## On the Costs and Benefits of Money at Different Points in Life

Recently one of my colleagues at RWM asked for my thoughts on a problem one of our clients was facing. Our client had recently been informed that their pension was shutting down and they had to decide on how to be paid out. They were given two options:

**Lump Sum:**Receive $138,000 today of qualified money (not taxable until withdrawals are made in retirement), or**Annuity:**Receive $1,800 a month for life starting 17 years from today (this is when our client would reach age 62)

While a situation like this might never occur for you, deciding between a lump sum and an annuity is common for many people with pensions who are approaching retirement. So, what should our 45 year-old client do?

If you’re a numbers fiend like me (note: they call me Nicky Numbers at RWM), then your first instinct will be to value the Annuity. How much is $1,800 a month for life worth 17 years from now?

To do this we need to estimate: (1) how long our client live will past age 62 (when they start getting the Annuity) and (2) what return will they get on their money in retirement.

For life expectancy, we assumed that if our client made it to age 62 *she* would live 23 more years to be 85 (this comes from this actuarial life table from the Social Security Administration). For the rate of return, we conservatively assumed 5% annually on a 60/40 portfolio (with stocks earning 7% and bonds earning 2%).

Putting this all together, at the moment our client retires at age 62 their $1,800 monthly payments (or $21,600 annually) for 23 years (while earning 5%) would be worth ~$306,000 (assume annual payment at year start).

Great now, we have to compare this Annuity amount ($306,000) with what we would expect the Lump Sum to grow to by the time our client retires 17 years from today. The Lump Sum ($138,000), if compounded at 5% for 17 years would grow into ~$316,000. This is a good check on our math as both the Annuity and Lump Sum tend to be actuarially similar with a 5% growth rate and an appropriate life expectancy.

Visually you can compare the Lump Sum to the Annuity by looking at how they both grow and draw down before and after our client’s retirement at age 62 [Note: the vertical line is when our client starts taking annual withdrawals of $21,600 in retirement]:

So, we tell our client to take the Lump Sum, right?

Not so fast. The Lump Sum has a problem. If you assume the same spending rate as the Annuity, the Lump Sum would run out of money before our client turns 87. This is not an issue for the Annuity which makes payments for life.

So, we have to ask, what is the probability that our 45 year-old client makes it to age 87 and beyond? Using the SSA life tables, there is a 43% chance that our client outlives what the Lump Sum would provide (all else equal). And if our client lives to age 62, the probability that she lives past age 87 is 46%. More importantly, if our client makes it to age 87, her life expectancy is *another* 6 years.

If we re-run our simulation with a life expectancy of 87, you can see that the Annuity is now worth more than the Lump Sum:

So the Annuity wins then right?

Well, not exactly. What if our client dies *before* they reach age 62? According to the SSA actuary tables, there is a 7% chance that this will occur, leaving our client’s heirs with nothing [Note: This assumes our client chooses a *single life* annuity option and not a *joint life* annuity option with a lower future payout].

So, with the 7% chance of dying early, but a 43% chance of outliving the money, our client should obviously take the Annuity, right? Not necessarily.

**The one thing that the Lump Sum offers that the Annuity doesn’t is optionality.** With the Lump Sum, our client would have a choice in how to invest, spend, and bequest their money. This flexibility would allow our client to spend more in the early years of their retirement when they are in better health than they will be in later years. It also provides more flexibility with tax planning compared to the Annuity since the Lump Sum can be rolled into an IRA or other qualified retirement plan.

In addition, the Lump Sum would not have limits on the upside. Since a 60/40 portfolio has returned 9% historically, it is not out of the question for it to return 6% over the next 17 years and provide far more income in retirement than the Annuity.

But all of these questions come down to making tradeoffs. The question you have to consider when choosing between an Annuity and a Lump Sum is: **what risk do you want to take?**

- With the Lump Sum there is the risk of outliving your money either due to long life or subpar investment returns.
- With the Annuity there is the risk of dying before retirement age and the risk of seeing your income lose its purchasing power due to inflation.

In the end, we told our client to go with the Lump Sum because of the combined flexibility and the belief that it would outperform 5% annually. Given that a 60/40 portfolio has returned 6.5% over the last 5 years and 8% since the early 1990s, this assumption seemed reasonable.

**I Can’t Get No Satisfaction**

When it comes to the Lump Sum vs. Annuity decision, as I mentioned above, it all comes down what risks you want to take. I can understand how unsatisfying this answer is for those looking for a silver bullet. But if you approach retirement looking for the perfect solution, you won’t get it. Why?

Because as William Sharpe, the Nobel Laureate, notes, retirement is the “nastiest, hardest problem in finance.” And I agree. With the multiple layers of uncertainty (inflation, life expectancy, returns, and lifestyle choices) the problem is not solvable in the strict sense. There is always risk that you cannot eliminate. There are things that are beyond all expectations. As the famous phrase goes:

Man plans, God laughs

Special thanks to Gary Pulford and Dan LaRosa for providing inspiration for this post and thank you for reading!

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This is post 131. Any code I have related to this post can be found here with the same numbering: https://github.com/nmaggiulli/of-dollars-and-data

Hi,

When a pension plan offers a lump sum option and an annuity option, is it not their objective to make them as equivalent as possible? I suppose that is what this example is illustrating, although it appears that the lump sum is of slightly higher value than the annuity.

I assume most people in this type of situation would take the lump sum, and I was wondering that to balance the two options that people choose, might the goal posts move slightly in favor of promoting the annuities (provide more incentives to do so) in the years to come?

