In order to calculate the tax-drag on a taxable account, you need to compare the net after-tax future value of a taxable account to the future value of a tax-free account. These values are then plugged into the following formula:
Where:
We can define the ending value of a tax-free account as follows:
The formula above is essentially the future value formula with a different set of variables. Recall, that the future value of a taxable account adjusts the rate of return by a quantity that takes into account annual accrual based taxation:
Assume you made a $1,000 investment into a security that was projected to pay a 4% dividend for ten years, with an annual dividend tax of 30%. What is the tax-drag on the taxable account relative to the tax-free account?
In order to calculate the tax-drag we need to plug the variables into both future value formulas:
Plugging those same values to solve for the ending value of the taxable account yields the following:
Now that we have calculated the ending values for both the tax-free and taxable accounts, we can plug those values into the tax-drag formula:
Notice that the tax-drag of 33.7% is higher than the annual tax rate of 30%. The additional tax erosion above and beyond the 30% annual rate of taxation is due to paying 30% every year in the taxable account, relative to not paying any taxes in the tax-free account.
We can illustrate the longer term detrimental effects of tax-drag by constructing a tax-drag table. Using Excel, let’s compute a future value table for a tax-free account, assuming an annual tax rate of 30%:
| Rate | ||||||
| 2% | 3% | 4% | 5% | 6% | 7% | |
| Year | ||||||
| 1 | $ 1,020.00 | $ 1,030.00 | $ 1,040.00 | $ 1,050.00 | $ 1,060.00 | $ 1,070.00 |
| 2 | $ 1,040.40 | $ 1,060.90 | $ 1,081.60 | $ 1,102.50 | $ 1,123.60 | $ 1,144.90 |
| 3 | $ 1,061.21 | $ 1,092.73 | $ 1,124.86 | $ 1,157.63 | $ 1,191.02 | $ 1,225.04 |
| 4 | $ 1,082.43 | $ 1,125.51 | $ 1,169.86 | $ 1,215.51 | $ 1,262.48 | $ 1,310.80 |
| 5 | $ 1,104.08 | $ 1,159.27 | $ 1,216.65 | $ 1,276.28 | $ 1,338.23 | $ 1,402.55 |
| 6 | $ 1,126.16 | $ 1,194.05 | $ 1,265.32 | $ 1,340.10 | $ 1,418.52 | $ 1,500.73 |
| 7 | $ 1,148.69 | $ 1,229.87 | $ 1,315.93 | $ 1,407.10 | $ 1,503.63 | $ 1,605.78 |
| 8 | $ 1,171.66 | $ 1,266.77 | $ 1,368.57 | $ 1,477.46 | $ 1,593.85 | $ 1,718.19 |
| 9 | $ 1,195.09 | $ 1,304.77 | $ 1,423.31 | $ 1,551.33 | $ 1,689.48 | $ 1,838.46 |
| 10 | $ 1,218.99 | $ 1,343.92 | $ 1,480.24 | $ 1,628.89 | $ 1,790.85 | $ 1,967.15 |
Let’s do the same for a taxable account:
| Rate | ||||||
| 2% | 3% | 4% | 5% | 6% | 7% | |
| Year | ||||||
| 1 | $ 1,014.00 | $ 1,021.00 | $ 1,028.00 | $ 1,035.00 | $ 1,042.00 | $ 1,049.00 |
| 2 | $ 1,028.20 | $ 1,042.44 | $ 1,056.78 | $ 1,071.23 | $ 1,085.76 | $ 1,100.40 |
| 3 | $ 1,042.59 | $ 1,064.33 | $ 1,086.37 | $ 1,108.72 | $ 1,131.37 | $ 1,154.32 |
| 4 | $ 1,057.19 | $ 1,086.68 | $ 1,116.79 | $ 1,147.52 | $ 1,178.88 | $ 1,210.88 |
| 5 | $ 1,071.99 | $ 1,109.50 | $ 1,148.06 | $ 1,187.69 | $ 1,228.40 | $ 1,270.22 |
| 6 | $ 1,087.00 | $ 1,132.80 | $ 1,180.21 | $ 1,229.26 | $ 1,279.99 | $ 1,332.46 |
| 7 | $ 1,102.21 | $ 1,156.59 | $ 1,213.25 | $ 1,272.28 | $ 1,333.75 | $ 1,397.75 |
| 8 | $ 1,117.64 | $ 1,180.88 | $ 1,247.23 | $ 1,316.81 | $ 1,389.77 | $ 1,466.24 |
| 9 | $ 1,133.29 | $ 1,205.68 | $ 1,282.15 | $ 1,362.90 | $ 1,448.14 | $ 1,538.08 |
| 10 | $ 1,149.16 | $ 1,231.00 | $ 1,318.05 | $ 1,410.60 | $ 1,508.96 | $ 1,613.45 |
With these two tables, we can now compute a tax-drag table using the values above:
| Rate | ||||||
| 2% | 3% | 4% | 5% | 6% | 7% | |
| Year | ||||||
| 1 | 30.00% | 30.00% | 30.00% | 30.00% | 30.00% | 30.00% |
| 2 | 30.21% | 30.31% | 30.41% | 30.51% | 30.61% | 30.71% |
| 3 | 30.42% | 30.62% | 30.83% | 31.03% | 31.23% | 31.43% |
| 4 | 30.63% | 30.93% | 31.24% | 31.55% | 31.85% | 32.15% |
| 5 | 30.83% | 31.25% | 31.66% | 32.07% | 32.47% | 32.87% |
| 6 | 31.04% | 31.56% | 32.08% | 32.59% | 33.10% | 33.61% |
| 7 | 31.26% | 31.88% | 32.50% | 33.12% | 33.73% | 34.34% |
| 8 | 31.47% | 32.20% | 32.92% | 33.65% | 34.37% | 35.08% |
| 9 | 31.68% | 32.51% | 33.35% | 34.18% | 35.00% | 35.82% |
| 10 | 31.89% | 32.83% | 33.77% | 34.71% | 35.64% | 36.57% |
As you can see, the importance of sheltering gains from taxation (in a legal manner of course) becomes extremely important the longer the time frame, the higher the tax rate, and the higher the expected level of return. Based on the table above, the tax-drag on an investment with a 7% rate of return over 10 years is 36.57%, which is much higher than 30%.
Understanding the impact of tax-drag illustrates the importance of having a tax-diversification strategy in addition to an asset diversification strategy. For instance, hold longer term capital appreciating securities which pay no dividends or interest in a taxable account, while investing in interest bearing and dividend paying securities inside of tax-sheltered accounts such as Traditional IRAs and Roth IRAs or employer sponsored retirement plans.
Generally speaking, if taxes are paid on an annual basis the tax-drag will be greater than the tax rate. Conversely, if taxes are deferred until the end of the period the tax-drag will be equal to the tax rate.
A copy of the Excel model used to construct the tax-drag table can be found here.