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Simple Accounting Question (Recieveable and Payables)

Wanted to make sure I am thinking about how Payables and Receivables affect cash. Could anyone comment on the below?

With receivables (for example Accounts Receivables), the offsetting balance sheet entry for a decrease in AR is an increase in cash, and the offsetting entry an increase in AR is an increase in Retained Earnings (Revenue flowing through NI statement).

For payables (for example Accounts Payable), the offseting balance sheet entry for an decrease in AP is a decrease in cash, and the offsetting entry for an increase in AP is a decrease in Retained Earnings (Expense flowing through NI statement).

With WCInv:

Decreased AR, decreases WCInv, Increases cash, Increased FCFF
Increased AR, increases WCInv, NI is overstated on a cash basis, Decreased FCFF

Decreased AP, increases WCInv, Decreases cash, Decreased FCFF
Increased AP, decreases WCInv, NI is understated on a cash basis, Increased FCFF

> an increase in AR is an increase in Retained Earnings

Not necessarily. An increase in AR comes from sources like decrease in inventory or decrease in cash or other assets. It can have all kinds of impact on Retained Earnings, not necessarily an increase.

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