Reading 9 Taxes and Private Wealth Management in a Global Context
by Stephen M. Horan, PhD, CFA, CIPM, and Thomas R. Robinson, PhD, CFA
Stephen M. Horan, PhD, CFA, CIPM, is at CFA Institute (USA). Thomas R. Robinson, PhD, CFA, is at AACSB International (USA).
© 2008 CFA Institute. All rights reserved.
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The candidate should be able to:
compare basic global taxation regimes as they relate to the taxation of dividend income, interest income, realized capital gains, and unrealized capital gains;
determine the effects of different types of taxes and tax regimes on future wealth accumulation;
calculate accrual equivalent tax rates and after-tax returns;
explain how investment return and investment horizon affect the tax impact associated with an investment;
discuss the tax profiles of different types of investment accounts and explain their impact on after-tax returns and future accumulations;
explain how taxes affect investment risk;
discuss the relation between after-tax returns and different types of investor trading behavior;
explain the benefits of tax loss harvesting and highest-in/first-out (HIFO) tax lot accounting;
demonstrate how taxes and asset location relate to mean–variance optimization.
Private wealth managers have the basic goal of maximizing after-tax wealth subject to a client’s risk tolerance and portfolio constraints. Portfolio managers can add value in a number of ways, such as buying undervalued securities, selling overpriced securities, and improving asset allocations. This is challenging in highly efficient markets where informational advantages are difficult to exploit as market participants compete with each other in search of abnormal returns. Managing a portfolio efficiently from a tax perspective, however, is a reasonable goal in almost all markets. In most economies around the world, taxes have a significant impact on net performance and affect an adviser’s understanding of risk for the taxable investor. Tax rates, particularly those for high-net-worth (HNW) individuals, are non-trivial and typically affect returns more than portfolio management costs.
Despite a long history of high tax rates on investment returns, most modern portfolio theory is grounded in a pretax framework. This phenomenon is understandable because most institutional and pension portfolios are tax-exempt. As more wealth becomes concentrated with individuals, it is important to examine the impact of taxes on risk and return characteristics of a portfolio and wealth accumulation. The purpose of this reading is to outline basic concepts that serve as the foundation for building tax-aware investment models that can be applied in a global environment.
The approach developed here is valuable for several reasons. First, it can be applied in a broad range of circumstances representing different taxing jurisdictions, asset classes, and account types. Second, it can provide a framework with which advisers can better communicate the impact of taxes of portfolio returns to private clients and develop techniques to improve their after-tax performance. Third, tax codes change over time. The models developed here provide the adviser a framework to manage changes should they occur.
2. OVERVIEW OF GLOBAL INCOME TAX STRUCTURES
Tax structures (the specifics of how governments collect taxes) are determined by national, regional, and local jurisdictions in order to meet governmental funding needs. Major sources of government tax revenue include:
Taxes on income. These taxes apply to individuals, corporations, and often other types of legal entities. For individuals, income types can include salaries, interest, dividends, realized capital gains, and unrealized capital gains, among others. Income tax structure refers to how and when different types of income are taxed.
Wealth-based taxes. These include taxes on the holding of certain types of property (e.g., real estate) and taxes on the transfer of wealth (e.g., taxes on inheritance).
Taxes on consumption. These include sales taxes (which are taxes collected in one step from the final consumer on the price of a good or service) and value-added taxes (which are collected in intermediate steps in the course of producing a good or service but borne ultimately by the final consumer).
This reading’s focus will be on the taxes that most directly affect tax planning for investments, specifically taxes on investment income to individuals and, secondarily, wealth-based taxes.
In many cases, the tax system is used to encourage or discourage certain activities (for example, investing in domestic companies or encouraging retirement savings). Tax structures vary globally and can change as the needs and objectives of the governmental jurisdiction change. In such a dynamic environment, the investment manager needs to understand the impact of different tax structures on investment returns and wealth. Rather than delineate specific country tax rules, this reading provides a framework for managers to understand and implement investment strategies in a dynamic environment where different tax environments may apply to different clients and tax environments can change over time.
2.1. International Comparisons of Income Taxation
We reviewed the taxation of different types of income, particularly investment income, around the world in order to summarize the major tax regimes.1 The review was based on data from over 50 countries as reported in the Deloitte Touche Tohmatsu International Business Guides, which were available during the summer of 2007. This summary provided the basis for our discussion of the common elements of individual income taxation around the world and our classification of different countries into general income tax regimes.
