Shortfall Base Q

[VeryOldMan]

Can someone comment on the attached shortfall summary. It seems that my outstanding balance in 2018 is less than the sum of the annual charges. Don't see where my calc went wrong!

2018-SHORTFALLBASE Sheet1.pdf

[C. B. Zeller]

Looks fine to me. There's no requirement that the sum of the installments be less than the sum of the PV of the outstanding bases for any given year.

[VeryOldMan]

Isn't that mathematically unsound?

 

[C. B. Zeller]

I don't think so. You are amortizing 3 separate bases. It just so happens that you have one large positive base and 2 smaller negative ones. The positive base has a smaller duration (in the Macaulay sense) than the negative bases, so it contributes less to the outstanding balance, but a larger payment so it contributes more to the current installment. It is weird but, as you've shown, clearly not impossible.

Editing my reply to add that the sum of the outstanding bases, although it is required to be reported on the Schedule SB, is not a number with any real actuarial significance. You can't use it to determine anything useful on its own, which is presumably why you are required to attach the schedule of bases to the SB.

[VeryOldMan]

Thanks for your comments--makes sense to me.