Clicking the Attribution button at the bottom of the Accrual Rates dialog box of an accrual definition type of Benefit Formula Component leads to the Accrual Rate Proration dialog box, used to specify custom attribution of liabilities under the unit credit (pension modes only) and/or projected unit credit liability methods. Note that it is only the calculation of the actuarial accrued liability and normal cost under these two liability methods that is affected by custom attribution: calculation of present value of future benefits and calculation of liabilities under other methods (e.g., entry age normal) are not affected by custom attribution rates.

• Under the projected unit credit cost method, custom attribution rate parameters apply only under the accrual rate proration option.

• Under the unit credit cost method, custom attribution rate parameters are used to determine the accrued benefit under the accrual rate proration option and the linear proration options.

The methodology of accrual rate proration attribution is discussed briefly at the end of this article. For more detailed information about this methodology and information about the methodology used for the other (linear) options afforded by the attribution parameters of a pension mode Benefit Definition or the attribution parameters of an OPEB mode Benefit Definition, see our Technical Reference article entitled PUC and UC attribution.

In the pension modes, attribution may be specified independently for unit credit and projected unit credit liabilities. For both cost methods, there are two options for the structure of attribution rates. The first option, For Projected Unit Credit accrual rate proration and For Pure Unit Credit proration, to use accrual rates, indicates that attribution rates are the same as benefit accrual rates and that attribution service is the same as benefit service (as determined by the Benefit service based on parameter selection in the Accrual Rates dialog box). Under this option, benefits are attributed under the cost method as they accrue. To specify a different basis for attribution service and/or different attribution rates, select the custom rates that vary by rate structure.

The custom rates option allows for rates that vary over “years of service” or “age” or “points (age + service)”, including caps (for example, the rate becomes zero after a maximum number of years). This rate structure also allows access to rate schedules that differ by calendar year of decrement and permits you to apply new rate schedules for future calendar years of decrement that will replace the old rates for all service, age or points, including attribution periods prior to the effective date of the change. To enter a constant attribution rate that differs from the specified accrual rates, simply enter the constant rate in the first row of the grid and do not create any new rates.

When the custom rate option is selected, the Attribution service based on parameter (discussed below) determines the starting point for attribution of the benefit. Thus you may indicate that attribution begins at a different point in time from benefit accrual.

Type values only in the From and Rate columns; the Up to column will be filled in automatically. Enter percentages as their decimal equivalents. If you are entering additional rate schedules that start at different calendar dates, then the schedule on the main attribution rates screen should reflect the original attribution pattern before any changes.

The with new rates as of parameter lists the dates of any subsequent changes to the rates. To modify an existing schedule of rate change, click the date; to add a new rates schedule, click the New button.

Each new attribution rate table will have the same structure as the first one – Service-based rates, Age-based rates or Points-based rates.

The Effective date for each new rate table is the calendar date on which rates begin to follow the new schedule. The Effective date is entered directly in the text field.

The breakpoints and rates are entered in the table in the same manner as on the main attribution rates screen and the Attribution service based on parameter (discussed below) from the main screen applies to all attribution rate tables.

You may Apply rates to just the Years after the effective date of the rate change (the benefit attributed up to the effective date is not changed) or to All years (the benefit attributed up to the effective date is recomputed according to the new rate pattern). The latter option represents a change in attribution rates for the active member’s entire attribution period and can cause the attributed benefit to increase sharply at the effective date of the change, producing a possibly undesirable attribution pattern. Furthermore, if changing attribution rates for all years produces a decrease in the attributed benefit as of the decrement date, ProVal considers the attributed benefit up to that date to be the attributed benefit as of the prior decrement date (one year earlier), if greater. This is done to avoid the illogical result of a previously attributed benefit becoming “unattributed” a year later (which implies that the previous funding or expensing of the attributed benefit is reversed). Thus the typical choice is expected to be a change in attribution rates only prospectively.

