Question

A firm has sales of \(3 million, and 10 percent of the sales are for cash. The year-end accounts receivable balance is \)285,000. What is the average collection period? (Use a 360-day year.)

Short answer

The average collection period of the firm is 38 days.

Step-by-step solution

Net credit sales 

$\begin{array}{rcl}\mathrm{Net}\mathrm{credit}\mathrm{sales}& =& \mathrm{Total}\mathrm{sales}\times \left(1-\mathrm{Cash}\mathrm{sales}\right)\\ & =& \$3,000,000\times \left(1-0.10\right)\\ & =& \$2,700,000\end{array}$

Average receivable turnover ratio

$\begin{array}{rcl}\mathrm{Average}\mathrm{receivable}\mathrm{turnover}\mathrm{ratio}& =& \frac{\mathrm{Net}\mathrm{credit}\mathrm{sales}}{\mathrm{Average}\mathrm{accounts}\mathrm{receivable}}\\ & =& \frac{\$2,700,000}{\$285,000}\\ & =& 9.47\end{array}$

Average collection period

$\begin{array}{rcl}\mathrm{Average}\mathrm{collection}\mathrm{period}& =& \frac{360\mathrm{days}}{\mathrm{Average}\mathrm{receivable}\mathrm{turnover}\mathrm{ratio}}\\ & =& \frac{360}{9.47}\\ & =& 38\mathrm{days}\end{array}$