Answer:
Consider the following calculations
Explanation:
First calculate the Economic Order Quantity (EOQ) ignoring the discount.
Economic Order Quantity (EOQ)= √ (2DS/H)
D- Demand per year= 3400 pounds
S- Ordering cost per year= $100
Per unit cost= $3 per pound
H- Holding (carrying) cost per unit per year=$0.51( 17% of purchase price)
So by applying the above formula, we get the following answer:
EOQ= SQRT (2*3400*100/0.51)= 1154.70 units
Economic Order Quantity (EOQ)= 1154 units
Discounted Order Quantity (DOQ) = 1500 units
Annual Orders under EOQ = Demand ÷ EOQ = 3400 ÷ 1154 = 3 orders
Annual Orders under DOQ = Demand ÷ DOQ = 3400÷ 1500 = 2.40 or 3 orders
Average Inventory under EOQ = EOQ ÷ 3 = 1154 ÷ 3 = 384.90 units
Average Inventory under DOQ = DOQ ÷ 3 = 1500 ÷ 3 = 500 units
A-Saving from reduction in Price
= Demand × Full Price × Discount Rate
= 3400× 3 × 0.33 = $ 3366
B-Saving from reduction in orders
= Orders reduced × Order Cost
= (3− 3) × 100 = 0
C-Increase in holding cost
= Increase in average inventory × holding cost per unit per annum
Holding cost is 17% of purchase price
So for 500 units it is=$170 (17% of $2 per pound)
For 384.90 units= $196.30 (17% of $3 per pound)
Increase in holding cost= 170-196.30= $-26.30
Net savings on discount order quantity = A + B − C = 3366 + 0 – (-26.30) = $3392.30
Since the net effect on income is positive, the store should place the order for quantity discount.
