Jordan Air Inc. has average inventory of $1,000,000. Its estimated annual sales are $10 million and the firm estimates its receivables conversion period to be twice as long as its inventory conversion period. The firm pays its trade credit on time; its terms are net 30 days. The firm wants to decrease its cash conversion cycle by 10 days. It believes that it can reduce its average inventory to $863,000. Assume a 365-day year and that sales will not change. By how much must the firm also reduce its accounts receivable to meet its goal of a 10-day reduction in its cash conversion cycle?
A) $ 101,900
B) $1,000,000
C) $ 136,986
D) $ 333,520
E) $ 0

Question

Quizplus · Accepted Answer

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

CCC = Inventory conversion period + Receivables conversion period - Payables deferral period

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

Receivables conversion period = 2 x Inventory conversion period = 2 x 36.5 days = 73 days

Payables deferral period = 30 days (given)

CCC = 36.5 + 73 - 30 = 79.5 days

To reduce CCC by 10 days, the firm needs to reduce the sum of its inventory conversion period and receivables conversion period by 10 days. We know that the firm plans to reduce its inventory conversion period by $1,000,000 - $863,000 = $137,000. Let's assume that accounts payable remain the same.

So, we need to find how much the firm should reduce its accounts receivable to reach the goal:

New inventory conversion period = $863,000 / ($10,000,000 / 365) = 31.59 days

New receivables conversion period = 2 x 31.59 days = 63.18 days

New CCC = 31.59 + 63.18 - 30 = 64.77 days

To reduce CCC by 10 days, we need:

79.5 - 64.77 = 14.73 days

The firm should reduce the sum of its inventory and receivables conversion periods by 14.73 days. Since we already reduced inventory conversion period by 4.91 days (from 36.5 to 31.59), we need to reduce the receivables conversion period by the remaining 9.82 days:

9.82 days = (New receivables conversion period - Current receivables conversion period)

New receivables conversion period = Current receivables conversion period - 9.82 days = 73 - 9.82 = 63.18 days

Now we can calculate the new accounts receivable level:

New accounts receivable = (New receivables conversion period / 365) x Annual sales = (63.18 / 365) x $10,000,000 = $1,093,151

To reach the goal of a 10-day reduction in CCC, the firm should reduce its accounts receivable to $1,093,151 - $1,000,000 = $93,151.

Therefore, choice C is the correct answer.