# Growth versus income: comparing "apples and oranges." (Personal Financial Planning)

Who was it who said that compound interest is the "eighth wonder of the world"? Whoever it was, he or she was among the few people who really appreciate the impact of long-term compounding.An investor was curious about the long-term difference between letting money accumulate in tax-deferred growth stocks versus fixed-income investments that generate taxable income. Others gave me cause to compare taxable and tax-exempt investments versus qualified plan investments such as a pension plan.

To answer these questions I used a Lotus 1-2-3 spreadsheet. From having done so, a few lessons were learned.

Adjusted Yield Rates Can Be Misleading

It's easy to compare a taxable bond investment to a tax-free investment where there is no deferral of taxes involved. You just need to adjust the after-tax yield for the investor's tax bracket. Where a taxable investment pays a 6% return and the investor has an effective rate of 33%, the after-tax return is 4%. Any tax-exempt yield of 4% or more is going to produce a higher net return, as long as you assume an equal risk factor for both investments.

But how can you compare a tax-deferred investment to a currently taxable investment? What about the impact of time? Stock funds are not subject to a tax until sold. If a $1,000 investment is compounded at 10% for 10 years, the result is about $2,600. If we assume a 30% tax bracket on the $1,600 of gain, the tax will be $480, and the after-tax investment will be worth $2,120.

What if you could find a fixed-income investment that paid 7% per year? It would be worth $1,967 after 10 years of compounding. The taxable stock investment results in more money than the tax-free investment with the same after-tax yield rate. Comparing after-tax rates doesn't give the full story. With longer periods of time and with higher assumed tax rates, the differences will be more dramatic.

The "real rate of return" is generally deemed as the gross yield (income plus growth), minus the rate of inflation. Please note that the rate of return ignores taxes.

On the other hand the after-tax rate of return ignores inflation.

What is seldom discussed by anyone is the after-tax real rate of return. That's the after-tax rate of return minus the inflation rate. Table 1 presents a few comparisons where the gross rate of return increases by the same rate as the inflation rate.

As the rate of inflation increases, the after-tax real rate of return decreases, even though the nominal rate of return increases in exact proportion to the inflation rate.

However, if the tax burden can be deferred, the real rate of return will adjust for any inflation. (If inflation rates do not exceed about 5% to 7%.)

Making Long-Term Comparisons

Over time, inflation takes its toll in different ways depending on the type of investment and how taxes are being deferred.

In order to compare tax-deferred investments and taxable investments for periods of more than a year, I created a worksheet template to make the projections for up to 25 years. I made calculations for four types of investments: fully taxable in the year income is received, fully tax exempt in the year received, tax deferred on the income until the end of the period, and investments held in a qualified retirement plan. The results, are examples of one set of possibilities to compare the after-tax inflation adjusted benefits of the four different types of savings alternatives for up to 25 years.

The "balance at 25 years" is the amount left in each account. The "balance after tax" is the amount that would be left if the total account were cashed in and any deferred taxes paid. In the first two columns, the taxes have already been taken into account. In the third column, it's assumed that the balance is cashed in and taxed at a long-term capital gain rate of 28%. For the qualified retirement plan column, the initial investment is "grossed up" to reflect the pre-tax equivalent of the after-tax investment in the other three columns. Then, the same income tax rate is used to reduce the account balance as if it were cashed in. The tax rate would not be at capital gain rates, but at the ordinary income rates in effect at the time the account was paid.

Thc "inflation adjusted" row is based on a discounted index factor computing by discounting the previous year's index by 1, minus the assumed inflation rate.

The "CPI adj. draws" is an abbreviation for "consumer price index adjusted withdrawals." The amounts withdrawn each year are multiplied by the CPI discount rate for that year and then added together.

The last row for "25 year adj. totals" represents the after-tax, inflation-adjusted balance in each account, plus after tax, inflation adjusted withdrawals from each account.

TABLE 1 REAL AFTER-TAX RETURN Gross rate of return 3.00% 5.00% 7.00% Inflation rate none 2.00% 4.00% Real rate of return 3.00% 3.00% 3.00% Gross rate of return 3.00% 5.00% 7.00% Income tax rate 30% 30% 30% After-tax rate of return 2.10% 3.50% 4.90% Inflation rate none 2.00% 4.00% After-tax real rate of return 2.10% 1.50% .90% TABLE 2 COMPARISON OF REAL AFTER-TAX RETURN Qualified Retirement Taxable Exempt Deferred Plan Beginning fund $100,000 $100,000 $100,000 $100,000 Gross yield 8.00% 8.00% XXXX 8.00% Growth rate XXXX XXXX 8.00% XXXX Tax rate 28.00% XXXX XXXX 28.00% Withdrawal rate 5.00% 5.00% 5.00% 5.00% Inflation rate 4.00% 4.00% 4.00% 4.00% Capital gain rate XXXX XXXX 28.00% XXXX Balance at 25 years $120,838 $209,378 $209,378 $209,802 Balance after tax 120,838 209,378 178,969 209,378 Inflation adjusted 43,549 75,459 64,500 75,459 CPI adj. draws 82,853 105,175 102,924 105,175 25 year adj. totals $126,402 $180,634 $167,424 $180,634

Taxable Savings Projection

To replicate my computations, you would need to set up a worksheet with the input data shown above. Then you would create four separate sections to project the income, taxes, withdrawals, and inflation over 25 years. In my case, I used separate columns for each year instead of running the years down a single column. (I put the time factor on the horizontal axis.)

