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On the other hand, SS is progressive in the way it allocates benefits; low-income individu-
als receive a relatively larger share of preretirement income upon retirement. Of the SS tax of
7.65%, 6.2% goes toward the retirement benefit and 1.45% toward retirement healthcare
services provided by Medicare. Thus, combining your payments with your employer™s, the
real retirement annuity is financed by 2 6.2 12.4% of your income (up to the aforemen-
tioned cap); we do not examine the Medicare component of SS in this chapter.
SS payments are made throughout one™s entire working life; however, only 35 years of
contributions count for the determination of benefits. Benefits are in the form of a lifetime real
annuity based on a retirement age of 65, although you can retire earlier (as of age 62) or later
(up to age 70) and draw a smaller or larger annuity, respectively. One reason SS is projected
to face fiscal difficulties in future years is the increased longevity of the population. The cur-
rent plan to mitigate this problem is to gradually increase the retirement age.
Calculation of benefits for individuals retiring in a given year is done in four steps:
1. The series of your taxed annual earnings (using the cap) is compiled. The status of this
series is shown in your annual SS statement.
2. An indexing factor series is compiled for all past years. This series is used to account for
the time value of your lifetime contributions.
3. The indexing factors are applied to your recorded earnings to arrive at the Average
Indexed Monthly Earnings (AIME).
4. Your AIME is used to determine the Primary Insurance Amount (PIA), which is your
monthly retirement annuity.
All this sounds more difficult than it really is, so let™s describe steps 2 through 4 in detail.

The Indexing Factor Series
Suppose your first wage on which you paid the SS tax was earned 40 years ago. To arrive
at today™s value of this wage, we must calculate its future value over the 40 years, that is,
FV wage (1 g)40. The SS administration refers to this as the indexed earnings for that
year, and the FV factor, (1 g)40, is the index for that year. This calculation is made for each
year, resulting in a series of indexed earnings which, when summed, is the value today of the
entire stream of lifetime taxed earnings.
A major issue is what rate, g, to use in producing the index for each year. SS uses for each
year the growth in the average wage of the U.S. working population in that year. Arbitrarily,
the index for the most recent two years is set to 1.0 (a growth rate of zero) and then increased
each year, going backward, by the growth rate of wages in that year. For example, in the year
2001 the index for 1967 (35 years earlier) was 6.16768. Thus the 1967 wage is assumed to
have been invested for 35 years at 5.34% (1.053435 6.16768). The actual average growth
rate of wages in the U.S. over the years 1967“2001 was 5.48%8; the index is slightly lower be-
cause the growth rate in the two most recent years prior to retirement has been set to zero.
Wage growth was not constant over these years. For example, it was as high as 10.07% in
1980“1981, and as low as 0.86% in 1992“1993. At the same time, the (geometric) average
T-bill rate over the years 1967“2001 was 6.53% and the rate of inflation 4.92%, implying a
real interest rate of 1.53%. For retirees of 2002, the average real growth rate applied to their
SS contributions is about 0.40% (depending on how much they contributed in each year), sig-
nificantly lower than the real interest rate over their working years, but closer to the longer-
term (1926“2001) real rate of 0.72%. (See Table 5.2).

We use a wage growth rate of 7% in our exercises, assuming our readers are well educated and can expect a higher
than average growth. Special attention must be given to this input (and the others) if you advise other people.
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18 Taxes, Inflation, and Investment Strategy

TA B L E 18.5
Calculation of the retirement annuity of representative retirees of 2002

Low Average High Maximum

AIME rank:
% of Average Wage 45 100 160 Max*
AIME ($ month) 1,207 2,683 4,145 5,489
PIA formula:
90% of the first $592 532.80 532.80 532.80 532.80
32% of AIME over $592 through $3,567 196.80 669.12 952.00 952.00
15% of AIME over $3,567 0 0 86.70 289.80
Total PIA ($/month) 729.60 1201.92 1571.50 1774.60
Real retirement annuity PIA 12 8,755 14,423 18,858 21,295
Income replacement (%) 60.45 44.80 37.91
IRR** assuming longevity 81; inflation 3% 7.44 6.20 5.49 4.72
IRR** assuming longevity 84; inflation 3% 7.76 6.56 5.89 5.18
Longevity implied by SS (years) for IRR 6% 11 15 18 23

*Income is above the maximum taxable and income replacement cannot be calculated.
**Internal Rate of Return.

