A pension plan may require actuarial increases after Normal Retirement Date (NRD) and under certain conditions a plan must provide actuarial increases after NRD.  ProAdmin performs late retirement calculations within a Late Retirement Benefit Formula Component (BFC).

ProAdmin supports three (3) general approaches for direct actuarial equivalence calculations using annuity factors where one is cumulative and two are annual calculations. (ProAdmin also supports calculations based on tables and interest-only, but these are outside the scope of this discussion.)  The general actuarial equivalence increase rate formula for each of the annuity-based approaches are:

1. At commencement age:  The cumulative increase rate formula is an immediate annuity at NRD (N) divided by an annuity deferred from NRD to the commencement age (B):   /  _B-N|.  If commutation factors are calculable (i.e., static mortality and interest rates apply), this formula reduces to: N_NRD / N_B.


2. Annually using factors from NRD:  The increase factor for a year is the ratio of the commencement age factor for that year (as calculated above) divided by the commencement age factor for the prior year.  So if normal retirement age is 65 and we want the annual increase factor from age 66 to age 67, the formula is : (  /  2|) / (  / ₁|), which reduces to 1| / 2| and can be seen to be equivalent to    /₁|. If commutation factors are calculable (i.e., static mortality and interest rates apply), this formula reduces to: N₆₆ / N₆₇.


3. Annually using factors from the beginning of the plan year:  With static interest and mortality, this approach is mathematically equivalent to the formula derived above for calculating the factors annually from NRD, but instead of going through all of the gyrations, it directly, in the case of a factor moving from age 66 to age 67, uses the    /₁| formula. Accordingly, the increase rate formula for each full plan year after NRD is:  /  ₁|. The nice thing about taking this approach directly when the mortality is dynamic and/or the interest rates are segment rates is that only the current plan year's calculation reflects that plan year's interest and mortality, as opposed to using a methodology that uses the current year's interest and mortality for factors that span more than just the current plan year. 

To completely define late retirement, ProAdmin needs to know:

• The value of the accrued benefit at any point in time through decrement.  Note: This is another Benefit Formula Component, but not a late retirement BFC.
• The Normal Retirement Age (NRA) and Date (NRD), which is usually the plan's Normal Retirement Date, but can be defined within the Late Retirement parameters using a different Eligibility Definition with a Service Definition Set to evaluate any service condition(s). 
• The Actuarial Equivalence assumptions upon which the accrued benefit is increased.  This is also known as the basis.
• The approach for comparing accrued benefits to the actuarially increased benefits.  ProAdmin's available approaches for performing the calculations are: 
  • at commencement date,
  • annually using factors from NRD, or
  • annually using factors from the beginning of the plan year.

Please note that if there are intermediate dates in a plan year, the calculation does not flow from one date to the next.  Rather, the calculations for  each date within a plan year are independent and start from the beginning of that plan year.

The basic steps of the late retirement calculation are:

1. Determine the participant's Normal Retirement Date (NRD) for the Late Retirement Benefit Formula Component.   This is the date after which actuarial increases will be applied and benefits compared.
2. Using the Actuarial Equivalence assumptions (or basis) in effect at each calculation date after NRD (that is: at each "requested" Benefit Commencement Date (BCD)), develop two annuity factors: an immediate annuity factor and a deferred annuity factor.  
3. Using the two factors, divide the deferred annuity into the immediate annuity to provide the increase factor. 
4. The increase factor will be either a cumulative late retirement or an incremental late retirement factor.  This depends on the parameter selected for Calculation performed, which provides the methodology for applying increase factors and comparing intermediate results to determine the benefit payable at each commencement date.

After NRA, NRD and actuarial equivalence has been determined, computing the two annuity factors and the resultant actuarial increase are next.  For details on the methodologies, please select:

• Calculation performed: At commencement date ​or Annually using factors from NRD
• Calculation performed: Annually using beginning of plan year factors

On the detailed report for Late Retirement, ProAdmin writes output into the following columns:

1. Date - calculation date
2. Member Calc. Age - the member's age at the calculation date
3. BOY calc Age - the member's age at the beginning of the plan year. (Note: this column only appears when Calculation performed parameter is Annually using factors from the beg of plan year)
4. Accrued Benefit - the value at each date of the BFC defined as the accrued benefit in the late retirement component.
5. Change in Accrued Benefit - shown only if late retirement computations are done annually, is the Accrued Benefit minus the previous Accrued Benefit
6. Interest Rate - the interest rate in effect at each calculation date used in the basis for the both annuity factors.
   1. 2nd Interest rate - appears only when using spot interest rates
   2. 3rd Interest Rate - appears only when using spot interest rates
7. Immediate Annuity at NRD - the immediate annuity factor for NRA using the basis in effect at each date.
8. Annuity
   1. deferred from NRD - the deferred annuity factor from NRA to the Member's Age using the basis in effect at calculation date.  (Note: this column appears when Calculation performed parameter is at Commencement age or Annually using factors from NRD)
   2. deferred from NRD at boy - the deferred annuity factor from NRA to the Member's Age at the beginning of the period (typically the prior year) using the basis in effect at calculation date.  (Note: this column only appears when Calculation performed parameter is Annually using factors from NRD).  The incremental late retirement factor listed below, while not actually internally calculated this way, is the ratio of this deferred annuity factor at the beginning of the period to the deferred annuity factor from NRD (at the calculation date). This is useful when interest rates and/or mortality vary from calculation date to calculation date.
   3. Annuity def'd 1 yr or to date - deferred annuity from NRD or the beginning of plan year (Note: this column only appears when Calculation performed parameter is Annually using factors from the beg of plan year)
9. Late Retirement Factor -
   1. Cumulative Late Retirement Factor - this is used when Calculation performed parameter is At commencement age
   2. Incremental Late Retirement Factor - his is used when Calculation performed parameter is Annually . . .
10. Factor Adjusted Benefit -
    1. When Calculation performed parameter is At commencement age, it is the accrued benefit at NRD multiplied by the Cumulative Late Retirement Factor
    2. When Calculation performed parameter is Annually using factors - from NRD or from beg of plan year, it is the Benefit Component at previous end of plan year multiplied by the Incremental Late Retirement Factor
11. Benefit Component - at any date is the larger of two values -
1. the Accrued Benefit (d) computed at the date (a), using plan provisions (i.e., without actuarial increases)
2. the Factor Adjusted Benefit (j)