Nerd Alert!

This article is a follow-up on the lump sum case study I conducted for the ChooseFI listener, Tess, in Part 11 of the Pension Series. If you missed it, that case study also aired as Episode 58R on the ChooseFI Podcast. I mentally debated if I should make this Part 11a considering the links between the two articles.  However, given this article’s length, and the alternate pension lump sum analysis method it outlines, I decided it warrants its own part in the series.

I’ll warn you now, this article is another deep dive into the world of pension lump sum offers. It won’t be my last either. Pension lump sum analysis is a rabbit hole. As I pointed out in my previous article, there’s no one correct method. A lot depends on what the pensioner values and the questions they are trying to answer. Proper analysis is also based on the strings attached to either the lump sum or the annuities.

Fortunately, as a result of my appearance on ChooseFI 58R, several people reached out to discuss methods of calculating pension value and conducting lump sum analysis. We are currently in the process of compiling a spreadsheet with many of those methods baked in. It’s not quite ready though. So, for now, you have to put up with another wordy pension lump sum analysis from yours truly. Forewarned is forearmed.

The Problem Bounded

For those that missed my previous post, or who just need a refresher, these are the quick facts surrounding Tess’s pension and my calculations. Tess’s company offered her a pension cash lump sum of approximately $75.7K. Alternately, she could wait 7, 12, or 17 years until she is 55, 60, or 65 years old for monthly annuity payouts to start. Tess stated those three waiting periods would result in monthly payouts of $690, $1066, or $1254 respectively. Her pension doesn’t have a Cost of Living Adjustment (COLA) to fight inflation, and she stated survivorship was not a consideration.

For my calculations in Part 11, I used a 2% average rate of inflation. As a result, 7, 12, or 17 years of inflation eating away at (i.e. deflating) the value of those monthly payments would result in $601, $841, or $896 respectively in today’s dollars. Converted into annual amounts that’s $7212, $10092, and $10752 in today’s dollars. Finally, I used the Social Security Administration’s actuarial table to project a reasonable average life expectancy for Tess of 83 years old.

As a result, my calculations showed that $7212 x 28 years, $10092 x 23 years, and $10752 x 18 years of retirement, adjusted again for 2% inflation by using my TDV formula as described in Part 11 of the Pension Series, equals $152,672 , $183,785, and $160,617 respectively in today’s dollars. Thus, depending on which annuity payment scenario Tess prefers, and assuming she lives to at least 83, her company owed her approximately $153K, $184K, or $160K in future payments at today’s dollar price compared to the $75.7K they were willing to pay her as a lump sum right now.

Listener Feedback

This was an incredibly simplified scenario, mostly because I didn’t have a lot of the information required to judge whether I should use a more complicated calculation method. Thus, I made a lot of assumptions. I stated as much in the case study. Most importantly I assumed Tess’s pension was 100% safe and would pay out as promised. I also referred people to Part 8 of my Pension Series if they had a pension situation more advanced than the one Tess described.

Despite that, my method and the answer did not satisfy everyone. Actually, it’s probably more accurate to state that my method left some people wanting more. Several people asked why I didn’t compare future annuity values to an invested lump sum? A follow-up post in the ChooseFI Facebook group by a listener named Allen encapsulated this sentiment perfectly:

Grumpus Maximus the way the analysis was done assumes that the lump sum scenario would only yield the rate of inflation correct? What if the lump sum were invested at either an annuity rate or a normal 60/40 stock/bond allocation to get a higher return… Would it grow to more than the PV (Present Value) of cash flows at age 55, 60, 65? Or, alternatively, what is the ROI (Return on Investment) the lump sum would have to achieve to be favorable to the annuity scenarios?

To be clear, I didn’t compare the lump sum’s future value to the annuities’ Present Value, and explained why to Allen in the following terms:

Negative, to your first question. My method brings the future value of the pension into today’s current dollar value. It assumes no rise in the lump sum’s value (inflation or otherwise) because the lump sum is already in today’s dollar value. Therefore, I deflate the future value of the annuity payouts down to today’s dollar value in order to get an apples to apples comparison of the current value of the lump sum compared to the current value of the future annuity payments that are owed (to Tess in this case). Apparently, this is a similar method as using the XNPV function in excel as Actuary On Fire’s article suggests to do.

