Question

A business currently orders 1,000 units of product ZETA at a time. It has decided that it may be better to use the Economic Order Quantity method to establish an optimal reorder quantity. Information regarding inventories is given below:
Purchase price K15 per unit
Fixed cost per order K200
Holding cost 8% of the purchase price per annum
Annual demand 12,000 units
Current annual total inventory costs are K183,000, being the total of the purchasing, ordering and holding costs of product ZETA.
Required:
(a) Calculate the Economic Order Quantity. [2 Marks]
(b) Using your answer to (a) above calculate the revised annual total inventory costs for product ZETA and so establish the difference compared to the current ordering policy.

(c)Describe ways in which discounts might affect this Economic Order Quantity calculation and subsequent inventory costs. [4 Marks]

Answer 1

a) Annual consumption (A) = 12,000 units

Ordering cost per order (O) =`K200

Carrying cost (C) = 8% of K15 = K1.2

EOQ = = = 2,000 units

b) Calculation of annual total inventory costs:

Particulars	Current System	EOQ
No. of Orders (Annual demand / Order Quantity)	12,000 / 1,000 = 12	12,000 / 2,000 = 6
Average Inventory	1,000 / 2 = 500	2,000 / 2 = 1,000
Ordering Cost (number of orders * K200) (a)	12orders * K200 = K2,400	6orders * K200 = K1,200
Carrying cost (C * Average Inventory) (b)	K1.2 * 500 = K600	K1.2 * 1,000 = K1,200
Total Cost (a+b)	K3,000	K2,400

Based on above calculations total inventory cost under EOQ is K2,400 and under current system is K3,000. The savings of K600 under EOQ are due to reduced ordering costs. Although carrying cost has increased by K600 under EOQ but ordering cost has decreased by K1,200, which has increased savings. Purchase price will remain same i.e. K180,000

c) EOQ generally minimizes the total inventory cost. However, EOQ may not be optimal when discounts are factored into the calculation. The optimal order quantity when discounts are involved is either:

• EOQ; or
• Any one of the minimum order quantities above EOQ that qualify for additional discount.

Now, suppose supplier offers a discount of 5% on orders of 3,000 units and above. In this case costs shall be as follows:

Order Quantity	EOQ = 2,000 units	For 5% Discount = 3,000 units
Number of orders (Annual demand / Order Quantity)	12,000 / 2,000 = 6	12,000 / 3,000 = 4
Ordering Cost (number of orders * K200)	6 * 200 = K1,200	4 * 200 = K800
Carrying Cost (8% * Purchase Price * Average Inventory)	0.08*(15*1)*(2,000/2) = K1,200	0.08*(15*0.95)*(3,000/2) = K1,710
Cost of Purchase (Purchase Price * Annual Demand * (100 - discount%)	15*12,000*(1 - 0) = K180,000	15*12,000*(1.0-0.05) = K171,000
Total Inventory Cost	$182,400	$173,510

In above calculation, inventory cost under EOQ is K2,400 and under discount quantity it is K2,510, that is higher than EOQ. But still discount quantity is more beneficial because the overall cost is much lesser than under EOQ quantity. Hence, under EOQ inventory cost will always be minimum but overall cost may be more than other options, if discount is given.