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write-off: revenue vs cash collected

vol2 pg383 says "write-offs will reduce the gross accounts receivable balance" -- this I understand.
"We can infer a $0.025 billion write-off from the decrease in the allowance for doubtful accounts" -- I thought allowance for doubtful accounts was used to reduce accounts receivable. Shouldn't a write-off be the case where such allowance increased, unless the write-off refers to the allowance itself? Because of this I am not getting the formula on the next age.

You set up an allowance first.

then you decrease it.

when you decrease the allowance - the flip side is a decrease due to doubtful accounts.

Accounts Receivable XXX
Doubtful Accounts (YYY)
Allowance for Doubtful accounts (YYY) <- This is the balancing entry for the line immediately above.


Balance sheet
Accounts Receivable XXX
Doubtful Accounts (YYY)
-------------------------------
Net Accounts Receivable XXX - YYY

Doubtful accounts (YYY) would be on the Asset side of the Balance sheet - shown immediately below the Accounts Receivable and then there would be a Net Accounts Receivable.

The Allowance for Doubtful accounts would show a Decrease year on year when this transaction is complete.

CP

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What's the difference between Allowance for Doubtful accounts and just Doubtful Accounts?

So write-off just means decreasing the allowance for doubtful accounts? It sounds to me like the write-off in the first sentece refers to writing off accounts receivable, but the write-off in the second sentence and in the formula on the next page refers to writing off doubtful accounts. The formula (Revenue - Cash collected = Increase in gross accounts receivable + Write offs - Increase in unearned revenue) seems to imply write off = decrease in allowance = increase in receivables reported.

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