## It’s complicated, it requires detailed work—but it’s all right here in a how-to-do-it format. So, get out your calculators (one that can solve for exponentials) …

More than any single factor, money will determine when people will retire and the type of lifestyle they will have during retirement. This article is designed to help you determine your income needs during retirement and create a plan to achieve your objective.

## An Overview of the Process

The process is complex and will be described in detail. But let’s start with an overview. The steps in the analysis can be summarized:

- First determined are what your income needs would be if you were to retire today;
- Next, the future value of those dollars upon retirement are determined;
- The amount of capital needed at retirement to produce that future income need over the course of retirement is then calculated;
- Sources of income during retirement, expressed in terms of retirement date dollars, must be subtracted from this capital need;
- Also subtracted from this capital need are cash ﬂows expected up to retirement age, any future contributions to retirement plans and the future value of any current capital;
- If you have a surplus, great!
- If more capital is required upon retirement, determine how much more must be saved each year to reach the required level. Much of the analysis is dependent upon certain formulas, and these are summarized in
**Table 1**The variables in the formulas are described in the text, since they will vary depending upon how they are used.

Finally, the analysis is dependent on many assumptions and parameters. These include:

- Inﬂation rate,
- Aftertax rate of return,
- Mortality age,
- Social Security benefit amount and rate of increase,
- Income from employee benefit plans,
- Existing working capital (i.e., assets that will grow and be available for use in providing income at retirement),
- Growth rate for existing working capital,
- Projected liabilities at age of retirement,
- Future annual cash ﬂow margin, (i.e., annual amounts available for accumulation for retirement use),
- Future annual contributions to employee benefit/retirement plans, and
- Rates of return on future annual cash flow margin and future annual employee benefit/retirement plans.

The prospective retiree must determine these assumptions and parameters for his own situation; growth and inﬂation rates should be figures you feel are realistic. We will go through an example in this article, which will provide you with an indication of how these parameters and assumptions affect the analysis.

## Your Income Needs

The first step in estimating your future income needs is determining what your present needs are. To do this, one must create a “budget” or, rather, a summary of what your current expenses are. Begin making a list of all expenses you incur according to your current standard of living and record these along the left-hand side of a piece of paper. Try to include as much detail as possible and account for every expense, including income taxes. Add an expense item labeled “cash” to account for cash expenditures that you cannot specifically retrieve from past records. The total of this column should accurately represent your total current expenditures, which, indirectly, represent the lifestyle you lead.

Now comes the creative part. Next to each expenditure listed, make an estimate of what you would like that expense to be if you were retired now, in today’s dollars. For example, you might currently spend $1,000 per year on vacations. However, if you were retired today you may want to travel more, and thus you allocate $3,000 per year to this expense during retirement (please remember, this is in today’s dollars). You may spend $2,500 per year on clothing now because of your employment, yet during retirement you estimate a need for less formal attire; thus, you allocate $1,000 per year to this expense. The key here is to mentally picture yourself retired, this very moment, and create the expenditures you would like to have. Of course, you should be realistic with your “wants.”

This method allows you to create the lifestyle you would like during retirement by establishing an estimate of your desired retirement cash allocations now, rather than waiting until retirement. Too often, people retire, gather up all their assets, determine their monthly estimated income from employee benefit plans and Social Security and then create their lifestyle around what they have. They are then in a situation where their finances control them and, by extension, their lifestyles during retirement. Using the above method, you can quantify the lifestyle you would like during retirement and then plan for the sum to be accumulated by retirement in order to achieve this lifestyle.

## Converting to Future Dollars

At this point, if you’ve done your homework, you have an approximate gross (before-tax) income need during retirement in today’s dollars. We will call this the *current annual* need. However, inﬂation will erode this figure by the time you hit retirement age. Therefore, we must project this need out to your anticipated retirement date and beyond, to determine its equivalent purchasing power in future dollars.

Let’s take an example. John and Mary would like to retire at John’s age 60; currently he is 53. Let’s assume they have determined their gross annual income need for retirement in today’s dollars to be $30,000. We also have to make some other assumptions and parameters—these are presented in **Table 2**.

The *future need* to maintain today’s buying power will be the result of applying the future value formula to the current annual need. In this instance, the *n* in the formula represents the number of years from today until retirement; the *i* represents the assumed rate of inflation, in this instance 6% [Note: The current inflation rate for the U.S. is 2.2% for the 12 months ended September 2017]. **Table 3** presents the future need assuming a 6% inflation rate for various points in John and Mary’s retirement years. It indicates that they will need $45,109 when John reaches 60 to equal the buying power in today’s dollars.

## Determining Capital Needs

Once the future need has been determined, John and Mary need to determine how much will be needed upon retirement to sustain the future need each year for all the years of retirement. This can be determined by applying the formula for the present value of annuity due; the *n* in this formula is the number of years for the period, which in this case is from retirement age until mortality.

