What is the age 65, immediate annuity to lump sum conversion factor as

[JDuns]

What is the age 65, immediate annuity to lump sum conversion factor assuming 83 GAM (unisex) and 8 1/2% interest?

I have been told both 9.6156 and 9.4903

In the future, how would I combine interest and mortality assumptions to verify the correct conversion factor?

[Mike Preston]

My calculation routine doesn't get either of your numbers.

Where did you get yours?

Note that there are two 83GAM-Unisex tables in common use. Sometimes this causes confusion. One is based on 50/50 mortality and is called, as you mentioned it, 83GAM-Unisex. There is another that is slightly different, used for some IRS and plan purposes, which I generally refer to as GATT, although it is supposed to be based on 83GAM and be a unisex mortality table.

The difference between the two, however, isn't as big as the difference between the two rates you show. I get 9.34685 under GATT and 9.34679 under 83GAM-Unisex.

There really isn't any way for you to do the calculations unless you have a copy of the underlying mortality factors for each year from age 65 to the end of life-span and a desire to write a calculation routine (such as in excel). The mortality tables are available at the Society of Actuaries' website. At least the 83GAM rates are. You may need to find an IRS Revenue Ruling for the GATT mortality rates.

[David]

FWIW, the 9.34679 number is the value of an annual annuity due rather than an annual annuity immediate. 9.34679 is the number I get based on the q's given in Rev Rul. 95-6 (GATT table). Actually I get 9.34676. The annual annuity immediate is 8.34676.

[Mike Preston]

David, ignoring the terminology, do you concur that the appropriate rate to use for conversion is the annuity due rather than the immediate (which is really one year deferred) annuity rate?

Also, what do you get using the 50/50 table?

I think we can safely ignore the 5th digit to the right of the decimal as being due to rounding rules.

[David]

Mike, I think the appropriate rate to use depends on when the annuity which is being converted is defined as being payable, end of year, beg of year, end of month, beg of month, etc.

If the actuarial equivalence basis were "GATT" mortality and 8.5% interest, I would use the 9.34676 if I wanted to calculate the single sum value of an annuity which is payable once a yr. at the first day of the year and further that is payable now (in other words not defered, I am trying not to use the word "immediately").

I think I once heard an explanation of why "annuity due" and "annuity immediate" were adopted as standard actuarial terminology but it sure seems counter-intuitive.

Also, the only 83GAM tables I have plugged in are the GATT basis and 83GAM(M & F) so I can't develop the other factor you mentioned.

[JDuns]

I am trying to determine the factor used to convert DC contributions to an annuity for purposes of the average benefits test. Last year, the actuary stated that the 7-1/2% + gam 83(unisex) conversion factor was 9.5237.

This year, they increased the interest assumption to 8-1/2% but still indicated that they were using gam 83 (unisex) and stated that the conversion factor was 9.6156. Since when interest rates increase, the conversion factor decreases, I was trying to find the "right" factor.

Several years ago in connection with a different calculation, the same actuary gave me the 9.4903 conversion factor at 8-1/2% and GAM83 (without reference to male, female, blended, unisex or any other variation). My assumption is that they used a different variant of the GAM 83 mortality assumptions to get that number.

Thank you for your help in confirming that the 9.6156 factor they used would appear to be incorrect.

[Mike Preston]

9.5237 is indeed 7.5% GATT.

9.6156 is indeed 8.5%, 83IAM-F.

9.4903 is indeed 8.5%, 83GAM-F.

All of these are not true annual annuities, but 1/12 the monthly annuity due factors. In most cases using the monthly annuity due factors divided by 12 will be the correct factors.

It sounds ike the actuary mis-identified, or you misunderstood, the table names.

Note that the first one, the GATT rate, is not a "standard" mortality table under the non-discriimination regs. That doesn't necessarily mean that the table can't be used for any purpose because there are certain assumption sets that merely need to be reasonable, as opposed to being forced into the use of "standard."

[MGB]

I have a very, very bad feeling about an actuary that used 7.5% in 2001 and 8.5% in 2002 for nondiscrimination testing. The only rational reason for this would be to manipulate results. There is no justification for this change in the current markets.

[Mike Preston]

Current market rates have no bearing on the selection of standrd asumptions. Standard assumptions are also a safe harbor for reasonaable assumptions under the regs. Manipulation in this context doesn't apply.