# The 30-Year Value of a Single Roth Conversion

Many financial advisors, tax preparers, and investors vastly under estimate the value of systematic Roth conversions. Optimizing Roth conversions requires sophisticated analysis unavailable with most commercial software.

If you haven’t done the analysis before, it can be difficult to see the benefit on Roth conversions. The temptation is to use a simple calculation based on the immediate tax owed. But any time you zoom in on only the downside of Roth conversions, you will find yourself irrationally critical. You need to look at the whole tax picture to see the benefit of Roth conversions.

Although we recommend many complicated and customized systematic Roth conversion plans, this article is intended to zoom in on a simple example: the value of a single year’s Roth conversion.

### Assumptions for our example

Imagine a single 69-year-old who will start Required Minimum Distributions next year. He has a single choice: Should he do a \$20,000 Roth conversion this year?

In one scenario, he converts \$20,000 from his traditional IRA to Roth IRA and pays the income tax on that one conversion.

In the other scenario, he does not do a Roth conversion.

He faces a marginal income tax burden of 29.75% (24% federal and 5.75% Virginia state) and qualified tax rate (used for dividends and capital gains) of 20.75% (15% federal and 5.75% Virginia state).

His \$20,000 conversion owes \$5,950 in state and federal taxes (29.75% of \$20,000). This means that he has a taxable brokerage account worth \$5,950 in the no conversion scenario and worth \$0 in the conversion scenario.

From these assumptions, we can compare the after-tax value of a \$20,000 Roth verses a \$20,000 traditional IRA and a \$5,950 brokerage account for a now 70-year-old.

For all accounts, I assume a total return of 8.5% annually which is itemized as 2.0% inflation, 4.3% growth, and 2.2% interest and dividends. I assume that most capital gains tax can be delayed, but that the interest and dividends in the taxable brokerage account are taxed every year.

Here is the benefit to the client over 30 years (until they reach age 99) of this one Roth conversion.

### Calculations

#### Roth Conversion Scenario

The conversion scenario is easy to calculate. The client only has one account: the Roth IRA. The dividends, interest, capital gains, and distributions in a Roth IRA are all free of tax. This means that both the nominal and after-tax value of the Roth IRA are the same. To calculate the value after the 30 years, we just have to grow the \$20,000 by 8.5% annually. Here is how that growth looks:

Age Nominal / After-Tax Value of  Roth IRA
69 Assumptions \$20,000
70 \$21,700
71 \$23,545
72 \$25,546
73 \$27,717
74 \$30,073
75 \$32,629
76 \$35,403
77 \$38,412
78 \$41,677
79 \$45,220
80 \$49,063
81 \$53,234
82 \$57,759
83 \$62,668
84 \$67,995
85 \$73,774
86 \$80,045
87 \$86,849
88 \$94,231
89 \$102,241
90 \$110,931
91 \$120,361
92 \$130,591
93 \$141,691
94 \$153,735
95 \$166,803
96 \$180,981
97 \$196,364
98 \$213,055
99 \$231,165

The 30 years of tax-free 8.5% growth results in a final nominal value of \$231,165. Because no taxes are owed on this balance, this means that the 30-year after-tax value is also \$231,165.

#### No Conversion Plan

Without the conversion, the client has two accounts: a Traditional IRA worth \$20,000 and a brokerage account that is still flush with \$5,950 because it did not have to pay a tax for a Roth conversion.

The Traditional IRA is subject to a Required Minimum Distribution (RMD) starting at age 70 for this client, the year after our year of conversion. The RMD is taxed at income rates, which for this client means a rate of 29.75%. In “The Complete Guide to Timing Your RMD” we suggest that, if you are not doing a conversion, you benefit from taking your RMD as late in the year as possible.

For this reason, we first grow the Traditional IRA by the 8.5% growth. The dividends and interest of a Traditional IRA are not taxed as they accrue, so we do not need to tax any of this growth. After the growth, we are required to take out that year’s RMD, which is calculated by dividing last year’s value by this year’s RMD divisor. Traditional IRA distributions are taxed at income tax rates. That means that 29.75% of the RMD is lost to taxes and the remainder is deposited into the taxable brokerage account.

