Normalizing Factors (EBAR)

[Below Ground]

Does anyone know where I can access the tables that list the factors used to calculate "EBAR Values"? I would like to be able to check values that the "program spits", using a table of factors. Thank you in advance.

[Jim Chad]

What software are you using?

[Below Ground]

In-house, custom program. EBAR Programming by an EA. Any idea where a table of factors might be found?

[Tom Poje]

Hey Rocky, watch me pull a rabbit out of my hat....nothin up my sleave...presto, an actuarial factor!

awhile back someone asked where the actuarial factor came from, and I thought maybe Bullwinkle really did pull it out of the air. I'm used to calculating an EBAR another way, so I set the 2 equations equal to each other to discover where this mysterious critter came from, and ended up with the following:

the facts that were given:

For the individual age 55, the actuarial factor was .035155 and the years to retirement was 10. Where did the actuarial factor come from?

This walk through will use the 10 years to retirement and solve for the actuarial factor.

Allocation / (compensation * actuarial factor) =

[(allocation * 1.085 10 * 12 /95.38) ] / compensation the 95.38 is UP 84, 8.5% at age 65

Allocation is in the numerator of both formulas, and compensation is in the denominator so those terms can be eliminated.

This leaves one with

1/actuarial factor = (1.085 10 * 12 / 95.38)

1/ actuarial factor = .284460

or actuarial factor = 3.5155% or .03515.

Therefore, actuarial factor is simply the (APR) / [(1.0I) yrs to retirement] * 12

I = Interest rate.

APR is used to determine a monthly annuity. results will vary depending on the mortality table used and interest rate.

Compensation is an annual figure, so the factor of ‘12’ must be used to keep things consistent.

[Below Ground]

Thanks for the very good explanation, Tom. Could you tell me where you got the value 95.38 for UP 84? Is there a published table of these values for respective mortality tables? Again, thanks!

[Mike Preston]

Tom, an EBAR is a long way away from what you have described. The "EBAR" is the "Equivalent Benefit Accrual Rate" and most of the time it is calculated on a basis which includes permitted disparity. It makes the formula quite lengthy.

However, if you want to determine the EBAR on the basis of "NO permitted disparity" it is simply:

The Participant's Annual Additions times the factor determined as (1 plus the 401(a)(4) Pre-Retirement Testing Interest Rate raised to the Number of Years to Testing Age) divided by the Single Life Annuity Purchase Rate determined at the 401(a)(4) Testing Age using the 401(a)(4) Post-Retirement Testing Interest Rate and the 401(a)(4) Testing Mortality Table) and then divided by 401(a)(4) Testing Compensation * 12

Let's call the above the "Above Factor".

However, if developing the EBAR on the basis of permitted disparity (almost always the right thing to do), the formula gets much more complicated. It is easier to break down the development of the EBAR into two potential formulas, only one of which is applied to any given individual:

If the 401(a)(4) Testing Compensation is less than the 401(l) Covered Compensation (you have to look this up for each participant, based on their year of birth) for this individual applicable to this testing year then:

Take the minimum of (the Above Factor times two) or (the Above Factor plus the Permitted Disparity Factor (0.65, 0.70 or .075 in most cases) applicable for this individual for this testing year)

However, if 401(a)(4) Testing Compensation is greater than the 401(k) Covered Compensation for this individual applicable to this testing year then:

Then take the minimum of:

a) (The Above Factor times 401(a)(4) Testing Compensation divided by the quantity determined as (401(a)(4) Testing Compensation in excess of Covered Compensation)

or

b) (The Above Factor times 401(a)(4) Testing Compensation) plus (Covered Compensation times the Permitted Disparity Factor applicable for this individual for this testing year) and then divide the result it by 401(a)(4) Testing Compensation.

All of this is quite simple compared to determining EBAR's and MVAR's for defined benefit plans. I'm presuming that you have no interest in a detailed description of how to do that.

