Question

Costco carries an average inventory of $3,000,000. Its annual sales are $20 million and its gross profit margin is 45%. The receivables conversion period is half of its inventory conversion period. Costco’s trade terms with its suppliers is net 30 and it always pays on time. Costco’s new CFO wants to improve the cash conversion cycle by 25 days, based on a 365-day year. His first strategy is to reduce the amount of inventory to $2,500,000 while maintaining the same level of sales. His second strategy is to negotiate longer credit term with the suppliers, and he expects this move will increase his account payable balance by 10%. By how much must the firm also reduce its accounts receivable level to meet its goal of a 25-day reduction in the cash conversion cycle?

You must show all calculation steps, providing a final answer only will not get you full marks.

Answer 1

Cash conversion cycle = receivable days + inventory days - payable days

Now COGS = (1-45%)*$20 million = $11,000,000

Thus inventory days = 365/(11,000,000/3,000,000)

= 99.5455

Thus receivables conversion period = 1/2*inventory days = 1/2*99.5455 = 49.7727

Payable days = 30. Thus cash convesrion cycle = 99.5455+49.7727-30

= 119.3182 days

Now desired level of new cash conversion cycle = 119.3182-25 = 94.3182 days

New inventory days = 365/(11,000,000/2,500,000) = 82.9545 days

Now we will have to compute payables amount in the past. Days payable outstanding = 30 and so payable turnover = 365/30 = 12.17. Now COGS/payables = 12.17 and so 11,000,000/payables = 12.17. Thus payables = 11,000,000/12.17 = $904,109.59

Thus new balance of payables = 1.1*$904,109.59 = $994,520.55. Thus days payable outstanding = 365/(11,000,000/994520.59) = 33 days

Thus using the equation of cash convesrion cycle we have: 94.3182 days = 82.9545 days + receivable days - 33 days

or receivabe days = 44.3636 days

Thus earlier receible days was 49.7727 days and now it is 44.3636 days

We know that receivable days = 365/(sales/receivables)

Thus 49.7727 = 365/(20,000,000/receivables). Or receivables = 2,727,272.73

Receivables now: 44.3636 days = 365/(20,000,000/receivables). Or receivables = 2,430,884.18

Thus reduction in receivables = 2,727,272.73 - 2,430,884.18

= $296,388.54

Thus receivables will have to decline by $296,388.54 to $2,430,884.18