I believe the method you are referring to is the one Financial Samurai uses, and I referred to in the case study as the ROI method. Sticking with my analogy, I believe (although not a math major here, so I could be mistaken) that the ROI method is an oranges to oranges comparison of future value in future dollars since it requires growing (inflating) an invested lump sum via investing in order to compare to an annuity’s future dollar value at a future date in time.

Neither is more correct over the other as I pointed out in the case study. However, assuming I have my facts correct, if you start to mix both methods I think you’d get an apples to oranges comparison.

My preference (much like Tom Brady’s and the New England Patriots) is to deflate everything … into today’s dollars. … I think it’s easier to show people what the current value comparisons are.

Friendly Banter

First off, Allen mustn’t be a Patriots fan because he didn’t rise to my bear baiting. That’s OK because as I described in a separate post, we cut the cable cord last year as a time and money saver. We don’t even have an HD antenna. Therefore, I have no idea what is going on in the NFL. A school kid could talk rings around me right now when it comes to football. A co-worker had to tell me the other day who made it to the Super Bowl this year. Ignorance is bliss … and frees up a lot of time to study things like future values of lump sums and pensions.

More importantly, Allen continued to press me in a friendly manner on what he saw as the usefulness of running a future value scenario between an invested lump sum and the annuities. Despite my preference for current values, I agreed with him that some people might find that useful. I just didn’t know how to figure it out.

Of course, I had the Financial Samurai article as a reference. However, upon closer inspection it turns out Financial Samurai’s method wasn’t built to answer a lump sum vs. annuity question per se — it simply allows you to value your pension annuity based on different Reasonable Rates of Return (R³) and a discount rate based on pension safety. That didn’t suit the purpose here.

I wasn’t aware of any other methods for calculating the future value of a pension. I messaged back and forth with Allen for a bit, who suggested a method. Honestly, though, I couldn’t understand it. Thus, I resorted to dinking (vice drinking) around with some online calculators, and working through the problem logically. Hours after a real mathematician would have worked it out, it finally clicked in my head. What can I say? Liberal Arts major here!

Restating the Question

I basically had to re-state Allen’s questions above in a manner that made sense to a guy like me who prefers inflation-adjusted current value scenarios. Thus, despite a college professor failing one of my essays for reformulating one of his questions; I reformulated what Allen asked:

• • If a person invested the $75.7K lump sum over the 7, 12, or 17 year periods; could any of those scenarios result in an inflation-adjusted future value big enough to sustain withdrawals equal or greater to the annual annuity amounts above ($7212, $10092, and $10752)?
  • If so, what is the required ROI?

Rates of Return

In order to answer Allen’s questions though, I needed to determine a reasonable rate of return. My preferred first stop for something like that is Early Retirement Now. In Big ERN McCracken’s  Safe Withdrawal Rate (SWR) series he uses a long-term inflation-adjusted projection of 6.6% for equity returns. So assuming Tess invested her lump sum in 100% equities (stocks), she could project a 6.6% annual return after adjusting for inflation (known as the real return). It’s a number with a lot of analysis behind it, so I decided to use it as my best case scenario.

However, anyone who knows much about individual investors knows that the average investor returns far less than what the market averages. In fact, Dalbar’s Quantitative Analysis of Investor Behavior (QAIB) 30-year average real return for “average investors” is only 1.9%! The Dalbar number represents the worst tendencies among investors, which ChooseFI listeners are especially keen to avoid. Despite that, I decided to use it to represent a worst-case scenario. I would’ve preferred a number with a longer history, but it seems that Dalbar dominates analysis about this niche area of the market, and they only do 10, 20, and 30 year looks (from what I can determine).

