To Roth or Not to Roth

(C) 2011 - William L. Bahn

(Last Mod: 14 March 2011 02:44:59 )


Executive Summary

Unless your are in a situation in which some of the 'fine print' rules apply -- which includes having your tax-deductible contribution limits to a traditional plan reduced or eliminated -- and are important, in almost all cases you are better off placing the bulk of your funds in a Traditional1 retirement account and not a Roth account.

The reasons for this are three:

  1. Multiplication is both associative and commutative.

  2. Funds are contributed at or near the marginal tax rate and withdrawn at or near the average tax rate.

  3. The U.S. has a very progressive income tax rate schedule.

The first of these leads to the conclusion that, by far, the primary (and usually only) consideration that determines which type of plan outperforms the other is the relationship between the effective tax rate on the funds when they are contributed (in the case of a Roth plan) and the effective tax rate on the funds when they are withdrawn (in the case of a Traditional plan).

The second of these results from the fact that contributions are generally a relatively small fraction of total income while withdrawals are frequently a considerable fraction of total income in retirement.

The third, combined with the other two, means that effective tax rate when funds are contributed is almost always significantly higher than than when the funds are withdrawn.

Note that "almost all cases" is not the same as "all cases". There are certainly going to be cases in which the Roth is the preferred option. However, it is difficult to construct such a case that would be applicable to any significant fraction of account holders a significant fraction of the time. There are, however, situations in which it can make sense to either contribute to a Roth or convert funds from a Traditional to a Roth. These situations are generally temporary in nature and would likely only apply to only a portion of the funds being contributed. However, by being aware of them, it is possible to selectively contribute to both types of account in such a way as to get better performance than either one could provide by itself.


Most tax-favored retirement plans offer two basic variants, namely a Traditional1 tax-deferred plan or a non-tax-deferred Roth version. In both variants, funds (contributions plus the earnings on those contributions) are never taxed as long as they remain in the plan. In a Traditional plan, the funds are generally tax deductible in the year they are contributed and everything drawn from the account during retirement is taxed as normal income. In a Roth plan, normal income taxes are paid on the contributed funds in the year they are contributed, but then anything that is withdrawn during retirement, including earnings, is free of further taxes.

There are some general rule differences that usually, though not always, go along with the two options. For instance, in a Traditional plan you are usually prohibited from withdrawing any of the funds before you reach the age of 59.5 without incurring taxes and penalties. In most Roth plans, on the other hand, you are generally able to withdraw the contributed funds -- but not the earnings on those funds -- after they have been invested for at least five years. Another difference is that the contribution limits on how much you can contribute to each type of plan, at least while taking advantage of the tax deduction differ between them. Many people find themselves in a situation in which they can not make tax deductible contributions to a Traditional plan because of income limitations while they may still contribute to a Roth. For those people, this discussion is irrelevant because it is pointless to compare two plans when only one of them is an option for you.

While these differences in rules can be significant if they apply to your situation, the vast majority of funds fall into the basic situation in which none of these differences matter; namely, funds are invested into the plan (fully tax-deductible in the case of the Traditional plan or fully taxed in the case of the Roth), allowed to grow for the minimum amount of time, and then withdrawn after the person has reached the necessary age. Therefore, the remainder of this discussion will concern itself solely with the performance of the two variants in that situation.

If you listen to many 'professionals' discuss the differences between a Traditional and a Roth, you will hear many really tout the Roth as the only plan you should consider, provided it is an option in your situation, because everything is tax free after you make the contributions. Others will babble on about how lots of factors influence which is the better choice, usually focusing on how long you will be able to let the money sit and grow. They are basically claiming that if you choose a Roth, your funds suffer an initial loss in value that has to be allowed to grow for some minimum amount of time in order to recover the upfront taxes and then, after that, you are money ahead.

Here's a newsflash: The bulk of this is utter nonsense. Very seldom will you hear any of these 'professionals' even mention the one and only factor that matters: Which end has the higher effective tax rate? If the effective tax rate at the time you contribute the funds is the same as the effective tax rate when you withdraw the funds, then they will perform exactly the same whether you leave them in for five years or fifty years. The reason is very simple: multiplication is both commutative and associative.

Remedial Math for Financial Advisors

Consider the following two cases:

Person A, Alice, takes an amount of money, M, and invests it into a Traditional plan. While invested, the money grows tax-deferred by a factor G. When it is withdrawn, it is taxed leaving her with a fraction TA. The total funds she has at the end, FA, is therefore given by:

FA = (M*G)*TA

Person B, Bob, on the other hand, takes the same amount of money but invests it into a Roth account. As a result, it is first taxed, leaving him with a fraction TB to actually invest in the account. The invested amount then grows by the same growth factor G before being withdrawn with no further taxes. The total funds he has at the end, FB, is therefore

FB = (M*TB)*G

Since multiplication is both commutative and associative, this may be rewritten as:

FB = (M*G)*TB

Now, we stipulated that both allocated the same amount of money, so each have the same value of M. Assuming that they both follow an identical investment strategy, there is no reason to believe that Alice's value for G will be appreciably different than Bob's. Each will probably incur some management fees, but as long as they are the same percentage, that will not matter. If teh percentages aren't the same, then it is most likely that Alice will have the smaller percentage since she will have the larger amount invested. If the expenses are a fixed amount, then Alice will be better off yet again because they will be a smaller percentage of her total invested funds compared to Bob. But, for simplicity, we will assume that both accounts are subjected only to expenses that are a fixed percentage of the total account value.

Clearly, if TA = TB, then FA = FB and they are equivalent. On the other hand, TA > TB, then the Traditional plan will outperform the Roth while, conversely, if TA < TB, then the Roth will be the better choice.

So how do we determine TA and TB? The simple answer is that T = (1-R) where R is the effective tax rate that applies. So if the effective tax rate that applies to the funds with Alice withdraws them is RA, then TA=(1-RA). Similarly, if the effective tax rate that applies when  Bob contributes the funds are RB, TB=(1-RB).

It should be clear that if RA<RB, then TA>TB and the Traditional plan would be the preferred choice.

As an example, if the effective tax applied to the funds when they are deposited is 25%, then TB = 0.75, while if the effective tax rate during retirement is 15%, then TA = 0.85. For these example numbers, the Traditional plan would be the better choice and, in fact, would result in the Traditional plan effectively having TA/TB=1.13 times the buying power of the Roth account (or 13% more).

