User:Fyre4ce/Traditional versus Roth

It is a common investment decision whether to use a Traditional or Roth account. You must make this decision if your employer offers both a Traditional and Roth 401(k), or when you can invest in either your Roth IRA or your employer's Traditional 401(k), or when you consider a Roth IRA conversion.

In a Traditional retirement account such as a deductible Traditional IRA or Traditional 401(k), your contributions are deductible, taxes (such as dividends and capital gains) are deferred until withdrawal, and eventual withdrawals are taxed as ordinary income. In a Roth retirement account such as a Roth IRA or Roth 401(k), your contributions are not deductible, but all future growth and withdraws are tax-free in retirement  Either one may be a better investment choice; here are some of the considerations.

General Guidelines
The following guidelines are relevant for most investors. See below for explanations, and remember to check your own situation.

Non-tax considerations (401(k) vs. IRA, regardless of whether traditional or Roth):
 * If your employer matches 401(k) contributions, put enough to get the maximum match in the 401(k) before contributing to any IRA.
 * If you have inferior options in the 401(k), prefer an IRA to unmatched 401(k) contributions.

Tax considerations:
 * Prefer Traditional savings during higher earning years, and prefer Roth savings and conversions during lower earning years, such as during school and training, early in your career if you expect your income to rise, during lower-income years with disability or sabbatical, while working part-time, or in retirement prior to taking Social Security benefits.
 * Most investors benefit from having at least some money in Traditional accounts (401(k), IRA, etc.). If you currently have no Traditional savings, prefer Traditional.
 * If you are currently living in a high-tax state and plan to retire to a lower-tax or tax-free state, prefer Traditional. If you currently live in a low-tax state and plan to retire to a high-tax state, prefer Roth.
 * If you will have a traditional account or a pension large enough to meet your expected retirement expenses (and you expect to take that pension shortly after retiring), prefer a Roth.
 * If you expect to leave your estate to heirs who will have a higher marginal tax rate than you, prefer Roth. If you expect them to have a lower marginal rate, prefer Traditional.
 * Both Traditional and Roth are generally superior to non-qualified accounts (taxable accounts, variable annuities, etc) for retirement savings, so maximize retirement account contributions (even if the Traditional/Roth trade is suboptimal) before investing elsewhere.

Marginal Tax Rates
The main reason to prefer one type of account over the other is the comparison of marginal tax rates. If your marginal tax rate now is higher than your estimated marginal tax rate at retirement, then the traditional account is better; if it is lower, then the Roth account is better.

The simplest equations for the after-tax amount one gets, after growth and taxes are considered:


 * Traditional = Original_amount * Growth_factor * (1 - withdrawal_tax_rate)


 * Roth = Original_amount * (1 - contribution_tax_rate) * Growth_factor

The Growth_factor can be calculated as either:
 * (1 + r)^t, for periodic compounding, where r is the periodic rate of return (eg. annual) and t is the time in terms of number of periods (eg. years)
 * e^(r * t) or EXP(r * t), for continuous compounding

When the tax rates are equal, thanks to the commutative property of multiplication (i.e., A * B * C = A * C * B) the Traditional and Roth results are equal.

The reason to use marginal tax rates in this decision, as opposed to average tax rates, is that you can make the decision separately for every dollar you invest. If the next dollar you invest will be taxed at 22% now and 24% when you retire, there is a slight advantage for the Roth account. Your future effective or average tax rate (total tax divided by taxable income) will likely be much lower than 24%, perhaps only 10%. But nonetheless, you are still better off contributing to Roth, because each additional dollar invested is a new investment, and would be taxed at a higher rate in the future than now.

This common misunderstanding about Traditional accounts is sometimes described as, "contributions are taken from the top tax rate and are withdrawn later at the average rate". In other words, that one saves a marginal rate when contributing but pays only an average rate (starting at 0% for the first dollar withdrawn) when withdrawing. This is only true for the first dollar you contribute to Traditional accounts. After that, subsequent contributions will be withdrawn on top of the withdrawals due to previous contributions. One must therefore calculate the marginal withdrawal tax rate due to those subsequent contributions. But, this is why it's a good idea for most people to have at least some Traditional investments, to take advantage of and "fill up" the lower brackets in retirement.

