Pbo calculation

CFA Level I FRA
#1

-) One way to calculate PBO in each year

  • we discount all expected future payments into year 1, we calculate PBO in year 1 after workers have worked 1 years.
  • we discount all expected future payments into year 2, we calculate PBO in year 2 after workers have worked 2 years.
    -) Another way to calculate PBO in year 2 from PBO in year 1
    PBO in year 2 = PBO in year 1 + PBO in year 1 x discount rate + service cost in year 2. However this this larger than PBO calculated above because PBO in year 1 + PBO in year 1 x discount rate = PV of all expected future payments into year 2
    Whar are your opinions?
#2

No, it isn’t.

It’s the PV of all previously earned expected future payments into year 2, but not those earned in year 2.

#3

-For example, we have a pension contract that define annual end of year payment of 1% of final salary for each year of service, until death.
-Assumption:

  • current salary: 100,000
  • salary growth rate : 3%
  • Disocunt rate : 7%
  • year till retirement: 15
  • years till death : 10
  • from those assumptions, we calculate each year employee will receive 1,558 per year for 10 years → it’s also expected future payment.
    There is only one expected future payment, i don’t understand which expected future payments yoy are mention?
#4

So . . . year 1 each employee will earn 1,558 (which seems paltry, by the way) discounted for 15 years at 7% per year.

If we increase that by 7% we get the year 2 PV of what they earned in year 1. But they’ll earn another year’s benefits in year 2: 1,558 (still paltry) discounted for 14 years @ 7% per year.

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#5

However, i remember definition of DBO: company promises to pay a fixed future benefit to employee in the future after they retire.
And fixed future benefit here is 1,558 per year for 10 years. I don’t undersand why they’ll earn another year’ benefits in year 2: 1,558
PV here is PV (1,558 in year 1) + PV (1,558 in year 2) +…

#6

The future benefit isn’t fixed; it depends on how many years the employee works.

A common formula is along these lines:

Benefit=1\%\times years\ worked\times final\ salary
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#7

It means that, for example,
in year 1: expected future payment : 1558 per year for 10 years
in year 2: expected future payment: 3116 (1558 x 2) per year for 10 years
in year 3: expected future payment : 1558 x 3 per year for 10 years
Do i understand correctly?