Calculations Of Great Interest
The Age
Sunday September 6, 1992
VERY few people can expect to have enough money on retirement to live for long just on their savings and superannuation payouts. Most have to progressively eat into their capital upon retirement.
So you expect to receive _ or have already got $100,000 or $200,000 or whatever _ when you retire. But for how long will this money provide you with an acceptable standard of living?
The answer depends on many factors among which are: the rate of return which your funds can earn, the rate of inflation, the expense of your acceptable standard of living, your eligibility for a full or part government pension, what taxation will be deductible from income and what other assets or sources of income you have or will have.
Even if all but the first three of these factors are ignored, most retirees would find it difficult to work out how long their funds will last, unless they have access to a computer or calculator which is programmed for amortisation calculations _ and know how to use it. Furthermore, rates of return, rates of inflation, and what at any time one might contemplate spending, are all subject of change, requiring a revision of budget decisions.
However, the requisite calculations can easily by made by anyone armed with a cheap pocket calculator and the accompanying table _ or at least reasonably correct answers can be obtained.
What the table indicates is the number of years that will elapse before an initial sum of $100,000 would be reduced to zero for different real rates of return and different sums withdrawn per annum, in today's dollars. For example, if withdrawals are increased annually in money terms to keep pace with inflation. An investment's real rate of return is approximately its nominal rate of return (as quoted by the financial institution in which one has invested) less the rate of inflation.
By way of illustration of one of the ways in which the table can be used, suppose for the moment that there is no inflation and that an investment fund is earning three per cent per annum and can be expected to continue to do so.
The table indicates that a person with $100,000 in this fund could withdraw $8850 for 14 years, or $7,270 for 18 years, and so on. If the available capital in the fund was not $100,000 but $275,000 the withdrawable amounts would be 2.75times larger, or if the person's capital was $143,500 then the annual withdrawals which could be made for 14 years are equal to $143,500 divided by $100,000 multiplied by $8850 i.e. $12,700. (All sums of money are rounded off to the nearest $10).
What if inflation is not zero but a steady twoper cent per annum? The table is based on real earning rates and all one needs to do to use it when there is inflation is to deduct the annual rate of inflation from the nominal earning rate on funds to obtain the real earning rate.
To take the example just considered, if the fund's earning rate reflects the two per cent inflation rate and it earns five per cent in nominal terms, it is still returning three per cent each year in real terms. The same amounts as previously calculated can be withdrawn over the same periods in real terms.
THAT is to say, an initial capital of $143,500 would allow withdrawals of $12,700 plus two per cent at the end of the first year, and plus a further two per cent in the following year, and so on for 14 years. The annual withdrawals in money terms can grow at a rate which maintains the purchasing power that $12,700 has today.
Once one knows how much capital one has, its nominal earning rate and the rate of inflation, the table enables a simple calculation to determine how much can be withdrawn each year, in terms of what dollars can buy today, and for how long. Or, given a level of withdrawals for, say, 20 years as an objective, one can use the table to calculate how much capital in today's dollars one would need, depending on the real return one expects to earn. Of course what a fund actually earns and what is the annual rate of inflation can only be known with hindsight. Also, what a person may wish to (or have to) spend in any one year can also change; which leads to another helpful way in which the table can be used.
At the beginning of any year you can ascertain the value of your capital and make some assumptions as to its likely earning rate and the likely rate of inflation _ what happened last year is as good a guide as any unless there are clear indications to the contrary. Consulting the table and using that pocket calculator you can decide how much to withdraw, depending on how long you wish to continue that level of withdrawals. If last year's budget decision was made in the same way but the earning rate on funds or the rate of inflation proved to be different from what was previously expected, an over or under estimate of how long the money would last will have arisen. If it was underestimated, you might decide to raise the amount withdrawn this year, or maintain it because then the capital will last longer, and vice versa.
You might decide on a ``binge" year _ an overseas trip, say. How many years will this use up, or what future ``belt tightening" will pay for it? The table facilitates the calculation.
For example, say you have $186,000 and expect that the funds will earn four per cent per annum in the next and subsequent years in real terms. You hope to draw out $15,000 in other years, but are going to spend an additional $8000 this year for an overseas trip. Since $23,000 is taken out for the trip, this will leave you with $163,000 of capital.
To use the table, convert the $15,000 to the equivalent annual withdrawls with $100,000 of capital: $100,000 $163,000 x $15,000 = $9200 and by consulting the table you find that $100,000 would last a little over 14 years if $9200 is withdrawn anually. So $163,000 of capital would permit $15,000 to be drawn out each year for the same period.
Once the method of calculations is understood, any alternative numbers for capital, withdrawals, years, nominal interest rates and inflation can be substituted, and calculations made.
Lump sum calculator for capital of $100,000
Real rates of
return
(per annum) 2% 3% 4% 5% 6%
Years
capital Annual amounts withdrawable in present dollar values
lasts
6 17,850 18,460 19,080 19,700 20,340
8 13,650 14,250 14,850 15,470 16,100
10 11,130 11,720 12,330 12,950 13,950
12 9,460 10,050 10,660 11,280 11,930
14 8,260 8,850 9,470 10,100 10,760
16 7,370 7,960 8,580 9,230 9,900
18 6,670 7,270 7,900 8,550 9,240
20 6,120 6,720 7,360 8,020 8,720
22 5,660 6,270 6,920 7,600 8,300
24 5,290 5,900 6,560 7,250 7,970
(Note: All money sums have been rounded off to the nearest $10 and it is
assumed that withdrawals are taken as a lump sum at the end of the year
and earn no interest. Returns in the fund have been compounded annually.)
© 1992 The Age