[Tom Poje]

Below Ground:

I am not sure exactly where you would find the 'factors' you want, for example the 95.38 is for UP 84 at 8.5% and age 65 and would be different if you used 7.5% or a different retirement age.

the 'table values' just for ages 60 - 65 for UP 1984 are as follows:

60 0.014162

61 0.015509

62 0.017010

63 0.018685

64 0.020517

65 0.022562

and then somehow these are converted to an APR depending on interest rate and age (e.g. 95.38 at 8.5%).

probably more importantly, the tables that you are allowed to use are found in 1.401(a)(4)-12 "Standard Mortality Tables" - I believe the tables which produce the greatest extreme would be 1983 IAF and UP 1984.

as for Mike's explanantion, while it is true you can impute disparity, I'd hold the way the regs do - that would be an 'adjustment' to the accrual rate (found in 1.401(a)(4)-7), not the actual equivalent accrual rate.

and it is true, in the DB would you would also have a further adjustment for the MVAR (most valuable accrual rate), but I didn't take your question as referring to that animal.

As a side note, going one step further, the regs don't even use the term EBAR - they refer to things as 'eqivalent accrual rate' (see 1.401(a)(4)-8(b)(2), but then we would have to abbreviate them and call them 'EARs', and who would 'listen' to something like that?

[Below Ground]

I see under Standard Morality Table that I can get these tables from the Society of Actuaries. I also see I can use the table under 417(e)(3)(A)(ii)(I). Anyway, my goal was to obtain a better understanding of these concept. For me, that would be doing the computation by hand. My big problem was:

"and then somehow these are converted to an APR depending on interest rate and age (e.g. 95.38 at 8.5%)."

and

"[(allocation * 1.085 10 * 12 /95.38) ] / compensation the 95.38 is UP 84, 8.5% at age 65"

Getting that 95.38 is my problem. No matter. Both you and Mr. Preston provided excellent explanations. My thanks to both.

[Mike Preston]

Keep in mind that if everybody's current age is less than the testing age, the APR itself is irrelevant. That is, there is a constant multiplier/divisor based on the APR and if it is changed, it is changed for everybody. Hence, a shortcut you can use is to just assume that the APR is 100 for everybody. Again, as long as everybody's age is less than the testing age a test that would pass if the APR is 95.38 will also pass if the APR is 100.

[Below Ground]

I think I now understand why my very good EA friend says that the mortality table really has no impact, unless person is over NRD (testing age). Basically, it's all discount rate for period to NRD? Again, thanks to both. You are both truely gentlemen and scholars!

[Tom Poje]

actually, the mortality table makes a difference if you impute disparity even if all have the same retirement age.

1983 IAF sometimes gets someone into the rate group while up 1984 might not.

gentleman and scholar??? ha. you never met this idiot. as for Mike...I suspect he has already actuarily calculated Michigan's chances of winning the Big 10 this fall.

[Below Ground]

I must admit, that Mike did lose me a little as my understanding of imputted disparity is more in line with "I'd hold the way the regs do - that would be an 'adjustment' to the accrual rate (found in 1.401(a)(4)-7), not the actual equivalent accrual rate." My question now becomes if you are adjusting the rate, would the mortality table have an impact? Wouldn't you then apply the imputted disparity as if you were testing on a "contribution basis", and normalize this adjusted allocation?

[Mike Preston]

Got time for a quick example, Tom? Something tells me we agree, but we are just expressing it differently.

[Mike Preston]

BG, I'm confused. The methodology I described is straight from the regs. How is what you are describing different?

[Tom Poje]

Consider the following, retirement age is 65. Calculation assume interest rate of 8.5%

owner gets 20% contribution, the guy who does all the work gets 5%.

