Suppose the Campus Bookstore purchases 50,000 boxes of writing tablets every year.Ordering costs are $100 per order and carrying costs are $0.40 per box.Moreover,management has determined that the EOQ is 5,000 boxes.The vendor now offers a quantity discount of $0.02 per box if the company buys tablets in order sizes of 10,000 boxes.Determine the before-tax benefit or loss of accepting the quantity discount.(Assume the carrying cost remains at $0.40 per box whether or not the discount is taken. )
A) $1,000 loss
B) $1,000 benefit
C) $500 loss
D) $500 benefit
E) $0 (The change would not affect profits. )

Question

Quizplus · Accepted Answer

Without the discount:
Annual demand = 50,000 boxes
Ordering cost = $100 per order
Carrying cost = $0.40 per box
EOQ = 5,000 boxes

Using the EOQ formula:

EOQ = sqrt[(2 x 50,000 x 100) / 0.40]
EOQ = 5,000 boxes

Therefore, the company should place 10 orders of 5,000 boxes each year.

Total annual ordering cost = 10 x $100 = $1,000
Total annual carrying cost = 50,000 x $0.40 = $20,000

Total cost without discount = $1,000 + $20,000 = $21,000

With the discount:
Order size = 10,000 boxes
Ordering cost = $100 per order
Carrying cost = $0.40 per box
Annual demand = 50,000 boxes

Using the EOQ formula:

EOQ = sqrt[(2 x 50,000 x 100) / (0.40 + 0.02)]
EOQ = 10,000 boxes

Therefore, the company should place 5 orders of 10,000 boxes each year.

Total annual ordering cost = 5 x $100 = $500
Total annual carrying cost = 50,000 x $0.40 = $20,000

Total cost with discount = $500 + $20,000 - ($0.02 x 50,000 x 0.5) = $19,500

The discount reduces the cost by $1,500.

Therefore, the before-tax benefit of accepting the quantity discount is $500.

Suppose the Campus Bookstore Purchases 50,000 Boxes of Writing Tablets