The impact of the Tax Cut and Jobs Act on IRA choice for moderate income investors Timothy Manuela,*, Lee Tangedahla, Kent Swifta aCollege of Business Administration, University of Montana, Missoula, MT 59812, USA Abstract While the choice of appropriate individual retirement account (IRA) type involves many factors, it is well known that differences in tax rates during the working and retirement years impact the optimal choice. Lower rates of return on investment may cause an investor to prefer a Traditional IRA whereas higher rates of return often result in higher after-tax future wealth for the Roth IRA. The lower statutory tax rates for individuals resulting from the 2018 Tax Cut and Jobs Act raises the breakeven rate of return where the Roth becomes preferable for many moderate income individuals who invest the amount of the deduction generated by the Traditional IRA. The new tax law significantly increases the breakeven rates for investors who begin investing at an older age. Moderate income investors are defined as those who will be in the 22% marginal tax bracket during their working years. Many investors do not invest the tax savings generated by a qualifying Traditional IRA. For these individuals a spreadsheet model is used to compare contribution and retirement real consumption. The Traditional IRA can be a better choice for many moderate income individuals who want to maximize their total lifetime real consumption rather than retirement consumption, and the compression in tax rates of the new tax law increases the number of outcomes where the Traditional IRA yields higher total consumption. © 2018 Academy of Financial Services. All rights reserved. JEL classification: Paper classifications; G110 portfolio choice; Investment decisions; D140 household saving; Personal finance Keywords: Financial planning; Retirement account; Personal finance; Personal savings * Corresponding author. Tel.: �1-406-243-2511; fax: �1-406-243-6925. E-mail address: tim.manuel@business.umt.edu (T. Manuel) Financial Services Review 27 (2018) 345-365 1057-0810/18/$ – see front matter © 2018 Academy of Financial Services. All rights reserved. 1. Introduction Contributions to Roth individual retirement accounts (IRAs) are not tax deductible, while for many moderate income investors contributions to a Traditional IRA are deductible. Subject to certain rules the withdrawals from a Roth IRA are not taxed, whereas Traditional IRA withdrawals are taxable. The new Tax Cut and Jobs Act (TCJA) generally increases the number of moderate income individuals who may prefer the Traditional over the Roth IRA. Moderate income investors are defined as those who will be in the 22% marginal tax bracket during their working years.1 When determining whether to choose a Traditional IRA or a Roth IRA conventional wisdom indicates one should consider the individual’s tax rate today versus their expected future tax rate (VanZante and Fritzsch, 2013). If a person believes the future tax brackets and tax rates will be lower, or if they will have lower income in retirement, then a Traditional IRA may be the best choice (Grossman and Rose, 2012). In comparison, higher rates of return and contribution amounts lead to higher tax rates on Traditional IRA withdrawals and, thus, favor the Roth IRA. Similarly, lower rates of return on investment and smaller contributions favor the Traditional IRA. The compression of the tax brackets, and the general reduction of the marginal tax rates in the new law, raises the breakeven rate of return beyond which an investor may achieve a higher after-tax future value with a Roth IRA. The breakeven rates of return are calculated before and after the new tax law. The new tax law favors the Traditional IRA for a broader range of returns for individuals who invest the deduction. For older investors with only 15 years to retirement the breakeven rate of return where the Roth provides a greater future value is as high as 21.95% under the new tax law. Most investors are not likely to achieve an average return this high and may be better off with a Traditional IRA. Adelman and Cross (2010) and Beshears, Choi, Laibson, and Madrian (2017) indicate that many people do not actually invest the deduction generated by contributions to a Traditional IRA, preferring instead to consume the extra income. When comparing future values of the two types of IRAs, the Roth IRA yields higher futures values than the Traditional IRA without the deduction invested in the majority of cases. This has led some authors such as Beshears et al. (2017) to conclude that the Roth provides consis- tently higher future savings than the Traditional IRA. However, choosing the Roth reduces an investor’s real consumption during their working years compared with a Traditional IRA because the Roth contributions are not deductible. Even with the higher future value of a Roth IRA, the Traditional IRA could provide a higher level of lifetime consumption. Monte Carlo simulations were used to determine whether lifetime real consumption is maximized with a Traditional or a Roth IRA for investors who do not invest the deduction generated by a Traditional IRA under various return scenarios. The Traditional IRA provided higher median lifetime consumption than the Roth IRA in the majority of our simulations for moderate income individuals who reduce the risk of their portfolios as they age. The Traditional IRA can be a better choice for many moderate income individuals, regardless of whether they invest the deduction from Traditional IRA contributions if current spending is a concern along with funding retirement. This has not generally been discussed in the literature on retirement investing.2 346 T. Manuel et al. / Financial Services Review 27 (2018) 345-365 2. IRA usage According to the Report on the Economic Well Being of Households in 2016 by the Board of Governors of the Federal Reserve System (2017) about 31% of households have an IRA. The most common type IRA is the Traditional IRA, and only a subset of households has a Roth IRA or both types. About half of households have a 401(k), and about 25% have a defined benefit plan, whereas about 28% of households have no retirement investments. The report shows that investors with Roth IRAs are more likely to be higher income, more financially sophisticated and have utilized a financial planner than those who have a Traditional IRA. Smith, Finke, and Huston (2012) find similar results. They show that investors with Roth IRAs were much more likely to be “financially sophisticated” as measured by the extent of their equity investments and/or had consulted a financial planner. Roth IRAs are apparently still not well understood by many households who do not use financial planners, or perhaps planners favor Roth IRAs for their clients. For many investors the best IRA choice depends on many factors such as age, expected portfolio returns over time, risk aversion, liquidity needs, and the willingness to engage in tax management strategies, particularly during retirement. For more on some of the factors that favor the Traditional IRA see Saunders (2018). 