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> Analyze lifetime savings plans.


> Account for inflation in formulating savings and investment
plans.


> Account for taxes in formulating savings and investment
plans.

> Understand tax shelters.


> Design your own savings plan.




624
Bodie’Kane’Marcus: VI. Active Investment 18. Taxes, Inflation, and © The McGraw’Hill
Essentials of Investments, Management Investment Strategy Companies, 2003
Fifth Edition




http://www.ssa.gov
Related Websites
Visit the above site to find information on
http://www.tamasset.com
Social Security.
This site contains information on asset class returns
http://www.bloomberg.com
and studies on portfolio management.
http://www.morningstar.com
http://www3.troweprice.com/retincome/RIC
http://www.quicken.com
The above site has a simulation retirement planner that
can be used to assess the ability to meet goals under The sites listed above contain information on personal
different allocation strategies. financial planning.
http://flagship.vanguard.com/VGApp/hnw/
PlanningAndAdvice
Here you will find general educational information on
financial planning.




n previous chapters we concentrated mostly on the role of professional manage-

I ment of investments. In this chapter we are concerned with individual investors™
management of their overall lifetime savings plans. Our major objective is to
introduce you to the principles of managing personal savings in a complex environ-
ment in which taxes and inflation interact, rather than to provide a detailed analysis
of the (ever-changing) tax code.
Retirement, purchase of a home, and financing the education of children are the
major objectives of saving in most households. Inflation and taxes make the task of
gearing investment to accomplish these objectives complex. The long-term nature of
savings intertwines the power of compounding with inflation and tax effects. Only the
most experienced investors tend to fully integrate these issues into their investment
strategies. Appropriate investment strategy also includes adequate insurance cover-
age for contingencies such as death, disability, and property damage.
We introduce some of these issues by focusing on one of the long-term goals:
formulating a retirement plan. We investigate the effect of inflation on the savings
plan and examine how tax shelters may be integrated into one™s strategy.1 Next we in-
corporate Social Security and show how to generalize the savings plan to meet other
objectives such as owning a home and financing children™s education. Finally, we dis-
cuss uncertainty about longevity and other contingencies. Understanding the spread-
sheets we develop along the way will enable you to devise savings/investment plans
for yourself and other households and adapt them to an ever-changing environment.



1
Readers in other countries will find it easy to adapt the analysis to the tax code of their own country.
Bodie’Kane’Marcus: VI. Active Investment 18. Taxes, Inflation, and © The McGraw’Hill
Essentials of Investments, Management Investment Strategy Companies, 2003
Fifth Edition




626 Part SIX Active Investment Management


18.1 SAVING FOR THE LONG RUN
In Chapter 17 we described the framework that the Association of Investment Management
and Research (AIMR) has established to help financial advisers communicate with and
involve client households in structuring their savings/investment plans.2 Our objective here
is to quantify the essentials of savings/investment plans and adapt them to environments in
which investors confront both inflation and taxes. As a first step in the process, we set up a
spreadsheet for a simple retirement plan, ignoring for the moment saving for other objectives.
Before diving in, a brief word on what we mean by saving. Economists think of saving as
a way to smooth out the lifetime consumption stream; you save when you have high earnings
in order to support consumption in low-income years. In a “global” sense, the concept implies
that you save for retirement so that consumption during the retirement years will not be too
low relative to consumption during the saving years. In a “local” sense, smoothing consump-
tion implies that you would finance a large purchase such as a car, rather than buy it for cash.
Clearly, local consumption smoothing is of second-order importance, that is, how you pur-
chase durable goods has little effect on the overall savings plan, except, perhaps, for very large
expenditures such as buying a home or sending children to college. We begin therefore with a
savings plan that ignores even large expenditures and later discuss how to augment the plan to
account for these needs.


