J. Welch October 12, Measuring the Financial Consequences of IRA to Roth IRA Conversions

Transcription

1 Measuring the Financial Consequences of IRA to Roth IRA Conversions Executive Summary The tax code permits the conversion of IRA funds to a Roth IRA provided that personal income taxes are paid on the IRA distributions. Common motivations for IRA to Roth IRA conversions are to increase retirement disposable income, ensure against future tax increases, and allocate retirement savings to minimize combined taxes for retirees and their heirs. This paper quantitatively assesses the financial consequences of making conversions with respect to these motivations. Our laboratory was a linear programming retirement planning calculator that, given a set of assumptions and constraints, computes retirement cash flow that maximizes disposable income by minimizing taxes and maximizing compounded asset returns. Disposable income is our metric for evaluating different assumptions, such as doing or not doing conversions. Our results are that partial conversions early in the optimal plan increases disposable income by around 1% in most situations. Conversions reduce total income taxes paid by 19% as it shifts them from later in retirement to early in retirement. Prepositioning savings for inheritance purposes can be accomplished with minor reductions in disposable income. However, if the retiree does not live out the full term of the plan, i.e. live to age 92, then her estate at age 80, for example, can be reduced by up to 8%. 1 Introduction The objective of retirement planning is to maximize disposable income 1 from all sources; Social Security benefits, pensions, sale of illiquid assets, and the distribution of retirement savings (liquid assets). Retirees have little control over Social Security benefits and pension income because they are fixed at the age of retirement. In contrast retirement savings distributions are at the retiree s discretion. It is in the retiree s interest to maximize disposable income by minimizing personal income taxes while maximizing returns on retirement savings. Because tax-deferred account withdrawals are subject to personal income taxes a suboptimal distribution schedule will decrease disposable income. We assume three retirement savings accounts 2 : 1. Tax-deferred account (IRA) 3 contributions from wages are exempt from personal income taxes. Distributions are taxed as personal income. After age 70 ½ IRA distributions are forced by the IRA s Required Minimum Distribution (RMD). 2. Roth IRA (Roth) 4 contributions from wages are subject to personal income taxes. Asset returns and distributions are not taxed. The Roth has no RMD. 3. After-tax Account 5 contributions can be from any source and are assumed to be already taxed as appropriate. Profits are taxed as incurred. Distributions are not taxed, i.e. distributions are after-tax. 1 Disposable income is the money available for personal consumption after taxes have been paid. 2 See the Glossary in Appendix A. 3 We refer to the collection of tax-deferred accounts as the IRA. 4 We use the term Roth to designate the Roth IRA savings account. 1

2 Retirement savings are the sum of the account balances for these three accounts. Federal and state tax codes permit the IRA to Roth IRA conversion of funds providing that personal income taxes are paid on the IRA withdrawals.. Our interest is in measuring the consequences to disposable income caused by IRA to Roth IRA conversions. We explore this question using a linear programming (LP) model that, for a given set of assumptions, maximizes disposable income. We report the results of some tests that address this issue. Each test compares optimal plans with and without conversions. Motivations for making IRA to Roth conversions are: 1. Increase retirement disposable income. 2. Pre-position savings in the retiree s estate to reduce the heirs personal income tax liability. 3. Preserve savings for heirs by avoiding the IRA s RMD In anticipation of increases to personal income tax rates during retirement. This paper focuses on motivations 1 through 3. Motivation 4 is not considered because future personal income tax changes are likely to increase rates in the upper brackets which are not a factor in our scenarios where taxable income is in the lower brackets. For planning purposes projecting the current progressive tax structure into the future is a valid assumption. We are reporting on computational experiments, each with two components: 1. No Conversion Option (NCO) is a retirement plan in which no IRA to Roth conversions are permitted. 2. Conversions Enabled Option (CEO) is a retirement plan in which IRA to Roth conversions are allowed during retirement. We compare the difference in annual retirement disposable income between NCO and CEO. Our laboratory was the Optimal Retirement Planner (ORP) 7, an LP based retirement calculator that maximizes retirement disposable income by minimizing income taxes on savings account withdrawals and other sources of income. Minimizing income taxes influences the order and amount of saving account distributions. The optimizer computes the values of variables which are pre-specified assumptions by the simulators more commonly used in retirement planning. We find that the optimal plan will perform partial conversions early in retirement 8 at a level and duration that maximizes disposable income. Conversions increase taxes in the year in which they occur but reduce taxes paid later in retirement when Roth IRA distributions are used to provide disposable income. The optimizer will include conversions only when they increase disposable income. For example, conversion will be avoided of the IRA Rate of Return (ROR) is greater that the Roth IRA ROR. A onetime conversion of the entire IRA during the first year of retirement is technically feasible, 5 What we are calling the After-tax Account is referred to as the taxable account in some sources. We prefer Aftertax because all three accounts are taxable; during accumulation, during compounding, or during distribution. 6 The IRA is subject to the RMD but the Roth is not. The purpose of the RMD is to force the IRA account balance to near zero at the account holder s actuarial life expectancy. 7 ORP is available on the Internet without registration or fee at i-orp.com 8 As a simplifying assumption we do not model conversion before retirement begins. 2

