The Administration Factors tool generates annuity, lump sum and insurance present value factors, factors for converting from one payment form to another (conversion factors) and commutation functions. Factors are developed for the ages that you request and the payment forms that you specify. Payment forms are defined in a manner similar to that of defining pension mode payment forms for inactive plan members (under the Inactive Data topic of the Census Specifications) and defining a Payment Form Definition for active plan members, with some differences, discussed below in the Payment Forms section of this article. Present values, for annuity factors, and the ratio of present values, for conversion factors, are as of a “current age” that typically would be the member’s age on his or her termination date (and is presumed to be so in the rest of this article). This date is analogous to the valuation date for an inactive payment form or to the decrement date for ProVal’s active Payment Form Definition.

Name may be any descriptive phrase, including spaces, under which to save this entry in the Administration Factors library.

Select the calculations to perform by checking one or more of the boxes for:

• Annuity Factors: the factor value is the present value of the annuity or insurance at the member’s termination date;

• Conversion Factors: the factor value is the ratio of 1) the present value, at the termination date, of the annuity or insurance you are converting from to 2) the present value, again at the termination date, of the annuity or insurance you are converting to;

• Commutation Functions for annuities and insurance.

Select a topic to edit contains entries for each category of information (topic) found under the Administration Factors command. The available topics differ according to which of the three factor types you have selected. Click the name of a topic to access its parameters, which are described in separate sections (below) of this article. The topics are:

Current Ages

Interest Rates

Mortality and Timing Parameters

Payment Forms – not applicable if the Commutation Functions box has been checked

Commutation Functions – if the Commutation Functions box has been checked

In the following discussion of these topics, a reference to factors also applies to commutation functions, unless noted otherwise.

After entering all relevant parameter values, click the Run button to execute the selected calculations. ProVal will check for completion of all specified parameters and then, if no errors are found, calculate the factors and or functions. When the calculation is complete, ProVal displays, in the output, the parameter settings and the results for the factors or functions requested.

 

Current Ages

Under the Current Ages topic, you set the ages for which to generate annuity (present value) factors and/or conversion factors. Either you indicate the Age ranges, or combination of age ranges for the plan member and the member’s spouse or beneficiary if any factors involve joint life annuities, or you provide Specific ages / age combinations for the plan member, and for the spouse or beneficiary if joint life annuities are involved.

If you select Age ranges, ProVal will generate factors for a range of ages entered for the Primary Annuitant (the plan member), and reflecting, for each Primary Annuitant age, a range of ages entered for the Contingent Annuitant (the member’s spouse or beneficiary, presumed to be of opposite sex) if joint life factors are to be generated. For each annuitant, in the box to the right of From, enter the first age for which you wish to generate a factor and, in the box to the right of To, enter the last age for which you wish to generate a factor. You may enter only whole numbers (for example, 55, not 55.5).

Alternatively, if factors are to be generated for joint life annuities, you may define the Contingent Annuitant age range by selecting the Age differences up to option and entering, in the text field, the largest age difference between the primary and contingent annuitants (member and spouse / beneficiary), n, to consider. ProVal will generate factors for 2n+1 sets of age differences (-n…, -1, 0, 1…, n). Note that you specify the fixed range as a positive number; ProVal will generate factors for a contingent annuitant up to n years older and up to n years younger than the primary annuitant.

Check the Include monthly ages box to indicate that you want ProVal to calculate factors for (besides integral ages) all "fractional ages" of the primary and contingent annuitants, that is, ages in years and months in-between the integral ages. For example, if the Primary Annuitant (member) age range is 55 to 70 and the Contingent Annuitant (spouse, or beneficiary of opposite sex) age range is 50 to 75, ProVal will generate factors at age 55, at age 55 and 1 month, at age 55 and 2 months, etc., for the primary annuitant, up to and including age 70. For each of these primary annuitant ages, ProVal will also generate factors at contingent annuitant ages 50, 50 and 1 month, etc., up to and including age 75.  The factors generated at months in-between the integral ages are linearly interpolated between the factors at integer ages.  For a joint and survivor annuity, interpolation is performed first on the member age and then on the spouse age. 