A Hypothetical Household
Imagine you are now 30 years old and have already completed your formal education, accu-
mulated some work experience, and settled down to plan the rest of your economic life. Your
plan is to retire at age 65 with a remaining life expectancy of an additional 25 years. Later on,
we will further assume that you have two small children and plan to finance their college
education.
For starters, we assume you intend to obtain a (level) annuity for your 25-year retirement
period; we postpone discussion of planning for the uncertain time of death. (You may well live
to over 100 years; what then?) Suppose your gross income this year was $50,000, and you
expect annual income to increase at a rate of 7% per year. In this section, we assume that you
ignore the impact of inflation and taxes. You intend to steadily save 15% of income and invest
in safe government bonds that will yield 6% over the entire period. Proceeds from your in-
vestments will be automatically reinvested at the same 6% until retirement. Upon retirement,
your funds in the retirement account will be used to purchase a 25-year annuity (using the
same 6% interest rate) to finance a steady consumption annuity. Let™s examine the conse-
quences of this framework.


The Retirement Annuity
We can easily obtain your retirement annuity from Spreadsheet 18.1, where we have hidden
retirement
the lines for ages 32“34, 36“44, 46“54, and 56“64. You can obtain all the spreadsheets in this
annuity
chapter from the Web page for the text: http://www.mhhe.com/bkm.
Stream of cash
Let™s first see how this spreadsheet was constructed. To view the formulas of all cells in
flows available for
an Excel spreadsheet, choose “Preferences” under the “Tools” menu, and select the box
consumption during
one™s retirement years. “Formulas” in the “View” tab. The formula view of Spreadsheet 18.1 is also shown on the
next page (numbers are user inputs).
2
If you skipped Chapter 17, you may want to skim through it to get an idea of how financial planners articulate a
saver™s objectives, constraints, and investment policy.
Bodie’Kane’Marcus: VI. Active Investment 18. Taxes, Inflation, and © The McGraw’Hill
Essentials of Investments, Management Investment Strategy Companies, 2003
Fifth Edition




627
18 Taxes, Inflation, and Investment Strategy



S P R E A D S H E E T 18.1
The savings plan


A B C D E
1 Retirement Years Income Growth Savings Rate ROR
2 25 0.07 0.15 0.06
3 Age Income Savings Cumulative Savings Consumption
4 30 50,000 7,500 7,500 42,500
5 31 53,500 8,025 15,975 45,475
6 32 57,245 8,587 25,520 48,658
9 35 70,128 10,519 61,658 59,608
19 45 137,952 20,693 308,859 117,259
29 55 271,372 40,706 943,477 230,666
39 65 533,829 80,074 2,457,518 453,755
40 Total 7,445,673 1,116,851 Retirement Annuity 192,244


A B C D E
1 Retirement Years Income Growth Savings Rate ROR
2 25 0.07 0.15 0.06
3 Age Income Savings Cumulative Savings Consumption
4 30 50000 =B4*$C$2 =C4 =B4-C4
5 31 =B4*(1+$B$2) =B5*$C$2 =D4*(1+$D$2)+C5 =B5-C5
39 65 =B38*(1+$B$2) =B39*$C$2 =D38*(1+$D$2)+C39 =B39-C39
40 Total =SUM(B4:B39) =SUM(C4:C39) Retirement Annuity =PMT($D$2,$A$2,-$D$39,0,0)




Inputs in row 2 include: retirement years (cell A2 25); income growth (cell B2 .07);
Age (column A); and income at age 30 (B4 50,000). Column B computes income in future
years using the growth rate in cell B2; column C computes annual savings by applying the
savings rate (cell C2) to income; and column E computes consumption as the difference be-
tween income and savings: column B column C. Cumulative savings appear in column D.
To obtain the value in D6, for example, multiply cell D5 by 1 plus the assumed rate of return
in cell D2 (the ROR) and then add current savings from column C. Finally, C40 shows the
sum of dollars saved over the lifetime, and E40 converts cumulative savings (including inter-
est) at age 65 to a 25-year annuity using the financial function PMT from Excel™s function
menu. Excel provides a function to solve for annuity levels given the values of the interest
rate, the number of periods, the present value of the savings account, and the future value of
the account: PMT(rate, nper, PV, FV).
We observe that your retirement fund will accumulate approximately $2.5 million (cell
D39) by age 65. This hefty sum shows the power of compounding, since your contributions to
the savings account were only $1.1 million (C40). This fund will yield an annuity of $192,244
per year (E40) for your 25-year retirement, which seems quite attractive, except that the stan-
dard of living you™ll have to get accustomed to in your retirement years is much lower than
your consumption at age 65 (E39). In fact, if you unhide the hidden lines, you™ll see that upon
retirement, you™ll have to make do with what you used to consume at age 51.3 This may not
worry you much since, with your children having flown the coop and the mortgage paid up,
you may be able to maintain the luxury to which you recently became accustomed. But your
projected well being is deceptive: get ready to account for inflation and taxes.