3 sometimes practiced, but rarely part of an optimal plan. (It could occur if the IRA was small, that is below the retiree s personal exemption and standard deduction, and there are other sources of income not subject to taxation.) We also find that in comparing two optimal plans, differing only in whether or not conversions are allowed, that there is less that a 1% improvement in the conversion plan vs the non-conversion plan. The optimizer rearranges taxes paid to compensate for the differences in IRA distributions. In the next section we review the literature concerned with quantitative evaluation of conversions. We begin our evaluations by examining the details of a typical conversion and its effect on the big picture. Then a sensitivity analysis compares the disposable income consequences of varying plan assumptions. Next we study the financial consequences of prepositioning account balances for inheritance purposes. We conclude with some summary remarks. 2 Literature Review The literature and popular press are rife with advice on how and when to do IRA to Roth conversions. There is very little published that quantifies the consequences of conversions. Clayton, Davis and Fielding [2012] developed a simulator that applied the Monte Carlo method to determine the break-even age of conversions using randomized RORs. They conclude that the conversion decision is a function of current vs future tax rates. If future tax rates are less than current tax rates then conversions offer no advantage. If future tax rates are projected to be greater than current tax rates then conversions should be considered. LP is a useful method of modeling retirement cash flow. The computation of progressive Federal income taxes and the RMD is a natural fit for an LP model. Thus LP schedules withdrawals from the three savings accounts in a manner that minimizes income taxes while at the same time maximizing asset return compounding. The LP models in the literature maximize Final Total Account Balance (FTAB) for a specified level of disposable income. In other words, the FTAB is used to measure the performance of a model. Ragsdale, Seila and Little [1993] modeled retirement cash flow with an LP model. They demonstrated that their LP optimal withdrawal plan is superior to two heuristic withdrawal methods. Their model fixed the withdrawal rate and maximized the FTAB. They computed personal income taxes on withdrawals, met the RMD, minimized the Excess Distribution Penalty (no longer a feature in the tax code), and minimized estate taxes. They modeled two IRAs with different RORs and concluded that distributing the lower performing IRA account first is optimal. Coopersmith and Sumutka [2011] developed an LP retirement planning model to schedule withdrawals from the IRA and After-tax Account in a tax efficient way that maximized the FTAB. They found that the LP results were superior to the common practice, which is to deplete the After-tax Account first, deplete the IRA next, and finally the Roth. Their implementation computed personal income taxes on IRA withdrawals plus Social Security benefits, satisfied the RMD, transferred RMD amounts in excess of spending to the After-Tax Account, and minimized estate taxes. They showed improvement over common practice for situations where: The After-tax ROR is greater than the tax-deferred ROR. 3

