In Service Distribution

[Guest MikeMiller]

I have a plan that allows for in-service distributions once the participant hits normal retirement age. How do you calculate the accrued benefit for the year following the first year of distributions?

Example:

Plan Year = 3/1 - 2/28

Normal Retirement Date = 3/1/2000

Accrued Benefit as of 3/1/2000 = $2,500

Accrued Benefit as of 3/1/2001 = $3,000

Distributions of $3000 per month begin on 3/1/2001

What is the procedure for calculating his accrued benefit as of 3/1/2002 ???

[AndyH]

An increasingly popular phrase on these boards is relevent here, "What does the plan say?".

There are a number of possible approaches, which all depend upon what the plan says.

[Blinky the 3-eyed Fish]

Mike, what are the provisions in the document regarding the benefit for working past normal retirement? Most plans we have give the participant the greater of the prior year's benefit actuarially increased to the next year or the benefit under the plan.

If you provide that information, I or someone else can chime in on the calculation methodology. I would suspect the document is silent regarding the specifics of the calculation.

[Guest MikeMiller]

Blinky,

Actually the document reads the following:

"At the close of the Plan Year prior to his Actual Retirement Date, such participant shall be entitled to a monthly retirement benefit payable each subsequent Plan Year equal to the greater of (1) his monthly retirement benefit determined at the close of the prior Plan Year, or (2) his accrued benefit determined at the close of the Plan Year, offset by the actuarial value of the total benefit distributions made by the close of the Plan Year."

I'm assuming that I take last year's benefit at the valuation date and subtract out the actuarial equivalent of the payments that have been made to the start of the current Plan Year and then actuarially increase that for one year. Is this correct?

[Blinky the 3-eyed Fish]

Mike, you will take the value of the accrued benefit at 2/28/01 ($3,000) and actuarially increase that to 2/28/02. Compare that to his accrued benefit under the plan benefit formula at 2/28/02 and take the greater value. Then subtract off the actuarial equivalent value of the distributions already taken. The net result is your accrued benefit at 2/28/02 (3/1/02).

[ishi]

I agree with Blinky, but I don't think the final calculation can be less than $3,000 (the accrued benefit at 2/28/01). The participant makes out in this case.

[MGB]

As a follow up to ishi's statement:

Assume there is no further accruals and there is only an actuarial increase. When you actuarial increase a benefit, and then subtract the actuarial value of the prior benefit paid, you arrive back to the original benefit amount. That is a mathematical fact. The only time that the subtraction would result in a lower amount (or higher amount) is if you are using different assumptions for the actuarial increase than the conversion of the actuarial equivalent of the prior payments. However, when this occurs, I think you have problems with plan design.

The only time that the new calculation should be different is if the new accruals are greater than the actuarial increase...but note that the person loses out on the accruals up to the amount of the actuarial increase (I have said repeatedly since OBRA '86 that this was a poor result of the language of that law...people effectively do not get the continued accruals when you do this offset for the actuarial increase, even though that is what everyone says this law provided...which is false.)

Perhaps there is some type of actuarial increase described elsewhere in the document, but it is not encapsulated here.

Having said all that, I am only responding to the prior two responses. I do not think that the language in the plan document does this. It does not provide for an actuarial increase in the prior accrued benefit. Therefore, there needs to be separate language in the plan for suspension of benefits and there must have been a suspension of benefits notice provided to the participant at NRA. If such notice was not provided, you are not allowed to subtract off the actuarial value of benefits already paid.

[Blinky the 3-eyed Fish]

Oops, looks like I didn't read the language provided by Mike very carefully. I agree with MGB's statement.

As far as the mathematical fact, I am not sure that is entirely correct because of the fact the person did not die. An annuity amount payable at n would be less valuable than the same benefit annuity amount at n+1 plus the money received for the year.

But it's late, and I could just be loopy.

[MGB]

The whole point of giving an "actuarial increase" is to recognize the that the earlier payment is now worth more due to both interest and the benefit of survivorship. Offsetting for the "actuarial value" of prior payments does the same thing.

