Measuring the Efficiency of Tax-Favored Investments

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$1.75. $2.07. $1.99. $2.55. 20 Years: Investment will grow to: 2.38. 2.97. 4.30. 6.14. Minus taxes. 0.00. 0.00. 1.08. 1.84. Net Amt. After Taxes. $2.38. $2.97. $3.22.
Measuring the Efficiency of Tax-Favored Investments by Glenn Wood, Ph.D., and Mohsen Attaran, Ph.D.

nvestments can be classified for income tax purposes into four basic categories: (1) taxable, (2) tax-free, (3) tax-deferred, (4) tax-deductible and deferred. 1 Taxable investments have no basic tax advantages and are illustrated by many transactions. A bank CD, for example, requires after-tax dollars and the income it provides is currently taxable. The income on tax-free investments escapes taxation completely, although purchases are made with after-tax dollars. Municipal bonds are the classic example in this category. Tax-deferred investments require after-tax dollars but accumulate on a tax-free basis; that is, taxes are postponed. Annuities and life insurance cash values are good examples. The fourth category is illustrated by qualified retirement plans, individual retirement accounts, simplified employee pensions, and Section 403(b) plans. They are made with before-tax dollars and accumulate on a tax-free basis. Most investors are well aware of the various categories of taxation and the tax advantages of qualified retirement plans. However, a method of measuring the tax efficiency of all the various approaches is not readily apparent. Furthermore, in comparing tax-free with tax-deferred investments, it is not always easy to know which is preferable. An additional complication is the proper evaluation of the

August 1997

ten-percent premature distribution tax associated with qualified retirement plans. Many young investors, for example, are reluctant to maximize their qualified plan and 403(b) plan salary reductions because of the "lack of liquidity." Proposed Approach

Glenn Wood, Ph.D.

One relatively easy method of measuring the efficiency of the various classifications is to use pre-tax dollars that are available for investment. This approach makes the various tax categories comparable. Table 1 is based on this approach and uses the following assumptions: z Tax rate Pre-tax interest rate Tax-free interest rate

30 % 9.0% 7.5%

The gain on taxable investments is taxed each year. Therefore, the after-tax accumulation of taxable investments is simply the amount that will accumulate at the after-tax rate. For purposes of comparability, for each $1 of earnings, only $.70 is available for investment. In Table 1, the net amount after taxes in 30 years for a taxable investment is $.70(1 +.063)3°, or $4.38. The formula for the taxable approach is

MohsenAttaran, Ph.D.

(PV)(1 - t)(1 + kat)n

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amount is available for investment. The tax upon withdrawal is computed only on the gain. W h e n k bt is the before-tax interest rate, the formula is

TABLE 1 The Tax Efficiency of the VariousApproaches

Taxable

Tax Free

Tax Deductible Deferred and Deferred

$1.00 .30 .70

$1.00 .30 .70

$1.00 .30 .70

$1.00 0.00 1.00

Pre-tax Interest Rate After-tax Interest Rate

9.0% 6.3%

7.5% 7.5%

9.0% 9.0%

9.0% 9.0%

5 Years: Investment will grow to: Minus taxes Net Amt. After Taxes

.95 .00 $ .95

1.00 .00 $1.00

1.08 .11 $.97

1.54 .46 $1.08

10 Years: Investment will grow to: Minus taxes Net Amt. After Taxes

1.29 .00 $1.29

1.44 .00 $1.44

1.66 .29 $1.37

2.37 .71 $1.66

Pre-tax $ Available Minus Taxes Net Amt. Availablefor Investment

(PV)(1 - t)(1 + kbt)n t[(PV) (1- t)(1 +kbt)n PV(1 - t)] -

-

-

Without any initial taxation, investments that are both tax-deductible and deferred allow the full one dollar to be invested. Of course, the full amount accumulated, as well as the gain, will be taxed when withdrawn. N e t accumulations with qualified retirement plans can be calculated in this manner: (PV)(1 + k) n

-

-

t[(PV)(1 + k)n].

