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Employee contribution methodology

In a Valuation or Core Projection, ProVal calculates an employee contribution offset to the normal cost as of the valuation date and displays this offset as a negative number. Under the “level contributions for NC with accrued liability” methodology option, ProVal also calculates an employee contribution accrued liability, i.e., the accumulation (to the valuation date) of normal costs for years prior to the valuation date.

You may select employee contribution timing to be either the beginning of the year or the middle of the year, for purposes of the employee contribution normal cost calculations. If contributions are assumed to be middle of year, the annual employee contribution amount will be discounted with interest to reflect mid-year timing. If contributions are assumed to be beginning of year, no interest discount will be applied (see calculation details below).

You can view the employee contribution normal cost offset value (and accrued liability value, if calculated) by using the Valuation Output or Core Output command (or Output pane), selecting the normal cost variable for the appropriate liability method (e.g., PUC, UC, EAN$ or EAN%) and, to see the accrued liability, the Active liability variable, and then turning on "Details" for the "EEC" benefit. You may also select the Present Value of Future Employee Contributions.

In a Valuation Set or Deterministic Forecast, the mid-year cash flow value is shown. If employee contributions are assumed to be middle of year, then the cash flow value can be derived by multiplying the Valuation or Core Projection normal cost offset value by (1+i) ^ (1/2). If contributions are assumed to be beginning of year, then the cash flow value will equal the normal cost offset value.

You can view the employee contribution cash flow value by using the Valuation Set Output or Deterministic Forecast Output command (or Output pane) and selecting the Expected Employee Contributions variable.

The exact calculation used in a Valuation or Core Projection is discussed below. These formulas are for an individual record and vary according to the timing of decrements (beginning or middle of year), the timing of employee contributions (beginning or middle of year) and the liability method used for valuing plan benefits (e.g., PUC / UC, EAN$ / EAN%). Employee contributions may be adjusted by interest and/or survivorship by selecting one of the following employee contribution timing options:

For example, the “Middle of year” option above would indicate middle of year timing for the interest discount and no adjustment (no discount) for survivorship, that is, survival in active status to the middle, or the end, of the year is not required for the (full) annual employee contribution amount to be paid by the employee.

By contrast, the “Beginning of year, except survivorship at end of year” option would indicate beginning of year timing for the interest discount (thus no discount) and adjustment (discount) for survivorship, to reflect the required survival in active status to the end of the year in order to make (any) employee contributions for the year.

The following examples are based on a valuation as of 1/1/2011 with a 5% of pay contribution for the first 15 years of service and a funding span that ends at the 100% retirement age, which is 65. The employee is age 60 with 13 years of service on 1/1/2011 and a $28,382.52 current salary. As of 1/1/2011, the annual employee contribution is therefore 5% * 28,382.52 = 1,419.13.

 

BEGINNING OF YEAR DECREMENTS

EECx = contribx x survivorship adjustment x interest adjustment

where:

The examples illustrate the formula above for two employee contribution timing options: 1) “Beginning of year” and 2) “Middle of year, except survivorship at end of year”.

 

PUC / UC (and Attained Age %)

Beginning of year employee contribution timing

EECx = contribx

For example, if x = 60 and contrib60 = 1,419.13, then

EEC60 = 1,419.13.

Thus, under this option, the expected employee contribution is the same as the annual employee contribution computed by the benefit formula.

Note: Because the timing of decrements and employee contributions is identical, an assumption had to be made about which occurs first. The premise underlying this option is that the entire year’s employee contributions are paid first, before the employee decrements from active status (and, of course, the full year employee contributions are paid by employees who continue in active status throughout the year).

By contrast, the premise underlying the “Beginning of year, except survivorship at end of year” option is that the decrement occurs first, so that no employee contributions are paid for the year by employees who decrement from active status during the year. Therefore EECx = contribx* px

Middle of year employee contribution timing, except survivorship at end of year

EECx = contribx * px * v1/2

For example, if x = 60, contrib60 = 1,419.13, p60 = 0.925505 and i = 8%, then

EEC60 = 1,419.13 * 0.925505 * 1.08 -1/2 = 1,263.83.