2.1. Traditional IRA An IRA is not an investment per se, but is a tax advantaged investment vehicle. For a Traditional IRA, all deductible contributions and account earnings are subject to income taxation upon disbursement. Thus, an IRA is a type of tax-deferred savings account. If an amount is withdrawn before age 591⁄2, the taxpayer is required to pay tax on the amount withdrawn along with a 10% penalty for the early withdrawal.3 At age 701⁄2 an investor in a Traditional IRA must begin making withdrawals from the IRA. The withdrawals are termed required minimum distributions (RMDs). RMDs are calculated as the balance from the end of the previous year or life expectancy from the IRS’ Uniform Lifetime Table. The table can be found at https://www.irs.gov/pub/irs-tege/uniform_rmd_wksht.pdf. Failure to make the RMD results in a 50% excise tax. Additional tax details are available from the IRS’s publication on IRAs found at https://www.irs.gov/retirement-plans/individual- retirement-arrangements-iras. Roth IRAs do not require the investor to make RMDs during their lifetime. A beneficiary of a Roth IRA must make RMDs over the beneficiary’s expected life span, but if the beneficiaries are children the required withdrawal is usually small because of a long expected life span. Roth IRAs can, thus, be better for individuals who wish to fund a bequest to their heirs rather than provide funding for their own retirement. Individuals can open a Traditional IRA as long as they are not older than 701⁄2. In 2018 contributions to IRAs are limited to the lesser of $5,500 ($6,500 if 50 or older) or their taxable compensation for the year; although our model assumes that the IRS, in accordance with Congressional mandates, increases the allowable contribution amount over time to keep up with inflation. The new TCJA calculates the indexing of contribution amounts and tax brackets using the Chained CPI-U index rather than the Traditional CPI-U.4 The other main tax feature of the Traditional IRA is that, subject to the investor’s income and pension 347T. Manuel et al. / Financial Services Review 27 (2018) 345-365 contribution, the contributions to a Traditional IRA may be tax deductible in the year of the contribution. 2.2. Roth IRA In a Roth IRA the contributions are never tax deductible. However, the contributions and account earnings are not taxable when withdrawn as long as the individual has had the Roth IRA for five years or more and does not make withdrawals before age 591⁄2. Under these conditions, Roth IRA distributions are not subject to income taxation. 2.3. Additional tax considerations for a Traditional IRA Contributions to a Traditional IRA can usually be used to reduce an individual’s Modified Adjusted Gross Income (MAGI). Table 1 Filing Status and Deductibility provides the 2018 taxable year table applicable for individuals that are, or are not, covered by a retirement plan at their place of employment. Table 1 Filing status and deductibility with a retirement plan at work (2018 tax year) Panel A: Filing status and deductibility with a retirement plan at work For 2018 if your filing status is . . . AND your MAGI is. . . THEN you can take Single or head of household $63,000 or less A full deduction up to your contribution limit More than $63,000 but less than $73,000 A partial deduction $73,000 or more No deduction Married filing jointly or qualified widower $101,000 or less A full deduction up to your contribution limit More than $101,000 but less than $121,000 A partial deduction $121,000 or more No deduction Married filing separately Less than $10,000 A partial deduction $10,000 or more No deduction Panel B: Filing status and deductibility without a retirement plan at work In 2018 if your filing status is . . . AND your MAGI is. . . THEN you can take Single, head of household, or qualifying widower Any amount A full deduction up to your contribution limit Married filing jointly or separately with a spouse who is not covered by a plan at work Any amount A full deduction up to your contribution limit Married filing jointly with a spouse who is covered by a plan at work $189,000 or less A full deduction up to your contribution limit More than $189,000 but less than $199,000 A partial deduction $199,000 or more No deduction Married filing separately with a spouse who is covered by a plan at work Less than $10,000 A partial deduction $10,000 or more No deduction Note: MAGI � Modified Adjusted Gross Income. 348 T. Manuel et al. / Financial Services Review 27 (2018) 345-365 Panel A of Table 1 provides deductibility of a Traditional IRA for various filing statuses for individuals that are covered by a retirement plan at work and Panel B of Table 1 provides similar information for those who do not have a retirement plan at work. Withdrawals from a Traditional IRA in retirement can cause Social Security benefits to be taxable, although Adelman and Cross (2010) suggest that this does not usually result in a very large increase in taxes. Medicare premiums may also increase with increased income resulting from a Traditional IRA withdrawal, but not from a Roth. A Traditional IRA also has a valuable option component (Baxendale and Coppage, 2014). Under existing tax rules all or part of Traditional IRAs can be converted to Roth IRAs (termed an IRA rollover). This option is preserved under the 2018 TCJA, although the ability to switch back to a Traditional IRA was eliminated in the new tax bill. 2.4. Additional tax considerations for Roth IRAs Unlike a Traditional IRA, the principal invested in a Roth IRA can generally be withdrawn without taxation before age 591⁄2 if the funds have been invested for at least five years. Not all investors can make Roth contributions. If an investor makes more than $199,000 in 2018 and has a tax status of married filing jointly then the person cannot contribute to a Roth IRA account, although this income level increases over time. If a person is single, head of household or married filing separately the individual cannot contribute to a Roth if they make more than $135,000, although this income level also increases over time.5 The contribution limits are the same for the Traditional and the Roth IRA and the limit is cumulative for the two in a given tax year. Excessive contributions to either type of IRA result in a six percent tax penalty that is imposed each year until the excessive contribution and its earnings are removed. An investor must also file Form 5329, or face an additional tax of up to 25% of the excise tax. See the IRS explanation titled, “About Form 5329, Additional Taxes on Qualified Plans (including IRAs) and Other Tax-Favored Accounts” found at https://www.irs.gov/forms-pubs/ about-form-5329 or the general discussion provided by Reichert (2011). 2.5. Math models of future values of traditional and Roth IRAs with constant returns and the impact of the TCJA Examining mathematical models comparing the future value of a Traditional and a Roth IRA can highlight the impacts of the new tax law on the choice. One cannot compare equal dollar investments in a qualifying Traditional and Roth IRA because investments in the Roth are after-tax, but are pre-tax in a Traditional IRA. Most literature comparing the two performs an adjustment to put the two on the same after-tax basis.6 Because investing X dollars in a Traditional IRA generates a tax deduction that can be invested, many models compare the future value at retirement (or an annuity beginning at retirement) of the Traditional IRA after-tax plus the future value of the extra amount invested as the result of the deduction (see for instance Horan, 2002, 2003). Because the value of the deduction is the tax rate at contribution times the deduction, it is easy to set up a comparison of the future values after-tax of the two alternatives. The latter amount is usually assumed to be invested 349T. Manuel et al. / Financial Services Review 27 (2018) 345-365 in a taxable account. One then compares this sum to the future value of X dollars invested in a Roth IRA. In particular, the Traditional IRA combined with a taxable investment will be preferable to the Roth IRA if the Future Value of Traditional IRA � Future Value of Taxable Investment � Future Value of Roth IRA or if (1 � r)n �1 � tw� � tc�1 � r�1 � tc�� n � �1 � r�n (1) where r is the constant pre-tax rate of return, n is the number of years to retirement, tc is the tax rate at contribution and tw is the tax rate upon withdrawal.7 Withdrawals are assumed to begin after age 591⁄2 and at least 5 years after the funds are invested so that there are no tax penalties. Sibley (2002) and various others model the future values of the two in this way. If the savings from the Traditional IRA are invested in an account with tax deferral benefits, such as non-dividend paying stocks or certain stock mutual funds, then the model understates the future value of the Traditional IRA. For details see Horan (2003, 2006). Higher rates of return, r, and time invested, n, favor the Roth over the Traditional IRA (Al Zaman 2008; Cook, Meyer, and Reichenstein, 2015; Horan, 2003; Horan and Al Zaman, 2009; Reichen- stein, 2006; Reichenstein, Horan, and Jennings 2015; Sibley 2002). Funds invested in any