The following discussion pertains to Benefit Component Tables and Reference Tables.

• Benefit Component Tables are used primarily in Benefit Formula Components and Accrual Basis Components. They can also be used in Benefit Definitions to adjust a 415(b) Maximum Benefit Limit (in the U.S. qualified and U.S. public pension modes) or an ITA Maximum Pension Limit (in the Canadian registered pension mode), in OPEB mode Plan Definitions to define Full Eligibility, in pension mode active member Payment Form Definitions to reduce post-decrement death benefits and, under the pension mode Inactive Benefits topic of the Census Specifications, to reduce post-decrement death benefits.

• Reference Tables are used primarily in Valuation Assumptions and Projection Assumptions. ProVal has Reference Tables for decrements (containing rates for mortality, disability, retirement or termination), salary merit scales, mortality improvement scales, election probabilities, lapse probabilities, COLA rates, increase rates, fraction married, husband/wife age difference, yield curves used in forecasting, and some regulatory data items. This article does not pertain to the table interface for increase rates, which is covered instead under the Increase Rates topic of the Reference Tables command, for custom regulatory tables or for forecast yield curves.

Benefit Component Tables and Reference Tables are entered into spreadsheets that contain values, not formulas. Generally, these values may depend on age, service (duration for COLA rate reference tables), sex or any combination of the three. For example, in a select and ultimate table, the values depend on both age and service (or duration for COLA rate tables).

Some reference tables have other dimensions for “looking up” values in these tables (hereinafter referred to as table “lookups”). Mortality rate table values may depend on pre/post-commencement status, year of birth or duration from decrement, in combination with age and/or sex. Mortality improvement scale table values may depend on year of improvement, in combination with age and/or sex. Disability rate table values may depend on year of birth, again, in combination with age and/or sex.

ProVal computes table lookup values for these various dimensions as follows:

• Age is based on the member’s age as defined by the date of birth (or attained age) parameter of the Active Data, Inactive Data - pension modes or Inactive Data - OPEB mode topic of the Census Specifications. Note that ProVal uses this input value to compute the member’s rounded attained age on the valuation date. ProVal then projects this age forward (and backward) by 1 every year to the relevant decrement or payment date. Thus the lookup age is, in insurance parlance, age nearest birthday and is a whole (not fractional) number.  (Note that this age is determined as of a valuation date anniversary, regardless of whether decrement timing is beginning or middle of year.)

In OPEB mode, if an inactive Benefit Definition’s payment form is payable to the spouse, then ProVal looks up table values based on the spouse’s age as defined by the date of birth (or attained age) parameter of the Covered Spouses section of the Inactive Data - OPEB mode topic of the Census Specifications. ProVal uses this input value to compute the spouse’s rounded attained age on the valuation date and projects and “looks up” as previously discussed for member age.

• For active members, service is based on one of two values, depending on the ProVal mode of operation: in all modes other than the German pension mode, the member’s service is defined based on the date of hire (or hire age) parameter of the Active Data topic of the Census Specifications; in the German pension mode, the member’s service is defined based on the Teilwert First Funding Age. ProVal uses this input value of service to compute the difference between rounded attained age and rounded hire age on the valuation date (or, in German mode, the difference between rounded attained age and First Funding Age). ProVal then projects this service value forward (and backward) by 1 every year to the relevant decrement or payment date. Thus the lookup service is a whole (not fractional) number.  (Note that this service is determined as of a valuation date anniversary, regardless of whether decrement timing is beginning or middle of year.)

Alternatively, you may define service for table lookups by reference to a database field, containing a service start date or numeric service as of the valuation date, or by reference to a Service Definition. If a Service Definition is specified, ProVal may project service, from the valuation date, using a value other than 1 and special rounding rules may apply. However (see the discussion in the following paragraph), regardless of whether you have (or have not) referenced a service field or Service Definition, the value used for the table lookup will be a whole (not fractional) number.

