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Most Americans keep their retirement savings in an employer-sponsored 401(k) or in a traditional IRA that works the same way. To manage that money well, it is critical that the account’s benefits are understood: What is the net, after-tax outcome at the end of the day when you access your money? Does it save you taxes? How?
The model
The following model of tax-shelters shows the math and logic of what happens. The example uses one set of input assumptions, but the relationships hold true for all assumptions. The benefit from the tax-shelters is calculated as the difference in outcomes versus the taxed account.
The normal taxable and Roth accounts are well understood. Both are funded with $600 after-tax savings. The Roth grows at the nominal rate of return of its investments because no profits are taxed. The taxable account grows slower because its profits are taxed. The $560 net benefit of the Roth is from sheltering profits from taxation. The 401(k) is funded with $1,000 because the $400 income tax is not deducted from wage income. The account grows tax-free. The account total is taxed at withdrawal.
How the account is funded
There is an equality of value between the after-tax $600 funding the Roth and taxable account, and the before-tax $1,000 funding the 401(k). As will be shown, not all the account is ”your money.” The same savings behavior results in each. The 401(k) needs to be larger because its dollars cannot be accessed without first paying tax. The inherent liability for withdrawal tax exists from the very start. It does not show up at the last minute.
The taxman’s share
The 401(k) is best understood by thinking of it as the sum of a Roth account plus a difference. The difference is your best friend Bob, who gives you his money ($400) to invest for him, alongside your own $600. Bob has no say about investments; he gets what he gets. Since your money grows at 8%, so too does Bob’s. Since he funds 40% of the account at the start, at the end he takes back his 40% ($1,864) of the resulting value. His repayment is an allocation of principal between the account’s two owners.
You neither benefit nor lose from the arrangement with Bob. The $400 he gives you is not a gift or a benefit. It is never a reason for you to enter the arrangement. His repayment is not your expense. It is always exactly covered by Bob’s original funding. There is no way you can strategize this arrangement to create a benefit.
While Bob’s money was coming and going, your own $600 was growing tax-free just like a Roth. The most important benefit from a 401(k) is the same $560 benefit from tax-free growth in a Roth. When there is no change in tax rates between contribution and withdrawal, the accounts will have the same dollar outcomes.
You have figured out by now that Bob = Taxman?
Understanding tax-free growth
The calculation of the benefit from tax-free growth uses standard time-value-of-money equations two ways. The benefit equals the difference between the future value of a dollar using before-tax and after-tax rates of return. Or you can calculate it directly with the future value of a growing annuity. The annuity is the $7.20 tax paid in year one. Its growth rate is the 6.8% of the taxed account. The compounding rate is the 8% of the Roth account.
What if tax rates change?
A lower tax rate on withdrawals is a bonus. The reverse is also possible. This possible difference in tax rates is completely independent of the benefit from tax-free growth. Often this factor is attributed to the deferral of tax. That misrepresents it. A withdrawal delayed three decades may still not produce any bonus, and a withdrawal next year could produce a large bonus. It depends on tax rates, not time.
The math is simple. An x% change in tax rates creates an x% bonus or penalty, calculated on the account’s total. If a math model starts with the calculated outcome of a Roth, the 401(k) outcome requires only the additional bonus = $Roth / (1-cont’nTx% ) multiplied by (cont’nTx% less drawTx%).
The industry practice
Before- versus after-tax funding
At least three important industry sources (Vanguard, Betterment, Kitces) give equal weight to after-tax and before tax dollars. This error reverses the asset location conclusions. It can result in 15% reduced outcomes from asset allocation.
Bob’s funding
Contributions to 401(k) accounts are promoted by the government (in Canada and the UK also) with the claim that the $400 tax reduction at contribution is a benefit – a reason to contribute. According to IRS literature, “a traditional IRA is a way to save for retirement that gives you tax advantages. Contributions you make to a traditional IRA may be fully or partially deductible“. That is false. Bob’s $400 will be returned to him along with all the profits it earns. You don’t get to keep it.
Individual steps in the life cycle versus net benefits
That same IRS page continues with a second advantage, that “earnings and gains are not taxed until distributed.” Most in the investment industry think that is damning with faint praise. They warn that profits are taxed on withdrawal, and at full rates, not the preferential rates for dividends and capital gains. In the asset location literature, a common argument is that owning stocks in the traditional IRA or 401(k) accounts eventually turns what would have been a tax preference item into ordinary income. But none of this matters. These are just individual steps in the account’s life cycle. They cancel out each other.
As shown on the right side of the example above, the $1,464 is what the industry thinks of as the ”profits taxed on withdrawal.” It always equals the value of the deferral of tax on contributions (the profits earned by the $400 in the deferral period). The $400 that the industry thinks of as the withdrawal tax on contributions always equals the contribution’s tax reduction that the industry thinks is a benefit. These four factors always exactly equal and offset each other, creating no benefits and no cost.
Wikipedia
The Wikipedia pages for 401(k) and IRAs lack any section on benefits. The IRA page is completely silent. The 401(k) page acknowledges a potential bonus from withdrawal at a lower tax rate, without mention of the penalty. It claims that “less taxes are paid overall with the 401(k) due to the ability to avoid taxes on capital gains.” ……. No comment.
Conclusions
The 401(k) benefits are quite different from what is commonly understood. What matters for strategies and optimizing benefits is:
- The account’s life cycle has three steps – addition, growth and withdrawal. Tax that happens at one step can get reversed at a later step. It is only the net result at the end that matters.
- The 401() holds before-tax dollars. It must be bigger than Roth or taxable accounts just to be equal. It has an inherent liability for withdrawal tax, right from the start.
- Conceptually, the government partially funds the account and continues to own its share.
- The account’s universal benefit is from tax-free growth (of the after-tax savings) – permanently tax-free. This benefit always exactly equals the same benefit from a Roth.
- There is a possible bonus (or penalty) from an effective tax rate at withdrawal lower (or higher) than at contribution.
What does not matter are the tax rules and procedures at individual steps in the account’s life cycle:
- The tax reduction at contribution is not a benefit or reason to contribute. It perfectly funds the eventual withdrawal tax (at the same tax rate).
- There is no benefit from deferral of tax, neither the tax on the original wages nor the tax on profits.
- The withdrawal tax (at the same tax rate) does not include a ”tax on profits – at full rates.” It is an allocation of principal between the account’s two owners, from which you neither gain nor lose.
Chris Reed is an independent retired investor. –Comments and email are encouraged and can be sent to [email protected].
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