415 Calculations

[FAPInJax]

Has anyone seen or willing to admit understanding how to value 415 lump sums when segmented interest rates are involved?

For example, assume the interest segments are 4.5%, 5% and 5.5% (funding). Now, a 62 year old retiring at 65 has a maximum benefit and the stream of payments begins discounting using the 4.5% for 2 years commencing at 65, 5% for 15 years and then the 5.5% for the remainder. The 415 lump sum limit is computed using 5.5% for all years. Which present value stream is adjusted OR am I missing something??

[SoCalActuary]

Has anyone seen or willing to admit understanding how to value 415 lump sums when segmented interest rates are involved?

For example, assume the interest segments are 4.5%, 5% and 5.5% (funding). Now, a 62 year old retiring at 65 has a maximum benefit and the stream of payments begins discounting using the 4.5% for 2 years commencing at 65, 5% for 15 years and then the 5.5% for the remainder. The 415 lump sum limit is computed using 5.5% for all years. Which present value stream is adjusted OR am I missing something??

I am not sure which issue you are discussing, so here's a few questions.

1. Are you using a lesser of two values approach?

2. Are you valuing the probability of a lump sum payment?

3. How does your example change if the segments are 6.0, 6.5, 6.6?

My understanding is that the maximum lump sum is a known quantity at each future age where the plan has a fixed AE definition. If you are using a dynamic mortality table for valuation, I would have to think this trhough a little more.

You determine the current 415 unisex mortality table value at 5.5% for each age where a potential lump sum is payable.

You determine the maximum benefit available at that age, presumably the lesser of the age-adjusted dollar limit or the 100% of pay limit. If a prior benefit has been paid, then you must adjust for the value of prior benefits, apparently in a separate manner for 100% of lay benefits vs dollar limit benefits.

Now you have a known quantity for a maximum lump sum at each age.

For valuation, you determine the probability of a lump sum payment at each age, and discount those payments back using your segment rates. You also determine the probability that an annuity payment (limited to 415) commences at each age and determine the future annuitized payments resulting from that event. Those are separately discounted back using your segment rates.

What am I missing in your question?

[Blinky the 3-eyed Fish]

A present value determination of an annuity is merely the total present values of each annuity payment (obviously).

With a single interest rate it's simpler because most valuation programs can get you the purchase rate and you simply discount it with interest (if no pre-retirement mortality) to get a present value.

With segment rates the simplicity is gone. Each payment is discounted at the appropriate segment rate. For example a $1 payment at age 65 with interest rates of 4.5%, 5% and 5.5% is the sum of these 3 segments for a 62 year-old:

1/(1.045^3) + 1/(1.045^4)*l66/l65 ---- segment 1

1/(1.05^5)*l67/l65 + 1/(1.05^6)*l68/l65 + ... + 1/(1.05^19)*l81/l65 ---- segment 2

1/(1.055^20)*l82/l65 + ... + 1/(1.055^n)*ln/l65 ---- segment 3

(I don't know how to do the fancy subscripts Andy the A does)

We wrote an Excel spreadsheet that calculates the amounts in a jiffy. We also have ProVal to be able to compare the values to. Luckily they match, which is nice.

[FAPInJax]

1 The approach is to use the greater of AE or the 417(e) rates.

2 Yes, we are valuing the probability of a lump sum.

The problem is not with the present value of the annuity as I understand that part. The problem is when does the 415 limit trigger.

For example, a participant is at some 415 maximum benefit. Let's say for the sake of argument that the greater of the AE or 417(e) produces an amount which is in excess of the 415 lump sum at 65. Therefore, the lump sum is limited at 65 to the 415 lump sum using 5.5%, etc. Can this number be discounted for cost purposes using the 4.5% funding interest segment (assuming again the participant is 61 years old)? This produces a number larger than the lump sum 415 at his current age (because discounting at 4.5 instead of 5.5).

Thanks for all your comments.

[Blinky the 3-eyed Fish]

If your question is relating to how to perform the actuarial valuation, the answer is this. Compare the lump sum value at the assumed retirement age (65) determined using the valuation segment rates (4.5%, 5%, 5.5%) and the Applicable Mortality Table versus the 415 lump sum using 5.5% and the Applicable Mortality Table versus the lump sum determined using AE. Take the lesser of the three. Discount from that point at the appropriate segment rate to current age.

So to your last question, yes, that amount is discounted at the 4.5% rate to current age. Yes, it is greater than discounting at 5.5% but keep in mind you are valuing a lump sum at retirement age, not current age. If the assets grew at 4.5% to retirement age, you get there.

Anyway, a current 415 lump sum calculation for distribution purposes is not valuing at retirement age and discounting to attained age either. It's a value determined at attained age.

[SoCalActuary]

If your question is relating to how to perform the actuarial valuation, the answer is this. Compare the lump sum value at the assumed retirement age (65) determined using the valuation segment rates (4.5%, 5%, 5.5%) and the Applicable Mortality Table versus the 415 lump sum using 5.5% and the Applicable Mortality Table versus the lump sum determined using AE. Take the lesser of the three. Discount from that point at the appropriate segment rate to current age.

So to your last question, yes, that amount is discounted at the 4.5% rate to current age. Yes, it is greater than discounting at 5.5% but keep in mind you are valuing a lump sum at retirement age, not current age. If the assets grew at 4.5% to retirement age, you get there.

Anyway, a current 415 lump sum calculation for distribution purposes is not valuing at retirement age and discounting to attained age either. It's a value determined at attained age.

I agree with this post.