate for a married couple goes all the way up to $321,450 of income. So if you are a super high income earner above that, you may have a problem.
Some more thoughts on RMDs:
1) RMDs don’t kick in until 70.5 years of age
2) RMDs for this example start at around $100,000 a year and then scale up, but you wouldn’t start taking out $200,000 until age 85, assuming you didn’t withdraw anything before 70.5. There’s a cool calculator for this too (source)
3) If you actually retire at 60, per our example assumptions, you still have a solid 10.5 years of throttled withdrawals that will reduce the account balance even more.
4) You could optimize how much you take out before 70.5, keeping your withdraws under a particular tax bracket and then contribute that amount to a Roth IRA.
5) Bonus: There is a rule of 55 that allows you to start taking your money out of your 401(k) if you leave your job after 55. I’m suspecting that people with multi-million dollar 401(k)s would consider retiring early. That further provides the opportunity to start optimally extracting money out of the 401(k).
6) RMDs of $200,000 a year are ultimately a good problem that few people will have. If I have this “problem” at 85 years old and if Congress jacks tax rates up significantly, the thought that I might not have optimized my tax savings over the prior decades won’t be high up on my priority list. 🙂
Thanks for that analysis! I forgot to mention this, but such a high earner would probably have high social security benefits as well (assuming we still go on with social security, which I know you mentioned in another comment may not be the case). If you have both RMD’s and security benefits kicking into the same year, wouldn’t the arbitrage benefit be offset by the additional taxes you pay on the social security? Let’s use the same example for consistency. Your first RMD kicks in age 70.5. To make it harder for my cases, I’ll assume you reduced funds to 1 mill by taking out funds after 60 like you mentioned. The RMD is 40K at year 70 and let’s assume the social security benefit is 80K (conservative estimate using https://smartasset.com/retirement/social-security-calculator). The taxes you’d be paying on the benefits at age 70 would be ~7K more than if you were taking out the same 40K from a Roth account. Even assuming a generous tax arbitrage of 10%, the 7K loss outweighs the 4K gain on a 40K withdrawal. Let me know if there are any holes in my analysis!
P.S – I think you mentioned this in the comment earlier that social security and how much you have in your 401K on retirement is hard to predict. But I think a safe bet for high earners would be to put in money in both, with an emphasis on Roth. Would you agree?
I’m actually glad you brought the social security argument back into the fold.
The maximum benefit allowed by law if social security is deferred to 70.5 would be $82,000. To get that amount it would require the earner to have earned more than the maximum tax cap of $137,700 for 30 years adjusted for inflation. (If it is not deferred and instead taken at 65 it would be a starting benefit of about $55k) (Social Security Tables)
So, if the family earned between $137,000-171,000 for the 30 years, they would have paid (Roth) or saved (traditional) the marginal tax rate of 22%.
When they take it out, with a deferred $80,000 yearly social security pension, it would push them right back into the same 22% tax rate. They could have a maximum of $91,000 in taxable income from all sources and remain in the same tax bracket. Consequently, there would be no benefit from either account type from a Federal tax standpoint.
+If you factor in the Medicare plan B discussion in the comment above, it tips the scales slightly into the Roth account by 1-2%.
+But if you move from a state paying 5% tax to a tax free state in retirement like a lot of retirees do, it tips the scales back into the regular 401(k) camp even with the medicare plan B.
+If your family earns more than $171,000 now, you are in the next tax bracket (24%) and the traditional account is the winner again.
The nice thing about the traditional 401(k) is you have more flexibility for strategy in your later years. With the Roth, you pre-pay the tax upfront at the highest rate and there is nothing else to be done. When you retire and defer taking social security, you will have a number of years (as many as 15 if retiring at 55) to take the maximum amount that would keep you under the prior high tax rate, about $104,000 (80,000+24,000), and transfer some or all of it to a traditional IRA and then do an immediate conversion to a Roth. This way you will end up with Roth assets during your RMD years anyway.
And remember, the RMD is only the minimum. If you have a $1,500,000 account at 70, you are only required to take out about $55,000. You could take out an extra $35,000 and that would keep your RMDs under the $91,000 threshold for a lot longer than if you only took out the minimum and let the balance continue to grow.