4 The initial After-tax balance is greater than 10 percent of total retirement savings. Itemized deductions are greater than the standard deduction. Their paper includes the equations that comprise their LP implementation. In an earlier paper [Welch 2015] we reported an LP implementation that extended this prior work by: Fixing the FTAB and maximizing disposable income, Modeling all three retirement savings accounts, Implementing IRA to Roth conversions, Adding other sources of taxable income to the model, such as pensions and earnings from post retirement employment. We showed that the LP approach computed disposable income schedules that were 3% to 34% greater than a common practice simulator. We demonstrated the implementation s credibility by showing its internal consistency and by comparing its income schedules to those published in two previously mentioned publications. ORP is deterministic, i.e. non probabilistic, and assumes a fixed inflation rate and fixed RORs on investments. Appendix C reviews this assumption. 3 Baseline Scenario In this section we define a baseline scenario (Baseline), solve it for NCO and CEO, and examine the details of the optimal plans generated by the LP. 3.1 Baseline Definition The Baseline is for a single, 65 year old retiree, just beginning retirement, with one million dollars in savings. The IRA contains $750,000 and the After-tax Account balance is $250,000. Initially there is no Roth account. Other assumptions are a 5% ROR on all savings accounts, 2.5% inflation, retirement lasts to age 92, and the FTAB will be zero, i.e. savings will be depleted at the end. We used the 2015 Federal income tax tables. ORP maximizes disposable income for the first year of retirement. We assume the constant spending model where subsequent years income are the first year s disposable income indexed to inflation. 3.2 Baseline Evaluation We solved the LP model representing the Baseline scenario with no conversions (NCO) and with conversions implemented (CEO) to measure the economic advantage of doing IRA to Roth IRA conversions. We examined the resulting distribution schedules to compare the dynamics of the optimal solutions for the no conversions case and the case with conversions Income and Distributions The Baseline results are that NCO s maximum initial disposable income is $44,487 vs $45,049 for CEO. Initial disposable income is the maximum amount available for personal consumption in the first year of retirement. This gives a 0.6% economic advantage to enabling conversions. Lifetime NCO disposable income was $1,786,000 compared to $1,797,000 for CEO. Lifetime tax payments are 19% less with CEO 4

5 than NCO. Lower taxes paid are due to CEO shifting savings account balances out of the IRA to the Roth IRA where asset returns are not taxed. Figure 1 charts the savings account balances over retirement with and without conversions. Figure 1: Savings Account Balances Assumptions Baseline scenario. Y-axis is savings balance in thousands of dollars ($000) 1000 NCO CEO Age Age Discussion Initial account balances at age 65 reflect that the first year distributions have already been made. In the CEO case the steep rise in the Roth IRA balance before the age of 70 indicated conversions while the After-tax distributions satisfy disposable income. The balances for all accounts go to zero at the end because of the zero FTAB requirement. The NCO panel reflects but does not follow the conventional practice of depleting the After-tax Account before distributing the IRA. In the beginning, disposable income requirements are satisfied from the After-tax Account while the IRA continues to appreciate through the compounding of IRA assets.. The After-tax Account is not fully depleted until the end of retirement. Some After-tax money is held in reserve, i.e. not distributed, so that it is available later for meeting disposable income requirements while holding IRA distributions at the top of the 15% tax bracket (see Figure 2) without allowing any income to spill over into the 25% bracket. The CEO panel shows the Roth playing a significant role in the plan. The IRA balance falls right from the start as funds are transfered to the Roth IRA while the After-tax Account is distributed. The After-tax Account is fully depleted by age 70 because the Roth is available to help minimize taxes on IRA distributions. At age 78, in the CEO option, the Roth balances exceeds the IRA and the two are distributed in parallel due to conversions and compounding. Figure 2 demonstrates the saving account distribution schedules for Baseline with and without IRA to Roth conversions. 5

6 Figure 2: Baseline Income and Distributions Assumptions: Baseline, same test as Figure 1. Y-axis is in thousands of dollars ($000) NCO CEO After-tax Age NCO 0 Age CEO % Exempt Discussion: The upper panels show disposable income and savings distributions. IRA withdrawals exceed disposable income when taxes are paid out of IRA distributions. The lower panels show income as it is subject to income taxes. In the CEO panels the dip in IRA distributions and taxable income at age 71 is caused by simultaneous final distribution from the After-tax Account and the termination of IRA to Roth IRA conversions. Before the age of 70 while the After-tax Account is meeting disposable income needs the CEO panels show IRA distributions for conversions to be in the $50,000 to $60,000 range. Early in retirement parallel IRA and After-tax Account distributions satisfy NCO disposable income requirements. In the CEO option the amounts of the conversions are held in check by the IRA distribution tax brackets and the funds available in the After-tax Account. IRA distributions are high during the first five years of the plan because the After-tax Account provides for spending and the IRA is making annual conversions to the Roth Exempt

