Projection and Freeze Ages, Crediting Frequency and Indexation Timing
The “Projection & Freeze Ages” topic is part of final average, career average and cash balance format accrual definition Benefit Formula Components. This topic is entitled “Projection & Freeze Ages, Crediting Frequency” for cash balance accrual definitions, because of the availability of an interest crediting frequency parameter. In the universal pension mode, for career average accrual definitions with indexation selected, this topic is entitled “Projection & Freeze Ages, Indexation Timing”, because of the availability of an indexation parameter (typically used to code pension plans of the Netherlands).
The parameters of this topic deal with continued accumulation of benefit credit, in some manner, after decrement. The benefit credit accumulated or granted after decrement is added to the accrued benefit as of the decrement date to determine the value of the Benefit Formula Component at the time of decrement.
Project service to (final average format, career average format, universal mode career average format if no indexation) lets you compute the value of an accrual definition format Benefit Formula Component as if service continued to accumulate after the decrement age and up to the constant age or age in database field specified, with the accrual basis “frozen” no later than the decrement year. (For decrement ages after the projection age, the component value will be the same as at decrement.)
If the component’s format is final average, the accrual basis used for projection is frozen in decrement year (that is, the accrual basis value for years after decrement is the same as the accrual basis value associated with the decrement year).
If the component’s format is career average, you may specify whether the accrual basis used for projection should be the accrual basis frozen in the decrement year or frozen in the year before the decrement year.
Lastly, specify times what percentage (usually 100) future accrual rates should be prorated.
For example, for a final average format, if the accrual basis is 5 #FAS 5, the value of the projected component will be based on the value of this final average salary operator at decrement. If instead you want the final average salary to be based on level pay each year from decrement, this can reasonably be approximated by using 1 #FAS 1 as the accrual basis (this is exact except for participants within five years of the projection age, for which this approximation overestimates the benefit under an increasing salary scale). Note that to base final average salary on level pay for each year after decrement, you would need to use two Benefit Formula Components, one for accruals up to decrement, with 5 #FAS 5 in the basis, and one for projected accruals after decrement, with 1 #FAS 1 in the basis.
Project to (cash balance format, universal mode career average format with indexation) lets you compute the value of an accrual definition format Benefit Formula Component as if 1) interest crediting (cash balance format) or indexation (career average format) continued after the decrement age and up to the constant age or age in database field specified, or 2) with service accruals (career average format) or pay credits (cash balance format) accumulating after decrement (until the projection age) or 3) both interest crediting / indexation and service / pay credits continued after decrement up to the projection age. (For decrement ages after the projection age, the component value will be the same as at decrement.)
In the case of cash balance components, you may elect to project interest and/or pay credits to the specified age. If the interest credits box is checked, interest will be credited on the cash balance amount beyond decrement. If the pay credits box is checked, pay credits will be granted beyond decrement. Enter the (integer) age to which interest and/or pay credits should be projected when evaluating the accrual definition. Projection is for the number of whole years until the participant’s rounded age reaches the specified age. If the participant continues in active service beyond that age, the component will continue to accrue benefit credit past that age, because of accumulating interest credits and/or pay credits. Pay credits may be projected using the accrual rate at decrement (the accrual rate in effect on the first day of the decrement year) or projected accrual rates (as if service were ongoing). In either case, the accrual basis (e.g., each year’s pay) may be frozen (“frozen” as defined above) in the year prior to decrement or in the decrement year.
In the case of career average components with indexation, you may elect to project indexation and/or service to the specified age. If the indexation box is checked, the career average benefit will be increased beyond decrement at the indexation rate. If the service accruals box is checked, service will continue to accrue beyond decrement. Enter the (integer) age to which indexation and/or service accruals should be projected when evaluating the accrual definition. Projection is for the number of whole years until the participant’s rounded age reaches the specified age. If the participant continues in active service beyond that age, the component will continue to accrue benefit credit past that age, because of accumulating indexation and/or service accruals. Service accrual may be projected using the accrual rate at decrement (the accrual rate in effect on the first day of the decrement year) or projected accrual rates (as if service were ongoing). In either case, the accrual basis (e.g., each year’s pay) may be frozen (“frozen” as defined above) in the year prior to decrement or in the decrement year.
