Hello there. I am trying to figure out one piece of a pension calculation. It is regarding a Deferred Lump Sum Factor using Pre-PPA Assumptions. To calculate this factor it uses the mortality and interest discount from age 65 to 36.9167 using 1.36% discount rates and the GAR94 table (unisex) here: https://www.irs.gov/pub/irs-drop/rr-01-62.pdf. The factor comes out to 125.39772. Can you please help me understand how this might be calculated in some detail? Thank you!
Welcome. I don’t whether I’ll work on this, but it might help with more complete info. Especially there is apparently a typo.
[quote] To calculate this factor it uses the mortality and interest discount from age 65 to 36.9167 using 1.36% discount rates and the GAR94 table (unisex) here: https://www.irs.gov/pub/irs-drop/rr-01-62.pdf.
[/quote]
Maybe you mean 66.6197, or maybe 73.9167 or maybe even more of a typo.
It would also help to have a more complete description of the factor and the benefit. Presumably the lump sum at the end of the deferral period is the factor times something, but what is the something?
Also, do you elect the benefit age 65? What happens if he dies before the end of the deferral period?
Finally, it is far easier to reverse-engineer factors if you know several factors. E.g if you also gave factors for deferral until 66, 67, 68, 69, 70. (Or even some of them if not all).
Again, I may not get a chance to work on ir or may not be able to solve it, but that info could help anyone who wants to try
Thank you for your reply and my apologies for not providing enough information. Let me try to paint a more complete picture of what I’m dealing with.
This Lump Sum Factor is used to calculate an immediate lump sum payout if someone leaves the company before age 65. I’m assuming because it would be early “retirement” you can’t choose to calculate with a deferral past 65, but I could be wrong. The person is age 36.9167 as of the pension analysis.
The pension calculation creates an estimated deferred balance at Age 65 based on a formula encompassing things like years of service and last four years average salary. Let’s assume this person has a current pension balance of $100k at age 36.9167 and this “deferred to age 65 balance” is $400k.
Next, the calculation uses an “Age 65 Annuity Factor” of 200.00052 to calculate an annuity deferred to age 65, which in this example would be $1999.99 / mo. (400k/200.00052)
Next, the calculation uses a “Deferred Lump Sum Factor“ of 125.39772 to get the immediate lump sum payout, which in this example would be $250,794.79. (1999.99*125.39772)
The one thing I can’t figure out is how this “Deferred Lump Sum Factor“ of 125.39772 is calculated. (FYI, I do understand how the Age 65 Annuity Factor is calculated).
Does this answer your questions or help?
Thank you!
Ah. Now I understand the situation much better.
One minor point, that perhaps other readers would have grasped immediately. I interpreted “factors” as something you multiply by, and yours are things you divide by. Now I see that clearly.
I also totally misunderstood the setup. I thought the person, upon reaching 65, could start a pension, or could (perhaps) take a lump sum right away, or could (what you were interested in) elect to take a lump sum to be received at a later date. In all situations involving annuities and lum sums to be paid, it is important to consider when the election is made, since otherwise those in poor health (whose future payments on average would be shorter) will take the lump sum.
As to the actual case, I now think this is just a calculation of value of some sort. This is NOT an amount the person could take in cash now, is it?
I’m traveling for the next week and am unlikely to do anything on this until back home. Perhaps someone else can help.
I’m glad it makes more sense :). And just to be clear when you say “or could (what you were interested in) elect to take a lump sum to be received at a later date", if I’m understanding you then this is not correct. This lump sum would not be received at a later date. This calculation is if someone were to take a lump sum immediately, as in when they are age 36.9167, their present age, as of this calculation. It would be as if they left the company now they would receive an “immediate” lump sum pension payout soon after leaving.
So then, yes it would be the amount the person would take in cash now. I assume it would probably be rolled into something like a Traditional 401k or IRA to avoid taxes, but that would be left up to the individual what to do with it. Yes I believe you are correct, I think this probably is just simply a calculation of value of some sort.
I am not in any hurry so if you are able to get back to this sometime later I would greatly appreciate it! If not, if someone else is able to help that would be great too!
What is this being used for? Actuaries don’t give actuarial advice without knowing how their work will be used, and also not for free. If this is being used for financial planning or in a divorce, you’ll need to work with your planner or lawyer, for example.
It’s not a simple factor if you’re not an actuary. It is the annuity factor using that mortality table assuming no payments from current age until 65, discounted to today at the interest rate you stated.
