# How do I Value a Defined Benefit Plan

## Background

My "side hustle" for a while has been the US Navy Reserve. I think I've stopped having fun, and I'm ready to quit and devote that time to my main job, my family, etc.

However, one of the major benefits of the Reserves is the retirement - If you complete 20 years of service, you get a pension worth some fraction of your rank's base pay, starting at 62.

I'd like to understand what the value of that retirement is. I get that it's a nice perk, but how should I think of it to understand what I'm missing out on if I do leave the service?

## The Question

How do I put a dollar value on a defined benefit of ~25k a year, from 62 until I die?

The typical way to value such payments is to think about it from an investment standpoint. Meaning, how much would I pay for an annuity (which is just a fixed series of payments) with some interest rate `r` that paid `P` dollars for `n` years?

The rate of return can be either a "risk-free" rate of return like you'd get from a savings account, or if you want to compare it to what you'd make investing the money yourself with a little more risk, use a higher number. 5% is a fairly conservative rate to use if you take a moderate amount of risk.

So, given that, let's say you live for 20 years after age 62. The value of that investment at age 62 would be

``````PV = P/r * (1- (1+r)^(-n))
``````

or

``````25k/.05 * (1- (1.05^-20))  ~= 250k
``````

But that's the value at age 62. What's the value now? To get that you'd discount that value back to the present, which means using a similar formula with n being the number of years between now and when you turn 62. Let's say that's 25 years:

``````PV = FV*(1+r)^(-n)

= 250k * (1.05)^(-25) ~= 74k
``````

That is analogous to saying if you had 74k now, you could invest it at 5% per year for 25 years, and have enough money (still earning 5%) to pay you 25k for another 20 years.

The discount rate and longevity are significant variables here. With a 10% discount rate, the present value actually drops to 39k (since you don't need to invest as much now to get to the annuity value), and if you plan to live longer than 82 the value goes up since it obviously will pay out more.

• "annuity" is the key term here. I'm not sure why you use 5% as the discount rate though. Since there's no opportunity cost to consider, wouldn't it make more sense to use a risk free rate, for example 1.6% for 10Y treasurys? Also, I would use a range of scenarios for longevity. Another factor to consider might be survivor benefits, if they're entitled to the pension. Commented May 6, 2021 at 19:44
• See also: Present Value of an Annuity Commented May 6, 2021 at 19:46
• @0xFEE1DEAD 1.6% would certainly be reasonable for a guarantee that the plan is viable, but there's an opportunity cost if you compare it to, say, a traditional retirement plan with a 20y+ horizon. I can put it in an S&P 500 ETF and be pretty secure in getting 8-10% on average with moderate risk. Over 20 years that's a massive difference. So I chose 5% as an arbitrary, conservative discount rate. Commented May 6, 2021 at 22:30
• The thing is there are only two options in this case: take it (by remaining a reservist) or leave it (by walking away from the pension). Unless I misunderstood, OP can't just cash out the money now and invest it somewhere else. Commented May 7, 2021 at 11:05
• @0xFEE1DEAD Then what's the point of knowing the "current value"? Many pension plans offer a lump-sum payment, which is where these calculations are handy (and too conservative with risk-free rates). Commented May 7, 2021 at 12:56

A practical way to value this retirement benefit might be to use an Income Annuity calculator. Here's one from Schwab: https://www.schwab.com/annuities/fixed-income-annuity-calculator

Entering some test cases for someone now in their 40s gives values (today) of \$200k-300k. That's what the person could pay now for the future benefit.

For what it's worth, this is the process I settled on.

## Convert to a Retirement Fund Equivalent

The rule of thumb is that 4% withdraws are sustainable long term. So to get an additional 25k a year, your retirement fund needs to be: 25 / 0.04 = 625k larger.

## And from there, to Years

Based on your target retirement nest egg, you can see how long it would take to grow it by 625k while continuing to work.

If you planned to retire with 1M, 10% annual growth takes you a little under 6 years to get to 1.6M - call it 5 years if you're making good contributions.

If you're planning on retiring with 5M, then the extra 25k a year is only worth about one year of additional work.

And, obviously, if you expect to have little or no retirement savings, the defined benefit could be worth decades of extra work.