Example
You can either contribute $5,000 pre-tax earnings to a 401(k) as Traditional or Roth. Your marginal tax rate is 22% now, predicted to be 12% in retirement. The investment is expected to grow at 8% in either case, and be withdrawn in 20 years. Contributing as Traditional means the entire earnings ($5,000) goes into the account now, grows to $24,765.16 ($5,000 * EXP(8% * 20)), and will be worth $21,793.34 ($24,765.16 * (1 - 12%)) in retirement after-tax. If you instead contribute as Roth, you will only be able to invest $3,900 ($5,000 * (1 - 22%)), because you must pay income tax on the earnings. That contribution will grow to $19,316.83 ($3,900 * EXP(8% * 20)) in retirement, and will be able to be withdrawn tax-free. The Traditional contribution results in more after-tax money, due to the difference in marginal tax rates.

Note: This calculation assumes you have not reached the contribution limits for your retirement accounts. If you can maximize your 401(k) and IRA contributions, see below.

Marginal Tax Rate Now
Your marginal tax rate now is relatively easy to determine. It is not necessarily your tax bracket, because of phase-ins and phase-outs of tax benefits; see Marginal tax rate for a more detailed explanation. You can ask your accountant, or use tax software to recalculate your return using a small (typically a few hundred dollars) increase in income. Most of the phase-outs (Child Tax Credit, Student Loan Interest Deduction, Section 199A deductions, etc) apply more often to taxpayers in their working years rather than in retirement, so pay careful attention to these phase-outs, and don't assume your marginal tax rate now is simply your tax bracket. Some specific considerations are listed below.

Child Tax Credit
One of the most important phase-outs is the child tax credit. The credit is increased to $2,000 per child and $500 per non-child dependent, but the phase-out begins at $400,000 for married filling jointly, $200,000 for all others, which means that it affects primarily taxpayers in the 32% and higher tax brackets. Investors with income that high are unlikely to prefer a Roth IRA in any case, but the phase-out gives a further advantage for traditional contributions if doing reduces their adjusted gross income and makes them eligible for the credit, or for a larger credit. Since the phase-out rate is 5%, your marginal tax rate is 5% higher than your tax bracket if your MAGI is in the phase-out range

Many of the education tax credits also phase out for middle-income taxpayers, so you might prefer traditional contributions when you expect to take those credits.

Saver's Credit
Saver's Credit is effectively a match from the IRS on your retirement contributions if you have a relatively low income. The credit is given for contributions to either traditional or Roth accounts. However, there are two advantages which may make traditional contributions more attractive. If you cannot afford to contribute $2000 to a Roth account, then you can contribute more to a traditional account for the same out-of-pocket cost to get a larger match. In addition, the credit is based on your adjusted gross income; contributions to a Traditional IRA or 401(k) reduce your adjusted gross income and may make you eligible for the credit, or for a larger credit.

The saver's credit is one reason that someone in a low tax bracket might have a high marginal savings rate and thus prefer using a traditional account.

College Aid
While the Expected Family Contribution for college financial aid is not a tax, it works the same way as a tax, as it is calculated based on a percentage of your income from the year before you file the form. But it counts after-tax income, including retirement contributions, and thus creates an advantage for the Roth as long as the Roth contribution does not cause education tax credits to phase out. For example, if you are in a 22% tax bracket and contribute $10,000 to a Traditional 401(k), the $10,000 is not subtracted from your income, and the $2200 tax savings is added to your income, so your EFC for the next year is increased by $1034 if you are subject to the 47% marginal rate. If you instead contribute $7500 to a Roth 401(k) for the same out-of-pocket cost, your EFC is not increased.

Do not convert a deductible Traditional IRA to a Roth while you have children in college; the amount of the conversion is counted in your income for both EFC and tax purposes, so it will increase your EFC as well as possibly causing education benefits to phase out. (There is no disadvantage to using the Backdoor Roth IRA; converting a non-deductible IRA to a Roth IRA does not create income.)