7 Age 78 is the pivot age for CEO. IRA and Roth distribution switch places, with Roth taking over the majority of supplying disposable income and IRA distributions dropping to the top of the 10% income tax bracket. In Figure 2 NCO shows significantly more money being taxed in the 15% bracket than does CEO because tax bracket upper bounds are indexed to inflation. Conversions take place as long as the After-tax Account is not depleted. From ages 72 to 77 low level distributions from the Roth are sufficient to fill in the gap between disposable income requirements and IRA distributions at the top of the 15% income bracket. Despite rearranged IRA distributions and differences in taxes paid NCO and CEO have similar disposable income graphs across retirement. This is consistent with initial income differences being less than 1% and the constant income assumption. Taxes drive the process. For the first ten years NCO income is mostly from the After-tax Account but supplemented by IRA distributions, first at the top of the exempt tax bracket then at the top of the 10% bracket. At age 70 IRA distributions rise into the 15% bracket. Sufficient funds are retained in the Aftertax Account so that at age 76 it can supplement IRA distributions to keep them within the ceiling of the 15% bracket throughout the remainder of retirement. This is contrary to convention practice which would have the retiree deplete the After-tax Account before beginning IRA distributions. At age 77, in Figure 2, CEO panel, IRA withdrawals drop to the top of the 10% bracket for the duration of the plan since there are sufficient funds in the Roth to meet the disposable income requirements. Identification of this pivot age is key to the successful implementation of CEO and has to be identified with some precision. Make the pivot too early and there will be insufficient funds in the Roth to carry out its mission to bridge the gap between disposable income and IRA withdrawals at the top of the 10% bracket. Make the pivot too late and extra taxes will have been paid on IRA withdrawals in the 15% bracket, thereby reducing disposable income. It is interesting to note that the After-tax Account is a holding place for funds early in the plan so that it can be used to keep IRA withdrawals at the top of the 10% income tax bracket after age 78. The Roth serves the same function with CEO, but more efficiently. 7

8 3.2.2 Taxes Paid Figure 3 compares NCO and CEO taxes paid annually and cumulative. 10 Figure 3: Nominal Taxes Paid Baseline scenario, same as Figure 1 and Figure 2 Y-axis is in thousands of dollars Annual Taxes 0 Age The left panel shows taxes paid each year of the plan. The right panel shows cumulative taxes paid. Before age 77 both options support spending from the After-tax Account, where distributions are not taxed. NCO has smaller IRA distributions and thus lower taxes. CEO is paying higher taxes because of conversions. At age 77, for NCO the IRA is the sole provider for spending and taxes go up accordingly. CEO IRA distribution and taxes are reduced as the Roth begins distributions. NCO and CEO cumulative taxes take two different paths with trajectories changing at age 77. NCO total taxes end up 19% higher than CEO Cumulative Taxes 0 Age

9 4 Sensitivity Analysis Sensitivity analysis is changing one assumption of the Baseline at a time and measuring the effect that it produces on income. Table 1 summarizes a set of trials each with a different Baseline assumption value changed. Each trial computes NCO and CEO maximum disposable incomes and compares their percent difference shown in the Benefit column. Table 1: Summary of Consequences of Conversions, Single Retiree Assumptions Baseline scenario Each trial has one modified Baseline assumption. Assumption Benefit Description of How One Assumption was Modified. Baseline 0.6% Baseline: 5% ROR, 2.5% inflation, 0 FTAB. Accounts 0.0% $1M IRA, 0 Roth, 0 After-tax. Accounts 0.0% $400K IRA, $350K Roth, 250K After-tax. Earned Income 0.9% Earn $ annual income until age 70. FTAB 0.6% $100,000 Final Total Account Balance. Illiquid Asset 0.9% $400,000 house sold at age 85. Inflation 1.5% The inflation rate is set to 0%. Inflation 1.1% The inflation rate is set to 10%. Large Savings 1.3% Multiply initial account balances by 10, i.e. $10M in total savings. Longevity 0.7% Plan ends at age 80. Longevity 0.9% Plan ends at age 100. Pension 0.4% $100,000 pension income, beginning at age 65, adjusted for inflation. Retire Early 0.6% Current age is 55 and retire at the age of 55. ROR 0.0% 0% rate of return. ROR 1.3% 10% rate of return. Social Security 1.2% $23,000 Primary Insurance Amount (PIA) beginning at age 62. Social Security 0.6% $23,000 PIA beginning benefits at age 70. State Tax 0.7% $4,300 exemption and 9% state tax rate. Discussion Benefit values are the percent difference between CEO disposable income and NCO disposable income. (CEO income NCO income)/nco income. Negative benefits do not occur because if the conversion consequence is unfavorable the optimizer will simply not do the conversion and the CEO results are the same as NCO. Table 2 presents the same set of trials as Table 1 but for a married couple. Introducing marriage into the picture changes the income tax computations. The exempt bracket is larger with two personal exemptions and two people over age 65. 9

