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of Individual Retirement Accounts (IRAs) which we discuss later, so we will describe this
structure as having an “IRA style.”
To examine the impact of an IRA-style structure (assuming you could shelter all your sav-
ings) in a situation comparable to the nonsheltered flat-tax case, we maintain the same con-
sumption level as in Spreadsheet 18.4 (flat tax with no shelter), but now input the new,
sheltered savings plan in Spreadsheet 18.5. This focuses the entire effect of the tax shelter onto
retirement consumption.
In this sheet, we input desired real consumption (column H, copied from Spreadsheet 18.4).
Taxes (column E) are then calculated by applying the tax rate (E2) to nominal consumption
less the exemption (H C D). The retirement panel shows that you pay taxes on all with-
drawals”all funds in the retirement account are subject to tax.
The results are quite surprising. The tax protection means faster accumulation of the re-
tirement fund, which grows to $3.7 million (column G), compared with only $1.9 million
without the shelter, but you also owe taxes on the entire amount. You pay taxes as you draw
income from the retirement funds, and this tax load results in an effective tax rate of about
20% on your withdrawals (E68/B68). Still, your real retirement annuity ($60,789) is far
greater than the average $35,531 absent the shelter, a result of the earning power of the sav-
ings on which you postponed taxes. Note that the source of effectiveness of the shelter is
twofold: postponing taxes on both savings and the investment earnings on those savings.


>
5. With the IRA-style tax shelter, all your taxes are due during retirement. Is the trade-
Concept
off between exemption and tax rate different from the circumstance where you
CHECK have no shelter?


The Effect of the Progressive Nature of the Tax Code
Because of the exemption, the flat tax is somewhat progressive: taxes are an increasing frac-
tion of income as income rises. For very high incomes, the marginal tax rate (25%) is only
slightly higher than the average rate. For example, with income of $50,000 at the outset, the
average tax rate is 17.5% (.25 35,000/50,000), and grows steadily over time. In general,
with a flat tax, the ratio of the average to marginal rate equals the ratio of taxable to gross

4
Bankruptcy or death can erase some tax liabilities, though. We will avoid dealing with these unhappy outcomes.
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Fifth Edition




633
18 Taxes, Inflation, and Investment Strategy



S P R E A D S H E E T 18.5
Saving with a flat tax and an IRA-style tax shelter


A B C D E F G H
1 Retirement Years Income Growth Rate of Inflation Exemption Now Tax Rate Savings Rate ROR rROR
2 25 0.07 0.03 15000 0.25 0.15 0.06 0.0291
3 Age Income Deflator Exemption Taxes Savings Cumulative Savings rConsumption
4 30 50,000 1.00 15,000 5,016 9,922 9,922 35,063
5 31 53,500 1.03 15,450 5,465 10,724 21,242 36,224
9 35 70,128 1.16 17,389 7,628 14,600 83,620 41,319
19 45 137,952 1.56 23,370 16,695 31,106 438,234 57,864
29 55 271,372 2.09 31,407 34,952 65,205 1,393,559 81,773
39 65 533,829 2.81 42,208 71,307 135,087 3,762,956 116,365
40 Total 944,536 1,773,854 Real Annuity 76,052
41 RETIREMENT
42 Age Nom Withdraw Deflator Exemption Taxes Funds Left rConsumption
43 66 220,420 2.90 43,474 44,236 3,768,313 60,789
47 70 248,085 3.26 48,931 49,789 3,720,867 60,789
52 75 287,598 3.78 56,724 57,719 3,455,127 60,789
57 80 333,405 4.38 65,759 66,912 2,856,737 60,789
62 85 386,508 5.08 76,232 77,569 1,774,517 60,789
67 90 448,068 5.89 88,374 89,924 0 60,789
68 Total 8,036,350 1,612,828


A B C D E F G H
1 Retirement Years Income Growth Rate of Inflation Exemption Now Tax Rate Savings Rate ROR rROR
2 25 0.07 0.03 15000 0.25 0.15 0.06 =(G2-C2)/(1+C2)
3 Age Income Deflator Exemption Taxes Savings Cumulative Savings rConsumption
4 30 50000 1 =$D$2*C4 =(H4*C4-D4)*$E$2 =B4-E4-H4*C4 =F4 35062.5
5 31 =B4*(1+$B$2) =C4*(1+$C$2) =$D$2*C5 =(H5*C5-D5)*$E$2 =B5-E5-H5*C5 =G4*(1+$G$2)+F5 36223.7712378641
39 65 =B38*(1+$B$2) =C38*(1+$C$2) =$D$2*C39 =(H39*C39-D39)*$E$2 =B39-E39-H39*C39 =G38*(1+$G$2)+F39 116364.980523664
40 Total =SUM(E4:E39) =SUM(F4:F39) Real Annuity =PMT($H$2,$A$2,-$G$39/$C$39,0,0)
RETIREMENT
41
42 Age Nom Withdraw Deflator Exemption Taxes Funds Left rConsumption
43 66 =$H$40*C43 =C39*(1+$C$2) =$D$2*C43 =MAX(0,(B43-D43)*$E$2) =G39*(1+$G$2)-B43 =(B43-E43)/C43
44 67 =$H$40*C44 =C43*(1+$C$2) =$D$2*C44 =MAX(0,(B44-D44)*$E$2) =G43*(1+$G$2)-B44 =(B44-E44)/C44
67 90 =$H$40*C67 =C66*(1+$C$2) =$D$2*C67 =MAX(0,(B67-D67)*$E$2) =G66*(1+$G$2)-B67 =(B67-E67)/C67
68 Total =SUM(B43:B67) =SUM(E43:E67)




