Wharton Financial Institutions Center Personal Finance. Measuring the Tax Benefit of a Tax-Deferred Annuity

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1 Wharton Financial Institutions Center Personal Finance Measuring the Tax Benefit of a Tax-Deferred Annuity David F. Babbel* The Wharton School of Business University of Pennsylvania 3620 Locust Walk, SH-DH Suite 3000 Philadelphia, Pennsylvania babbel@wharton.upenn.edu Ravi Reddy* CRA International John Hancock Tower 200 Clarendon Street, T-33 Boston, Massachusetts hdreddy@yahoo.com August 21, 2009 * Mr. Babbel is Professor of Insurance and Finance at the Wharton School at the University of Pennsylvania, and Senior Advisor to Charles River Associates. Mr. Reddy is a financial engineer at Charles River Associates. They received helpful comments from Mark Meyer, Joseph Paster and Miguel Herce, and especially from the referees to this Journal. The authors take full responsibility for the opinions expressed in this study and any remaining errors.

2 ABSTRACT Measuring the Tax Benefit of a Tax-Deferred Annuity David F. Babbel The Wharton School, University of Pennsylvania Charles River Associates Ravi Reddy Charles River Associates We show how to measure the size of tax benefit arising from the purchase of fixed annuities relative to holding a taxable account composed of stock and fixed income assets o whether traditional or equity-indexed o for both deferred and immediate annuities We demonstrate how the size of tax benefit available from tax deferral depends on five factors: o the length of time the annuity is held during the accumulation and decumulation phases of ownership o whether a deferred annuity is annuitized at the end of the surrender period, or taken as a lump sum distribution o the level of yields net of expenses o tax rates on ordinary income o the differential between tax rates on ordinary income and taxpreferred treatment of dividends and capital gains The impact of tax deferral can be positive or negative, depending on how the aforementioned factors interact Under some circumstances, the benefits from tax deferral can amount to the equivalent of earning more than 200 extra basis per year relative to the taxable alternative This tax advantage can be reduced or increased by embedded expense differentials between insurance products and alternative investments, depending upon the products utilized We analyze how the size of benefits from tax deferral will change if the current tax code reverts to the pre-bush levels, as scheduled We provide a set of formulae that can be used to estimate the size of tax benefit arising from tax deferral under varied scenarios

3 1 Measuring the Tax Benefit of a Tax-Deferred Annuity ABSTRACT In this study, we show how to measure the size of tax benefit arising from the purchase of fixed annuities whether traditional or equity-indexed, and for both deferred and immediate annuities relative to holding a taxable account composed of stock and fixed income assets. We demonstrate how the size of tax benefit available from tax deferral depends on five factors: (1) the length of time the annuity is held during the accumulation and decumulation phases of ownership; (2) whether a deferred annuity is annuitized (either by conversion or by a 1035 exchange) at the end of the surrender period, or taken as a lump sum distribution; (3) the level of yields net of expenses; (4) tax rates on ordinary income; and (5) the differential between tax rates on ordinary income and tax-preferred treatment of dividends and capital gains. We provide a set of formulae that can be used to estimate the size of tax benefit arising from tax deferral under varied scenarios. 1. Introduction Is there a tax benefit for individuals who place their non-qualified funds in tax-deferred vehicles such as traditional fixed annuities (TFAs) or fixed indexed annuities (FIAs, formerly called equity-indexed annuities) as opposed to taxable accounts such as mutual funds? If there is a benefit, how large is it, what factors influence its size, and how does one measure it? Hogan (1994) provides one such measure cross over years which represents the number of years it takes for a tax benefit in tax-deferred accounts to overcome a higher net investment yield in taxable accounts. His analysis is limited primarily to variable annuities, where the yield differential that exists between variable annuities and their taxable counterparts accounts for insurance expense. Moreover, Hogan treats all returns as ordinary income. Preferred tax treatment of equity dividends and capital gains is not considered. Wood and Attaran (1997) compare four different account types taxable, tax-free, tax-deferred (e.g., annuity), and tax-deductible and deferred (e.g., 401(k) plans). They show that taxable accounts are the least efficient of the four with respect to taxes. Their analysis is also based on the assumption that all returns are taxed as ordinary income and not preferentially as capital gains or dividends. Hogan (1994) and Neimeyer (1999) mention that an individual can attain an additional tax benefit by opting for a payout in the form of an immediate annuity; however, neither author attempts to quantify this added benefit. In this study we provide a general framework to assess the tax benefit of tax-deferred accounts relative to taxable accounts. This is done by distinguishing the returns in the taxable accounts to be of three kinds: (1) ordinary income taxed immediately at the investor s marginal tax rate, (2) capital gains taxed only at the end of the investment time horizon at a preferred tax rate (i.e., we assume no turnover in the taxable account, thereby inflating somewhat the assumed performance of that account), and (3) dividends taxed immediately at a preferred tax rate. We consider the tax benefit over both the accumulation and decumulation periods. Our concern here is with living benefits available through both taxable and tax-deferred accounts. We do not consider the stepped-up basis for bequest in the case of death of the owner of a taxable account.