Note that, under this option, employee contributions are assumed made only by employees who survive all decrements to the end of the year.

By contrast (as noted above for beginning of year employee contribution timing), under the “Middle of year” option, the (full) annual employee contribution amount is assumed paid by all employees, regardless of whether they decrement from active status during the year. Therefore EECx = contribx * v1/2

 

EAN$ / EAN%

Employee contributions under EAN may be calculated using one of three methods:

If “expected contributions for the year” is selected, the employee contribution offset to normal cost is calculated in the same manner as for PUC / UC (described above).

If “level contributions over career ($ or % of pay)” or “level contributions for NC with accrued liability” is selected, the employee contribution offset to normal cost is determined as follows:

Repeat the calculation of EECx (shown above for PUC / UC) for every age from plan entry to the age at which the retirement rate becomes 100%, or from entry to the last age with a future employee contribution, depending on the selection for the EAN funding span parameter. Then calculate an EAN "normal cost" in the usual fashion, i.e., NC = [PVFEC / PVFS] * S, where PVFEC and PVFS are at entry age (denoted as funding age in sample life reports). PVFS is the present value of future salaries (EAN % liability method) or the present value of future service (EAN $ liability method) and S is the current year valuation salary or valuation number, respectively. (Note: for display purposes, ProVal “normalizes” the calculation and shows values as of the valuation date, rather than as of the entry date.) This is expected employee contributions, or employee normal cost (an offset to employer normal cost), for the valuation year (2011 in our example).

There is no accrued liability for an employee contribution Benefit Definition under the “level contributions over career ($ or % of pay)” or the “expected contributions for the year” methods. In other words, the liability for employee contributions is zero.

Under the “level contributions for NC with accrued liability” method, the accrued liability for an employee contribution Benefit Definition is the difference between the present value of the expected employee contributions and the present value of the (level contribution) employee contribution offsets to normal cost, i.e., AL = PVFB – PVFNC = PVFEEC – [PVFS * (NC rate per life or NC%)].

The following two examples (excerpts from the EAN sample life report, with some columns not directly related to this discussion omitted for simplicity) develop the employee contribution normal cost under the “Beginning of year” and the “Middle of year, except survivorship at end of year” employee contribution timing options. The examples also develop the employee contribution accrued liability under the “level contributions for NC with accrued liability” methodology.

For both employee contribution timing examples below, you can check the 2011 value in the Expected Contrib. column – it is the same as under PUC / UC above.

Beginning of year employee contribution timing

If beginning of year employee contribution timing is selected, the calculation of the employee contribution normal cost under the EAN level percent of salary method will yield 1,300.43, as developed in step 8 below.

Year Member Age PV Salary Interest Discount Prob. of Remaining Active Annual Contrib. Expected Contrib. PV Expected Contrib.
1998 47 122,640.19 2.719624 2.645492 117.35 117.35 -844.30
1999 48 99,775.04 2.51817 2.235044 971.05 971.05 -5,465.28
2000 49 85,556.09 2.331639 1.99024 1,009.90 1,009.90 -4,686.46
2001 50 74,300.49 2.158925 1.794885 1,050.29 1,050.29 -4,069.90
2002 51 65,831.55 1.999005 1.651465 1,092.30 1,092.30 -3,606.00
2003 52 59,274.49 1.85093 1.544164 1,136.00 1,136.00 -3,246.85
2004 53 54,806.58 1.713824 1.482685 1,181.44 1,181.44 -3,002.11
2005 54 50,632.45 1.586874 1.422445 1,228.69 1,228.69 -2,773.45
2006 55 46,713.98 1.469328 1.362837 1,277.84 1,277.84 -2,558.82
2007 56 43,041.05 1.360489 1.303978 1,328.95 1,328.95 -2,357.62
2008 57 39,107.45 1.259712 1.230374 1,382.11 1,382.11 -2,142.16
2009 58 35,469.21 1.1664 1.15883 1,433.46 1,433.46 -1,937.55
2010 59 31,767.32 1.08 1.077803 1,419.13 1,419.13 -1,651.91
2011 60 28,382.52 1 1 1,419.13 1,419.13 -1,419.13
2012 61 25,295.26 0.925926 0.925505 1,475.89 1,475.89 -1,264.76
2013 62 23,184.47 0.857339 0.880901 1,342.01 1,342.01 -1,013.53
2014 63 17,296.59 0.793832 0.682466 0.00 0.00 0.00
2015 64 14,463.87 0.73503 0.592646 0.00 0.00 0.00
2016 65 0.00 0.680583 0.455794 0.00 0.00 0.00
Total   917,538.60         -42,039.82

