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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