I suppose there is a battle over this field position from the wealth management firms (lump sum proponents) and the annuity firms (insurers).

Just wondering if you have any comments on this and as well as the potential of interest rate cuts rocking the pension world due to the sudden spike in commuted values of active pension plan members. And what would negative interest rates do to commuted values and how are other regions (ie. Europe) handling this type of scenario?

I understand that annuities are paid by PRIVATE insurance companies. Are annuities insured? If the annuity company goes bankrupt, what happens? How often do annuity companies go bankrupt?

Then there’s always a consideration of something called a pension max using some type of life insurance. Of course the client has to meet certain criteria health wise and be able to decide which annuity option fits the bill. I have found on a few occasions in my career 23+ years that a client would be able to have their cake and eat it too when using life insurance as a component piggy backing on top of the annuity (especially when no lump sum option is offered) At the end of the day, our clients want peace of mind and there’s some great combinations available for them.

How is this process work point to point relative to change in s&p and russel on daily basis. It open +or – and closes +or – daoly. Does it mean my annuity earn money with the Insurance company. My is 1 year point to point and also monthly point to point. When do I earned money on my annuity.

The lump sum has bigger upside, but higher variability. The guarantee provided by the annuity is worth something – it can be counted upon. I’m surprised not to see a price/value put upon that certainty.

Great post Nick. Many people unfortuantely wouldn’t do the analysis correctly. And, many people are incapable of managing money themselves or hiring a good management firm, so for them it isn’t about more vs less, it is giving them a monthly check or a stick of dynamite. I took a lump sum at coincidentally 45 years of age and one of the big deals was the optionality you speak of. I was also completely detached from an unfunded pension with my lump sum, vs waiting 10-20 years to collect a promised benefit. But, the real kicker was at 45 you have to think about survivor benefit. And, since the qualified lump sum went straight to my IRA it went in at full life-only value and the survivor benefit (and heirs!!!) is already waiting. Not even a survivor pension benefit choice gives $1 to non-spouse heirs, but the lump rolled-over does.

Very nice job of examining the options! Good writing: clear and jargon-free. It sure points out the complexities of investing for an unknown future.

We’re facing a simpler version of this problem. My spouse has just retired at 63 and she will elect an option (many choices, including SLAnnuity and lump sum) at 65.

She wants the annuity, unlike most of her fellow employees. She likes the predictable return and her family, especially the women, live long (grandmothers 87 and 92, mother still healthy at 89). So this will be the very conservative part of our portfolio.

If it were my choice I’d take the lump sum. Low discount interest rates mean lump sum would be bigger now, so kind of missing out. However, we do like the thought that we could live an okay, reduced lifestyle on just the annuity and the two Soc Sec checks.

Great article and analysis.

A great start but-

1. You provide sensitivity analysis around death but what market returns? At what stock market return will the annuity make sense.

2. Which strategy would allow the guy to delay social security claiming so he can get something like a 7% increase in benefits.

3. What is your spend down strategy? And if the market tanks?

4. What would it cost to buy this annuity in the open market as an individual- is he getting a “wholesale proce”

Interesting but maybe the best of both worlds. 17 years more to investin 501k IRA etc. So take the annuity and don’t look back. Treat it as bond fund. Annuity is ok to 250,000 depends on the state insurance on accounts.

Lovely pix and explanation of risks and consequences. Since you said you were a numbers guy….

What about a differential approach, chart the difference between annuity/lump sum as a function of death date? This would reveal the penalty and reward consequences between the two if you die before retirement or outlive the annuity. It also explicitly shows the zero point, where the two strategies have similar outcomes and how broad the “sweet spot” is where there is little or no difference between the two strategies.

To complicate matters further, use the cumulative probability function from the morbidity/mortality rate to weight the differential outcome by that death date. I’m thinking of a death weighted Net Present Value of the differential.

I’m not sure how to include the conditional actuarial probability you mentioned…if our client lives to age 62, the probability that she lives past age 87 is 46%

Thoughts?

tom luther

I was faced with this choice a couple of years before I took early retirement in 2000. I looked at what annuity the lump sum would buy at the time, and it was a great deal less than the pension payment. Since I was unmarried with no children I didn’t care about leaving an inheritance. I took a chance on inflation and took the pension. I have not regretted the choice.

The times I have looked at friends offers of lump sum buyouts for their pensions the answer has always been obvious. Decline the buyout and keep the fixed pension. This isn’t because the pension (annuity) option is inherently a better choice. It is because the buyout offers are so ridiculously awful that the the companies are clearly only looking for a way to reduce their pension obligation. A fair buyout offer would allow you to take the proceeds and go to immediateannuities.com and buy an equivalent annuity to replace the pension. I have yet to see a buyout that would replace more than two thirds of the pension that is being given up.

What happens if the insurance companies can’t meet their obligations because life expectancy is higher than they predicted among their customers or future returns of their investments are lower than they predicted?

I could never recommend straight annuities for most people. There should be a 2% inflation adjustment to reflect the Fed/Euro inflation targets. You still run the risk of those inflation targets being abandoned or the insurance company going bankrupt, but those are inescapable risks, which someone must bear and might as well be the policy holder to keep costs down. Annuities without 2% inflation adjustments are inherently complicated beasts, because monthly payout is constantly decreasing in purchasing power based on initial assumptions (certain decline, versus risk factor decline). Why even bother with analysing something so complicated?