Jordan Air Inc.has average inventory of $1,000,000.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 $900,000.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?
A) $101,900
B) $1,000,000
C) $291,667
D) $333,520
E) $0

Question

Quizplus · Accepted Answer

First, we need to find the current cash conversion cycle (CCC):

Inventory conversion period = (average inventory / cost of goods sold) x 360
= ($1,000,000 / 0.8 x 15,000,000) x 360
= 30 days

Receivables collection period = 2 x inventory conversion period
= 60 days

CCC = Inventory conversion period + receivables collection period - payable deferral period
= 30 + 60 - 30
= 60 days

To reduce the CCC by 10 days, the firm needs to reduce its inventory conversion period and/or its receivables collection period by a total of 10 days. Given that average inventory can be reduced to $900,000, we can calculate the new inventory conversion period:

New inventory conversion period = ($900,000 / 0.8 x 15,000,000) x 360
= 27 days

So the firm can reduce its inventory conversion period by 3 days. Therefore, it needs to reduce its receivables collection period by 7 days (10 - 3) to meet its goal.

The current accounts receivable balance can be calculated as:
Accounts receivable = (annual sales / 365) x receivables collection period
= (15,000,000 / 365) x 60
= $2,465,753

To reduce the receivables collection period by 7 days, the new accounts receivable balance must be:
New accounts receivable = (annual sales / 365) x (60 - 7)
= (15,000,000 / 365) x 53
= $2,173,972

Therefore, the firm must reduce its accounts receivable balance by $291,781 ($2,465,753 - $2,173,972) to meet its goal.

The closest answer option is C) $291,667.