Mea Culpa

This is a substantive revision to the original article I published on 01 October 2017 entitled “The Pension Series (Part 4): Total Dollar Value (TDV) of Your Pension.” I am making this substantive revision because I have updated the formula to calculate the Total Dollar Value (TDV) for pensions without a Cost of Living Adjustment (COLA).

In my two-and-a-half years of blogging, this is only the second major revision I’ve made to an article. However, as a result of updating the formula, it will not be my last. Several other articles in which I attempt to calculate the TDV of people’s pensions also need to be changed. I will update and re-publish those articles, much as I did with this one, with notifications to all my readers. But, since this article explains TDV calculations of no COLA pensions, I needed to start with this one.

My Continued Commitment to Quality and Accuracy

When I revised my first article, I stated that I was committed to ensuring the information shared on this blog was as accurate as possible. I remain so. I also remain committed to updating my readership whenever I make substantive changes to an article. In my opinion, the below changes (also in blue) meet that threshold. Not all bloggers do that, but in the profession from which I recently retired, you tell people when the information you previously provided them changed or was wrong. That way, they don’t act on stale or erroneous data. I see no need to lower those standards simply because I’m retired.

I apologize to anyone who may have used my previous method for calculating the TDV of their no COLA pension. When I originally wrote this article, it was the only method I could devise to account for a pension’s total value over the estimated life span of a retiree, while still deflating its purchasing power due to inflation. I created it with good intentions based on the information and tools I had available at the time. However, as I submitted the first drafts of my upcoming book (which contained the prior TDV method) for review and publication, it came under the scrutiny of people with far better math skills than myself.

Fortunately, one of the reviewers (a polymath) not only caught my error but grasped what I was attempting to do. As a result, he provided me with a much more accurate method for calculating the TDV of a no COLA pension. Having tested it out over the last several months during re-writes of my book, I’ve come to believe that it’s a far more accurate method than my own. Thus, the need to update this article. I hope that I explain the changes below (from the old formula to the new) well-enough that you can understand the ramifications.

Finally, this issue also serves as a good reminder of what I note on my disclosures page, and routinely try to remind people in my articles. I have no formal finance or pension training. Other than laboring for a pension myself, and researching pensions for the blog, I’m not certified in anything. Apart from the occasional guest post, I am also a one-person show here at GM HQ, which means I don’t have a deep bench of reviewers and editors. As a result, as you read through the blog you are doing so for informational purposes only. You shouldn’t take action based on the information on this blog without first consulting a certified financial advisor, planner, accountant, or some other accredited agent familiar with the specifics of your pension and financial state of affairs. Now, with all that said, enjoy the newest version of this article!

Determining Total Dollar Value (TDV)

My original intent for Part Four of this series was to write about good pension calculators found on the web that could help you place a Total Dollar Value (TDV) on your pension.  In fact, I was building up to it from Part One onward.  I felt my topics had a nice and natural progression beginning with pension safety, moving on to whether or not your pension is worth it, and then analyzing the three most important factors in determining your pension’s worth: the Initial Dollar Value (IDV) formula, inflation’s effect, and the Immediacy Effect.

However, it turns out that most generic pension calculators on the web stink, if you can find one at all.  It also turns out, that most pension plans have their own calculators.  In hindsight, that makes sense because as we discussed in Part Three, each pension plan has its own formula to calculate IDV.  My oversight aside, it doesn’t decrease the importance of determining the TDV of your pension.  In fact, there are several good reasons for doing so, even if the process might prove different than I first imagined.

Reason #1: Reduces The Potential For Miscalculation

The most import reason for calculating your pension’s TDV is to ensure your Human Resources (HR) and/or pay department give you what you are entitled to upon retirement.  This may seem like obvious advice, but I am not so sure.  The Department of Labor’s (DOL’s) Employee Benefits Security Administration (EBSA), the federal office designed to protect employee’s retirement benefits, has a web page with the 10 Common Causes Of Errors In Pension Calculation.  It’s worth a read, especially since 2 of the 10 most common errors are due to simple math.