2.2. Common Elements
In most tax jurisdictions, a tax rate structure applies to ordinary income (such as earnings from employment). Other tax rates may apply to special categories of income such as investment income (sometimes referred to as capital income for tax purposes). Investment income is often taxed differently based on the nature of the income: interest, dividends, or capital gains and losses. Most of the countries examined in our review have a progressive ordinary tax rate structure. In a progressive rate structure, the tax rate increases as income increases. For example:
Taxable Income (€)Tax on
Column 1Percentage on Excess
Over Column 1OverUp to015,000–2315,00028,0003,4502728,00055,0006,9603855,00075,00017,2204175,00025,42043
In such an environment, if an individual has taxable income of €60,000, the first €15,000 is taxed at 23 percent; the next €13,000 (i.e., from €15,000 to €28,000) is taxed at 27 percent; and so on. The amount of tax due on taxable income of €60,000 would be €17,220 + 0.41(€60,000 − €55,000) or €19,270. This would represent an average tax rate of €19,270/€60,000 or 32.12 percent. In tax planning for investments, it is useful to think about how much tax would be paid on additional income, known as the marginal tax rate. The marginal rate, or rate on the next €1 of income, would be 41 percent in this example. This taxpayer could have €15,000 more in income before moving into the next tax bracket (a new marginal rate of 43 percent). Some countries do not have a progressive tax system and instead impose a flat tax. In a flat tax structure, all taxable income is taxed at the same rate. For example, at the time of this writing, Russia had a flat tax rate of 13 percent.
Many countries provide special tax provisions for interest income. These special provisions included an exemption for certain types of interest income (for example, Argentina exempted interest income from Argentine banks for residents), a favorable tax rate on interest income (for example, Italy taxed some interest income at 12.5 percent even though the minimum marginal rate is 23 percent), or an exclusion amount where some limited amount of interest income is exempt from tax (for example, Germany provided such an exclusion). Some fixed income instruments are indexed for inflation and this inflation adjustment may not be subject to taxation in some jurisdictions. Unless special provisions exist, interest income, including inflation adjustments, is taxed at the tax rates applicable to ordinary income (ordinary rates).
Similarly, dividend income may have special provisions. In some cases there are exemptions, special tax rates, or exclusions as described above for interest income. In other cases, there may be provisions for mitigating double taxation because dividends are a distribution of company earnings and the company may have already paid tax on the earnings. Tax credits can be used to mitigate the effects of double taxation. For example, the dividend can be taxed at ordinary rates but the individual is entitled to a credit for a portion of the taxes paid by the company (referred to as “franking” in some jurisdictions such as Australia). As with interest income, absent special rules dividend income is taxed at ordinary rates.
Finally, capital gains (losses) may have special provisions or rates. These often vary depending upon how long the underlying investment has been held. Generally, long term gains are treated more favorably than short term gains. Long term is defined differently in different jurisdictions; for example, in the data examined, we observed required holding periods of six months, one year, two years, and five years. Special provisions observed included total exemption of capital gains or long-term capital gains from taxation (for example, Austria exempted long-term gains), exemption of a certain percentage of gains from taxation (for example, Canada exempted 50 percent of gains), a favorable tax rate on capital gains (for example, Brazil provided a flat 15 percent rate for capital gains), or indexing the cost of the investment for inflation (for example, India permitted inflation indexing for some investments). In some cases, countries provided more favorable provisions for domestic companies or companies traded on a local exchange (sometimes applied to both dividend income and capital gains). In most cases, only realized gains were taxed (when the investment was sold). In rare cases, countries impose a tax on unrealized gains (appreciation of the investment prior to sale) either annually, upon exiting the country to relocate domicile, or upon inheritance.2
Vanessa Wong is a new client living in a jurisdiction with a progressive tax rate structure. She expects to have taxable ordinary income of €70,000 this year. The tax rate structure in her jurisdiction is as follows:
Taxable Income (€)Tax on
Column 1Percentage on Excess
Over Column 1OverUp to030,000–2030,00060,0006,0003060,00090,00015,0004090,00027,00050
Wong’s marginal tax rate is closest to:
Wong’s average tax rate is closest to:
Solution to 1:
B is correct. Wong’s marginal tax rate is 40 percent. Because Wong’s income is over €60,000 but below €90,000, her next €1 of income would be taxed at 40 percent.