Average and Marginal Tax Rates

Now, notice that the term 'effective tax rate' was used and not just 'tax rate'. The distinction is critical any time different portions of the money in question are taxed at different rates. The term 'average tax rate' is the tax rate that would need to be applied to the entire amount of money in question to result in the same taxes as the non-uniform tax schedule results in. The term 'marginal tax rate', on the other hand, refers to the tax rate that would be applied to a small change in the money in question. This is sometimes known as the 'tax rate on the next dollar'.

The term 'effective tax rate' refers to the average tax rate on the money in question when all other factors are kept the same. The significance of this last proviso should become evident as we work through several scenarios later on.

To understand why the distinction between average and marginal tax rates is so important to this discussion, it is important to understand the nature of the progressive tax system that is applied at either end. To have solid numbers to work with, let's look at the 2010 tax rate schedule (see p98) for people that are single.

Between and taxed at
0 8,375 10%
8,375 34,000 15%
34,000 82,400 25%
82,400 171,850 28%
171,850 373,650 33%
373,650 higher 35%

For those that are married filing jointly, it is:

Between and taxed at
0 16,750 10%
16,750 68,000 15%
68,000 137,300 25%
137,300 209,250 28%
209,250 373,650 33%
373,650 higher 35%

It is next important to note that these rates apply to 'taxable income', which is 'Adjusted Gross Income' (AGI) less deductions and exemptions. For simplicity, we will assume that all of our filers only clam the standard deduction, which is $5,700 for people that are single and $11,400 for people that are married filing jointly, and the standard exemption, which is $3,650.

Alice and Bob

Soon we will be examining a number of scenarios in which we want to compare the performance of a Traditional plan to that of a Roth. Let's assume we have our two taxpayers from before, Alice and Bob. Alice has decided to invest all of her retirement contributions in a Traditional account while Bob has chosen to use a Roth exclusively.

To keep things simple, we will assume that they are using Individual Retirement Accounts (IRAs) that they are contributing to completely separate from their employer (in fact, let's assume that their employer doesn't offer any form of retirement plan). This has the effect of taking off the table the issue of whether or not payroll taxes are an issue since both people are using money on which payroll taxes were paid in full. We will examine the impact of payroll taxes elsewhere, as well as the impact of exploiting employee matching contributions.

To further keep things simple, we will assume that Alice and Bob both live in a state with no income tax (and a few of those do exist).

Now, Alice and Bob are both single and each earns a gross income of $45,000/yr (which is in the ballpark of the median income for established wage earners). We will assume that neither has any adjustments to income and therefore their AGIs are also $45,000. However, this is not their taxable income since they are allowed to deduct $9,350, which represents the combined value of their standard deduction and single exemption they each get to claim. Thus, if they were to forego any retirement contributions, their taxable income would be $35,650, which places them in the 25% marginal income tax bracket.

However, their average income tax would be considerably less. Using the tax schedule given above (and noting that taxes are rounded to the nearest dollar), we can determine that their total income tax would be

10%*$8,375 + 15%*($34,000-$8,375)+25%*($35,650-$34,000) =  $5,094

This is the total income tax that they paid on their gross income of $45,000, hence their average income tax is only

$5,094/$45,000 = 11.32%

While this is the effective tax rate applied to all of their earnings, what we are really interested in is the effective tax rate applied to just that portion of their earnings that they contribute to their IRAs.

Let's first consider Alice, who chooses to invest $4,000 in a Traditional IRA. Assuming that this is completely tax deductible for her, doing so reduces her taxable income by $4,000 to $31,650 and her income tax will be reduced to

10%*$8,375 + 15%*($31,650-$8,375) =  $4,323

Thus, the last $4,000 of income was taxed at an effective rate of

($5,094-$4,323)/$4,000 = $771/$4,000 = 19.28%

Now let's consider Bob, who has chosen the Roth. Can he invest $4,000? Not if we are trying to make an apples-to-apples comparison. Consider that Alice, by making a tax-deductible contribution, reduced her tax burden by $771. In essence, she only reduced her take-home funds by $3,229, with the other $771 coming from the tax savings she received on this end. Bob, on the other hand, doesn't get a tax savings and so can only contribute $3,229 to his Roth account if he is going to keep his take-home funds equal to Alice's. So both are contributing $4,000 of their income to their retirement plan, but Bob is being assessed a 19.28% tax on the front end. This makes his tax factor equal to

TB = 1-0.1928 = 0.8072

Now for the trickier case of determining the effective tax factor on the back end. Since we are talking about something that will not happen for many years, perhaps even several decades, there are huge uncertainties in what fundamental changes will happen, both in our lives and in the tax code. We will discuss a few of them later, but for now, since we don't have a good crystal ball to gaze into, we will assume that the current tax rates remain unchanged in real dollars (meaning that the break points between brackets adjust to match inflation) and that the standard deductions and exemptions likewise increase to match inflation. This allows us to work in today's dollars, even when talking about the situation in retirement decades down the road, since the inflation factor will cancel out from everything.

We will further assume, for now, that we want to withdraw funds from our accounts so as to make the same income that we presently do and that they are the only source of income we will have. Under these assumptions, the effective tax rate on the money that is withdrawn will be the same as the current average tax rate of 11.32%, yielding a tax factor for Alice of

TB = 1-0.1132 = 0.8868

Hence there would be a significant advantage to putting the funds in a Traditional account. In fact, Alice would effectively have 0.8868/0.8072 = 1.099 times as much money in retirement as Bob, or said another way, she would have 10% more purchasing power than Bob.

Crystal Ball Gazing

Now let's consider some of those crystal ball assumptions.

As you can see, there are a number of considerations that affect the effective tax rate down the road and most of them you can only take a weak guess at. This is one of the more rational arguments for favoring the concept of a Roth over the Traditional plan in that it renders most of these questions academic since, once you pay the up front taxes, changes in the tax code or in your tax situation can be expected to have little effect, making your planning decisions at least somewhat more reliable.

However, nothing is engraved in stone and potential changes to the tax code could be devastating to Roth holders. For instance, what if the country manages to replace the income tax with a national sales tax? If that happens, the money that you paid taxes on will get taxed all over again. Even though there are certain to be transition rules of some kind to deal with this, it is unlikely that you will escape unscathed. Next, consider that the fact that Roth accounts are distributed tax-free is an artifact of current tax law and can be changed by Congress at any time. Don't think this could possibly happen? Consider the case of Social Security benefits. Presumably, these are funds "contributed" to "your" account and upon which you paid full income tax the year in which it was earned. Thus, originally, Social Security benefits were distributed tax free. That was the case for over four decades, but along came 1983 and the country found its favorite Ponzi scheme in trouble. Therefore they changed the law (P.L. 98-21) to not only increase the SS tax rate (which, in and of itself, was nothing new), but to also expand the pool of new participants (classic goal of any Ponzi scheme) by forcing new groups, such as the military and most other federal employees, to contribute, and made up to 50% of social security benefits taxable. Then, in 1993, they further raised the amount that could be taxable to 85% (P.L. 103-66). There are occasional calls to simply make it all taxable, so don't think that there is no chance that Roth payouts could become taxable down the road. 