If pay credits (cash balance format) or service accruals (career average format with indexation) are projected, select an option for determining the basis to use after decrement, either the Accrual Basis frozen in the decrement year (“frozen” as defined above) or frozen in the year before the decrement year.
If pay credits (cash balance format) or service accruals (career average format with indexation) are projected, also select an option for determining the rates that apply after decrement: 1) “projected accrual rates”, in which case ProVal will accumulate benefit accruals by following the pattern of Accrual Rates that would have applied had the member remained active until the projection age, or 2) “accrual rate at decrement”, in which case future benefit accruals will be at the same rate as in effect at decrement (i.e., level accrual rates after decrement).
In either case, specify times what percentage (usually 100) future accrual rates should be prorated.
Here are some examples of how ProVal accumulates benefit credit past decrement to a projection age of 65 (which accumulation, again, depends on the accrual format and, where available, the selected options for the basis and/or the rates):
A final average accrual definition, for which service is projected using projected accrual rates and the basis is frozen in the decrement year.
Example: 2% * years of service * final average pay
Member Age at Decrement Benefit Service Cumulative Accrual Rate Accrual Basis Accrued Benefit Projected Accrual Rates Projected Accruals Benefit Component 62 10 0.20 100,000 20,000 0.06 6,000 26,000 63 11 0.22 105,000 23,100 0.04 4,200 27,300 64 12 0.24 110,000 26,400 0.02 2,200 28,600 65 13 0.26 115,000 29,900 0 0 29,900 Projected Accruals as of decrement age 62 = Accrual Basis * Projected Accrual Rates =
100,000 * 0.06 = 6,000Benefit Component value at age 62 = Accrued Benefit + Projected Accruals =
20,000 + 6,000 = 26,000
A career average accrual definition (in universal mode, without indexation), for which service is projected using projected accrual rates. The accrual basis in Example 1 is frozen in the year prior to decrement and the accrual basis in Example 2 is frozen in the decrement year.
Example 1: 2% * pay for each year of service, $40,000 accrued benefit at decrement age 62
Member Age at Decrement Accrual Rate Accrual Basis Annual Accrual Accrued Benefit Projected Accrual Rates Projected Accruals Benefit Component 61 100,000 62 0.02 110,000 2,200 40,000 0.06 6,000 46,000 63 0.02 120,000 2,400 42,200 0.04 4,400 46,600 64 0.02 130,000 2,600 44,600 0.02 2,400 47,000 65 47,200 0 0 47,200 Projected Accruals as of age 62 = Accrual Basis (for prior year) * Projected Accrual Rates =
100,000 * 0.06 = 6,000Benefit Component value at age 62 = Accrued Benefit + Projected Accruals =
40,000 + 6,000 = 46,000Example 2: 2% * pay for each year of service, $40,000 accrued benefit at decrement age 62
Member Age at Decrement Accrual Rate Accrual Basis Annual Accrual Accrued Benefit Projected Accrual Rates Projected Accruals Benefit Component 61 100,000 62 0.02 110,000 2,200 40,000 0.06 6,600 46,600 63 0.02 120,000 2,400 42,200 0.04 4,800 47,000 64 0.02 130,000 2,600 44,600 0.02 2,600 47,200 65 47,200 0 0 47,200 Projected Accruals as of age 62 = Accrual Basis (for current year) * Projected Accrual Rates =
110,000 * 0.06 = 6,600Benefit Component value at age 62 = Accrued Benefit + Projected Accruals =
40,000 + 6,600 = 46,600
A cash balance accrual definition in which both interest credits and pay credits are projected. In this example, the accrual basis is frozen in the year prior to decrement and the accrual rates entered are constant (therefore the projected rates that apply in the future are the same as the rate at the decrement age, 62), so the result is the same regardless of whether the rates parameter is set to “accrual rate at decrement” or “projected accrual rates”.
