Financial Management and Strategic Management · Management of Inventory

Economic Order Quantity (EOQ) Formula and Numericals for CA Inter FM

Updated 4 October 2026 · Fact-checked

EOQ is the order size that makes the total of ordering cost and carrying cost the lowest. Use EOQ = √(2 × A × O ÷ C), where A is annual demand, O is cost per order and C is carrying cost per unit per year. Then find the number of orders and total cost.

Understand Economic Order Quantity (EOQ)

Every business that holds stock faces two opposing costs. If you order often, you pay ordering cost many times: placing the order, transport, inspection and paperwork. If you order in big lots, you pay more carrying cost: storage, insurance, obsolescence and interest on money locked in stock.

The Economic Order Quantity (EOQ) is the order size at which these two costs balance. Ordering cost falls as order size rises. Carrying cost rises as order size rises. Total cost is lowest where the two are equal.

That is why the formula works. At EOQ, annual ordering cost = annual carrying cost. You never need to try different order sizes. The formula finds the point directly.

The model rests on assumptions: demand is known and constant, price is fixed (no quantity discount), lead time is constant, there are no stock-outs, and ordering cost per order and carrying cost per unit are fixed. The whole order arrives at once. If a question gives a discount, you must compare total costs at different order sizes.

Key rules to remember

Economic Order Quantity: EOQ = √(2 × A × O ÷ C); A = annual demand in units, O = ordering cost per order, C = carrying cost per unit per year. If carrying cost is given as a percentage, C = percentage × purchase price per unit.
Number of orders per year: Number of orders = A ÷ EOQ; Time between orders = 12 months ÷ number of orders, or 365 days ÷ number of orders.
Annual ordering cost: Ordering cost = (A ÷ Q) × O; Q is the order size actually used.
Annual carrying cost: Carrying cost = (Q ÷ 2) × C; Average stock is Q ÷ 2 because stock falls steadily from Q to zero.
Total inventory cost: Total cost = Purchase cost (A × P) + (A ÷ Q) × O + (Q ÷ 2) × C; Include purchase cost when comparing different prices, as in quantity discount problems. For EOQ alone, ordering plus carrying cost is enough.
Total relevant cost at EOQ: At Q = EOQ: Ordering cost = Carrying cost = (EOQ ÷ 2) × C, so Ordering cost + Carrying cost = EOQ × C; This holds only at Q = EOQ, because only there are the two costs equal. At any other order size, calculate each cost separately. EOQ × C is the sum of ordering cost and carrying cost only. It excludes purchase cost, so add A × P separately if the question asks for total cost including purchase. At EOQ the ordering and carrying costs are equal, so this is a quick check.

How to solve Economic Order Quantity (EOQ) questions

Use this method for any EOQ question, with or without a quantity discount.

1Write down A (annual demand), O (cost per order) and C (carrying cost per unit per year). Convert monthly demand to annual and percentages to rupees.
2Check units. If carrying cost is a percentage of price, compute C = percentage × price.
3Compute EOQ = √(2AO ÷ C). Round only at the end, as the question or practice requires.
4Find the number of orders = A ÷ EOQ and the gap between orders.
5Compute ordering cost, carrying cost and total cost at EOQ. Check that the first two are equal.
6If a discount is offered, compute total cost (purchase + ordering + carrying) at EOQ and at each discount quantity. Use EOQ only if it qualifies for that price; otherwise use the minimum qualifying quantity.
7Pick the lowest total cost, state the order size and write a one-line conclusion.

Quickest way: Square root, then check equality

When to use it: Use this for MCQs and for the first part of long numericals.

Compute 2 × A × O first, divide by C, then take the square root. Many exam values are perfect squares, so test quickly.
For MCQs, find total ordering plus carrying cost as EOQ × C. This avoids two separate calculations.
In a quantity discount MCQ, check whether EOQ at each price lies in that price band before computing any cost.
For written answers, show the formula, the substitution and the result on separate lines. Label ordering cost, carrying cost and total cost clearly to earn step marks.
End with a conclusion sentence: order X units, Y times a year.