tax deferred annuity (TDA) grow at the pre-tax interest rate r while funds invested in a fully taxable account grow at the after tax rate r(1�tc). Because of the difference, at higher rates of return the Roth IRA can generate higher retirement income than the after tax value of the combination of the Traditional IRA and a taxable investment even when the tax rate is lower during retirement. Previous literature such as Horan (2003) has shown that while it is often the case that the Traditional IRA combined with a taxable account will yield a higher future value than a Roth IRA if tw � tc, sometimes the Roth is better even when the tax rate at withdrawal is lower than at the point of contribution if r is high enough. Before the TCJA many moderate income investors were likely to be in the 25% tax bracket during their working years and in the 15% bracket upon retirement. Table 2 compares the breakeven rates of return (r) under the old and new tax laws. At r � 9% or higher the Roth is preferred even if the tax rate at contribution is 25% and at withdrawal is substantially lower at 15%. Before the TCJA of 2018 the personal marginal tax rates started at 10%, increased to 15%, then to 25%, then to 28% and so on up to a maximum of 39.6%. Under the TCJA the personal marginal rates start at 10%, then progress to 12%, 22%, 24%, and so on, up to 37%. As shown in Table 2 the generally lower tax rates under the new law favor the Traditional IRA over the Roth IRA for a broader range of returns earned on invested funds with a given investment horizon.8 For a 25 year investment horizon under the 2017 tax rates an investor who had a 25% tax rate during the contribution years and 15% during retirement and who earned a pre-tax rate of return r � 8% on all investments would have been better off in a Traditional IRA. The Traditional is better because the sum of the after-tax future value per dollar invested in the Traditional IRA plus the after-tax future value of the taxable account (� 6.89417) is greater than the future value of the Roth IRA (� 6.848475). If 350 T. Manuel et al. / Financial Services Review 27 (2018) 345-365 the investor earned nine percent on all alternatives; however, then the Roth generates a higher future value. Panel A of Table 3 contains the breakeven rates of return under the old and the new tax rates for various investment periods if the deduction generated by the Traditional IRA is invested and is fully taxable at tc. For instance, with a 25 year time horizon to retirement, the breakeven r under the old tax rates is 8.8024%. At all lower rates of return the Traditional IRA is preferable, but at rates above the breakeven the Roth IRA is preferred, even though the tax rate is substantially lower during retirement. With the new tax law a similar investor may face tc of 22% and tw of 12%. In this case the breakeven rate of return is increased to Table 2 Future value of equal after-tax investments in Traditional IRA plus taxable account compared with future value of Roth IRA FV Traditional IRA FV taxable account FV Traditional IRA � taxable account FV Roth Tax law tc tw r rA-T n (1�r)n(1�tw) tc(1�rA-T)n Sum (1�r)n Preference 2017 25% 15% 7.00% 5.25% 25 4.61332 0.89845 5.51177 5.427433 Traditional 25% 15% 8.00% 6.00% 25 5.82120 1.07297 6.89417 6.848475 Traditional 25% 15% 9.00% 6.75% 25 7.32962 1.27979 8.60940 8.623081 Roth 25% 15% 10.00% 7.50% 25 9.20950 1.52458 10.73408 10.83471 Roth 2018 22% 12% 8.00% 6.24% 25 6.02666 0.99914 7.02579 6.848475 Traditional (TCJA) 22% 12% 9.00% 7.02% 25 7.58831 1.19963 8.78794 8.623081 Traditional 22% 12% 10.00% 7.80% 25 9.53454 1.43844 10.97298 10.83471 Traditional 22% 12% 11.00% 8.58% 25 11.95521 1.72254 13.67775 13.58546 Traditional 22% 12% 12.00% 9.36% 25 14.96006 2.06009 17.02014 17.00006 Traditional 22% 12% 13.00% 10.14% 25 18.68288 2.46065 21.14353 21.23054 Roth 22% 12% 14.00% 10.92% 25 23.28649 2.93541 26.22190 26.46192 Roth 22% 12% 15.00% 11.70% 25 28.96868 3.49745 32.46613 32.91895 Roth Note: IRA � individual retirement account; TCJA � Tax Cut and Jobs Act; tc � tax rate at time of contribution; tw � tax rate upon withdrawal; r � pre-tax rate of return, assumed constant; rA-T � after tax rate of return on earnings using tc; n � number of years until retirement. Table 3 Breakeven return r vs. years to retirement with reinvestment pre- and post-TCJA Panel A: Breakeven returns with tax deduction invested in a fully taxable account Years to retirement � 15 years 25 years 30 years 35 years 40 years Breakeven r old tax law 15.4637% 8.8024% 7.2425% 6.1522% 5.3472% Breakeven r new tax law 21.9536% 12.2185% 10.0010% 8.4647% 7.3376% Increase in breakeven r 6.4899% 3.4161% 2.7585% 2.3126% 1.9904% Panel B: Breakeven returns with tax deduction from Traditional IRA invested with an effective tax rate (ti) of 10% Years to retirement � 15 years 25 years 30 years 35 years 40 years Breakeven r old tax law 50.3346% 25.3536% 20.3129% 16.9441% 14.5337% Breakeven r new tax law 65.5725% 31.4991% 25.0028% 20.7278% 17.7013% Increase in breakeven r 15.24% 6.15% 4.69% 3.78% 3.17% Note: IRA � individual retirement account; TCJA � Tax Cut and Jobs Act. 351T. Manuel et al. / Financial Services Review 27 (2018) 345-365 12.2185%, and the Traditional IRA is preferred over a broader range of returns. As time to retirement (n) increases, the breakeven rates fall under both tax regimes because higher after-tax future values are produced by the Roth at longer n. The difference between the breakeven rates of return induced by the lower tax rates under the new law is thus reduced as n is increased. This implies that the new tax law should not have as large an influence on the choice of IRA for younger investors. However, older investors facing the same tax rates as depicted above who are starting to invest with a shorter time to retirement such as 15 years may prefer a Traditional IRA for almost all investment portfolios. In this case the breakeven r where the Roth provides a higher future value is 21.95% under the new tax law. Most investors are unlikely to achieve this large of an average return. Panel B of Table 3 depicts the various breakeven rates of return under the old tax law and the new assuming that the deduction generated by the Traditional IRA is invested in a tax-advantaged investment.9 Horan (2003, 2006) and others have shown that the ability to invest the deduction in a mutual fund with a tax deferral feature, or in a tax advantaged investment increases the future value of the Traditional IRA. To illustrate the impact on the breakeven rate of return the effective tax rate on the amount invested (ti) is assumed to be 10% to generate the results in Panel B. The breakeven rates of return are substantially increased under both the old and the new tax rates and the Traditional IRA would likely provide a higher after tax future value under most return scenarios. Recent work by Adelman and Cross (2010) and Beshears et al., (2017) indicate that many people do not invest the tax savings from the Traditional IRA, preferring instead to consume the extra income. This possibility complicates the choice of the two types because future retirement income will vary with investor behavior.10 The FV of the Roth will be greater than the FV of the Traditional IRA at lower breakeven rates of return if investors do not reinvest the tax savings because in this case the future value of the Traditional IRA per dollar is (1�r)n(1�tw) � tc, which is less than the future value of the Roth IRA of (1�r)n if tc/tw � (1�r)n.11 The Roth will generally provide a higher future value under a broad range of investment returns, especially if n is large. Table 4 provides data on the future values of the Roth and Traditional IRAs for a 20 year work period at different r when the tax savings from the Traditional IRA are not reinvested under the old and the new tax law.12 When an individual does not invest the tax savings from the Traditional IRA, the Roth is preferred if (1�r)n � tc/tw. The top part of Table 4 depicts rates of return where the Table 4 Future value of equal after-tax investments in Traditional IRA with tax savings not invested compared with future value of Roth IRA Tax