Regular 401k & IRA: The Undeniable Math To Avoid The Roth
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Updated on November 12th, 2021
Retirement planning does not come easy for most people and there are a plethora of choices to make in the process. If you have ever asked, “Should I do a Roth or traditional 401k,” this article is for you.
This article is not about discussing whether you should pick an Individual Retirement Account (IRA) versus a 401(k). Instead, it’s about whether you should pick the Roth or traditional style of either account type.
The obvious question is “Which account style leads to more money?” And the answer we will prove herein is that it’s the traditional 401k or standard IRA, and not the Roth account style, contrary to popular opinion and finance gurus.
What Is The Difference Between a 401(k) or IRA
For a quick recap on the difference between the two, your options are to either choose a Roth 401k (Roth IRA), where contributions are after-tax, or choose a traditional 401k (traditional 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 401k is handled through your employer and for 2020 & 2021 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 & 2021. Sadly the limit was not increased for 2021.
The options inside an employer 401k are usually pretty limited to a handful of funds, but with an IRA you can buy almost anything exchange traded.
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The Roth variation has only existed since 1997.
Which is Better Roth or Traditional?
Almost all the personal finance gurus out there favor the Roth account type 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. In fact, quite the opposite.
I go against the herd and explain why most people should skip the Roth option and pick the traditional type because, for most people, it will lead to more money. This is explained through the concept of tax arbitrage.
Tax Arbitrage: 401k Math
The fundamental idea is whether you pay taxes now or pay taxes later.
Mathematically, if the tax rate is the same in the contribution period and the withdrawal period, the after-tax value of both account styles will be exactly the same from the commutative property of multiplication:
When is the Traditional 401k Better Than the Roth?
When your retirement tax rate is lower than your contribution rate.
This is the concept of tax arbitrage: You contribute during your peak earning years, taking a higher income tax rate deduction (saving more tax dollars now) and take distributions during retirement paying a lower income tax rate.
How Tax Arbitrage 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 a single bracket, 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.
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Of course, by retirement, the assumption is that you are actually retired. If you continue working while taking distributions from your retirement accounts, your regular working income will push up your marginal tax rate reducing the tax arbitrage benefit being described now.
The valuation formulas become:
Since Retire_Avg_Rate <= Marginal_Rate, mathematically 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 marginal tax rate during your working years, such as if future tax rates increase substantially. This is a commonly cited reason for choosing the Roth: risk aversion on future tax rates. I address this possibility in a section below, but first an example illustrating with numbers.
Example With Median Earning Family
Let’s say you are a median working family in America earning $55,000 annually and taking the standard deduction (and ignoring credits for children, etc., which will drop your adjusted income further).
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. Alternatively, you could think about it in a simple two year period: your last working year and your first year of retirement.
At $55,000, your marginal federal income 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 (12%) 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 regular 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 required tax of $3,325 is about half the amount one is required to pay immediately if they choose a Roth account type.
In this median case you can save nearly 50% in taxes by choosing a traditional, standard retirement account!
When will there be no advantage of a traditional 401k over a Roth?
If you are a low income earner and only make income in the lowest tax bracket then neither account has an advantage over the other. 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, pushing your income above the lowest marginal rate, or you are worried about higher tax rates in the future, this would be the time to choose the Roth retirement account.
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What if Taxes Increase?
The most commonly cited reason for choosing a Roth 401k is the risk that tax rates will increase in the future because of the national debt. They may or they may not. Remember, taxes have been decreasing in the United States for decades now, so if someone chose a Roth account back when they were introduced in 1997, they left a lot of money on the table.
With interest rates near zero for the foreseeable future, the national debt servicing costs is the lowest it has been in the country’s entire history. If taxes are to be raised, it will be for other reasons, but I guarantee that paying down the national debt will take last priority.
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 as they are today, since presidential cycles are the primary cause for adjustments.
But we can play with this assumption: What if the income tax rates were to double during your retirement years?
There are two parts to the tax brackets: the rates and how wide the brackets are, 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 be lamenting today’s Roth 401k choice in this scenario? As the table below shows, not really. The after-tax value is almost the same (an extra $50 a year in taxes paid with the Traditional), which is a pretty strong result.
Think about 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, which is usually an extra 5%.
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% federal 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.
So far this has only been an analysis related to the after-tax value of the account types, which is the main difference between the Roth and traditional IRA & 401K.
Roth accounts do have some other advantages, such as a lack of required minimum distributions (RMDs) in retirement, being able to withdrawal contributions for specific purposes without penalty, and income that doesn’t count towards Medicare Plan B payments. However, when you stack these all up, you find they are largely minor benefits that don’t skew the analysis away from the biggest 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 into the account since you pay the taxes from funds outside of the retirement 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 today for a low tax tomorrow. And there is another way to look at it: if you contribute $19,500 to a Roth today and pay an extra $4,290 in taxes today is the contribution really only $15,210?
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A lot of people overlook this concept as if the tax 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 are saving for retirement 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. The whole pre tax vs Roth discussion is moot if you decide not to use a retirement account at all.
But the conclusion is that you’ll have more money in retirement if you 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 income 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. You are paying the tax dollars anyway in this situation, so at least you can save on the back end with the backdoor IRA Roth option.
This article puts some analysis to the Roth vs traditional 401k decision instead of just making assumptions that not paying taxes in the future is the preferable route.
Taxes are complex and there is a whole menu of credits and deductions that change from year to year.
Also, if your employer 401k is loaded with fees, or doesn’t offer a contribution match, it can wipe out the tax savings, and so you may want to go the IRA route. Similarly, if you load up your 401k or IRA with the wrong type of investments, your account could under-perform enough to wipe out any tax arbitrage advantage.
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Continue on into the comments where we discuss high income earners mixed with Social Security, Medicare Plan B and Required Minimum Distributions in retirement. If you don’t want to read through all the details, know that the conclusion still stands: the Regular 401k is the winner!
An investment that defers taxes like a retirement account (and eliminates tax upon death), is the Master Limited Partnership (MLP).
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