why do we have to reclassify shortfall in total periodic pension cost from CFO to CFF?

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Because it is viewed as borrowing the money from the plan; money borrowed is CFF.

this is an analyst adjustment that is made. You (as an analyst) are saying that the money that the Company had contractually agreed to pay (the pension cost), it should have paid. If the company did not - the extra money was used for some other “financing” activity. It did not disappear into thin air.

so is it always an requirement that the firm have the necessary cash on cash to meet its total periodic pension cost?

It’s not a requirement.

But if their contribution falls short any year, they should expect analysts to reduce their CFO and increase their CFF.