If you select Specific ages / age combinations, ProVal will generate factors for (only) the ages you enter in the grid, in years and months, for the Primary Annuitant, and reflecting the ages you enter (also in years and months) for the Contingent Annuitant if joint life factors are to be generated. For example, to generate life annuity factors for a Primary Annuitant who is age 55.5, enter 55 in the years column and 6 in the months column. To also generate joint life annuity factors for a married primary annuitant of the same age with a spouse age 52.25, enter in the Contingent Annuitant columns 52 for the years and 3 for the months.  The factors generated at months in-between the integral ages are linearly interpolated between the factors at integer ages.  For a joint and survivor annuity, interpolation is performed first on the member age and then on the spouse age. 

 

Interest Rates

The Interest Rates topic provides the following options for defining the interest assumption to be used in your calculations:

• Static Rate, to use the same (i.e., a constant, or single) interest rate for all years after the member’s termination date up to the date of each benefit payment, regardless of the benefit payment dates. To choose an interest rate on the “GATT” basis, which is the interest basis typically used for U.S. minimum lump sum present values under the law in effect prior to the Pension Protection Act of 2006 (PPA), click the GATT rates button, which accesses the “Look up 30-year Treasury rates” dialog box. Looking up, and pasting into the text field, a GATT interest rate for calculation of minimum lump sum present values is done in similar fashion to looking up segment rates for minimum lump sum present values under PPA (see Looking up PPA interest rates for more information). Alternatively, you may type the desired rate in the text field. Note, however, that ProVal will not prevent you from computing lump sum present values using an interest rate not matching the acceptable GATT rate for the relevant calendar month.

• Variable Rate, to use rates that depend on duration from the current age (that is, from the member’s termination date, or time 0) to the year associated with the interest rate. If, for the Input is parameter, you select the forward rates option, then the rate specified at a particular duration is used for all discounting at that duration for all payments made at or after that duration from the current age. For example, if 0.06 is entered at duration 2-3, indicating the time interval from 2 to 3 years after current age, then all benefit payments made at time 2 or later are discounted at 6% for the year running from time 2 to time 3. If you select the spot rates option, then the rate specified at a particular duration is used to discount benefit payments made at that duration for the entire period back to the current age. For example, if 0.06 is entered at duration 2-3, indicating the time interval from 2 to 3 years after the termination date, then all benefit payments made at or after time 2 but before time 3 are discounted at 6% for all years back to time 0. For further discussion of variable interest rates, including how to enter values in the three-column grid, see the sections on variable interest rates in the Help article for the Lump Sum & Optional Payment Forms topic of Valuation Assumptions. If the spot rates option is selected, the PPA rates button is accessible; click it to enter the “Look up PPA corporate bond yield curve” dialog box, in which you can look up historical U.S. PPA spot rate curves (discussed in the next paragraph below) and paste them into the grid.

• Segment-style rates, to enter U.S. PPA minimum lump sum present value segment rates or, more generally, to use rates with the duration structure of PPA segment interest rates, that is, a 1st segment rate for benefit payments made at durations less than 5 years after the member’s termination date, a 2nd segment rate for benefit payments made at durations at least 5 years after the termination date but less than 20 years after, and a 3rd segment rate for benefit payments made at durations at least 20 years after the termination date. For further discussion of segment-style rates, see the section on PPA interest rates in the Help article for the Interest Rates topic of Valuation Assumptions. See also the discussion of variable by duration interest rates in the Help article for the Lump Sum & Optional Payment Forms topic of Valuation Assumptions, inasmuch as coding interest rates to be used for annuity present values is similar to defining valuation lump sum interest rates (coding the latter to match the U.S. PPA minimum lump sum segment rates is accomplished by a three-row grid, one for each segment rate). If the Segment-style rates option is selected, the PPA rates button is accessible; click it to enter the “Look up Minimum lump sum segment rates” dialog box, in which you can look up historical PPA segment rates for calculating statutory minimum present values for lump sum benefit payments (see Looking up PPA interest rates for more information). Alternatively, you may type the desired rates in the text fields. Note, however, that ProVal will not prevent you from computing lump sum present values using interest rates not matching the acceptable segment rates for the relevant calendar month.