Common mistakes in Economic Order Quantity (EOQ)

Using monthly demand as A without converting to annual.
The question gives monthly usage and the carrying cost is annual.
Fix: Convert A and C to the same period, normally one year, before using the formula.
Taking carrying cost percentage as the rupee value of C.
The problem says carrying cost is 10% and students put C = 10.
Fix: Multiply the percentage by unit price to get C in rupees per unit per year.
Dividing by two twice or forgetting to divide by two for average stock.
Mixing up the EOQ formula with the carrying cost formula.
Fix: The 2 in EOQ is inside the root. Carrying cost uses Q ÷ 2 for average stock.
Leaving out purchase cost in quantity discount problems.
Students are used to ordering plus carrying cost only.
Fix: When prices differ, include A × P in total cost for every option.
Using EOQ in a discount question even when it is below the discount threshold.
The EOQ value looks neat and students stop.
Fix: Check whether EOQ qualifies for the price used. If not, test the minimum quantity that earns the discount.
Forgetting assumptions when asked to state them.
Students focus only on numericals.
Fix: Learn the list: constant demand, fixed cost per order, fixed carrying cost per unit, constant price and lead time, no stock-outs.

Worked examples

Example 1

A firm uses 24,000 units of a component a year. Ordering cost is ₹150 per order. Carrying cost is ₹6 per unit per year. Calculate the EOQ, the number of orders per year, and the total of ordering and carrying cost.

Show the solution

A = 24,000 units, O = ₹150, C = ₹6.
EOQ = √(2 × 24,000 × 150 ÷ 6) = √(72,00,000 ÷ 6) = √12,00,000.
2 × 24,000 × 150 = 72,00,000. Divided by 6 = 12,00,000. √12,00,000 ≈ 1,095 units.
Number of orders = 24,000 ÷ 1,095 ≈ 21.9, about 22 orders.
Ordering cost = (24,000 ÷ 1,095) × 150 ≈ ₹3,288. Carrying cost = (1,095 ÷ 2) × 6 = 547.5 × 6 = ₹3,285.
Total ≈ EOQ × C = 1,095 × 6 = ₹6,570. The small difference between the two costs is rounding.

Answer: EOQ ≈ 1,095 units; about 22 orders a year; total ordering plus carrying cost ≈ ₹6,570.

Example 2

A company needs 3,600 units a year. Ordering cost is ₹100 per order. Carrying cost is 10% of purchase price. The supplier charges ₹50 per unit for orders below 600 units and ₹48 per unit for orders of 600 units or more. Find the best order size.

Show the solution

A = 3,600, O = ₹100.
At ₹50: C = 10% × 50 = ₹5. EOQ = √(2 × 3,600 × 100 ÷ 5) = √(7,20,000 ÷ 5) = √1,44,000 ≈ 379.5 units. This is below 600, so it qualifies for ₹50.
At ₹48: C = ₹4.80. EOQ = √(7,20,000 ÷ 4.8) = √1,50,000 ≈ 387.3 units. This is below 600, so it does not qualify for ₹48. Test Q = 600.
Option 1, Q = 379.5 at ₹50: Purchase = 3,600 × 50 = ₹1,80,000. Ordering + carrying = EOQ × C = 379.5 × 5 ≈ ₹1,897. Total ≈ ₹1,81,897.
Option 2, Q = 600 at ₹48: Purchase = 3,600 × 48 = ₹1,72,800. Ordering = (3,600 ÷ 600) × 100 = 6 × 100 = ₹600. Carrying = (600 ÷ 2) × 4.8 = 300 × 4.8 = ₹1,440. Total = ₹1,74,840.
Option 2 costs less by about ₹7,057.

Answer: Order 600 units at a time at ₹48 per unit. Total annual cost is ₹1,74,840, lower than ₹1,81,897 at EOQ.

Exam tips

Write the formula and the substitution in the answer book. Even if arithmetic slips, you still earn method marks.
In MCQs, check the carrying cost basis first. Percentage of price versus rupees per unit changes the answer completely.
For discount questions, make a small table of price, order size, purchase cost, ordering cost, carrying cost and total. It is quick and clear.
Check your result by confirming ordering cost equals carrying cost at EOQ.
Be ready to state the assumptions and limits of the model in a short theory answer.

Practice questions from Management of Inventory

Economic Order Quantity (EOQ) in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Economic Order Quantity (EOQ): frequently asked questions

What is the EOQ formula?

EOQ = √(2 × A × O ÷ C). A is annual demand, O is ordering cost per order and C is carrying cost per unit per year. Keep all three in the same time period and rupee basis.

How do I solve EOQ with quantity discount?

Compute total cost for each price, including purchase cost, ordering cost and carrying cost. Use EOQ for a price only if it falls in that price's quantity band. Otherwise test the minimum quantity for the discount. Choose the lowest total cost.

What are the assumptions of the EOQ model?

Demand is known and constant, and price per unit is fixed. Ordering cost per order and carrying cost per unit are constant. Lead time is constant, the full order arrives at once and there are no stock-outs.

Why is average stock taken as Q ÷ 2?

Stock starts at Q when an order arrives and falls steadily to zero. The average over the cycle is therefore half of Q. Carrying cost is charged on this average stock.