Solution to 2:
A is correct. Wong’s tax liability would be €15,000 + 0.40 (€70,000 − €60,000) = €19,000. With a tax liability of €19,000 and taxable income of €70,000, her average tax rate would be about 27 percent (€19,000/€70,000).
2.3. General Income Tax Regimes
Each country’s income tax structure can be classified as either progressive or flat. Income tax regimes can be further distinguished based on the taxation of investment returns in taxable accounts. Interest income is either taxed at ordinary rates or at favorable rates under special provisions. In this review, interest income is considered to be taxable at ordinary rates unless significant exceptions apply. Similar classifications were used for dividends and capital gains. Seven different tax regimes were observed in the sample of countries examined. Exhibit 1 classifies common elements of tax regimes and is further explained below.
Exhibit 1. Classification of Income Tax Regimes
Regime1 — Common Progressive2 — Heavy Dividend Tax3 — Heavy Capital Gain Tax4 — Heavy Interest Tax5 — Light Capital Gain Tax6 — Flat and Light7 — Flat and HeavyOrdinary Tax Rate StructureProgressiveProgressiveProgressiveProgressiveProgressiveFlatFlatInterest IncomeSome interest taxed at favorable rates or exemptSome interest taxed at favorable rates or exemptSome interest taxed at favorable rates or exemptTaxed at ordinary ratesTaxed at ordinary ratesSome interest taxed at favorable rates or exemptSome interest taxed at favorable rates or exemptDividendsSome dividends taxed at favorable rates or exemptTaxed at ordinary ratesSome dividends taxed at favorable rates or exemptSome dividends taxed at favorable rates or exemptTaxed at ordinary ratesSome dividends taxed at favorable rates or exemptTaxed at ordinary ratesCapital GainsSome capital gains taxed favorably or exemptSome capital gains taxed favorably or exemptTaxed at ordinary ratesSome capital gains taxed favorably or exemptSome capital gains taxed favorably or exemptSome capital gains taxed favorably or exemptTaxed at ordinary ratesExample CountriesAustria
Saudi Arabia (Zakat)Ukraine
Sources: Classified based on information provided in International Business Guides from Deloitte Touche Tohmatsu (available at www.deloitte.com) and online database of worldwide taxation provided by PricewaterhouseCoopers (www.taxsummaries.pwc.com).
Common Progressive Regime: This regime has progressive tax rates for ordinary income, but favorable treatment in all three investment income categories: interest, dividends, and capital gains. This was the most common regime observed. Even though categorized as “common,” there is variation within this regime with some countries treating some interest income as ordinary and other interest income as tax exempt, while other countries provide for exemption or special treatment for all interest.
Heavy Dividend Tax Regime: This regime has a progressive tax system for ordinary income and favorable treatment for some interest and capital gains but taxes dividends at ordinary rates.
Heavy Capital Gain Tax Regime: This regime has a progressive tax system for ordinary income and favorable treatment for interest and dividends, but taxes capital gains at ordinary rates. Only one such country was observed.
Heavy Interest Tax Regime: This regime has a progressive tax system for ordinary income and favorable treatment for dividends and capital gains, but taxes interest income at ordinary rates.
Light Capital Gain Tax Regime: This regime has a progressive tax system for ordinary income, interest, and dividends, but favorable treatment of capital gains. This was the second most commonly observed regime.
Flat and Light Regime: This regime has a flat tax system and treats interest, dividends, and capital gains favorably.
Flat and Heavy Regime: This regime has a flat tax system for ordinary income, dividends, and capital gains. It does not have favorable treatment for dividends and capital gains, but has favorable treatment for interest income.
2.4. Other Considerations
In addition to the different tax regimes in which different types of income are taxed at possibly different rates, there are other important dimensions in tax planning for investments. Some countries permit the use of tax deferred retirement accounts. A tax deferred account
defers taxation on investment returns within the account;
may permit a deduction for contributions;
may occasionally permit tax free distributions.
On the other hand, a few countries impose a wealth tax on accumulations on a periodic basis which reduces after-tax returns and accumulations similar to income taxes.
