Discount Rate - Periodic Pension Cost ( US GAAP)

CFA Level II
#1

Hi,

Statement qouted from the CFA Text:

[content removed by moderator]

I find this statement from the CFA text to be opposite of what I thought a lower discount rate would do.

If you calculate periodic pension cost (US GAAP) on the Income Statement like this:

Service cost

+ Interest Cost ( Discount rate * PBO beginning of year)

  • Expected Return on plan Assets.

= Periodic Pension Cost

To me it looks like a lower discount rate would reduce the Interest Cost and not Increase it?

Thanks for the help!

#2

The point is that a lower discount rate will increase the PBO. A lot.

For example, if your obligation in 20 years is expected to be $10,000,000 and you’re comparing annual discount rates of 5% and 8%. At 5% the PBO is $10,000,000 / 1.05^20 = $3,768,895; this year’s interest cost is $3,768,895 × 5% = $188,445. At 8% the PBO is $10,000,000 / 1.08^20 = $2,145,482; this year’s interest cost is $2,145,482 × 8% = $171,639.

The interest cost is higher when the discount rate is lower.

#3

Thank you S2000magician. That makes sense.

Increase in Discount rate : PBO down

Decrease in Discount rate: PBO up

However the effect on Interest cost must be a function of both the discount rate and the change in PBO. Right?

I have included an example here comparing discount rates of 6 and 7% where the IR cost is higher under 7% which is inconsistent with the statement " The interest cost is higher when the discount rate is lower". Do you care to take a look at my example? I would appreciate your thoughts on this.

Edit: I was not able to paste my full table. But the key points are -

Opening PBO under a discount rate of 6%: 77394

Ir cost of 6%: 4643

Opening PBO under a discount rate of 7%: 68 205

Ir cost: 4774.

This is from an example in the CFA text.

#4

Obviously if the discount rate is higher the interest cost must be higher eventually:

  • To get from a present value of $3,768,895 to a future value of $10,000,000 in 20 years requires an average annual interest charge of $311,555
  • To get from a present value of $2,145,482 to a future value of $10,000,000 in 20 years requires an average annual interest charge of $392,726

Therefore, eventually, the 8% discount rate will have to generate higher annual interest costs than the 5% discount rate.

You should create a table in Excel: calculate the present value of a $10,000,000 pension obligation 20 years from today under various discount rates, then compute the interest charge each year for 20 years and compare those annual interest charges. It’ll be enlightening.