To calculate the firm's year-end balance in accounts receivable, we can use the formula for the average collection period (ACP):
\[ \text{ACP} = \frac{\text{Accounts Receivable}}{\text{Credit Sales per Day}} \]
We need to first determine the Credit Sales per Day. Given that the total credit sales for the year are $50 million, we can calculate the Credit Sales per Day as follows:
\[ \text{Credit Sales per Day} = \frac{\text{Total Credit Sales}}{365} \]
Substituting the value:
\[ \text{Credit Sales per Day} = \frac{50,000,000}{365} \approx 136,986.30 \]
Now, we can use the Average Collection Period to solve for Accounts Receivable:
\[ \text{ACP} = \frac{\text{Accounts Receivable}}{\text{Credit Sales per Day}} \] \[ 20 = \frac{\text{Accounts Receivable}}{136,986.30} \]
Now, we can solve for Accounts Receivable:
\[ \text{Accounts Receivable} = 20 \times 136,986.30 \approx 2,739,726 \]
Rounding to two decimal places:
\[ \text{Accounts Receivable} \approx 2.74 \text{ million} \]
Thus, the firm's year-end balance in accounts receivable is approximately $2.74 million, which corresponds to option C.
The final answer is C) $2.74 million.
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