It is even less inconceivable that some form of "means testing" could get applied to Roth distributions in order to "make the rich pay their fair share". The same is more likely to happen with Social Security benefits -- and sooner.

In general, unless you have strong visibility, or at least convictions, into at least some of these issues, you are probably best assuming that many of them will average out in the end. Having said that, you can probably make a few reasonable assumptions, such as you are likely to need moderately less income in retirement than you do now, particularly if you work toward living in a home with no mortgage.


To get a feel for how some of these issues impact the Roth/Traditional decision, let's look at a few scenarios. In all of these scenarios we will use Alice and Bob, so let's recap their basic situation. They are both single, earn $45,000 today, and live in a state with no income tax. They both pay the 7.65% FICA tax on their gross income. If they didn't invest anything, they would each pay $5094 in federal income tax.

Alice will invest $4000 into a Traditional IRA. In doing so, she saves $771 which adds to her take-home income giving a net result of $37,234. Bob, on the other hand, will take contribute $3229 to a Roth IRA, thereby leaving him with the same take-home pay as Alice. The effective tax that applies to both people's $4000 contributions is 19.28%, or $771. In Alice's case, this is the amount she saved due to her $4000 contribution and now has available as take-home income. In Bob's case, this is the amount of tax he had to pay out of his $4000 contribution to pay the up-front taxes on it.

In figuring taxes, we will always assume that both Alice and Bob claim only the standard deduction of $5,700 and a single exemption of $3,650, both now and in retirement.

Since Bob's situation is very static, we will usually be asking how a slightly changed set of assumptions affects Alice and then asking either how the effective tax rate on her withdrawals compares to the 19.28% Bob paid upfront, or asking how much Alice would have to withdraw before her effective tax rate became equal to Bob's upfront 19.28%.

Scenario 1

Alice is currently paying $1,000/mo on a mortgage (principal and interest portion) and plans to retire it before she retires herself. She also plans to stop contributing to her retirement plans at that point. Other than that, she wants to maintain the same take-home pay as now. All of her income will be from her Traditional retirement plans.

What is the effective tax rate on her IRA withdrawals? ANSWER: 7.03%

First, let's figure out Alice's current take-home pay. She grosses $45,000 and, from that, pays 7.65% in FICA taxes. This reduces her pay by $3,443. She then is paying $4,323 in federal income tax (we are assuming she lives in a state with no state income tax). So her take-home pay is presently $37,234. Since $4,000 of that is presently going into her retirement plan and $12,000 is going to her mortgage company, her desired take-home pay in retirement can be reduced to $21,234.

Next, she needs to draw out of her retirement plan enough funds to cover both the $21,234 and the taxes on it. The easiest way to determine how much she should withdraw is to first see how much she will be short if she simply withdraws the $21,234. After doing so, her taxable income will be this less the $9,350 combined standard deduction and exemption she has to reach before any of her income becomes taxable at all, making her taxable income just $11,884. The tax on this income, using the Single tables above, is $1,364. She therefore has to draw an additional $1,364 plus even more to pay that tax on that. However, since this is comfortably in the 15% marginal bracket, determining the necessary amount is trivial. Basically, she needs an amount X such that 0.85X is $1,364 or an additional $1,605. The bottom line is that she needs to withdraw a total of $22,839 from her retirement accounts and will pay a total of $1,605 in taxes on it, making the effective tax rate on her withdrawal just 7.03%.

Note how poor a choice Bob made in choosing the Roth IRA. Alice effectively has 15% more in retirement funds than Bob does.

Scenario 2

Same as Scenario #1 except that Alice also expects to receive about $1,200/mo in Social Security benefits (which is close to the present average benefit and about half the maximum benefit amount). Other than that, all of her income will still be from her Traditional retirement plans.

What is the effective tax rate on her IRA withdrawals? ANSWER: 0%

First, note that her desired take-home pay remains $21,234, the same as the last scenario.

Next, she expects to receive $1,200/mo in SS benefits, or $14,400/yr. For this example, this will be tax free (more on this in a bit). Thus she needs to draw out of her retirement plan enough funds to cover the remaining $6,834 plus enough to pay any taxes on it.

But wait! If she is only drawing $6,834 in taxable retirement benefits and her SS benefits are nontaxable, then she is well below the $9,350 combined standard deduction and exemption she has to reach before any of her income becomes taxable at all! So her effective tax rate is 0%.

Think about the implications of this -- she paid no tax on the money when she put it in and she paid no tax on the money when she pulled it out. Bob, on the other hand, paid nearly 20% in tax on the money he put in just so that he could pull it out tax free, even though it would have been tax free anyway. The effect is that Alice now effectively has 23.9% more in retirement funds than Bob.

Scenario 3

Again, the same basic situation as Scenario #1, except that Alice wants to draw out enough money each month so that her effective tax rate on it will make the Traditional/Roth decision moot.

What is the retirement take-home income level at which the Roth/Traditional decision yield the same performance? ANSWER: $82,466

First, let's determine which tax marginal tax bracket she will be in when this occurs. We can tabulate the average tax at the bottom of each bracket by taking the total tax at that point and dividing by the total income, including the standard deduction and exemption, associated with it. The results are shown below:

Between and taxed at Avg
0 8,375 10% 0.00%
8,375 34,000 15% 4.72%
34,000 82,400 25% 10.80%
82,400 171,850 28% 18.29%
171,850 373,650 33% 23.08%
373,650 higher 35% 28.31%

We therefore see that Alice will need to be somewhere in the 28% tax bracket to reach the target 19.28%. At the floor of this bracket, she would be withdrawing $91,750 -- $82,400 + $5,700 + $3,650 -- from her account and paying $16,781 in taxes. At the target 19.28%, she would be paying $17,689. As she draws more funds, they will be taxed at 28%. The first 19.28% of that goes to track the desired average tax rate and the remaining 8.72% makes up for the $908 shortfall that existed at the bracket floor. Thus she needs to withdraw $908/8.72% =  $10,413 above and beyond the $91,750, for a total of $102,163. Her effective take-home income would then be $82,466.

