Our professor posted this practice exam question, and I'm having trouble understanding why the answer key is correct:

The balance in Accounts Receivable was $650,000 at the beginning of the year and $350,000 at the end of the year. Sales for the year totaled $4,100,000. How much cash was collected from customers during the period?

A) $4,400,000

B) $4,000,000

C) $3,750,000

D) $4,800,000

E) None of the above.

If sales totaled $4.1m, then that figured is composed of the following:

  • $X of direct cash debits

  • $Y of accounts receivable

But my professor said we can just assume "sales for the year" is referring to accounts receivable, put the $4.1m on the debit side of the Accounts Receivable T-chart, and then solve that way (getting A, $4.4m). I don't quite understand why this works, as it seems to overlook key information about cash transactions.

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    I'm voting to close this question as off-topic because Accounting homework questions appear off-topic based on money.stackexchange.com/help/on-topic – RonJohn Feb 2 '18 at 17:47
  • To be fair, I classified it as homework, but it's an in-class practice exam that our instructor went over with us during lectures. It's just I didn't understand her explanation very well. – AleksandrH Feb 2 '18 at 22:11

We make $4.1M in sales during the year, all of it goes to AR, plus we had a beginning AR balance of $650k. If no cash was collected, our AR balance at year end would be $4.75M. We know that our AR balance is $350k at year end, so we know that we must have collected the difference in cash over the year, $4.4M.

Alternatively, if none of the $4.1M went to AR, but was all paid cash, then you collected $4.1M in cash. Add the difference between beginning and ending AR balances, $300k, for $4.4M cash collected.

The split between cash sales an AR sales is immaterial.

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    I see, I think I understand now. – AleksandrH Feb 2 '18 at 17:26
  • Hey! It's me again. I found a way to solve this mathematically, and I figured I'd mention it here. Let CashCollected = DirectCashReceipts + CollectionsFromAR. [CC = DCR + CAR]. Let DirectCashReceipts = $4.1m - DepositsToAR. [DCR = $4.1m-DAR]. And let CollectionsFromAR = $650k+DepositsToAR-$350k = $300k+DepositsToAr. [CAR = $300k+DAR]. Then CC = ($4.1m - DAR) + (DAR + $300k) = $4.4m. So you're right, the split is immaterial because DAR gets canceled out. – AleksandrH Feb 5 '18 at 12:01

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