Social Security Benefits
One important exception is the phase-in of taxation of Social Security benefits. If you are in the phase-in range, you may experience a marginal rate in retirement of 22.2% or 40.7% despite being in the 12% or 22% brackets. The 22.2% "spike" is not much of a concern, because it blends in smoothly with the 22% bracket. But, the 40.7% spike is worth taking care to avoid. Those most likely to be affected by the 40.7% spike are as follows:

If you are reasonably close (10-15 years or less) to retirement and are in the benefits and income range where you may be affected by the 40.7% spike, you should try to either come in under the spike, or go far above it, depending on which option is easier. For those making Traditional contributions, switching to Roth to lower taxable income in retirement might be the easiest option.

Marginal Tax Rate In Retirement
In general, most retirees have the same or lower marginal tax rate than when they were working, and thus should prefer a Traditional account to a Roth if the options are comparable. When you retire, you will only pay tax on income earned outside a retirement account, and on the money you actually withdraw for spending. In addition, if any of your retirement spending comes from Roth accounts, it will not be taxed, and if it comes from taxable capital gains or qualified dividends, it will be taxed at a lower rate than your marginal tax rate. Therefore, you can spend the same amount but have less taxable income. For this reason, in the absence of a more rigorous analysis, most investors should prefer Traditional contributions during their peak earning years. For those seeking a more accurate estimate, an analysis method follows.

Estimating your marginal tax rate in retirement is considerably harder. For one, tax laws may change, and the further you are from retirement, the more likely this becomes. As a starting point, it makes sense to assume the current tax code will still be in place in retirement, but if you have strong feelings that taxes will go up or down in the future, you could make adjustments to these numbers. In any case, you should adjust the bracket thresholds for inflation, which historically has averaged about 3% per year. You may also be living in a different state. Some states (Florida, Texas, Washington, South Dakota, Nevada, Wyoming, Alaska) don’t charge any income tax, while others charge high taxes (eg. California charges up to 13.3%).

You will need to estimate your taxable retirement income. If you have, or plan to have, a large tax-deferred investment, then withdrawals will require you to pay substantial taxes in retirement. You can use the Future Value function in Excel to estimate future balances. For example, for an investor with $250,000 saved in tax-deferred investments, retiring in 20 years, contributing $19,000 per year, expecting 8% growth before inflation and 5% growth after inflation, the function “=FV(5%,20,-19000,-250000)” gives an inflation-adjusted balance in retirement of $1,291,578. Assuming a 4% withdrawal rate, this investment would yield about $51,663 of annual income in retirement.

Next, add to this value any taxable income from other sources, including pensions, rental properties, part-time work, investment income, etc. Also add in 85% of your expected annual Social Security benefit (85% of Social Security benefits are taxable, unless your other income is very low). Then subtract either the standard deduction or what you know to be your itemized deductions. If you currently have very little tax-deferred retirement savings, your calculated retirement tax rate will be very low, so you’ll get a big value by contributing more. In fact, due to the federal standard deduction, the first $12,200 or $24,400 you withdraw in retirement each year should be tax-free. Assuming a 4% withdrawal rate, that corresponds to an account balance of $305,000 or $610,000 that can be accessed federally tax-free, and these figures should grow with inflation. As your tax-deferred balance rises, so will your expected tax rate, but as long as it’s less than your marginal tax rate now it still makes sense to contribute to tax-deferred accounts. If your expected retirement marginal tax rate ever reaches or exceeds your current marginal tax rate, and you still want to save more, then additional savings should be done in a Roth account.