10 Table 2: Summary of Consequences of Conversions, Married Couple Assumptions Baseline scenario but for a 65 year old retired married couple. Each trial has one modified Baseline assumption. Assumption Benefit Description Baseline 0.9% Baseline, except for a spouse, age 65, retired at age 65. Accounts 0.0% $1M IRA, 0 Roth, 0 After-tax. Accounts 0.2% $400K IRA, $350K Roth, 250K After-tax. Earned Income 0.5% Earn $100,000 annual income until age 70. FTAB 0.9% $100,000 Final Total Account Balance. Illiquid Asset 0.7% $400,000 house sold at age 85. Inflation 0.7% Inflation rate is set to 0%. Inflation 0.6% Inflation rate is set to 10%. Large Savings 1.1% Multiply initial account balances by 10, i.e. $10M in savings. Longevity 0.4% Plan ends at age 80. Longevity 1.1% Plan ends at age 100. Pension 0.1% $100,000 pension income, beginning at age 65, adjusted for inflation. Retire Early 0.7% Retire at the age of 55. ROR 0.0% 0% ROR. ROR 0.7% 10% ROR. Social Security 0.1% $23,000 PIA beginning at age 62. Social Security 0.1% $23,000 PIA beginning at age 70. State Tax 1.3% $4,300 exemption and 9% state tax rate. Discussion The Benefit column is the percent increase in income for CEO and NCO, i.e. (CEO income NCO income)/nco income. There is some variation in the Benefits values between the two scenarios but overall there is not much difference between being married or single, at least from a conversion perspective. 5 Pre Positioning of Savings in Retirement Accounts A popular motivation for employing IRA to Roth conversions is to arrange savings so that the retiree and heirs pay a minimum of combined income taxes. A second violist in the Dayton Symphony is going to have a relatively low income compared to his sister the cosmetic surgeon in Beverly Hills, or even to the retiree. The violist s portion of retiree s estate is best left in the IRA because his distributions will fall into his low marginal income tax bracket. His sister is better off receiving a Roth IRA from the estate with the retiree bearing the income tax burden of conversion while the surgeon s subsequent distributions are tax free [Potts and Reichenstein 2015]. Modeling the heirs income taxes is beyond the scope of our study. Assuming that the retiree knows how she wants to divide up her bequest our interest is to measure the financial consequences of shifting part of the FTAB from the IRA, where the optimal solution will normally leave it, to the Roth for the heirs benefit. 10

11 We address this issue by specifying a Minimum Roth Balance (MRB) that must be carried in the Roth throughout retirement and into the FTAB. The MRB and FTAB are indexed to inflation. Since the Aftertax Account is distributed early in retirement normally only the IRA will contain any remaining FTAB balance. Leaving the FTAB in the IRA is optimal, from the retiree s perspective, because it leaves the paying of income taxes on IRA distributions to the heirs. Because of the uncertainty as to when the last will and testament will actually be read the retiree s estate at any age is the total of all three savings accounts. The MRB will be part of that estate throughout retirement. To establish the MRB the initial IRA to Roth IRA conversion may made during the first year of retirement. Additional partial conversions will cause the Roth balance to rise substantially above the MRB during the course of the plan. Roth distributions cannot take the Roth balance below the MRB. Positioning funds for the FTAB reduces disposable income during retirement because income taxes on the conversion reduces disposable income. 5.1 Comparison of Prepositioning Plans In this section we evaluate the results of applying different FTAB options through manipulation of the MRB. With MRB as the independent variable we consider four cases: the Baseline scenario plus three FTAB Options: 1. Baseline: The FTAB is fixed at $100,000. IRA to Roth conversions are not allowed. There is no MRB. 2. All-IRA: The MRB is zero and the Roth balance can take on its optimal level %-Roth: The MRB is $50,000, or 50% of the planned $100,000 FTAB. The remainder will be in the IRA since the After-tax Account is the first to be depleted. 4. All-Roth: The entire $100,000 FTAB will be in the Roth and there will be no IRA balance in the FTAB. 11

