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3 Points

Determining the Present Value of a Future Pension Benefit

Posted by FinanceMom on 10/7/2007 at 7:15 PM | 3 comments | 23856 views
I imagine that many members of NetworthIQ have pensions as well as 401(k) plans. These are very difficult to value, because they haven't been completely earned yet. However, your employer should be able to tell you how much your annual pension benefit will be AT EARLIEST FULL RETIREMENT AGE if you were to quit TODAY. (The assumption here is that you are already vested.) Your employer has to be able to determine this number because people quit all the time. Once they can give you that information, this is how you can calculate the present value of your pension:

The basic formula is two-fold:

1) You calculate the present value of the annuity you will be receiving at the time of your retirement.
2) Using that lump sum as a future value, you then discount that to the present time period.

I think it is best to illustrate this using an example.

Let's say that as of today you are 45 years old. According to your employer, if you stopped working today, 15 years from now you could receive an annual payment of $25,000. They are using 5% as the discount rate. (If you can't get this rate, 4.5 to 6.5% are typical discount rates used for annuity calculations.) Since you will be 60 as of retirement, you would use the life expectancy tables to figure out the total time period of retirement, but for now we'll just say you expect to live until age 85. That's 25 years.

STEP 1: Using a financial calculator, you put in 25,000 as PMT, or payment. Then you input the time frame N, as 25. Next, you input 5 as i, or annual interest rate. You then press the PV (Present Value) key to get the value of the annuity at age 60. In this case, you should come up with $352,349.

STEP 2: Clear the registers on your calculator. Now you take the $352,349 and put it in as FV (Future Value). Input 5 again as the i, interest rate. Put in 15 as N, the time period, since you have 15 years until retirement. Now, press the PV key to get the present value of that future lump sum. In this case, you should come up with $169,486.

This, of course, is an approximate value, but it is a reasonable way to calculate it. In the event of a divorce, lawyers often use rates & annuity tables published by the Pension Benefit Guarantee Corporation. Actually, they hire professional actuaries. If there are any actuaries here, I love to know if they would have anything to add or change to what I have written here.

Comments

Thanks FM!

One interesting point, which I found counterintuitive at first, is that the lower the discount rate applied, the higher the present value works out to be. So, the higher the discount rate used, the more conservative the calculation.

This ultimately makes sense if you think of how much money you would have to invest today, if grown at annualized rates of return (i), results in those future cash flows.

Thanks again,

Toad
Excellent, excellent post. More and more pensions these days are going the way of the dinosaur, but folks who have them would do well to read this and get a better understanding of how the benefit is calculated and what it means in todays dollars.

FinanceMom, this was some pretty serious math you put on us...I was taken aback until I saw that you were a CPA, MBA, and gearing up for the CFP. Figures!
I think what you calculated is the accrued liability (AL) instead of the present value of future benefits (PVFB). PVFB should be the sum of AL and all future normal costs for someone who is still active. For someone who already terminated, AL = PVFB since there will be no future benefits to be accrued. Using your example, to calculate PVFB for this active employee, the benefit payable at retirement should consider all compensation and service projected from his date of hire to expected date of retirement. Some assumptions such as salary increase will be adopted. I agree with the way you calculated AL assuming 0 mortality, although in reality we should probably make some mortality assumptions since 85 is considerably higher than current life expenctancy. Most of the time there will be two differnt tables for pre and post retirement mortality. For the QDRO cases I've seen, lump sums are normally calculated with 417(e) segment rates and mortality.

Just my 2 cents. :)

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