income. This ratio becomes .89 at age 45 (check this) at which point the average tax rate is
above 22%. The current U.S. tax code, with multiple income brackets, is much more progres-
sive than our assumed structure.
In Spreadsheet 18.6 we work with a more progressive tax structure that is closer to the progressive tax
U.S. Federal tax code augmented with an average state tax. Our hypothetical tax schedule is Taxes are
described in Table 18.1. an increasing
Spreadsheet 18.6 is identical to Spreadsheet 18.4, the only difference being the tax built fraction of income
as income rises.
into column E according to the schedule in Table 18.1.
Despite the more progressive schedule of this tax code, at the income level we assume, you
would end up with a similar standard of living. This is due to the large lower-rate bracket.
Although the lifetime tax rate is higher, 34.66% compared with 32.13% for the flat tax, you
actually pay lower taxes until you reach the age of 41. The early increased savings offset some
of the bite of the overall higher tax rate. Another important result of the nature of this code is
the lower marginal tax rate upon retirement when taxable income is lower. This is the envi-
ronment in which a tax shelter is most effective, as we shall soon see.
Spreadsheet 18.7 augments the progressive tax code with our benchmark (IRA-style) tax
shelter that allows you to pay taxes on consumption (minus an exemption) and accumulate tax
liability to be paid during your retirement years. The construction of this spreadsheet is iden-
tical to Spreadsheet 18.5, with the only difference being the tax structure built into column E.
We copied the real pre-retirement consumption stream from Spreadsheet 18.6 to focus the
Bodie’Kane’Marcus: VI. Active Investment 18. Taxes, Inflation, and © The McGraw’Hill
Essentials of Investments, Management Investment Strategy Companies, 2003
Fifth Edition




634 Part SIX Active Investment Management



S P R E A D S H E E T 18.6
Saving with a progressive tax


A B C D E F G H
1 Retirement Years Income Growth Rate of InflationExemption Now Tax rates in Savings Rate ROR rROR
2 25 0.07 0.03 10000 Table 18.1 0.15 0.06 0.0291
3 Age Income Deflator Exemption Taxes Savings Cumulative Savings rConsumption
4 30 50,000 1.00 10,000 8,000 6,300 6,300 35,700
5 31 53,500 1.03 10,300 8,716 6,718 13,396 36,958
9 35 70,128 1.16 11,593 12,489 8,646 51,310 42,262
19 45 137,952 1.56 15,580 32,866 15,763 248,018 57,333
29 55 271,372 2.09 20,938 76,587 29,218 731,514 79,076
39 65 533,829 2.81 28,139 186,335 52,124 1,833,644 104,970
40 Total Total 632,759 2,116,533 799,371 Real Annuity 37,059
41 RETIREMENT
42 Age Nom Withdraw Deflator Exemption Taxes Fund Left rConsumption
43 66 107,408 2.90 28,983 16,207 1,836,254 31,467
47 70 120,889 3.26 32,620 15,371 1,813,134 32,347
52 75 140,143 3.78 37,816 13,083 1,683,643 33,599
57 80 162,464 4.38 43,839 8,831 1,392,054 35,045
62 85 188,341 5.08 50,821 1,757 864,701 36,714
67 90 218,338 5.89 58,916 0 0 37,059
68 Total 3,916,018 227,675




Taxable Income** Over But Not Over The Tax Is of the Amount Over
TA B L E 18.1
$ 0 $ 50,000 $ 0 20% $ 0
Income tax schedule
50,000 150,000 10,000 30 50,000
used for the
progressive 150,000 ... 40,000 40 150,000
tax*


*The capital gains tax rate is assumed to be 8% when income is in the low two brackets and 28% for the highest bracket.
**Current exemption with this code is assumed to be $10,000. The exemption and tax brackets are adjusted for future inflation.


effect of the tax shelter on the standard of living during the retirement years. Spreadsheet 18.7
shows that the lower tax bracket during the retirement years allows you to pay lower taxes
over the life of the plan and significantly increases retirement consumption. The use of the
IRA-style tax shelter increases the retirement annuity by an average of $34,000 a year, a bet-
ter improvement than we obtained from the shelter with the flat tax.
The effectiveness of the shelter also has a sort of hedge quality. If you become fortunate
and strike it rich, the tax shelter will be less effective, since your tax bracket will be higher at
retirement. However, mediocre or worse outcomes will result in low marginal rates upon re-
tirement, making the shelter more effective and the tax bite lower.