Example: 2% * pay for each year of service, $40,000 accrued benefit at decrement age 62, 6% interest credits
Member Age at Decrement Accrual Rate Accrual Basis Annual Accrual Interest Rate Accrued Benefit Projected Interest Projected Accruals Benefit Component 61 100,000 62 0.02 110,000 2,200 0.06 40,000 1.191016 6,367.20 54,007.84 63 0.02 120,000 2,400 0.06 44,600 1.123600 4,532.00 54,644.56 64 0.02 130,000 2,600 0.06 49,676 1.060000 2,400.00 55,056.56 65 55,257 1.000000 0.00 55,256.56 Projected Interest as of age 62 = (1+i) ** (Projection Age – Member Age at decrement) =
1.06 ** (65-62) = 1.191016Projected Accruals as of age 62 = Sum of (Projected Interest * Accrual Rate) for years after the decrement year (i.e., years when the participant is age 63, 64 or 65) =
(1.1236 * 0.02 + 1.06 * 0.02 + 1 * 0.02) * 100,000 = 6,367.20Benefit Component value at age 62 = (Accrued Benefit * Projected Interest) + Projected Accruals =
40,000 * 1.191016 + 6,367.20 = 54,007.84
Note that the Accrued Benefit, if provided (for career average and cash balance accrual definitions), should exclude projected accruals. ProVal computes projected accruals on an “expected value” basis, even for ages in the past (for entry age normal cost method calculations).
Under the accrual rate proration attribution method, the projected unit credit Cumulative Accrual Rate = Cumulative Accrual Rate + Projected Accrual Rates. Thus PUC values will be fully attributed, as of the valuation date, for decrement ages prior to the projection age (i.e., these values will be allocated to the accrued liability, rather than to future normal costs); see PUC and UC attribution for details.
Freeze accrual basis and rates at age allows you to freeze the accrual definition component value at a specified age. If this box is checked, both the accrual basis and the accrual rates will freeze when the member’s rounded age reaches the age indicated. This may be useful when applying actuarial increase factors to a benefit frozen at a particular age, for example, to calculate an increased delayed retirement benefit amount for an annuity commencing after the normal retirement age. See the Frequently Asked Questions article entitled Late retirement increase for coding suggestions.
In the event that accruals are projected (that is, either the Project service to age box or the Project to age box is checked), the freeze age must be greater than or equal to the specified projection age.
Crediting frequency determines the frequency of interest compounding and accruals (e.g., salary credits) for cash balance accrual definitions. Mathematically, it is as if the interest crediting rate were set to (1+ i/m) ** m – 1 and the accrual basis were multiplied by [(1+i/m) ** m – 1] / i, where m is the number of credits per year and i is the interest crediting rate. Accruals are assumed to occur at the end of each period. No special adjustments are made for partial years (e.g., the year of hire).