Additionally, I haven’t done the precise math, but that’s an extremely high deferred annuity factor for that age, even at that interest rate. The only way I can get in the ballpark is by assuming no mortality before 65, but I still don’t match precisely. There is missing information here, and would need clarification from the plan administrator or plan actuary on methodology for determining the deferred lump sum factor.
You can use this public calculator to get pretty close to the 200 value at age 65. Anything beyond that I’m not comfortable opining on.
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I share NerdAlert’s concern about the purpose of the calculation.
I also observe that if this lump sum is a distribution from the plan, as a cash payment or a rollover, the amount will depend on the plan provisions, including for example vesting.
You mentioned the last 4 year’s salary. Depending on purpose, that could mean 4 year’s ending on the as of date of the calculation, salaries which are known, or 4 year’s ending at normal retirement date. If this involves an actual distribution from a plan, using projected salaries seems unlikely, but again plan provisions would govern.
And as NerdAlert said, for most purposes mortality before age 65 would be considered. For an actual distribution from a pla, plan provisions would govern.
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I can reassure you that this “200” is the correct annuity factor, even though it seems very high. I am looking at a detailed pension calculation and on this step of the calculation basically it says “Age 65 Annuity Factor using GAR94U tables and unisex rates (50% male / 50% female) and 1.36%): 200.00052” However, this is not the factor I am looking for. It is the Deferred Lump Factor which is 125.39772.
SteveWhite: the 4 years salary is using only the avg salary as of the date of the calculation, not some assumed future increased salary.
Maybe the following will help explain things further. If I had to sum up in brief detail how the calculation works it is as follows:
- [Current pension balance] = [Current years of service] * [Last four years average salary as of pension calculation] / 10
- [Pension balance deferred to Age 65] = [Assumed years of service at 65] * [Last four years average salary as of pension calculation] / 10
- [Annuity deferred to Age 65] = [Pension balance deferred to Age 65] / [Age 65 annuity factor]
- [Immediate Lump sum payment at current age (pre-PPA assumptions)] = [Annuity deferred to Age 65] * [Deferred Lump Sum Factor]
- Immediate lump sum payout pre-retirement age = MAXIMUM of ( [Immediate Lump sum payment at current age (pre-PPA assumptions)] OR [Current pension balance] )
This is being used to create an estimator that I can use to calculate future lump-sum payouts from our company given things like projected 30 year treasury rates, projected three segment rates, salary, years of service, etc. I have been working with our pension department to try to gather these kinds of details so that I can provide something to people in my group who are on this specific pension plan.
This last factor (Deferred Lump Sum Factor) I have been asking for here is the last step I believe I need before I can have a complete and useful calculator and our pension department said they cannot provide this. Once I have this I should be good to go and that is why I came here asking for help :). Even if I was to be able to calculate a factor that was pretty close using a more simplified method I would be happy with that. I don’t necessarily need something ultra-precise. Even though I am not an actuary, I do fully understand the actuarial calculations used to calculate the Age 65 annuity factor, and can personally calculate it precisely. I do understand though that for a non-actuary it may be uniquely difficult to understand calculations for this Deferred Lump Sum Factor (though I believe I could understand them :)).
I do understand if you folks here are not interested in helping me out with this given your role as a actuary. If this is the case, would you at least be willing to provide the options on the afc.soa.org Calculator you would suggest using to get a number close to 125.39772? Maybe since I’m ok getting pretty close this calculator would serve my purposes quite well. If you are not comfortable providing those I understand that too and I will promptly go away and not bother you all anymore :). Either way, I appreciate the help that you all have been able to provide!
I am not a pension actuary, though I know some about pension actuarial connections. Nor is pensions NerdAlert’s primary practice area. She may be more familiar with pensions than I am. We both are in the US.
You seem to know one, and only one, deferred lump sum factor, and are trying to understand how it was calculated. Who calculated it, and how did you find it out?
This plan seems unusual to me. It appears to accumulate funds to a balance at age 65, then convert the balance to an annuity if an annuity is wanted. Am I interpreting the plan correctly?
If yes, then in the US such plans normally involve an interest rate in the accumulation process. Yours doesn’t seem to.
I am aware of another deferred lump sum factor of 49.01928 that uses the same calculation method. It is for someone age 40.33 using GAR94U unisex rates, this time with a rate of 4.28%. This deferred lump sum factors (125.39772 and 49.01928) were calculated at different times (ages as of both calculations were about 3.5 years apart). The interest rates (4.28 and 1.36) are different due to the 30-year treasury rate being different at those times.