law tw tc r n tc/tw (1�r)n Preference 2017 15% 25% 2.00% 20 1.6667 1.48595 Traditional 15% 25% 3.00% 20 1.6667 1.80611 Roth 15% 25% 4.00% 20 1.6667 2.19112 Roth 2018 12% 22% 2.00% 20 1.8333 1.48595 Traditional (TCJA) 12% 22% 3.00% 20 1.8333 1.80611 Traditional 12% 22% 4.00% 20 1.8333 2.19112 Roth 12% 22% 5.00% 20 1.8333 2.65330 Roth Note: IRA � individual retirement account; TCJA � Tax Cut and Jobs Act. 352 T. Manuel et al. / Financial Services Review 27 (2018) 345-365 Traditional or the Roth IRA are preferred for an investor under the old tax law who is in the 25% tax bracket during their working years, and is in the 15% tax bracket during retirement with 20 years to retirement. In this case the investor should prefer the Roth IRA if their pre-tax rate of return is expected to be 3.00% or higher. The breakeven return is actually 2.5870% as shown in Table 5. Once again the impact of the TCJA is to raise the breakeven rate of return where the Roth is preferable. With the new tax rates the Traditional IRA is still preferred at a 3.00% rate of return, but at a 4.00% return the Roth again provides a higher future value assumption. The actual breakeven rate of return is 3.0771% as shown below, which is the case where (1�r)20 � 1.8333. The breakeven rates in Table 5 indicate that in most return scenarios the Roth is likely to provide more retirement income than the Traditional IRA given the low breakeven rates even with the new tax law. 3. Lifetime consumption versus retirement consumption Choosing the Traditional IRA generates more spending power in the working years than the Roth on a dollar for dollar basis. Varying time preference for consumption and liquidity needs may still cause an investor who does not reinvest the tax savings to prefer the Traditional IRA even at rates of return above the breakeven rates shown above. It is possible to model real consumption over the working and retirement years from the two alternatives. The Traditional IRA can be optimal with a lifetime consumption decision variable, partic- ularly given uncertain reinvestment rates and low tolerance for risk, both of which will reduce the average return earned. Consider the case for a couple who are married filing jointly, neither of whom are covered by a plan at work, who do not reinvest the tax savings generated by the deductibility of contributions to a Traditional IRA. Choosing this filing status limits the likelihood of running afoul of income limits on deductibility of IRA contributions. It is assumed that the couple will use the standard deduction under the new TCJA, and then real consumption in year t during their working years after investing in a Traditional IRA is: Real Consumptiont � Incomet � Standard Deductiont � Traditional IRA Contributiont � Taxest � Standard Deductiont �1 � Deflator�t (2) where the deflator represents cumulative inflation so that real consumption is measured in terms of the date when the IRA contributions begin. This model is drawn from Bodie, Kane, and Marcus (2008). The Traditional IRA contribution reduces the couple’s taxable income and, thus, taxes owed in year t because these IRA contributions are deductible. The sum of Table 5 Breakeven return vs. years to retirement without reinvestment Years to retirement � 15 years 20 years 25 years 30 years 40 years Breakeven r old tax law 3.4642% 2.5870% 2.0643% 1.7173% 1.2853% Breakeven r new tax law 4.1237% 3.0771% 2.4542% 2.0410% 1.5269% Difference 0.6595% 0.4900% 0.3899% 0.3237% 0.2416% 353T. Manuel et al. / Financial Services Review 27 (2018) 345-365 the first three terms in the numerator of Eq. (2) is taxable income in year t. The Standard Deduction in time t is then added back after taxes are calculated on taxable income. Ignoring Social Security benefits and other income during retirement, the cumulative savings from the future value of the invested IRA contributions can be annuitized upon retirement. For simplicity our hypothetical couple retires at the same time. A Nominal Annuity amount is then used as the only source of income during retirement. Real Con- sumptiont in year t during retirement is thus: Real Consumptiont � Nominal Annuity � Standard Deductiont � Taxest � Standard Deductiont �1 � Deflator�t (3) If the couple chooses a Roth IRA instead of the Traditional IRA then Real Consumptiont during the working years is found as: Real Consumptiont � Incomet � Standard Deductiont � Taxest � Roth IRA Contributiont � Standard Deductiont �1 � Deflator�t (4) In this case the Taxest are calculated from the Income minus the Standard Deduction before considering the Roth IRA contribution as Roth contributions are not tax deductible. Real Consumptiont in year t during retirement for the Roth is thus: Real Consumptiont � Nominal Annuity �1 � Deflator�t because no taxes are owed on the Roth withdrawals. Compared with the Roth, the Traditional IRA provides extra real consumption during the working years (t � 1 to n), but at a cost of reduced consumption during the retirement years (t � n�1 to End of Life) because of taxes that will have to be paid as shown below: �t�1 n tc�Traditional IRA Contributiont� �1 � Deflatort� � �t�n�1 Life tw�Nominal Annuity � Standard Deductiont� �1 � Deflatort� (5) The additional consumption during the working years is tc(Traditional IRA Contributiont) per year, but choosing the Traditional IRA results in additional taxes in retirement on the annuity as compared with the Roth. This retirement income is taxed at the rate tw. The taxable income is the Nominal Annuity – Standard Deductiont. The size of the Nominal Annuity is dependent on the number of years of retirement, the returns on the contributions, the number of years of contributions and the contribution amount. To have a net gain in Real Consumption the additional consumption during the working years (the first term above) must be larger in aggregate than the additional taxes that occur during retirement (the second term). The larger the Nominal Annuity the less likely the net gain will be positive, although this can be offset by a higher Standard Deduction if tax law allows indexing the deduction. In addition, if tw is sufficiently lower than tc the net gain can be positive. A lower tax rate in retirement may occur because the investor will be in a lower tax bracket, or because 354 T. Manuel et al. / Financial Services Review 27 (2018) 345-365 statutory tax rates are lower. Higher inflation will increase the deflator more rapidly and will reduce the real value of consumption in retirement for both IRA types. However, if higher inflation raises the investment rate of return, then inflation will favor the Roth because higher average nominal returns generate more taxes in retirement and favor the Roth in general. Greater risk aversion, as indicated by reducing risk at an earlier age and, thereby, lowering the average return, favors the Traditional IRA because it lowers the lifetime average return on investment and, thus, potentially, the taxes paid in retirement. 