In the taxable account section, the initial (after tax) "beginning fund" is invested at the rate shown for the gross yield. That income amount is then used to compute the income tax. The result is multiplied by the withdrawal rate and the withdrawal amount is deducted from the balance after taxes. An inflation index factor is computed for each year by multiplying the previous year's index by 1 minus the assumed rate of inflation. That index is then multiplied by the account balance to get the inflation adjusted balance. Any withdrawals are multiplied by the inflation index for the year of the withdrawal and then added to the accumulated withdrawals from the previous year. Thus, each withdrawal is adjusted for the inflation index rate for the year of the withdrawal.

Tax-Exempt Savings Projections

This section is identical to the previous one except that the gross yield is assumed to be the after-tax yield. The input data for the tax rate and for the capital gains tax rate are set to zero. In most cases, a tax-exempt yield will be significantly lower than a taxable yield, but the example above shows an exempt yield that is equal to a taxable yield. Any variations in the differential in yield rates is part of the input data.

Tax-Deferred Savings Projections

The tax deferred (growth) column is based on the concept of a growth stock (or fund) that does not produce any taxable income. As income is needed for current expenses, part of the accumulated principle is cashed in.

In the deferred (growth) account, the account balance is first increased by the gross yield of 8%. The 5% withdrawal is based on the year-end balance of $108,000, resulting in a draw of $5,400. Only 8% of the draw is assumed to be taxable. The $432 of assumed capital gain is then subject to a tax rate of 28%, resulting in a current tax of $120.96. This method results in a larger annual distribution than the taxable account would generate. Since the distributions are not equal, the accumulated distributions must be added back to the ending balance to make a valid comparison at any point in time.

The taxable account results in a current tax of $2,240, whereas the growth account results in a tax of $120 on just 8% of the amount withdrawn. Each year, the taxable percentage of the total tax deferred growth account will increase of course, but this concept still offers substantial tax deferral. A step-by-step explanation of the worksheet mechanics of adjusting the tax deferred account for a constantly changing tax basis is beyond the size limitations of this discussion; but one important point should be made. Because the rate of withdrawal can be more than, equal to, or less than the growth rate, the adjustment of the tax basis each year has to be based on the lesser of the amount withdrawn or the amount of the current year growth in the account.

Tax Qualified Retirement (Pension) Plan

The fourth comparison assumes that the amount invested is either before tax or deductible against taxable income and the income is not taxable until it is withdrawn. In order to make that choice comparable to the other three, you either need to reduce the amount available for investment by an income tax rate or you need to "gross up" the amount invested in the retirement account. Thus, with a tax rate of 28%, the pre-tax equivalent of a $100,000 after-tax investment would be $138,889 ($100,000/.72). Any distributions are assumed to be fully taxable at that time.

Taxable Versus Tax Deferred

In the example shown, the gross yield is equal for each of the four types of investments. The tax-deferred (growth) investment provides 73% more retirement income than the taxable Investment plan. In addition, the tax-deferred (growth) fund provides 24% more than the taxable investment in after-tax withdrawals, adjusted for inflation. The combined account balance and accumulated withdrawals under the tax deferred plan provide $41,022 more, after taxes and after inflation. Table 3 presents how those amounts and percentages are computed.

The difference is entirely due to taxes because inflation will treat the two accounts the same if all other factors are the same. The taxable account is analogous to the idea of investing your principal and spending your income. At 8% before taxes, the account is increased by 5.76% after taxes and is reduced by 5% for withdrawals. For example, In the first year, the account balance is increased by $8,000 and is reduced by $2,240 in taxes leaving a balance of $105,760 before withdrawals. The 5% withdrawal is based on that balance, resulting in a draw of $5,288.

TABLE 3 COMPARISON OF TWO TYPES OF INVESTMENT Income Income Taxable Deferred Difference Balance at 25 years $120,838 $ 209,378 73.27% CPI adj. draws 82,853 102,924 24.22% 25 year adj. totals 126,402 167,424 $ 41,022

These projections lead me to believe that an investor will have more retirement income by investing for growth than by investing for income because of the differences in taxes. This assumes that the pre-tax yield on the growth investments is equal to the pre-tax yield on the taxable investments. It's even more true when you factor in an adjustment for inflation.

Taxable Versus Pension

In the example shown above, the pension savings account would provide significantly more after-tax income adjusted for inflation than either the taxable or the tax deferred growth fund. The taxable account would produce $126,402 of benefits. The growth fund would produce $167,424 and the pension fund would produce $180,634 of after-tax benefits adjusted for inflation.

In this example, the tax-exempt account would generate the same results as the tax-deductible account because the input data used the same gross yield rate for both accounts. In the real world, the yield available on tax-exempt investments is usually two or three points lower than the yield on taxable investments.

Vernon K. Jacobs, CPA, provides personal financial planning services for individuals and small-business owners. He is the software columnist for a prominent professional journal and is the author/publisher of a newsletter on advanced concepts in financial planning. A copy of the author's worksheet template, catalog, and his newsletter are available to The CPA Journal readers from Research Press, Inc. Box 8194, Shawnee Mission, Kansas. A copy of the Lotus template created for this article can he obtained for a nominal fee.

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Author: | Jacobs, Vernon K. |
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Publication: | The CPA Journal |

Date: | Nov 1, 1994 |

Words: | 2173 |

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