Determination of Present Value of Accrued Benefit

[MarZDoates]

First let me say that DB is definitely not my area of expertise!! Can anyone give me a mathematical formula to determine the present value of an accrued benefit. I have the monthly benefit amount and the participant's date of birth and normal retirement age. My assumptions are: 1983 Group Annuity Mortality Table and the applicable interest rate is the rate on 30 Year Treasury Securities. Sorry if this sounds like a stupid question. Thanks to any and all who care to reply!!!

[Guest flogger]

What is the form of the annuity (straight life, period certain, J&S?), and what happens in the event of death prior to the annuity starting date?

[MarZDoates]

Problem is I do not have a document to refer to. I didn't know if there was a way to make a calculation to get a "ballpark" amount. I do not have the answers to your questions. Sounds like I need to get more information, huh?

[Blinky the 3-eyed Fish]

And you need to know when the determination of the applicable interest rate is.

[Effen]

If MarZDoates, do DoeZEoates? Sorry, couldn't resist.

[david rigby]

Ball park:

If recipient is age 65, multiply the monthly benefit by 128.218.

If the recipient is age 50, and the benefit is assumed to start at age 65, multiply by 54.867.

Assumptions: 1983 GAM Table (male, not unisex), 5.0%.

Obviously, more information is needed to provide a "better ballpark".

[SoCalActuary]

The choice of mortality table deserves more discussion.

The 1983 Group Annuity Table blended 50% male/female was mandated for lump sum payments from 1995 to 2001. In 2002, the table could be used, or the new 1994 Group Annuity Reserving Table, which became mandatory for lump sums and 415 limits in 2003.

You calculations on a different table are interesting, perhaps for evaluation in a divorce, or for funding purposes or financial reporting. It just is not useful for lump sum valuation.

How did you decide which assumptions to use, and what is the purpose of your calculation?

Generally, for disclosure, the actuary picks assumptions appropriate for the purpose.

For lump sums, the actuary is governed by plan documents and the appropriate 417(e) tables and interest rates. For other purposes, it depends whether an annuity will be paid.

To answer your original question, the mathematics of computing annuity payments is found in many text books. Generally, you figure the probability of future payments each year, taking into account the age of the participant, gender (if it matters), the form of payment including any guaranteed payments, and any other beneficiaries. The probability tables can even be more distinct, based on the generation (year of birth) of the benefiting person.

These probable future payments are discounted back to current date, using the one (or more) interest rates for discount purposes.

Now, I keep mortality probabilities in a data base, import them into a spreadsheet, and apply them to the calculation needed, with the interest rates desired. (From this you could tell that I am not a civilian, but a long time actuary who still likes computer programs.)