• PBGC-style rates, to enter U.S. lump sum present value interest rates on the PBGC basis or, more generally, to use interest rates that vary by year according to whether the year is during the benefit payment period or is during a deferral period, and if within a deferral period according to how many years prior to benefit commencement the year occurs. In the Immediate rate text field, enter the interest rate to be used once payments commence. Enter in the Prior 7 years (K1) text field the (deferred) interest rate to be used for the first 7 years prior to when payments commence. Enter in the Prior 8 years (K2) text field the (deferred) interest rate to be used for the next 8 years prior to when payments commence. Enter in the All Prior years (K3) text field the (deferred) interest rate to be used for the remaining years, that is, all years at least 15 years prior to when payments commence. To choose interest rates in accordance with the PBGC basis, click the PBGC rates button, to access the “Look up PBGC-style annuity rates” dialog box, which contains rates published through December 2007. Looking up, and pasting into the text field, PBGC interest rates for calculation of minimum lump sum present values is done in similar fashion to looking up segment rates for minimum lump sum present values under PPA (see Looking up PPA interest rates for more information). Alternatively, you may type the desired rates in the text fields. Note, however, that ProVal will not prevent you from computing lump sum present values using interest rates not matching the acceptable PBGC rates for the relevant calendar month.

Enter all interest rates as numbers between 0 and 0.40 (not as percentages).

 

Mortality and Timing Parameters

Under the Mortality and Timing Parameters topic, you define the mortality assumption to be used in your calculations, as well as the timing of annuity payments within each payment year. Thus the dialog box is divided into two sections, Mortality and Timing Parameters.

In the Mortality section, unless all payment forms defined under the Payment Forms topic are payable only for a certain period (that is, life contingencies do not apply), you must select the mortality rate reference table (from among those unhidden in the current Project) that you wish to use for the Primary Annuitant (the plan member), and if joint life factors are to be generated you must select a mortality table for the Contingent Annuitant (the member’s spouse or beneficiary, presumed to be of opposite sex). For either the primary or the contingent table selection, the button provides access to the Mortality Rate Table Library, in which you may create new tables or modify existing ones. If an “Age by Duration from Decrement” table is selected, duration is measured from the member age (entered under the Current Ages topic) at which the factor is being calculated. You may not use a service-based mortality table, because a service dimension does not apply to inactive plan members and the factors being developed are presumed to be for inactive members (computed “as of” the termination date).

The Valuation year text field is accessible only for dynamic, fully generational and age by year of birth mortality tables. Enter the calendar year, for example, 2013, you wish ProVal to assume is the year that corresponds to the attained ages specified under the Current Ages topic.

For fully generational mortality tables, choose whether to Generate factors for an individual age x in valuation year, and if selected, specify the desired age. If this option is selected, all factors generated will be for the same individual. If this option is not selected, the factor for each age entered under the Current Ages topic will be for different individuals attaining each age in the applicable valuation year. For example, if the valuation year is 2015 and factors are generated for an individual age 60 in valuation year, then an age 60 factor will be for someone who is attained age 60 in 2015 and an age 61 factor will be for someone whose attained age is 61 in 2016. If this option is unchecked, then an age 60 factor will still be for someone who turns 60 in 2015, but an age 61 factor will be for someone who turns 61 in 2015. 

For an age by year of birth mortality table, choose whether to Generate factors for year of birth. Similar to the example above for projected mortality improvements, if this option is selected, all factors generated will be for the same individual.  If the option is not selected, the factor for each attained age specified under the Current Ages topic will be for an individual attaining that age in the valuation year. For example, if the valuation year is 2015, an age 65 factor would be for someone born in 1950, an age 64 factor would be for someone born in 1951, and so forth.

See Decrement Tables, in particular, the Mortality Projection and Dynamic Mortality sections, for more information about these tables.

Check the Use zero mortality in the deferral period (if any) box to assume zero mortality rates, for all payment forms, during the payment form’s entire deferral period (if any) for both the primary and contingent annuitants.

In the Timing Parameters section, your selection for the Payment Frequency parameter indicates, for all payment forms, how often payments are made within each payment year. ProVal assumes that benefit payments will be made in equal installments throughout the year and will adjust the present value of each payment form to account for multiple payments during the year. The available frequencies are “Annual”, “Semi-annual”, “Quarterly”, “Monthly” and “Continuous”. For details about the adjustment methodology, see the Technical Reference article entitled “Present Values: Benefits payable (m)thly”.

Your selection for the Annuity Payment Timing parameter indicates, for all annuity payment forms and all payment years, whether each payment is made at the beginning of each period or at the end of each period – for example, for 12 (monthly) payments each year, whether payments are made at the beginning or end of each month. Select “Beginning of Period” for an annuity-due or “End of Period” for an annuity-immediate. ProVal will adjust the present value of each annuity payment form to account for the indicated timing. The length of each period (a year, half year, quarter, month, or a fraction of an instant for the continuous frequency) is determined by the setting of the Payment Frequency parameter. Note: the Annuity Payment Timing parameter does not affect a life insurance benefit, which is always assumed to be payable at the end of the period. Again, for details about the adjustment methodology, see the Technical Reference article entitled “Present Values: Benefits payable (m)thly”.