3.1. The impact of the TCJA on lifetime consumption for the Traditional and Roth IRA The model can be used to demonstrate the impact of the TCJA on the choice of Traditional and Roth IRA on lifetime real consumption. In the model, tax brackets are assumed to be indexed to inflation as they have been in the past.13 Investment returns are based on historical geometric average returns, correlations, and standard deviations of major asset classes such as stocks, bonds and bills using data from Damodaran (2018). The model incorporates the concept of reducing portfolio risk as the investors approach retirement. All contributions cease at retirement. The model ignores other income and Social Security benefits. The invested amount at retirement is annuitized over the remaining expected lifetime. The model used allows an investor to choose at what age they plan to reduce risk in the portfolio by shifting more of the portfolio from stocks to Treasury bonds and Treasury bills. The return data and portfolio weights based on Damodaran’s (2018) data are given in Table 6. The asset allocation is shown above for assumed high risk, medium risk, and low risk portfolios. The choice of age at which an investor switches from a high to medium to low risk fund is a proxy for risk aversion. Greater risk aversion is indicated by reducing risk at an earlier age and/or choosing a lower percentage in stocks in each portfolio. The spreadsheet model provides stochastic rates of return to determine future values based on the input data. This is substantially different than in much of the literature where many studies assume a fixed rate of return, or allow only a small amount of variation in returns.14 For simplicity the Table 6 Portfolio risk and return based on Damodaran data Stocks Long term (LT) government bonds T-bills Stocks LT government bonds Stocks T-bills LT government bonds T-bills Average return 9.65% 4.88% 3.39% � �0.028 �0.030 0.296 � 19.62% 7.72% 3.05% Cov �0.000418339 �0.000178894 0.000698036 High risk 70% 30% 0% 0.0192257 Medium risk 60% 40% 0% 0.0146133 Portfolio variances Low risk 30% 50% 20% 0.0049861 Risk Portfolio average return Portfolio � High 8.22% 13.87% Medium 7.74% 12.09% Low 6.01% 7.06% 355T. Manuel et al. / Financial Services Review 27 (2018) 345-365 model does not have any excess contributions, which are rare in practice (see Sibley, 2002), and there are no RMDs because of the focus on lifetime real consumption rather than bequests. 3.2. Impact of IRA choice on consumption pre- and post-TCJA The real consumption outcomes for a hypothetical married couple filing jointly that are not covered by a plan at work who are 30 years old, will retire at age 65, and fund their retirement to age 90 is shown below using the 2017 tax rates and rules. In 2018 the life expectancy of a 30 year old U.S. male is 71 and for a female is 75 according to coun- tryeconomy.com. Funding to age 90 should be amply sufficient to ensure an investor’s funds do not run out. The 2017 progressive tax rates and brackets are used and the brackets are indexed to inflation as per IRS practice as mandated by Congress. The IRS normally adjusts the standard deduction for inflation as well, and it is also increased at age 65, and is higher for taxpayers that meet certain conditions.15 The couple starts with a high risk portfolio that has an average return of 8.22% with a standard deviation of 13.87%, reduces to medium risk at age 50 with an average return of 7.74% with a portfolio standard deviation of 12.09%, and reallocates to a low risk portfolio at retirement that has an average return of 6.01% and a standard deviation of 7.06%. The couple’s starting income is $80,000 between the two of them at age 30; subsequently, their income grows at six percent per year and inflation is three percent per year. The couple contributes $10,000 total to either a Roth or a Traditional IRA each year until they retire. Annual rates of return are generated from a normal distribution with the given geometric average return and standard deviation using Monte Carlo simula- tion. The cumulative savings at retirement is annuitized over the given life expectancy using the low risk portfolio return. A simulation of 500 different outcomes was created with a spreadsheet macro.16 The results are presented in Table 7. Each row in Table 7 gives the results of 500 different trial runs with different returns in each trial. Table 7 shows that using the 2017 tax rules in place before the TCJA, the Traditional IRA provided higher lifetime consumption in 383 out of the 500 trials (77%), with the Roth IRA doing better in only 117 runs (23%). The median lifetime consumption from the Roth was $5,059,391 whereas the median consumption for the Traditional IRA was $5,078,552.17 The second row replicates the results using the same inputs except that the TCJA progressive tax rates and the new standard deduction (with no personal exemptions) was used. In this case the Traditional IRA provided higher lifetime real consumption in 361 (72%) out of the 500 trials and the Roth Table 7 Representative simulation of Traditional vs. Roth IRA lifetime consumption pre- and post-TCJA No. runs Traditional IRA had higher lifetime consumption No. runs Roth had higher lifetime consumption Median lifetime consumption traditional Median lifetime consumption Roth Difference in median lifetime consumption Pre TCJA choice of IRA 383 (77%) 117 (23%) $5,078,552 $5,059,391 $19,161 Post TCJA choice of IRA 361 (72%) 139 (28%) $5,049,170 $5,015,551 $33,619 Note: IRA � individual retirement account; TCJA � Tax Cut and Jobs Act. 356 T. Manuel et al. / Financial Services Review 27 (2018) 345-365 provided more consumption in 139 trial runs (28%).18 The TCJA modestly increases the median lifetime consumption, but the simulation indicates the TCJA does not have a major impact on IRA choice when the decision variable is lifetime consumption. Higher rates of return and higher incomes will increase the number of times that the Roth provides more favorable outcomes. Similarly if Congress decides to not increase the brackets or the standard deduction with inflation, then the Roth IRA will provide better outcomes in the large majority of simulation runs because the retirement tax liability is then much greater for the Traditional IRA. Calculations for the scenario outputs shown below are provided in the Appendix. In the majority of cases the Traditional IRA provided higher median lifetime consumption than the Roth IRA pre- and post-TCJA. For moderate income individuals where current spending is a primary concern as much as funding retirement, the Traditional IRA can be the better choice. Higher levels of starting income imply a higher tax burden in retirement and favor the Roth IRA. 4. Conclusions The impact of the new lower rates in the TCJA should make the Traditional IRA more attractive for moderate income investors who invest the tax deduction. The impact of the tax law is to raise the breakeven rates of return where the Roth IRA becomes the better alternative in terms of future value for many investors who may be in the 22% tax bracket in their working years and in the 12% tax bracket in retirement. This is likely to include a large number of investors. Depending on the length of the contribution period, the breakeven rate of return is increased by between 2% to as much as 6.5% for individuals who invest the tax savings from their Traditional IRAs. There are only small changes in breakeven for investors who do not invest the difference and are looking to maximize retirement income. Individuals of modest income who are seeking to maximize their lifetime consumption, however, may still prefer the Traditional IRA to the Roth. Simulations with reasonably realistic investment strategies that reduce risk as the investor ages and incorporate the new tax brackets and standard deduction indicate that in many cases the Traditional IRA provides greater median lifetime consumption than the Roth. This result does not hold in simulations where tax brackets are not indexed and/or when the standard deduction is not increased by inflation, so future tax rules are critical in the choice of IRA. Finally, investors and planners should be aware that many variables should be considered in the choice of IRA, and analyzing after tax returns is not sufficient to fully inform the decision. Behavioral characteristics such as whether the tax savings will be invested, the investor’s risk tolerance, their desire to fund working years’ consumption versus retirement consumption, expected market returns and the investor’s willingness and ability to engage in tax management strategies should be considered in the choice (Horan, 2006). If investors (or their planners) are willing to engage in tax management strategies then having both may be optimal; nevertheless, the Traditional IRA remains a good choice for many investors. 357T. Manuel et al. / Financial Services Review 27 (2018) 345-365 Notes 1 For the 2018 tax year a moderate income investor that is married and is filing jointly must have modified adjusted gross income (MAGI) over $77,401 according to the IRS. 2 In reality many factors other than future value or consumption can affect the optimal IRA type as discussed below. Beshears et al. (2017) indicate that factors other than future value should be considered in the choice of IRA type. 3 There are several “personal hardship” and other exemptions that allow an investor to withdraw money before age 591⁄2 without facing a tax penalty. Nevertheless, it is generally not a good idea to withdraw funds invested for retirement unless absolutely necessary. 