4 In Section 2, we discuss the major factors that influence the size of tax benefit from a tax-deferred account over a taxable account. i Next, in Section 3, we present methodology and formulae to compute after-tax payouts for both account types (tax-deferred and taxable) and two payout options (lump sum or immediate annuity). ii The after-tax payout for an individual electing the immediate annuity payout option is computed after determining her exclusion ratio, which dictates the percentage of annuity income excluded from taxable income. Finally, in Section 4 we present the results using these formulae. The tax benefit of a tax-deferred account is expressed in terms of a yield spread. The yield spread is defined as the additional yield, net of expenses, that an alternative, taxable account must earn in order to match the after-tax performance of a taxdeferred account. We show that in some situations this yield spread is negative while in other situations it can exceed 200 basis points per year under today s yield and tax environment. Over the past several years, the benefit of tax deferral has been lower than historically, and probably lower than what will unfold in the future. This can be traced primarily to two factors. First, tax rates particularly dividend and capital gains tax rates are at historic lows. Second, interest rates are flirting with low levels not seen since the 1950s. Our study is written at a time when tax schedules are likely to change. Coupled with the unprecedented borrowing requirements of our federal government, interest rates are unlikely to remain where they are currently. If tax rates and interest rates both rise, the tax benefit of annuities will increase beyond its current levels. The analysis that follows will provide charts and formulae that will enable the reader to estimate the tax benefit as these changes unfold. 2. Factors Several factors influence the yield spread that measures the tax benefit of tax-deferred annuities over taxable accounts, including: 1. Investment yield 2. Investment time horizon (accumulation phase) 3. Portfolio mix of the taxable account 4. Payout option lump sum or conversion to an immediate annuity 5. Tax regime capital gains tax, dividends tax, and ordinary income tax Although the investment yield is stochastic in nature, in order to focus solely on the tax benefit it is best initially to hold yields constant and equal across the two accounts. iii Investment horizon will also be set equal for both accounts. Portfolio mix refers only to the taxable account, since all gains in the tax-deferred account are treated as ordinary income. The portfolio in the taxable account is allocated between two types of assets: (1) those that generate interest income, and (2) those that generate tax-preferred income such as capital gains and dividends. We will examine various combinations of ordinary and tax-preferred income in the taxable account. Insofar as taxpreferred equity income factors into the taxable portfolio, we will assume that one-fourth stems from dividend payments, while three-fourths relate to capital gains. iv Because of the capital gains component in these yields, over time the asset values in the tax-preferred portion of the taxable account will climb to the extent that equity income plays a role. This will require a small amount of rebalancing each year in order to maintain constant proportions between ordinary income and tax-preferred income in the taxable account. In this study we will ignore the tax consequences of rebalancing, which would otherwise favor tax-deferred annuities by 5 to 7 basis points per year over the accumulation period. 2

5 3 We found that the tax benefit depends mainly on two factors: (1) the share of assets that generate returns with a preferred tax rate, and (2) the method of payout lump sum or immediate annuity. Other factors, such as investment yield, investment time horizon (also referred to as accumulation period), and tax regime also influence the extent of the benefit and in a few cases can reverse the tax benefit. Because of the considerable uncertainty that exists regarding our current tax regime, we will ignore the traditional attraction of deferring income into a future period when individuals historically expected to face lower marginal tax rates. 3. Methodology The primary motivation of this study is to measure tax benefit, whether positive or negative, in terms of yield spread. We assume equal initial investments in the taxable account and the tax-deferred annuity, and equal pre-tax yields, net of expenses. As the tax benefit depends on several factors mentioned above, we studied the effect of each factor independently while others were held constant. The following is a list of constant values assumed in our base case: 1. Investment yield of 6% 2. Accumulation period horizon of 14 years 3. Portfolio mix of 50%-50% in fixed income and equities, or 100% in fixed income and 0% in equities. 4. Tax regime a. Capital gains tax of 20% (5% state tax included) b. Dividends tax of 20% (5% state tax included) c. Ordinary income tax of 40% (5% state tax included) 5. Age at end of accumulation period is 65 years. These base case assumptions facilitate the isolation of any tax benefit. Elsewhere, we determine how much more a taxable account would need to yield, pre-tax, to offset the benefits of tax deferral. Later, each of these factors will be changed so that we can examine its effect on the value of tax deferral. The formulae used in this study are presented in Appendix A. There are four formulae for two payout options and two account types tax-deferred and taxable accounts. The yield for the taxable account is changed until its payout equals the tax-deferred annuity payout. The yield spread is calculated as the difference between the two yields. Both payouts are calculated on an after-tax basis. In the case of an immediate annuity payout election, the after-tax income is calculated by factoring in the exclusion ratio that determines the taxable portion of the income. A positive yield spread indicates the taxable account would need to yield more in order to purchase an after-tax payout equal to that from the tax-deferred account. A negative yield spread indicates the opposite Exclusion Ratio Calculation For non-qualified accounts under the annuity payout election, both taxable and tax-deferred accounts provide the benefit of some income being excluded from taxes. The portion of annuity income excluded is determined by an exclusion ratio, which is aimed at returning principal (i.e., tax basis) over time without incurring double taxation. In the case when a tax-deferred account is converted into an immediate annuity, either through the exercise of its annuitization provision or through a 1035 exchange, tax on the gains is further deferred until the gains are received as income. The equivalent of a 1035 exchange does not exist when converting a taxable account to an immediate annuity. Therefore taxes are paid when the taxable account is liquidated,