In the next section we will examine how taxes affect after-tax returns and accumulations. We also examine the impact of tax deferred accounts and wealth taxes. In a later section we will discuss planning opportunities suitable for the various tax regimes.3
3. AFTER-TAX ACCUMULATIONS AND RETURNS FOR TAXABLE ACCOUNTS
Taxes on investment returns have a substantial impact on performance and future accumulations. This section develops models to estimate the tax impact on future accumulations in various tax environments. These models enable the investment adviser to evaluate potential investments for taxable investors by comparing returns and wealth accumulations for different types of investments subject to different tax rates and methods of taxation (accrued annually or deferred).
3.1. Simple Tax Environments
As the preceding analysis of global tax regimes suggests, investment returns can be taxed in a number of different ways. This section begins with some straightforward methods that illustrate basic concepts and serve as building blocks for more complex environments.
All but four of the countries studied in the tax regime analysis have a progressive income tax system.4 The discussion in this section assumes uniform marginal tax rates based on the investor’s current tax bracket which is effectively flat for some range of income. Models that accommodate multiple tax brackets grow in complexity very quickly. Also, investors are often subject to a single rate on the margin, limiting the usefulness of an analysis based on multiple tax brackets. Finally, much of the intuition and analysis that is derived in a flat tax framework applies in a setting with multiple tax brackets.
3.1.1. Returns-Based Taxes: Accrual Taxes on Interest and Dividends
One of the most straightforward methods to tax investment returns is to tax an investment’s annual return at a single tax rate, regardless of its form. Accrual taxes are levied and paid on a periodic basis, usually annually, as opposed to deferred taxes that are postponed until some future date. Most of the countries examined above tax interest income on an accrual basis annually, either at ordinary rates or at favorable rates as the result of special provisions. Germany, Greece, Canada, Colombia, and the United States, for example, tax most interest income at ordinary rates, although some interest income may receive favorable tax treatment. Japan, China, Finland, the Czech Republic, and the United Kingdom tax interest income at a special fixed rate. Dividends, like interest income, are typically taxed in the year they are received, albeit often at different rates.
When returns are subject to accrual taxes, the after-tax return is equal to the pretax return, r, multiplied by (1 − ti) where ti represents the tax rate applicable to investment income. For the purposes of this section, we consider an investment with a return that is entirely taxed at a single uniform rate.
The amount of money accumulated for each unit of currency invested after n years, assuming that returns (after taxes at rate ti are paid) are reinvested at the same rate of return, r, is simply
FVIFi = [1 + r(1 — ti)]n
Equation 1 is simply a future value interest factor (FVIF) based on an after-tax return. For example, €100 invested at 6 percent per annum for ten years in an environment in which returns are taxed each year at a rate of 30 percent will accumulate to be €100[1 + 0.06(1 − 0.30)]10 = €150.90. Had returns not been taxed, this investment would have grown to €100[1 + 0.06(1 − 0.00)]10 = €179.08, a difference of €28.18. Notice that taxes reduce the potential gain on investment by (€179.08 − €150.90)/(€179.08 − €100.00) = €28.18/€79.08 = 35.6 percent, which is more than the ordinary income tax rate. This suggests that the tax drag on capital accumulation compounds over time when taxes are paid each year. (Tax drag refers to the negative effect of taxes on after-tax returns.) By contrast, when taxes on gains are deferred until the end of the investment horizon, the tax rate equals the tax drag on capital accumulation as we shall see in the next section.
Exhibit 2 illustrates the impact of taxes on capital growth for various investment horizons and rates of return and demonstrates several conclusions. First, when investment returns are taxed annually, the effect of taxes on capital growth is greater than the nominal tax rate as noted above. Second, the adverse effects of taxes on capital growth increase over time. That is, the proportional difference between pretax and after-tax gains grows as the investment horizon increases. Third, the tax drag increases as the investment return increases, all else equal. Fourth, return and investment horizon have a multiplicative effect on the tax drag associated with future accumulations. Specifically, the impact of returns on the tax effect is greater for long investment horizons, and the impact of investment horizon is greater for higher returns because figures in the bottom right corner change more rapidly than figures in the upper left corner.