Here is how the Traditional IRA nominal value is calculated:

Age Nominal IRA RMD Divisor IRA RMD RMD Tax
69 Assumptions \$20,000 0 \$0 \$0
70 \$20,970 27.4 \$730 (\$217)
71 \$21,961 26.5 \$791 (\$235)
72 \$22,970 25.6 \$858 (\$255)
73 \$23,993 24.7 \$930 (\$277)
74 \$25,024 23.8 \$1,008 (\$300)
75 \$26,058 22.9 \$1,093 (\$325)
76 \$27,089 22 \$1,184 (\$352)
77 \$28,113 21.2 \$1,278 (\$380)
78 \$29,118 20.3 \$1,385 (\$412)
79 \$30,100 19.5 \$1,493 (\$444)
80 \$31,049 18.7 \$1,610 (\$479)
81 \$31,953 17.9 \$1,735 (\$516)
82 \$32,801 17.1 \$1,869 (\$556)
83 \$33,576 16.3 \$2,012 (\$599)
84 \$34,264 15.5 \$2,166 (\$644)
85 \$34,862 14.8 \$2,315 (\$689)
86 \$35,352 14.1 \$2,472 (\$736)
87 \$35,719 13.4 \$2,638 (\$785)
88 \$35,943 12.7 \$2,813 (\$837)
89 \$36,003 12 \$2,995 (\$891)
90 \$35,905 11.4 \$3,158 (\$940)
91 \$35,632 10.8 \$3,325 (\$989)
92 \$35,167 10.2 \$3,493 (\$1,039)
93 \$34,493 9.6 \$3,663 (\$1,090)
94 \$33,635 9.1 \$3,790 (\$1,128)
95 \$32,583 8.6 \$3,911 (\$1,164)
96 \$31,330 8.1 \$4,023 (\$1,197)
97 \$29,870 7.6 \$4,122 (\$1,226)
98 \$28,202 7.1 \$4,207 (\$1,252)
99 \$26,390 6.7 \$4,209 (\$1,252)

The taxable brokerage account has interest, dividends, and capital gains all taxed. In reality, taxable interest and ordinary dividends are taxed at income rates while capital gains and qualified dividends are taxed at the lower qualified rates. For the purpose of this example, we have assumed that interest and all dividends are taxed at the more favorable qualified rates. This gives a slight unfair advantage to the No Conversion Plan over the Conversion Scenario, but you will see that the advantage does not help it enough.

Also, with careful capital gains management, you can dodge the capital gains tax for a while. For this reason, we tax the 2.20% of dividends and interest at the qualified rate of 20.75% each year but allow the remaining 6.3% of growth to compound without the burden of taxation. It is only during the after-tax calculation that we calculate what it would cost to realize the unrealized capital gains at the 20.75% qualified rate. This is slightly more favorable than the reality of regularly realized and taxed capital gains as a part of withdrawals and rebalancing, but again you will see that the advantage does not help this plan enough.

For the brokerage account, first we grow the assets by 6.3% without tax. Then, we add in 2.20% of dividend and interest growth decreased by a 20.75% tax. Finally, we deposit the after-tax proceeds from the RMD into the account.

Here is how that taxable brokerage account calculation works out:

