Copyright 1992 by Edward A. Chang
All rights reserved.
This article appeared in the February 1992 NAPFA News. NAPFA is the National Association of Personal Financial Advisors. An updated analytical model is available through my Spreadsheets page.
Index funds tend to have low portfolio turnover, resulting in fewer realized
gains that must be distributed to shareholders. Realized gains are
immediately taxable. Unrealized gains provide a tax-deferred, compounding
effect.
A variable annuity is a vehicle primarily used to defer taxes on gains. It is similar to a non-deductible IRA. However, even if you could invest in your favorite mutual fund, the annual expense ratio would be higher than the same fund without the variable annuity feature.
Many investment advisors use the Standard & Poor's 500 (S&P 500) Composite Stock Price Index as a benchmark for equity investments. It is therefore appropriate to examine the results of investing in an S&P 500 index mutual fund and the same fund offered through a variable annuity.
As you'll see from the analysis of investments of $1 per year, the benefits of using a variable annuity are questionable. In both cases, I assumed the historical S&P 500 total return (capital appreciation + dividends) of 10 percent.
Without Variable Annuity
Based on the Vanguard S&P 500 Index fund distributions of the past decade, I assumed 50 percent of the total return (minus expenses) will be distributed and taxed each year. Note the low .2 percent annual expense ratio. The distribution can be reinvested, but the taxes should be sub-tracted from the value of the account. This results in the figures for the column labeled "End." Assuming a 40 percent tax rate during the life of the investment and a 30 percent retirement tax rate on the accumulated appreciation upon full withdrawal, the account would be worth $102.02 after 30 years ("TV" column).
With Variable Annuity
Here I assumed the variable annuity would have no distributions until termination. The annual expense ratio is 1 percent. With a 30% tax rate upon full withdrawal, the account would be worth $113 after 30 years.
Is having 10.8 percent more after 30 years worth the lack of liquidity?
Note: an enhanced spreadsheet, similar to the one that generated the following analysis, is available through my Spreadsheets page. Bold text items could be changed in the original spreadsheet.
| WITHOUT VARIABLE ANNUITY | WITH VARIABLE ANNUITY | |||||
| F | 50% | Fraction of (Return-Expenses) Paid Out | F | 0% | Fraction of (Return-Expenses) Paid Out | |
| I | $1 | Annual Investment | I | $1 | Annual Investment | |
| T | 40% | Tax Rate for Distributions | T | 40% | Tax Rate for Distributions | |
| E | 0.2% | Expenses | E | 1.0% | Expenses | |
| R | 10% | Return | R | 10% | Return | |
| TF | 30% | Tax Rate for accumulated appreciation | TF | 30% | Tax Rate for accumulated appreciation | |
| * | Value after paying taxes on distributions | * | Value after paying taxes on distributions | |||
| ** | Termination Value after taxes on dist. & apprec. | ** | Termination Value after taxes on dist. & apprec. |