Exhibit 2. Proportion of Potential Investment Growth Consumed by Annual Taxes on Return
Investment Horizon in Years (n)r (%)51015202530354020.3080.3190.3300.3400.3510.3620.3730.38440.3170.3380.3590.3810.4030.4250.4470.46960.3250.3560.3890.4210.4540.4860.5180.54980.3330.3750.4180.4610.5030.5450.5840.622100.3410.3930.4460.4990.5500.5980.6430.684120.3480.4110.4740.5350.5930.6460.6940.737140.3560.4290.5010.5690.6330.6890.7390.781160.3640.4460.5260.6010.6690.7270.7760.818180.3710.4620.5510.6310.7010.7600.8080.848
Note: The calculations assume a 30 percent annual tax rate on investment returns.
Conceptually, this framework could apply to securities, such as fixed-income instruments or preferred stock, in which most or possibly all of the return is subject to annual taxes. This is an oversimplification, of course, but we will address that concern below.
Vladimir Kozloski is determining the impact of taxes on his expected investment returns and wealth accumulations. Kozloski lives in a tax jurisdiction with a flat tax rate of 20 percent which applies to all types of income and is taxed annually. Kozloski expects to earn 7 percent per year on his investment over a 20 year time horizon and has an initial portfolio of €100,000.
What is Kozloski’s expected wealth at the end of 20 years?
What proportion of potential investment gains were consumed by taxes?
Solution to 1:
FV = €100,000 × FVIFi
= €100,000 × [1 + 0.07(1–0.20)]20
Solution to 2:
Ignoring taxes, FV = €100,000 [1 + 0.07]20 = €386,968. The difference between this and the after tax amount accumulated from above is €89,611. The proportion of potential investment gains consumed by taxes was €89,611/€286,968 = 31.23 percent.
3.1.2. Returns-Based Taxes: Deferred Capital Gains
Another straightforward method of taxing returns is to focus on capital gains, the recognition of which can usually be deferred until realized, instead of interest income and dividends, which are generally taxable each year. A portfolio of non-dividend-paying stocks could fall under this type of framework. The analysis of global tax systems in the previous section indicates that it is very rare for unrealized investment gains to be taxed, so this implicit deferral mechanism has nearly universal application.
If the tax on an investment’s return is deferred until the end of its investment horizon, n, and taxed as a capital gain at the rate tcg, then the after-tax future accumulation for each unit of currency can be represented in several ways, including the following:
FVIFcg = (1 + r)n — [(1 + r)n — 1]tcg
FVIFcg = (1 + r)n(1 — tcg) + tcg
The first term of Equation 2a represents the pretax accumulation. The bracketed term is the capital gain (i.e., future accumulation less the original basis), while the entire second term represents the tax obligation on that gain. Viewed differently, the first term of Equation 2b represents the future accumulation if the entire sum (including the original basis) were subject to tax. The second term returns the tax of the untaxed cost (also known as cost basis or basis) associated with the initial investment.
For example, €100 invested at 6 percent for ten years in an environment in which capital gains are taxed at the end of that time at a rate of 30 percent will accumulate to be €100[(1 + 0.06)10(1 − 0.30) + 0.30] = €155.36. Notice that this sum is greater than the €150.90 accumulated in the previous example using Equation 1, where returns are taxed annually at the same rate. This comparison illustrates the value of tax deferral.
Notice, as well, that the after-tax investment gain equals the pretax investment gain multiplied by one minus the tax rate. That is, €55.36 = €79.08 × (1 − 0.30). Whereas the tax drag on after-tax accumulations subject to annual accrual taxes compounds over time, the tax drag from deferred capital gains is a fixed percentage regardless of the investment return or time horizon. In other words, when deferral is permitted, the proportion of potential investment growth consumed by taxes is always the same as the tax rate, 30 percent in this case, which is less than that presented in Exhibit 2 when there was annual taxation.
Because the tax drag in Exhibit 2 increases with the investment return and time horizon, the value of a capital gain tax deferral also increases with the investment return and time horizon. One implication of the value of tax deferral is that investments taxed on a deferred capital gain basis can be more tax efficient (i.e., tax advantaged) than investments with returns that are taxed annually, all else equal, even if the marginal tax rate on the two is the same. Moreover, the difference compounds over time. The tax regime analysis from Exhibit 1 reveals that relatively few jurisdictions tax components of equity returns (dividends and capital gains) more heavily than interest income. There are rare exceptions where dividends (but usually not capital gains) are taxed to a greater extent than interest (such as the Heavy Dividend Tax Regime countries in Exhibit 1). Moreover, even if the tax rate on deferred capital gains is greater than the tax rate on interest income, the value of the deferral can more than offset a lower tax rate on annually taxed income, especially over time.
