Potential Mistake in FSA Notes

I am looking at a summary of how changes in pension assumptions impact the balance sheet and income statement. A higher discount rate means a lower obligation and lower service costs. However, wouldn’t it mean higher interest costs? Is there a mistake in this table?

It depends on the amount of time over which you’re discounting. If the time’s long enough, then a higher discount rate will lead to a lower interest cost; if not, then the interest cost will be higher.

Yeah, that does not make any sense to me. If the discount rate is higher, the specific length of time seems to make no difference. Keep in mind, from Investopedia, interest costs refer to “The annual interest accumulated on the unpaid balance of the PBO as an employee’s service time increases.” If we are discounting at a higher rate, that seems to imply that the unpaid balance will grow at a correspondingly higher rate.

It also implies that the beginning value is smaller. Competing conditions.

Time to whip out Excel.

Say you have $1,000,000 due in the future, and you change the discount rate from 5% to 6%.

First, figure out the present value under each discount rate if the $1,000,000 is due in 25 years.

Then, create an amortization table for each discount rate: beginning value, interest, ending value. The beginning value in year 1 is the PV you calculated. The ending value in year 1 is the beginning value plus the interest. The beginning value in year 2 is the ending value in year 1. If you’ve done it correctly, the ending value in year 25 should be $1,000,000.

Compare the interest cost each year under a 5% discount to the interest cost that same year under a 6% discount.

Please report your findings.

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I see. That is clearer, so the outcome is ambiguous.