In the curriculum, P. 533 of Volume 2, The present value of the eternal benefit obligation attributable to future wage growth (this does not include the accrued benefit portion of the liability) for s years till retirement but starting in d years equals Vld = B / (r - g) * ((1 + g)^s - 1) / (1 + r)^d Could anyone help me with why is (1 + g)^s and not (1 + g)^d? Thank you.
derive the formula step by step and you will see why. it is coming from a lcm of the denominators.
Sorry, I don’t understand what you mean by “lcm of the denominators”.
I already tried to derived step by step, but when I derive the present value of the eternal benefit obligation attributable to future wage growth (this does not include the accrued benefit portion of the liability) for s years till retirement but starting in d years, I believe it should be
Vld = B / (r - g) * ((1 + g)^d - 1) / (1 + r)^d But the derivation in the curriculum said otherwise.
My question is why B only needs to grow for s years but discount for d years? Should both be d?
For example, when deriving the present value of the eternal benefit obligation attributable to future wage growth (this does not include the accrued benefit portion of the liability) for s years till retirement,
Vld = B / (r - g) * ((1 + g)^s - 1) / (1 + r)^s --> Both grow for s years and discount for s years --> Why is not it the case for above?
future wage growth. and does not include the accrued portion of the liability. (this has already grown upto some value now).
you need to thus grow the liability only for s more years.
but for the present value it needs to be discounted the full d years.
you have a benefit B - growing at g.
B grows for d years with s years to retirement - B grows for s years with s years to retirement = obligation due to wage growth.
B grows for d years with s years to retirement is necessary - only because you need to pay the benefit up until the employee retires. beyond that there is no need to build up the liability.
I understand the need to take out (hence, minus) the part beyond d years, and that is not my question.
My question is how to calculate the benefit from d years and beyond.
Maybe answer the following multiple choice may help me:
When the employee retires s years from now (current time is year 0), what are the benefit for year s and year s+1,
A. B * (1 + g)^s for year s and B * (1 + g)^(s+1) for year s+1
B. B * (1 + g)^s for year s and B * (1 + g)^s for year s+1
C. Others, please specify.
Answer is A, B, or C?
the benefit grows for s years - but needs to be discounted for d years completely. (and d > s).
benefit grows for 1 year -> B (1+g) and is discounted for 1 year -> B (1+g) / (1+r)
benefit grows for 1 year, discounted for 2 years - and this is the case because your plan employees retire at the end of year 1 -> B (1+g) / (1+r)^2
(and let’s please stop decrypting that meaningless formula)
guys, do we need to know these formulas for the exam?