Not satisfied with a best and worst case scenario, I also chose a middle range number to represent a reasonable rate of return for a stock/bond portfolio mix (like the kind Allen inquired about). I went with a 4.2% annual real return because it seemed perfectly plausible. It was also the average of the best and worst case scenarios.

Alternate Method

The analysis method I happened upon isn’t anything fancy. I essentially decided to grow the lump sum via a compound interest calculator by 7, 12, and 17 years at 1.9%, 4.2%, and 6.6%. That gave me nine values that corresponded to a set number of years in Tess’s retirement (28, 23, or 18) and one of the three inflation-adjusted annuity values ($7212, $10092, or $10752). This resulted in a chart that looked like this:

	Lump Sum Real Rate of Return
Years $75.7K Invested (Years of Retirement)	1.90%	4.20%	6.60%	Yearly Annuity Amounts
7 (28)	$86,360.50	$101,304.40	$118,412.16	$7,212
12 (23)	$94,882.49	$124,740.83	$162,998.02	$10,092
17 (18)	$104,245.43	$153,599.20	$224,371.85	$10,752

After doing this I tested all nine scenarios in my preferred retirement calculator, Flexible Retirement Planner (FRP). By zeroing out many of the categories on FRP, I was able to run a simple nest egg drawdown scenario. I tested each of the nine scenarios using their projected real rate of return (i.e. 1.9%, 4.2%, or 6.6%)  while making yearly withdrawals equivalent to the corresponding yearly annuity amounts from the chart above. This allowed me to plot which scenarios could sustain the annual withdrawals over the defined period, and which ones could not. The results are reflected in the chart below where Red is a failure and Green is a success.

	Lump Sum Real Rate of Return
Years $75.7K Invested (Years of Retirement)	1.90%	4.20%	6.60%	Yearly Annuity Amounts
7 (28)	$86,360.50	$101,304.40	$118,412.16	$7,212
12 (23)	$94,882.49	$124,740.83	$162,998.02	$10,092
17 (18)	$104,245.43	$153,599.20	$224,371.85	$10,752

Results

What does the above chart tell me? For starters, it tells me if Tess took the lump sum and invested it, with the intent to create the equivalent amount in yearly withdrawals to the annuities offered by her company, she needs to average above a real return of 4.2% for any reasonable chance of success. The chart also tells me that a 6.6% real return works for all three annuity/retirement year scenarios.

In fact, 6.6% more than works because in all three scenarios a 6.6% real return preserves 100% of the lump sum. In one scenario 6.6% actually grows the lump sum by a significant amount. I have no idea if that’s important to Tess, but people who wish to pass on generational wealth may find this of particular value. I’ve taken screenshot the charts from each 6.6% test in FRP to show what I mean:

Next Step

The next logical step was determining the break-even point, in case Tess doesn’t want to preserve the principle lump sum. In other words, if Tess was willing to spend the invested lump sum down to zero by 83 (the end of my projected lifespan for Tess), what would the required real rate of return need to be to build that lump sum just big enough for each scenario? I ran the numbers and came up with the following chart. The informative numbers are in Green:

	Lump Sum Real Rate of Return Zero Spend
Years $75.7K Invested (Years of Retirement)	4.00%	5.40%	5.50%	Yearly Annuity Amounts
7 (28)			$110,119.00	$7,212
12 (23)		$142,292.00		$10,092
17 (18)	$147,456.00			$10,752

Thus, if Tess wishes to spend her lump sum down to zero using one of the yearly annuity amounts as a guide, she should strive for a 5.5%, 5.4% or a 4.0% real rate of return respectively. For example, if she was to start annual withdrawals of $10,092 after 12 years of investing (in line with when the annuity would start), and wanted it to last 23 years until she was 83 years old, it would have to grow to $142,292 in those 12 years (equaling a 5.4% real return). So on and so forth for the other two scenarios.

