Using the logic used to derive EOQ formula,
The total annual cost would be least when Annual Setup Costs= Annual Holding Costs,
If we solve this further,
(No. of Setups in a year) x (Cost per setup) = (Cost of holding one unit of inventory per annum) x (Average inventory)
Solving this further, (Annual Demand/batch quantity) x (Cost per setup) = (Cost of holding one unit of inventory per annum) x (Batch quantity/2)
i.e., Batch quantity^2 = (2 x Annual Demand x Cost of one setup) / Cost of holding one unit of inventory per annum
The reason why we are averaging the inventory is because we are assuming inventory reduction due to sale, which is evenly spread throughout the year. Now, once we are dividing the inventory by 2 to arrive at the average inventory, it's duplication to further deduce it by (1-Demand/Capacity).
From a reference book, reviewed by ACCA, refer the following example.
The following is relevant for Item X:
• Production is at a rate of 500 units per week.
• Demand is 10,000 units per annum; evenly spread over 50 working
• Setup cost is $2,700 per batch.
• Storage cost is $2.50 per unit for a year.
Calculate the economic batch quantity (EBQ) for Item X.
The answer after multiplying the denominator by (1-Demand/Capacity) for this question is EBQ = 6000 units.
The answer without multiplying the denominator by (1-Demand/Capacity) for this question is EBQ = 4648 units. (approx)
Now look at the total setup + holding costs for both these quantities:
Batch Quantity (Q) = 6000 units
Set up Cost (Annual Demand/Q x 2700) = $4500
Holding Cost (Q/2 x 2.5) = $7500
Total Holding + Setup Cost = $12000
Batch Quantity (Q) = 4648 units
Set up Cost (Annual Demand/Q x 2700) = $5809
Holding Cost (Q/2 x 2.5) = $5809
Total Holding + Setup Cost = $11619
Is it appropriate to use (1 - Demand/Capacity) in the denominator when we are already dividing the quantity by 2 to arrive at average inventory?