Example
A single investor earns $200,000 gross income and has a marginal tax rate of 32%. He plans to retire in 25 years. He currently has $150,000 in Traditional (tax-deferred) savings, expected to grow at 8% after fees, and has been making the $19,000 maximum yearly contributions. He also has a $50,000 taxable account, to which he expects to contribute $5,000 per year, with an expected growth of 8%, a yield of 2%, and a dividend tax rate of 15%. He also expects to receive a $3,000 per month inflation-adjusted Social Security benefit, of which 85% will be taxable. He does not expect any additional income in retirement, from part-time work, investments income other than tax drag from the taxable account, rental properties, pensions, etc. His 401(k) allows either Traditional or Roth contributions; which should he be making? His predicted retirement marginal tax rate could be calculated as follows:

Under the current tax bracket structure, his future marginal rate is predicted to be only 22% (just below the 24% threshold), and since his current marginal rate is 32%, he should prefer Traditional contributions to Roth.

Straddling Brackets
Note that the marginal tax rates now and in the future can be affected by the amount contributed to Traditional accounts. For example, contributing the full $19,000 to a Traditional 401(k) might bring an investor down from the 32% bracket into the 24% bracket. Likewise, contributing more to Traditional accounts might raise the predicted future marginal tax rate such that it might cross into a higher bracket. In these cases, the Traditional vs. Roth analysis should be done for each dollar invested; contributions can be divided in any proportion. The higher the investment performance, longer the time horizon, and higher the contribution limit to Traditional accounts, the more likely straddling becomes.

Example
A married couple earns $400,000 gross income. They currently have $350,000 in Traditional (tax-deferred) savings, expected to grow at 9% after fees. They contribute $37,000 each year into their Traditional 401(k), and can each contribute $19,000 into their 401(k) as either Traditional or Roth. They also have a $50,000 taxable account, to which they expect to contribute $5,000 per year, with an expected growth of 8%, a yield of 2%, and a dividend tax rate of 15%. They expect to each receive a $3,000 per month inflation-adjusted Social Security benefit, of which 85% will be taxable. They do not expect any additional income in retirement, from part-time work, investments income other than tax drag from the taxable account, rental properties, pensions, etc. Should they make Traditional or Roth 401(k) contributions with their $38,000 per year? For fully Traditional contributions, their predicted retirement marginal tax rate could be calculated as follows:

Assuming the current tax system remains in effect, their future marginal rate is predicted to be 32%. Their current marginal tax rate with full Traditional contributions would be 24% ($400,000 - $37,000 - $38,000 - $24,400 = $300,600). It appears as though they should prefer Roth contributions.

However, if the calculation is run assuming 100% Roth contributions, the result is different:

Their future marginal rate would therefore be only 24%, and their current marginal rate with full Roth contributions would be 32% ($400,000 - $37,000 - $24,400 = $338,600), the opposite of before. The optimal solution is to split contributions between Traditional and Roth contributions. For simplicity, we can check six possible proportions, although in practice, spreadsheet or optimization software could automate this calculation to be more precise:

Note that this analysis is extremely imprecise; it depends on future contributions being made, investments performing as expected, and the tax code remaining the same, most of which are very unlikely to occur. The proper strategy is to repeat this analysis every few years, or when there are major changes to your situation, booms or busts in the market, and changes to the tax code. Through iterative adjustments, you can home in on the optimal answer as you near retirement.

State Taxes
Consider state taxes as well as federal taxes in your tax rate comparisons, both for the state you live in and for the state you expect to retire in.

Some states do not allow deductions for traditional account contributions, or only allow them for some types of contributions (New Jersey, for example, allows deductions for 401(k) but not 403(b) or IRA contributions); if you live in such a state, the Roth has an advantage. If your state allows a deduction but you might retire in a state which has no tax or will not tax your Traditional IRA withdrawals, then the Traditional IRA has a potential advantage; conversely, if your state has no income tax but you might retire in a state which taxes Traditional IRA withdrawals, the Roth has a potential advantage.

Estate Planning
For those planning on leaving a significant estate to their heirs, multigenerational affects should be considered. For example, if you are a high earner in the 32% tax bracket, and expect to be throughout retirement, but your heirs are lower earners in the 12% tax bracket, you should prefer Traditional contributions - your heirs will receive a larger inheritance after tax. Likewise, if you are in the 12% bracket but your heirs are in the 32% bracket, you should prefer to contribute to Roth accounts.