The bottom line here is that Alice would have to draw, in retirement, well over twice her present gross income (giving her a take-home income of nearly four times the $21,234 that she expects will give her a comparable lifestyle to today) before she reached the point where the Roth would have been the better choice.

Scenario 4

This is the same basic situation as Scenario 2, in which Alice receives $1,200/mo in SS benefits. Like the previous scenario (Scenario 3), she now plans to draw enough from her retirement account so that the Roth/Traditional decision is moot.

What is the retirement take-home income level at which the Roth/Traditional decision yield the same performance? ANSWER: $58,114

If her SS benefits remained untaxed, then this computation would be identical to Scenario 3 with the only difference being that now her effective take-home income would be the SS benefits of $14,400 plus the $82,466 from Scenario #3 for a total of $96,866.

Unfortunately, her SS benefits will become largely taxable well before this point. Determining how much of her SS benefits are taxable involves a rather convoluted worksheet contained in the IRS Form 1040 Instructions. Reviewing the instructions, we discover that, at most, 85% of the SS benefits will become taxable. This would mean that 85%*$14,400=$12,240 would get included in our taxable income. Assuming this to be the case (and at this level of taxable income, it's a good assumption), we need to find the amount of income from the retirement plan must be pulled such that:

Tax(0.85*S + P) = 19.28%P

Here Tax(AGI) is a function that returns the tax on the adjusted gross income amount AGI.

We can use a technique similar to that used in the previous scenario, although it is a bit more obscure. The basic idea is to create a faux tax table in which all of the thresholds are reduced by the amount of the SS tax that is taxable, namely $12,240. Doing so, we discover that at the bottom of the 28% tax bracket Alice would be drawing $79,510 from her plan and paying $16,781 in taxes, for an effective tax rate 21.11%. This is an excess amount of $1,451 over the $19.28%*79,510 = $15,330 target that she was aiming for. As she reduces her draw below this, she reduces her tax burden by 25% of the reduction (until she hits the next bracket floor). Thus each dollar of reduction chips away $1*(25%-19.28%) = $0.0572 of the excess. She therefore need to reduce her draw by $25,367 to $54,153.

Since her effective tax rate on the $54,153 of withdrawn funds is the target 19.28%, she will be paying $10,439 in taxes. Thus her effective take-home income is $14,400 + $54,153 - $10,439 = $58,114. Thus, even if her Traditional distributions result in her Social Security benefits becoming taxable to the maximum degree possible (something that Roth distributions -- under present law -- don't impact), she can increase her take-home income in retirement to more than half again (56%) its present level of $37,234 before she approaches the point where the Roth was the better option.

Scenario #5

In this scenario, Alice attempts to achieve the same take-home income as in Scenario #1, namely $21,234, but we will assume that the tax rates increase proportionately so as to erase the advantage of the Traditional over the Roth.

How much would tax rates in retirement need to increase, across the board, to render the Traditional/Roth performance the same? ANSWER: A factor of 2.39 (or, equivalently, 139% higher than today)

Since all of her income is from her retirement withdrawals and we want an effective tax rate on those withdrawals to be 19.28%, Alice will be withdrawing $21,234/0.8072 = $26,306 from her account each year. Of this, she will be paying $5,072 in taxes. Under the present tax rate schedule, she would only pay $2,125 in taxes on this amount. This means that all of the tax rates would need to go up by a factor of 2.39 to make this happen. Thus the lowest tax rate would be 24%, the second would be 36%, and the top rate would be $84% (which is actually below the historic high for the top marginal income tax rate).

Once again, it is clear that the Traditional account was, by far, the better choice.

Scenario #6

In this scenario, Alice withdraws funds so as to match her full taxable working income of $45,000. She plans to use the FICA taxes that she will now not be paying, together with money she will not paying toward her mortgage or into her retirement plans, to better enjoy her retirement, at least for a few years. She is also electing to delay drawing her Social Security benefits during this time. She also has a retirement plan from her employer that provides 2/3 of her target income, or $30,000/yr, all of which is taxable.

What is the effective tax rate on her IRA withdrawals? ANSWER: %

In this scenario, Alice is withdrawing the last $15,000 of her income from her IRA. Her taxable income is $45,000-$9,350=$35,650. While she is in the 25% tax bracket, only $1,650 of her withdrawals will be taxed at that rate. The remaining $13,350 of her withdrawal will be taxed at the 15% rate. Thus her total taxes on her IRA withdrawal will be

25%*$1,650 + 15%*$13,650 = $2,460

This results in an effective tax rate of 16.40%, which is still significantly below the 19.28% rate that it would to break even.

Thus, even by pushing hard to move the IRA withdrawals toward the marginal tax rate, the Traditional account is still the better choice.

The obvious next scenario would be to ask how much she would have to decrease her IRA withdrawals (while increasing her draw from her employer-sponsored plan by the same amount) in order to be at the break even point for the Roth. However, this question has an obvious answer -- namely, the same amount that she contributed, or $4,000/yr. Now, this is a direct consequence of how we set up the problem, namely having her want to match her full working income while deriving the rest of it entirely from taxable sources. If she reduced her draw by just half of the $3442 she no longer pays in FICA taxes (or $1721), then she would drop below the 25% floor and all of her IRA withdrawal would be taxed at no more than 15%.

Once again, it is clear that the Traditional account was, by far, the better choice.

Why People Wrongly Love the Roth

It's perfectly reasonable to ask why so many "professionals" are enamored with the Roth if it can be expected to underperform a Traditional plan for the majority of investors that could choose to make qualified contributions to either. , then why are so many "professionals" so in love with them. Put a little more bluntly, if I am going to say that all of those people are wrong, then it is perfectly reasonable to expect me to debunk their arguments in favor of their position.

While I certainly haven't heard all of the arguments in favor of the Roth, here are the ones I have heard:

  1. The Roth allows you to pay tax on a much smaller amount of money.

  2. Tax rates are going to go up in years to come.

  3. You can put more money to work for you in a Roth if you pay the taxes with other funds.

Let's take these one at a time, but before we do, keep in mind that I have never claimed that the Roth never makes sense or that it is always the worse option. As we shall see, there are times when the Roth is the better option. The point is that we need to understand how to determine, or at least estimate, when that is likely to be the case.

The Roth allows you to pay tax on a much smaller amount of money

While technically true, it is also totally irrelevant. This claim is usually followed with an example along the lines of the this: You put $3,000 into an IRA at the age of 30 and, after 40 years of compound interest at 5%, it has grown to about $21,000 before you pull it out at age 70. If it was a Traditional IRA you would pay taxes on the entire $21,000 while, if it was Roth IRA, you would only pay taxes on the original $3,000. Assuming you are in the 33% tax bracket, that's $7,000 in taxes compared to just $1,000. Which would you prefer?