6 which in this study is assumed to occur at the end of the accumulation period to enable the purchase of the immediate annuity. v The exclusion ratio for an immediate annuity is defined by the following formula: 4 Exclusion Ratio = Net Cost Annuitant's Life Expectancy Annual Income Basis Value of Expected Benefits Net cost, or basis, is the original principal of the deferred annuity (for tax-deferred accounts) or the total accumulated value less taxes (for taxable accounts). vi The annuitant s life expectancy is determined by Table V of IRS Publication 939 and is the same regardless of the source of the funds (taxable or taxdeferred accounts). Annual income can be derived by multiplying the accumulated value (less tax) by the annuity factor. vii For example, a 65-year-old male who purchases a $100,000 immediate annuity will receive income of $8,704 annually. This individual has a life expectancy of 20 years according to the IRS, which implies that the individual has an expected lifespan of 85 years (20 years beyond age 65). Using the formula above, we obtain an exclusion ratio of 0.57, implying that 57 percent of the income generated through the immediate annuity is excluded from taxes for all payments until the individual reaches life expectancy. An 80-yearold male purchasing the same $100,000 immediate annuity would receive $12,287 of income annually. This individual s life expectancy is 9.5 years. Using the formula above, we can determine that 86 percent of that individual s annuity income will be excluded from taxes. The exclusion ratio allows for the return of already-taxed principal (basis) over the remaining expected lifetime of the individual. The exclusion ratio is higher for the 80-year-old individual than for the 65-year-old because the expected remaining lifetime is shorter for the 80-year-old (9.5 years) than for the 65-year-old (20years) Effect of Exclusion Ratio The tax-deferred account can be converted into an immediate annuity directly or through a 1035 exchange. Neither of these is a taxable event. Therefore, the annual income (in the denominator of the exclusion ratio) for the tax-deferred account is derived using the entire accumulated account value, whereas the annual income for the taxable account is derived using the accumulated account value, less taxes paid. The result is a higher gross monthly income for the tax-deferred account compared to the taxable account. viii Conversely, the exclusion ratio is greater for immediate annuities purchased entirely from cash after fully liquidating a taxable account than for an immediate annuity purchased using existing annuity funds that already have an embedded tax-deferred gain. This is due to two factors a higher numerator and a lower denominator. For immediate annuities purchased through taxable accounts, the basis (numerator) is defined as the accumulated balance less taxes; for immediate annuities purchased through tax-deferred accounts, it is defined as the original principal used to purchase the tax-deferred annuity. Therefore, unless all of the portfolio gains on the taxable account were lost to taxes, the basis for taxable accounts is larger than that for tax-deferred accounts, assuming positive returns on investment. Additionally, the annual income (denominator) is smaller when one liquidates a taxable account to purchase an immediate annuity than when one liquidates a tax-deferred account to do so. This is because converting the tax-deferred account into an immediate annuity does not trigger a tax event, but liquidating a taxable account will result in ordinary income tax as well as capital gains tax. This leaves a smaller amount in the taxable account with which to purchase the annuity, resulting in a lower pre-tax annual income.

7 At this point it is useful to introduce a numerical example to illustrate how the factors interact to produce tax-advantaged income. Consider a 51-year-old male who opens two accounts with $100,000 in each. The first account is tax-deferred and the second account is taxable. Both accounts earn 7% per year during the accumulation phase, which spans 14 years. In addition, this individual is taxed at 40% on ordinary income and 20% on dividends and capital gains during the entire accumulation and decumulation phase. We will assume for the purposes of this example that the taxable account produces only ordinary income. At age 65, the individual draws down the accumulated value in both accounts using an immediate annuity that provides him with constant periodic income for the rest of his life. 1. Amount available to purchase immediate annuity at the end of 14 years: a. Tax-deferred account = $100,000 x = $257,853 b. Taxable account = $177,889 (Refer to Part III in the formulae section of Appendix A.) c. Note that the tax-deferred account is before tax and the taxable account is after tax. This is because tax-deferred accounts can be converted into immediate annuities without triggering a tax event. d. Also, note that the taxable account formula takes into account an implicit rebalancing each year. 2. Gross Income a. Tax-deferred account = $257,853 x = $22,444 b. Taxable account = $177, 889 x = $15,484 c. The annuity factor is from Vanguard.com (February 2008). This represents the amount of income that can be received by purchasing immediate annuity with $1. d. The gross income is different for the tax-deferred account and taxable account since the amount available to purchase the immediate annuity is different for both the accounts. 3. Exclusion Ratio: a. Tax-deferred account = 22% b. Taxable account = 57% c. Refer to exclusion ratio formula in Part IV and Part V of the formulae section at the end of the paper. In this case, the man will have a remaining life expectancy of 20 years. d. These exclusion ratio figures should not be confused with other exclusion ratio figures presented in the paper since they correspond to a different example, where the immediate annuity was purchased entirely with after-tax dollars. 4. Net Income: a. Tax-deferred account = $15,467 b. Taxable account = $12,848 c. Refer to Part IV and Part V of the formulae section at the end of the paper. These formulae were used to convert the gross income into net income. d. The difference between the two accounts is approximately $2,500 and this is the amount we revisit in Section 4.1, in the paragraph preceding Figure 1. With an understanding of these numerical relationships, we proceed to the results of our analysis. The next section presents our results using the assumptions stated here in Section 3 and formulae from Appendix A. 4. Results We first outline the results from adjusting the factors affecting the tax benefit of a tax-deferred annuity. Our analysis looks at a taxable portfolio with 50% to 100% of ordinary income. We do not analyze a taxable portfolio that has no ordinary income, because we are comparing the tax implications of fixed annuities 5