Opportunity to Convert Later
If you contribute to a traditional IRA, you can convert to a Roth IRA in a later year. If you contribute to a traditional 401(k) and leave your employer, you can roll the 401(k) into a traditional IRA and then convert it later, or roll it directly to a Roth IRA. Your income (and therefore marginal tax rate) might be lower in a year when you separate from an employer. In either case, you may come out ahead if you can convert in a lower tax bracket, because you pay the taxes in the year of conversion instead of the year of contribution.

This increases the benefit from using traditional accounts when you retire in a low tax bracket. If you retire in a 12% tax bracket before taking Social Security, and don't need the whole 12% tax bracket for living expenses, you can convert part of your Traditional IRA to a Roth at 12%, reducing the amount you will have in the IRA when you start taking Social Security.

But if you expect to retire in the same tax bracket, this is not a significant extra advantage for the traditional accounts. If you are usually in a 22% tax bracket and retire in a 22% tax bracket but happen to have some years in a 12% bracket (large deductions, unemployed part of the year, one spouse takes off from work or works part-time to care for children), you can convert up to the top of the 12% bracket in those years, and you can make those conversions from any traditional accounts you have, whether or not you have Roth accounts.

Required Minimum Distributions
Traditional accounts have the disadvantage of having Required Minimum Distributions (RMDs) begin at age 70.5. (Roth 401(k)'s have RMD's as well, but can easily be rolled over into a Roth IRA upon retirement, and Roth IRA's do not have RMD's). RMD's are a reasonable percentage of the account balance, but if you expect to want to leave large IRAs as part of your estate and RMD's would hinder this goal, then prefer Roth contributions.

Tax Risk
If all else is equal (that is, you expect to retire in the same bracket, and never to have the opportunity to convert in a lower bracket), the Roth account has a slight advantage because there is less tax risk. You might not retire with the same marginal tax rate that you expect, either because tax rates change or because your taxable income is higher or lower.

If you will have a lot of money in retirement, it is desirable to have some Roth money because of Required Minimum Distibutions. If all of your retirement money is in traditional accounts, you will have to take the RMDs even if that is more than you need to live on, and thus pay tax prematurely. If you have Roth accounts which you do not need in your own retirement, you can leave them for your heirs.

Another risk for MFJ filers is the death of one spouse, leaving the survivor with single filing status and its higher marginal rates.

Tax Diversification
Tax Diversification is the principal that having assets spread across different kinds of accounts (Traditional, Roth, taxable, etc) give you an extra dimension of flexibility in retirement. The further you are from retirement, the harder it is to predict what tax law will be. It may be the case that there will be certain "spikes" in marginal rates in the future (eg. the current Social Security taxation spike), and having the flexibility to control your taxable income to some degree might allow you to optimize around future tax laws. Conversely, if you only have Traditional investments, you will be required to withdraw RMD's or whatever you need to live on, and pay whatever tax results. Even if the Traditional vs. Roth analysis described above favors one type or the other, there is a potential large advantage to having a mix.

Investment options
You may have different investment options in traditional and Roth accounts. If your employer offers a Traditional 401(k) but not a Roth 401(k), then you must use Traditional accounts if you invest in the 401(k). If you are over the income limit for a deductible Traditional IRA, then you must use a Roth account if you invest in an IRA (a non-deductible IRA cannot be better than either a deductible or Roth account). The choice of account, or benefits within the account, may be more important than the different tax treatment of traditional and Roth accounts.

Employer match
If your employer matches 401(k) contributions, this is by far the best investment you can make, as it has an immediate return equal to the match rate. Therefore, regardless of the quality of your employer's plan, you should get the maximum match before investing anywhere else.

If your employer offers both traditional and Roth accounts, any match goes to a traditional account. Therefore, if you cannot contribute enough to a Roth to get the maximum match, you should prefer the traditional account. For example, if you are in a 12% tax bracket and your employer will match 100% of your contributions up to $4000, then you can contribute $3520 out of pocket to a Roth 401(k) and get a $3520 match in the Traditional 401(k), or $4000 to a Traditional 401(k) (with $480 in tax savings) and get a $4000 match.