4 The CBO estimates the Chained CPI (C-CPI-U) results in about a 0.25% lower average inflation rate than the CPI. The chained version is thought to be more accurate because it allows for substitutions to lower cost items as relative prices change and corrects for a small size sampling bias whereas the traditional CPI measure does not. For more detail see CBO’s Projections of Demographic and Economic Trends found at https://www.cbo.gov/system/files?file�2018-06/53919-2018ltbo-appendixa.pdf. 5 A phase-out of the amount contributed applies for lower income limits regardless of filing status. An investor can still create a “backdoor” Roth IRA if their MAGI is too high to directly contribute to a Roth IRA. The procedure is to contribute to a non-deductible IRA and then roll it over to a Roth IRA. There is no MAGI limit on the rollover. If the investor has a deductible IRA then part of the rollover is taxable. For more information see https://www.irs.gov/retirement-plans/retirement-plans-faqs- regarding-iras-rollovers-and-roth-conversions or the discussion in Harline (2014). 6 An exception is Horan (2003) who compares equal pre-tax investments as well as equal after-tax investments. The pre- or after-tax method of comparisons are equiv- alent assuming that the tax deductions generated by the Traditional IRA are invested in the pre-tax case. Thus, one need only compare an equivalent pre-tax investment amount in the Traditional and Roth IRA and vary whether the deduction is invested. 7 This model assumes the money in both IRAs is withdrawn upon retirement. Alterna- tively, n may be considered the time to when the investor begins withdrawing from the IRAs. This is the time to age 701⁄2 at the maximum for the Traditional IRA, but n could be longer for a Roth IRA. 8 Throughout the discussion it is assumed that the changes in the tax code from the TCJA will persist after 2025 when they are scheduled to sunset. This discussion centers on investors who are in the 25%/15% pre-TCJA tax brackets and 22%/12% post-TCJA brackets during their working years and retirement years, respectively. Post-TCJA this includes investors whose gross income is up to $165,000 in their working years and $77,400 during their retirement years in today’s dollars. The same income numbers for pre-TCJA were $153,100 and $75,900, respectively. 9 The breakeven interest rate is found by solving the following for r: (1�r)n (1�tw)�tc[1�(r(1�ti)] n � (1�r)n where ti is set to 10% and n is varied as shown in the table. 10 It is likely that many investors do not think about the tax savings as an amount that could be invested unless a planner points this out. 358 T. Manuel et al. / Financial Services Review 27 (2018) 345-365 11 The future value component [1 � r(1�tc)] n drops out if the tax savings are not reinvested. 12 Alternatively, once could compare a $5,000 qualifying contribution to a Traditional IRA versus $5,000(1–22%) � $3,900 in a Roth IRA. Some investors may choose this alternative rather than investing the deduction generated by the Traditional IRA. The relative advantage in future value of the two IRA types in this case is completely determined by whether tc is greater than or less than tw. Using the $5,000 pre-tax contribution amount, the future value of the Traditional IRA is greater than the future value of the Roth IRA if $5,000(1�r)n(1�tw) � $5,000(1�tc)(1�r)n, which holds if tc � tw and not otherwise. Adelman and Cross (2010) make a similar point. In the literature it is more common to model the comparison of not investing the deduction as done here: $5,000(1�r)n(1�tw)�tc � $5,000(1�r)n. 13 The model incorporates the higher deduction upon retirement and the additional amount that can be contributed from age 50 onward. The model also incorporates indexed standard deductions and IRA contributions. Results are available from the authors. Indexing deductions tends to favor the Traditional IRA by reducing taxes due in retirement. Indexing contributions favors the Roth IRA because bigger contributions increase retirement income and thus taxes in retirement. The Roth avoids these higher taxes in retirement. 14 The option value of the ability to convert a Traditional IRA to a Roth IRA (the rollover option) is ignored. 15 The spreadsheet incorporates the increase in deduction at age 65. 16 Providing a simulation of multiple outputs is a better method to evaluate the preferable type of IRA than providing a single point estimate of future value. Note that the model uses realistic estimates of portfolio returns at the chosen risk levels and starts with a modest income amount. 17 The simulation contains some runs with high returns. For the Roth these tend to result in higher consumption, whereas for the Traditional the higher incomes that result lead to higher taxes that offset at least some of the income. Thus, choosing the Roth IRA can result in higher average lifetime consumption, even though the median is lower. In other words choosing the Traditional IRA forfeits the positive skewness of returns and consumption that the Roth may generate. 18 Simulation results (not shown) indicate that higher returns increase the number of trials where the Roth provided higher consumption, but the Traditional IRA still pre-dominates. However, when the brackets and/or the deductions are not indexed with inflation the Roth dominates in almost all scenarios. Appendix: Scenario calculations 1. More on the spreadsheet model and simulation Larger contribution amounts favor the Roth IRA in the spreadsheet outcomes, which is consistent with most of the literature that concentrates on maximizing retirement income. A 359T. Manuel et al. / Financial Services Review 27 (2018) 345-365 A pp en di x T ab le 1 Si m ul at io n re su lts an d sa m pl e ca lc ul at io ns se le ct ed ye ar s pr e- T C JA E nt er nu m be r of tr ia ls (m ax � 1, 00 0) : 50 0 L if et im e re al co ns um pt io n A ge st ar t co nt ri bu tio n A ge m ed iu m ri sk A ge lo w ri sk A ge re tir e L if e ex pe ct an cy T ra di tio na l R ot h R un si m ul at io n 30 50 60 65 90 M in im um 4, 33 9, 99 1 4, 25 6, 48 8 St ar tin g in co m e In co m e gr ow th R at e of in fla tio n C on tr ib ut io n M ax im um 7, 17 0, 88 0 7, 64 3, 98 8 50 0 M ed ia n 4, 97 4, 77 6 4, 92 9, 16 3 $8 0, 00 0 6. 00 % 3. 00 % $1 0, 00 0 A ve ra ge 5, 07 8, 55 2 5, 05 9, 39 1 D ed uc tio n ad ju st m en t 10 0% B et te r 38 3 11 7 C ha ng e in ta x ra te af te r re t 0. 00 % 3. 00 % B ra ck et ad ju st m en t 3. 00 % W or ki ng R et ir ed L if et im e C um ul at iv e sa vi ng s 1, 78 2, 73 8 A ge st ar t co nt ri bu tio n A ge m ed iu m ri sk A ge lo w ri sk A ge re tir e L if e ex pe ct an cy In co m e ye ar s 35 25 60 L if et im e ta x ra te N om in al an nu ity 13 9, 63 0 In co m e 9, 52 9, 66 9 3, 49 0, 75 2 13 ,0 20 ,4 22 R ea l an nu ity 49 ,6 22 30 50 60 65 90 T ax es , T ra di tio na l IR A 1, 31 0, 34 2 63 ,9 81 1, 37 4, 32 3 14 .4 2% R is k A ve ra ge re tu rn St an da rd de vi at io n St ar tin g in co m e In co m e gr ow th R at e of in fla tio n C on tr ib ut io n � ag e 50 St an da rd de du ct io n an d ex em pt io n T ax es , R ot h IR A 1, 46 5, 91 5 0 1, 46 5, 91 5 15 .3 8% H ig h 8. 22 % 13 .8 7% R ea l co ns um pt io n, T ra di tio na l IR A 3, 96 6, 69 7 84 5, 51 9 4, 81 2, 21 6 B et te r M ed iu m 7. 74 % 12 .0 9% $8 0, 00 0 6. 00 % 3. 00 % $1 0, 00 0 $2 5, 20 0 R ea l co ns um pt io n, R ot h IR A 3, 88 3, 19 5 86 4, 07 9 4, 74 7, 27 4 L ow 6. 01 % 7. 06 % G ro w th in ta x ra te af te r re tir em en t 0. 00 % 3. 00 % B ra ck et ad ju st m en t 3. 00 % In co m e, co nt ri bu tio ns , ex em pt io ns T ra di tio na l IR A R ot h IR A In ve st m en t/s av in gs A ge In co m e D efl at or In de xe d IR A co nt ri bu tio ns In de xe d de du ct io n T ax ab le in co m e M ar gi na l ta x ra te T ax es R ea l co ns um pt io n T ax ab le in co m e M ar gi na l ta x ra te T ax es R ea l co ns um pt io n A ve ra ge re tu rn St an da rd de vi at io n C um ul at iv e sa vi ng s 30 80 ,0 00 1. 