12 Table 3 summarizes initial disposable income and taxes paid by the options as compared to the Baseline. Table 3: Cost of MRB, Baseline vs Alternative Options Baseline scenario with a $100,000 FTAB, no conversions. MRB is the independent variable. All Options permit IRA to Roth conversions. Option Income Taxes All-IRA 0.6% -38.5% 50%-Roth 0.1% -33.7% All-Roth -1.2% -29.0% Option identifies the allocation of Roth balance in the FTAB. The Income column is the percent difference of the Option s initial disposable income and the Baseline s initial disposable income. A positive value indicates increased disposable income compared to Baseline. Taxes is the percent difference of the Option s total taxes and the Baseline s total axes. A negative value indicates that the Option reduces total taxes paid. The IRA to Roth conversion to satisfy the MRB occurs in the first year of retirement. The All-IRA Option is the same as Baseline in Table 1, FTAB trial. The lower two rows of the income column shows that there is a cost to forcing the MRB into the FTAB. The All-IRA solution is the true optimum which takes advantage of the Roth IRA to maximize disposable income but leaves no balance in the FTAB s Roth IRA. Adjusting the composition of the FTAB forces the solution away from the true optimum by increasing taxes paid, thereby reducing maximum disposable income. The additional cost is born by the retiree, every year of retirement. The tax percentages are negative, i.e. total taxes paid by the Options are smaller than for the Baseline. Conversions early in retirement reduce the size of the IRA, which pays taxes on distributions, and increases the size of the Roth, whose distributions are not taxed. This decreases the taxes paid on compounded asset returns. The large tax reductions are consistent with the 19% reduced taxes as shown in Figure 3. 12

13 Figure 4 shows cumulative taxes paid for the three FTAB Options as they relate to the Baseline. Figure 4: Cumulative Taxes Paid for FTAB Options. Assumptions Baseline scenario with $100,000 FTAB MBR as the independent variable. Each line is cumulative taxes from retirement to the end in thousands of dollars. 150 Cumulative Taxes ($000) Age Discussion The Baseline pays no taxes until age 69 because After-tax distributions are not taxed and IRA distributions are at the top of the exempt tax bracket. The 50%-Roth Option establishes the $50,000 MBR, 50% of the FTAB, in the first year (in case the retiree dies in the second year) which puts some taxable income into the 15% bracket. The All-Roth Option establishes the $100,000 MBR in the first year (in case the retiree dies in the second year) which puts some taxable income into the 28% bracket. Baseline cumulative taxes don t exceed the Options taxes until the retiree is in her mid-80 s. At that point the Options are making parallel distributions from the IRA and Roth with IRA distributions at the top of the 10% bracket compared to Baseline IRA distributions which are at the top of the 15% bracket. 5.2 The Cost of Prepositioning Life is uncertain. All three FTAB Options pay higher taxes early in retirement while Baseline pays higher taxes toward the end of retirement (Figure 4). Should the retiree demise prior to the end of the planning period the prepaid taxes stay with the government instead of going to the heirs. Figure 5 shows the difference between the FTAB Options saving balances and the Baseline saving balance as a percentage of the Baseline balance for each year of retirement. 13

14 Figure 5: Saving Account Balances as a Percentage Difference of the Baseline Assumptions Baseline with $100,000 FTAB MRB as the independent variable. 1.0% -1.0% -3.0% -5.0% -7.0% Age Discussion Higher prepaid taxes results in reduced savings account balances as compared to Baseline. Comparing the prepositioned FTAB options to the Baseline shows that: 1. The Options disposable incomes are similar (Table 3). 2. The Options savings balances are lower than Baseline during much of retirement (Figure 5). 3. Total Options taxes for the full plan are lower than Baseline (Figure 4). If, as is most likely, the retiree does not survive to the end of the planning period then the heirs may prefer she follows the Baseline model where taxes are pushed to the end of the plan. 6 Conclusions Modifying base scenario assumptions shows that IRA to Roth IRA conversion increase disposable income by zero to 1.5% (Table 1 ). IRA to Roth IRA conversions protect against future tax increases by relying on a reduced taxable balance in the IRA later in retirement. The open issue is how much of a tax increase and to which tax brackets, warrant conversions. (Figure 3) Directing savings to the Roth IRA with the intention reducing the tax burden for the heirs incurs a small reduction in retirement disposable income. (Table 3) There is, as yet, no rule of thumb for identifying the optimal age (Figure 2, CEO option) to lower IRA distributions and increase Roth IRA distributions to meet disposable income requirements while minimizing taxes. Given: -9.0% 14

