Finance: Approximating the Value of Pensions and Required Contributions

Greetings everyone!

Last week I was at a finance conference in Costa Mesa, CA for my work. It is a general accounting and tax conference that is held by my employer every year and topics covered range from sales tax, year-end reporting, using Microsoft Office to streamline processes, and the speech of why the university system I work for is important.

Unlike most attendees, I was invited last hour. 4:00 on the Friday before the conference. Despite having to reserve a room at the hotel across the street who at first mistakenly put my reservation for one month later, I had a great time.

One of the workshops I went to was about accounting for pensions (an area I usually don't work with at my job, it is good to step out of the comfort zone). There are two accounting regulations GASB 67 & 68 that were put into place in 2012. GASB is short for Governmental Standards Accounting Board. Both deal with how government entities valued pensions, determine pension liability, and make footnotes about them in the financial statements. I will include a link for reference for those who are interested:

GASB 67

GASB 68

Again, I don't claim to be an expert with either GASB 67 or 68, as my job usually doesn't involve working with pensions.

This workshop lead me to try to get an understanding of how pensions are valued. The examples I present on this blog entry is for one employee, not for an entire system of employers. Hopefully this will provide some sort of an introduction to anyone interested in pensions.

Types of Pensions

To my understanding, there are two general types of pensions:

Defined Benefit Plan: This plan details a promised payment (pension benefit) to an employee when the employee retires. The amount itself is determined in various ways, such as a percentage of a salary.

Defined Contributor Plan: The pension that is needed for the employee is funded by payments that contributed by the employer while the employee is working.

It would not surprise me if there are pension plans that have characteristics of both a defined benefit and defined contributor plans.

Valuing Pensions

In simple terms, pensions can be thought of a "deferred annuities". Pensions have two parts to them:

* Before retirement, where the employee works. Pensions can be funded by a one-time deposit or by monthly contributions. My pension is the latter.

* After retirement, where the employee receives the pension benefits. The length of time when the employee receives benefits is determined by professional actuaries.

I am going to use my trusty HP 12C calculator for these examples, but any financial calculator will do. Again, the examples I list here are simplified.

Example 1

Situation and Assumptions:
* An employee is currently 42 years of age and wants to retire at the age of 67.
* An actuary determines that the employee will live to the age of 90. Hence, the length of pension benefits will be for 23 years. Assume that this is going to be pretty certain (see note below).

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In reality, actuary use probability factors that an employee lives to certain age. Higher ages of mortality receive less probability than younger ages. I think the standard highest age anyone is considered to live is 110 years.

Often determining the value of present value will involve calculating a factor, determine by actuaries, to be used in the formula:

PV of Pension Benefits Paid after Retirement = Payment × Pension Factor

In our example, we will assume each payment will occur with 100% certainty.

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* The discount rate is 5% compounded annually. (The periodic rate would be about 0.4167%)
* The monthly payment is determined to be $3,000 paid at the end of the month. Pensions benefits can also be paid at the beginning of the month as well.
* The employer plans to make a one-time deposit in account that accrues a safe 5% interest rate.

What is the current value of the pension (when the employee is at age 42)?

We divide this problem into two calculations:
1. Present Value of the pension benefits paid from age 67 to age 90.
2. Present Value of the "lump sum" discounted back to age 42 to determine the one-time required contribution, when the employee turns 42.

Part 1:
n = 23 × 12 = 276
i = 5 ÷ 12 = 0.4167 (I/YR = 5, P/PY = 12)
PMT = 3,000.00
FV = 0.00
Calculated PV = -491,476.19 This amount becomes the FV in Part 2. I enter this amount as a positive in Part 2.

Part 2:
n = 25 × 12 = 300
i = 5 ÷ 12 = 0.4167 (I/YR = 5, P/PY = 12)
PMT = 0.00
FV = 491,476.19
Calculated PV = -141,176.44

The employer will have to deposit $141,176.44 into an account paying 5% interest. It is the current value of this pension.

Example 2

Situation and Assumptions:
* An employee is currently 37 years of age and wants to retire at the age of 67.
* An actuary determines that the employee will live to the age of 92. Hence, the length of pension benefits will be for 25 years.
* The discount rate is 5% compounded annually. (The periodic rate would be about 0.4167%)
* The monthly payment is determined to be $3,000 paid at the end of the month.
* The employer plans to make monthly contributions to the pension. We assume that the employee will be working for the entire 30 years.

What is the required monthly payment while the employee is working?

We divide this problem into two calculations:
1. Present Value of the pension benefits paid from age 67 to age 92.
2. Present Value of the "lump sum" discounted back to age 37 to determine the monthly contributions.

Part 1:
n = 25 × 12 = 300
i = 5 ÷ 12 = 0.4167 (I/YR = 5, P/PY = 12)
PMT = 3,000.00
FV = 0.00
Calculated PV = -513,180.14 This amount becomes the FV in Part 2. I enter this amount as a positive in Part 2.

Part 2:
n = 30 × 12 = 300
i = 5 ÷ 12 = 0.4167 (I/YR = 5, P/PY = 12)
PV = 0.00
FV = 513,180.14
Calculated PMT = -616.61

At the end of each month, the employer contributes $616.61 to the pension.

That is my introduction to pensions, hope you find this helpful.

Eddie

Resources (retrieved during 3/10/14 - 3/15/14)

Determining the Present Value of a Pension Benefit - FinanceMom

Pension Value of a Defined Benefit Pension - Pension Analysis Consultants, Inc. See section 16.13



This blog is property of Edward Shore. 2014