Discount Rate - Periodic Pension Cost ( US GAAP)

[archived_user]

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!

 

[archived_user]

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.

 

[archived_user]

S2000magician wrote:
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.

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.

 

[archived_user]

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.