QUOTE (Andy the Actuary @ Sep 14 2010, 03:53 PM)

QUOTE (My 2 cents @ Sep 14 2010, 05:31 PM)

Wouldn't the normal approach be a straight life annuity? Say annuity value at age x = 100 and at age x+1 = 98.
current benefit = $100. With actuarial increase for a year, $108.16.
value now of immediate benefit = 100*100 = 10,000
value now of one year deferred benefit = 108.16 * 98/1.06 = $10,000
No gain or loss (OK, I did massage the factors a bit, but they are reasonably representative of what you might see)
Wouldn't a 20 year certain only form without an actuarial increase be a bit, shall we say, unfair? Plus, when would you ever see that as the normal form?
The example was for the sake of illustrative ease. In your example, we would have:
PV
x=100x100=10,000
PV
x+1=100x98=9,800
PV
x+1 of increased benefit=108.16 x 98 = 10,600
What is 10,600 - 9,800 = 800?
Unless you have special provisions, $9800 is irrelevant.
PV is $10,000 and one year later it is $10,600. The $100 benefit payable at x is identical in value to the 108.16 payable at x + 1, because you did not receive the payments.
Andy, your example twists up the normal perception of late retirement equivalence.
Is it because of your perception that Assumed retirement age is x + 1,
and by delay in retirement the next valuation assumes payment starts at x+2?
I have a participant eligible at age x, and I assume they will retire at x + 1.
The assumed benefit of $100 at x must be converted into 108.16 at x + 1.
I grant the exception where someone is at their 415 limit,
in which case you will have a gain when they don't take the required payments.
If I assume at x + 1 that the $108.16 is payable at x + 1, then my assumptions are met.
You are implying that valuation at x + 1 assumes payment at x + 2.
So you should be valuing the equivalent of the $108.16 (roughly $117) payable at x + 2.