If the “level contributions over career ($ or % of pay)” method is selected, the calculations stop with step 8 below. If the “level contributions for NC with accrued liability” method is selected, the accrued liability is developed in steps 9 through 12 below. The present values in steps 9 and 10 (which, for a funding span to 100% retirement age, are developed in the "PV of Future Service, Salary & Employee Contributions" sample life report) are accumulated from age on the valuation date, rather than from funding age as for steps 4 and 5.

1. Age     60            
2. Entry age   47            
3. Funding age   47            
4. PV Expected Contrib. from funding age -42,039.82            
5. PV Salary from funding age   917,538.60            
6. Normal Cost rate: (4) / (5)   -0.045818            
7. Valuation Salary   28,382.52 PV Salary term at Valuation Date      
8. Normal Cost: (6) x (7)   -1,300.43            
9. PV Future Employee Contributions   -3,697.42        
10. PV Salary   108,622.72        
11. PV Normal Cost: (6) x (10)   -4,976.88            
12. Liability: (9) - (11)   1,279.46            

Middle of year employee contribution timing, except survivorship at end of year

If this option is selected, the calculation of the employee contribution normal cost under the EAN level percent of salary method will yield 1,158.04, as developed in step 8 below.

Year Member Age PV Salary Interest Discount Prob. of Remaining Active Annual Contrib. Survival Probability Annual Interest Discount (mid-year) Expected Contrib. PV Expected Contrib.
1998 47 122,640.19 2.719624 2.645492 117.35 0.84485 0.96225 95.40 -686.38
1999 48 99,775.04 2.51817 2.235044 971.05 0.89047 0.96225 832.05 -4,682.95
2000 49 85,556.09 2.331639 1.99024 1,009.90 0.901843 0.96225 876.39 -4,066.90
2001 50 74,300.49 2.158925 1.794885 1,050.29 0.920095 0.96225 929.89 -3,603.33
2002 51 65,831.55 1.999005 1.651465 1,092.30 0.935027 0.96225 982.77 -3,244.42
2003 52 59,274.49 1.85093 1.544164 1,136.00 0.960186 0.96225 1,049.59 -2,999.89
2004 53 54,806.58 1.713824 1.482685 1,181.44 0.959371 0. 96225 1,090.65 -2,771.41
2005 54 50,632.45 1.586874 1.422445 1,228.69 0.958095 0. 96225 1,132.76 -2,556.92
2006 55 46,713.98 1.469328 1.362837 1,277.84 0.956811 0. 96225 1,176.50 -2,355.88
2007 56 43,041.05 1.360489 1.303978 1,328.95 0.943555 0. 96225 1,206.60 -2,140.57
2008 57 39,107.45 1.259712 1.230374 1,382.11 0.941851 0. 96225 1,252.60 -1,941.43
2009 58 35,469.21 1.1664 1.15883 1,433.46 0.930078 0. 96225 1,282.90 -1,734.04
2010 59 31,767.32 1.08 1.077803 1,419.13 0.927814 0. 96225 1,266.98 -1,474.80
2011 60 28,382.52 1 1 1,419.13 0.925505 0. 96225 1,263.83 -1,263.83
2012 61 25,295.26 0.925926 0.925505 1,475.89 0.951806 0. 96225 1,351.73 -1,158.36
2013 62 23,184.47 0.857339 0.880901 1,342.01 0.774736 0. 96225 1,000.45 -755.57
2014 63 17,296.59 0.793832 0.682466 0 0.868389 0. 96225 0 0
2015 64 14,463.87 0.73503 0.592646 0 0.769084 0. 96225 0 0
2016 65 0 0.680583 0.455794 0 0 0. 96225 0 0
Total   917,538.60             -37,436.70

