need $10,000 more than normal to pay for it, the extra withdrawals represent lumps in the otherwise smooth payment stream.
Fortunately, mathematical programming can solve this sort of problem. Unfortunately, like many high-level mathematical tech- niques, it is not easily understood. The formulations and solution algorithms are admittedly complex. It is a little like playing the vio- lin: It only looks easy by someone who knows how to do it. Anyone who has had a course that includes mathematical programming can testify to its complexity (unfortunately, I am convinced that some of my MBA students never really catch on). So the actual calculations are best left to a computer, which is exactly what Chapter 8 describes how to do.
activities, or whatever else turns them on. Volatility should no longer bother them, nor should the puzzling prognostications of the market pundits. By dedicating their assets, they have locked in a plan that will automatically take care of them for the next 5 years. Sometime in the fifth year, they will need to withdraw $56,180 to support their sixth year of retirement and reload the portfolio for the next 5 years.
They have answered the three classic retirement questions:
1. How much can I spend?
Answer:Recall from Chapter 5 that 10 years earlier, the Browns estimated that they would need the equiva- lent of about $70,000 gross annual income when they retired. Under their plan, that income would be supplied from three sources: $30,000 from their retirement portfo- lio, $20,000 from Social Security, and $20,000 from other pensions. Adjusting for 4 percent inflation increases this
$70,000 gross to $103,617.10After taxes, this would leave them a net spending budget of $82,894 per year, or $6908 per month. They do not have to spend every penny, of course, and they could always plow any leftover money back into the growth portion of their portfolio. But this is what they had planned for.
2. How long will my money last?
Answer:If all their projections and assumptions hold true, their income should last until they reach their hun- dredth birthdays.
The Distribution Phase: Dedicating Assets to Do Their Job 147
Table 7.3
The Browns’ First 5 Years of Withdrawals after Retirement
Income Withdrawals Age Year with Inflation
66 0 $44,400
67 1 $46,176
68 2 $48,023
69 3 $49,944
70 4 $51,942
71 5 $54,019
Total, Years 1–5: $250,104
3. How much does my portfolio have to earn?
Answer:The growth portion will have to earn a total return of 11 percent per year, and the overall portfolio, 8 percent.
By monitoring their portfolio as they withdraw funds from it, the Browns can follow the critical path that their portfolio has to trace out if it is to remain on target. Table 7.4 shows what their portfolio ought to be worth every 5 years of their retirement.
Figure 7.1 charts the critical path from age 56 through age 102. The left-hand portion represents the preretirement critical path from age 56 to 66 and is the same as Figure 6.1. Note that it began at $275,000 and, with their additional savings and growth, grew to $866,687 on the day of their retirement. It then continues to grow because the initial withdrawals are less than the annual growth. By the time the Browns reach age 86, the portfolio reaches the maximum estimated value shown, $1,264,942. At this point, they are probably feeling very comfortable.
But their portfolio begins to decline after they reach age 86, as the income withdrawals (including inflation) begin to outpace growth. The decline is not a surprise. Recall that they deliberately chose to withdraw more than the recommended 4 percent neces- sary for a self-sustaining portfolio that would probably never run
Table 7.4
Critical Path of Nest Egg Balance after Retirement
Critical Path = Nest Egg Income Balance before Age Withdrawals Withdrawals
66 $44,400 $866,687
72 $56,180 $1,025,634 77 $68,352 $1,146,459 82 $83,160 $1,238,306 87 $101,177 $1,264,942 92 $123,098 $1,162,785
97 $149,767 $828,388
102 $94,918 $94,918
out. They planned for their portfolio to last until they were age 100.
That is, they had planned their last withdrawal for their ninety- ninth birthday. At that point, they expected the account to be com- pletely liquidated.
It may be exhausted a little sooner or a little later. Projections can be made assuming that market conditions remain the same over time. For example, the Browns can assume that the yield curve on interest rates will remain exactly the same in the future as it was on the day they started their retirement, that the 11 per- cent total return on the growth portion remains the same, and that inflation remains the same at 4 percent. They can plug the ending values of their growth portfolio after each planning horizon into the input screen, and also plug in what their withdrawals will be in future dollars. Chapter 8 will project their retirement experience if these assumptions hold and they survive beyond the 99th per- centile life expectancy. It turns out that under these assumptions, their portfolio will last a little beyond age 100. At about that time, their funds will become exhausted and they will be broke. But the portfolio did the job it was designed to do: It supported them to age 100 and actually a little bit beyond.
There is no way to know what interest rates or rates of return will be in the future, of course, so the portfolio may or may not last exactly to their ninety-ninth birthdays. These projections are only estimates, of course. Because future interest rates and rates of return cannot be predicted with accuracy, there is no way to know
The Distribution Phase: Dedicating Assets to Do Their Job 149
Target
Safety Zone
Danger Zone
$1,400,000
$1,200,000
$1,000,000
$800,000
$600,000
$400,000
$200,000
$0
56 61 66 71 76 81 86 91 96 101
Figure 7.1
The Critical Path before and after Retirement
exactly what each successive 5-year income bridge will cost. Market conditions will differ at each point in time. During 2003, bond yields dropped to near historic lows as the Fed cut its lowest lending rate to 1 percent, a rate that had not been seen since the 1940s. This low spot appeared to end the long, slow decline of interest rates that occurred during the 1990s and continued until 2004. But who knows what the future holds? The further out you go, the hazier it gets.
The important thing for the Browns is for their portfolio to stay above this critical path. It will then continue to supply the needed income over their lifetimes. They need not worry about financial problems so long as their portfolio stays in the Safety Zone shown in Figure 7.1.
If they have not yet done so, they must arrange their wills, trusts, and other legal documents to legally transfer their assets to their heirs. This is one of those life tasks that must be taken care of to make sure the transfer phase goes smoothly. If they have not done this by now, they need to do it because time is beginning to run out for the Browns.