# Defined Benefit Lump Sum calculation

I have a Defined Benefit Pension Plan. I know how to calculate my monthly annuity (single life annuity), but can't figure out how the Lump Sum is calculated from the monthly annuity.

I have been trying to get this calculation for close to two years (for our union members) from our company and Fidelity and still do not have the calculation. The Fidelity printout they give me shows a Lump Sum Factor. I know that Lump Sum Factor x 12 x monthly annuity is my Lump Sum Value. What I don't know is how that Lump Sum Factor is calculated.

I also know that it uses three interest rates that are published in August of each year and a mortality rate that is published once per year.

Can anyone shed light on this for me?

Welcome to Money.StackExchange!

Unfortunately, I won't be able to help you 100%, partly because you haven't really given any numbers to ground this against... But mostly, because there is a LOT of math that goes into those Lump Sum Factors, much of which is proprietary to Fidelity.

What I can do is walk through the basics of the theory and put together a simplified example. Hopefully that makes you more comfortable with the analysis that Fidelity has done when it presents you with a declarative page of numbers by age... it can be frustrating when a significant financial decision like your retirement is told to you with what feels like very little input.

## Key "academic" concepts: (1) Time value of money (2) Age/date groupings

Time Value of Money There are plenty of resources available on the internet to explain this in more detail.

The most important concept is that the \$1,000 you would receive in December 2018 is more valuable to you, and your pension administrator, than the same \$1,000 they will pay to you in December 2048. By December 2048, they've had 30 more years of investment returns and inflation to make it easier to pay that \$1,000.

Mathematically, the "today" value = \$231.38 for your December 2048 \$1,000 payment, assuming a 5% interest rate.

The formula for this 2018 vs 2048 question with annual compounding is:

[Present Value] = [Future Value] / (1 + interest rate) ^ (# of years)

[231.377] = [\$1,000] / ((1 + 0.05) ^ 30)

Note that it is very sensitive to changes in inputs.... a 10% interest makes the \$1,000 value 30 years away... just \$57 today. (The pension company could invest \$57 for 10% return each year to pay you \$1,000 in 30 years if you live that long.)

Or, you can keep the 5% interest but calculate the present value of the Dec. 2038 Payment (20 years)... \$377 vs. \$1,000.

You are welcome to use the formula, or you can use "discount factor tables" like the one here.

Age/Date Groupings Another important aspect is the way payout values are discounted. First the years of a payout are grouped by "pre-retirement", "early retirement", "standard retirement", and then discounted differently

Below, I have modified the example used in the US Government's Pension Benefit Guaranty Corporation explanation:

Assume the participant is age 40 on the valuation date and the normal retirement age is 65. The 25‑year period between the valuation date and normal retirement date is called the "deferral period." The deferral period is divided into three time periods. Assuming that... [mortality rate changes at about age 58]... those time periods are:

• The 7-year period from age 58 to age 65.
• The 8-year period from age 50 to age 58
• The rest of the time period (i.e. from age 40 to age 50).

The payments in each year "bucket" are treated differently because (a) the mortality rate changes, (b) the interest rates change, and (c) the number of years discounted changes. Another way to think of it is that a, b, and c influence the likelihood the pension company would have to pay you and everyone else in the plan consistent payouts by the time you hit age 95.

Let's say my pension is really simple: I get \$200K every 10 years. I'm currently 40, and my first payout would be age 50. I'm probably going to kick the bucket before 80, so three payouts.

First Age bucket: 41-50 years of age This bucket of \$200K that would pay out in 2028 is "worth" \$110K today.

• Assumption 1: 5% interest rate. This is aligned with short-term inflation
• Assumption 2: 90% chance of survival / 10% mortality rate
• Assumption 3: 10-years-away-5%-discount factor is 0.6139 (see linked table)

[ \$110K ] = [90% x [\$200K x 0.6139]]

Second Age Bucket 51-60 years of age This bucket of \$200K that would pay out in 2038 is "worth" \$77K today.

• Assumption 1: 4% interest rate. This is aligned with more mid-term growth and inflation
• Assumption 2: 85% chance of survival / 15% mortality rate
• Assumption 3: 20-years-away-4%-discount factor is 0.4564 (see linked table)

[ \$77K ] = [85% x [\$200K x 0.4564]]

Third Age Bucket 61-70 years of age This bucket of \$200K that would pay out in 2048 is "worth" \$17K today.

• Assumption 1: 7% interest rate. This is aligned with more long-term growth rate expectations.
• Assumption 2: 65% chance of survival / 35% mortality rate
• Assumption 3: 30-years-away-7%-discount factor is 0.1314 (see linked table)

[ \$17K ] = [65% x [\$200K x 0.1314]]

The Lump Sum Total The total amount this 30-year deal would bring me is \$600K in 3 payments of \$200K each. I can only calculate this because I made up the "know I will die between 71-79 but not 80".

If the pension companies and I could agree, I should be happy to trade +/- \$204K [\$110K + \$77K + \$17K] to exchange \$600K over 30 years for cash today.

## So What

This is the same thing that is taking place with your Lump Sum Factor. Fidelity and its team of actuarial scientists have calculated out this example for every. single. payment. Every month. For all the plan participants.

My example (\$204K offer) could be summed up in a table as a 1.02 multiplier at age 40. (\$204K/\$200K) A 1.018 multiplier at age 41, 1.015 multiplier at age 42, etc.

To steal from your question... "You take the multiplier x payment monthly x months to get your Lump Sum"...

Every year when the new interest rates get published, the math from my example gets re-run. Higher long-term interest rates mean overall lower Lump Sums. Lower long-term interest rates mean high overall Pension Lump Sum payments.

• Thanks, THEAO for the response. It helps some but not entirely. Here are my specifics: My Single Life Annuity at age 62 if I stop working on 6/30/19 will be \$4355.55. Lump Sum Estimate Calculated to commence on 7/1/19 and I will be 60 years old. The interest rates used to calculate my lump sum were: 1.93%, 3.57%, 4.36%, but those values will not be used for my actual calculation. It will use the August 2018 interest rates, which have gone up. The Lump Sum factor I have been given is: 135.3519 and the Lump Sum value was \$589,532.02. Aug 11, 2018 at 15:12
• I'm trying to get an idea of how the Lump Sum Factor is calculated so I can estimate how much my Lump Sum will be affected by: 1) interest rate changes and 2) staying longer and 3) if my earnings in my Accrued Benefit calculation change. Aug 11, 2018 at 15:14