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Total periodic pension cost formula

Hello, 

Can someone help me understand this formula (regarding total periodic pension cost):

In the Kaplan book, it says that total periodic pension expense is:

Employer Contribution - (ending funding status - beginning funding status)

However, in the CFAI text I found the formula for total periodic pension cost to be:

Ending funding status - employer contributions - beginning funding status.

Could anyone help how to get from the first to second formula? I get confused and maybe my algebra is off.

Thanks,

"Wiley's prep material was a huge part of my success." - Lindsey G., USA

You can’t get from the first to the second.

The CFA Institute text used to have an inconsistency: at one point they defined funded status as:

Plan liabilities – Plan assets

and at another point they defined it as:

Plan assets – Plan liabilities

The CFA Institute formula you cite uses the former definition.

Kaplan’s formula is based on the latter definition.

Use the latter formula; it makes more sense.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

In this case, how would the change in the funded status be directly proportional to the total periodic pension cost? It would make more sense that the higher the funded status, the lower the required total periodic pension cost.

keep_running wrote:
In this case, how would the change in the funded status be directly proportional to the total periodic pension cost? It would make more sense that the higher the funded status, the lower the required total periodic pension cost.

It isn’t.

You need to be careful when you use terms such as “directly proportional”.  They have a very specific meaning (if x doubles, then y doubles) that isn’t what you mean.

Suppose that the beginning plan assets have a FMV of $100 and your beginning pension liability is $80; the beginning funded status is $20 (= $100 − $80).

During the year your pension liability increases by $50, the return on your plan assets is $10, and the employer contributes $30.  The ending plan assets have a FMV of $140 (= $100 + $10 + $30) and the ending pension liability is $130 (= $80 + $50); the ending funded status is $10 (= $140 − $130).  The change in the funded status is −$10 (= $10 − $20).

The pension cost is $40 (= $50 − $10): the change in the liability less the change in the assets.

The pension cost is also $40 = $30 − (−$10): the employer contribution less the change in the funded status.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

Ok makes sense, so the total pension cost calculation is not directly proportional to ending funded status (in the usual terms) because it also depends on the increase in pension obligation during the period.

Correct.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

The pension cost is also $40 = $30 − (−$10): the employer contribution less the change in the funded status.

Based upon this definition, this would fit in line with the definition from Kaplan, the first formula that has the employer contribution less the change in the funded status from Kaplan.

Employer Contribution - (ending funding status - beginning funding status)