Exhibit 3 illustrates the value of tax deferral and its compounding effects more generally by presenting the ratio of after-tax accumulation in a deferred capital gain regime to after-tax accumulation in a regime in which returns are taxed annually. For example, with a 6 percent annual return, 20-year time horizon and a 30 percent tax rate, the accumulation of €100 in a deferred capital gain environment, is €100[(1 + 0.06)20(1 − 0.30) + 0.30] = €254.50. In an annual taxation environment, it is €100[1 + 0.06(1 − 0.30)]20 = €227.70. Therefore, a deferred capital gain environment accumulates €254.50/€227.70 = 1.118 times the amount accumulated in an annual taxation environment. The relative accumulations can be substantially larger when gains are deferred for long time horizons, especially for high returns. It is important to note, however, that the advantages of tax deferral can be offset or even eliminated if securities taxed on an accrual basis have greater risk-adjusted returns.
Exhibit 3. Ratio of Future Accumulations: Accumulation in a Deferred Capital Gain Environment to Accumulation in an Annual Taxation Environment
Investment Horizon in Years (n)r (%)51015202530354021.0011.0041.0081.0151.0231.0331.0451.05841.0031.0141.0311.0561.0861.1231.1651.21361.0071.0301.0671.1181.1811.2571.3461.44781.0121.0501.1131.1981.3051.4321.5821.754101.0181.0751.1691.2941.4531.6441.8712.136121.0251.1041.2321.4051.6241.8922.2142.598141.0331.1371.3031.5291.8182.1772.6163.149161.0411.1721.3801.6662.0352.5003.0803.799181.0501.2101.4641.8142.2732.8623.6124.561
Note: The calculations assume a 30 percent annual tax rate on investment returns and a 30 percent tax rate on deferred capital gains.
In many countries, the rate applied to capital gains is lower than the rate applied to interest income. In such cases, the investor gets a dual benefit from returns in the form of capital gains: deferral of taxation and a favorable tax rate when gains are realized. The capital gain tax rate may also vary depending on the holding period. Longer holding periods may receive a lower tax rate to encourage long-term rather than short-term investment. Australia, for example, taxes short-term gains (i.e., holding period less than 12 months) at ordinary rates. Only half the gains on assets held for more than 12 months are taxed, however, making the effective long-term capital gain tax rate half of the rate on ordinary income. In such cases the investor gets a dual benefit; deferral of taxation and a favorable rate on realized gains. The holding period can vary. Belgium and the Czech Republic, for example, require a five-year holding period to receive preferential tax treatment on capital gains.
Deferred Capital Gains
Assume the same facts as in Example 2. Kozloski invests €100,000 at 7 percent. However, the return comes in the form of deferred capital gains that are not taxed until the investment is sold in 20 years hence.
What is Kozloski’s expected wealth at the end of 20 years?
What proportion of potential investment gains were consumed by taxes?
Solution to 1:
FV = €100,000 × FVIFcg = €100,000 × [(1 + 0.07)20(1 — t) + t]
= €100,000 × [(1 + 0.07)20(1–0.20) + 0.20] = €329,575.
Solution to 2:
Ignoring taxes, FV = €100,000 [1 + 0.07]20 = €386,968. The difference between this and the after-tax amount accumulated from above is €57,393. The proportion of potential investment gains consumed by taxes was €57,393/€286,968 = 20.0 percent. This result compares favorably to the potential investment gains consumed by taxes in Example 2.
3.1.3. Cost Basis
In taxation, cost basis is generally the amount that was paid to acquire an asset. It serves as the foundation for calculating a capital gain, which equals the selling price less the cost basis. The taxable gain increases as the basis decreases. In consequence, capital gain taxes increase as the basis decreases. In some circumstances, this basis may be adjusted under tax regulations or carry over from another taxpayer. The previous capital gains examples assume that cash is newly invested so that the cost basis was equal to the current market value. That is, the tax liability at the end of the investment horizon is based on the difference between the pretax ending value and the current market value today.
