# 4.2. Economic Order Quantity

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The total cost of inventories is the summation of these rising and declining costs, or the total costs curve. It has been shown that, under reasonable assumptions, the minimum point on the total costs curve can be found by an equation called the EOQ formula:

EOQ = Square Root (2FU/CP)

Where: EOQ is the economic ordering quantity, or the optimum quantity to be ordered each time an order is placed.

F = fixed costs of placing and receiving an order.

U = annual usage in units.

C = carrying cost expressed as a percentage of inventory value.

P = purchase price per unit of inventory.

For any level of usage, dividing U by EOQ indicates the number of orders that must be placed each year. The average inventory on hand (the average balance sheet inventory figure) will be

Average inventory = EOQ/2

**Use of EOQ Model in the Computer Technology Industry**

Let us assume that you will sell 1000 units of a laptop over the next year. The laptop is priced at R2,000. The cost of placing an order is estimated at R17.50. The critical calculation is the carrying costs. Costs such as interest, insurance and warehousing can probably be estimated at 20% of the price of a unit. But what about obsolescence? How much is a one-year-old laptop worth? Obsolescence can be calculated by estimating the “depreciation” over a yearâ€™s time. If we assume the laptop will lose 50% of its value in a year, the total carrying costs will be equal to 70% (20% plus 50%). The calculation of the EOQ is as follows:

2FU = 2 X R17.50 X 1,000 = 35,000

CP = 70% X R2,000 = 1,400

2FU = 35,000 divided by 1,400 = 25

CP

The square root of 25 is 5.

The calculation shows that the EOQ = 5. The average inventory level should be half of the EOQ or 2 to 3 units. Therefore, if 1,000 units are sold throughout the year, the average daily unit sales will be 4 (1,000 divided by 260 business days per year). What this illustration points out is that the risk of obsolescence is far greater than the cost of placing orders.