00 00 0 10 ,0 00 25 ,2 00 44 ,8 00 15 % 5, 78 8 64 ,2 13 54 ,8 00 15 % 7, 28 8 62 ,7 13 10 ,0 00 31 84 ,8 00 1. 03 00 0 10 ,3 00 25 ,9 56 48 ,5 44 15 % 6, 32 1 66 ,1 93 58 ,8 44 15 % 7, 86 6 64 ,6 93 8. 21 9% 13 .8 66 % 21 ,4 83 32 89 ,8 88 1. 06 09 0 10 ,6 09 26 ,7 35 52 ,5 44 15 % 6, 89 2 68 ,2 31 63 ,1 53 15 % 8, 48 4 66 ,7 31 8. 21 9% 13 .8 66 % 33 ,2 35 33 95 ,2 81 1. 09 27 3 10 ,9 27 27 ,5 37 56 ,8 17 15 % 7, 50 4 70 ,3 29 67 ,7 45 15 % 9, 14 3 68 ,8 29 8. 21 9% 13 .8 66 % 48 ,8 59 34 10 0, 99 8 1. 12 55 1 11 ,2 55 28 ,3 63 61 ,3 80 15 % 8, 15 8 72 ,4 88 72 ,6 35 15 % 9, 84 6 70 ,9 88 8. 21 9% 13 .8 66 % 55 ,0 78 35 10 7, 05 8 1. 15 92 7 11 ,5 93 29 ,2 14 66 ,2 52 15 % 8, 85 7 74 ,7 09 77 ,8 44 15 % 10 ,5 96 73 ,2 09 8. 21 9% 13 .8 66 % 57 ,4 39 48 22 8, 34 7 1. 70 24 3 17 ,0 24 42 ,9 01 16 8, 42 1 25 % 27 ,5 96 10 7, 92 0 18 5, 44 6 25 % 31 ,8 52 10 5, 42 0 8. 21 9% 13 .8 66 % 45 0, 11 1 49 24 2, 04 8 1. 75 35 1 17 ,5 35 44 ,1 88 18 0, 32 5 25 % 30 ,1 37 11 0, 85 0 19 7, 86 0 25 % 34 ,5 21 10 8, 35 0 8. 21 9% 13 .8 66 % 60 8, 61 4 (c on ti nu ed on ne xt pa ge ) 360 T. Manuel et al. / Financial Services Review 27 (2018) 345-365 A pp en di x T ab le 1 (C on tin ue d) In co m e, co nt ri bu tio ns , ex em pt io ns T ra di tio na l IR A R ot h IR A In ve st m en t/s av in gs A ge In co m e D efl at or In de xe d IR A co nt ri bu tio ns In de xe d de du ct io n T ax ab le in co m e M ar gi na l ta x ra te T ax es R ea l co ns um pt io n T ax ab le in co m e M ar gi na l ta x ra te T ax es R ea l co ns um pt io n A ve ra ge re tu rn St an da rd de vi at io n C um ul at iv e sa vi ng s 50 25 6, 57 1 1. 80 61 1 19 ,0 61 45 ,5 14 19 1, 99 6 25 % 32 ,6 06 11 3, 45 0 21 1, 05 7 25 % 37 ,3 72 11 0, 81 2 7. 74 2% 12 .0 89 % 78 0, 97 0 51 27 1, 96 5 1. 86 02 9 19 ,6 03 46 ,8 79 20 5, 48 3 25 % 35 ,5 16 11 6, 56 5 22 5, 08 6 25 % 40 ,4 17 11 3, 93 1 7. 74 2% 12 .0 89 % 85 9, 26 1 56 36 3, 95 1 2. 15 65 9 22 ,5 66 54 ,3 46 28 7, 03 9 25 % 53 ,3 80 13 3, 54 6 30 9, 60 5 25 % 59 ,0 22 13 0, 93 0 7. 74 2% 12 .0 89 % 1, 52 8, 33 7 57 38 5, 78 8 2. 22 12 9 23 ,2 13 55 ,9 76 30 6, 59 8 25 % 57 ,7 19 13 7, 24 3 32 9, 81 1 25 % 63 ,5 22 13 4, 63 0 7. 74 2% 12 .0 89 % 1, 58 6, 66 5 58 40 8, 93 5 2. 28 79 3 23 ,8 79 57 ,6 56 32 7, 40 0 25 % 62 ,3 51 14 1, 04 7 35 1, 27 9 28 % 68 ,3 51 13 8, 42 4 7. 74 2% 12 .0 89 % 1, 41 7, 59 8 59 43 3, 47 1 2. 35 65 7 24 ,5 66 59 ,3 85 34 9, 52 0 25 % 67 ,2 96 14 4, 96 1 37 4, 08 6 28 % 73 ,8 36 14 2, 18 5 7. 74 2% 12 .0 89 % 1, 33 5, 64 5 60 45 9, 47 9 2. 42 72 6 25 ,2 73 61 ,1 67 37 3, 04 0 28 % 72 ,6 16 14 8, 97 0 39 8, 31 2 28 % 79 ,6 93 14 6, 05 5 6. 01 3% 7. 06 1% 1, 45 4, 96 8 61 48 7, 04 8 2. 50 00 8 26 ,0 01 63 ,0 02 39 8, 04 5 28 % 78 ,6 63 15 2, 94 9 42 4, 04 6 28 % 85 ,9 43 15 0, 03 7 6. 01 3% 7. 06 1% 1, 41 8, 92 5 62 51 6, 27 1 2. 57 50 8 26 ,7 51 64 ,8 92 42 4, 62 8 28 % 85 ,1 22 15 7, 04 3 45 1, 37 9 28 % 92 ,6 13 15 4, 13 4 6. 01 3% 7. 06 1% 1, 63 1, 54 7 63 54 7, 24 7 2. 65 23 4 27 ,5 23 66 ,8 39 45 2, 88 5 28 % 92 ,0 21 16 1, 25 5 48 0, 40 8 28 % 99 ,7 28 15 8, 35 0 6. 01 3% 7. 06 1% 1, 67 4, 73 0 64 58 0, 08 2 2. 73 19 1 28 ,3 19 68 ,8 44 48 2, 91 9 28 % 99 ,3 87 16 5, 59 0 51 1, 23 8 28 % 10 7, 31 6 16 2, 68 7 6. 01 3% 7. 06 1% 1, 60 0, 10 0 65 61 4, 88 7 2. 81 38 6 29 ,1 39 77 ,9 44 50 7, 80 4 28 % 10 5, 28 0 17 0, 75 0 53 6, 94 3 28 % 11 3, 43 9 16 7, 85 1 6. 01 3% 7, 06 1% 1, 78 2, 73 8 W or ki ng 9, 52 9, 66 9 64 8, 75 9 1, 60 1, 58 8 7, 27 9, 32 1 22 % 1, 31 0, 34 2 3, 96 6, 69 7 7, 92 8, 08 1 23 % 1, 46 5, 91 5 3, 88 3, 19 5 1, 78 2, 73 8 R et ir em en t T ra di tio na l IR A R ot h IR A A ge N om in al w ith dr aw D efl at or In de xe d de du ct io n T ax ab le in co m e M ar gi na l ta x ra te T ax es R ea l co ns um pt io n T ax ab le in co m e M ar gi na l ta x ra te T ax es R ea l co ns um pt io n 66 13 9, 63 0 2. 89 82 8 80 ,2 82 59 ,3 48 15 % 6, 20 0 46 ,0 38 0 48 ,1 77 67 13 9, 63 0 2. 98 52 3 82 ,6 91 56 ,9 39 15 % 5, 75 7 44 ,8 45 0 46 ,7 74 68 13 9, 63 0 3. 07 47 8 85 ,1 72 54 ,4 59 10 % 5, 44 6 43 ,6 40 0 45 ,4 11 69 13 9, 63 0 3. 16 70 3 87 ,7 27 51 ,9 03 10 % 5, 19 0 42 ,4 50 0 44 ,0 89 70 13 9, 63 0 3. 26 20 4 90 ,3 58 49 ,2 72 10 % 4, 92 7 41 ,2 94 0 42 ,8 05 71 13 9, 63 0 3. 35 99 0 93 ,0 69 46 ,5 61 10 % 4, 65 6 40 ,1 72 0 41 ,5 58 72 13 9, 63 0 3. 46 07 0 95 ,8 61 43 ,7 69 10 % 4, 37 7 39 ,0 83 0 40 ,3 47 73 13 9, 63 0 3. 56 45 2 98 ,7 37 40 ,8 93 10 % 4, 08 9 38 ,0 25 0 39 ,1 72 84 13 9, 63 0 4. 93 41 2 13 6, 67 5 2, 95 5 10 % 29 5 28 ,2 39 0 28 ,2 99 85 13 9, 63 0 5. 08 21 5 14 0, 77 6 0 10 % 0 27 ,4 75 0 27 ,4 75 86 13 9, 63 0 5. 23 46 1 14 4, 99 9 0 10 % 0 26 ,6 74 0 26 ,6 74 87 13 9, 63 0 5. 39 16 5 14 9, 34 9 0 10 % 0 25 ,8 97 0 25 ,8 97 88 13 9, 63 0 5. 55 34 0 15 3, 82 9 0 10 % 0 25 ,1 43 0 25 ,1 43 89 13 9, 63 0 5. 72 00 0 15 8, 44 4 0 10 % 0 24 ,4 11 0 24 ,4 11 90 13 9, 63 0 5. 89 16 0 16 3, 19 7 0 10 % 0 23 ,7 00 0 23 ,7 00 N ot e: IR A � in di vi du al re tir em en t ac co un t; T C JA � T ax C ut an d Jo bs A ct .S el ec te d ye ar sa m pl e ca lc ul at io ns fo r on e ru n fo r th e pr e- T C JA sc en ar io fo r re al co ns um pt io n. 361T. Manuel et al. / Financial Services Review 27 (2018) 345-365 A pp en di x T ab le 2 Si m ul at io n re su lts an d sa m pl e ca lc ul at io ns se le ct ed ye ar s po st -T C JA E nt er nu m be r of tr ia ls (m ax � 1, 00 0) : 50 0 L if et im e re al co ns um pt io n A ge st ar t co nt ri bu tio n A ge m ed iu m ri sk A ge lo w ri sk A ge re tir e L if e ex pe ct an cy T ra di tio na l R ot h R un si m ul at io n 30 50 60 65 90 M in im um 4, 37 9, 63 1 4, 30 8, 33 3 St ar tin g in co m e In co m e gr ow th R at e of in fla tio n C on tr ib ut io n M ax im um 7, 76 7, 85 0 8, 30 1, 18 3 50 0 M ed ia n 5, 04 9, 17 0 5, 01 5, 55 1 $8 0, 00 0 6. 00 % 3. 00 % $1 0, 00 0 A ve ra ge 5, 14 8, 77 1 5, 13 4, 02 9 D ed uc tio n ad ju st m en t 10 0% B et te r 36 1 13 9 C ha ng e in ta x ra te af te r re t 0. 00 % 3. 00 % B ra ck et ad ju st m en t 3. 00 % W or ki ng R et ir ed L if et im e C um ul at iv e sa vi ng s 2, 70 1, 44 9 A ge st ar t co nt ri bu tio n A ge m ed iu m ri sk A ge lo w ri sk A ge re tir e L if e ex pe ct an cy In co m e ye ar s 35 25 60 N om in al an nu ity 21 1, 58 7 In co m e 9, 52 9, 66 9 5, 28 9, 66 6 14 ,8 19 ,3 35 L if et im e ta x ra te R ea l an nu ity 75 ,1 94 30 50 60 65 90 T ax es , T ra di tio na l IR A 1, 12 9, 43 6 26 2, 25 7 1, 39 1, 69 2 14 .6 0% R is k A ve ra ge re tu rn St an da rd de vi at io n St ar tin g in co m e In co m e gr ow th R at e of in fla tio n C on tr ib ut io n � A ge 50 St an da rd de du ct io n an d ex em pt io n T ax es , R ot h IR A 1, 26 2, 64 6 0 1, 26 2, 64 6 13 .2 5% H ig h 8. 22 % 13 .8 7% R ea l co ns um pt io n, T ra di tio na l IR A 4, 05 5, 19 1 1, 24 0, 65 1 5, 29 5, 84 2 B et te r M ed iu m 7. 74 % 12 .0 9% $8 0, 00 0 6. 00 % 3. 00 % $1 0, 00 0 $2 4, 00 0 R ea l co ns um pt io n, R ot h IR A 3, 98 3, 89 3 1, 30 9, 37 1 5, 29 3, 26 4 L ow 6. 01 % 7. 06 % G ro w th in ta x ra te af te r re tir em en t 0. 00 % 3. 00 % B ra ck et ad ju st m en t 3. 00 % In co m e, co nt ri bu tio ns , ex em pt io ns T ra di tio na l IR A R ot h IR A In ve st m en t/s av in gs A ge In co m e D efl at or In de xe d IR A co nt ri bu tio ns In de xe d de du ct io n T ax ab le in co m e M ar gi na l ta x ra te T ax es R ea l co ns um pt io n T ax ab le in co m e M ar gi na l ta x ra te T ax es R ea l co ns um pt io n A ve ra ge re tu rn St an da rd de vi at io n C um ul at iv e sa vi ng s 30 80 ,0 00 1. 00 00 0 10 ,0 00 24 ,0 00 46 ,0 00 12 % 5, 13 9 64 ,8 61 56 ,0 00 12 % 6, 33 9 63 ,6 61 10 ,0 00 31 84 ,8 00 1. 03 00 0 10 ,3 00 24 ,7 20 49 ,7 80 12 % 5, 58 1 66 ,9 11 60 ,0 80 12 % 6, 81 7 65 ,7 11 8. 21 9% 13 .8 66 % 21 ,4 01 32 89 ,8 88 1. 06 09 0 10 ,6 09 25 ,4 62 53 ,8 17 12 % 6, 05 4 69 ,0 22 64 ,4 26 12 % 7, 32 7 67 ,8 22 8. 21 9% 13 .8 66 % 36 ,5 05 33 95 ,2 81 1. 09 27 3 10 ,9 27 26 ,2 25 58 ,1 29 12 % 6, 55 9 71 ,1 93 69 ,0 56 12 % 7, 87 0 69 ,9 93 8. 21 9% 13 .8 66 % 42 ,5 22 34 10 0, 99 8 1. 12 55 1 11 ,2 55 27 ,0 12 62 ,7 31 12 % 7, 09 9 73 ,4 28 73 ,9 86 12 % 8, 44 9 72 ,2 28 8. 21 9% 13 .8 66 % 62 ,6 01 35 10 7, 05 8 1. 