Question

A firm ended the year with an average collection period of 20 days. The firm's credit sales were $50 million. What is the firm's year-end balance in accounts receivable?

A) $1.46 million
B) $2.50 million
C) $2.74 million
D) $4.00 million

Answer 1

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**.