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Monday, April 30, 2012

Spending the Nest Egg

Considerable research efforts have been directed to determine the appropriate nest egg withdrawal rate.  Many people seem to believe there is a single answer.  In truth, of course, there are too many unknowns including life expectancy, the rate of inflation, and market performance to produce a single number.  These unknowns give the problem a dynamic nature and mean that the retiree has to continually make adjustments.

In fact, there are two questions that sometimes are treated as the same. Some people want to know what rate can they spend at and have a high probability of not running out of funds.  Others are interested in the optimal rate of spending. T hey want to spend their last dollar as the plug is pulled.  If they follow the 4% rule-of-thumb and find they have $2.0 million on their death bed, they'll be upset and rant and rail about all the trips they could have taken, etc.

With this said, it is useful to run scenarios if for no other reason to at least get a feel for the nature of the problem.  As an added bonus, some readers will get some useful exposure to the arithmetic and issues involved.  The particular scenario I want to consider is as follows.  Suppose we are retiring today with a nest egg of $1.0 million, and we need an inflation adjusted cash flow of $40,000.  Note that I am conveniently neglecting taxes.  This is significant because taxes are the biggest single expense of retirees!  That's right - it's not medical expenses or anything else - it's taxes.  But taxes are messy, so we'll neglect them.

Let's assume 3% inflation.  The rate of inflation we assume is important because we are looking at a long run (hopefully!) situation.  Just as Enron was able to manipulate earnings by changing market assumptions on long-term contracts by a miniscule amount, the numbers will change here in a meaningful way if the inflation assumption is changed.  Keep that in mind.

To make this a bit different from other analyses of this type, let's think of matching our first 10-year payment needs ($40,000 adjusted annually for 3% inflation) with zero coupon Treasuries.  How much would this cost?  The Table shows the set-up.  It shows that, if inflation rises 3%/year, then by 2015 we'll need $43,709 to keep up.  To generate that payment of $43,709 in 2015, we can buy a zero coupon Treasury for $43,082.

Matching the required payments over the 10 years in this way requires $430,440.  This leaves $569,560 to invest today.  Working backwards, we ask the question of what return would it take to get us to our original $1.0 million by the end of the 10 years?

This is easy:  ($1,000,000/$569,560)^.10 = 1.057, or 5.7%.  In other words, if we can achieve an average annual return of 5.79%, we will be back to our original $1.0 million after satisfying our income needs for 10 years.

So, the good news is that we are 10 years older, have our $1.0 million in hand (especially good news for potential heirs), and have control of our money (in contrast to an annuity).  The bad news is that we have to generate $52,191 to start the next 10 years.

We'll continue with this next time.

The table presented here is really easy to do in a spreadsheet.  If anyone has questions, feel free to ask. Again, this whole exercise is useful, I think, in coming to understand the problem and challenge of generating an income off of a nest egg.

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