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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).

8

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

NA*

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%

9

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

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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

longevity

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

expectancy.

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

income.

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

10

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.

11

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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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

CHECK

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?

18.7 CHILDREN™S EDUCATION AND

L ARGE PURCHASES

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

12

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.

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644 Part SIX Active Investment Management

S P R E A D S H E E T 18.10

Financing children™s education