CA Intermediate · Financial Management and Strategic Management

Management of Inventory: formula sheet

Full chapter guide

Key formulas

Total inventory cost: Total cost = Ordering cost + Carrying cost (+ Purchase cost, if it varies with order size); Stock-out cost is added where the question mentions it. Purchase cost matters when quantity discounts exist.
Annual ordering cost: Number of orders × Cost per order = (A ÷ Q) × O; A = annual requirement, Q = order quantity, O = cost per order.
Annual carrying cost: Average inventory × Carrying cost per unit per year = (Q ÷ 2) × C; Assumes steady usage and no safety stock. Carrying cost can also be given as a % of unit price.
Opportunity cost of inventory: Average inventory value × Cost of funds (%); Include this in carrying cost when interest rate is given.
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.
Reorder level (ROL): ROL = Maximum consumption × Maximum lead time; If the question gives only a normal rate and a lead-time range, use the highest lead time and the highest usage given.
Minimum level: Minimum level = ROL − (Normal consumption × Normal lead time); Normal lead time is often the average of the minimum and maximum lead time, if the question says so.
Maximum level: Maximum level = ROL + ROQ − (Minimum consumption × Minimum lead time); ROQ is the reorder quantity. It is often the EOQ given or computed.
Average stock level: Average level = (Minimum level + Maximum level) ÷ 2; Another form is Minimum level + ½ × ROQ. The two can give different answers, so use the form the question points to. (Min + Max) ÷ 2 is the usual default.
Danger level: Danger level = Average (or normal) consumption × Emergency lead time; Emergency lead time is the time an urgent purchase takes. Use the consumption rate the question gives. The danger level is normally set below the minimum level.
Annual consumption value: Annual consumption value = Annual usage (units) × Unit price; Use this to rank items for ABC analysis. Rank in descending order.
Cumulative percentage for ABC: Cumulative % = Running total of value ÷ Total value × 100; Typical illustration: A about 70% of value from about 10% of items; B about 20% of value from about 20%; C about 10% of value from about 70%. These are indicative, not fixed rules. Follow the figures in the question.
Inventory turnover ratio: Inventory turnover = Cost of goods sold ÷ Average inventory; Average inventory = (Opening + Closing) ÷ 2. If the question gives sales only, state your assumption.
Inventory holding period: Holding period (days) = 365 ÷ Inventory turnover; Use 360 days if the question says so. Equivalent: Average inventory ÷ COGS × 365.
Two-bin system: second bin: Second bin quantity = Reorder level (stock to cover consumption during the lead time, plus any buffer the firm sets); This is a practical set-up, not a fixed formula. The reorder level is usually worked out as Maximum usage × Maximum reorder period. The first bin holds the rest of the stock.

Quick revision

Inventory objectives: avoid stock-outs, keep investment low and keep total cost minimum.
Total inventory cost = ordering cost + carrying cost (+ purchase cost where relevant).
EOQ = √(2AO ÷ C).
At EOQ, total ordering cost equals total carrying cost. This holds in the basic EOQ model, with constant price, constant carrying cost per unit and no quantity discounts.
Number of orders per year = A ÷ EOQ.
Stock levels (mainly Paper 4 support): reorder level = maximum usage × maximum lead time.
Minimum level = reorder level − (normal usage × normal lead time).
Maximum level = reorder level + reorder quantity − (minimum usage × minimum lead time).
Danger level = normal (average) consumption × maximum reorder period for emergency purchases. This is the convention used here. Some books use minimum consumption × emergency lead time, so follow the one the question or your Paper 4 notes use.
ABC ranks by value, VED by criticality, FSN by speed of movement.
JIT aims at near-zero stock by receiving material only as production needs it.

Common mistakes

Treating the objective as minimising inventory. Fix: Write the objective as minimising total cost while avoiding stock-outs. Zero stock risks production stoppage and lost sales.
Putting storage or insurance under ordering cost. Fix: Ask whether the cost depends on the number of orders or on stock held. Storage, insurance and interest are carrying costs.
Using monthly demand as A without converting to 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. Fix: Multiply the percentage by unit price to get C in rupees per unit per year.
Using normal consumption in the reorder level formula. Fix: ROL covers the worst case during delivery, so it is max consumption × max lead time. Normal figures appear only inside the minimum level.
Subtracting the wrong pair in the maximum level. Fix: Maximum level = ROL + ROQ − (minimum consumption × minimum lead time). Use the slowest usage and shortest delivery.
Ranking items by unit price or quantity instead of annual consumption value. Fix: Always multiply units by price first. Rank only on that product.
Using fixed 70-20-10 cut-offs when the question gives different limits. Fix: Treat the split as indicative. Apply the cut-offs stated in the question. If none are given, say you assume a typical split.

Exam tips

Theory questions often ask for motives, types or costs as short notes. Use bold headings, one line each, and an example for every point.
In MCQs, test whether a cost is per order or per unit held. This settles most ordering vs carrying questions.
Always write average inventory as Q ÷ 2 in numericals, and show the substitution for step marks.
Link every answer to working capital: inventory ties up funds, so efficient control raises liquidity and returns.
Before moving to numericals, learn this page well, since EOQ and stock level questions depend on the same cost logic.
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.