Defined Benefit Liability formula reading, service, amount, question, official

stockjaguar

Hello all, I have a question about the DB Liability formula from the Employee Compensation reading.

the official text's formula for a DB Liability(Asset) is as follows

Defined Benefit Obligation from Balance Sheet
+ unrecognized actuarial gains (or less unrecognized losses)
– unrecognized past service cost
– value of plan assets from Balance Sheet
= Defined Benefit Liability (or if this amount is negative, DB Asset)

Intuitively, this seems backwards to me; A past service cost seems to me as something that must be paid out; it seems like it's a liability that must be expensed.

According to this formula, if I have a lot of unrecognized past service costs, my liability is decreasing, or even becoming an asset if I owe my employees a lot more than what I've funded my plan Assets with!
here's what I mean:
say my DBO is $500. I've been naughty, and not recognized my employee's services for a while, so that figure is $700. furthermore, I've only tucked away $50 into their plan assets.
According to the formula;
$500 - 700 - 50 = (-$250)
So, according to this, I would post to my balance sheet a Defined Benefit Asset of $250 (ie plan is in an overfunded position of $250).
I owe this fund a hell of a lot of money to be where I need to be relative to the benefits my employees are owed, so how is it that I have an Asset to declare?

Conversely, let's leave everything the same, but change the unrecognized past service cost to only $25.
$500 - 25 - 50 = $375
In this case, I would post a Defined Benefit Liability of $375 (Plan is underfunded by $375). wtf? I owe less money than in the other world, so why do I post a Liability in this circumstance, and an Asset in the other one?

scarecrow

if you started with a sign on the DBO - it is a liability - so it has to be negative...

so -500 -725 = -1225 (a bigger liability).

CP

MiniMe7

Here's another way to look at it

Funded Status (FV plan assets- PBO)

+/- Unrecognized deferred (gains) and loses
+ unrecognized past service cost
+/- unrecognized transition (assets) or liabilites
= Net Pension asset(liabilites) reported on balance sheet

losses are added and gains are subtracted because G/L are not recognized immediatley. This will keep the accounting equation in balance.

ryanlb

CP, I realize it was strange of me to give the formula in such a way that makes a negative value an asset, and a positive value a liability, but that's how they did it in the example. Hendriar14 has put it in terms of a positive being an asset, but he had the signs wrong on it unfortunately, which is my dilemma; it seems more right the way he's put it, but the text says otherwise. Here's the same formula to solve having a positive be an asset, and a negative be a liability:

Fair value of Plan Assets
– Unrecognized actuarial gains (or plus losses)
+ unrecognized past service cost
+ unrecognized transition (assets) or liabilites
– Defined Benefit Obligation
= Defined Benefit Asset (negative value is a liability)

So in my example, world 1 (high service cost) still gives:
50 + 700 – 500 = $250 Asset (overfunded position)

and world two
50 + 25 – 500 = -$425 Liability (underfunded position)

note that I made a mistake when I calculated world 2 in my initial post, the figure for the net underfunded position should have been a liability of 425, not 375, idk why I thought $500 - 25 - 50 = $375, it's not, it's 425 (ie liability of 425)

To see more specifically what I'm talking about, look at examples one and two on pages 199-201 of the CFAI readings (reading 24).

here are the figures for example 1:
DBO = 5485
unrec. transition liability = 50
unrec. actuarial losses = 59
unrecognised past service cost = 70
fair value of plan assets = 5798

they solve for a liability as a positive value, asset value as negative, but I'll do it so that an asset is positive here:

Fair value of Plan Assets 5798
– Unrecognized actuarial gains (or plus losses) +59
+ unrecognized past service cost +70
+ unrecognized transition (assets) or liabilites +50
– Defined Benefit Obligation -5485
= Defined Benefit Asset (negative value is a liability) =492 Asset

They are clearly showing that having more unrecognized costs/losses makes the fund's asset position greater (or liability position smaller) which seems counter intuitive to me.
If anyone understands that and can explain it, I'm all ears! for now, i'm gonna go robot on the formula!

tianxin

Simply put, the reason why it seems counter intuitive is because we're dealing with "unrealized gains and loses. If we didn't add back loses and subtract gains it would through off our accounting equation. Does this help?

thecfawannabe

Sorry brah, your formula just isn't right : /

again, here are the figure's we're working with for example 1:
DBO = 5485
unrec. transition liability = 50
unrec. actuarial losses = 59
unrecognised past service cost = 70
fair value of plan assets = 5798

here's the math using your formula:

Funded Status (FV plan assets- PBO) = 5798 - 5485 = 313

+/- Unrecognized deferred (gains) and losses – 59
+ unrecognized past service cost + 70
+/- unrecognized transition (assets) or liabilites – 50
= Net Pension asset(liabilites) reported on balance sheet = 274

That's just not right; you're supposed to get a net pension asset of 492, not 274

19831985

we can just save ourselves a lot of time by accepting the following as IFRS's formula for a Defined Benefit Asset:

Fair Value of Plan Assets
+ unrecognized actuarial losses (or less unrecognized gains)
+ unrecognized past service cost
+ unrecognized transition liabilities (or less gains)
– Defined Benefit Obligation from B.S.
= Defined Benefit Asset (negative value is a DB Liability)

If the figure is indeed an Asset, IFRS requires the company to report the lower of that item, or this one here:

Unrecognized net actuarial losses
+ unrecognized past service cost
+ PV of any economic benefits available in the form of refunds or plan reductions in future contributions to the plan (from what I understand, this = Plan Assets - DBO)
= DB Asset

IFRS further states that if the bottom thing is the lower item, you have to post the difference between this item and the upper item in the footnotes, though the text doesn't say explicitly what you post it as, only that the difference is posted there.

GAAP seems easier to me in this topic by just not allowing the unrecognized losses/gains to be deferred. the key to me understanding what is going on with this stupid formula has something to do with deferring those expenses and that somehow being an asset (I think, obviously not too sure tho).

I know what to do, I'm just not sure why it's being done.

ninja1024

Trust me it is correct, If you treat a Asset and Liability as a minus. If you subtract at liability (minus) you actually add it, not subtract. I know it seems weird, but the point is you need to add loses and liabilites and subtract gains and liabilites.

here's the math using your formula:

Funded Status (FV plan assets- PBO) = 5798 - 5485 = 313

+/- Unrecognized deferred (gains) and losses – 59
+ unrecognized past service cost + 70
+/- unrecognized transition (assets) or liabilites – 50
= Net Pension asset(liabilites) reported on balance sheet = 274

That's just not right; you're supposed to get a net pension asset of 492, not 274


Here's the correct math. 5798-5485=313 add back 59 (unrec. actuarial losses),add back 50 (unrec. transition liability), and 70 (unrecognized past service cost)= 492

CP was trying to explain the same thing above....

Re: Defined Benefit Liability formula
Posted by: cpk123 (IP Logged)
Date: January 3, 2011 06:54AM


if you started with a sign on the DBO - it is a liability - so it has to be negative...

so -500 -725 = -1225 (a bigger liability).

CP

I guess I didn't do a good job of explaining it before. The point being as long as you add back loses and subtract gains you'll get the right answer.

BelalM

ok, that's different than what you posted initially then. It's confusing because if you have a formula that is solving for a DB Liability as a positive value, and a DB asset as a negative value (as is done in the example in the text), you have to subtract unrecognized losses:

Defined Benefit Obligation from Balance Sheet
– unrecognized actuarial losses (or plus unrecognized gains)
– unrecognized past service cost
– value of plan assets from Balance Sheet
= Defined Benefit Liability (or if this amount is negative, DB Asset)

If you're doing it the way people seem most comfortable here, which is to solve for DB asset as a positive value, then it's basically just the reverse:

Fair value of Plan Assets
+ unrecognized actuarial losses (or less gains)
+ unrecognized past service cost
+ unrecognized transition (assets) or liabilites
– Defined Benefit Obligation
= Defined Benefit Asset (negative value is a liability)

The formula you just used is basically the same as this one here, because
funded status = Fair V of plan Assets - DBO, sooo

Funded Status
+ unrecognized actuarial losses (or less gains)
+ unrecognized past service cost
+ unrecognized transition (assets) or liabilites
= Defined Benefit Asset (negative value is a liability)


Still leaves me with the same dilemma of not really understanding why having more unrecognized losses and costs increases your DB Asset tho... still hazy on that.

bdavi77962

Yeah sorry. I pulled that formula from Schweser. I'm using a combo of CFAI materials and Schweser for the exam. THey sometimes write the equations different from the CFAI, but I think it's easiers to understand sometimes.

I think in Schweser they said that you have to do the opposite mathematically because the G/L are unrealized and if you didn't do it that way the whole accounting equation (A=L + OE) would be off. Let me know if you want me to post the example verbatum from the material.

I think the way I'm going to memorize it as they way of your last post.

Funded Status
+ unrecognized actuarial losses (or less gains)
+ unrecognized past service cost
+ unrecognized transition (assets) or liabilites
= Defined Benefit Asset (negative value is a liability)

Are you using any other materials besides the stuff from CFAI??