The Average Indexed Monthly Income
The series of a retiree™s lifetime indexed contributions (there may be zeros in the series for
periods when the retiree was unemployed) is used to determine the base for the retirement
annuity. The 35 highest indexed contributions are identified, summed, and then divided by
35 12 420 to achieve your Average Indexed Monthly Income (AIME). If you worked less
than 35 years, all your indexed earnings will be summed, but your AIME might be low since
you still divide the sum by 420. If you worked more than 35 years, your reward is that only
the 35 highest indexed wages will be used to compute the average.

The Primary Insurance Amount
In this stage of the calculation of monthly SS benefits, low-income workers (with a low
AIME) are favored in order to increase income equality. The exact formula may change from
one year to the next, but the example of four representative individuals who retired in 2002
demonstrates the principle. The AIME of these individuals relative to the average in the pop-
ulation and their Primary Insurance Amount (PIA) are calculated in Table 18.5.
Table 18.5 presents the value of SS to U.S. employees who retired in 2002. The first part of
the table shows how SS calculates the real annuity to be paid to retirees.9 The results differ for
the four representative individuals. One measure of this differential is the income replacement
rate (i.e., retirement income as a percent of working income) provided to the four income
brackets in Table 18.5. Low-income retirees have a replacement rate of 60.45%, more than
1.5 times that of the high-wage employees (37.91%).
The net after-tax benefits may be reduced if the individual has other sources of income,
because a portion of the retirement annuity is subject to income tax. Currently, retired house-
holds with combined taxable income over $32,000 pay taxes on a portion of the SS benefits.
At income of $44,000, 50% of the SS annuity is subject to tax and the proportion reaches 85%

The annuity of special-circumstance low-income retirees is supplemented.
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Fifth Edition

642 Part SIX Active Investment Management

at higher income. You can find the current numbers and replicate the calculations in Table 18.5
by logging on to http://www.ssa.gov/OACT/ProgData/nominalEarn.html. This website also
allows you to project Social Security benefits at various levels of sophistication.
When evaluating the attractiveness of SS as an investment for current retirees (the bottom
part of Table 18.5), we must consider current longevity figures. For a male, current remaining
life expectancy at age 65 is an additional 15.6 years, and for a female 19.2 years. Using these
Remaining life
figures, the current PIA provides male retirees an internal rate of return on SS contributions in
the range of 7.44“4.72%, and female retirees 7.76“5.18%.10 These IRRs are obtained by
taking 12.4% (the combined SS tax) of the series of 35 annual earnings of the four employees
as cash outflows. The series of annuity payments (16 years for males and 19 for females), as-
suming inflation at 3%, is used to compute cash inflows.
To examine SS performance another way, the last line in the table shows the longevity
(number of payments) required to achieve an IRR of 6%. Except for the highest income
bracket, all have life expectancy greater than this threshold. Why are these numbers so attrac-
tive, when SS is so often criticized for poor investment performance? The reason benefits are
so generous is that the PIA formula sets a high replacement rate relative to the SS tax rate, the
proportion of income taxed. Taking history as a guide, to achieve an IRR equal to the rate of
inflation plus the historical average rate on a safe investment such as T-bills (with a historical
real rate of 0.7%), the formula would need to incorporate a lower replacement rate. With a
future rate of inflation of 3%, this would imply a nominal IRR of 3.7%. Is the ROR assumed
in our spreadsheets (6%) the right one to use, or is the expected IRR based on past real rates
the correct one to use? In short, we simply don™t know. But averaging across the population,
SS may well be a fair pension plan, taking into consideration its role in promoting equality of
The solvency of SS is threatened by two factors: population longevity and a below-
replacement growth of the U.S. population. Over the next 35 years, longevity is expected to
increase by almost two years, increasing steady-state expenditures by more than 10%. To keep
a level population (ignoring immigration) requires an average of 2.1 children per female, yet
the current average of 1.9 is expected to decline further.11 The projected large deficit, begin-
ning in 2016, requires reform of SS. Increasing the retirement age to account for increased
longevity does not constitute a reduction in the plan™s IRR and therefore seems a reasonable
solution to deficits arising from this factor. Eliminating the deficit resulting from population
decline is more difficult. It is projected that doing so by increasing the SS tax may require an
increase in the combined SS tax of as much as 10% within your working years. Such a simple
solution is considered politically unacceptable, so you must expect changes in benefits.
The question of privatizing a portion of SS so that investors will be able to choose port-
folios with risk levels according to their personal risk tolerance has become a hot public policy
issue. Clearly, the current format that provides a guaranteed real rate is tailored to individuals
with low risk tolerance. Although we advocate that at least a portion of SS be considered as a
safety-first proposition (with a very low-risk profile), investors who are willing to monitor and
rebalance risky portfolios cannot be faulted for investing in stocks. The main point with
respect to this option is that the media and even some finance experts claim that a long-term
investment in stocks is not all that risky. We cannot disagree more. We project that with

