short answer is that it is the rule, better to memorize.
If you want to know the intuition, let's consider the accounting equation:
A = L + SE
=> change in A = change in L + change in SE
=> change in cash + change in non-cash assets = change in L + change in SE
=> change in cash = change in SE + change in L - change in non-cash assets
net income results in a change in SE, that is why we need to start from the net income.
change in L includes the change in accounts payable
change in non-cash assets includes change in accounts receivable.
Here the change can be either an increase or decrease. Regarding your question, if you have a increase in accounts payable, you can consider it as you purchased more inventory on accounts than the amount you pay to your supplier. You may somehow sell the extra amount of inventory for cash, which results in the increase in cash.
Hope this helps.
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