For past service liabilities: Its: m/80 (multiply by) salary factors (the S, s and the z....) (multiply by) The probability employee will die at a time t (multiply by) discount factor (multiply by) annuity factor We sum this for all values of t to get the past service liability. NOW for Future service liability why do we need to Sum the M bar Commutation factor (to get the R bar factor) the CMP justifies this by saying: "We now need to consider all of the future years of service"....... have these years of service not been considered when we summed the C Commutation factor. After all we did sum for all values of t; i.e. from 0 to NPA-x Kindly can anyone pretty please explain this in words (instead of notation) as i did for the above Past service lib benefit valuation.
At the outset, let’s consider past service liability when an employee can retire at ‘exact age 65’ and at ‘any age after 60’. Ordinarily, an individual employee’s EPV of benefit for either of these conditions shouldn’t materially be different. Isn’t it? But if you see the results M65 and M60, the numerators are very different and hence the EPV of an employee who retires at exact age 65 is approx 1/3rd of the employee who can retire at any age between 60and 65. I have now concluded that the EPV benefit is from a company’s/ sponsor’s standpoint, not the employee’s! (It seems logical – else how can an employee who retires at 64 receive benefit 3 times more than the one who retires at 65?). The company should sum over the years from 60 to 65 years for all the employees who will retire at these ages. And assuming this is the right diagnosis: The future service liability (FSL) is again (from the hopefully right conclusion above) from a pension provider/ company standpoint, not from an employee’s. So the company considers all employees who would retire from ages 60 through 65. FSL is thus the sum of all C-bars i.e. M-bars. To answer your question “why do we sum the M-bars?”, let us break the answer into two parts: up to age 60 and from age 60 through 65. a. Up to age 60: as per pension tables there are no retirements up to age 60 i.e. nothing populated in rx. If an employee is 40 years now, the company will accrue the same level of benefits for him up to age 60 i.e. 128026 (M40, M41, …) in the numerator for each year. Note there’s NIL in C40, C41, … - so the C-bars couldn’t be summed up for the service from age 40 to 60. These M-bars have to be summed up for each year and they are a big sum – beyond a million. Also note that the number of years of future service is not multiplied: it’s already considered in this ‘large million’ number. Example, for PSL we used n/80 x Mx, but for FSL we will use 1/80 x Rx. The missing n is explained by the ‘large million’ factored in Rx (crude explanation, but I hope to have made a point). b. From age 60 through 65, we are using the logic of estimating EPV for the company/ pension provider and not for the employee, and hence adding up the M-bars. I trust this helps. Best regards, A
Hmmm now I'm a bit confused. Hi5, from what I understand, the formula for past service liability is as you explained - you probably mean the probability the employee will retire at time t by the way, not die. Then we sum over all values of t to allow for all possible ages the employee can retire at, based on the fixed past service (m). Now for future service liability, consider one particular year of service (t,t+1). Calculate the EPV of all retirement benefits with respect to that year - i.e. assume the employee only works one more year, the first sum (to get M) is to allow for all possible ages the employee can retire at BUT with respect to that one year of service. Then we need to sum over all future years of service (t,t+1(, (t,t+2)...(NPA-1, NPA). I'm not sure I've explained this clearly. But the way I think about it is: the past service is a fixed number (m). The future service for any 1 year would be calculated similar to the past service, hence the M function. But then we need to sum all of the possible future years of service (hence the R function). Hope this helps. I've not 'revised' this yet, hopefully it will be clear in time for the exam :-s
Well I'm still wondering, if you only work for one more year, why would you need to sum over all the future yrs. of service, since wouldn't this be your last yr. of service? I'd think you'd only need to now sum all the yrs. from now that you can retire... Any help?
Assumming that you're comfortable with past service, ie summing the value of retiring at a specific year to get the value of retiring at any point in the future. For future service, you're looking at each individual year of service and summing these to get all future service. The embedded discount rates, and decrement tables take care of all the neccesary time values and probablilities of surviving and working that year, and then surviving to receive a pension etc. There is a typo in part you're quoting, should be sum of (t,t+1),(t+1,t+2)...(NPA-1,NPA) When you look at one year, it is just like for past service. Instead of x years its just 1 year. Important thing is that its a fixed period of service. To recap, but first for simplicity I'm going to leave out the divided by Dx for the following expressions. Loosely speaking C,D Benefit of 1 at future date on death/survival M Benefit of 1 at all possible future date R Benefit of ALL future service (at rate of 1 per year of service) starting at ALL possible future dates The later is really sum of all possible benefit values each summed over all possible times it can be paid
Hmm ok, so it's basically the 1/80 for the one yr. of future service earned, and for that yr (and for every yr following), the employee can retire and they'd be entitled to 1 yr fut. serv. benefit only. So really it's a sum of all the possible values the pension benefit can take for every yr that it's possible to retire with one 1 yr entitlement, then sum all possible yrs. of entitlement. Right?
future service benefits I just didn't get future service benefits... like why can't we directly calculate EPV of future benefits by first considering benefit payable due to future service...like: .5*S*(z <x+.5>/s <x-1>) pa if the person dies in x→x+1 till the end of person's life, similarly 1.5 *S*(z <x+1.5>/s <x-1>) if dies in x+1→x+2...and so on... then multiplying the discount and prob. factors? and then finding some appropriate commutation functions??
Table: the pension benefits accrued from the year of future service relating to x to x +1. gives the future service period relating to service done in between age x to x+1. Now, if (s)he died between (x,x+1), the service period would be 0.5..... But if (s)he died later than x+1, the service period relating to service done in (x,x+1) would be 1..........(as stated in tables with Scaled Salary.) Same way for future service benefit got from service done in x+t to x+t+1. For your previous Q(nice Q):-(I skip Scaled Salary and all for now for simplicity) when employee died between (x,x+1), future service benefit period will be 0.5. when employee died between (x+t,x+t+1), future service benefit period will be t+0.5.(subject to regulations for limit)... you can provide commutation function as \( R_x=0.5C_x+1.5C_{x+1}+2.5C_{x+2}+.........=\Sigma C_x +\Sigma C_{x+1}+.......-(0.5C_x+0.5C_{x+1}+0.5C_{x+2}+........)=\Sigma M_x -0.5\Sigma C_x\) (C represents general form as given in notes)......