However, income is correlated with longevity and with durability of marriage. This means that wealthy retirees and
their spouses draw longer annuities than the poor do. It is suggested that this difference may as much as completely
offset the progressivity built into the PIA schedule.
Fertility rates in Europe, Japan, and (until recently) in China are even lower, exacerbating the problems of their
Social Security systems.
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Fifth Edition

18 Taxes, Inflation, and Investment Strategy

appropriate risk adjustment, future retirees will find it difficult to beat the SS plan and should
be made fully aware of this fact.12

9. Should you consider a dollar of future Social Security benefits as valuable as a Concept
dollar of your projected retirement annuity? For example, suppose your target is a
real annuity of $100,000 and you project your SS annuity at $20,000. Should you
save to produce a real annuity of $80,000?

Sending a child to a private college can cost a family in excess of $40,000 a year, in current
dollars, for four years. Even a state college can cost in excess of $25,000 a year. Many fami-
lies will send two or more children to college within a few years, creating a need to finance
large expenditures within a few years. Other large expenditures such as a second home (we
deal with the primary residence in the next section) or an expensive vehicle present similar
problems on a smaller scale.
The question is whether planned, large outflows during the working years require a major
innovation to our planning tools. The answer is no. All you need to do is add a column to your
spreadsheet for extra-consumption expenditures that come out of savings. As long as cumula-
tive savings do not turn negative as the outflows take place, the only effect to consider is the
reduction in the retirement annuity that results from these expenditures. To respond to a lower-
than-desired retirement annuity you have four options: (1) increase the savings rate, (2) live
with a smaller retirement annuity, (3) do away with or reduce the magnitude of the expendi-
ture item, or (4) increase expected ROR by taking on more risk. Recall though, that in Section
18.2, we suggested option 4 isn™t viable for many investors.
The situation is a little more complicated when the extra-consumption expenditures create
negative savings in the retirement plan. In principle, one can simply borrow to finance these
expenditures with debt (as is common for large purchases such as automobiles). Again, the
primary variable of interest is the retirement annuity. The problem, however, is that if you
arrive at a negative savings level quite late in your savings plan, you will be betting the farm
on the success of the plan in later years. Recalling, again, the discussion of Section 18.2, the
risk in later years, other things being equal, is more ominous since you will have little time to
recover from any setbacks.
An illuminating example requires adding only one column to Spreadsheet 18.2, as shown
in Spreadsheet 18.10. Column G adds the extra-consumption expenditures. We use as input
(cell G2) the current cost of one college year per child”$40,000. We assume your first child
will be collegebound when you are 48 years old and the second when you are 50. The expen-
ditures in column G are inflated by the price level in column C and subtracted from cumula-
tive savings in column E.
The real retirement annuity prior to this extra-consumption expenditure was $48,262, but
“after-children” only $22,048, less than half. The expenditure of $320,000 in today™s dollars
cost you total lifetime real consumption of 25 ($48,262 $21,424) $6,710,950 because

Here, again, we collide with those who consider stocks low-risk investments in the long run (some of them esteemed
colleagues). One cannot overestimate the misleading nature of this assessment (see the Appendix to Chapter 6). The
difference between the 35-year average real rate over 1967“2001 (1.53%) and 1932“1966 ( 1.05%), was 2.58%!
Over long horizons, such a difference has staggering effects on retirement income. Check your spreadsheets to see the
impact of a 1% change in ROR.
Bodie’Kane’Marcus: VI. Active Investment 18. Taxes, Inflation, and © The McGraw’Hill
Essentials of Investments, Management Investment Strategy Companies, 2003
Fifth Edition

644 Part SIX Active Investment Management

S P R E A D S H E E T 18.10
Financing children™s education


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