Question
Margetis Inc. carries an average inventory of $750,000. Its annual
sales are $10 million, its cost of goods sold is 75% of annual sales,
and its average collection 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 $647,260 with no effect on sales. By how much must the
firm also reduce its accounts receivable to meet its goal in the
reduction of the cash conversion cycle?
a. $123,630
b. $130,137
c. $136,986
d. $143,836
Explanation / Answer
According to the given information, Cost of gooods sold = 75% ($10,000,000) = $7,500,000 Inventory turnover ratio = Cost of goods sold / Average inventory = $7,500,000 / $750,000 = 10 times Days sales ininventory = 365 / Inventory turnover ratio = 365/ 10 = 36.5 days But the average collection period is twice of the inventory conversion period. Average collection period = 2 (36.5 days) = 73 days From Average collection period = (Accounts receivables * 365) / Credit sales 73days = (AR * 365) / $10,000,000 $730,000,000 = AR * 365 AR = $2,000,000 Average collection period is same as DAys sales outstanding. Since the payables are paid in time, the days payable outstanding is 30 days Cash conversion cycle = DSO + DIO - DPO Where DSO = Days sales outstanding DIO = Days inventory outstanding DPO = Days payable outstanding CAsh conversion cyle = 73 days + 36.5 days - 30days = 79.5 days If the CCC is reduced by 10 days, then the average inventory comes to $647,260 keeping sales constant. Therefore, there exists a change in the DAys inventory outstanding. DAys inventory outstanding = (365 / Inventory turnover) = 365 / (Cost of goods sold / Average inventory) = 365 / ($7,500,000 / $647,260) = 365 / 11.59 = 31.5 days TheDIO has decreased by 5 days and the DSO has to be reduced by another 5 days to reduce the CCC by 10 days. DSO =(Accounts receivables * 365) / Credit sales 68 = (AR * 365) / $10,000,000 $680,000,000 = AR * 365 AR= $680,000,000 / 365 = $1,863,014 Therefore, the accounts receivable should be reduced by $2,000,000 - $1,863,014 = $136,986 The correc option is c) $136,986