Plan Year is 2005. HCE age 62, comp =210000, contrib = 42,000

NHCE age 47, comp = 20000, contrib = 1000

APR for UP 84 is 95.38, APR for 1983 IAF is 115.38.

working through one of the calculations you get the following

42000 * (1.085^3) / 95.38 * 12 / 210000 = 3.214%

assuming folks can work through the calculation you would have:

HCE EBAR = 3.214 (UP 84) or 2.657 (1983 IAF)

NHCE EBAR=2.732(UP 84) or 2.258(1983 IAF)

in both cases, you would fail testing because the NHCE is not in the rate group.

if you 'adjust' these EBARs by imputing disparity the NHCE has comp below the covered comp level, so the NHCE gets adjusted by .65 no matter what mortality table is used.

the HCE has comp above the covered comp, so imputing disparity gets adjusted by the lesser of the C rate or the D rate.

for lack of boring you to death and to save a step or two, the D rate produces the smaller rate

cov comp for 2005, age 62 = 55464

permitted disparity factor for the HCE is .7 (since SSRA = 66)

so the adjustment is

55464 * .7 / 210000 = .185

up84 HCE = 3.214 + .185 = 3.399

up84NHCE=2.732 + .65 = 3.382

NHCE is not in the rate group

1983 IAF HCE = 2.657 + .185 = 2.842

1983 IAF NHCE=2.258 + .65 = 2.908

NHCE is in the rate group!!!!!!!!!!!!!!!!

[Below Ground]

I thought that:

For below TWB you use lesser of (A) 2 times allocation rate or (B) the allocation rate plus permitted disparity rate....

and

For above TWB you use lesser of © Allocation/(Compensation - (50% of TWB)) or (D) (Allocation+5.7%TWB)/Compensation.

You then apply this rate to Compensation to to get a dollar value which is then normalized.

Is that wrong? Is it necessary to use a "permitted disparity factor" like DBP when Testing Age is not SSRA? If so, where can you get that factor?

Sorry if these questions sound dumb. I am a "DCP Person" so DB stuff, while interesting, does create a mental block for me.

[Tom Poje]

if ee is born before 1938 the SSRA is 65

between 1938 - 1954 it is 66

and after that it is 67.

the tables of permitted disparity factors for different retirement ages are found at 1.401(l)-3(e)

I am not a DB person either.

You could impute disparity in the DC world as you indicated, but you would not then convert that value to a E-BAR.

its detertmine the e-bar first then 'adjust' for disparity. e.g. if you were doing a combo dc/db you would determine cross test the dc to determine the 'accrual', add that to the db accrual and then impute disparity.

[Below Ground]

While I am sure that you are right, I am having a hard time grasping this. Am I right in saying that:

1) If you are NOT imputting disparity you simply project forward the allocation value for testing on the benefits level.

2) If you ARE imputting disparity you simply adjust the allocation (as stated in the formula in my previous post) for testing on the contribution level.

3) If you ARE imputting disparity you can NOT simply adjust the allocation (as stated in the formula in my previous post) and project that value forward for testing on the benefits level.

4) What you DO need to do if testing on a benefits level is to first project forward the allocation and then impute disparity to that benefit using the formula used for DBP's.

Doesn't that seem "inconsistent"? While I am NOT an authority in ANY respect, it just makes sense that you would project the adjusted allocation since that is what you do if you are not imputting disparity. Afterall, if testing without imputting disparity you are using the allocation whether testing is on a benefits or contribution basis. Why can't you just adjust the allocation and project that value for a benefits basis test.

Anyway, I know that things don't have to make sense to me. I just wanted to make sure that I understand how this works, and confirm that my orginal thoughts on how this works were totally wrong.

So, is it just wrong to project forward the allocation after making the adjustment as done for the contribution basis testing as stated in #2 above. Thanks again!

Last question: Are you the co-author of a book that I frequently use on CCH? If so, great job!

[Mike Preston]

Tom, of course. The permitted disparity amount is an "addon" that doesn't vary as the mortality table/interest changes. Hence, if the other portion of the calculation is compressed (or expanded) the permitted disparity portion conversely expands or contracts (in relative terms). If the compression (or expansion) is not uniform between participants then you get different results with a change in the underlying mortality/interest.