I doubt the EBSA would waste time stating the obvious in a list of 10 Common Errors if it was not happening, so make sure the administrators are doing the basics correctly.  It so happens that I have a pension administrator in my Golden Albatross Facebook Group and after I sent her the link she advised:

…I would definitely recommend that everyone … do their own basic pension calculation. I’ve had very few people I’ve worked with over the years do this … Our process is to have our outside administrator do the calculation … we also independently do the calculation before we review theirs. The idea being that it’s unlikely both will make the same error, so if we match we’re good to go. If not, we investigate until we find the error. This has worked well for me … Still, while this makes me confident that we’re providing accurate calculations, I think everyone should understand their own calculation and be able to challenge it if they’re not confident in the accuracy.    — Michelle 

I think that is great advice, especially since I doubt everyone’s organization has someone as conscientious as Michelle looking out for their best interest.  Also, I presume it’s hard, if not impossible, to fix an error in your pension calculation after you’ve retired, signed all the paperwork, and started to receive checks.  Which means it’s probably best to save yourself a headache, if not a heart attack, and calculate your pension’s TDV before you sign anything.

Reason #2: Survivorship Cost Comparisons

The second reason why it’s important to determine a TDV for your pension is the issue of survivorship.  If you are married or have children, then by law your pension plan must offer some sort of survivorship plan.  Survivorship essentially acts as an insurance policy, allowing you to select a certain percentage of your pension to pass to your spouse and/or minor children when you die.  In turn, this reduces the total monthly payment to you while living (akin to a monthly premium).

Thus, if you don’t know the TDV of your pension, you’ll have no idea if electing the survivorship benefit is a good value for money.  Or, if alternatively, you might find better value for money through something like term insurance.  It’s not a direct apples to apples comparison, as inflation plays a role in this determination as well.  This is a topic I explore at length in Part 5 of the Pension Series, but until then just keep in mind that some of the values you calculate when determining TDV can help you decide when to elect survivorship.

Reason #3: The Lump Sum Offer

Another topic I explore in the Pension Series is that of the lump sum offer.  It is also the third major reason why I think it’s important to calculate a TDV for your pension.  Many pension plans these days, including public pensions, offer the opportunity to take some, or all, of your future pension’s value in the form of a lump sum payment immediately upon retirement.  As discussed in my Pension Safety article, there is a good reason why pension plans do this.

Pension plans offer lump sums as a method to transfer risk and to reduce future financial liability to shore up their finances.  This means it’s cheaper to pay you a reduced amount of money at retirement in order to reduce or eliminate the liability of paying you (or your survivors) a larger amount of money spread out over the remainder of your lifetime.  Now, there might be good reason for you to take a lump sum (which is why I explore it so much in the Pension Series), but without knowing your pension’s TDV, you’ll have no idea as to just how much money the pension plan stands to save (and you stand to lose) from their lump-sum offer.

 

Inflation Paced Calculations

So if those are three good reasons as to why it’s in your best interest to calculate your pension’s TDV, let’s see if we can actually do it.  As you will recall from Part Three of the Pension Series, the first thing we must do is calculate Initial Dollar Value (IDV), which is based on your pension formula.  Since different pension systems have different pension formulas, it’s best to check your pension’s website or annual literature to find out what yours is.

While on the website, you will hopefully find a calculator that will at least calculate the IDV for you.  If not, go back to Part Three of this series, and review how to draft a mathematical formula yourself.  Even if you find a calculator, you may still want to conduct the calculations by hand just to be safe.  Who knows how the calculator on the website was programmed?  This is your pension, after all, no one besides you and your family has more of a vested interest in ensuring the calculations are correct.

Grumpus’s IDV Calculations

Grumpus’s Calculator		Before Taxes
Years Out	Year	Monthly Pay	Annual Pay	Cumulative
1	2020	$4,731.54	$56,778.47	$56,778.47
10	2029	$5,699.22	$68,390.66	$624,254.36
20	2039	$7,011.21	$84,134.48	$1,392,050.44
30	2049	$8,625.41	$103,504.90	$2,336,655.14
40	2059	$10,611.25	$127,335.04	$3,498,696.08

When you calculated your IDV did it come out in a monthly or yearly amount?  The U.S. military’s pension calculator spits out results like the above chart.  It provides both a monthly and an annual value as highlighted in the red text in the chart.  If your calculator only provides a monthly amount, go ahead and calculate the annual amount since it is what we will need for our calculations below.  Ignore the rest of the chart, for now, I will refer back to it as needed.