<
1. If you project an ROR of only 5%, what savings rate would you need to maintain Concept
the same retirement annuity?
CHECK


3
It would make sense (and would be easy) to rig the retirement fund to provide an annuity with a choice growth rate
to allow your standard of living to grow with that of your social circle. We will abstract from this detail here.
Bodie’Kane’Marcus: VI. Active Investment 18. Taxes, Inflation, and © The McGraw’Hill
Essentials of Investments, Management Investment Strategy Companies, 2003
Fifth Edition




628 Part SIX Active Investment Management


18.2 ACCOUNTING FOR INFL ATION
Inflation puts a damper on your plans in two ways: First, it erodes the purchasing power of the
cumulative dollars you have so far saved. Second, the real dollars you earn on your portfolio
each year depend on the real interest rate, which, as Chapter 5 showed, is approximately equal
to the nominal rate minus inflation. Since an appropriate savings plan must generate a decent
real annuity, we must recast the entire plan in real dollars. We will assume your income still is
forecast to grow at a 7% rate, but now you recognize that part of income growth is due to in-
flation, which is running at 3% per year.

A Real Savings Plan
To convert nominal dollars to real dollars we need to calculate the price level in future years
relative to today™s prices. The “deflator” (or relative price level) for a given year is that year™s
price level divided by today™s. It equals the dollars needed at that future date which provide
the same purchasing power as $1 today (at age 30). For an inflation rate of i 3%, the defla-
tor for age 35 is (1 i)5, or in Excel notation, (1 i)^5 = 1.03^5 1.16. By age 65, the de-
flator is 2.81. Thus, even with a moderate rate of inflation (3% is below the historical average,
as you can see from Figure 5.4), nominal dollars will lose a lot of purchasing power over long
horizons. We also can compute the real rate of return (rROR) from the nominal ROR of 6%:
rROR (ROR i)/(1 + i) 3/1.03 2.91%.
Spreadsheet 18.2, with the formula view below it, is the reworked Spreadsheet 18.1
adjusted for inflation. In addition to the rate of inflation (cell C2) and the real rate of return
(F2), the major addition to this sheet is the price level deflator (column C). Instead of nominal
consumption, we present real consumption (column F), calculated by dividing nominal
real consumption
consumption (column B column D) by the price deflator, column C.
Nominal consumption
The numbers have changed considerably. Gone is the luxurious retirement we anticipated
divided by the price
earlier. At age 65 and beyond, with a real annuity of $49,668, you will have to revert to a
deflator.
standard of living equal to that you attained at age 34; this is less than a third of your real
consumption in your last working year, at age 65. The reason is that the retirement fund of
$2.5 million (E39) is worth only $873,631 in today™s purchasing power (E39/C39). Such is the
effect of inflation. If you wish to do better than that, you must save more.


S P R E A D S H E E T 18.2
A real retirement plan

A B C D E F
1 Retirement Years Income growth Rate of Inflation Savings rate ROR rROR
2 25 0.07 0.03 0.15 0.06 0.0291
3 Age Income Deflator Saving Cumulative Savings rConsumption
4 30 50,000 1.00 7,500 7,500 42,500
5 31 53,500 1.03 8,025 15,975 44,150

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