15 92 7 11 ,5 93 27 ,8 23 67 ,6 43 12 % 7, 67 5 75 ,7 28 79 ,2 35 12 % 9, 06 7 74 ,5 28 8. 21 9% 13 .8 66 % 84 ,4 92 48 22 8, 34 7 1. 70 24 3 17 ,0 24 40 ,8 58 17 0, 46 4 22 % 23 ,6 77 11 0, 22 2 18 7, 48 9 22 % 27 ,4 22 10 8, 02 2 8. 21 9% 13 .8 66 % 58 6, 72 2 49 24 2, 04 8 1. 75 35 1 17 ,5 35 42 ,0 84 18 2, 42 9 22 % 25 ,8 94 11 3, 27 0 19 9, 96 4 22 % 29 ,7 52 11 1, 07 0 8. 21 9% 13 .8 66 % 66 8, 70 2 50 25 6, 57 1 1. 80 61 1 19 ,0 61 43 ,3 47 19 4, 16 3 22 % 28 ,0 48 11 5, 97 4 21 3, 22 4 22 % 32 ,2 42 11 3, 65 2 7. 74 2% 12 .0 89 % 80 7, 05 3 (c on ti nu ed on ne xt pa ge ) 362 T. Manuel et al. / Financial Services Review 27 (2018) 345-365 A pp en di x T ab le 2 (C on tin ue d) In co m e, co nt ri bu tio ns , ex em pt io ns T ra di tio na l IR A R ot h IR A In ve st m en t/s av in gs A ge In co m e D efl at or In de xe d IR A co nt ri bu tio ns In de xe d de du ct io n T ax ab le in co m e M ar gi na l ta x ra te T ax es R ea l co ns um pt io n T ax ab le in co m e M ar gi na l ta x ra te T ax es R ea l co ns um pt io n A ve ra ge re tu rn St an da rd de vi at io n C um ul at iv e sa vi ng s 51 27 1, 96 5 1. 86 02 9 19 ,6 03 44 ,6 47 20 7, 71 5 22 % 30 ,5 90 11 9, 21 4 22 7, 31 8 22 % 34 ,9 03 11 6, 89 5 7. 74 2% 12 .0 89 % 76 2, 89 5 56 36 3, 95 1 2. 15 65 9 22 ,5 66 51 ,7 58 28 9, 62 7 22 % 46 ,2 04 13 6, 87 4 31 2, 19 2 22 % 51 ,1 69 13 4, 57 2 7. 74 2% 12 .0 89 % 1, 45 5, 91 3 57 38 5, 78 8 2. 22 12 9 23 ,2 13 53 ,3 11 30 9, 26 4 22 % 49 ,9 99 14 0, 71 8 33 2, 47 7 22 % 55 ,1 06 13 8, 41 9 7. 74 2% 12 .0 89 % 1, 51 3, 68 8 58 40 8, 93 5 2. 28 79 3 23 ,8 79 54 ,9 10 33 0, 14 5 22 % 54 ,0 52 14 4, 67 4 35 4, 02 5 22 % 59 ,3 05 14 2, 37 8 7. 74 2% 12 .0 89 % 1, 67 6, 05 8 59 43 3, 47 1 2. 35 65 7 24 ,5 66 56 ,5 58 35 2, 34 8 22 % 58 ,3 79 14 8, 74 5 37 6, 91 3 22 % 63 ,7 83 14 6, 45 1 7. 74 2% 12 .0 89 % 1, 87 9, 84 9 60 45 9, 47 9 2. 42 72 6 25 ,2 73 58 ,2 54 37 5, 95 2 22 % 62 ,9 98 15 2, 93 3 40 1, 22 5 24 % 68 ,5 72 15 0, 63 7 6. 01 3% 7. 06 1% 1, 79 9, 64 9 61 48 7, 04 8 2. 50 00 8 26 ,0 01 60 ,0 02 40 1, 04 5 22 % 67 ,9 27 15 7, 24 3 42 7, 04 6 24 % 73 ,9 38 15 4, 83 9 6. 01 3% 7. 06 1% 2, 01 9, 08 0 62 51 6, 27 1 2. 57 50 8 26 ,7 51 61 ,8 02 42 7, 71 8 24 % 73 ,2 42 16 1, 65 6 45 4, 46 9 24 % 79 ,6 63 15 9, 16 3 6. 01 3% 7. 06 1% 2, 26 5, 82 0 63 54 7, 24 7 2. 65 23 4 27 ,5 23 63 ,6 56 45 6, 06 8 24 % 79 ,1 64 16 6, 10 3 48 3, 59 1 24 % 85 ,7 70 16 3, 61 2 6. 01 3% 7. 06 1% 2, 24 1, 13 5 64 58 0, 08 2 2. 73 19 1 28 ,3 19 65 ,5 66 48 6, 19 7 24 % 85 ,4 86 17 0, 67 8 51 4, 51 6 24 % 92 ,2 83 16 8, 19 0 6. 01 3% 7. 06 1% 2, 36 5, 91 8 65 61 4, 88 7 2. 81 38 6 29 ,1 39 74 ,8 49 51 0, 90 0 24 % 90 ,4 79 17 6, 01 1 54 0, 03 8 24 % 97 ,4 72 17 3, 52 5 6. 01 3% 7. 06 1% 2, 70 1, 44 9 W or ki ng 9, 52 9, 66 9 64 8, 75 9 1, 52 5, 93 9 7, 35 4, 97 1 19 % 1, 12 9, 43 6 4, 05 5, 19 1 8, 00 3, 73 1 20 % 1, 26 2, 64 6 3, 98 3, 89 3 2, 70 1, 44 9 R et ir em en t T ra di tio na l IR A R ot h IR A A ge N om in al w ith dr aw D efl at or In de xe d de du ct io n T ax ab le in co m e M ar gi na l ta x ra te T ax es R ea l co ns um pt io n T ax ab le in co m e M ar gi na l ta x ra te T ax es R ea l co ns um pt io n 66 21 1, 58 7 2. 89 82 8 77 ,0 94 13 4, 49 2 12 % 15 ,0 35 67 ,8 17 0 73 ,0 04 67 21 1, 58 7 2. 98 52 3 79 ,4 07 13 2, 18 0 12 % 14 ,7 24 65 ,9 46 0 70 ,8 78 68 21 1, 58 7 3. 07 47 8 81 ,7 89 12 9, 79 7 12 % 14 ,4 04 64 ,1 29 0 68 ,8 14 69 21 1, 58 7 3. 16 70 3 84 ,2 43 12 7, 34 4 12 % 14 ,0 75 62 ,3 65 0 66 ,8 09 70 21 1, 58 7 3. 26 20 4 86 ,7 70 12 4, 81 6 12 % 13 ,7 35 60 ,6 53 0 64 ,8 63 71 21 1, 58 7 3. 35 99 0 89 ,3 73 12 2, 21 3 12 % 13 ,3 85 58 ,9 90 0 62 ,9 74 72 21 1, 58 7 3. 46 07 0 92 ,0 55 11 9, 53 2 12 % 13 ,0 25 57 ,3 76 0 61 ,1 40 73 21 1, 58 7 3. 56 45 2 94 ,8 16 11 6, 77 0 12 % 12 ,6 54 55 ,8 09 0 59 ,3 59 84 21 1, 58 7 4. 93 41 2 13 1, 24 8 80 ,3 39 10 % 8, 03 4 41 ,2 54 0 42 ,8 82 85 21 1, 58 7 5. 08 21 5 13 5, 18 5 76 ,4 01 10 % 7, 64 0 40 ,1 30 0 41 ,6 33 86 21 1, 58 7 5. 23 46 1 13 9, 24 1 72 ,3 46 10 % 7, 23 5 39 ,0 39 0 40 ,4 21 87 21 1, 58 7 5. 39 16 5 14 3, 41 8 68 ,1 69 10 % 6, 81 7 37 ,9 79 0 39 ,2 43 88 21 1, 58 7 5. 55 34 0 14 7, 72 0 63 ,8 66 10 % 6, 38 7 36 ,9 50 0 38 ,1 00 89 21 1, 58 7 5. 72 00 0 15 2, 15 2 59 ,4 35 10 % 5, 94 3 35 ,9 52 0 36 ,9 91 90 21 1, 58 7 5. 89 16 0 15 6, 71 7 54 ,8 70 10 % 5, 48 7 34 ,9 82 0 35 ,9 13 N ot e: IR A � in di vi du al re tir em en t ac co un t; T C JA � T ax C ut an d Jo bs A ct . Sa m pl e ca lc ul at io ns fo r on e ru n of th e po st -T C JA si m ul at io n. 363T. Manuel et al. / Financial Services Review 27 (2018) 345-365 shorter time to retirement favors the Traditional IRA in terms of lifetime consumption. Consistent with the literature, a lower tax rate during retirement than in the working years favors the Traditional IRA, but this situation does not always hold. At longer times to retirement, larger investment amounts, greater income and higher investment returns the Roth IRA performs increasingly well even if tax rates fall during retirement. At lower amounts saved the Traditional IRA can be better even with higher tax rates in retirement. These results are consistent with most of the prior literature and help validate the model. The model is not a complete, or even a nearly complete, depiction of which type of IRA is preferable for all investors. The model is not for those who wish to maximize retirement consumption income rather than overall lifetime income. The spreadsheet model only applies for investors that are married, filing jointly, and are not covered by a plan at work. The model does not allow contributions to continue after retirement, nor ensure that RMDs are made. It also does not consider estate planning, other income and the impact on taxation of Social Security benefits. However, the model indicates that from the perspective of lifetime consumption, the Roth IRA is not necessarily always the best choice. Simulating a large variety of returns using actual market data also gives a richer understanding than assuming a fixed return with no risk. In Appendix Table 1 above Taxable Income � Income – Standard Deduction – IRA Contributions for the Traditional IRA and Income – Standard Deduction for the Roth IRA, respectively, for one run of the simulation. The taxes used are from the 2017 progressive tax table for married filing jointly (see www.IRS.gov) with the tax rules in place before the TCJA. In the contribution years Real Consumption � Income – IRA contributions – Taxes, adjusted for inflation with the deflator column. Annual rates of return are drawn from a normal distribution with the given geometric average return and standard deviation. The cumulative savings at retirement is annuitized over the given life expectancy. The nominal annual withdrawal during the retirement years is a constant amount as shown and real consumption declines each year because of inflation. The low amount of taxation during the retirement years for the Traditional IRA is an artifact of indexing the tax brackets and the standard deduction to match inflation. If the brackets or the deductions are not indexed the Roth IRA pre-dominates in most scenarios. The choice of IRA is thus very dependent on whether the IRS will continue to index deductions and tax brackets. The consumption outcomes at the top of the table are for one trial run. Providing a simulation of multiple outputs rather than a single point estimate of future value is a better method to determine the preferred choice. Note that the model uses realistic estimates of portfolio returns at the chosen risk levels. This provides investors better information to choose between the IRA types. 2. Post-TCJA scenario In the following scenario the same inputs were used, but the new TCJA tax brackets and standard deduction were applied. Rates of return are randomly drawn so they are different from the pre-TCJA scenario. Nevertheless, the Traditional IRA still pre-dominates in terms of real consumption in 361 out of the 500 trials. See Appendix Table 2. 364 T. Manuel et al. / Financial Services Review 27 (2018) 345-365 References Adelman, S. W., & Cross, M. L. (2010). 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