If you are one of the lucky ones I described in Part Three of this series whose pension starts immediately upon retirement and has a Cost of Living Allowance (COLA) linked to inflation as listed in the Consumer Price Index (CPI), your task is simple.  You can calculate TDV in today’s dollars by multiplying the yearly total for your IDV by the number of years you think you are going to live.  So if I were to take the annual amount highlighted in red text above ($56,778.47) and multiply it by 40 (putting me at the ripe old age of 85) my TDV in today’s dollars would be $2,271,138.80.  Notice that is a different amount than the cumulative value calculated in green in the lower right-hand corner of the chart.

Why?  Well, an inflation-linked COLA is built into the military pension calculator, so the payments increase by some nominal amount representing inflation every year.  The calculator doesn’t tell me what value is used for inflation, but in truth, it doesn’t matter.  Since my pension payments will keep pace with inflation, it essentially eliminates the need to consider inflation’s effect.  And since my pension starts immediately, I don’t need to discount it for the Immediacy Effect either.  Thus, in any circumstance where a person has a CPI-linked COLA pension that starts immediately upon retirement, IDV multiplied by your Expected Life-Span (ELS) equals TDV (minus any survivorship payments one elects to make). Mathematically it looks like this:

• • TDV= IDV x Expected Life Span (ELS)

This is especially handy when comparing TDV to any lump sum offer.  It allows you to make a dollar for dollar comparison in today’s dollars, without the need for any funky inflation calculations.  So, if your pension has a CPI-linked COLA and your work’s lump-sum offer is $200K, but you just calculated a $1 million TDV (without survivorship), that means the offer is 80% less than what you are owed over your expected lifetime.

Non-Inflation Paced TDV Calculations: The Wrong Way

The correct TDV formula I’m about to show you (in the next section) came from one of the math geniuses who proof-read my upcoming book, The Golden Albatross: How To Determine If Your Pension Is Worth It (scheduled for release in early-2020 by ChooseFI Publishing). I like to call him Billy the Kid, and if you want the blow-by-blow as to how he devised the formula, then read the book once it’s released. Suffice it to say, though, that in the original version of this post, and therefore early drafts of my book, I got the method for calculating the TDV for no COLA pensions wrong.

It was wrong because I failed to realize that the method did not account for inflation’s effect on an annual basis. Instead, the original method calculated the entire value of a lifetime of pension payments first, by using the TDV formula above (TDV = IDV * ELS). It then took that sum and devalued the purchasing power due to inflation all in one shot by using an inflation calculator.

The method was simple, but inaccurate, because as Billy so eloquently pointed out, “this should … be an exponentiation operation, as each year of inflation compounds against the prior year.” He was right. Just like compound interest, inflation also compounds over time. Unlike compound interest though, inflation devalues purchasing power fractionally. So, according to Billy, what I needed to:

…figure out this value is much more akin to calculating the future value of an investment with regular contributions coming into a portfolio, where the growth rate is simply negative [due to] inflation.

Non-Inflation Paced TDV Calculations: The Correct Way

Pensioners without COLAs and pensioners with some sort of flat rate COLA, it’s your turn. Roll up your sleeves and get ready to do some math. That said, my big hope is that your pension’s website has a calculator that does all this for you. That way you will at least have a value to compare yours to, once you make the calculations.

Although, if you do find a pension calculator on your pension fund’s website, don’t cop-out and just rely on those figures! If nothing else, remember the list of the 10 most common mistakes made with people’s pensions that I mentioned above. It’s in your best interest to understand how and why the pension fund is offering to pay you the amount in your pension statement.

So, here it is:

• • *No COLA Pension TDV = IDV[((1-r)^(ELS+1)-(1-r))/-r]

• • • IDV = annual pension payment
    • r = annual inflation rate (negative growth)
    • ELS = Expected Life Span (or any number of years you want to use)

*Note: this formula starts inflation with the first year’s payment, which essentially means your pension payment devalues throughout the first year, in real-time. In my opinion, this is the more accurate way to calculate inflation’s effect since real-world inflation’s effect doesn’t wait until the end of the year to impact your household budget for staples like food.

Does This Look Familiar?

For the math lovers out there, who think this formula looks vaguely familiar, it’s a modified equation for investment growth with regular contributions, like the one below. However, the TDV formula above drops the initial principle represented by “P” in the below formula, since there is none. The no COLA TDV formula above also switches out “c” for the IDV acronym that I like to use. Finally, the formula above turns the growth rate, represented by (r), below, negative to simulate inflation.

