Jordan Air Inc.has average inventory of R1,000,000.Its estimated annual sales are 15 million and the firm estimates its receivables collection period to be twice as long as its inventory conversion period.The firm pays its trade credit on time; its terms are net 30.The firm wants to decrease its cash conversion cycle by 10 days.It believes that it can reduce its average inventory to R900,000.Assume a 360-day year and that sales will not change.Cost of goods sold equal 80 percent of sales.By how much must the firm also reduce its accounts receivable to meet its goal of a 10-day reduction?

Question

Quizplus · Accepted Answer

First, we need to calculate the current cash conversion cycle (CCC) of the firm:

Inventory conversion period = average inventory / cost of goods sold per day = R1,000,000 / (0.8 x 15,000,000 / 360) = 30 days
Receivables collection period = 2 x inventory conversion period = 60 days
Payables deferral period = 30 days (given in the problem)

CCC = inventory conversion period + receivables collection period - payables deferral period
CCC = 60 days

Next, we need to find the new inventory conversion period after the firm reduces its average inventory to R900,000:

New inventory conversion period = R900,000 / (0.8 x 15,000,000 / 360) = 27 days

Now we can calculate the new CCC that the firm wants to achieve, which is 10 days lower than the current CCC:

New CCC = CCC - 10 days = 50 days

Finally, we can solve for the new receivables collection period that the firm needs to achieve the target CCC:

New receivables collection period = New CCC - new inventory conversion period + payables deferral period
New receivables collection period = 50 - 27 + 30 = 53 days

The firm needs to reduce its receivables collection period from 60 days to 53 days, which is a reduction of 7 days. Using the formula for average daily sales, we can calculate the reduction in accounts receivable that the firm needs:

Average daily sales = 15,000,000 / 360 = R41,667
Reduction in accounts receivable = 7 x average daily sales = R291,667

Therefore, the answer is choice C) R291,667.