This example, while it sounds compelling on the surface, actually has several flaws. The first is that it asks an irrelevant question. My decisions shouldn't be based on how much I end up paying in taxes, but rather how much I get to keep and use after taxes, however much and whenever they are paid. Second, if we going to compare apples to oranges, we can't contribute the $3,000 to either type of account because, if we put it into a Roth, we have to pay out the taxes first. So here is the proper way that this example plays out: You have $3000 available for investing into an IRA. If you invest in a Traditional IRA, you put in the entire $3,000 and, after the 40 years at an effective 5% annual return, it has grown to $21,000 and you withdraw it and pay $7,000 in taxes leaving you with $14,000. If you invest in a Roth IRA, you pay $1,000 in taxes leaving you with $2,000 to actually invest, which then grows to $14,000 of which you get to keep everything. So, yes, you paid a lot less in taxes, but you ended up with the same amount so it doesn't matter.

A third mistake that this, and almost all comparisons that come out in favor of the Roth, makes is that of assuming that the taxes levied on either end are done at the full marginal rate. While this is usually true at the front end (i.e., for the Roth contributions), it would seldom be expected to be the case at the back end (i.e., for the Traditional withdrawals). The reason is that the disbursements will generally make up a larger fraction of your retirement income than the contributions represented for your working income, therefore at least part of them will be in a lower bracket and, very likely, some of them will even be all the way into the 0% bracket due to your deductions and exemptions. For this example, let's assume that the effective rate at withdrawal from the Traditional works out to 30% instead of 33%, meaning that it is almost all being taxed at the marginal rate. Now you taxes would amount to $6,300. If we ask the question as the Roth proponents posed it, we would ask if you would rather pay $1,000 in taxes or $6,300. If we ask it the right way, we would ask whether you would rather pay $1,000 in taxes to keep $14,000 or $6,300 in taxes to keep $14,700.

Tax rates are going to go up in years to come

While this involves crystal ball gazing, let's go ahead and stipulate that it is likely to be the case. Under that assumption, then the comparison certainly shifts toward the Roth. If you assume that everything, on both ends, is going to be taxed at the full marginal rate and that your retirement income puts you in the same marginal tax bracket ('same' in terms of position within the tax rate schedule), then the Roth would clearly win. However, for most investors, their withdrawals will almost certainly be taxed at a lower effective bracket, so the rates will probably not increase enough to make the Roth the better choice. Go back and review Scenario #5 to get a feel for how much rates would have to change by to tip the scales.

You can put more money to work for you in a Roth if you pay the taxes with other funds

This is true in some sense, but is generally thrown out fairly carelessly. Let's look at this claim fairly carefully.

At the present time, the limitation on contributing to either a Traditional IRA or a Roth IRA is $5,000 (if you are under 50). If Alice and Bob both actually put $5,000 into the account and do nothing else, then Bob will end up better off in retirement. because he paid the 25% tax ($1,250) from other funds and therefore has 33% more money effectively invested ($5,000 instead of $3,750).

However, that is very apples-to-oranges. You can't simply ignore the factor, TB, that Bob pays up front and this is what this analysis does. The fact remains that Alice got a tax savings of $1,250 that she could do something with. Even if she spends it on clothes or a vacation, she is receiving a benefit from her investment decision that has value and that Bob has forfeited. To make it more apples-to-apples, let's have Alice decide to invest that $1,250 into a normal account that is not tax-deferred and leave it there until retirement. In that case, it would still grow and become available as taxable income at retirement, but it would not grow as much. To see how much of an effect it has, let's assume that all of the funds, Traditional, Roth, and taxed-account, grow at a 5% return. If we assume that Alice's other investments are taxed every year on the earnings at her full marginal rate of 25%, her effective return on those funds is only 3.75%. However, that only affects a portion of her invested funds.

To see the impact down the road, we need to do the math. First, let's derive the applicable general expressions.

Bob takes an amount of money, M, and invests it in a Roth. Since he paid the taxes out of other funds, we'll set TB=1, so he gets the full MG at retirement. Up to this point we have ignored the details of calculating G,  but they now become important. G is simply the annual rate of return, I, compounded over Y years:

G = (1+I)Y

Hence, in retirement, Bob's available funds, FB, are:

FB = M(1+I)Y

Alice took the same amount of money, M, and invested it and her tax savings, MRB (which equals the amount Bob paid in taxes) , as follows:

She took M and invested it into a tax-deferred account that has an average annual return of I. She then took her tax savings, MRB, and invested it into a non tax-deferred account making the same return. The earnings on it, however, are taxed each year at RG, so her effective return each year (on those funds) is I(1-RG). At the end of the first year, the value of her account is:

M(1+I) + MRB[1+I(1-RG)] = M{(1+I) + RB[1+I(1-RG)]}

Over Y years, this becomes:

M{(1+I)Y + RB[1+I(1-RG)]Y}

At the end of this time, she must still pay taxes at the retirement rate, RA, leaving her with:

FA = M{(1+I)Y + RB[1+I(1-RG)]Y}(1-RA)

We can determine which is the better choice by taking the ratio of Alice's available funds to those of Bob. If the quantity is greater than 1, Alice is better off. If it is less than one, then Bob's option (the Roth) is better.

FA/FB = {(1+I)Y + RB[1+I(1-RG)]Y}(1-RA)/(1+I)Y

Expanding this slightly, we get:

FA/FB = {(1+I)Y - RA(1+I)Y + (1-RA)RB[1+I(1-RG)]Y}/(1+I)Y

We can now take the denominator inside the numerator to get:

FA/FB = 1  + {(1-RA)RB[1+I(1-RG)]Y - RA(1+I)Y }/(1+I)Y

Now note that if the quantity in curly braces is positive, then the overall ratio will be greater than 1 (and the Traditional will be preferred), while if it is negative, the overall ratio will be less than 1 (and the Roth will win). This then reduces to the following inequality which, when true, favors the Roth:

(1-RA)RB[1+I(1-RG)]Y < RA(1+I)Y

While this is a fairly nasty looking expression, it can actually be solved for RA (though not RB).

 RA >  RB * [1+I(1-RG)]Y/{(1+I)Y + RB[1+I(1-RG)]Y }

From an evaluation standpoint, this can be expressed a bit more friendly as:

 RA >  { 1  +  (1+I)Y / RB [1+I(1-RG)]Y }-1

This is very straightforward to evaluate for specific numbers and fairly easy to answer some very telling questions for some special cases.