 

Payment Forms

Under the Payment Forms topic, you define the annuity, lump sum and insurance payment forms whose present values you wish to calculate and you indicate, for conversion factors, which payment form to convert from. There are also parameters to blend male and female factor values and/or to blend life with joint life factor values.

Select a payment form to modify contains entries for each payment form you have already defined, if any. To add a new payment form, click the Add button and complete the parameters in the Payment Form Definition dialog box. To change the order of payment forms in the list, click the Reorder button.

For details about completing the parameters to define an Administration Factors payment form, see the discussions of payment forms for inactive members and Payment Form Definitions (for active members). However, there are some differences – in available parameters, their options and their treatment – between payment forms defined within this tool and either active Payment Form Definitions or payment forms defined for Inactive Benefits:

• You cannot select a payment form Type that is a modified cash refund annuity or a post-decrement death benefit.

• There are some parameters available for defining active or inactive plan member payment forms that (because of the nature of the Administration Factors tool) are not supported. In particular, because member data does not come from a database, but instead from specified current ages, options are not available to define joint life continuance fractions and deferral, temporary and certain periods by reference to a database field. Nor are options available to define the deferral, temporary and certain periods by reference to either a specific date (because the “as of” date for present values is determined by current ages that you input, rather than specific termination dates) or to a Benefit Component Table (which applies to look ups at future decrement dates, whereas, under this tool, the decrement from active status is assumed to have already occurred and thus present values are determined at current age on the termination date).

• For joint life payment forms, the Beneficiary determined parameter is accessible only for deferred annuities, that is, if the Benefit commences parameter is not set to the immediately option. This parameter indicates whether marital status, and thus the existence of a beneficiary (assumed to be of opposite sex from the plan member), will be determined at current age (for which input values have been entered under the Current Ages topic), and beneficiary mortality applied starting at that time, or at commencement (that is, at the age when benefit payment starts, according to the value entered for the Benefit commences parameter), and beneficiary mortality not applied until the end of the deferral period (which is, of course, the start of the payment period). Thus, if at commencement is selected, marital status, and the existence of a beneficiary, is determined at the payment start date; only primary annuitant mortality will apply during the deferral period and if the member dies during the deferral period, there will be no benefit payable to a beneficiary.

• Whereas COLA parameters (sometimes complex) for active Payment Form Definitions or payment forms defined for Inactive Benefits are associated with the payment form, not included within its parameters, the tool supports only COLA assumptions that can be specified within the payment form. The COLA rate during payment period is used to index benefits after payment has commenced. Select the Constant option to specify a single COLA rate to apply to all years after payments start. If there is no payment period COLA, enter zero as the COLA rate.  Enter COLA rates as numbers (not percentages), for example, 0.03 for a 3% COLA. Select the Variable option to access COLA rate tables that have been entered under the Reference Tables command of the Input menu. Select from the list of all COLA rate reference tables in the current Project or click the  button to create a new table. COLA rate tables for payment periods may vary by age, sex and duration (time elapsed) since the commencement of payments.  Also, you may specify, for deferred payment forms, a (perhaps different) COLA rate during the deferral period (to increase benefit payment amounts, again by the same rate of increase each year, between the current age and the age annuity payments or insurance coverage commences). Select the Constant option to specify a single COLA rate to apply all years before payments start. Enter the COLA rate as a number (not as a percentage). Select the Variable option to access COLA rate tables that have been entered under the Reference Tables command of the Input menu. Select from the list of all COLA rate reference tables in the current Project or click the  button to create a new table. COLA rate tables for deferral periods may vary by age and sex.     

If the Conversion Factors box has been checked, the Normal Form of Payment parameter is accessible, for you to select the payment form you wish to convert from. Once you have defined at least one payment form, you may select from the drop down list of payment forms unhidden in the current Project. As previously alluded to in this article, only payment forms that are an annuity or insurance Type will appear in the list. Neither will a joint life payment form Type appear in the list, because ProVal does not support conversion from a joint life annuity to another payment form, although you can generate factors to convert to a joint life payment form. ProVal will produce factors to convert from the selected normal form to each other payment form listed in this (Payment Forms) dialog box.