Parameters for selection of alternative service are not specified in the Benefit Component Table or Reference Table itself but, rather, are specified where the table is used (provided that an alternative definition of service is an available option). Alternative service may be specified for Benefit Component Tables used in Benefit Formula Components, Accrual Basis Components or Full Eligibility definitions (OPEB mode). Alternative service may be specified for decrement rate reference tables used under the Decrements topics of the Valuation Assumptions and Projection Assumptions. Generally, you have a choice of “<rounded attained age – rounded hire age>”, a service field or a Service Definition.

If a service field or a Service Definition is selected, ProVal truncates service. Therefore, truncated service measured from the date specified for the date of hire (or hire age) parameter of the Active Data topic of the Census Specifications may differ, by one year more or less, from the value resulting from selection of the “<rounded attained age – rounded hire age>” option. For example, consider an active member with a birth date of 3/5/1967 and a hire date of 4/15/1997. Given a valuation date of 1/1/2000, ProVal computes an exact attained age of 32.8251 and a rounded attained age of 33. ProVal also computes an exact hire age of 30.1120 and a rounded hire age of 30. Exact service at 1/1/2000 is 2.7131 (32.8251 – 30.1120). The effect of using service defined by “<rounded attained age – rounded hire age>” versus a service field is demonstrated as follows:

Date	<Rounded Attained Age – Rounded Hire Age>	Exact service from hire	Truncated service from hire
1/1/1997	0 (30-30)	-0.2869	0 (as not <0)
1/1/1998	1 (31-30)	0.7131	0
1/1/1999	2 (32-30)	1.7131	1
1/1/2000	3 (33-30)	2.7131	2
1/1/2001	4 (34-30)	3.7131	3
Etc.

• For mortality and disability rate tables that vary by year of birth, the year is taken directly from the date of birth (or attained age) parameter of the Active Data, Inactive Data - pension modes or Inactive Data - OPEB Mode topic of the Census Specifications. If a numeric age is provided, then a date of birth is calculated according to the specified valuation date.

• For mortality improvement scale tables that vary by year of improvement, the improvement rate or factor from year 2011 to 2012, for example, should be entered for year 2012, not 2011. See the Technical Reference article entitled “Mortality improvement (generational mortality)” for further information.

• For COLA rate reference tables that vary by duration (permissible for payment period COLAs only), duration is based on the date benefit payments commence, as specified by the active member Benefit Definition’s payment form parameters or the inactive member Inactive Benefit’s payment form parameters (included under the Inactive Data topic of the Census Specifications). Therefore, if your COLA varies by duration, be sure to specify, for currently inactive members, a commencement date prior to the valuation date for benefits that are already in pay status.

• In OPEB mode, if the payment form of the Benefit Definition is “to the spouse” (rather than “to the member”), then the table lookup for a sex-distinct table is performed using the spouse’s sex, not the member’s sex.

• For replacement ratio retirement tables, replacement ratio is calculated as:

 

Where: 

The accrued benefit is the sum of all benefits that are payable immediately upon retirement. If specifying rates by benefit, the accrued benefit is the sum of all benefits for which the table or the <total retirement decrement> is selected.

Salary is the salary for the year prior to the year of retirement. This is based on the valuation salary parameter of the Active Data topic of the Census Specifications. Alternatively, you may specify a salary definition under the the Decrements topics of the Valuation Assumptions and Projection Assumptions. 

Member contributions are the contributions for the year prior to the year of retirement. These are the sum of any employee contributions specified in the Plan Definition. These will be determined as of the beginning of the year, regardless of any timing parameters.

You must specify an age to assume 100% retirement at age. 100% retirement will be assumed at this age, regardless of replacement ratio. 

Once age and/or service/duration/year/replacement ratio at the relevant decrement or payment date has been computed, as integral values (whether rounded or truncated), ProVal returns table values as follows:

• In an age-based table, a value of zero will be returned for ages younger than the first age found in the table (preset at 15, the youngest age ProVal can handle, for a new table). Table lookups for ages older than the last age (preset at 120 for a new table) will return the value for the last age.

• In a service-based or duration-based table, the first row represents zero years of service/duration. Table lookups for service/duration greater than the highest number of years found in the table will return the value for that highest number.