In many cases, an investment being evaluated today was purchased some time ago and has a cost basis that is different from the current market value. If a security has risen in value since its initial purchase, the cost basis may be less than its current market value. Cost basis affects an investment’s after-tax accumulation because it determines the taxable capital gain. Specifically, the after-tax cash flow from liquidation increases as the cost basis increases, holding all else equal. Put differently, an investment with a low cost basis has a current embedded tax liability because, if it were liquidated today, capital gain tax would be owed even before future capital growth is considered. Newly invested cash has no such current tax liability.
If the cost basis is expressed as a proportion, B, of the current market value of the investment, then the future after-tax accumulation can be expressed by simply subtracting this additional tax liability from the expression in either Equation 2a or 2b. In other words,
FVIFcgb = (1 + r)n(1 — tcg) + tcg — (1 — B)tcg
Notice that if cost basis is equal to the initial investment, then B = 1 and the last term simply reduces to Equation 2b. The lower the cost basis, however, the greater the embedded tax liability and the lower the future accumulation. Distributing and canceling terms produces
FVIFcgb = (1 + r)n(1 — tcg) + tcgB
This form resembles Equation 2b, and the last term represents the return of basis at the end of the investment horizon. The lower the basis, the lower is the return of basis. For example, suppose an investment has a current market value of €100 and a cost basis of €80. The gain when realized will be subject to a capital gains tax of 30 percent. The cost basis is equal to 80 percent of the current market value of €100. If it grows at 6 percent for 10 years, the future after-tax accumulation is €100 [(1.06)10(1 − 0.30) + (0.30)(0.80)] = €149.36, which is €6 less than the €155.36 accumulation that would result if the basis were equal to €100. The €6 difference represents the tax liability associated with the embedded capital gain.
Express the cost basis as a percent of the current market value.
What is Kozloski’s expected wealth after 20 years?
Solution to 1:
Cost basis/Current market value = B = €80,000/€100,000 = 0.80.
Solution to 2:
FV = €100,000 × FVIFcbg
= €100,000 × [(1 + 0.07)20(1–0.20) + 0.20(0.80)]
This amount is €4,000 smaller than Kozloski’s expected wealth in Example 3, in which it was assumed that the cost basis equaled the current market value.
3.1.4. Wealth-Based Taxes
Some jurisdictions impose a wealth tax, which is applied annually to a specific capital base. Often the wealth tax is restricted to real estate investments (e.g., Australia, Singapore, Belgium, Germany, and the United Kingdom). In other countries, it is levied on aggregate assets including financial assets above a certain threshold (e.g., Colombia). If limited to real estate holdings, the tax may be levied at the federal level or a municipal level. In any case, the wealth tax rate tends to be much lower than capital gains or interest income rates because it applies to the entire capital base — i.e., principal and return — rather than just the return.
The expression for an after-tax accumulation subject to a wealth tax is therefore different from the previous scenarios in which only incremental gains are taxed. If wealth is taxed annually at a rate of tw, then after n years each unit of currency accumulates to
FVIFw = [(1 + r)(1 — tw)]n
For example, if wealth capital is taxed at 2 percent, then €100 invested at 6 percent for ten years will grow to [(1.06)(1 − 0.02)]10 = €146.33. Because the form of a wealth tax differs from the form of taxes on either investment returns or deferred capital gains, this figure is not comparable to the previous two examples. This figure is substantially less than the pretax accumulation of €179.08, however. In other words, the two percent wealth tax consumed 41.4 percent of the investment growth that would have accrued over ten years in the absence of a wealth tax (i.e., (€79.08 − €46.33)/€79.08).
Exhibit 4 illustrates the impact of a wealth tax on investment growth for various rates of return and investment horizons. Because wealth taxes apply to the capital base, the absolute magnitude of the liability they generate (measured in units of currency) is less sensitive to investment return than taxes based on returns. Consequently, the proportion of investment growth that it consumes decreases as returns increase. Viewed differently, a wealth tax consumes a greater proportion of investment growth when returns are low. In fact, when returns are flat or negative, a wealth tax effectively reduces principal. Like the previous two types of taxes, however, the wealth tax consumes a greater share of investment growth as the investment horizon increases.
Exhibit 4. Proportion of Investment Growth Consumed by Wealth Taxes
Investment Horizon in Years (n)r (%)51015202530354040.5400.5640.5880.6110.6350.6570.6790.70060.3800.4140.4490.4830.5170.5500.5830.61480.3010.3410.3820.4230.4640.5050.5440.581100.2530.2980.3440.3900.4370.4820.5260.567120.2220.2700.3200.3710.4210.4700.5170.560140.2000.2500.3040.3580.4120.4640.5120.557160.1830.2370.2930.3500.4060.4600.5100.556180.1710.2260.2850.3450.4030.4580.5080.555
Note: The calculations assume a 2 percent annual wealth tax.
