Actuarial Equivalance

Defined Benefit plan.

Actuarial Assumptions for all purposes (not just lump sums) :  mortality rates = applicable mortality table.    interest rates = applicable segment rates.  The stability period is the calendar year.

Normal retirement age = 65 and NRD = 9/1/2015   Participant's actual retirement age = 73 with a commencement date of 3/1/2023

Benefits were frozen before the participant reached age 65.  The plan states that benefits are actuarially increased with interest and mortality from normal retirement date to date of actual retirement.  

Assuming the life annuity at age 65 is $1,000 per month, what is the monthly amount beginning at 3/1/23?

I have seen at least 3 methods - based on the 2015 rates, based on 2023 rates. or based on a different rate for mortality and interest for each year.  As an aside, how would you determine the lump sum at age73?  Do you start with the first five years or year 9?  Of course these rates should match the rates used for any optional form.

Thanks to anyone who is bold enough to answer because I'm so confused at this point. 

I'll take a stab at it and I'm assuming a calendar year plan since you said calendar is stability period. This is how I would calculate it.

Take the benefit at 9/1/2015 and adjust to 12/31/2015 at the AE in the document for 2015 (2015 table and rates)

This becomes his protected floor benefit at 1/1/2016.

Actuarial increase from 1/1/2016 to 12/31/2016 at the AE in the document for 2016 (2016 table and rates)

Repeat each year until 12/31/2022

Actuarial increase from 1/1/2023 to 3/31/2023 at 2023 rates.

Check each benefit to make sure you don't exceed 415. You "probably" don't, given the starting point, but the with 9 years of increase the 100% of pay limit could come into play.

As for lumpsum. 3/1/2023 benefit from above times the APR using the 2023 AE and check against the 415 lump sum max.

Which of the 3 segment rates would you use for adjustment?  I guess you could argue the 1st segment since you are really determining the value of payments missed within that year. 

I like the year by year approach with a new rate/table each year, as Lou stated.

I like year-by-year approach, it is solid.   I am OK with calculations based on the 2023 basis (rates, mortality, etc.) using the logic is that is when the calculations are done.  I would not use "old" rates.

On 2/3/2023 at 4:17 PM, Effen said:

Which of the 3 segment rates would you use for adjustment?  I guess you could argue the 1st segment since you are really determining the value of payments missed within that year. 

I would use the ratio of an immediate factor to a deferred factor.

I largely agree with what has been said - year-by-year adjustments using a ratio of immediate to deferred factors is my preferred approach. I can't see any way that someone can find issue with it. I have seen plans that adopted an administrative practice of saying late retirement will be based on the rates in effect at the NRD for all years of late retirement and others that used rates in effect on the actual retirement date. I can kind of get behind using the factors at NRD. I have a hard time with the factors at actual commencement date as it is possible that in a year where interest rates go down the benefit payable in the Normal Form would be less than if they had commenced during the prior year which I don't think is permissible.

Sorry, but I am old, and I want to clarify something related to the statement that you are "using the ratio of immediate to deferred factors" to determine the rolled up amount.  The ratio of the immediate to deferred factors only gives you the change in value of the annuity.  It is not the same ratio as the change the the amount of the annuity.    I assume what you are doing is taking the annuity, then determining the lump sum value of it, then doing your ratio of immediate to deferred factors, then dividing back by the current immediate value to arrive at the newly rolled up month amount.  I just wanted to clarify that the change in the monthly amount will be greater than the "ratio of immediate to deferred factors".

20 hours ago, Effen said:

I assume what you are doing is taking the annuity, then determining the lump sum value of it, then doing your ratio of immediate to deferred factors, then dividing back by the current immediate value to arrive at the newly rolled up month amount.

Not really. Annuity multiplied by a ratio of immediate to deferred factor will give me an actuarially increased annuity which will be compared to an accrued benefit. The greater of amount will be the starting point for the next year comparison. 

Sorry, I was misunderstanding what you meant, I agree that the ratio of the (immediate factor at NRA) / (Deferred factor from NRA to AA) is the same as an Nx(nra)/Nx(aa). 

I was thinking you were saying the( Immediate at AA)/(deferred from NRA to AA) - which reduces to Dx/Dx which is not correct when adjusting monthly annuities. 

Thanks for pushing back.  Just wanted to make sure it was clear for future readers.