Margetis Inc.carries an average inventory of $1,000,000.Its annual sales are $10 million,and its receivables conversion period is twice as long as its inventory conversion period.The firm buys on terms of net 30 days,and it pays on time.Its new CFO wants to decrease the cash conversion cycle by 10 days,based on a 365-day year.He believes he can reduce the average inventory to $863,000 with no effect on sales.By how much must the firm also reduce its accounts receivable to meet its goal of a 10-day reduction in the cash conversion cycle?

Question

Quizplus · Accepted Answer

To calculate the current cash conversion cycle, we need to determine the inventory conversion period and the receivables conversion period. The inventory conversion period is:

Inventory conversion period = (Average inventory / Cost of goods sold) x 365 days
Inventory conversion period = ($1,000,000 / ($10,000,000 / 365)) = 36.5 days

The receivables conversion period is twice as long as the inventory conversion period, which means:

Receivables conversion period = 2 x 36.5 days = 73 days

The cash conversion cycle is the sum of the inventory conversion period and the receivables conversion period, minus the payables deferral period (which is assumed to be zero in this case since the company pays on time):

Cash conversion cycle = 36.5 days + 73 days - 0 days = 109.5 days

To decrease the cash conversion cycle by 10 days, the company needs to reduce either the inventory conversion period or the receivables conversion period (or both) by 5 days each. The CFO believes that he can reduce the average inventory to $863,000 with no effect on sales, which means:

New inventory conversion period = ($863,000 / ($10,000,000 / 365)) = 31.4 days

This is a reduction of 5.1 days from the current inventory conversion period of 36.5 days. To calculate the necessary reduction in the receivables conversion period, we can use the following formula:

Cash conversion cycle = Inventory conversion period + Receivables conversion period - Payables deferral period
New cash conversion cycle = (31.4 days) + (Receivables conversion period) - 0 days
New cash conversion cycle = 109.5 days - 10 days = 99.5 days

Solving for the new receivables conversion period, we get:

New receivables conversion period = 68.1 days

This is a reduction of 4.9 days from the current receivables conversion period of 73 days. Therefore, the company needs to reduce its accounts receivable by:

Reduction in accounts receivable = (Current accounts receivable / Current receivables conversion period) x Reduction in receivables conversion period
Reduction in accounts receivable = ($1,000,000 / 73) x 4.9 = $67,123
Rounding up, the answer is $68,000 or approximately $136,986 if we assume a 365-day year (as stated in the problem).

Therefore, the best answer is C.