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#1




Optional Form of Pmt Factor Decreasing with Later BCD
Hi all, I'm not an actuary but work in the pension administration space. I have a conceptual question that I'm hoping someone can help me with.
A pension plan participant is questioning the difference between two benefit estimates. His plan offers full early retirement at Age 62. He terminated at 62 and is comparing estimates at a BCD of age 62.5 and age 63. Say his accrued benefit is $500 at age 65. Since this is unreduced if he commences at 62.5 or 63, the SLA value at either BCD is still $500. However, his optional form factors are decreasing as he gets older. The forms offered are Joint and Survivor and Certain and Life annuities. Typically when someone commences later rather than earlier, the reduction is less or if over 65 an increase is applied, so his SLA value is greater at the later BCD, and this is usually enough to offset the slight decrease in the optional form factors at a later age. Since he is unreduced at either age, he is noticing this decrease. I understand that this has something to do with the plan makes less payments if he is older (stream of $1 annual payments from start age to end of mortality table is less, so the factor (sum of $1 pmts discounted by interest rate and mortality) is going to be smaller) but I'm not sure of the best way to explain this concept to participants. These participants are highly educated business professionals so they would understand a complex answer. Can anyone help explain? Thanks. 
#2




In most cases, optional forms are calculated as being actuarially equivalent, based on some mortality table and interest rate assumption.
What’s the present value of $500 as a life annuity payable at age 62.5? What’s the present value of $500 as a life annuity payable at age 63? The former is going to be larger than the latter, correct? What’s the present value of $1 payable as a x years certain and life annuity at 62.5 vs 63.5? The 62.5 amount is going to be more valuable than 63.5, but not by as much of a magnitude as the life annuity, because of the ten years certain aspect. There’s a higher chance of the 63 dying between 63 and 73 (assuming x = 10) than a 62.5 year old dying between 62.5 and 72.5. To convert these optional forms at each age, you’d multiply the $500 by the life annuity factor and divide by the certain factor. The ratio of SLA/CC is going to be larger at 62.5 than 63 for the reasons above. Say SLA at 62.5 is 12, and 10cc is 12.5 (no idea if this math checks out, just for illustrative purposes), and SLA at 63 is 11.5 and 10cc is 12. Conversion factor is going to be 12.5/12 = 0.96 at 62.5 for a 10cc and 11.5/12 = 0.958 at 63. For the joint and survivor annuity, I imagine there’s a similar line of logic as well, but without exact ages and an annuity calculator at my disposal, it’s difficult to say.
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#3




NerdAlert, this is great. Totally understand what you're saying and can craft a response based on this. Thanks very much.

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factor, optional form, pension 
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