Investment Quality and Fees
Many 401(k) plans, and even more retirement plans of other types such as 403(b) plans, have inferior investment options. If you invest in high-cost funds in a 401(k), you will usually lose more to the high costs than you can gain from any tax difference between the 401(k) and IRA. Some plans have only high-cost options; in such a plan it is better to max out your IRA (Traditional or Roth) before making unmatched contributions to the 401(k). Other plans have some low-cost options, but have no options or high-cost options in some asset classes; in such a plan, you should prefer to invest enough in an IRA (Traditional or Roth) to cover the asset classes with no good option in the 401(k). Once your IRA is maxed out, it is usually worth contributing even to a bad 401(k). Conversely, some retirement plans, such as the Thrift Savings Plan, have better options than are available to retail investors in IRAs. If you have such a plan, you may prefer that plan to an IRA, even at a tax cost. Investment quality and tax considerations can be combined into the same calculation, by using the Growth_factor in addition to the marginal tax rates.

Example
You can either contribute $5,000 pre-tax earnings to a Traditional 401(k) or a Roth IRA. Your marginal tax rate is 22% now, predicted to be 12% in retirement. The investment is expected to grow at 8% before fees in either case, but the Traditional 401(k) charges a 1.00% expense ratio, and the Roth IRA charges a 0.04% expense ratio. Either investment would be withdrawn in 20 years. The future after-tax values of the two investments will be as follows:
 * Traditional 401(k): $5,000 * EXP((8% - 1%) * 20) * (1 - 12%) = $17,842.88
 * Roth IRA: $5,000 * EXP((8% - 0.04%) * 20) * (1 - 22%) = $19,162.91.

Assuming the investments are held for the full 20 year term, the fees in the 401(k) outweigh the tax savings, and the Roth IRA is a superior investment. However, the tax savings from the Traditional contribution is immediate, whereas the fees reduce performance gradually over time. In this circumstance, if you expected to separate from your employer well before the 20 year term, you could roll the 401(k) into either a low-expense Traditional IRA, or the 401(k) at your new employer. Depending on how long the money remained in the high-expense 401(k), you might come out ahead contributing to the 401(k) now.

Maxing Out Your Retirement Accounts
The IRS sets a maximum contribution to retirement accounts. If you have reached this maximum, anything else you contribute must be in a taxable account that will (if you pay more than 0% on annual earnings or capital gains) lose money to taxes not incurred in either a Traditional or Roth account. The IRS contribution limits do not distinguish between Traditional (pre-tax) and Roth (after-tax) accounts. Because after-tax money is worth more than pre-tax money, Roth accounts effectively allow you to contribute more than Traditional accounts. For example, if your marginal tax rate is 32%, a $19,000 Roth 401(k) contribution will tax-shelter $27,941.18 ($19,000 / (1 - 32%)) of pre-tax earnings, whereas a Traditional 401(k) contribution can only tax-shelter $19,000. A fair comparison between Roth and Traditional contributions when at a fixed-dollar limit must therefore also take into account the performance of the remaining money in a taxable account.

Taxable Investment Performance
Calculating the performance of taxable investments is considerably more complicated than for Traditional or Roth investments. The tax rules for taxable investments are as follows:


 * Taxable investments are made with after-tax money
 * Interest, dividends and capital gains generated by the taxable investment are taxed as income in that year, either as ordinary income (for interest, ordinary dividends, and short-term capital gains), or at a reduced rate for long-term capital gains and qualified dividends
 * When the investment is sold, the difference between the sale price and the cost basis is taxed as either short-term (if held for <=1 year) or long-term (if held for >1 year) capital gains. Because this analysis is for retirement savings, long-term rates will be assumed.