Age Nominal Taxable Account Nominal Dividend Growth Nominal Dividend Tax RMD Proceeds Unrealized Gain
69 Assumptions \$5,950 \$0 \$0 \$0 \$0
70 \$6,941 \$131 (\$27) \$513 \$375
71 \$8,056 \$153 (\$32) \$556 \$812
72 \$9,306 \$177 (\$37) \$603 \$1,320
73 \$10,708 \$205 (\$42) \$653 \$1,906
74 \$12,278 \$236 (\$49) \$708 \$2,581
75 \$14,033 \$270 (\$56) \$768 \$3,354
76 \$15,994 \$309 (\$64) \$832 \$4,238
77 \$18,178 \$352 (\$73) \$898 \$5,246
78 \$20,613 \$400 (\$83) \$973 \$6,391
79 \$23,320 \$453 (\$94) \$1,049 \$7,689
80 \$26,326 \$513 (\$106) \$1,131 \$9,159
81 \$29,662 \$579 (\$120) \$1,219 \$10,817
82 \$33,361 \$653 (\$135) \$1,313 \$12,686
83 \$37,458 \$734 (\$152) \$1,414 \$14,788
84 \$41,992 \$824 (\$171) \$1,522 \$17,147
85 \$46,996 \$924 (\$192) \$1,626 \$19,793
86 \$52,513 \$1,034 (\$215) \$1,737 \$22,754
87 \$58,591 \$1,155 (\$240) \$1,853 \$26,062
88 \$65,279 \$1,289 (\$267) \$1,976 \$29,753
89 \$72,634 \$1,436 (\$298) \$2,104 \$33,866
90 \$80,695 \$1,598 (\$332) \$2,219 \$38,442
91 \$89,521 \$1,775 (\$368) \$2,335 \$43,526
92 \$99,176 \$1,969 (\$409) \$2,454 \$49,165
93 \$109,727 \$2,182 (\$453) \$2,573 \$55,414
94 \$121,215 \$2,414 (\$501) \$2,663 \$62,326
95 \$133,713 \$2,667 (\$553) \$2,747 \$69,963
96 \$147,294 \$2,942 (\$610) \$2,826 \$78,387
97 \$162,037 \$3,240 (\$672) \$2,896 \$87,666
98 \$178,026 \$3,565 (\$740) \$2,955 \$97,875
99 \$195,303 \$3,917 (\$813) \$2,957 \$109,090

By adding together these two nominal account values, we get the total nominal value of this plan.

Although you can avoid capital gains tax for a while, chances are you are going to need to realize gains as you rebalance or withdraw from your account. In this way, we can calculate the after-tax taxable account value by reducing the account value by the 20.75% tax on the unrealized capital gains.

The tax on a pre-tax traditional IRA is never avoided. Even your heirs must take RMDs and pay income tax on those distributions. In this way, there is always a significant part of your traditional IRA which is best thought of as the government’s money and not yours. The U.S. government will take its share each time you reach in to take yours. In this way, the after-tax value of your Traditional IRA is your traditional IRA minus your marginal income tax rate. In this case, it would be the traditional IRA minus 29.75%.

As a result, in addition to the nominal value of this plan, we can also calculate the after-tax value of the plan where the traditional IRA and taxable account have been reduced in this way.

Here are those two numbers for the No Conversion Plan:

Age Nominal No Conversion Plan After-Tax No Conversion Plan
69 Assumptions \$25,950 \$20,000
70 \$27,911 \$21,595
71 \$30,017 \$23,315
72 \$32,276 \$25,169
73 \$34,701 \$27,167
74 \$37,301 \$29,321
75 \$40,091 \$31,643
76 \$43,082 \$34,144
77 \$46,291 \$36,839
78 \$49,731 \$39,742
79 \$53,419 \$42,869
80 \$57,375 \$46,237
81 \$61,615 \$49,865
82 \$66,161 \$53,771
83 \$71,034 \$57,977
84 \$76,257 \$62,505
85 \$81,858 \$67,380
86 \$87,866 \$72,627
87 \$94,310 \$78,276
88 \$101,222 \$84,355
89 \$108,637 \$90,899
90 \$116,600 \$97,941
91 \$125,153 \$105,521
92 \$134,343 \$113,679
93 \$144,220 \$122,460
94 \$154,850 \$131,911
95 \$166,296 \$142,085
96 \$178,624 \$153,038
97 \$191,908 \$164,831
98 \$206,229 \$177,529
99 \$221,693 \$191,206

At the end of 30 years, this plan only has \$221,693 nominally and \$191,206 after-tax, which is \$9,472 and \$39,959 less than the Roth conversion plan, respectively.

