Today’s short post involves calculating the present value of my pension. Present value is a formula used in finance that calculates the present day value of an amount that is received at a future date. The premise behind the calculation is the concept of the “time value of money” or in other words, that it’s more valuable to receive something today than to receive the same value at a future date (which is why it’s important to get started saving your first $100,00 dollars).
Before I go any further, I imagine most lawyers reading this are surprised to see that I have a pension that needs to be calculated. Believe me, I felt the same way when I discovered I had a pension during a job change. Pensions are typically from a bygone era and I didn’t even realize I was accruing a pension (how’s that for my firm not doing a great job of advertising your benefits).
As part of my exit package, I was handed a statement of my pension amount, the date that the payments would begin and the percentage that had vested. Not one to leave money on the table, I’ve done my best to keep good records of the pension benefit. Why? Because it won’t begin payment until April 1, 2046. But that’s not going to stop me from collecting!
The amount I’m slated to receive on that great day is a payment of $1,300 a month, which I will then receive each month until my death. It’s hard to say how much $1,300 a month will be worth 30 years from now. Obviously inflation will eat away at its purchasing power (the pension is not linked to inflation – I will receive a fixed $1,300 a month).
Using the federal government’s inflation calculator, I can see that $590 in 1986 has the same buying power as $1,299.66 today. If I work backwards, I could guess that $1,300 in the 2046 will be equal to $590 a month in 2016. While I won’t be living the high life on $590 a month, that’s enough to easily cover my grocery bills for a month for a family of two. So I better keep great paperwork!
Next, I wanted to figure out how much my pension was worth today. In other words, how much money would I need today in order to provide a benefit of $590 a month in 2046?
To do the calculation, I opened up Excel and loaded up the trusty present value formula. Present value is calculated as PV = FV / (1 + i)^n, where the present value equals the future value divided by one plus the expected interest rate over “n” number of years.
You can see right away that the first thing I needed to know was the future value of the pension in 2046. Not too easy since all I know is that I’ll be receiving $1,300 a month in the future.
To calculate the future lump sum amount that equates to receiving $1,300 a month, I first tallied up the yearly value of the payments, which is equal to $15,600 ($1,300 x 12). Assuming that you can safely withdraw 4% of a portfolio annually without touching the principal, I would need a portfolio of approximately $390,000 in 2046 to withdraw $15,600 a year.
Now that I know the future value of the pension, I need to assume an interest rate. I’ll use 8% since that’s a reasonable return to expect from equities. I also know that there are 30 years between today and 2046, so I have my “n” number of years.
The formula is PV = FV / (1 + i)^n and with my numbers it is PV = $390,000 / (1 + 0.08)^30.
Adding the formula to Excel leads a value of $38,757.16. Impressive! That’s a lot of money for a benefit I didn’t realize existed. My firm really should have done a better job advertising this perk to associates. The only flaw in my calculation is that upon my death I won’t have the $390,000 to distribute to my heirs, but that’s okay – I’ll be dead anyway!
You can check the work by loading a compound interest calculator, inserting the current principal and your assumed interest rate plus the number of years to grow.
Joshua Holt is a practicing private equity M&A lawyer and the creator of Biglaw Investor. Josh couldn’t find a place where lawyers were talking about money, so he created it himself. He convinces the student loan refinancing companies to give you cashback bonuses for refinancing your student loans and looks forward to you discovering how easy it is to track your net worth with a free tool like Personal Capital.
Thirteen thoughts on Calculating Present Value of a Pension
Really odd to know you have a pension. I didn’t know this was a perk in private practice at all. This is a good example of making sure you know your benefits. My guess is very few people have ever looked into this perk.
Very odd indeed. The vesting started at 20% after three years of practice, so most of the junior associates weren’t aware of it because it didn’t apply to them. I thought it was pretty strange to figure all this out as I was leaving.
We have a pension but like much of the US I suspect ours will be taken away at some point with an optional lump sum buyout. You give a great example of how you can determine whether the assumptions they make on interest and inflation are giving you a fair shake with their lump sum (here is a hint, its probably in the companies best interest for you to take the lump sum).
I use NPV a lot. Any time I make a decision to invest in changes at work part of the analysis of whether it is worth to pursue needs to look at NPV. A personal finance example might be whether to refinance versus the cost of the refinance.
Its worth saying that a lump sum offer is not necessarily zero sum. i.e. Company wins/you lose. There are all sorts of costs the company incurs keeping your pension that you won’t as an individual. (PBGC premiums, admin, actuarial fees) .
But you still have to do the math and weigh up the risk transfer from sponsor to participant.
I think you’re under-selling the benefit! By discounting at an equity return you are assuming the benefit is as risky as stocks. But the pension is almost risk free. So I discount my pensions at a high quality long duration bond yield 4%.
Really good point. 8% is too high for something like a pension. If I had used 4%, the present value of my pension is $120,244.28. You just tripled the value of my pension!
Your formula is wrong, the correct formula is PV = FV / (1 + i)^n . This formula will result in the $38,757.16 number that you came up with.
Thanks for pointing out the typo Dave. Really appreciate that. I’ve fixed it in the post.
Assume a 35-year old investor wants to retire in 25 years at the age of 60. She expects to earn 12.5% on her investments prior to her retirement and 10% thereafter. How much must she deposit at the end of each year for the next 25 years in order to be able to withdraw $25 000 per year at the beginning of each year for 30 years help guys with this question
Using the 4% safe withdrawal rate, you need a nest egg of $625,000 to be able to withdraw $25,000 per year. If you have zero savings today, you’d only need to save about $4,350 a year at a 12.5% rate of return to have $625,000 when you turn 60.
A couple of thoughts on your plan:
– Will $25,000 a year be enough when you’re 60 after factoring in inflation? Or do you want $25,000 per year in today’s dollars? If so, the math is a little different.
– 12.5% is a very aggressive return on investments. I don’t think you’ll be able to achieve that.
You can play around with the calculators here to explore different scenarios:
If one is already drawing a pension of $5500/month today as part of an early retirement (age 58), how is the NPV calculated on it?
Thanks for the post. I’m thinking through a slightly different version of this situation.
My partner has to decide whether it’s worth it to contribute 6% of her salary to her new job’s pension scheme. She vests in 4 years, which is the maximum she’s likely to stay at this job. The plan pays her 2.4%*years worked*salary (I’m simplifying slightly), which works out to a meagre $9k/yr. She’s 30, so let’s say benis start in 2050 and run till 2070, for a total undiscounted, nominal value of $9k*20=$180k. To get this, she has to contribute 6%*$75k=$4500/yr for the next 4 years, or $18k. Without taking any discounting or inflation into account, it looks like a neat way to 10x a year’s 401k contribution limit. But is it actually a good alternative to a 401k or other investment option? If you discount those future cash flows, starting when she’s 60 and going till she’s 80, you actually have to assume only a 5.5% nominal return on your alternative investments in order to come up with a positive net present value (NPV) for the pension! I think I can do better than that…
Government Attorney here! I have a pension. Vested in 5 years. IMO, a great benefit as I’m planning on it as part of our FI stash.
Very helpful info. I think if you’re interested in FI and retiring early it is hard to evaluate what you’ve got. Or if you need to stick out a job for a few more years to vest. Kind of like social security.
Big Ern over at early retirement now dot com has some analysis on how Pensions and SS affect the 4% withdrawal rate.