8 (traditional or indexed) to taxable portfolios. A taxable portfolio with no ordinary income would most likely be comprised of municipal bonds and/or equities. Municipal bonds do not provide the same pre-tax yields as taxable bonds of similar tenor and credit quality. Equity returns are vastly different from the returns and guarantees associated with TFAs, although under certain conditions a 50% weight on equities and a 50% weight on fixed income securities can approximate the initial hedge ratio of the equity derivative element of certain FIAs. Accordingly, we referenced the fixed annuities to a taxable portfolio comprised of either 0% equities or 50% equities After-Tax Annual Income We compare the after-tax annual income of both the tax-deferred annuity and the taxable account after they are converted to an immediate annuity. In later sub-sections we present the results for both payout options immediate annuity and lump sum payout. Although both payout options exist, converting some of one s accumulated savings to an immediate annuity is a logical choice for an individual whose goal is to maintain his current income level during retirement. Because the exclusion ratio is different for the two accounts, using before-tax annuity income to assess the tax advantage could yield inaccurate results. Therefore, we use after-tax income to compare the tax advantage between the two accounts. We assume that the individual who is converting is a 65-year-old male. Our conclusions are similar for females. In Section 4.5 we adjust the age of the individual and present our results. Figure 1 shows the after-tax annual income from both account types for $100,000 invested at the beginning of a 14-year accumulation phase. We show these figures across a wide range of yields from 3% to 10%. This is the range reflecting historical yields since 1995 on fixed annuities, both traditional and indexed. ix Regardless of the pre-tax yield, the after-tax annual income is greater for the tax-deferred account than that of the taxable account when payouts are received via annuitization. x For example: a taxable account with 100 percent ordinary income and a yield of seven percent will produce $2,500 less in annual after-tax income than a tax-deferred account with the same yield. This difference increases as the yield rises. Figure 1: After-Tax Annual Income per $100,000 Invested 6

9 4.2. Investment Time Horizon Here we measure the tax benefit in terms of the yield spread as the accumulation horizon is adjusted from five to thirty years, while assuming the base case where both accounts earn 6% annually. Again, a positive yield spread means the taxable account must out-perform the tax-deferred account in terms of pre-tax yield, while a negative spread indicates the opposite. Figure 2 shows results for both payout options lump sum and immediate annuity. Figure 2: Effect of Time Horizon on Yield Spread 7 If the payout is taken as a lump sum (Panel A), the yield spread is positive provided that the time horizon is greater than 20 years or if 100 percent of the assets produce ordinary income, but the yield spread is negative for durations less than 20 years and where only 50 percent of the assets produce ordinary income. If the payout is taken as an immediate annuity (Panel B), then the yield spread is positive for all time horizons and for any portfolio that has 50 percent or more returns as ordinary income. This spread is based simply on the after-tax account balances for both accounts at the end of the accumulation horizon. For example, under a 15-year accumulation period, if an individual purchased a taxable investment comprised entirely of assets that generate ordinary income and she decided to annuitize the payout at age 65, then she would need to earn an additional yield (yield spread) of around to two percent annually. The yield spread is close to one percent under the same accumulation period if she opts for a lump sum payout regardless of the age the payout is received. This figure shows that in many cases, assets invested in taxdeferred accounts will achieve greater after-tax yields than assets invested in taxable accounts when both accounts have equivalent pre-tax yields, under the assumption that any capital gains in the taxable account will be recognized on the eve of the individual s retirement. If a lump-sum payout is elected, an individual can match or exceed the yield she would achieve with tax-deferred assets only by purchasing in sufficient quantity assets that generate capital gains and/or dividends (generally these types of assets are considered to be riskier).