For additional information, such as input coding format, see the discussion under the Accrual Rates topic.

The Apply cash balance crediting rate (to attribution rate) check box, available for the projected unit credit cost method in the pension modes, is accessible if your accrual definition component has a cash balance accrual format (inapplicable to OPEB mode). Check the box if you wish to reflect the interest crediting rate, as well as the attribution service pay credit rate, in accrual rate proration attribution of the cash balance amount (i.e., the numerator and denominator of the accrual fraction will reflect interest credits).

The Attribution service based on parameter defines service for purposes of attribution and therefore determines when the attribution period commences. If custom rates vary by “years of service”, the Attribution service based on parameter also defines the service breakpoints, i.e., when the attribution rates change; if custom rates vary by points, this parameter similarly defines the service added to the age to obtain the points. This parameter may refer to a date from which to measure service or to the amount of service completed as of the valuation date. This service is then accumulated when ProVal calculates the attributed benefit. Typically, this parameter references a database Field that refers to either current service or a service start date. Select the desired field from among the numeric and date fields unhidden in the current Project. Alternatively, if you need fractional service attribution (e.g., hours-related service) or rounding (e.g., completed years), select from the library of Service Definitions. The button accesses the library to create and modify Service Definitions.

 

Notes regarding accrual rate proration attribution:

As mentioned at the beginning of this article, the methodology of accrual rate proration attribution, when custom attribution rates are used, is described briefly below. For more detail, see our Technical Reference article entitled PUC and UC attribution.

Projected Unit Credit (PUC)

The benefit formula component (BFT) with accumulated accrual rates (RATES) will be attributed as follows, in the absence of custom attribution rates, to derive PUC liabilities:

pucBFT[r] = BFT[r] * (RATES[x] / RATES[r])

where x is the age at the valuation date and r is the age at decrement.

If you click the Attribution button, you can substitute separate attribution rates for PUC. The revised equation becomes:

pucBFT[r] = BFT[r] * (pucRATES[x] / pucRATES[r])

For a cash balance component, BFT[r], of course, includes interest credits to decrement age r. pucRATES[x] and pucRATES[r] may include interest credits to decrement age r at your option. To reflect interest credits in the proration fraction’s numerator and denominator, check the Apply cash balance crediting rate (to attribution rate) box.

Unit Credit (UC)

Separate attribution rates generally are not needed to derive unit credit liabilities. If custom attribution rates are not defined, accrual rate proration will attribute BFT as indicated in the Technical Reference article, yielding:

ucBFT[r] = BFT[x]

For a cash balance component, BFT[x] will include interest to decrement age r.

However, if you

1. have separate attribution rates for PUC and

2. want UC liabilities to equal PUC liabilities without projected salary (i.e., without projected BASIS),

click the Attribution button and specify separate attribution rates for UC (presumably equal to the attribution rates for PUC). The modified formula becomes, as indicated in the Technical Reference article:

ucBFT[r] = BFT[x] * (ucRATES[x] / ucRATES[r]) / (RATES[x] / RATES[r]).

To see how this works, consider a component with a final average accrual format. We know that BFT[age] = RATES[age] * BASIS[age], so this equation reduces to:

ucBFT[r] = (RATES[x] * BASIS[x]) * (ucRATES[x] / ucRATES[r]) / (RATES[x] / RATES[r])

 = (RATES[r] * BASIS[x]) * (ucRATES[x] / ucRATES[r])

 = (RATES[r] * BASIS[x]) * (pucRATES[x] / pucRATES[r]).

The PUC formula reduces to:

pucBFT[r] = BFT[r] * (pucRATES[x] / pucRATES[r])

 = (RATES[r] * BASIS[r]) * (pucRATES[x] / pucRATES[r])

Comparing the two formulas, we see that UC uses BASIS[x] and PUC uses BASIS[r]. That is, they are the same except for the BASIS projection, which is what we wanted.