Analysis

I’ve refined the above valuation method for over a week now. As a result, I’ve realized two things. First, the lump sum vs. future annuity valuation method that I outlined in Part 11 of the Pension Series answers a different question than the above method. The Total Dollar Value (TDV) calculation I demonstrated in Part 11 answers the question of what a company owes a pensioner in future annuity payments adjusted to today’s dollars. It allows a pensioner to compare a lump sum offer to a future annuity on a dollar for dollar basis. The method is based on a few key assumptions, any of which might change during the life of an annuity. The most important assumption I made in Part 11 was that Tess’s pension was 100% safe.

The method I just finished outlining above answers a different, but related question. Instead of answering “what is a pensioner owed?”, it answers “what can a lump sum do?” In other words, if a person takes a lump sum, what can they do with it?

It turns out, a person can do quite a bit with it. A person like Tess could conceivably invest the lump sum and reproduce the annuity payments all within the same timelines as it takes the annuities to start. Not only that, but she could also preserve or grow the lump sum amount for future generations or other retirement costs. Conversely, the above method also helps to inform someone in a situation like Tess about the difficulty required to reproduce annuity payments on their own. It primarily does this by providing two things:

1. 1. 1. The target value that a lump sum needs to grow to by a certain time
      2. The real rate of return required to achieve that lump sum

A Few Thoughts on Risk

Of course, difficulty is subjective. Some investors in 2018 may look at a 5.4% real rate of return and think “no big deal especially with how strong the market’s performed since 2008.” Others may look at it and realize “that’s a 7.4% return prior to adjusting for inflation, just to achieve a zero-sum spend plan, which is difficult to achieve in any scenario, but especially when a Bull market is as long in the tooth as this one.”

You know what I say? To each their own — which of course is the beauty of taking a lump sum — it offers flexibility and the ability to tailor to personal preferences. There’s a lot to be said for flexibility, especially if you’re a savvy investor with a proven record in overcoming the human foibles which earn the average investor 1.9% real returns.

Yet, I’d be remiss if I didn’t mention some of the assumptions and problems built into this model. Since I addressed the assumptions and problems built into my calculations in Part 11, it’s only fair I do the same here. Thus, the biggest problem I see with my above method for projecting lump sum growth and drawdown is that it completely ignores Sequence of Returns Risk (SRR).

For those unfamiliar with SRR, you can read all about its impact on Early Retirement Now or Can I Retire Yet?. However, all the uninitiated needs to know is that SRR is the bad luck that some people experience by retiring and starting withdrawals from their nest egg of investments just as a major market downturn or crash occurs. Starting withdrawals as the market crashes significantly increases the likelihood that the nest egg will run out of money in the future. Unless, of course, a person builds their nest egg to insure against the chance of SRR. The fixed withdrawals that I built into the above scenario with set times that mirror the annuity options in Tess’s pension don’t account for SRR.

I already mentioned the other obvious issue with this model: to be truly useful it assumes returns that far exceed what the average investor achieved over the past 30 years. That’s a big assumption. To achieve the above investing results requires a level of discipline, fortitude, and self-awareness that the average investor apparently lacks. I obviously don’t know if Tess is an above or below average investor. Nor do I know if you are, but the red highlighted values in the 1.9% real return column in my chart above should be flashing right now.

At the End of the Day…

I can’t tell Tess, or you, what to do when it comes to pension lump sums. All I can do is provide education and tools that help capture the seemingly unending variables involved in a lump sum decision. As mentioned at the top, I’m in the process of developing a spreadsheet with both Allen and another reader that captures many of the various methods for valuing pensions with built-in formulas. If you’re a math dunce like me, you’ll definitely find it of value once it goes live.

Ultimately, I’m pleased Allen made me examine Tess’s lump sum offer further. It forced me to develop yet another way to conduct pension lump sum analysis. Doing so helped me to see lump sum offers as the opportunity that some people view them to be. I now understand how people who are comfortable investing, who value generational wealth, and/or who like the implied flexibility that lump sums offer are drawn towards the lump sum rather than an annuity payout. It’s not necessarily my preference, but I value the insight into the other side of the issue. Hopefully, you do as well.