Lump Sum Methodology

[JAY21]

Time to do some lump sum term calcs for 2008 calendar year plans. Theoretical example/question that hopefully will serve for the methodology:

If I have a retiree at age 65 (plan's NRA also is 65) with a lump sum option, is the annuity factor at 65 a summation of the following annuities: (a) 5 year temporary life annuity at 1st segment rate, plus (b) 5 year deferred temporary life annuity payable for 15 years at 2nd segment rate, plus © a 20 year deferred life annuity at 3rd segment rate ?

If the above is correct, if I changed the terminated participant's age to 55 would it just be the same above annuity summation but discounted 10 years at the 2nd segment rate (let's assume no pre-mortality table and no forfeitures on death).

I'd appreciate any confirmations or corrections.

[Andy the Actuary]

First scenario sounds right on.

Second scenario. If I understand, we are determining a lump sum payable to a 55 year old of a benefit that is payable at 65. In such case, there are no payments during the first 5 years, so we wouldn't use the first segment interest rate. During the next 15 years there are 10 years of payments (from age 65 to 75) deferred 10 years from age 55. So, would concur that you are talking about a temporary 10-year annuity deferred 10 years determined at the second segment interest rate plus a life annuity deferred 20 years at the third segment interest rate. I believe this is what you had summarized so would concur.

[JAY21]

Andy, I don't think we get the same result on the 2nd scenario (age 55; benefits payable at 65) but I think that is my error. I was initially thinking the PV for the 55 year old was the lump sum for the 65 year old but just discounted 10 years from 65 to age 55 using 2nd segment rate. However, my 65 year old has the 1st segment rate for the first 5 years of expected payments, whereas, under your advice it appears the 1st segment rate is never used for a 55 year old terminated participant getting an immediate lump sum since initial payments are more than 5 years away.

That said, I'm sure that your approach is correct for the 55 year old, I just need to correct my visualization of this and maybe use a timeline from the current age at lump sum on out to when payments would be expected to begin (if paid as an annuity), and for how long they would be payable under each segment rate.

[ak2ary]

You have to be careful whe you say that you are not using pre-retirement mortality. First, there is a question as to whether the most valuable benefit rules require the use of preretirement mortality in your 417(e) calculations, but the IRS knows they need to issue guidance on this before they can do any enforcement since they have issued oh about a million favorable DL's the other way..

But my point was that you MUST recognize mortality post retirement in any case, so in the instant case, beyond age 65... for the age 65 participant it is

(N65-N70)/D65..........+.............. (N70 - N85)/D65 ............. + ............ N85/D65

1st seg rate ........... + ............. 2nd seg rate ............. + .............. 3rd seg rate

So the 2nd and 3rd segment rate pieces of benefit have a mortality discount back to age 65. Some have proposed

(N65-N70)/D65 .......... + .......... {(N70 - N85)/D70} / ((1+2nd rate) ^ 5) .......... + .......... [N85/D85] / ((1+3rd rate) ^ 20)

1st seg rate ................. ..... + ......................... 2nd seg rate ...................................... + .............. 3rd seg rate

for plans with no preretirement mortality, but its simply wrong since it both assumes and does not assume mortality after age 65 in the same calc.

For the age 55 guy with pre retirement mortality

(N65-N75)/D55 .......... + ........... N75/D55

2nd seg rate ..........+ ......... 3rd seg rate

Without pre-retirement mortality

[(N65-N75)/D65] / ((1+2nd rate) ^ 10) ............ + ............ [N75/D65] / ((1+3rd rate) ^ 10)

2nd seg rate ................................ + ..................................... 3rd seg rate

[Mike Preston]

Aw, what the heck. Might as well let this out, if anybody is interested in it.

PPAFormula.pdf

[Guest Judy S]

Why am I unable to download the PPAFormula PDF file?

[ak2ary]

That's beautiful, Mike, just beautiful...brings a tear to my eye

[Mike Preston]

Thought you'd like it, Tom.

Judy, if you send me your email address via a private message I'll forward it to you.

[Mike Preston]

BTW, soon I'm going to post on BenefitsLink (via an attachment to a message, like I did with the PDF above) a windows program which will allow people to check that their own spreadsheet and/or valuation system is correctly calculating present value factors for a limited range of single life and certain annuities (consistent with the PDF).

This will be a completely free program for anybody to use how they see fit and it will not expire. However, it will only operate on a limited range of age/certain period/segment rates/mortality table combinations. I will have a commercial version or two (with different features) available for purchase which I will not post on BenefitsLink. Of course, the commercial versions will be unrestricted in the sense that they will operate on any age and any certain period and provide for updating of interest rates and mortality tables and have a few other bells and whistles (like the built in ability to send the information to a file that can be formatted and saved in Word - something akin to a mail merge).

In case anybody is wondering, I already discussed posting the free program here on BenefitsLink with Dave Baker and he has no objection to me doing so. In fact, he was rather enthusiastic.

[John Feldt ERPA CPC QPA]

I luv ya man!

[JAY21]

thanks Mike, that will be much appreciated. Thanks for your input as well Ak2ary.

[Guest Judy S]

I tried the download later in the day yesterday and was able to get it. Thanks Mike.

[Andy the Actuary]

Aw, what the heck. Might as well let this out, if anybody is interested in it.

I remember seeing formulae like this scrawled on the blackboard by Dustin Hoffman in the 1970's movie Straw Dogs, only to be partially changed by his supple spousette (Susan George). Anyway, while I'd rather gaze at Susan George, thank you for your posting.

[Mike Preston]

LOL. Well, we have 136 downloads and counting. Strange that nobody thinks there is even the slightest error. :-)