Operating Cycle LIFESAVER!

QUESTION

LIFESAVER for work shown!Linear Technology had sales (all on credit) of $36 million and a gross profit margin of 30% last year. If Linear Technologys inventory averaged $3.9 million, and its accounts receivable were $5.0 million, what was the length of its operating cycle?
This ratio indicates the time between acquisition of inventory and the realization of cash from sales of inventory. For most companies, the operating cycle is less than one year, but in some industries it is longer. The formula for calculating the length of operating cycle is Operating cycle = Accounts receivable turnover in days Inventory turnover in days Accounts receivable turnover in days = 365 / Receivables turnover But Receivables turnover = Net sales / Accounts receivables Accounts receivable turnover in days = (365 * Accounts receivables)/ Net sales = (365 * $5,000,000) / $36,000,000 = 365 * 0.139 = 50.735 days Therefore, Accounts receivable turnover in days is approximately 51 days Now, we have to calculate inventory turnover in days: Inventory turnover in days = 365 / Inventory turnover ratio But Inventory turnover ratio = Cost of goods sold / Inventory To know the value of cost of goods sold, we need to find out the value of Gross profit. From, Gross profit ratio =

Gross profit / Net sales 0.30 = Gross profit / $36,000,000 GP = $10,800,000 Therefore the gross profit is $10,800,000 But we know that Sales Cost of goods sold = Gross profit $36,000,000 $10,800,000 = Cost of goods sold $25,200,000 = Cost of goods sold Therefore, the value of cost of goods sold is $25,200,000 Inventory turnover ratio = Cost of goods sold / Inventory = $25,200,000 / $3,900,000 = 6.46 times Days sales in inventory = 365 / Inventory turnover = 365 / 6.46 = 56.5 days Therefore, the number of days for days sales in inventory is 56.5 days. Operating cycle = 51 56.5 = 107.5 days Therefore, the length of the operating cycle is 107.5 days

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