If you look at this formula in **Table 1**, you will note that instead of *i* for an inﬂation rate, *iar* is used. This is the inﬂation adjusted rate, and is the real rate of return expected over the period in question, which in this instance starts with the retirement date. The reason for using this is straightforward: The future need figure has already been adjusted for any inﬂation between now and retirement age; the inﬂation adjusted rate accounts for inﬂation after retirement. For the *iar* formula, *r* is the before-tax, post-retirement expected rate of return and *i* is the annual inﬂation rate.

We now have a figure that accurately reﬂects capital needs at the beginning of retirement. From this, we must subtract all income sources over the course of retirement.

## Determining Income Sources

The value of income sources is determined in the same manner in which we determined need. First, these sources are totaled in current dollars. The future value of those dollars is determined using the future value formula, where *n* is the number of years between now and retirement, and *i* is the estimated annual increase (or return) for the source.

The value of this income source at the beginning of the retirement period is determined by applying the present value of annuity due formula. Here, again, *iar *adjusts the figure for inﬂation that occurs after the retirement date; for the *iar* formula,* i* is the estimated annual increase (or return rate) for the income source. In the present value of annuity due formula, *n* represents the number of years over which the income source is received.

The difference between the income need and all of the income sources is the total capital required at retirement.

## Retirement Phases

**Table 4** presents a real-life example of the calculations involved. The example recognizes the fact that many factors, such as income requirements, Social Security benefits and income from retirement plans, will change during retirement. Therefore, the retirement years in the example have been divided into four phases: Phase 1 lasts five years; Phase 2 lasts three years; Phase 3 lasts 22 years; and Phase 4 lasts two years, ending with Mary’s expected mortality age of 89.

For each of the phases, both income needs and sources have been determined, as described above. For instance, in Phase 2, John is age 65 to 67. The future value (upon retirement) of his currently desired $30,000 income is $60,366. The next calculation is the amount of capital required upon retirement age to produce this amount of income for the next three years of this phase, when he turns 68; this turns out to be $174,592. The income source over this three-year time period is currently worth $9,936; the future value of this source when he turns 65 will be $12,601. The total value of this source of income for this three-year phase, using the present value of annuity due formula, is $35,121. Similarly, his pension plan will be worth $16,413. The income sources, when subtracted from income needs, produce a net capital requirement of $123,058.

The capital needs for the different phases reflect values at the start of that phase. For instance, $123,058 represents the capital needed by John when he is 65. However, the overall planning process is based on John’s retirement age of 60. Therefore, when the final tally is made, the capital needs of the individual phases must be restated in age-60 dollars. The present value formula accomplishes this. For Phase 2, that discounted amount is $76,409.

If income sources over a particular phase produce a surplus over income needed, it is carried over to the next phase as an income source. However, its value at the beginning of the next phase must be determined by using the future value formula: *n* is the number of years between the two phases, or the age at the beginning of the next phase less the age at the beginning of the current phase;* i* is the expected rate of return for that period.

The bottom of **Table 4** presents a summary of the capital amounts necessary in each phase. The final sum is the total capital required at retirement, when John is 60.

## Taking Stock of Existing Capital

Up to this point, we have taken future income needs, subtracted all future income sources available during retirement and arrived at a lump sum of capital required at retirement.

But what about existing capital, and future sources of income that will accumulate before retirement?

**Table 5** continues the John and Mary example, with these new figures included. John and Mary’s current capital is determined, and its value upon retirement is calculated, using the future value formula; *r* is the assumed rate of return on the capital. From this figure, all liabilities remaining at retirement are subtracted. This produces a future value for *existing* *working capital*. In the same way, future values are determined for any future annual cash ﬂow and future contributions to any qualified retirement plans. In determining future values for cash ﬂow, you should remember to use an aftertax rate of return. These future values are then totaled.

## The End Is Near

The future value of net existing capital, and the future values of annual cash flows and pension contributions are subtracted from the lump sum of capital required upon retirement. This is the figure you have been working toward: the *total capital required* or *surplus.*

If there is a total capital requirement, you will need to determine a schedule of savings for this amount.

Annual investing schedules are calculated by dividing the total capital required by the factor determined in the future value of annuity formula, where *i* is the aftertax rate of return [(1 – marginal tax bracket) × rate of return], and *n* is the number of years before retirement age (retirement age less current age).

Once calculated, the annual investment schedules will tell you how much additional savings will be necessary each year to achieve your objective.

If you showed a capital surplus on your financial independence calculation, as did John and Mary, you are on your way to achieving your objective.

## This article was written by Michael E. Leonetti for the April 1986 issue of the

AAII Journal. At the time, he was president of Leonetti & Associates, a fee-only financial planning firm based in Arlington Heights, Illinois. Leonetti is currently the chief executive officer of Leonetti & Associates.

curious as to the calculation to get the 7.84% IAR for social security. I understand the 3.77 math and 10% but what numbers go into the calculation for the 7.84%?

I like this and just trying to reverse engineer and understand each step and the math.

Great article. Do you have this spreadsheet template available for download?

MUCH too complicated. You can do the same thing on one page using an Excell spreadsheet.