Each row represents a one-year range of actual service/duration. Consider our previous example of a 1/1/2000 valuation for which the Census Specifications refer to dates of birth and hire. The active member’s birth date is 3/5/1967 and hire date is 4/15/1997, so ProVal computes an attained age on the valuation date of 33 and a hire age of 30. If our definition of service is “<rounded attained age – rounded hire age>”, then, attained age and completed service at each decrement date are calculated as follows:

Date	Age	Service
1/1/1997	30	0
1/1/1998	31	1
1/1/1999	32	2
1/1/2000	33	3
1/1/2001	34	4
etc.	etc.	etc.

If this member’s actual hire date had been another day within a one year period “surrounding” 3/5/1997 (the anniversary of the birthday in the year of hire), ProVal would have computed the same value of integral service at a particular decrement date and therefore returned the same table value (for example, for a decrement occurring on 1/1/2000, the table value in the row labeled “3” years of service would be returned for hire dates falling about six months on either side of 3/5/1997). In effect, ProVal has assumed a hire date of 1/1/1997 for actual hire dates falling up to about 6 months before and 6 months after 3/5/1997. Consequently, if component values must reflect service from the exact date, not ProVal’s assumed date, accumulate service under an Accrual Definition instead of a table.

Because service is measured only over a period of active employment, the service dimension cannot be used for duration after a decrement occurs. Thus, a service-based table cannot be specified (under the Decrements topic of Valuation Assumptions or Projection Assumptions) for inactive mortality and active mortality after decrement has occurred.

• In an age by year of birth table, ages are in rows and years of birth are in columns. Years of birth earlier than the first year specified in the table will return values from the first year column in the table, and table lookups for years after the last year will return values from the last year column.

• In an age by service or age by duration table, ages are in rows and years of service/duration are in columns. The select period of a select and ultimate table is one year less than the number of columns. For example, if you create a new age by service table with a 3-year select period, the table will have four columns, representing “0”, “1”, “2” and “3 or more” years of service.

Mortality rate tables have parameters (that do not pertain to other decrement rate tables) for specifying projection of mortality improvement in the future. See Decrement Tables for more information about those parameters.

If a table has values that vary by age, service/duration or years, and sex, then only one of the two spreadsheets (male or female values) can be viewed at a time. The Rates for drop-down list therefore appears and allows you to toggle between the male and female values. (If you are creating a new table, initially the spreadsheet will contain only a “Unisex” column: click Options, point to Table Type and select “Sex Distinct” to generate “Male” and “Female” columns.)

The Options button provides access to commands that allow you to alter the table dimensions and their characteristics or to populate the table with values.

The Table Type command allows you to make two decisions about the structure of the table:

1. The first is to select an Age table, a Service table or Duration (from commencement) table, or an Age by Service table or Age by Duration (from commencement) table. Fraction married and age difference reference tables do not have a service dimension. There are two additional table type options for mortality rate reference tables: an Age by Year of Birth table and an Age by Pre/post-commencement table. The Age by Year of Birth table option is also available for disability rates. In OPEB mode, the Age by Pre/post-commencement table is applied pre-decrement and post-decrement, rather than pre-commencement and post-commencement. For mortality improvement scales, the only options available are the Age table and the Age by Year of Improvement table. See Decrement Tables for more information, particularly about the table options and parameters available only for mortality rate Reference Tables.

2. The second is to select a Unisex table (same rates for males and females) or a Sex-distinct table (separate sets of rates for males and females).

Checkmarks appear next to the current selections.

If you reduce the number of dimensions of the table (e.g., you change the table type from age by service to age), ProVal will ask an additional question:

If you eliminate the age dimension, ProVal needs to know which age row of the table to retain for all years of service/duration.

If you eliminate the service/duration dimension, ProVal needs to know which year of service/duration column to retain for all ages.

Similarly, if you eliminate the year of birth or year of improvement dimension, ProVal needs to know which year column to retain for all ages.

If you eliminate the differentiation between pre-commencement and post-commencement mortality, ProVal needs to know whether to retain the Pre-Commencement or the Post-Commencement column for all ages.