Case #1: Equal Effective Tax Rates Throughout 

First, let's consider the case where all of the tax rates involved are the same:  (i.e. R = RA = RB = RG):

To answer this question, it is easiest to start from the first inequality above, which reduces immediately to:

(1-R)[1+I(1-R)]Y < (1+I)Y

In this case, it is clear that the two perform equally only when R=0 and that the Roth wins for any R>0.

Case #2: Non tax-deductible contributions grow tax deferred

Now, let's consider the case where the earnings from the non tax-deductible contributions are allowed to grow tax-deferred (i.e., RG = 0).

Before we turn to the math, let's consider when this is even possible. If, for other reasons (such as income limits), you are not able to deduct the full amount of your contribution to a Traditional IRA, then you are still able to contribute up to the general limit and, while not enjoying the tax deductibility, will at least enjoy the benefit of having the earnings grow tax deferred until retirement. For example assume that your limit on tax deductible contributions is $4000. Then you could still contribute the additional $1,000 to the Traditional IRA and have it grow tax-deferred, but you would not be able to deduct it on your current tax return. However, because of the higher income limits that generally apply to Roth accounts, you could probably invest this portion into a Roth. For this case, we will assume that they are all placed in a Traditional account.

It might be tempting to assume that this case simply reduces to the general case explored previously. However, the balance still shifts toward the Roth because the non tax-deductible funds placed in the Traditional account are fully taxed twice -- once when they are contributed and again when they are withdrawn.

Starting with the any of the general case inequalities above, the following relationship falls out with a little arithmetic:

RA > RB / (1+RB)

Using the example we have been working with, if the contributions are being taxed at 25%, then the Roth will outperform the Traditional provided the effective tax rate applied to the withdrawn funds in retirement is at least 20%. As previous examples have shown, it is highly likely that the effective tax rate in retirement will be considerably less than this, and this will still be the case even with considerable increases in the tax rates, especially for people that are not too far above the median income level. However, it must be kept in mind that this option can almost certainly be performed by putting the tax savings into a Roth.

Case #3: Non tax-deductible contributions taxed at working tax rate, but with lower retirement tax rate.

Now, let's consider the case where the earnings are taxed at the working rate, RB, but that we expect a lower effective tax rate in retirement.

Our final general inequality changes only slightly in this case to:

 RA >  { 1  +  (1+I)Y / RB [1+I(1-RB)]Y }-1

Pulling a factor of RB out front, we have:

 RA >  RB / { RB  +  (1+I)Y / [1+I(1-RB)]Y }

The following table shows some required retirement tax rates needed to make the two options equivalent for various investment terms (in years, across the top) and current marginal tax rates. All of the values assume a real return rate (rate of return discounted for inflation) of 4%.

Tax Rate 5 10 20 30 40 50
0% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
10% 8.93% 8.78% 8.47% 8.18% 7.89% 7.62%
15% 12.72% 12.40% 11.79% 11.20% 10.64% 10.10%
25% 19.24% 18.50% 17.09% 15.76% 14.52% 13.36%
28% 20.96% 20.08% 18.40% 16.83% 15.37% 14.01%
33% 23.64% 22.51% 20.36% 18.36% 16.53% 14.84%
35% 24.65% 23.41% 21.07% 18.90% 16.91% 15.09%
39% 26.56% 25.11% 22.38% 19.86% 17.56% 15.48%

As shown earlier, it is not unreasonable to expect the effective retirement tax rate to be considerably less than your working marginal tax rate, and thus it is still likely that the Traditional will prove the better investment. However, the Roth gains ground for funds that are allowed to sit and grow longer. It is less clear what the trend is as you move up in the tax brackets because there are competing factors - in general, the higher tax bracket you or in now favors the Traditional because it is more likely that you will be able to achieve a considerably lower average tax rate in retirement. But, in the case we are discussing here, the higher your current tax bracket, the larger the portion of your funds that must exposed to tax on the earnings as they grow.

When a Roth Makes Sense

As established early on, contributing funds (that would otherwise be fully tax-deductible if contributed to a Traditional account) into a Roth account only makes sense when the applicable effective tax rate today is lower (or at least no higher) than the effective tax rate you expect in retirement. The one time that this is guaranteed to be the case is if you are in a position where your marginal tax rate today is 0%. This might happen for a number of reasons. Among them are:

It is also possible that your taxable income might be low enough so that even though you aren't in the 0% bracket, you are in a low bracket and you expect to be in a much higher bracket during retirement. But consider the results of Scenario #1 in which, even though all of the retirement income was coming from IRA savings, the effective tax rate was still well below the lowest marginal tax rate of 10%.

However, if you have expect to have significant other taxable income sources during retirement such that most or all of your IRA disbursements will be effectively taxed at your marginal rate, then investing in a Roth, especially whenever your marginal rate is lower than usual, may make sense. But even here it is deceptively easy to discount the combination of even relatively small amounts of nontaxable income and moderate lowering of retirement income to reflect no longer needing to pay FICA taxes.

Although technically a situation in which the fine print applies, you should also contribute into a Roth any funds that would be non tax-deductible if contributed into a Traditional account.

Arguably the best strategy is to use a combination of Traditional and Roth vehicles. The bulk of your contributions should be to Traditional accounts, but when the opportunity presents itself to do so sensibly, inject funds into Roth accounts. Then, during retirement, use the funds from the Roth accounts to limit your taxable income to the next lower bracket or to a point that reduces or eliminates having to pay taxes on any Social Security benefits.

Perhaps the strongest point to be made is that it is not a good idea to blindly assume that the effective tax rate applied to the funds when you withdraw them from a Traditional account will be the same, or even close, to your marginal tax rate, either now or even in retirement.

A Progressive and Comprehensive Case Study

As a self-employed consultant (in 2010), David typically receives $135,000 in gross revenue from his contract. Were he to simply accept this as his compensation, his self-employment taxes would be $13,064 (Multiply net profit by 92.35% then SE tax is 15.3% of the first $76,200 and 2.9% of everything above that). His AGI would be the $135,000 less half of the SE taxes, or $128,468. He is married with one child and files a joint return. Although he has some significant itemizable expenses, due to the AGI floors imposed on the medical and unreimbursed business expenses, they do not rise above the level of standard deduction of #11,400. Therefore, the sum of his standard deduction and three exemptions is $22,350, bring his taxable income down to $106,118. His income tax is $18,892 (14.7% of his AGI). His total tax federal liability is therefore $31,956, which represents 23.67% of his gross revenues. Living in Colorado, which (for most taxpayers) imposes a 4.63% income tax on whatever the federal taxable income was (adjusted for state tax refunds, if claimed on the federal return as an itemized expense). Since David didn't itemize, this places his state income tax at $4913 and his total fed/state tax burden at $36,869, or 27.31% of his gross revenue.