• • Balance = P(1+r)^Y+c[((1+r)^(Y+1)-(1+r))/r]

• • • P = Initial principal (not used in the TDV equation)
    • r = growth rate
    • Y = Years of compounding (what I called ELS above)
    • c = regular contributions

Or, as Billy related:

The equation … is basically the same equation as a compounded growth of [an] investment with periodic regular contributions, though in this case, the growth rate is inverted (inflation) and the contributions into the portfolio are … the pension’s payments.

An Example

To prevent all the non-math loving heads (like mine) from exploding while looking at the above formula, I plugged some numbers into the equation below as a practical example. To compare my result below to the full COLA pension calculation from four-sections ago, I used the same $56,778.47 as the annual payment. I also used the same 40-year ELS from above. Unlike the full COLA example though, I had to select an inflation rate. I chose 2% since it’s the U.S. Federal Reserve’s target rate.

Finally, I translated everything into Microsoft Excel syntax to make the calculation run on a spreadsheet. As a result, you can literally cut and paste everything below starting with the “=” symbol and continuing rightwards, plop it into your electronic spreadsheet of choice, and play around with it. When you do, what you’ll get is a result like this:

• • No Cola Pension TDV =56778.47*(((1-.02)^(40+1)-(1-.02))/-.02)
  • No Cola Pension TDV = $1,542,141.87

A TDV of $1,542,141.87 is a significantly smaller amount than the $2,271,138.80 TDV for the full COLA pension from earlier in this article. In fact, it’s 32% smaller. Such is the power of inflation, specifically inflation’s inverted effect on purchasing power. This is the reason why I covered it so extensively in Part 3 of the Pension Series.

A word of caution though, assuming the inflation rate is accurate, $1,542,141.87 represents a no COLA pension’s TDV in first retirement year dollars. If your retirement is still years off, you’ll need to deflate this value even further to put that value into today’s dollars. To do that, you can use an inflation calculator like the one linked here. All you need to do is plop in your TDV (i.e. $1,542,141.87 from the example above), set an inflation rate, and then enter the number of years your pension start date is offset from the present. Good luck!

Other Tips

What are some other tips I can give you? If your pension has a COLA that is linked only partially to CPI, or some other method, like a flat rate COLA increase of 1% or 2% per year, then you need to modify your inflation rate accordingly. For instance, in Part 3 of the Pension Series, I pointed out that one proposal for the latest military retirement system in the U.S. (which fortunately didn’t make the final draft) intended an annual COLA that would’ve been minus 1% of CPI. This essentially would’ve subjected future pension payments under this system to a 1% inflation rate in perpetuity.

Thus, if I were to calculate the TDV of that annual $56,778.47 pension using a 1% inflation rate over 40 years, it would equal a $1,860,732.43 TDV in year one dollars. Again, that’s a lot less than the $2.271 million in my CPI-linked COLA pension scenario. In fact, it’s approximately 18% less. On the other hand, it’s 17% more than the 2% inflation-adjusted TDV of $1,542,141.87 in my no COLA pension scenario above.

Delayed Pension Payouts

About the only scenario, I’ve not discussed is that of the delayed pension payout.  This is the type of pension which is vulnerable to the Immediacy Effect.  For those of you who’ve yet to read Part Three of this series, the Immediacy Effect is a term I use to describe the mathematical formula and calculations behind an important discovery made by Big ERN McCracken over at Early Retirement Now.  His calculations show that the further from your (early) retirement point your pension payments begin, the less those payments will mean to your successful employment of a Safe Withdrawal Rate (SWR).

As with the scenarios above, there are different considerations for pensions that have CPI-linked COLAs, and those that don’t. Since I describe those in detail in Part Three of the Pension Series, I won’t repeat them here.  What is worth repeating is that I address these specific scenarios in my upcoming book, The Golden Albatross. So, if you have a pension with a delayed start, you should check out the book. If you can’t wait until early 2020 though, you could always read Big Ern’s article describing his discovery and testing of the Immediacy effect.

Conclusion

That’s all I got folks.  It took a while for this article to gel, but I think I got there in the end, despite the substantive revision.  Turns out, that even without a calculator a person can determine the Total Dollar Value (TDV) of their pension.  Not only that but TDV has several important uses which include ensuring your pension administrator pays you the correct amount and valuing any lump sum offer that may come your way.

I also identified several potential future article topics for the Pension Series including survivorship calculations, lump-sum decisions, and developing a calculation for the Immediacy Effect.  Look for articles on those topics (and more) in the future.  Until then, I hope you found this article useful.  Feel free to comment, email, look me up on Facebook, or tweet me on Twitter.