QUESTION: Can I discount the projected benefit payments (output available in a Valuation or Valuation Set) to match my liabilities? Can I also discount projected salaries, projected head counts and projected employee contributions (output available in a Valuation) to match present value of future salaries, present value of future lives and present value of future employee contributions (respectively)?

ANSWER: You should be able to match liabilities to a reasonable degree and present values of salaries, head counts and employee contributions (PVFS, PVFL and PVFEC) more precisely.

 

Discounting projected benefit payments

Except for small variances that may arise if an estimated payment timing factor is used, the discounted projected benefit payments should match very closely to the liability value. Note that in U.S. Qualified mode, if the law type is "PPA", "PPA and CAS", or "Pre-PPA and PPA", the present value of future benefits (PVFB) is based on actuarial liability assumptions. ProVal calculates two sets of PVFB projected benefit payments: one using PPA mortality and interest and the other using actuarial liability assumptions. Be sure to use the correct set when discounting projected benefit payments to match the PVFB.

A simple method of discounting is as follows:

Discount = 1 / [ (1 + i) ^ (t+0.5) ], where t=0,1,2,3,….

A slightly more precise method for matching liabilities is to reflect the selection for timing of payments during the year, as follows:

Discount = 1 / [ (1 + i) ^ (t + TimingAdj) ], where t=0,1,2,3,… and

TimingAdj =

• Pension, valuing annuities: (m-1)/2m or (m+1)/2m if payment timing is Beginning or End of period, respectively, where m=number of payments per year. For the rationale, see Present Values: Benefits payable (m)thly.

• OPEB: 0, 0.5, or 1 if claims timing (entered under the Other Valuation Parameters topic of Valuation Assumptions) is Beginning, Middle or End of year, respectively.

For most plans, the value of discounted projected benefit payments will match very closely to the associated liability.

However, if a middle of year decrement timing assumption is used, a discrepancy has been observed for OPEB plans where active benefits are a function of decrement (i.e., the benefit paid depends on when you stopped working) if this plan provision has been coded by use of one of the operators #DECYEAR, #DECAGE, #DECSVC and #DECPTS instead of (the preferred coding) use of the eligibility parameters. This discrepancy reflects a distortion of liability values (not the projected benefit payments), caused by averaging of beginning and end of year benefits and payment form values; it can be substantial, particularly if benefits either commence or cease entirely in a particular decrement year. 

Also, please note that starting with version 3.07 of ProVal, if a middle of year decrement timing assumption is used, the Output value of expected benefit payments will not match precisely the value of projected benefits in the first year of the cash flow stream, because of a refinement to the projected benefit payments calculation to more closely match the discounted value to the liability.​

Discounting projected salaries, head counts and employee contributions

Some variance will be caused by scaling factors, if used (decrement timing should not affect matching present values).

The option to base projected salary and head count in Output on valuation salary / number, rather than on total salary / number, which is entered under a liability methods topic of Valuation Assumptions, must be selected in order to match the discounted values of projected salaries and head counts to PVFS and PVFL, respectively.

If the timing selected for PVFS, PVFL, valuation salary and valuation number, also entered under a liability methods topic of Valuation Assumptions, is the beginning of the year, a simple method of discounting to match PVFS or PVFL is as follows:

Discount = 1 / [ (1 + i) ^ t ], where t=0,1,2,3,….

If this timing parameter is set to the middle of the year, the discount factor instead would be:

Discount = 1 / [ (1 + i) ^ (t+0.5) ], where t=0,1,2,3,….

Lastly, if the timing parameter is set to the end of the year, the discount factor would be:

Discount = 1 / [ (1 + i) ^ (t+1) ], where t=0,1,2,3,….

Similarly, these methods of discounting can be used to match PVFEC; which method to use depends on the timing selected (under a liability methods topic of Valuation Assumptions) for employee contributions.