If the “level contributions over career ($ or % of pay)” method is selected, the calculations stop with step 8 below. If the “level contributions for NC with accrued liability” method is selected, the accrued liability is developed in steps 9 through 12 below. The present values in steps 9 and 10 (which, for a funding span to 100% retirement age, are developed in the "PV of Future Service, Salary & Employee Contributions" sample life report) are accumulated from age on the valuation date, rather than from funding age as for steps 4 and 5.

1. Age     60            
2. Entry age   47            
3. Funding age   47            
4. PV Expected Contrib. from funding age -37,436.70            
5. PV Salary from funding age   917,538.60            
6. Normal Cost rate: (4) / (5)   -0.040801            
7. Valuation Salary   28,382.52 PV Salary term at Valuation Date      
8. Normal Cost: (6) x (7)   -1,158.04            
9. PV Future Employee Contributions   -3,177.77        
10. PV Salary   108,622.72        
11. PV Normal Cost: (6) x (10)   -4,431.94            
12. Liability: (9) - (11)   1,254.17            

 

 

MIDDLE OF YEAR DECREMENTS

EECx = (contribx x survivorship adjustment x interest adjustment)

+ (contribx x (1 – survivorship adjustment) x interest adjustment 1/2) / 2

where:

Note that in U.S. public mode, the "Same as timing for PVFS, PVFL, valuation salary and valuation number" uses the alternate formula:

EECx = contribx x survivorship adjustment x interest adjustment

The examples illustrate the formula above for two employee contribution timing options: 1) “Beginning of year” and 2) “Middle of year, except survivorship at end of year”.

 

PUC / UC (and Attained Age %)

Beginning of year employee contribution timing

EECx = contribx

For example, if x=60, and contrib60= 1,419.13, then

EEC60 = 1,419.13.

Thus, under this option, the expected employee contribution is the same as the annual employee contribution computed by the benefit formula.

Note: The timing of decrements is half a year after employee contributions are made. The premise underlying this option is that the entire year’s employee contributions are paid by all employees, including those who decrement from active status in (the middle of) the year.

By contrast, the premise underlying the “Beginning of year, except survivorship at end of year” employee contribution timing option is that no employee contributions are paid for the remainder of the year after the decrement occurs by those employees who decrement from active status in (the middle of) the year. Therefore, EECx = contribx* px+ [(contribx * (1 – px)) / 2]

Middle of year employee contribution timing, except survivorship at end of year

EECx = contribx * px * v1/2 + [(contribx * (1 – px) * v1/4) / 2]

For example, if x=60, contrib60 = 1,419.13, p60 = 0.925505 and i = 8%, then

EEC60 = 1,419.13 * 0.925505 * 1.08 -1/2 + [(1,419.13 * (1 – 0. 925505) * 1.08 -1/4) / 2] = 1,315.68.

Thus, under this option, the (full) annual amount of employee contributions is assumed paid only by employees who survive all decrements to the end of the year, and half of this amount is assumed contributed (for the period prior to decrement) by employees who decrement from active status in (the middle of) the year.

Note: Because the timing of decrements and employee contributions is identical, an assumption had to be made about which occurs first. The premise underlying this option is that the decrement occurs first, so that employee contributions are not paid, by employees who decrement from active status, for the remainder of the year after the decrement occurs.