10 4.3. Percentage of Ordinary Income The percentage of ordinary income specifies the portion of the portfolio generating returns that are taxed at ordinary income tax rates (which currently are higher than the capital gains and dividends tax rate). The remainder of the portfolio generates returns that have a preferred tax rate. Figure 3: Effect of Ordinary Income on Yield Spread 8 The orange line in Figure 3 shows that for an annuitized payout option, the yield spread is positive and increasing as the portion of returns in taxable accounts attributed to ordinary income increases from 50 percent to 100 percent. The blue line shows that the yield spread is positive for lump-sum payouts when at least 64 percent of the returns in the taxable accounts are attributable to ordinary income. A positive yield spread implies that in order to match the periodic payouts of a tax-deferred annuity an individual investing in a taxable account must either invest more initial principal or seek investments with greater pre-tax yields than the tax-deferred investment Investment Yield In this section, we adjust the investment s assumed yield on both accounts over a range from three percent to ten percent and measure the impact on yield spread. Figure 4 shows the results of our analysis. If an investor elects a lump-sum payout (Panel A), the yield spread is positive when the portfolio assets yield is 100% ordinary income or, in the case of only 50% ordinary income, when the investment yield exceeds 9 percent. If an individual elects an annuitized payout (Panel B), then the yield spread is positive for all investment yields when the portfolio has 50 percent or more returns as ordinary income.

11 9 Figure 4: Effect of Investment Yield on Yield Spread This implies that the investor who purchases taxable investments will need to hold more of the assets that generate capital gains (which generally carry more risk) and opt for the lump-sum payout in order to match or exceed the performance of a tax-deferred annuity. The yield spread for individuals who receive all ordinary income and choose to convert to an immediate annuity is close to two percent even when the investment yield is about six percent. The yield spread is an increasing function of investment yield. This implies that the yield spread increases as investment yield increases regardless of the payout type or portfolio composition. Indeed, annual yield spreads exceed 3.5 percent in certain cases when the payout is taken in the form of an annuity (Panel B) Age at Conversion to an Immediate Annuity The age at conversion to an immediate annuity impacts the speed with which the tax benefit from the taxdeferred annuity is received. Federal law dictates that the principal used to purchase the annuity is returned to the annuity holder by the time she reaches her life expectancy. This return of principal is not taxed. This law is implemented in the exclusion ratio, which increases as one ages, all other variables remaining constant. Exclusion ratios are larger for taxable accounts than for tax-deferred accounts because the net basis is greater for taxable accounts (see section 3.1). Note that a larger exclusion ratio does not necessarily mean that annuities purchased through taxable accounts have a tax advantage. This is because the gross income would be lower for taxable accounts than for tax-deferred accounts, assuming that both accounts started with the same initial investment and earned the same gross rate of return during the accumulation phase. The exclusion ratio does not impact taxes after one reaches her life expectancy. At this age and beyond, all income is taxed. xi Therefore, beyond life expectancy, before-tax income is a good metric for comparing the two account types; after-tax income is a good metric for comparing the two account types before reaching life expectancy. Figure 5 shows the percentage by which annual income from a tax-deferred account exceeds (or lags) annual income from a taxable account.

12 10 Figure 5: Excess Income at Conversion to Immediate Annuity for Tax-Deferred Investments versus Taxable Investments In Panel A (50 percent ordinary income) at age 65, annual income from a tax-deferred annuity will exceed annual income from a taxable account by 20 percent on a before-tax basis and by 6 percent on an after-tax basis. We can infer from this figure that the only situation where an investor is better off purchasing a taxable investment, other things equal, is the case where 50 percent of the income generated is ordinary income and the investor converts to an immediate annuity at age 80 or older. xii In all other cases, our analysis shows the investor is better off purchasing a tax-deferred investment. This implies that in the only case when the taxable account is more favorable, seniors are required to hold a high percentage of assets in risky investments over an extended period of time because they generate tax-preferred returns Tax Rate Sensitivity Until now the tax rate used was 40% for the ordinary income tax and 20% for capital gains and dividends. Both of these combined tax rates include a 5% state tax. xiii To measure the sensitivity to tax, the tax rate is both lowered and raised, and the results are compared to those obtained in the previous sections. The lower combined tax rate is changed to 28% for the ordinary income tax and 18% for capital gains, including a 3% state tax. The higher combined tax rates, including a 5% state tax, are 44.6% and 25%, reflecting the combined tax rates scheduled to become effective when the Bush tax rates expire in The measure of the tax benefit is still expressed as yield spread. In some cases the higher tax regime has a larger yield spread than the lower tax regime. A larger yield spread does not necessarily imply a bigger after-tax payout difference because the level of the yields ultimately also impacts the payouts; instead, it merely implies that the benefit over a taxable account is bigger. Therefore, the yield spread of the lower tax regime may be lower but the payout could be larger than under the higher tax regime. The tax sensitivity results are presented here for two cases: (1) Varied time horizon, and (2) varied yield. The other results follow a similar pattern that leads to similar conclusions.