In practice, distributions from qualified retirement plans upon retirement may receive favorable tax treatment. 3

Observations 15 Years: Investment will grow to: Minus taxes Net Amt. After Taxes

1.75 0.00 $1.75

2.07 0.00 $2.07

2.55 .56 $1.99

3.64 1.09 $2.55

20 Years: Investment will grow to: Minus taxes Net Amt. After Taxes

2.38 0.00 $2.38

2.97 0.00 $2.97

4.30 1.08 $3.22

6.14 1.84 $4.30

25 Years: Investment will grow to: Minus taxes Net Amt. After Taxes

3.50 0.00 $3.50

4.27 0.00 $4.27

6.04 1.60 $4.44

8.62 2.59 $6.03

30 Years: Investment will grow to: Minus taxes Net Amt. After Taxes

4.38 0.00 $4.38

6.13 0.00 $6.13

9.29 2.58 $6.71

13.27 3.98 $ 9.29

where PV is the before-tax amount available for investment, t = marginal tax rate, and k at is the after-tax rate of return. The accumulation with tax-free investments is also quite easy to determine. Since these investments are made with after-tax dollars, only $.70 is available. As a general rule, these investments earn a return that is between 100 to 200 basis points lower

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than comparable taxable returns. The formula for the tax-free approach is (PV)(1 - t)(1 + k*)n where the terms are the same as before, except k* is the tax-free interest rate. Investments in the tax-deferred category accumulate at the pre-tax rate and again only the after-tax

Using Table 1 and 30 years, tax-free investments are 1.4 times more efficient than taxable investments. Taxdeferred vehicles are 1.5 times more efficient, and tax-deductible and deferred securities are 2.1 times more efficient than taxable investments. Note that taxes in the most efficient category have been calculated at the full 30 percent. Stated differently, using the 30-year period in Table 1, the net amount accumulated under each of the tax approaches is equivalent to the following compound annual interest rates: Taxable Tax-free Deferred Deductible & Deferred

5.05% 6.23% 6.55% 7.71%

Increasing the return more than 52 percent (266 basis points) by moving from taxable to deductible and deferred is impressive, indicating that tax-favored approaches may well be worth considerable effort to pursue. Conclusions Figure 1 illustrates the data in Table 1;

Journal of Financial Planning

several conclusions are possible. First, deductible and deferred investments accumulate the largest after-tax amount for all periods. Second, taxable investments accumulate the smallest after-tax amount for all periods. Third, the desirability of tax-free versus tax-deferred depends on the time period. For shorter periods, the tax-free approach is preferable. However, for longer periods, the deferral of the higher-interest return on the tax-deferred approach more than offsets the advantage of tax-free income. The critical factor here is the difference between the assumed tax-free rate of return (7.5 percent in our model) and the assumed rate of return on the tax-deferred investment. With a spread of 1.5 percentage points, as we have assumed, the break-even point is 20.8 years, as shown in Table 2. With a narrower spread--say, one percentage point--it takes more than 36 years for the tax-deferred return to overtake the tax-free return. However, with a spread of 2.5 percentage points, tax-deferred investments become advantageous in only five years. Some financial advisors use a rule of thumb of ten years as the approximate crossover point between tax-free and taxdeferred. Table 2 shows this rule has some basis but can be extremely dangerous under certain conditions. A common mistake is to place excessive importance on the wellknown ten-percent penalty tax on premature distributions from qualified plans. Using the original assumptions, Figure 2 includes all taxes, including the penalty tax, and the break-even point is 11 years between tax-free and tax deductible and deferred. Table 3 is a comparison between tax-free and tax-deductible and deferred with the ten-percent penalty tax. With a small spread--for example, one percentage point--the premature distribution penalty makes the deductible and deferred approach less desirable than the tax-free approach for the first 16.9 years. O n the other hand, with a larger spread, the penalty tax is overcome much faster. It is important to note that Table 3 is a function of the spread between

August 1997

TABLE 2 Tax Free Vs. Tax Deferred

Break-even Year

Interest Rate Spread

36.1 20.8 12.0 5.0

1.0 Point 1.5 Point 2.0 Point 2.5 Point

FIGURE 1 The Cumulative Total Return of $1 Investment (without penalty)

12

Deductible and Deferred 10

Tax Deferred

8!