>
6. Are you indifferent between an increase in the low-income bracket tax rate versus
Concept
an equal increase in the high bracket tax rates?
CHECK

18.5 A MENU OF TAX SHELTERS
Individual Retirement Accounts
Individual Retirement Accounts (IRAs) were set up by Congress to increase the incentives to
save for retirement. The limited scope of these accounts is an important feature. Currently,
annual contributions are limited to $3,000 with a scheduled increase to $4,000 in tax years
2005“2007 and then to $5,000 afterward. Workers 50 years of age and up can increase annual
Bodie’Kane’Marcus: VI. Active Investment 18. Taxes, Inflation, and © The McGraw’Hill
Essentials of Investments, Management Investment Strategy Companies, 2003
Fifth Edition




635
18 Taxes, Inflation, and Investment Strategy



S P R E A D S H E E T 18.7
The benchmark (IRA) tax shelter with a progressive tax code


A B C D E F G H
1 Retirement Years Income Growth Rate of Inflation Exemption Now Tax rates in Savings Rate ROR rROR
2 25 0.07 0.03 10000 Table 18.1 0.15 0.06 0.0291
3 Age Income Deflator Exemption Taxes Savings Cumulative Savings rConsumption
4 30 50,000 1.00 10,000 5,140 9,160 9,160 35,700
5 31 53,500 1.03 10,300 5,553 9,880 19,590 36,958
9 35 70,128 1.16 11,593 7,480 13,654 77,112 42,262
19 45 137,952 1.56 15,580 14,749 33,880 434,916 57,333
29 55 271,372 2.09 20,938 32,920 72,885 1,455,451 79,076
39 65 533,829 2.81 28,139 66,100 172,359 4,125,524 104,970
40 Total 632,759 879,430 2,036,474 Real Annuity 83,380
41 RETIREMENT
42 Age Nom Withdraw Deflator Exemption Taxes Funds Left rConsumption
43 66 241,658 2.90 28,983 49,311 4,131,398 66,366
47 70 271,988 3.26 32,620 55,500 4,079,381 66,366
52 75 315,309 3.78 37,816 64,340 3,788,036 66,366
57 80 365,529 4.38 43,839 74,588 3,131,989 66,366
62 85 423,749 5.08 50,821 86,467 1,945,496 66,366
67 90 491,241 5.89 58,916 100,239 0 66,366
68 Total 8,810,670 Total 1,797,848




contributions by another $1,000. IRAs are somewhat illiquid (as are most shelters), in that
there is a 10% penalty on withdrawals prior to age 591„2. However, allowances for early with-
drawal with no penalty for qualified reasons such as (one-time) purchase of a home or higher
education expenses substantially mitigate the problem.
There are two types of IRAs to choose from; the better alternative is not easy to determine.

Traditional IRA Contributions to traditional IRA accounts are tax deductible, as are the traditional IRA
earnings until retirement. In principle, if you were able to contribute all your savings to a tra- Contributions
ditional IRA, your savings plan would be identical to our benchmark tax shelter (Spreadsheets to the account and
18.5 and 18.7), with the effectiveness of tax mitigation depending on your marginal tax rate investment earnings
are tax sheltered until
upon retirement.
retirement.
Roth IRA A Roth IRA is a variation on the traditional IRA tax shelter, with both a draw- Roth IRA
back and an advantage. Contributions to Roth IRAs are not tax deductible. However, earnings Contributions are
on the accumulating funds in the Roth account are tax-free, and unlike a traditional IRA, no not tax sheltered, but
taxes are paid upon withdrawals of savings during retirement. The trade-off is not easy to eval- investment earnings
are tax free.
uate. To gain insight and illustrate how to analyze the trade-off, we contrast Roth with tradi-
tional IRAs under our two alternative tax codes.

Roth IRA with the Progressive Tax Code
As we have noted, a traditional IRA is identical to the benchmark tax shelter set up under
two alternative tax codes in Spreadsheets 18.5 and 18.7. We saw that, as a general rule, the
effectiveness of a tax shelter depends on the progressivity of the tax code: lower tax rates dur-
ing retirement favor the postponement of tax obligations until one™s retirement years. How-
ever, with a Roth IRA, you pay no taxes at all on withdrawals during the retirement phase. In
this case, therefore, the effectiveness of the shelter does not depend on the tax rates during the
retirement years. The question for any investor is whether this advantage is sufficient to com-
pensate for the nondeductibility of contributions, which is the primary advantage of the tradi-
tional IRA.
Bodie’Kane’Marcus: VI. Active Investment 18. Taxes, Inflation, and © The McGraw’Hill
Essentials of Investments, Management Investment Strategy Companies, 2003
Fifth Edition




636 Part SIX Active Investment Management

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