13 4.6.1 Investment Time Horizon and Tax Rate Change Under a 40 percent combined tax rate for ordinary income, the taxable account with 50 percent ordinary income and a lump sum payout has a tax benefit for cases where the investment time horizon is short. This benefit increases as combined tax rates rise. However, when the combined tax rate for ordinary income is 28 percent, the tax benefit of a taxable account is either reduced or entirely eliminated in some instances. This is because the spread between the ordinary income tax rate and the capital gains tax rate is diminished under the lower tax rate. For example: under the higher tax rate, some of the returns in the taxable account is taxed at a preferred capital gains rate of 20 percent, while the tax-deferred account is taxed at 40 percent. But, under the lower tax rate, some of the returns in the taxable account are taxed at 18 percent, while the returns in the tax-deferred account are taxed at 28 percent. Therefore, the size of the benefit to the taxable account is diminished under the lower tax rate when the taxable account generates 50 percent ordinary income. These results can be seen in the first panel in Figure 6. When the portfolio is 100 percent ordinary income, the lower tax rate reduces (but does not eliminate) the yield spread for the tax-deferred accounts (even for time horizons as short as five years). This is because with 100 percent of the taxable portfolio generating ordinary income, there is only one tax rate applied to all the returns in the taxable and tax-deferred portfolio. All other factors being equal, an individual who falls within the higher tax bracket can reinvest a larger portion of returns in the tax-deferred account than in a taxable account. This results in a bigger spread for the higher tax rate than for the lower tax rate. The second panel in Figure 6 shows these results. If the tax regime reverts to its pre-bush tax cuts levels, the yield spreads favoring annuitization will increase, regardless of the length of the accumulation period. Figure 6: Effect of Time Horizon on Yield Spread for Various Tax Rates 11

14 12 When the portfolio is 50 percent ordinary income and an individual elects payout through an immediate annuity, the results are mixed when the tax rate is reduced. For longer time horizons, the higher tax rate offers a greater yield spread; while for shorter time horizons, the lower tax rate offers a greater yield spread. The reason is that a longer time horizon enables more returns to be reinvested (and taxes deferred) when the tax rate is higher. Therefore, for long time horizons, a higher tax rate results in a larger yield spread. Conversely, for short time horizons, the deferral period is too short for a higher tax rate to have significant impact on the yield spread. The factor that impacts the yield spread at shorter time horizons is the difference between the ordinary income tax rate and preferred tax rate. Under lower tax rates, this difference is only 10 percent, compared to 20 percent at higher tax rates Investment Yield and Tax Rate Change The effects of adjusting the investment yield are similar to the effects of adjusting the investment time horizon (Section 4.6.1) and are presented in Figure 7. Under a 40 percent tax rate, the taxable account with 50 percent ordinary income and a lump sum payout has a tax benefit in certain instances when the investment yield is small. But, when the tax rate is 28 percent, the tax benefit of a taxable account is reduced or entirely eliminated in some cases. Again, this is because the spread between the ordinary income tax rate and the capital gains tax rate is less under the lower tax rate. When the portfolio is 100 percent ordinary income (Panel B), the lower tax rate reduces (but does not eliminate) the yield spread favoring the tax-deferred accounts (even for investment yields as low as 3 percent). Again, this is because when 100 percent of the returns on the taxable portfolio are in the form of ordinary income, there is only one tax rate applied to all the returns in the taxable and tax-deferred portfolio.

15 Figure 7: Effect of Investment Yield on Yield Spread for Various Tax Rates 13

16 14 The results above recreate results in two prior sections using different tax rates. All the conclusions from the prior sections still hold. But, the results expressed as a yield spread change in both directions (increases and decreases) depending on which factors are adjusted. In previous sections, the tax-deferred annuities had a negative yield spread in a certain instances. The occurrence of these instances falls when the tax rate is reduced. Where there is positive yield spread, the magnitude of this spread is reduced. Therefore, while the frequency of instances when tax-deferred annuities have an advantage is higher, the magnitude of this advantage is reduced to some extent. 5. Conclusions There are many situations when the tax benefit of a tax-deferred annuity outweighs those of a taxable account. This tax benefit can result in an annual yield spread of two percent or more, depending on how long the annuity is held, how high the yields are, and whether annuitization occurs as one reaches the end of his or her accumulation period. Our analysis shows two polar cases in which the tax-deferred annuity always has the tax advantage: 1. For individuals who are more risk averse and therefore prefer to invest in less risky assets, which generate ordinary income. Even for individuals who prefer to hold a portion of their assets in vehicles that produce tax-preferred income, the remaining assets that generate ordinary income provide better after-tax returns when they are in tax-deferred vehicles such as tax-deferred annuities. 2. For individuals seeking to convert their investments into immediate annuities to replace or add to retirement income. Payout through an immediate annuity extends the tax advantage since the conversion to a tax-deferred annuity can be done through the exercise of a contractual option within the deferred annuity, or through a 1035 exchange that does not result in an immediate tax event. Therefore, the taxes are deferred until the income is actually received. Of course, taxes are also deferred for anyone who systematically liquidates the taxable account over time as retirement income. However, in a volatile interest rate or stock return environment, such an approach subjects the individual to the yield erosion associated with reverse dollar-cost averaging, and this cost can be substantial. If the delay occurs over a market downturn, there may be inadequate resources remaining to guarantee an adequate lifetime income. It also subjects the individual to uncertainty regarding future annuity purchase rates. In both polar cases, independently or together, the tax-deferred annuity can provide the investor with a tax advantage. Additionally, by converting the investment into an immediate annuity instead of opting for a lump-sum payout, the individual also is protected from longevity risk. In conducting this study, we have necessarily abstracted from many complicating factors. These simplifications are necessary to keep the comparisons uncluttered by additional detail that may be important for an individual account. For example, we have assumed that at the time of a retirement, a lump sum of nonqualified savings is either fully liquidated or fully annuitized. We recognize that these two polar cases are not representative of the ways this decision would realistically be made. In many cases it could be preferable to systematically liquidate the taxable portfolio over time, thereby extending the time period for the beneficial tax rate differential between ordinary income and capital gains/qualified dividends, as well as the underlying tax deferral of capital gains themselves. This would lessen the advantage of the annuity approach for non-qualified savings.

