New Tool Allows Anyone to Calculate Basic Actuarial Liabilities

With every new version of our favorite technology – such as smartphones, televisions, and even cars – we can accomplish or experience something better than we were previously able. The computer has certainly helped the actuary by increasing the speed and accuracy in which calculations can be made.

But like many trade-specific tools, the available actuarial software was largely available only to actuaries and required more than just a general understanding of actuarial principles to properly utilize.

This has changed with a new website created by the Society of Actuaries, the main governing body for the actuarial profession. This site puts a simple yet powerful tool in the hands of non-actuaries. It can be found here: afc.soa.org/#Calculator.   (Note: if this direct link doesn’t work, use this link instead, www.soa.org/resources/tables-calcs-tools/act-practice-tools-landing/ and click the “learn more” link under the “Annuity Factor Calculator”.)  It allows the user to calculate an actuarial annuity factor. Having the annuity factor doesn’t do the non-actuary any good, unless the person knows how to apply that value. We hope to give you a basic understanding of how an actuary uses an annuity factor, enabling you to understand and reasonably approximate the numbers in a LOSAP valuation report.

The annuity value is used to determine the Actuarial Present Value (APV) of a future obligation. In our context, the obligation is a lifetime monthly service award benefit payment. The APV is then the current lump-sum cash value, in “today’s dollars” of that lifetime monthly service award.

If we remove the word “Actuarial” from APV, we are typically removing any decrements, like mortality (life expectancy), disability, and withdrawal (employment termination) from the calculation. Excel can easily calculate the present value of fixed-number of payments with a constant interest rate, whether a lump-sum payable in the future or a series of annual or monthly payments payable over a designated period. 

A simple example of present value would be to consider that you owe someone $1,000 one year from now. If we assume that we will earn 5% in our savings account during the year, the present value is about $952. If we have $952 in the bank, and earn 5% on that $952 during the year, we will have $1,000 at the end of a year. If we will only earn 1% on our savings account, then the present value increases to $990! That is because we will not earn as much interest, so we need to invest more in our savings account today to have the $1,000 one year from now. The complications ratchet up when we consider a payment that might be $1,000 per month for an individual’s lifetime starting a year from now, and not just a one-time payment. 

While there are other assumptions the actuary could make in the calculation, for most LOSAPs the two main assumptions are an interest rate and a mortality table. Some factors the actuary must consider:

• How long can we expect to pay a lifetime benefit? 
• How do we account for interest and the time value of money? 
• What death benefits, or payments that continue to a beneficiary, are provided?

Ultimately, the APV of a monthly service award is: Monthly Benefit x 12 x Annuity Factor = APV

​The Annuity Factor is where all of those assumptions are baked into one number.

​When you first access the tool online, you should see something like this:

There are several different options/assumptions that can be selected. For the more curious reading this article, in the header of the website there is a “Technical Terms” link. By clicking that link you will get more detailed information about some of these options.

In a typical actuarial valuation of a LOSAP, the actuary does not assume mortality before the entitlement age (the tool calls it Mortality Before BCA). The use of a projection method on the mortality varies. For our purposes, we made the following changes:

• Discount Rate (i.e., interest rate) to 5.00%
• Annuity Type to Certain and Life
• Certain Period to 10
• Primary Annuitant Gender to Male
• Mortality Before BCA to None
• Mortality After BCA to RP2014 Healthy Annuitant
• Projection Method to None

After making these changes, the resulting annuity factor is 5.7859. Note we did not change the “Primary Annuitant Age” from 45, which means this factor is only for a 45-year-old and based on the assumptions we noted. That being said, if this 45-year-old had accrued a $200 monthly benefit, the APV would be $13,886. In plain English, this essentially means we need $13,886 in the bank today in order to pay a 45-year-old male $200 per month for the rest of his lifetime beginning at age 62. 

Where you can experiment a bit with this tool is to make changes to the assumptions, such as:

• Lowering only the interest rate to 4.00% yields a factor of 7.4900, resulting in an APV of $17,976, which is roughly a 30% increase.
• Lowering only the Benefit Commencement Age to 60 yields a factor of 6.6002, resulting in an APV of $15,840, which is roughly a 14% increase.
• Using an older mortality table, such as the RP2000 Healthy Annuitant table, yields a factor of 5.4580, resulting in an APV of $13,099, or a roughly 6% decrease.

There are a couple limitations to this tool that you must be aware of, especially when trying to compare results to your actuarial report or participant statement:

• The tool only calculates the annuity factors for whole ages. When we calculate our annuity factors, we use the age in years and months. To approximate the APV of a pre-entitlement age participant from our reports, a user would have to interpolate between the participant’s current and age plus one.
• The tool only allows whole-number certain periods; therefore, calculating the APV for someone over the entitlement age will likely require more interpolations between whole-ages and whole-certain periods. However, the variance would be very small, thereby allowing you to validate the reasonableness of the values stated in the actuarial report. 

​This free tool from the Society of Actuaries is a valuable resource to help municipalities, participants, and auditors understand a bit of the actuarial mathematics and to verify that the calculations in the actuarial report. You will not likely get a 100% match on the APV you calculate compared the actuarial report, but you should end up with a reasonable approximation. We hope you will give it a try!
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