By contrast, the premise underlying the “Middle of year” employee contribution timing option is that the employee contributions are paid before the decrement occurs, so that the (full) annual amount of employee contributions is assumed paid by all employees, regardless of whether they decrement from active status in (the middle of) the year. Therefore EECx = contribx * v1/2

 

EAN$ / EAN%

As for beginning of year decrement timing, repeat the calculation of EECx (shown above for PUC / UC) for every age. Then calculate an EAN "normal cost" in the usual fashion, i.e., NC = [PVFEC / PVFS] * S. This is expected employee contributions, or employee normal cost (an offset to employer normal cost), for the valuation year (2011 in our example).

For both employee contribution timing examples below, you can check the 2011 value in the Expected Contrib. column – it is the same as under PUC / UC above.

Beginning of year employee contribution timing

If beginning of year employee contribution timing is selected, the calculation of the employee contribution normal cost under the EAN level dollar method will yield 915.61, as developed in step 8 below.

 Year Member Age  PV Service Interest Discount Prob. of Remaining Active Annual Contrib. Expected Contrib. PV Expected Contrib.
1998 47 7.208836 2.719624 2.650674 117.35 117.35 -845.96
1999 48 5.639244 2.51817 2.239421 971.05 971.05 -5,475.99
2000 49 4.64961 2.331639 1.994138 1,009.90 1,009.90 -4,695.64
2001 50 3.882611 2.158925 1.7984 1,050.29 1,050.29 -4,077.87
2002 51 3.307753 1.999005 1.6547 1,092.30 1,092.30 -3,613.06
2003 52 2.863739 1.85093 1.547189 1,136.00 1,136.00 -3,253.21
2004 53 2.546039 1.713824 1.485589 1,181.44 1,181.44 -3,007.99
2005 54 2.261663 1.586874 1.425231 1,228.69 1,228.69 -2,778.88
2006 55 2.006377 1.469328 1.365506 1,277.84 1,277.84 -2,563.83
2007 56 1.774048 1.360489 1.303978 1,328.95 1,328.95 -2,357.62
2008 57 1.549917 1.259712 1.230374 1,382.11 1,382.11 -2,142.06
2009 58 1.351659 1.1664 1.15883 1,433.46 1,433.46 -1,937.55
2010 59 1.164027 1.08 1.077803 1,419.13 1,419.13 -1,651.91
2011 60 1 1 1 1,419.13 1,419.13 -1,419.13
2012 61 0.856949 0.925926 0.925505 1,475.89 1,475.89 -1,264.76
2013 62 0.755231 0.857339 0.880901 1,342.01 1,342.01 -1,013.53
2014 63 0.541763 0.793832 0.682466 0.00 0.00 0.00
2015 64 0.435612 0.73503 0.592646 0.00 0.00 0.00
2016 65 0 0.680583 0.455794 0.00 0.00 0.00
Total   43.79508         -42,099.07
                   

(Note: The Annual Contrib. column is the same as in the EAN% examples above for beginning of year decrement timing, that is, we have assumed the same amount of annual employee contribution at each age, although the employee contributions might not be pay-related when a level dollar cost method is used.)

If the “level contributions over career ($ or % of pay)” method is selected, the calculations stop with step 8 below. If the “level contributions for NC with accrued liability” method is selected, the accrued liability is developed in steps 9 through 12 below. The present values in steps 9 and 10 (which, for a funding span to 100% retirement age, are developed in the "PV of Future Service, Salary & Employee Contributions" sample life report) are accumulated from age on the valuation date, rather than from funding age as for steps 4 and 5.

1. Age     60            
2. Entry age   47            
3. Funding age   47            
4. PV Expected Contrib. from funding age -42,099.07            
5. PV Service from funding age   43.79508            
6. Normal Cost rate: (4) / (5)   -915.61            
7. Valuation Number   1.00 PV Service term at Valuation Date      
8. Normal Cost: (6) x (7)   -915.61            
9. PV Future Employee Contributions   -3,697.42        
10. PV Service   3.589555        
11. PV Normal Cost: (6) x (10)   -3,286.62            
12. Liability: (9) - (11)   -410.79            

Middle of year employee contribution timing, except survivorship at end of year

If this option is selected, the calculation of the employee contribution normal cost under the EAN level dollar method will yield 891.12, as developed in step 8 below.