17 However, our analysis is really not limited only to the polar cases of fully liquidating or fully annuitizing the accumulated retirement savings. Rather, our analysis is robust and can be applied to any portion of accumulated non-qualified retirement savings that is either annuitized or left to accumulate in a taxable retirement account. The mathematics is the same, but performed in iterative pieces. Each piece faces the same economic factors, regardless of when they are implemented. What changes is the dimension of tax benefit. We have not discussed inflation and its impact on decumulation strategies. A financial planner is rightly concerned with steering his or her client into a product that locks the client into an income pattern that may not address future income needs in an inflationary environment. There are five approaches to the inflation problem in an annuity context that are useful to mention here. First, one can purchase inflation-indexed annuities. Three problems come to mind with this strategy: (1) the inflation rate applied in these policies is based on the consumer price index, which may diverge significantly from the inflationary costs of living for a retired person; (2) there are currently only a few providers of such annuities, subjecting the client to the credit risks of these providers; and (3) with few providers, pricing and product features may not yet have reached the competitive levels that has been achieved in more traditional products. A second strategy is to assist the client in purchasing a pre-specified escalation annuity, where the client selects a fixed rate of escalation (say, from 1% to 6% per year) for the level of annuity payments. Of course this places the client in the position of an economist for predicting future nominal income needs and inflation rates over a period of perhaps forty years. Admittedly, economists are not very adept at predicting inflation rates beyond about one year, much less forty. A third strategy is to steer the client to a product that has a one-time escalation feature, whereby annuity payments are increased by up to 500% or reduced by as much as to 80%. In such contracts, the individual needs to pre-select an age at which the change will be effected, as well as pre-select the amount of the increase or decrease. This approach has some cost advantages but is subject to the same difficulties as pre-selecting an annual escalation rate, plus the additional difficulty of pre-selecting a future age at which the change will be implemented. Nevertheless, this approach can be used to hedge much of the inflation risk and may be a satisfactory one for some clients, depending on their resources, needs, and other individual facts and circumstances. A fourth approach, and one that we favor, is to purchase a combination of immediate and several deferred annuities, diversified across a number of quality providers, and to annuitize the deferred policies only on an as-needed basis. This approach prolongs the tax deferral benefit, and the deferred policies can be annuitized based on the actual inflationary needs of the individual, rather than based on a price index that reflects an average consumer basket of consumption across the entire spectrum of consumers. The longer an individual can delay cashing or annuitizing one of these deferred annuities, the higher its monthly payouts will be due to (a) the accumulation of greater value over time, and (b) the aging of the annuitant, which elicits higher payments with each passing year, other things equal. Two additional advantages of this approach are that the products are priced in the sweet spot of the annuity market due to the vast competition in standard products, and that in the event of premature death, the deferred annuities are inheritable. A fifth approach is to purchase an annuity product whose returns are linked to something that might keep pace with inflation, such as 5-year Treasury yields, commodities, or even equities. In all cases, however, the annuitant would be subject to a high degree of tracking error in terms of hedging closely against the inflationary exposure of a given client over time. Nonetheless, a client may be willing to undertake such 15

18 exposure because of the returns expected weighed against the exposure absorbed. Product guarantees can help address the risk appetite. While we could not treat all of these complicating factors within the scope of our study, we caution the reader that when the principles elucidated in this study are applied to a given client, as always care must be taken to explore the individual client s needs, resources, exposure to risk, and risk appetite. Our only purpose was to give a sense of the dimensions of benefits from tax deferral that are available and conditions under which they accrue, which should not be ignored or dismissed as de minimis, but factored into the calculus of financial planning. 16

19 17 I. Variables Used: The following are variables used in the formulae: Formulae II. Formula for the value of tax-deferred annuity through lump sum payout The formulae that follow are all coded in MATLAB. The value of a tax-deferred annuity with a lump sum payout option: III. Formula for the value of taxable account through lump sum payout The value of taxable account with a lump sum payout option: IV. Formula for the value of tax-deferred annuity through annuitized payout The income generated by the purchase of an immediate annuity using funds in a tax-deferred annuity:

20 V. Formula for the value of taxable account through annuitized payout The income generated by the purchase of an immediate annuity using funds in a taxable account: 18

