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# Cost Accounting: The Economic Order Quantity Formula

Economic order quantity (EOQ) is a decision tool used in cost accounting. It’s a formula that allows you to calculate the ideal quantity of inventory to order for a given product. The calculation is designed to minimize ordering and carrying costs. It goes back to 1913, when Ford W. Harris wrote an article called “How Many Parts to Make at Once.”

EOQ is based on the following set of assumptions:

• Reorder point: The reorder point is the time when the next order should be placed. EOQ assumes that you order the same quantity at each reorder point.

• Demand, relevant ordering cost, and relevant carrying cost: Customer demand for the product is known. Also, the ordering and carrying costs are certain. A relevant cost refers to a cost you need to consider when you make a decision. The term is used throughout this book.

• Purchase order lead time: The lead time is the time period from placing the order to order delivery. EOQ assumes that the lead time is known.

• Purchasing cost per unit: The cost per unit doesn’t change with the amount ordered. This removes any consideration of quantity discounts. Assume you’ll pay the same amount per unit, regardless of the order size.

• Stockouts: No stockouts occur. You maintain enough inventory to avoid a stockout cost. That means you monitor your customer demand and inventory levels carefully.

• Quality costs: EOQ generally ignores quality costs.

Economic order quantity uses three variables: demand, relevant ordering cost, and relevant carrying cost. Use them to set up an EOQ formula:

• Demand: The demand, in units, for the product for a specific time period.

• Relevant ordering cost: Ordering cost per purchase order.

• Relevant carrying cost: Carrying costs for one unit. Assume the unit is in stock for the time period used for demand.

Note that the ordering cost is calculated per order. The carrying costs are calculated per unit. Here’s the formula for economic order quantity:

Economic order quantity = square root of [(2 x demand x ordering costs) ÷ carrying costs]

That’s easier to visualize as a regular formula:

Q is the economic order quantity (units). D is demand (units, often annual), S is ordering cost (per purchase order), and H is carrying cost per unit.

Don’t try this at home. You can research this formula, if you like, but be prepared to find the minimum point of the total cost curve by partially differentiating the total cost with respect to Q.

Say your clothing shop also sells men’s hiking shoes. The model you sell costs \$45 per pair. You sell 100 pairs of hiking boots a month, or 1,200 per year.

Your ordering cost is \$50 per order. You added up the total time spent by everyone who’s involved in the ordering process, and you figure that the combined time to process each order is one hour. Based on average salary and benefit costs, you assign a \$50 cost per order.

The carrying cost per unit is \$3. That rate covers the occupancy costs and insurance where the inventory is stored. The amount also accounts for the opportunity cost of carrying the inventory.

Based on the data for the hiking boots, here’s your economic order quantity:

Economic order quantity = square root of [(2 x demand x ordering costs) ÷ carrying costs]
Economic order quantity = square root of [(2 x 1,200 x (\$50)) ÷ \$3]
Economic order quantity = square root of [\$120,000 ÷ \$3]
Economic order quantity = square root of 40,000
Economic order quantity = 200

You just determined that the ideal order level is 200 units. At that level, you minimize ordering and carrying costs.

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