If you switch from sex-distinct to unisex values, ProVal needs to know how to weight, or blend (linearly), the sex-distinct values to determine the unisex ones. (Note: if you switch to unisex values in a Benefit Component Table containing annuity values, ProVal blends the annuity values, not the underlying mortality rates.)

The Row & Column Limits command allows you to set the youngest and oldest ages, the maximum service/duration of a service-based or duration-based table, the select period/maximum service of an age by service/duration table and the earliest and latest years of an age by year of birth or age by year of improvement table (mortality rate, disability rate and improvement scale tables only). Set these limits to encompass the spans of age, service/duration and/or years that your table requires. If you increase the size of your table, remember to scan for missing values before saving it. Blanks will not be permitted at execution and will abort the valuation run. If you reduce the size to remove a section of the table that contains values, ProVal will warn you that data in the rows and/or columns to be eliminated will be lost.

Because ProVal will reject tables with blanks, when entering values in the table, you must either fill the table with the appropriate defaults or trim the table to exclude all missing values. Right-clicking your mouse while in the spreadsheet will invoke a list of miscellaneous commands: edit, clear contents, duplicate cell down, copy, and paste.

The Interpolate command can be executed by either of two methods: linear or geometric interpolation of values. When you select one of the two methods, ProVal examines each column of your spreadsheet independently and fills in all embedded missing values. In other words, ProVal interpolates vertically, not horizontally. Thus, in an age by service table, values at intermediate ages, not intermediate years of service, are obtained (for each service column) by interpolation. Similarly, if there are imbedded missing values for both base rates and improvement rates in a dynamic mortality table, ProVal will interpolate, independently, both the Base Rates and Projection Scale columns.

The Adjust Values command, available in tables other than age difference tables, allows three ways to adjust table values. You can multiply all table values by a constant, add a constant to all values, or take reciprocal of each value (zero values are unchanged). If your table is sex-distinct, then the constants to use for adjustment may vary by sex.

To use the Perform Set Back command on a table with an age dimension, enter the number of years by which a value from the revised table should lag a value from the original table. For example, applying a setback (entered as a positive number) of 3 years will cause the resultant age 40 value to be the original age 37 value. Set backs may be positive or negative (ages “set forward”); if your table is sex-distinct, then the set backs may vary by sex. Because this command is not applicable to tables with a service/duration dimension, if you wish to convert an age-based table to one of these other types (e.g., to create an age by service or age by duration table), set ages back before you add a service/duration/year of birth dimension. Note that for mortality rate tables, age set backs are performed instead by use of the Link mortality base rates parameter; see Decrement Tables or more information.

If you are editing a Benefit Component Table, then you can use the Calculate Annuity Factors command to ask ProVal to compute values that depend upon mortality and interest rates and to fill the table with them automatically. See Calculating Annuity Values for details.

The Format Values command allows you to type a number for ProVal to use as a template for determining how to display (with respect to number of decimals, and presence of commas and dollar signs) table values. This entry will not affect the accuracy with which values are stored or calculated.

The Min/Max Allowed Values command, available in tables other than mortality improvement scales, sets the smallest and largest values that will be allowed in the table. You will be prevented from typing in new values outside the range, and you will not be allowed to adjust the table in a manner that would cause values to fall outside the range. Despite these constraints, ProVal will be permitted to produce values outside the range when taking reciprocals, calculating annuity factors or creating a unisex table from a sex-distinct table. If you set the minimum or maximum values such that existing table entries fall outside your range, ProVal will offer to adjust the table entries for you. (Note: the pre-set option for the minimum allowed value is zero; therefore, you must change this parameter to enter negative values.) Also note that this option is disallowed for mortality improvement scales, which have minimum and maximum values based on table type; see Mortality Improvement Scales for more information.

Finally, the Export and Import table commands allow you to export table values to a text file, or import values from a text file or file of another software application. To use this command, click Export or Import, indicate the location and name of the file to save values in or from which to take values, and save (to export) or open (to import) the file. Although table values may be imported from a text file or a csv file (with a fixed width or comma-delimited record format), the preferred method of entering values is to paste directly from the other software application or, for tables with only a few entries, to type in the values.