..................[ ]

-

I

5-Year

I

10-Year

I

15-Year

I

Tax Free

Taxable

I

20-Year

25-Year

30-Year

pie, the break-even point is 20.8 years in Table 2 with a 1.5 percent spread when the tax-free rate is 7.5 percent. However, if the tax-free rate is 5 percent and the taxable rate is 6.5 percent, the break-even year is 14. W h e n

the interest rates--not the level of interest rates. In other words, the break-even year is 11 with a spread of 1.5 percentage points when the taxfree rate is 7.5 percent and the taxable rate is 9 percent. The break-even year ~i(~ ii)/~i/i ~I::~ i !:i:i~: i ( / i ~::~~! : i/i

...................

:i

i:~~~(I:~I:I: i i i ( ! ! ~ iii

....i~i~/:;~'i~I i: •

..... •

Most investors are well aware of the various categories of taxation and the tax advantages of qualified retirement plans. However, a method of measuring the tax efficiency of all the various approaches is not readily apparent.

would be the same if the tax-free rate were, say, 5 percent and the taxable rate 6.5 percent. Interestingly, Table 2 is very sensitive to the level of interest rates--not only the spread. For exam-

the tax-free rate is 9 percent and the taxable rate is 10.5 percent (still a spread of 1.5 percentage points), the break-even year is 23. In general, the lower the level of interest rates, the

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is simply to decrease the investment return by the expense factor. For example, with the deductible and deferred approach, accumulations will be: (1 + k e)n _ t( 1 + k - e)% where "e" is the level percentage expense factor. Using the assumptions in Table 1 and a constant expense loading of 2.81 percent, the accumulation in 20 years with the deductible and deferred approach would be

TABLE 3 Tax Free Vs. Deductible & Deferred*

Interest Rate Spread

Break-even Year

1.0 Point 1.5 Point 2.0 Point 2.5 Point

16.9 11.0 8.4 6.7

* Assuming 10% penalty

(1 + .095 - .0281)i° -.3 (1 + .095 - .0281)2° = $2.55

FIGURE 2 The Cumulative Total Return of $1 Investment (with 10% penalty)

10 Deductible and Deferred 8

Tax Deferred

........ [] .............Tax Free 6

[] =

Taxable

4

2 •

......

I

0 5-Year

I

lO-Year

15-Year

20-Year

sooner the tax-deferred approach will overtake the tax-free approach. When fitting assumptions for current economic conditions, it may be important to recognize expenses. The administrative expenses associated with defined benefit pension plans, for example, can be onerous, especially in small plans. Defined contribution plans and IRAs are much less costly. Investment commissions and expenses also should be considered before reaching a final conclusion.41

Endnotes 1.

2.

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These are the basic categories. Some investments have combinations of these characteristics. The yield spread between taxable

25-Year

30-Year

and tax-free investments since 1990 has usually been one to two percent. Between 1951 and 1996, the spread averaged about 1.5 percent. See Moody's Municipal and Government Manual, Vol. 1,

1996, a9. Although the five-year forward averaging rule is being eliminated by recent legislation, some distributions are eligible for IRA rollover treatment and some people are still provided ten-year forward averaging. Recognizing expenses can be troublesome because of the many variations in expense charges. If the expenses are a constant percentage per year, the easiest method of adjusting for expenses

This is exactly the same amount (except for rounding error) that will be accumulated with the taxable approach. In other words, the accumulation will be greater with the deductible and deferred approach as long as the level expense loading is less than 2.81 percent. Note that this is the same answer provided by the growth rates given earlier in the paper; that is, 8.20% - 5.39% = 2.81%.

Glenn Wood has a Ph.D. from the Wharton School at the University of Pennsylvania and teaches at California State University, Bakersfield. He has published several books and numerous articles. His business experience includes ownership of a successful financial planning firm. Mohsen Attaran has a Ph.D. in systems science from Portland State University and teaches at California State University, Bakersfield. He is the author~co-author of 3 books, over 50 papers, and 6 commercial software packages. He has been a consultant for public and private organizations and has conducted numerous workshops and seminars for Fortune 500 companies.

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