; FAQ 1095: Mortality Tables - Checking a 2-D Generational PVF

FAQ 1095: Mortality Tables - Checking a 2-D Generational PVF

Problem:

We are using 2-D Generational projection scales with our FASB/ASC-715 valuation, and we would like to verify a 2-D projected present value factor (PVF) used for a participant. How do we check this in ASC?


Solution:

In using ASC > Access > Table Maintenance, we have the resources available for you to either do a quick check or a full review of a 2-D Generational PVF.

Background
Before we describe the two approaches, we recommend reviewing the DB Tables - Generational Mortality Projection Documentation.pdf from our Client Support Center Website > UPDATES & DOWNLOADS > ASC SYSTEM TABLES. This document provides detailed information about generational mortality projection scales.

Generational mortality tables depend on both the person's age and the year that age is attained (hence the 2-dimensional description). With generational mortality, the mortality rate for a 62 year old in 2021 will be different from a 62 year old in 2026, that is, each participant has an individual mortality table specific to that participant's age in the valuation year and subsequent years.

To generate the individual mortality table for each participant, you begin with a static (base) table then apply the 2-dimensional mortality improvement factors specific to that individual.

The Society of Actuaries (SOA) publishes the 2-D mortality improvement scales, and the 2-D projection tables are stored in Table Maintenance / Defined Benefit / Generational Mortality.

In the 2-dimensional mortality improvement table, the rows represent the age and the columns represent the year. The intersection of each row and column is the improvement factor for that specific age and year. Each decrement of the base table is projected with these factors.

The difference between the year benefit payments commence and the base year of the mortality table is the number of projection factors used for improving a base table mortality decrement. If a benefit payment is paid in a base year, no projection is applied. Each year after the base year will have one more projection factor.

The factors from the projection scale will be from the row of the participant's age as of the year of benefit payment. The factors from the year after the base year to the year of benefit payment are the factors used in projecting that decrement.

EXAMPLE
Base Table - PR12AAM (Pri-2012 Base table Annuitant Male Table Amounts weighted on Total dataset)
2-D Projection Scale - MP2020 M
Valuation Year - 2021
Participant Retirement Age - 65
Year Participant Attains Retirement Age - 2024

Base Table mortality Qx at age 65 - 0.010830
MP2020 M projection scale values from year 2013 to 2024 of age row 65: 0.0012, -0.0016, -0.0038, -0.0055, -0.0059, -0.0055, -0.0043, -0.0025, -0.0002, 0.0023, 0.0047, and 0.0069.
For each of the 12 projection scale values subtract the factor from 1. For the year 2013, take 1 - 0.0012 = 0.9988.
The projection factor to apply to the Base Table mortality Qx is the product of adjusted values from the previous step. That is, the product of 0.9988 and the other 11 factors for a projection factor of 1.014220
The projected Qx at age 65 = 0.010830 x 1.014220 = 0.010984
The resulting APR with an interest rate of 5% at age 65 is 147.271

Quick Check
Use the Access > Table Maintenance > Functions > Calc PV Factors menu. On the Calculate PV Factors screen, enter all the parameters (Base Table, Current and Retirement ages, 2-D Projection Type, Projection scale table, Val Year, interest, and annuity option) used in your FASB/ASC-715 valuation. To generate the specific PVF for the participant, enter their Current Age as of the valuation date. In the Mortality Projection Frame, the Val Year should correspond to the FASB/ASC-715 valuation date. Once all the relevant parameters have been entered press Calculate PVF.

Full Review
Use the Table Maintenance > Functions > Commutation Functions > Projection Factors report to review all the factors used to project a decrement. Once you have the Primary Mortality (Base Table), Primary Starting Age, and 2-D Mortality Projection parameters input, you can input up to three ages in the Projection Factors frame to generate a report that shows the base Qx decrement, factors from the projection scale, the projection factors, and the projected Qx.

The age input in the Prim Starting Age field is the age as of the Val Year. The First, Second, and Third input ages are the ages to illustrate the details used in the projection of these three decrement ages.

Once you have confirmed the projection on the base Qx values, you can proceed with using the commutation functions for generating the PVF. The Table Maintenance > Functions > Commutation Functions will print the standard commutation factors with the Qx decrements that have been improved by the 2-D projection scale. Performing the regular commutation arithmetic will produce the same PVF, as shown in the participant screen. The projected Qx decrements in the Projection Factors report are the same projected Qx decrements as shown in the commutation function report.

If you are unfamiliar with commutation functions, the SOA has published the Study Note 'Commutation Functions' to help individuals get accustomed to the commutation functions.

A simple example of a commutation function is to divide the N12x factor by the Dx factor of the same age. This produces an APR payable monthly. A second example is by dividing Dx over Dy, where the Dy is at a younger age. This will produce a discount factor that includes mortality. Multiplying the APR from the first example with the discount factor of the second example produces a PVF. That is, Dx / Dy x N12x / Dx produces the present value as of age y of the immediate monthly annuity payable at age x.

Please note, in general, 2-D projection scales are customized for each participant. Checking other participants will require you to input their age as of the valuation date to adjust the projection for that participant.