[Below Ground]

Okay, I think I'm lost. Compression and expansion? Doesn't vary with mortality and interest changes?? Not uniform... different results??? Am I missing something here???? Mike you are way beyond me!

Even so, it almost sounds like you are agreeing with what I was saying on consistency. Wishful thinking? Probably? Especially since I can't see how you would calculate the "most valuable accrual rate" or the "normal accrual rate", or items like "employer-provided accrual plus the permitted disparity factor times covered compensation divided by average annual compensation" as needed to input disparity for a DB Plan. While I can see how you could apply the "permitted disparity factor", and I can see how they apply to a DB Plan, I really don't see how this can be applied to a DC Plan.

Again, thanks! I really appreciate the time you have allowed for my questions. Hopefully, somebody else is also benefiting from this exchange. I know I am.

[Mike Preston]

My message was primarily aimed at Tom, in confirmation of the point he raised about the testing being dependent on the mortality table if, and only if, permitted disparity is being imputed.

I haven't the time today to review your latest exchange with Tom or to address the confusion. April 15th is fast approaching!

If you get no resolution on this by then, bump it.

[Tom Poje]

sorry I haven't been able to respond. was up in Pittsburgh to give a talk at an ABC meeting on cross testing. And then since the people who invited me up use Relius I also did an in house session on Crystal reports. hopefully I didn't bore either group too much - the Otis Redding song "Sittin in a Four-o-one Kay" seemed to go over well.

maybe this will help.

you allocate a profit sharing contribution. for whatever reason you need to run the nondiscrim test.

you can test on an allocation basis, and therefore determine an allocation rate. lets suppose the plan was 5.7% integrated (at 100% the Taxable wage base) If you test on an allocation basis you would fail. But if you impute disparity all the e-bars would be the same. try it. it will always work given those allocation conditions. it has to. the regs were, as far as I can tell written that way. note: imputing disparity is simply an adjustment to the allocation rate.

now, you could have cross tested (or converted the allocation to an accrual.) divide by the comp and you have an E-BAR. same as with the allocation, you can now adjust by imputing disparity - but since you are using accruals you use the DB adjsutment rather than allocation adjsutments. in other words, since you are 'pretending' the dc plan is really a db plan, use the db rules.

Below Ground: well, it is true I am responsible for some (but not all) of the stuff from the Coverage/Nondiscrim Answer Book. I'm a big one on examples, and probably did submit a greater portion of the book dealing with cross testing.

attached is a copy of the IRS notes pertaining with nondiscrim. Based onm its title, it is primarily intended to be used for Demo 6. 106 pages worth!. they walk through examples - the DB with disparity is page 103 or something like that. could have simply posted the link, but I guess maybe this is easier for most people.

[Below Ground]

I can see I have a good deal of reading to do.

I really find it odd that since you are testing allocations, why you can't test allocations adjusted for imputted disparity. That is, why not test contribution values that have been projected forward after they have been adjusted for imputted disparity. It just seems that you would continue forward with that logic for testing on a benefits basis. Am I making sense?

I think that projecting forward the "imputted allocations" would actually have less "allowed discrimination". While I can't prove that right now, I suspect that only imputting disparity under a DB Basis results in higher "allowed discrimination. Now I will need to check that out.

Regardless, if I'm wrong, I'm wrong. It won't be the first or the last time. I will read that big beast of a file, and let you know what I think.

Thanks for your patience and helpful replies. Thanks for the PDF File. And, thanks for your contributions to an excellent resourse in the Nondiscrimination Answer Book.

[Tom Poje]

well, look at it this way.

an ee receives a 5% contribution (e.g. $1000)

you impute disparity, which, since the ee is less than the TWB means his allocation w disparity is 2*5% or 10%. if you then were to cross test, you would still have the doubling effect.

on the otherhand if you cross test first, then you are only going to tack on an extra .65% at the most, certainly much less than the doubing effect.

hang in there. wait til you have to do db/dc combos.