21 19 References Bogle, John C. The Relentless Rules of Humble Arithmetic. Financial Analysts Journal (November / December 2005: Carter, W. K. and R. F. DeMong, Evaluating a Tax-Deferred Retirement Plan? Journal of the Institute of Certified Financial Planners (Winter, 1982): Drucker, D. J. and P. Sullivan, Choosing Among Taxable, Tax-Deferred, Tax-Exempt Fixed Income Investments Journal of Financial Planning (April, 1989): Hogan, S. Do Variable Annuities Make More Sense After 93 Tax Hike? Journal of Financial Planning (July, 1994): Kwall, J. L. The Value of Tax Deferral: A Different Perspective on Roth IRAs Journal of Financial Planning (December, 1998): Morrow, E. P. Section 1035 Policy Exchanges: Tax Techniques for Life Insurance Policy Surrenders Journal of Financial Planning (July, 1988): Milevsky, M. A. The Calculus of Retirement Income, Cambridge University Press, New York, NY (2006). Niemeyer, A. H. Variable Annuities: Are They Still Appropriate? Journal of Financial Planning (March, 1999): Wood, G. and M. Attaran, Measuring the Efficiency of Tax-Favored Investments. Journal of Financial Planning (August, 1997): i Our study does not take into account the implicit fees and commissions of annuities, nor the explicit loads and annual expense charges of competing mutual funds as well as other embedded costs in such products. All comparisons are net of such fees and expenses. The analysis of these costs and their relative impact upon returns is beyond the scope of this study, but all such costs will tend to offset the returns generated by the taxable and tax-deferred accounts. For example, Bogle (2005, p. 25) estimates that in the case of the average equity mutual fund, such explicit and embedded costs have consumed roughly three-fourths of the gross return investors would have earned in the market from , but for the costs of financial intermediation. ii We have chosen these two polar cases for payout options, recognizing that there are a number of hybrid alternatives, such as partial annuitization or systematic cash withdrawals over time that may also be chosen in practice. (Of course, systematic cash withdrawals over time within a volatile market context subjects the individual to reverse dollar-cost averaging, which can reduce the annual effective taxable yield over time by more than 100 basis points.) Worse, a sizable downturn in the portfolio value may occur during the delay to full annuitization which such a scheme would entail that the individual will not be able to purchase an annuity of sufficient size to satisfy required income needs over the remaining lifetime. A financial planner working with a client will obviously explore these and other strategies. Moreover, we are not implying in our study that all of one s income should be annuitized at retirement, or that all accumulated cash be taken in a lump sum. Rather, we are comparing the tax consequences of any amount that is annuitized versus taken in a lump sum. iii Later, we provide information that allows a financial planner to discern what yield spreads between taxable and tax-deferred accounts would be required to equate the after-tax income results that can be generated across both accounts.

22 20 iv Annual returns on the S&P 500 securities over the past several years have included an approximately 1.5% dividend yield as well as capital gains and losses. Because we will be assuming a 6% constant portfolio yield, the 1.5% historical dividend yield corresponds to one-fourth of the assumed total portfolio yield. v We are well aware that other liquidation strategies may be employed beyond a lump-sum withdrawal. For example, an individual may opt to take systematic withdrawals and tax harvest annually to further optimize cash flows and tax benefits. Such a strategy, however, incurs the yield erosion associated with reverse dollar-cost averaging in a volatile market and subjects the individual to uncertain purchase rates for annuities later on and, if annuitization is not done, the individual may run out of income before running out of life. To keep our comparisons simple and free of these complicating factors, we have opted to consider a lump-sum payout option for both polar cases treated in this paper, or for both the taxable and tax-free accounts to be converted into annuities. vi To be more precise, in the taxable account the accumulated value will include gross value purchases dividends and capital gains are not reinvested net of taxes; rather, the individual is given additional basis (shares or units purchased) at full value and then the individual pays taxes on his or her returns on the 1099 reported income. vii The annuity factor indicates how much annual lifetime income you can get per dollar of premium. For example, an annuitant may receive 8.6 per year for each premium dollar. For this analysis the source of the annuity factor is February viii We remind the reader that result holds under our assumptions that the entire accumulation account is liquidated in a single event of retirement, and that no capital gains have been realized prior to this event. If the individual takes systematic withdrawals from the accumulation account, steadily liquidating any gains over a period of years, the difference will be less. On the other hand, we have assumed that no capital gains taxes are incurred until retirement, an assumption that, when relaxed, is offsetting. The net result will depend on individual facts and circumstances. Other issues associated with a delay to full annuitization are discussed in endnote ii. ix We have paired up the after-tax annual income vertical bars assuming that the taxable and tax-deferred accounts both receive similar pre-tax yields. However, the charts also allow a reader to compare after-tax income levels across different account yields. For example, Panel B of Figure 1 shows a tax-deferral account earning 6% per year generating an annual after-tax income roughly equivalent to a taxable account earning 8% per year. Later, we explore in greater detail the breakeven yield spreads across a wide variety of tax rates, holding periods, portfolio mixes, and payout choices. x Here we compare the after-tax annuity payments only through life expectancy. Beyond life expectancy, the exclusion ratios no longer apply and both accounts are taxed identically. More will be said about this later. xi This is not true in some jurisdictions. For example, in Canada the exclusion ratio remains in effect for the remainder of one s lifetime. See Milevsky (2006, pp ). xii We again are holding accumulation periods constant at 14 years for comparison purposes. If the 80-year-old individual has been accumulating longer, the tax deferral advantage begins to dominate. xiii We do not take into account the deductibility of state tax from the federal taxable income, which can be achieved to some extent when the taxpayer itemizes his or her deductions.