| I | Start | Dist. | Apprec. | End* | TV** | I | Start | Dist. | Apprec. | End* | TV** | |||
| 1 | 1 | 1.00 | 0.049 | 0.049 | 1.08 | 1.06 | 1 | 1 | 1.00 | 0.000 | 0.090 | 1.09 | 1.06 | |
| 2 | 1 | 2.08 | 0.102 | 0.102 | 2.24 | 2.20 | 2 | 1 | 2.09 | 0.000 | 0.188 | 2.28 | 2.19 | |
| 3 | 1 | 3.24 | 0.159 | 0.159 | 3.50 | 3.40 | 3 | 1 | 3.28 | 0.000 | 0.295 | 3.57 | 3.40 | |
| 4 | 1 | 4.50 | 0.220 | 0.220 | 4.85 | 4.69 | 4 | 1 | 4.57 | 0.000 | 0.412 | 4.98 | 4.69 | |
| 5 | 1 | 5.85 | 0.287 | 0.287 | 6.31 | 6.06 | 5 | 1 | 5.98 | 0.000 | 0.539 | 6.52 | 6.07 | |
| 6 | 1 | 7.31 | 0.358 | 0.358 | 7.88 | 7.53 | 6 | 1 | 7.52 | 0.000 | 0.677 | 8.20 | 7.54 | |
| 7 | 1 | 8.88 | 0.435 | 0.435 | 9.58 | 9.09 | 7 | 1 | 9.20 | 0.000 | 0.828 | 10.03 | 9.12 | |
| 8 | 1 | 10.58 | 0.518 | 0.518 | 11.40 | 10.77 | 8 | 1 | 11.03 | 0.000 | 0.993 | 12.02 | 10.81 | |
| 9 | 1 | 12.40 | 0.608 | 0.608 | 13.38 | 12.56 | 9 | 1 | 13.02 | 0.000 | 1.172 | 14.19 | 12.64 | |
| 10 | 1 | 14.38 | 0.704 | 0.704 | 15.50 | 14.47 | 10 | 1 | 15.19 | 0.000 | 1.367 | 16.56 | 14.59 | |
| 11 | 1 | 16.50 | 0.809 | 0.809 | 17.80 | 16.52 | 11 | 1 | 17.56 | 0.000 | 1.580 | 19.14 | 16.70 | |
| 12 | 1 | 18.80 | 0.921 | 0.921 | 20.27 | 18.72 | 12 | 1 | 20.14 | 0.000 | 1.813 | 21.95 | 18.97 | |
| 13 | 1 | 21.27 | 1.042 | 1.042 | 22.94 | 21.08 | 13 | 1 | 22.95 | 0.000 | 2.066 | 25.02 | 21.41 | |
| 14 | 1 | 23.94 | 1.173 | 1.173 | 25.82 | 23.60 | 14 | 1 | 26.02 | 0.000 | 2.342 | 28.36 | 24.05 | |
| 15 | 1 | 26.82 | 1.314 | 1.314 | 28.92 | 26.31 | 15 | 1 | 29.36 | 0.000 | 2.642 | 32.00 | 26.90 | |
| 16 | 1 | 29.92 | 1.466 | 1.466 | 32.26 | 29.21 | 16 | 1 | 33.00 | 0.000 | 2.970 | 35.97 | 29.98 | |
| 17 | 1 | 33.26 | 1.630 | 1.630 | 35.87 | 32.33 | 17 | 1 | 36.97 | 0.000 | 3.328 | 40.30 | 33.31 | |
| 18 | 1 | 36.87 | 1.807 | 1.807 | 39.76 | 35.68 | 18 | 1 | 41.30 | 0.000 | 3.717 | 45.02 | 36.91 | |
| 19 | 1 | 40.76 | 1.997 | 1.997 | 43.96 | 39.28 | 19 | 1 | 46.02 | 0.000 | 4.142 | 50.16 | 40.81 | |
| 20 | 1 | 44.96 | 2.203 | 2.203 | 48.48 | 43.14 | 20 | 1 | 51.16 | 0.000 | 4.604 | 55.76 | 45.04 | |
| 21 | 1 | 49.48 | 2.425 | 2.425 | 53.36 | 47.30 | 21 | 1 | 56.76 | 0.000 | 5.109 | 61.87 | 49.61 | |
| 22 | 1 | 54.36 | 2.664 | 2.664 | 58.63 | 51.76 | 22 | 1 | 62.87 | 0.000 | 5.659 | 68.53 | 54.57 | |
| 23 | 1 | 59.63 | 2.922 | 2.922 | 64.30 | 56.56 | 23 | 1 | 69.53 | 0.000 | 6.258 | 75.79 | 59.95 | |
| 24 | 1 | 65.30 | 3.200 | 3.200 | 70.42 | 61.72 | 24 | 1 | 76.79 | 0.000 | 6.911 | 83.70 | 65.79 | |
| 25 | 1 | 71.42 | 3.500 | 3.500 | 77.02 | 67.27 | 25 | 1 | 84.70 | 0.000 | 7.623 | 92.32 | 72.13 | |
| 26 | 1 | 78.02 | 3.823 | 3.823 | 84.14 | 73.24 | 26 | 1 | 93.32 | 0.000 | 8.399 | 101.72 | 79.01 | |
| 27 | 1 | 85.14 | 4.172 | 4.172 | 91.81 | 79.66 | 27 | 1 | 102.72 | 0.000 | 9.245 | 111.97 | 86.48 | |
| 28 | 1 | 92.81 | 4.548 | 4.548 | 100.09 | 86.57 | 28 | 1 | 112.97 | 0.000 | 10.167 | 123.14 | 94.59 | |
| 29 | 1 | 101.09 | 4.953 | 4.953 | 109.01 | 94.01 | 29 | 1 | 124.14 | 0.000 | 11.172 | 135.31 | 103.42 | |
| 30 | 1 | 110.01 | 5.391 | 5.391 | 118.64 | 102.02 | 30 | 1 | 136.31 | 0.000 | 12.268 | 148.58 | 113.00 |