David notes that his marginal tax rate for business expenses is over 32.5%. Thus, if he were an actual business, anything he were to purchase for the business would effectively be reduced in price by that amount. However, he also realizes that there are numerous expenses he already incurs that are for the benefit of the business; thus he expects that by organizing his business activities as a sole proprietorship he should be able to quickly see a significant break on his taxes. At the same time, he sets aside the lower half of his home to be used regularly and exclusively for business purposes. After taking the proportionate share of taxes, insurance, mortgage interest, utilities, and home owners fees, plus the 2.564% depreciation on the portion of the home used for business, David is able to claim $12,800/yr as a home office business deduction. Office expenses and supplies total to $4000/yr. David is also a member of a few professional organizations, whose annual dues total to $200/yr. Furthermore, since his home office qualifies as his principal place of business, his 20 mile one-way trip to his typical job site is a deductible travel expense, for which he claims the standard mileage rate of $0.50/mi. Over the course of the year, this totals to approximately $5000. During a typical year, David purchases approximately $5000 in equipment, mostly lab equipment, which he expenses in the first year, using the provisions of Sec 179, instead of depreciating over time. Combined, these business expenses lower his net business income by $27,000, taking his net business profit to $109,000. The SE tax on this amount comes to $12,368. This, in turn, places his AGI at $102,816. While David still plans to only claim the standard deduction, he can now deduct the premiums he pays for his family's medical insurance as an adjustment to income (instead of an itemized expense subject to the 7.5% AGI floor). His annual premiums total $7000, thus his AGI is reduced to $95,816 and his taxable income is reduced to $73,466. His federal income tax becomes $10,731 and his state tax is $3,401. His total tax burden has therefore been reduced to $26,500 (19.63% of total revenue) and puts $10,369 more into his pocket each year, all without changing a single thing about what he does or spends.

At this point, David decides to look into his options for retirement savings. After doing some analysis of his expected needs after retirement and taking into account that he is not as young as he once was and therefore needs to aggressively save, he determines that he needs to save between $25,000 and $35,000 per year whenever possible. His plan for the next several years is to contribute approximately $20,000 and then, once his house is paid off, increase that to around $40,000 to make up the difference. Unfortunately, his net income from self-employment is well into the phase range (which, for married filing jointly, is  between $89,000 and $109,000), which would severely limit the amount he can contribute to a traditional IRA and deduct on his taxes. However, between he and his wife, they would be limited to only $10,000 per year anyway. Instead, he chooses to open a 401(k) plan (the so-called Solo 401(k)) for his business. Under that plan, he can put away up to $16,500 plus 20% of his net business earnings, as long as he doesn't exceed his total net income from the business or the $49,000 overall limit. He could therefore contribute $16,500 + 20%($102,816), which totals to  $37,063. Therefore, he chooses to contribute $20,000 to his 401(k). Since, as a self-employed person, he has to take this entire deduction only against his personal income tax, he must pay the SE tax on it and therefore his SE tax remains at $12,368. However, this reduces his AGI to $75,816 and his taxable income to $53,466. At this level, his federal income tax is $7,184 and his state tax is $2,475 bringing his total tax burden down to $22,027, a drop of $4,473, which means that his marginal savings on the contributions to his retirement plan was 22.37% and only reduced his take-home income by $15,527.

He now becomes aware of some provisions in the tax code that they can take advantage of if he formally employees his wife, Shari, in his business. Since she does not meet the criteria for having to consider her a co-owner, he can hire her as a common-law employee as long as she is paid reasonable pay for reasonable work. Since his wife already does much of the bookkeeping as an unpaid assistant, it is decided that she will be paid $25/hr for about 10 hrs per week and take on some additional office-management duties such as billing, bill paying, and paying taxes. This places her annual revenue at $13,000. Since these are W-2 wages, he must pay full 15.3% FICA on them, which is $1,989. It must be pointed out that the last $13,000 of his self-employment income was only 2.9% because he was above the Social Security ceiling on income, so this move costs actually costs him him $1,489. However, half of this tax, $995, is the employer portion and is deductible as a business expense, as is her entire wages. Thus his net business profit has been reduced to $95,005 and his SE tax is now $12,204. If this is all they planned to do, it would make more sense to have her remain unpaid, although it must be noted that previously all of the SE payments were being credited to David's Social Security account and none to his wife's; this at least now allows her to earn credit toward Social Security eligibility. But, this wasn't there primary motivation. Instead, his wife is now eligible to participate in the company 401(k) plan and chooses the full 25% profit sharing match, which allows the company to contribute $3,250 to her account pre-tax, meaning that neither she nor the company have to pay FICA taxes on that amount. She further elects to defer the maximum amount of her salary that is possible, which is $9,750 so that the total contributed does not exceed her income. This does not change the amount of FICA tax that either the business or her must pay on her wages, so it remains at $1989. But it reduces her W-2 wages to just $3,250. The net business profit has now been reduced to $91,755 and the SE tax has been lowered to $11,906. Since his wife was put away $13,000 toward retirement, David opts to only accept a $7,000 contribution. This makes their combined AGI $3,650 + $91,755 - 50%($11,906) - $7000 - $7000 = $75,452. Their taxable income is thus $53,102 and their federal tax is $7,131 and their state tax is $2,459. Added to the SE tax and his wife's full FICA amount, their total tax burden has now actually increased by $1,458 to $23,485. Again, if this was their only strategy, this would not be a good one.

However, with his wife now an employee, she is eligible to participate in a Medical Expense Reimbursement Program (MERP), meaning that, if it is set up correctly, she can be reimbursed for 100% of the qualified medical expenses for her, her spouse, and her dependents. The key point here is that a self-employed person is ineligible to participate in a MERP, but this allows him to be covered under his wife's MERP. In addition to the medical insurance premiums, which are presently deducted on their personal taxes, she can be reimbursed for most out-of-pocket medical expenses, which currently total to $5,000/yr since they chose a high-deductible health plan, HDHP, and David has some moderate on-going health issues. Not only are these now deductible, but they are a business deduction, which reduces SE tax. The effect of this $12,000 business expense is to reduce the net business profit to $79,755 and brings the SE taxes to $11,269. Their AGI is now $3,650 + 79,755 - 50%(11,269) - $7,000 = $70,771. Their taxable income is therefore $48,421 bring their federal/state taxes to  $6,426/$2,242 and their total tax burden to $21,926. While this represents only a slight decrease of only $101 from the situation when his wife was not an employee, it has set the stage for further reductions. For instance, the company can not set up a child care reimbursement plan and an educational benefits plan. All of these costs can now be written off as business expenses (provided they are legitimate and reasonable for the business). Furthermore, the business profit has now been reduced sufficiently so that all further business expenses reduce save the full 15.3% SE tax and, because they are still in the 25% tax bracket, their total savings on every dollar, accounting for state tax, is nearly 45%, meaning that anything they purchase for the business is nearly half off.