Olga Sanford lives in a country that imposes a wealth tax of 1.0 percent on financial assets each year. Her €400,000 portfolio is expected to return 6 percent over the next ten years.
What is Sanford’s expected wealth at the end of ten years?
What proportion of investment gains was consumed by taxes?
Solution to 1:
FV = €400,000[(1.06)(1 − 0.01)]10 = €647,844.
Solution to 2:
Had the wealth tax not existed, FV = €400,000(1.06)10 = €716,339. This sum represents a €316,339 investment gain compared to a €247,844 gain in the presence of the wealth tax. Therefore, the one percent wealth tax consumed 21.65 percent of the investment gain (i.e., (€316,339 − €247,844)/€316,339).
3.2. Blended Taxing Environments
The discussion in the previous section is an oversimplification because each model assumes that investment gains were taxed according to only one of a number of possible taxes. In reality, portfolios are subject to a variety of different taxes depending on the types of securities they hold, how frequently they are traded, and the direction of returns. The different taxing schemes mentioned above can be integrated into a single framework in which a portion of a portfolio’s investment return is received in the form of dividends (pd) and taxed at a rate of td; another portion is received in the form of interest income (pi) and taxed as such at a rate of ti; and another portion is taxed as realized capital gain (pcg) at tcg. The remainder of an investment’s return is unrealized capital gain, the tax on which is deferred until ultimately recognized at the end of the investment horizon.5 These return proportions can be computed by simply dividing each income component by the total dollar return.
Blended Tax Environment
Zahid Kharullah has a balanced portfolio of stocks and bonds. At the beginning of the year, his portfolio has a market value of €100,000. By the end of the year, the portfolio was worth €108,000 before any annual taxes had been paid, and there were no contributions or withdrawals. Interest of €400 and dividends of €2,000 were reinvested into the portfolio. During the year, Kharullah had €3,600 of realized capital gains. These proceeds were again reinvested into the portfolio.
What percentage of Kharullah’s return is in the form of interest?
What percentage of Kharullah’s return is in the form of dividends?
What percentage of Kharullah’s return is in the form of realized capital gain?
What percentage of Kharullah’s return is in the form of deferred capital gain?
Solution to 1:
pi = €400/€8,000 = 0.05 or 5 percent.
Solution to 2:
pd = €2,000/€8,000 = 0.25 or 25 percent.
Solution to 3:
pcg = €3,600/€8,000 = 0.45 or 45 percent.
Solution to 4:
Unrealized gain = €8,000 − €400 − €2,000 − €3,600 = €2,000. Expressed as a percentage of return, €2,000/€8,000 = 0.25, or 25 percent. The unrealized gain is the portion of investment appreciation that was not taxed as either interest, dividends, or realized capital gain.
In this setting, the annual return after realized taxes can be expressed as
r* = r(1 — piti — pdtd — pcgtcg)
In this case, r represents the pre-tax overall return on the portfolio. From the preceding example, note that the pre-tax return was 8 percent [(€108,000/€100,000) − 1], however there would be taxes due on the interest, dividends and realized capital gains. The effective annual after-tax return, r*, reflects the tax erosion caused by a portion of the return being taxed as ordinary income and other portions being taxed as realized capital gain and dividends. It does not capture tax effects of deferred unrealized capital gains. One can view this expression as being analogous to the simple expression in which after-tax return equals the pretax return times one minus the tax rate. The aggregate tax rate has several components in this case, but the intuition is the same.6
Blended Tax Environment: After Tax Return
Continuing with the facts in Example 6, assume that dividends and realized capital gains are taxed at 15 percent annually while interest is taxed at 35 percent annually.
What is the annual return after realized taxes?
Assuming taxes are paid out of the investment account, what is the balance in the account at the end of the first year?
Solution to 1:
r* = r(1 — piti — pdtd — pcgtcg)
= 8%[1 — (0.05 × 0.35) — (0.25 × 0.15) — (0.45 × 0.15)]
Solution to 2:
Using the income data from above,