Assume the original payment is P. The actuarial equivalent of prior payments since x, spread over an annuity at age x+t is (all N's are upper-12's):

P*(N(x)-N(x+t))/N(x+t).

The annuity payable at x, actuarially increased to be an annuity at x+t is:

P*N(x)/N(x+t).

If you take this actuarially increased amount and subtract the actuarial equivalent of the prior payments, you get:

P*N(x)/N(x+t) - P*(N(x)-N(x+t))/N(x+t) = P

(If you have access to old transcripts, these equations and examples of actual numbers are in the transcripts of a presentation I did for the 1990 Enrolled Actuaries meeting, session 4F, "Benefit Accruals after NRA," repeated in 1991 and are in those transcripts, too.)

[david rigby]

Looks pretty good.

But MGB, how can we old folks (OK, were not old, just "older") explain that to the younger crowd that did not learn commutation functions?

Hurray for Jordan!

[MGB]

I taught collegiate actuarial science using the current Actuarial Mathematics textbook. My suggestion to the students was to pick up an old copy of Jordan because they will run into commutation functions throughout their career.

This is especially true in pension actuarial work. One only needs to read the law (e.g., PBGC regulations) to run into numerous instances of commutation functions. Anyone entering the pension field must learn commutation functions, not to mention it makes writing formulas so much more efficient.

Of course, I could have broken the equations down into summations of discounted future probabilities, but it would have taken four or five times as much space (and probably introduce a dozen errors).

(I am currently writing a comment letter on the proposed 1.401(a)(9)-6 limitation on COLAs and am struggling with how to explain my position without using commutation functions -- it would only take a simple formula with them.)

[Larry M]

to pax and mgb,

"Jordan"???

You young whippersnappers, you should be reviewing Hall & Knight and Sturgeon - now, THOSE were texts!!

[Blinky the 3-eyed Fish]

I am trying to use this as a learning experience, so please tell me what is wrong with this logic. Here is a numerical example to illustrate what I was saying in my last post.

I will use the dates in the previous example, but just assume the payments were made annually for simplicity

Age 3/1/01 - 65

APR 65 - 11.992321 (83 GAM Unisex, annual payments)

APR 66 - 11.674182

Interest Rate - 5%

Benefit at 3/1/01 increased to 3/1/02

(3,000) * 11.992321/11.674182 * 1.05 = 3,235.84

Benefit paid at 3/1/01

(3,000 / 11.992321) = 250.16

Actuarial Increase of benefit paid to 3/1/02

250.16 * 11.992321/11.674182 * 1.05 = 269.83

Net benefit = 3,235.84 - 269.83 = 2,966.01

Therefore, 3,000 benefit still paid at 3/1/02 is worth more than 2,966.01 and the difference is the probability of dying while age 65. (1 - (2,966.01/3,000) = .01133

By the way, the Jordan book is 2 feet from me and is still on the reading list for the enrolled actuary exams. So, while us newer actuaries don't have to deal with commutation functions nearly as frequently as before, hope is not lost, because they must still be learned.

[MGB]

You have not given an actuarial increase in the first calculation -- you have only increased with interest. Same thing in the second calculation -- you are only bringing forward the payment with interest. This is not the actuarial value of the prior distribution. In each of these, you need to roll forward with the benefit of survivorship, not just interest. That is why the final calculation is off by the mortality factor.

[david rigby]

Correct. Or in actuarial terminology, use N's, not a's.

[Blinky the 3-eyed Fish]

MGB and pax, the logic of what you are saying makes perfect sense, but goes against how I was trained. It's like being told the Earth is flat, only to find out otherwise.

Another question, if you were to compute the dollar limitation past 65, what would be your methodology, with N's or a's?

[MGB]

It depends on the type of death benefit. The IRS wants you to take into account any preretirement death benefit in this actuarial adjustment. If you have a PVAB death benefit (no forfeit upon death), then you can only bring forward with interest (the calculation you were doing above).

Note that the "sample" good-faith amendments under EGTRRA are wrong on this point. The language in there states that mortality (additional increase based on the benefit of survivorship) is never used in the post-65 actuarial increase of the 415 limit. That is not what prior guidance on the issue has said.