Thus, one set of assumptions is age 36.9167, GAR94U unisex, 1.36%. The other set of assumptions is age 40.33, GAR94U unisex, 4.28%. Using the same calculation method should provide deferred lump sum factors of 125.39772 and 49.01928 respectively.
The pension department at my company will provide what they consider a “detailed” pension calculation upon request, and so that is who calculated it. It will list calculation steps along the way, including a number used for the different factors (such as deferred lump sum) but will not provide much as to how the different factors are determined. The only details they will tell you with regards to factors is what mortality table is being used and what interest rates are used.
You say “in the US such plans normally involve an interest rate in the accumulation process.” I can verify that the calculation steps I provided in the previous post are indeed how things are being calculated. However, I did intentionally leave out some of the earlier steps of the pension calculation because they don’t appear to typically factor into the final lump sum. Maybe this is what you are referring to. I will explain that here next:
The [Pension balance deferred to Age 65] I refer to above is determined by taking the minimum of two different calculations:
-
- [Assumed years of service at age 65] * [Last four years average salary as of pension calculation] / 10
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- [Current years of service] * [Last four years average salary as of pension calculation] * [Annuity Factor] / 10. The Annuity Factor here always assumes 5% (per our pension department this never changes) and does assume no pre-retirement mortality. For someone age 36.9167 this annuity factor is about 3.9703 and for someone age 40.33 it’s about 3.3460. I essentially understand how to calculate this annuity factor.
What I’ve seen so far with a couple of different calculations is #1 is usually lower than #2 and since the “Pension balance deferred to Age 65” takes the minimum of the two then #1 is the number that is used. I left this out intentionally to keep things simple because I’m not sure how relevant #2 will usually be in the final analysis. But if it does, my calculator will take that into account.
It will be over a week before I am able to try any calculations. Unfortunately, you apparently can only be sure that the age and 30-year treasury were different. Can you even be positive those were both used? (It does seem likely both were used.). You probably know years of service for both, and know that years of service would affect the deferred pension amount. You seem to think years of service would not affect the deferred lump sum factor. Maybe not, but maybe. I already pointed out that many plans would have vesting provision, lowering payouts on some early retirements. Could this plan have a vesting provision? If it has one, isn’t it likely, given the calculations as you have described them, that it’s part of the deferred lump sum factor?
Even for something as straightforward as the 30-year treasury, are you positive that calculations use it as the interest rate for taking present values? For example, if buried within the calculation they use 90% of the 30-year treasury, didn’t they still base the factor on the 30-year treasury?
ETA: or 110% of the 30-year treasury, which if used during the deferral period might produce a lower lump sum.
It’s very hard to understand the motivation for these very different formulas. Was there an earlier plan and a current plan, and some commitment that the current plan would always provide as much as the old?
If so, it would be nice to know how the pension amount and potential lump sum are calculated at actual retirement. (Also nice to know even if there was not an earlier plan). I was assuming just like the deferred calculation, but with age 65, but I’m not sure you said that.
And, for your actual deferred cases, are you sure the deferred lump sum factor would be calculated the same way, whichever of 1 and 2 was used?
No problem SteveWhite, I appreciate any help you are able to provide and I am not in any hurry. Thank you for all that you have done so far! I have put your statements or questions in bold with my responses following:
Can you even be positive those were both used? Yes, I do know that both scenarios used different 30 year treasury rates. I also know that the ages I provided for both scenarios are accurate (though it’s possible that maybe it’s off by a month due to rounding, but any rounding shouldn’t affect the factor calculation very much).
You seem to think years of service would not affect the deferred lump sum factor. I cannot say I know this for a fact but based on how they do other calculations, and some other information, I am pretty confident that it only looks at the time between current age and age 65. It appears like it probably uses survivability probability between current age and age 65 as well as a discount factor between those two ages, but I don’t know this for sure.
Could this plan have a vesting provision? Both of these scenarios assume full vesting on the pension. I know that the full vesting is pretty quick, though I’m not sure how quick, but I believe it fully vests after one year.
the 30-year treasury, are you positive that calculations use it as the interest rate for taking present values? Yes, I was told by our pension department that the Age 65 annuity factor uses the 30 year treasury rate. I’m not sure if they use some kind of factor applied to the 30 year treasury rate (such as 90%, 110%, etc.). I suspect not (see my modified calculation method below)
Was there an earlier plan and a current plan, and some commitment that the current plan would always provide as much as the old? I am not sure what dictates that these two calculations are done. The pension department told me by law that they have to take the highest when comparing. I know that the pension plans have changed throughout the company over time. It’s possible it’s because it must provide as much as the old plan. I am confident however that these two comparisons are being done and that the max is required because it does specify on this calculation step that it uses the maximum of these two values.