At this point, David and Shari pause to take stock of their situation. Originally, when David was simply claiming all of his pay as income, the money they were living on was:

Gross Revenue   $135,000
SE Tax $13,064  
Fed Tax 18,892  
State Tax 4,913  
TOTAL TAX   $36,869
Net Take-home Pay   $98,131

Included in this $98k are the expenses that David and Shari are presently paying, such as medical costs and office expenses regardless. They then look at their situation after the latest version of their plan:

Gross Revenue   $135,000
SE Tax $11,269  
FICA 1,989  
Fed Tax 6,426  
State Tax 2,242  
TOTAL TAX   $21,926
401(k) contributions $20,000  
Net Take-home Pay   $93,074

At this point they realize that although they have increased their retirement contributions $20,000, their available funds for all of their original expenses have only decreased by $5,047. Since they had allowed for a $20,000 contribution to their retirement plan, they review their options. First, they could contribute the remaining $14,953 to his retirement plan, or they could contribute $4,953 to his 401(k) and then $5000 each to their individual IRA accounts. However, any of these options would only save them the federal and state income taxes, which would be a savings of $4,431 (and which they could invest or use some other way). In fact, they could invest a total of $21,279 more into their plans, for a total of $41,279, while only decreasing their take home income by the allowed $20,000.

However, not want to leave that 15.3% SE tax on the table, they opt to instead budget for an additional $27,000 in business expenses of various kinds, as long as they are fully expensable. First, they then agree to allow for $18,000/yr for lab and office equipment that expands David's professional capabilities (and which will be first-year expensed). The remaining $9,000 is budgeted to allow each of them to attend a business-related conference, symposium, or training course.

After this change to the business plan, David's net business profit has been reduced to $52,755, on which his SE tax is now $7,454. Their AGI is now $45,678 and their taxable income is $23,328, on which their fed/state taxes are $2,661/$1,080, bringing their total tax burden to $13,184. However, they have now reduced their AGI to a point where they qualify for the Retirement Plan Contribution tax credit of $400. If they can get their AGI down to $36,000 they will qualify for another $400 and, if they can get it down to $27,750 they will qualify for yet another $1,200. Their situation is now summarized as follows:

Gross Revenue   $135,000
SE Tax $7,454  
FICA 1,989  
Fed Tax 2,661  
State Tax 1,080  
Retirement Contribution Credit <400>  
TOTAL TAX   $12,784
401(k) contributions $20,000  
Net Take-home Pay   $75,316

Notice that this has reduced their take-home pay by $2,915 more than expected. There are two reasons for this. The most significant is that, by expensing an additional $27,000, they reduced their SE tax deduction by $1,907. Furthermore, they are now down well into the 15% tax bracket and are therefore only seeing about a 35% savings on the last roughly ten thousand dollars of these new expenses instead of the prior 45%.

David and Shari spend $6,000 to send their child to a pre-school program that qualifies for consideration for the Child Care tax credit, however, after reviewing the limitation to the credit, it makes more sense for them to establish a Child Care Reimbursement program for the business, although the maximum benefit that can be deducted is $5,000, so that is where they set the limit.

Next David and Shari have each been taking one class each semester at the local college to enhance their skills within their respective professions. With tuition, books, fees, transportation, and supplies this typically totals to about $3,000 for each of them. Therefore, David sets up an educational reimbursement program for the company that covers these expenses.

Although these new programs represent an additional $11,000 in business expenses, they do not represent any new actual expenditures since these were costs that were being paid previously, just without any reimbursement.

The net effect of these new expenses is to reduce the net business profit to $41,755, on which his SE tax is now $5,900. Their new AGI is $35,455, making them eligible for an additional $400 on the retirement contribution tax credit. Their taxable income has been reduced to $13,105. Their new situation is summarized below:


Gross Revenue   $135,000
SE Tax $5,900  
FICA 1,989  
Fed Tax 1,313  
State Tax 607  
Retirement Contribution Credit <800>  
TOTAL TAX   $9,009
401(k) contributions $20,000  
Net Take-home Pay   $78,991

At this point, David starts eyeing the remainder of the retirement savings tax credit, which would save another $1,200 if he can manage to reduce his AGI by another $7,705. Of course, if he can reduce it by $6,505, then he can spend another $1,200 and have it immediately pay for itself. To reduce the AGI by $7,700, they will need to actually expense approximately $8,500 because of the lowered SE tax deduction. However, by spending this money, their total taxes will be lowered by approximately $4,000, which they decide is worth it.

With this change, the business profit is reduced to $33,255 and the SE tax to $4,699. Their AGI becomes $27,555 and their taxable income is reduced down to $5,205. This results in the following situation:

Gross Revenue   $135,000
SE Tax $4,699  
FICA 1,989  
Fed Tax 523  
State Tax 241  
Retirement Contribution Credit <2000>  
TOTAL TAX   $5,452
401(k) contributions $20,000  
Net Take-home Pay   $74,048

However, the above situation does not take into account that fact that the retirement contribution tax credit is nonrefundable, thus it cannot exceed the amount of the federal income tax. This, in turn, means that the taxable income must be at least $18,900 ($16,150 for a single person). This, in turn, means that the AGI must be at least $41,250 ($21,850 for a single person). Thus, while a single person could potentially take advantage of this tax credit to its maximum extent, out married couple with one dependent can't. Their optimal point is to shoot for a federal tax of $800, which requires a taxable income of $8,000 which, in turn, needs an AGI of $30,350.



While they are spending/investing $55,500 more each year, they are only reducing their available income by $24,083. The remaining $31,417 comes from their lowered tax liability. At this point, it is clear that any further savings would need to be as a result of lowering the SE Tax, but without lowering their AGI much more (since the tax credit is non-refundable).


1. The term "Traditional" is capitalized merely for aesthetics to balance the capitalized term "Roth".