[Below Ground]

Having had a chance to digest the Demo #6 PDF provided in Tom's April 14th post (Thanks Tom!), I find myself still somewhat confused. On page 10-53, the "Rate D Formula" for imputted disparity is:

(Accrual + (Factor x Covered Comp)) over Compensation.

In Tom's post #15, the factor used is ".7". Why isn't this value .007 as used in the example on page 10.53? (That example is (1,802 + (.0065 x 69012)) over 106,000; or 2.12%.) Why is the ".00" left out?

Also, is the "accrual" in the book's formula the "annual equivalent retirement benefit" provided by the $42,000 in Tom's post. I think that this value would be $6,749.40 (210,000 *.03214).

If followed through, you would get the same 3.4% that Tom got, but I am having trouble understanding "why". Also, the book's formula seems to be one simple step. Why not use that approach?

As stated in earlier posts, I am NOT trying to say anyone is wrong. To the contrary, I am trying to understand a concept that has previously escaped me. Thanks for your insights!

[Tom Poje]

Below Ground-

sometimes I get sloppy in my hurry posting calculations. the '.7' is really .7% which of course is equal to .007.

(sorry, at the moment I've got enough other projects on my desk, before I look at the pdf file example)

[Below Ground]

Understand the "projects on the desk". Thank you again for your help.

[AndyH]

Methinks that if Tom didn't have so many singing trips (e.g. Pittsburg) and wasn't such an incredible singer/songwriter then the desk might look better and he might elevate Below Ground even quicker. .......that and Mike might go easier on him .......

[Below Ground]

And he sings too? Now you are just messing with my head. Of course, Pittsburgh is a very nice city. Too bad about the Red Wings.

[Tom Poje]

Pittsburgh was a 'side trip' - the ABC group there wanted a talk on cross testing, so they grabbed me.

but since I am originally from Michigan, the hockey results were perfectly fine with me.

Andy way overrates any abilities I may have in regards to pension songs.

at the moment I seem to be struggling with some ideas for

Jimmy Buffet, "Jamaica Farewell"

Along the way I will squander my pay

For that fun that comes daily on the mountain top

I'll take expensive trips on sailing ships

I'll keep spendin' and spendin' and never stop

Now its sad to say

I'm in a four-oh-one K

I'm not deferring or puttin' away

My heart will be down

When 65 comes around

I'l have so little cash left to spend in town

(maybe someday I can actually finish such nonsense. at the moment I understand that 'Elvis' may come out of hiding and make the fall conference)

[Below Ground]

One can only hope.

[rcline46]

I believe Harry Belafonte sang that song long before dear Jimmie. Along with the Kingston Trio and quite possible the Beach Boys. Jimmy was a late comer to the tune.

[Mike Preston]

Pittsburgh was a 'side trip' - the ABC group there wanted a talk on cross testing, so they grabbed me.

but since I am originally from Michigan, the hockey results were perfectly fine with me.

Andy way overrates any abilities I may have in regards to pension songs.

at the moment I seem to be struggling with some ideas for

Jimmy Buffet, "Jamaica Farewell"

Along the way I will squander my pay

For that fun that comes daily on the mountain top

I'll take expensive trips on sailing ships

I'll keep spendin' and spendin' and never stop

Now its sad to say

I'm in a four-oh-one K

I'm not deferring or puttin' away

My heart will be down

When 65 comes around

I'l have so little cash left to spend in town

(maybe someday I can actually finish such nonsense. at the moment I understand that 'Elvis' may come out of hiding and make the fall conference)

I need a wav file of the above and I need it NOW! Hop to, Tom.

[Tom Poje]

"I've never written a song in my life. It's all a big hoax." - Elvis, but I plan on being at the ASPPA Conference.

[Below Ground]

Oh my!