And, for your actual deferred cases, are you sure the deferred lump sum factor would be calculated the same way, whichever of 1 and 2 was used? Yes, I am confident of this.
In addition to the answers to your questions above, there is one thing that may also help with all of this discussion. That is, I tried to create my own calculation that in essence seems like it might take into account both factors at the same time (annuity factor and deferred lump sum factor) without having to actually calculate both of these factors. I wonder if instead of taking a future lump sum and calculating an annuity and then converting that annuity back into a present lump sum, if you can essentially “bypass” the deferred annuity calculation step and combine both into a single step to go from future lump sum to present lump sum, if that makes sense.
Doing this actually comes up with a very close lump sum number. But…I’m not sure if I just got “lucky” with both of my scenarios. This is something that I came up with by doing some research on this topic, but I’m not sure if it’s valid (though it does seem reasonable and perhaps could be).
Here is how I’m doing it (you’ll see it looks very similar to the actual calculation steps above), the bolded part is my step that replaces the previous two steps :
- [Current pension balance] = [Current years of service] * [Last four years average salary as of pension calculation] / 10
- [Pension balance deferred to Age 65] = [Assumed years of service at 65] * [Last four years average salary as of pension calculation] / 10
- [Immediate Lump sum payment at current age (pre-PPA assumptions)] = [Pension balance deferred to Age 65] * [Interest only discount ] * [Survival probability to age 65 ]
- Immediate lump sum payout pre-retirement age = MAXIMUM of ( [Immediate Lump sum payment at current age (pre-PPA assumptions)] OR [Current pension balance] )
- Where, [Interest only discount ] = (1+30yrRate)^(-(65-age@calculation))
- Where, [Survival probability to age 65 ] = probability of surviving between [age of calculation and age 65] using the GAR94U table.
Basically, it takes these two steps:
- [Annuity deferred to Age 65] = [Pension balance deferred to Age 65] / [Age 65 annuity factor]
- [Immediate Lump sum payment at current age (pre-PPA assumptions)] = [Annuity deferred to Age 65] * [Deferred Lump Sum Factor]
and turns it into a single step, in effect “bypassing” the annuity calculation (and thus also bypassing the need to calculate a deferred lump sum factor):
- [Immediate Lump sum payment at current age (pre-PPA assumptions)] = [Pension balance deferred to Age 65] * [Interest only discount ] * [Survival probability to age 65 ]
When I compare the [Immediate Lump sum payment at current age (pre-PPA assumptions)] values from the actual pension calculation to my modified calculation for both of my scenarios, one is within 0.23% of the actual provided calculation and the other is within 0.03%. Thus, I’m wondering if this is a valid way to do the calculation?
If this is a valid way to do it then I wouldn’t necessarily need to calculate a deferred lump sum factor. When I look at the logic behind doing it this way, it at least make some sense to do it this way, especially when the values are so close, but I’m not an actuary :). And again, I don’t know if I’m just getting “lucky” with both of my scenarios. Though, it’s quite interesting to get that close using different assumptions in terms of salary, age, and quite different 30-year rates, and when the associated factors the pension department provides are so different, it seems like it very well could actually be valid.
Part or even most of my question was motivated by the possibility of bypassing the calculation of the deferred benefit. I thought that should be valid. If you are coming so close it probably is. On the other hand, it is very dangerous to draw conclusions based on only two data points. Even more so than usual (for me) since some of the calculations seem odd, especially that max of (1 and 2), and that 1 doesn’t use an interest rate. Also, full vesting after 1 year could be right, but I would certainly have to be sure of it before relying on it.
Even if you are sure your two known calculations are based on lives that are fully vested, you are planning to do calculations for other employees, you would need to consider their vesting situation, especially if prior employment is over one year but less than that in your two life sample.
You seem to be close to matching both sample lives, but not off by the same amount.on both. Those calculations are not for an integral number of deferral years. You have a mortality table for integral ages. There is no single method of calculating values at non-integral ages. They are very close, probably smaller than the differences you are getting (though I haven’t looked at your mortality table), but the could contribute something to the difference.