Year Member Age PV Service Interest Discount Prob. of Remaining Active Annual Contrib. Survival Probability Annual Interest Discount (mid-year) Expected Contrib. PV Expected Contrib.
1998 47 7.208836 2.719624 2.650674 117.35 0.84485 0.96225 104.33 -752.10
1999 48 5.639244 2.51817 2.239421 971.05 0.89047 0. 96225 884.21 -4,986.30
2000 49 4.64961 2.331639 1.994138 1,009.90 0.901843 0. 96225 925.01 -4,300.93
2001 50 3.882611 2.158925 1.7984 1,050.29 0.920095 0. 96225 971.05 -3,770.20
2002 51 3.307753 1.999005 1.6547 1,092.30 0.935027 0. 96225 1,017.58 -3,365.92
2003 52 2.863739 1.85093 1.547189 1,136.00 0.960186 0. 96225 1,071.78 -3,069.29
2004 53 2.546039 1.713824 1.485589 1,181.44 0.959371 0. 96225 1,114.19 -2,836.78
2005 54 2.261663 1.586874 1.425231 1,228.69 0.958095 0. 96225 1,158.02 -2,619.04
2006 55 2.006377 1.469328 1.365506 1,277.84 0.954941 0. 96225 1,202.44 -2,412.54
2007 56 1.774048 1.360489 1.303978 1,328.95 0.943555 0. 96225 1,243.39 -2,205.84
2008 57 1.549917 1.259712 1.230374 1,382.11 0.941851 0. 96225 1,292.02 -2,002.52
2009 58 1.351659 1.1664 1.15883 1,433.46 0.930078 0. 96225 1,332.06 -1,800.49
2010 59 1.164027 1.08 1.077803 1,419.13 0.927814 0. 96225 1,317.23 -1,533.29
2011 60 1 1 1 1,419.13 0.925505 0. 96225 1,315.68 -1,315.68
2012 61 0.856949 0.925926 0.925505 1,475.89 0.951806 0. 96225 1,386.62 -1,188.26
2013 62 0.755231 0.857339 0.880901 1,342.01 0.774736 0. 96225 1,148.73 -867.55
2014 63 0.541763 0.793832 0.682466 0.00 0.868389 0. 96225 0.00 0.00
2015 64 0.435612 0.73503 0.592646 0.00 0.769084 0. 96225 0.00 0.00
2016 65 0 0.680583 0.455794 0.00 0 1 0.00 0.00
Total   43.79508             39,026.75

(Note: The Annual Contrib. column is the same as in the EAN% examples above for beginning of year decrement timing, that is, we have assumed the same amount of annual employee contribution at each age, although the employee contributions might not be pay-related when a level dollar cost method is used.)

If the “level contributions over career ($ or % of pay)” method is selected, the calculations stop with step 8 below. If the “level contributions for NC with accrued liability” method is selected, the accrued liability is developed in steps 9 through 12 below. The present values in steps 9 and 10 (which, for a funding span to 100% retirement age, are developed in the "PV of Future Service, Salary & Employee Contributions" sample life report) are accumulated from age on the valuation date, rather than from funding age as for steps 4 and 5.

1. Age     60            
2. Entry age   47            
3. Funding age   47            
4. PV Expected Contrib. from funding age -39,026.75            
5. PV Service from funding age   43.79508            
6. Normal Cost rate: (4) / (5)   -891.12            
7. Valuation Number   1.00 PV Service term at Valuation Date      
8. Normal Cost: (6) x (7)   -891.12            
9. PV Future Employee Contributions   -3,371.50        
10. PV Service   3.589555        
11. PV Normal Cost: 6) x (10)   -3,198.73            
12. Liability: (9) - (11)   -172.77