So, if you are confident that you will earn the maximum social security benefit, your account balance will be more than $2,500,000 at age 70.4 when RMDs kick in, and IF you won’t move to a tax free state, then having a portion of that account in a Roth 401(k) could benefit you. It would require some great modeling with a lot of assumptions to determine what that optimal percentage is, of course.
But again, the state tax is SO critical to the analysis. Simply moving to a tax free state and saving 5%, you could have RMDs up to $222,601 a year (which would occur at year 14 with a $3 million starting account balance at age 70.5) and still do better with the traditional (32% bracket at 24k+80k+222k=326k).
So to answer your last question, I strongly believe that the odds are so stacked against the Roth account that I contribute nothing to a Roth 401(k) and max my traditional account, and that is the conclusion I think applies to most people.
Thanks again for taking the time to reply! I carefully read through you’re analysis and have to agree – odds are it’s better to go with a traditional. Unless you have 2.5 mil by 70 haha. I’m in a state without income tax right now though. So I guess the best strategy is to keep most of it in a traditional401K. But probably need to revisit it every year and adjust so that you’re going to hit the right numbers closer to age 70, updating it according to the latest laws.
On a side note, tax strategy would have been so much simpler if everything was a flat tax :D. The piecewise break up makes it a horribly non linear problem lol.
Glad to help! It’s been an interesting analysis problem to work through.
And you are absolutely right – taxes would be so much simpler with just a flat tax and say, a single standard deduction. Unfortunately we’ll never have that in this country though.
And like you also said, tax laws change every couple of years, so keeping up on the latest rules will help guide along the planning.
Feel free to comment on any other articles of interest 🙂
I am very intrigued by this article. While the tax savings math you used with the distribution amount example makes a lot of sense, it’s looking at the bigger picture that confuses me. Since I am 23 years old now, in theory I would have about 40 years to retirement. Using average stock market return rate of 7% shows me that the end result of contributing only 3k a year leaves me with an account balance of almost 600k, with total amount contributed at 120k. I can’t wrap my mind around any tax rate where it would be better to pay taxes on 600k vs paying for 120k. So I took to Google and ended up on Bankrate with a traditional vs roth calculator and found there that according to their calculations, roth comes out on top. The only caveat is that when selecting the option on the calculations to “invest immediate tax saving from traditional contributions” the traditional comes out on top by maybe a couple percent. However, this strategy seems a little to savvy for the average person as most people don’t just dump their tax return into an IRA or taxable. Curious on your thoughts.
Hi Jared,
That’s exactly the crux of the issue. Usually the comparison between the two account types only looks at the taxes not paid at the end of 30-40 years but ignores the reinvested tax savings over 30 years. Let’s say you make a commitment to contribute $10,000 a year into your 401(k). With the traditional, that $10,000 comes right out of your annual income. With the Roth, if you contribute that, then you need an extra say $2,000 to fund the tax bill. So if you only want $10,000 to come out of your paychecks you’d actually only contribute $8,000 to your Roth. So effectively with the traditional account, the government is giving you a $2,000 a year tax deferred loan to invest on their behalf, which a portion will have taxes taken out in the end. The real irony here is that you can end up paying a lot more in taxes than the taxes paid on the 120k contributed, but still have more after-tax money for yourself too. Conversely, you might not pay any taxes on the money at all in retirement if the account is appropriately throttled to stay under the lowest tax bracket. Good job on researching these issues early in your career!
OK Ryan:
My wife and I are 58. We have $1,300,000 in traditional 401 and IRA and another $250,000 in emergency savings. Own our home outright, $400K and have no debt. My wife is to retire at 62 and I will at 65, at least thats the plan. Should we continue the traditional route or go Roth? Should we consider a converstion? many tout the Roth. I am of the mind that the current tax savings, allowed to reinvest for years, is a big plus. Your thoughts?
Congrats on the successful retirement planning, you are in good shape! I am of the same opinion for current tax savings, as indicated from my lengthy post.
If you are 58, you are likely in your prime earning years, so your tax rate is high and when you both retire, your tax rate will be lower, so the regular 401k is the way to go. If you do a conversion, all that you convert will be taxed at your highest tax rate, which is not good. The only time a conversion makes sense is if someone has lower income relative to other years where they can sneak the converted amount into lower tax brackets, such as if they had a bout of unemployment, or are in retirement.