Question

Suppose Stanley's Office Supply purchases 50,000 boxes of pens every year. Ordering costs are $100 per order, carrying costs are 5% of the inventory value, and the price is of $2.00 per box. The vendor now offers a quantity discount of 1% per box if the company buys pens in order sizes of 20,000 boxes. Should the company accept the quantity discount? Show your calculations to justify your decision.

Answer 1

Economic order quantity (EOQ) = ((2 * annual demand * ordering cost) / carrying cost per unit)^(1/2)
= ((2 * 50,000 * 100) / (2 * 5%))^(1/2)
= (10,000,000 / 0.10)^(1/2)
= 100,000,000^(1/2)
= 10,000 boxes

Annual cost at 10,000 boxes (EOQ) = Annual Carrying cost + Ordering cost
= ((10,000 / 2) * 0.10) + ((50,000 / 10,000) * 100)
= 500 + 500
= 1000.

Annual cost on 20,000 boxes (quantity discount offer) = Annual Carrying cost + Ordering cost
= ((20,000 / 2) * 0.10) + ((50,000 / 20,000) * 100)
= 1000 + 250
= 1250.

Increase in annual cost = 1250 - 1000 = 250

Savings on price reduction = 50,000 * 2 * 1% = 1000

Net savings = 1000 - 250 = 750

Thus, the company should accept quantity discount.