dumb question re: how a lump sum value is computed

[Guest janie]

Here is a dumb question: if a DB plan provides for a lump sum payment option, and specifies that actuarial factors in general shall be computed on the basis of a specified interest rate and mortality table, does that mean that mortality is actually or necessarily taken into account in determining the lump sum amount to be paid where a participant who is retiring elects that option? I would have thought that the interest rate alone would apply in determining the lump sum value. Any help is greatly appreciated from someone who is definitely mathematically-challenged! :confused:

[david rigby]

Yes.

The determination of a lump sum equivalent is, at its most basic, a matter of how the Plan defines it. Most plans will define "actuarial equivalent" or some similar term. If that defintion includes reference to a mortality table, then it should be used. Should be NO discretion in this.

See my generic description here:

http://benefitslink.com/boards/index.php?showtopic=10579

[MGB]

Janie,

The normal form of payment must be a life annuity of some type. Most plans use a single life annuity. This means the defined monthly amount will be paid until the participant dies. No payments are made after that.

If the plan allows an optional lump sum, the lump sum must be calculated in a particular way. The theory is that it will be equivalent to the payment stream in the life annuity. If you were to only use interest to discount each future payment, there would be no way to incorporate the fact that the payments will not go on forever. Although it is mathematically possible to have a lump sum equal to an annuity that never ends (a perpetuity), we know that people don't live forever. The probability that a payment will be made when they are 100 yrs old, given that they are 65 or less now, is very small. The probability that they will still be alive to be paid next year or the year after is very high. These probabilities are based on the mortality table and that is how the mortality table enters into the calculation. A lump sum is the sum of present value of each individual possible payment out to the end of the mortality table. Each individual present value is the probability that the person will live until the payment is made times the present value of the payment (how much would need to be invested right now to produce that single payment in the future) based on a compounded discount using the stated interest rate.

A way to get an approximation to a lump sum is to know the life expectancy for the person under the mortality table being used. For example, assume the life expectancy of the person getting the lump sum at retirement is 20 years. If you assumed that the payments would last for 20 years and discounted these payments with interest only, you would get a very close approximation of the more complicated correct present value calculation described above. Although you are only using interest in this calculation, the mortality table was used to get the life expectancy.

The above assumes the lump sum is equivalent to an immediate payment of the annuity. Most lump sums are deferred annuities. I.e., the person is terminating before the normal retirement age and the annuity is assumed to not start until then. In this case, the calculation as of the normal retirement age (in the future) is the same as above. To discount from there to the actual age of payment, interest is again required. However, in this part of the calculation, a plan may or may not use mortality. Generally, if there is no death benefit prior to the assumed starting date of the annuity, mortality is again used in the discount. Plans with large death benefits may discount with interest only. This will create a larger lump sum to incorporate the value of the death benefit being given up when the lump sum is taken.

Another way to view the lump sum is from a grouped approach. Assume a 1000 people, the same age, took the same lump sum and pooled their money into a fund that received a fixed rate of interest that equals the interest rate used in calculating the lump sum. Have the fund pay out the annuities to each person. Some will only receive benefits for a short time, others for a very long time. The expectation is that the money in the fund will run out just as the last person finally dies.

[Guest janie]

Thank you Pax and MGB for your extremely helpful responses. I have a much better understanding now.