Incidentally, [(1+i/m) ** m – 1] / i can be derived as the sum of $1 credited and compounded mthly: (1/m) (1+i/m) ** (m-1) + (1/m) (1+i/m) ** (m-2) + … + (1/m) (1+i/m) ** 0 = [(1+i/m) ** m – 1] / i
Examples: 2% * pay for each year of service (no pay credits projected beyond decrement), $40,000 accrued benefit at decrement age 62, 6% interest credits
Annual crediting (m=1)
| Member Age at Decrement | Accrual Rate | Accrual Basis | Annual Accrual | Interest Rate | Benefit Component |
| 62 | 0.02 | 110,000 | 2,200 | 0.06 | 40,000 |
| 63 | 0.02 | 120,000 | 2,400 | 0.06 | 44,600 |
| 64 | 0.02 | 130,000 | 2,600 | 0.06 | 49,676 |
| 65 | 55,257 |
Annual Accrual at age 62 = Accrual Rate * Accrual Basis * {[(1+i/m) ** m – 1] / i} =
0.02 * 110,000 * {[(1+0.06/1) ** 1 – 1] / 0.06} = 0.02 * 110,000 = 2,200
Benefit Component value at age 63 = [Benefit Component value (prior year, at age 62) * [(1+i/m) ** m] + Annual Accrual (prior year, at age 62) =
40,000 * [(1+0.06/1) ** 1] + 2,200 = 42,400 + 2,200 = 44,600
Monthly crediting (m=12)
| Member Age at Decrement | Accrual Rate | Accrual Basis | Annual Accrual | Interest Rate | Benefit Component |
| 62 | 0.02 | 110,000 | 2,261.52 | 0.06 | 40,000.00 |
| 63 | 0.02 | 120,000 | 2,467.11 | 0.06 | 44,728.63 |
| 64 | 0.02 | 130,000 | 2,672.71 | 0.06 | 49,954.51 |
| 65 | 55,708.30 |
Annual Accrual at age 62 = Accrual Rate * Accrual Basis * {[(1+i/m) ** m – 1] / i} =
0.02 * 110,000 * {[(1+0.06/12) ** 12 – 1] / 0.06} = 2,261.52
Benefit Component value at age 63 = [Benefit Component value (prior year, at age 62) * [(1+i/m) ** m] + Annual Accrual (prior year, at age 62) =
40,000 * [(1+0.06/12) ** 12] + 2,261.52 = 44,728.63
In the universal mode, the Indexation occurs at parameter, for a career average accrual definition with indexation applied, indicates whether indexation is credited at the beginning of year (that is, a year of indexation is granted one year prior to when the year that would normally earn the indexation is completed) or at the end of year (that is, after the year that earns the indexation is completed). Indexation is credited at the beginning of the year in Example 2 and at the end of the year in Example 1.
Example 1: 2% of pay for each year of service (not projected beyond decrement), $40,000 accrued benefit at decrement age 62, 6% indexation
| Member Age at Decrement | Accrual Rate | Accrual Basis | Annual Accrual | Indexation Rate | Benefit Component |
| 62 | 0.02 | 110,000 | 2,200 | 0.06 | 40,000 |
| 63 | 0.02 | 120,000 | 2,400 | 0.06 | 44,600 |
| 64 | 0.02 | 130,000 | 2,600 | 0.06 | 49,676 |
| 65 | 55,257 |
Annual Accrual at age 62 = Accrual Rate * Accrual Basis * (1+i) =
0.02 * 110,000 * 1.06 = 2,200
Benefit Component value at age 63 = [Benefit Component value (prior year, at age 62) * (1+i)] + Annual Accrual (prior year, at age 62) =
40,000 * 1.06 + 2,200 = 42,400 + 2,200 = 44,600
Example 2: 2% of pay for each year of service (not projected beyond decrement), $40,000 accrued benefit at decrement age 62, 6% indexation
| Member Age at Decrement | Accrual Rate | Accrual Basis | Annual Accrual | Indexation Rate | Benefit Component |
| 62 | 0.02 | 110,000 | 2,200 | 0.06 | 40,000 |
| 63 | 0.02 | 120,000 | 2,400 | 0.06 | 44,732 |
| 64 | 0.02 | 130,000 | 2,600 | 0.06 | 49,960 |
| 65 | 55,714 |
Annual Accrual at age 62 = Accrual Rate * Accrual Basis * (1+i) =
0.02 * 110,000 * 1.06 = 2,200
Benefit Component value at age 63 = [Benefit Component value (prior year) + Annual Accrual (prior year, at age 62)] * (1+i) =
(40,000+ 2,200) * 1.06 = 42,200 * 1.06 = 44,732