Each year, taxes on interest, dividends, and capital gains (referred to as "dividends" from here forward, for simplicity) must be paid out of those earnings, reducing the rate of growth. Variables are defined as follows:


 * t = time
 * V(t) = investment value at time t
 * V(0) = initial investment value
 * B(t) = investment basis at time t
 * B(0) = initial investment basis
 * r = overall rate of return
 * y = yield
 * tr_now = marginal tax rate on ordinary income
 * tr_div = effective tax rate on dividends
 * tr_cg = effective tax rate on capital gains (when investment is sold)

The value of the investment at any time t can be calculated as follows:


 * V(t) = V(0) * EXP((r - (y * tr_div) * t))

Calculating the basis at any time t requires integration. The initial basis B(0) is assumed to be equal to V(0), and the rate of change of the basis over time is equal to:


 * dB(t)/dt = V(t) * y * (1 - tr_div) = V(0) * EXP((r - (y * tr_div) * t)) * y * (1 - tr_div)

Integrating this function from 0 to t gives:


 * B(t) = V(0) + V(0) * (1 - tr_div) * y * [ EXP((r - (y * tr_div) * t)) - 1] / [r - (y * tr_div)]

The after-tax value of the investment is therefore:


 * V(t) - (V(t) - B(t)) * tr_cg

Expressing this value in terms of pre-tax dollars, the after-tax value is:


 * (1 - tr_now) * [V(t) - (V(t) - B(t)) * tr_cg]

Example
You are deciding between Traditional and Roth contributions in your 401(k), with a contribution limit of $19,000. Your marginal rate now is 24%, your marginal rate in retirement is predicted to be 22%, your tax rate on dividends and long-term capital gains are both 15%. Your investments in any account are expected to return 8% with a yield of 2%. You plan to withdraw the money in 25 years. If you invest in Roth, you can effectively contribute $25,000 ($19,000 / (1 - 24%)) of pre-tax earnings, and your future after-tax value will be:


 * $25,000 * (1 - 24%) * EXP(8% * 25) = $19,000 * EXP(8% * 25) = $140,392.07

If you invest $19,000 in Traditional, your future Traditional after-tax value will be:


 * $19,000 * EXP(8% * 25) * (1 - 22%) = $109,505.81

In addition, you will invest the remaining $6,000 ($25,000 - $19,000) pre-tax money in a taxable account. After initial income taxes are taken, this amount becomes:


 * $6,000 * (1 - 24%) = $4,560

After 25 years, the value of the investment will grow to:


 * $4,560 * EXP((8% - (2% * 15%)) * 25) = $31,259.48

The basis of this investment will be:


 * $4,560 + (1 - 15%) * $4,560 * 2% * [ EXP((8% - (2% * 15%)) * 25) - 1] / [8% - (2% * 15%)] = $10,454.69

When sold, the future after-tax value of the investment will be:


 * $31,259.48 - ($31,259.48 - $10,454.69) * 15% = $28,138.76

Finally, we compare the two results and see that the Roth investment has an advantage, despite having an apparent disadvantage due to the higher marginal tax rate now:


 * Roth = $140,392.07
 * Traditional + taxable = $109,505.81 + $28,138.76 = $137,644.57

If the analysis were repeated with a wider spread in tax rates (eg. 22% and 12%, or 32% and 24%) then Traditional would retain the advantage. It's also worth noting that the Traditional and taxable investments both retain more flexibility for the future. The Traditional investment may be later converted to Roth, and the taxable investment may be sold and withdrawn without penalty at any time.

High Earners
High earners, who will be at or near the top tax bracket during working years and retirement, should generally prefer Roth investments. Such investors should expect little or no difference between their marginal rate between now and retirement, and because their tax rate is higher, they can tax-shelter lots more income with Roth than Traditional. A high earner with a 50.3% marginal tax rate (37% federal and 13.3% state) can tax-shelter $38,229.38 ($19,000 / (1 - 50.3%)) per year in a Roth account, more than double than with a Traditional.

Additional Resources
The 'Misc. calcs' tab (near row 150) in the Personal finance toolbox can be used to plug in your own numbers.

Another spreadsheet that does similar calculations:
 * Traditional versus Roth (401(k) or IRA)

Resources

 * Bogleheads' Guide to Retirement Planning, Chapter 10
 * Roth vs Traditional 401K on Bogleheads.org forum, 5 March 2008.
 * Why the Roth IRA bias? on Bogleheads.org forum, 14 October 2010.