#### Comparison

Here is the difference (Roth minus No Conversion) between the two plans over time both nominal and after-tax:

Age Nominal Difference After-Tax Difference
69 Assumptions -\$5,950 \$0
70 -\$6,211 \$105
71 -\$6,472 \$230
72 -\$6,730 \$377
73 -\$6,983 \$550
74 -\$7,228 \$752
75 -\$7,461 \$987
76 -\$7,679 \$1,259
77 -\$7,879 \$1,573
78 -\$8,054 \$1,935
79 -\$8,200 \$2,351
80 -\$8,311 \$2,826
81 -\$8,382 \$3,369
82 -\$8,403 \$3,988
83 -\$8,366 \$4,691
84 -\$8,262 \$5,490
85 -\$8,084 \$6,395
86 -\$7,821 \$7,418
87 -\$7,461 \$8,574
88 -\$6,991 \$9,876
89 -\$6,396 \$11,342
90 -\$5,668 \$12,990
91 -\$4,793 \$14,839
92 -\$3,752 \$16,912
93 -\$2,529 \$19,232
94 -\$1,115 \$21,824
95 \$507 \$24,718
96 \$2,357 \$27,943
97 \$4,457 \$31,534
98 \$6,827 \$35,526
99 \$9,472 \$39,959

You can see from these numbers that after the first year of equality, the after-tax No Conversion Plan value lags behind the Roth Conversion Scenario. Each year that passes, that gap just grows larger as the unpaid tax on the traditional IRA and taxable account looms larger and larger. At the end of the 30 years, the after-tax value of the Roth conversion is \$39,959.

Even in nominal terms, the Roth conversion is more valuable than having not done one. Although at first the account balance of the taxable account helps to keep the baseline plan ahead, eventually the income tax on the RMDs as well as the lost compounded growth in the taxable brokerage account swamp what little advantage the plan had. Thus, even the nominal value of the Roth conversion swings to positive eventually.

The longer the time frame, the more benefit that can be measured.

#### Conclusion

No matter the dollar amount, it is not uncommon to see Roth conversions that are worth close to twice the amount you are converting. Getting a million dollar IRA account converted before age 70 is often worth two million dollars in after-tax net worth.

In our scenario much of the value gained from converting is from paying the tax and reducing the taxable account. In the No Conversion Plan, the government’s lien on the traditional IRA means that the 69-year-old doesn’t own the entire \$20,000. However, after a conversion of the entire Roth account, he owns it all with no lien. Although he has to pay \$5,950 of tax from his taxable, it also means he has \$5,950 more in his Roth IRA than he owned outright in his Traditional IRA. Those extra lien-free assets then get to grow in a tax-free environment.

In this way, the tax effect of the Roth conversion is like having done a \$5,950 Roth contribution from the taxable account into your IRA. Through Roth conversion, you pay the tax from your taxable account to confiscate the government’s lien on your retirement assets.

Much of the remaining value of the conversion is gained from avoiding the required minimum distributions (RMDs) being put into your taxable account. When that first RMD gets deposited, its capital gains, interest, and dividends will be taxed for 30-years. This annual tax lowers the return, as the compounding growth on the tax is lost, and the capital gains tax lowers the value of any withdrawal you may need.

These two effects (confiscating the government’s lien while lowering your taxable account balance and avoiding the dribble of RMDs into your taxable account) are often the greatest benefits of a Roth conversion.

Tax preparers can be slow to see this benefit. Tax planning is very different than tax return preparation. The goal of tax preparation is to minimize your tax owed this year. The goal of tax planning is to maximize your after-tax net worth by minimizing your taxes owed over your lifetime. Roth conversions are smart tax planning but do result in more tax owed this year.

My hope is that this simple example will enlighten the hesitant to the benefits of systematic Roth conversions.

Photo by Joseph Gonzalez on Unsplash

##### David John Marotta

President, CFP®, AIF®, AAMS®

David John Marotta is the Founder and President of Marotta Wealth Management. He played for the State Department chess team at age 11, graduated from Stanford, taught Computer and Information Science, and still loves math and strategy games. In addition to his financial writing, David is a co-author of The Haunting of Bob Cratchit.