15 1. the retiree s aversion to using retirement savings to prepay taxes in a higher tax bracket early in retirement, 2. the potential reduction in the size of the estate in mid planning period, 3. the IRA vs Roth IRA withdrawal timing issue, and 4. the roughly 1% increase disposable income from doing partial IRA to Roth IRA conversions, the IRA to Roth IRA conversion decision should probably be made based on considerations other than increasing disposable income. 7 References Clayton, Ronnie J., Lemuel W. Davis, and William Fielding. (2012), Converting a Traditional IRA to a Roth IRA: Break-even Analysis, Journal of Personal Finance, Volume 11, Issue 2, page Coopersmith, Lewis W. and Alan R. Sumutka (2011), Tax-Efficient Retirement Withdrawal Planning Using a Linear Programming Model. Journal of Financial Planning, September Evensky,H.; Heading for Disaster; Financial Advisor, April 2001, pp Kingston, John D. (2001), Monte Carlo Simulation---Challenging the Sacred Cow, Journal of Financial Planning, November 2001, pages Potts, Tom L. and William Reichenstein. (2015), Which Assets to Leave to Heirs and Related Issues, Journal of Personal Finance, Volume 14, Issue 1, page Ragsdale, Cliff T., Andrew F. Seila, and Philip L. Little, Optimizing Distributions from Tax-Deferred Retirement Accounts. Personal Financial Planning, Welch, James S. (2015), Mitigating the Impact of Personal Income Taxes on Retirement Savings Distributions, Journal of Personal Finance, Volume 14, Issue 1, page Wikipedia (2015) June 8 8 Appendix A: Glossary After-tax Retirement Savings Account: Contributions to the After-tax Account can be from any source that has already been taxed. Taxes are paid annually on asset sale s profits, dividends and interest. Withdrawals are not taxed. When the IRA withdrawal exceeds income, say, due to the RMD, the surplus is transferred from the IRA to the After-tax Account. Taxes, at the capital gains rate, are assumed to be paid annually, thereby reducing the account s ROR. This reduced After-tax ROR is the main reason that both common practice and ORP distribute the After-tax Account first. After-tax Accounts typically include common stock, which often pay dividends that are subject to income taxes. We assume that the After-tax Account is invested only in growth stocks or mutual funds which pay insignificant dividends relative to the rest of the plan. Also, since the After-tax Account is depleted first there are no taxable dividends later in most plans. 15

16 The literature frequently uses the term taxable account for what we call the After-tax Account. In our view all accounts are taxable because they are taxed either as money enters the accounts or as it is distributed. Disposable Income: Money available for personal consumption after taxes have been paid. Estate: The money left in retirement savings at the end of the plan. This is a non-negative number specified as part of a scenario s assumptions. FTAB: Final Total Account Balance is the sum of all three savings accounts at the end of the plan. FTAB is also known as the plan s estate. FRA: Full Retirement Age is the age at which a person first becomes entitled to full or unreduced retirement benefits. IRA: A designator for all tax-deferred accounts. IRA to Roth IRA Conversion: The reclassification of IRA savings to the Roth IRA. Personal income taxes are paid on the reclassified amount. Linear Programming: A mathematical technique to describe a situation with a set of linear equation and an objective function to be maximized. Linear Programming has been an important Operations Research tool for over 50 years. Monte Carlo Method: A retirement simulator, with an assumed withdrawal rate, that is repeatedly solved, each time with a different set of randomly generated asset returns. Its results are a probability analysis of plan success or failure. Taxes are not considered by the simulators. Nominal Value: The measure of some economic activity indexed to inflation. As opposed to Real Value where the effects of inflation are removed. Objective Function: A linear function that spans the model LP and yields a single value. The LP optimizer maximizes this value. ORP s objection function is disposable income for the first year of retirement. Optimization finds the "best available" value of some objective function given a defined domain. For retirement savings distribution, the domain is the retiree s financial situation. The objective function (economic value) is disposable income available for spending. Optimization is the balancing of maximizing of asset compounding against minimizing taxes. PIA: The Principle Insurance Amount is the amount of Social Security benefits for which the retiree is eligible at FRA. ROR: The Rate of Return is the profit on an investment expressed as a percentage the of investment s nominal value. Real Value: The measure of some economic activity, usually disposable income in this study, in terms of current, not inflated, dollars. 16

