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Nov 1994 Growth versus income: comparing "apples and oranges." (Personal Financial Planning)by Jacobs, Vernon K.
An investor was curious about the longterm difference between letting money accumulate in taxdeferred growth stocks versus fixedincome investments that generate taxable income. Others gave me cause to compare taxable and taxexempt investments versus qualified plan investments such as a pension plan. To answer these questions I used a Lotus 123 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 taxfree investment where there is no deferral of taxes involved. You just need to adjust the aftertax 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 aftertax return is 4%. Any taxexempt 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 taxdeferred 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 aftertax investment will be worth $2,120. What if you could find a fixedincome 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 taxfree investment with the same aftertax yield rate. Comparing aftertax 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 aftertax rate of return ignores inflation. What is seldom discussed by anyone is the aftertax real rate of return. That's the aftertax 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 aftertax 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 LongTerm 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 taxdeferred 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 pretax equivalent of the aftertax 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 aftertax, inflationadjusted balance in each account, plus after tax, inflation adjusted withdrawals from each account. TABLE1 REALAFTERTAXRETURN
Grossrateofreturn3.00%5.00%7.00%
Inflationratenone2.00%4.00%
Realrateofreturn3.00%3.00%3.00%
Grossrateofreturn3.00%5.00%7.00% Incometaxrate30%30%30%
Aftertaxrateofreturn2.10%3.50%4.90% Inflationratenone2.00%4.00% Aftertaxrealrateofreturn2.10%1.50%.90% TABLE2 COMPARISONOFREALAFTERTAXRETURN
Qualified Retirement TaxableExemptDeferredPlan
Beginningfund$100,000$100,000$100,000$100,000 Grossyield8.00%8.00%XXXX8.00% GrowthrateXXXXXXXX8.00%XXXX Taxrate28.00%XXXXXXXX28.00% Withdrawalrate5.00%5.00%5.00%5.00% Inflationrate4.00%4.00%4.00%4.00% CapitalgainrateXXXXXXXX28.00%XXXX
Balanceat25years$120,838$209,378$209,378$209,802 Balanceaftertax120,838209,378178,969209,378
Inflationadjusted43,54975,45964,50075,459 CPIadj.draws82,853105,175102,924105,175 25yearadj.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. TaxExempt Savings Projections This section is identical to the previous one except that the gross yield is assumed to be the aftertax yield. The input data for the tax rate and for the capital gains tax rate are set to zero. In most cases, a taxexempt 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. TaxDeferred 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 yearend 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 stepbystep 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 pretax equivalent of a $100,000 aftertax 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 taxdeferred (growth) investment provides 73% more retirement income than the taxable Investment plan. In addition, the taxdeferred (growth) fund provides 24% more than the taxable investment in aftertax 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. TABLE3 COMPARISONOFTWOTYPESOFINVESTMENT
IncomeIncome TaxableDeferredDifference
Balanceat25years$120,838$209,37873.27% CPIadj.draws82,853102,92424.22% 25yearadj.totals126,402167,424$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 pretax yield on the growth investments is equal to the pretax 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 aftertax 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 aftertax benefits adjusted for inflation. In this example, the taxexempt account would generate the same results as the taxdeductible account because the input data used the same gross yield rate for both accounts. In the real world, the yield available on taxexempt 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 smallbusiness 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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