# Cost and Management Accounting

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LESSON# 9
ECONOMIC ORDERING QUANTITY
Economic order quantity refers to that number (quantity) ordered in a single purchase so that the
accumulated costs of ordering and carrying costs are at the minimum level.
In other words, the quantity that is ordered at one time should be so, which will minimize the total
of (i) Cost of placing orders and receiving the goods, and (ii) cost of storing the goods as well as
interest on the capital invested.
The economic order quantity can be determined by the following simple formula:
EOQ =
2xRUxOC
UC x CC%
Where;
EOQ =
Economic Order Quantity.
RU =
Annually Required Units.
OC =
Ordering Costs for one order.
UC =
Inventory Unit Cost.
CC =
Carrying Cost as %age of Unit Cost.
This formula is based on three assumptions:
1. Price will remain constant throughout the year and quantity discount is not involved.
2. Pattern of consumption, variable ordering costs per order and variable inventory carrying
charge per unit per annum will remain the same throughout, and
3. EOQ will be delivered each time the stock balance is just reduced to nil.
The Economic Order Quantity can be determined by applying the formula as under:
Suppose; the
Annual consumption is
80,000 units,
Cost to place one order is
Rs. 1,200
Cost per unit is
Rs. 50
Carrying cost is
6% of Unit cost
EOQ =
2xRUxOC
UC x CC%
EOQ =
2 x 80,000 x 1,200
50x6%
EOQ =
8,000
As stated above this formula holds good if changes in price are not likely in the near future and
consumption is regular. Otherwise, placing orders according to this formula may become
expensive.
Carrying cost of inventory consists of (i) the costs of physical storage such as cost of space,
handling and upkeep expenses, insurance, cost of obsolescence, etc., and (ii) interest on capital
invested (the opportunity cost of the capital blocked up). All these costs are expressed in %age of
the cost per unit.
Table of EOQ
Economic order quantity can also be proved through a table, by calculating total cost at different
order quantities.
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Following is a table that is showing total cost at five different order quantities, assuming that the
annual requirement of the units to be consumed remains the same. Here the total cost comprises
of ordering cost and carrying cost.
Total Ordering cost
Ordering cost is arrived by multiplying the number of orders in a year with the cost
per order. Number of order is calculated by dividing annually required units by the
order quantity.
Step I:
Required Units = Number of orders
Order Quantity
Step II: Number of orders x Cost per order
Total Carrying Cost
Carrying cost is arrived by multiplying the average ordering quantity with the
carrying cost per unit. Average ordering quantity is calculated by dividing the
ordering quantity by 2. (It is assumed that half of the ordering quantity is always kept into the
store, this is the reason the ordering quantity is divided by 2)
Step I:
Ordering Quantity = Average ordering quantity
2
Step II: Carrying cost per unit = Unit Cost x CC %age
Step III:
Average ordering quantity x Carrying cost per unit
Applying these steps at different presumed order quantities (inclusive of the
Economic Order Quantity) we can develop a table.
Required Number of  Total  Total Carrying
Total cost
Order
Cost
Quantity
Units
orders
Ordering
Avg Order qty x
Cost
Number of
Rs.3
orders x Rs.
1,200
20,000
80,000
4
4,800
30,000
34,800
10,000
80,000
8
9,600
15,000
24,600
8,000
80,000
10
12,000
12,000
24,000
5,000
80,000
16
19,200
7,500
26,700
4,000
80,000
20
24,000
6,000
30,000
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The above table shows that 8,000 is the economic order quantity because at this point total
cost is the minimum. At this point total ordering cost is equal to the total carrying cost.
If the order quantity is increased it will although result in reducing the total ordering cost but
at the same time more carrying cost will be incurred to store the inventory.
Whereas if the order quantity is decreased it will although result in reducing the total carrying
cost but at the same time more ordering cost will be incurred as the number of orders will
increase.
EOQ Graph
Economic order quantity can also be determined through a graph. Here the above
information is plotted in a graph for total ordering cost, total carrying cost and total cost at
different ordering quantities.
The point at which the line of total ordering cost intersects with the total carrying cost is the
EOQ. At this point the line of total cost will give a bend that shows the minimum cost.
COSTS
(000)
Total Cost
36
30
Total Carrying
Cost
24
18
12
6
Total Ordering
Cost
4
8 10
20
5
ORDER SIZE (Q) (000)
In the above graph line of total carrying cost intersects line of total ordering cost at 8,000 order
quantities, where both of the costs are Rs. 12,000. At this order quantity the total cost is Rs. 24,000
which is the minimum most.
If the order quantity is increased or decreased the total cost will be more than the cost at EOQ.
This is also evident from the above graph.
PROBLEMS
Q. 1
From the following data, you are required to determine the Economic Order Quantity.
Annual usage
8,000 units
Cost per unit
Rs. 30
Ordering cost
Rs. 7 per order
Storage and carrying cost as percentage of average inventory holding 15%
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Q. 2
What is Economic Order Quantity (EOQ)? Should the quantity ordered be always equal to EOQ?
Calculate EOQ from the following:
(a) RU
600 units
{b) Ordering cost
Rs, 12 per order
(c) Carrying cost
20%
(d) Price per unit
Rs. 20.
Q. 3
Annual requirement of Glass Limited is 100,000 units of product 10mm glass. Per unit cost of the
product is Rs. 10 and cost for each new order is Rs. 100. Carrying cost is 50%.
Required:
Calculate EOQ by table and by graph.
MULTIPLE CHOICE QUESTIONS
Q. 1
The demand for a product is 12,500 units for a three month period. Each unit of product has a
purchase price of Rs.15 and ordering costs are Rs.20 per order placed.
The annual holding cost of one unit of product is 10% of its purchase price.
What is the Economic Order Quantity (to the nearest unit)?
A  1,577
B  1,816
C  1,866
D  1,155
Q. 2
A company determines its order quantity for a raw material by using the Economic Order Quantity
(EOQ) model.
What would be the effects of a decrease in the cost of ordering a batch of raw material on the
ordering quantity and the total carrying cost?
Ordering quantity
Total carrying cost
A
Higher
Lower
B
Higher
Higher
C
Lower
Higher
D
Lower
Lower
Q. 3
A company uses the Economic Order Quantity (EOQ) model to establish reorder quantities.
The following information relates to the forthcoming period:
Order costs
Rs.25 per order
Carrying costs
10% of purchase price
Annual demand
20,000 units
Purchase price
Rs.40 per unit
EOQ
500 units
What are the total annual costs of stock (i.e. the total purchase cost plus total order cost plus
total holding cost)?
A
Rs. 22,000
B
Rs. 33,500
C
Rs. 802,000
D
Rs. 803,000
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