17 RMD: The Required Minimum Distribution is an amount that the IRS requires be withdrawn from the IRA annually beginning at the age of 70½. It is computed as the IRA balance on December 31 of the previous year divided by a life expectancy value taken from an IRS published table. The RMD is recomputed annually with a different (larger) life expectancy divisor. By IRS regulation IRA distributions made to satisfy the RMD cannot be converted to a Roth IRA. Roth IRA Retirement Saving Account: Income taxes are paid on the employment income contributions to a Roth IRA but there are no taxes on asset return compounding or withdrawals After age 59 ½, withdrawals can be made from the Roth IRA in any amount without penalty. Tax-deferred Retirement Savings Accounts (IRA): There are no income taxes on employment earnings contributed to the tax-deferred account but all withdrawals are taxed as personal income. This type of account includes IRA, 401k, 403b and a variety of others, all of which are generically equivalent for purposes of this study. The term IRA is used to denote the collection of these accounts since most are converted into an IRA before or at retirement. After age 59 ½ withdrawals can be made from the IRA in any amount without penalty. Tax Exempt Bracket: In computing personal income taxes the standard deduction, one or two personal exemptions, and one or two exemptions for being over the age of 65 are income that is not taxed. Withdrawal Plan: The schedule of distributions from retirement savings for all of retirement. The plan includes money used for taxes, income, and the FTAB. 9 Appendix B: Linear Programming We modeled retirement cash flow using Linear Programming (LP), an operations research tool with a 50 year history. LP is fundamentally different from a simulator. A simulator computes the unique solution to a process using the given set of assumptions. LP describes the process with a set of linear equations with more variables than equations and thus multiple solutions. A key feature of LP is its objective function. The objective function spans the model and yields a single value: the profit from doing the activities of the model. The LP optimizer finds a solution to these equations that maximizes the objective function. Our objective function is disposable income in the first year of retirement. The subsequent years disposable income is this value indexed for inflation. LP maximizes its objective function while satisfying the requirements (constraints) of the model such as the selected income model s requirements for each year of retirement while ending up with a zero FTAB ORP employs third party, off the shelf commercial software to input, solve, and report the results. The application s unique feature is a tailored, data preprocessor that prepares matrix-ready for input to the LP system. 10 Appendix C: Volatility A common criticism of deterministic retirement calculators is that the constant ROR assumption does not reflect the market volatility of asset returns. We argue that an asset with a low ROR is likely to be less volatile than market indexes (the S&P 500 for example) and thus our assumed constant, average ROR will reflect the future performance of the asset 9. Accordingly, active capital preservation portfolio 9 Investing in a low ROR, highly volatile asset would seem an unwise policy. 17

18 management can dampen the adverse effects of market volatility so that, when combined with a planning horizon of 25 years or more, the fixed ROR and inflation assumptions are valid for planning purposes. Given the Federal Reserve s commitment to maintaining an inflation rate of 2% to 2.5% we are comfortable with assuming a fixed inflation rate. Most quantitative studies appearing in the literature address volatility through the use of Monte Carlo method. The Monte Carlo method uses a simulator to model a process, runs it many times with randomly chosen input and the results are statistically evaluated. Monte Carlo models have their problems: Implementing Monte Carlo simulation is very difficult at best and can lead to incorrect decisions at worst. The problem is that the typical assumption set used in Monte Carlo simulation assumes normal distributions and correlation coefficients of zero, neither of which are typical in the world of financial markets. It is important for planners to realize that these assumptions can lead to problems with their analysis. Financial planners will find that exploratory simulation provides equivalent or better answers and is simpler to implement without assumptions [Nawrocki 2001). Kingston [2001] and Evensky [2001] further critique the Monte Carlo method. Most Monte Carlo methods derive their random RORs from historical S&P 500 data which is more volatile than conservatively managed retirement portfolios. Monte Carlo simulators do not include income tax computation, which as we can see these examples, ignores a significant factor in retirement planning. For purposes of this study our deterministic model gives more meaningful results. Deterministic calculators report the details of how they arrived at their final state, not just the probability of achieving an acceptable final state. Finally, we have yet to find a Monte Carlo based quantitative study that first validates its simulator. The validation requirement has been addressed for ORP [Welch 2015]. 18