Crystal Clear Company purchases 50,000 litres of distilled water each year.Ordering costs are $100 per order,and the carrying cost,as a percentage of inventory value,is 80%.The purchase price to CCC is $0.50 per litre.Management currently orders the EOQ each time an order is placed.No safety stock is carried.The supplier is now offering a quantity discount of $0.03 per litre if CCC orders 10,000 litres at a time.Should CCC take the discount?

A) No, the cost exceeds the benefit by $500.
B) No, the cost exceeds the benefit by $1,000.
C) Yes, the benefit exceeds the cost by $500.
D) Yes, the benefit exceeds the cost by $1,120.

First, we need to calculate the current EOQ using the formula:

EOQ = sqrt((2SD)/H)

Where:
S = Annual demand = 50,000 litres
D = Ordering cost = $100 per order
H = Carrying cost as a percentage of inventory value = 80% * $0.50 per litre = $0.40 per litre

Plugging in the values, we get:

EOQ = sqrt((2*50,000*100)/0.40) = 5,000 litres

This means that CCC currently orders 10 times a year (50,000/5,000).

Now, let's see what happens if CCC takes the quantity discount and orders 10,000 litres at a time. The new EOQ will be:

EOQ = sqrt((2SD)/H)

Where:
S = Annual demand = 50,000 litres
D = Ordering cost = $100 per order
H = Carrying cost as a percentage of inventory value = 80% * $0.50 per litre = $0.40 per litre - $0.03 per litre discount = $0.37 per litre

Plugging in the values, we get:

EOQ = sqrt((2*50,000*100)/0.37) = 5,399 litres

This means that CCC will now order 10 times a year (50,000/5,399).

The total cost of ordering and carrying inventory for both scenarios is:

Current scenario:
Ordering cost = 10*$100 = $1,000
Carrying cost = $0.50*5,000/2*0.80 = $125
Total cost = $1,125*10 = $11,250

New scenario:
Ordering cost = 10*($100/$0.03)*($0.03/$0.50)*($10,000/50,000) = $67
Carrying cost = $0.47*5,399/2*0.80 = $100
Total cost = $167*10 = $1,670

The cost savings from taking the quantity discount is therefore:

$11,250 - $1,670 = $9,580

Therefore, the benefit exceeds the cost by $1,120. So, CCC should take the quantity discount.