The Blending weights parameters allow you to blend male factor values with female factor values and/or to blend life factor values with joint life factor values. If conversion factors are to be produced (in addition to annuity factors), ProVal first blends the annuity factors for the normal form of payment and the payment form you are converting to, and then produces the (blended) conversion factor by taking the ratio of the blended annuity factors.

Check the Blend male and female annuity factors box to have ProVal weight the male and female annuity factors and blend them into a single factor. (Note that this parameter has no effect on results unless at least one of the mortality tables, or an underlying mortality improvement scale, selected under the Mortality and Timing Parameters topic is sex-distinct.) Enter the desired weight (a number between 0 and 1, inclusive) for a Male annuitant; ProVal will then enter the complement of this number for a Female annuitant. For example, if your payment form is a life annuity and you enter 0.5, for ProVal to weight male and female factor values equally, ProVal will compute separate male and female (primary) annuitant life annuity present values and then compute a blended value that is halfway between the male and female annuity present values. If your payment form is a joint life annuity and you enter 0.5, ProVal will compute separate factor values for 1) a male primary annuitant with a female contingent annuitant, and 2) a female primary annuitant with a male contingent annuitant, and then 3) compute a blended value that is halfway between the male and female primary annuitant joint life annuity values. Note that this parameter cannot be used to blend male and female mortality rates and then use the blended mortality rates to compute a single, blended, annuity present value factor; to achieve this result, you should first produce a unisex mortality table, select it under the Mortality and Timing Parameters topic and, consequently, not check the Blend male and female annuity factors box. (You can create a unisex mortality table from a sex-distinct table by use of the Table Type command behind the Options button available when you edit a Mortality Rate Table library entry; see Table Interface for details about constructing mortality rate tables.)

The Fraction of population receiving J&S (blends J&S factor with life annuity factor; applies only to the J&S forms) box applies only to joint life factors. Check it to have ProVal return joint life factor values computed by weighting each joint life annuity value towards the single life annuity value for the same primary annuitant current age. Presumably, you might not wish to use the “pure” joint life value if you are developing factors to compare to valuation results for a population that is not all married or that does not all elect a joint and survivor payment form. Enter the desired fraction (a number between 0 and 1, inclusive) that you wish ProVal to use to develop factors for a primary annuitant (plan member) who is Male; likewise, enter the desired fraction for ProVal to use for a Female primary annuitant / plan member. (Note: If a fraction of 1 is entered, that would denote a plan member population all of whom are married and/or electing the joint and survivor payment form, with thus no weighting towards the single life annuity value. However, in this situation, you need not check the Fraction of population receiving J&S box for ProVal to produce a “pure” joint life annuity value.) For example, if you enter 0.8 for a Male primary annuitant and 0.6 for a Female primary annuitant, for ProVal to weight joint life factor values by 0.8 for male plan members and by 0.6 for female members (and thus weight life annuity values by 0.2 for male members and by 0.4 for female members), ProVal will compute separate life annuity and joint and survivor annuity present values and then compute the weighted value. For male members, that value will be two tenths of the way from the male primary annuitant joint life value to the male annuitant life annuity value; for female members, that value will be four tenths of the way from the female primary annuitant joint life value to the female annuitant life annuity value.

If you check both the Blend male and female annuity factors box and the Fraction of population receiving J&S box, to blend male and female annuity factors and also to compute each joint life factor value as partly weighted towards a life annuity, ProVal will first weight each joint and survivor annuity factor value towards the life annuity factor value and then blend the male and female joint life factor values into a single (unisex) value.

 

Commutation Functions

Under the Commutation Functions topic, you may define commutation functions for ProVal to generate. You can select functions for (one or more of) the Primary Annuitant (the member, aged x), the Contingent Annuitant (the spouse or beneficiary, aged y) and, during the joint lifetime of the member and spouse / beneficiary, Joint Life (ages are x and y, respectively, denoted in the Joint Life column as xy).

The following commutation functions are available:

D, where D is the common denominator of commutation functions;

N, where N is an annuity factor numerator under which one payment is made per payment year;

N(m), where N(m) is the annuity factor numerator and m is the Payment Frequency entered under the Mortality and Timing Parameters topic, for example, if m=12, then N(m) represents a monthly annuity factor numerator;

S, where S is an increasing annuity numerator;

C, where C is an insurance utility numerator;

M, where M is the sum of Cx's;

R, where R is the increasing insurance numerator, the sum of Mx's;

e, where e is the curtate life expectancy.