CMA Intermediate · Financial Management and Business Data Analytics

Inventory Management: formula sheet

Full chapter guide

Key formulas

Annual ordering cost: (Annual demand ÷ Order size) × Cost per order; Number of orders per year × ordering cost per order. It falls as order size rises.
Annual carrying cost: (Order size ÷ 2) × Carrying cost per unit per year; Assumes steady usage, so average stock is half the order size. Per-unit cost may be given as a % of purchase price.
Carrying cost per unit when given as a percentage: Purchase price per unit × Carrying cost %; Use this to convert a percentage into rupees per unit per year.
Total inventory cost: Annual ordering cost + Annual carrying cost (+ stock-out cost, if given); Purchase cost is added only when prices differ between options, such as discount cases.
Average inventory: (Opening stock + Closing stock) ÷ 2; With uniform usage and no safety stock, it equals half the order size.
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. Keep A and C on the same unit and the same year.
Carrying cost per unit: C = carrying cost % × purchase price per unit; Use this when carrying cost is given as a percentage of price. If it is given in rupees per unit per year, use it directly.
Number of orders per year: N = A ÷ EOQ; If the answer is not a whole number in the question, state it as it is unless asked to round.
Time between orders: Days between orders = number of days in year ÷ N; Use 360 or 365 days as the question states. If nothing is stated, say which one you use.
Total ordering cost: (A ÷ Q) × O; Q is the order size.
Total carrying cost: (Q ÷ 2) × C; Based on average stock of Q ÷ 2, with no safety stock.
Total relevant cost at EOQ: Total relevant cost = √(2 × A × O × C) = EOQ × C; At EOQ ordering cost equals carrying cost, so each is half of this total.
Total inventory cost: Total cost = purchase cost (A × P) + ordering cost + carrying cost; Purchase cost is the same for every order size when there is no discount, so it does not change the EOQ.
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 C is a percentage of price, C = percentage × price of that band.
Carrying cost: Carrying cost = (Q ÷ 2) × C; Assumes steady usage, so average stock is half the order quantity Q.
Ordering cost: Ordering cost = (A ÷ Q) × O; A ÷ Q is the number of orders in a year. It can be a fraction in a calculation.
Purchase cost: Purchase cost = A × price per unit; Use the price of the band that Q falls in.
Total relevant cost: Total cost = A × P + (A ÷ Q) × O + (Q ÷ 2) × C; Compare this for each candidate order size. The lowest total is the best order size.
Validity check: EOQ is valid only if lower limit ≤ EOQ ≤ upper limit of its price band; If the EOQ is below the band, use the band's minimum quantity instead. If it is above the band, ignore it.
Reorder level (worst case): Reorder level = Maximum usage × Maximum lead time; This is the standard textbook formula. Use it when the question gives maximum usage and maximum reorder period and does not give safety stock separately.
Reorder level (with safety stock): Reorder level = Safety stock + (Normal usage × Normal lead time); Use when safety stock is given independently or you are asked to find it. It matches the worst-case formula only when safety stock is defined as worst-case consumption minus normal consumption.
Safety stock: Safety stock = (Maximum usage × Maximum lead time) − (Normal usage × Normal lead time); If only lead time varies: (Maximum lead time − Normal lead time) × Normal usage.
Minimum level: Minimum level = Reorder level − (Normal usage × Normal lead time); This always holds. It equals the safety stock when reorder level = safety stock + normal lead-time usage, for example when reorder level is built from maximum usage and maximum lead time.
Maximum level: Maximum level = Reorder level + Reorder quantity − (Minimum usage × Minimum lead time); Reorder quantity is usually the EOQ. Use minimum usage and minimum lead time here.
Danger level: Danger level = Usage figure named in the question × Emergency lead time; The usage is usually normal or average usage, but some questions name maximum usage. Use the figure the question names. Do not assume danger level is below minimum level.
Normal (average) lead time or usage: Normal = (Minimum + Maximum) ÷ 2; Use only when the question gives no normal figure and says average.
Annual consumption value: Annual consumption value = Annual usage (units) × Unit cost (₹); The base for ranking in ABC analysis.
Cumulative percentage: Cumulative % of value = Running total of value ÷ Total value × 100; Rank items in descending order of value first. Do the same for cumulative % of items.
ABC classes (typical guide): A: few items, high value | B: moderate items, moderate value | C: many items, low value; Percentages vary. Use the question's cut-offs if given.
VED and FSN bases: VED = criticality | FSN = rate of movement or issue; Neither depends on the value of the item.
Two-bin trigger: Second bin quantity = Consumption during lead time + Safety stock; Reordering is triggered when the first bin is empty.
Cost of issue (FIFO): Issue cost = units from oldest lot × its price + units from next lot × its price ...; Exhaust the oldest lot before moving to the next. Closing stock comes from the latest lots.
Cost of issue (LIFO): Issue cost = units from latest lot × its price + units from the previous lot × its price ...; In a perpetual (issue-by-issue) record, use the latest lot available on the date of that issue.
Weighted average rate (perpetual): Rate = Total value of stock on hand ÷ Total units on hand; Recalculate after every purchase. Issues do not change the rate.
Stock check: Opening stock + Purchases = Cost of issues + Closing stock; Use this to verify every method. The total must be the same.
Average inventory: (Opening inventory + Closing inventory) ÷ 2; Use the figures given. If only closing stock is given, use it and say so.
Inventory turnover ratio: Cost of goods sold ÷ Average inventory; Answer in times. Some questions use sales in the numerator. Follow the question.
Inventory holding period: Days in year ÷ Inventory turnover ratio = Average inventory ÷ COGS × days in year; Use 365 or 360 as the question states. If not stated, say which you assume.

Quick revision

EOQ = √(2AO ÷ C), where A is annual demand, O is ordering cost per order and C is carrying cost per unit per year.
At EOQ, total ordering cost equals total carrying cost.
Average stock under the basic model = order quantity ÷ 2.
Number of orders per year = annual demand ÷ order quantity.
Total cost = ordering cost + carrying cost (add purchase cost when comparing discounts).
With discounts, compare total costs at each price level and choose the lowest.
Reorder level has three standard forms: maximum consumption × maximum lead time; or (average consumption × average lead time) + safety stock; or minimum level + (normal consumption × normal lead time). Use the one that matches the data given: if only maximum figures are given, use the first; if average or normal figures and a safety stock are given, use the second; if the minimum level is given or computed, use the third.
Safety stock is the buffer held against variation in demand or lead time.
ABC ranks items by consumption value; VED by criticality; FSN by speed of movement.
Stock turnover ratio = cost of goods sold ÷ average inventory.
Inventory holding period = days in the year ÷ stock turnover ratio.
A very high turnover may signal stock-outs; a very low one signals overstocking.

Common mistakes

Classifying insurance, storage rent or obsolescence as ordering cost. Fix: Ordering cost arises from placing and receiving orders. Anything linked to holding stock is carrying cost.
Using full order size instead of half for carrying cost. Fix: Average stock is Q ÷ 2 when usage is uniform. Use it for carrying cost.
Using carrying cost percentage as the rupee value of C. Fix: Multiply the percentage by the purchase price first. 20% of ₹25 gives C = ₹5 per unit per year.
Mixing monthly demand with yearly carrying cost. Fix: Convert demand to an annual figure before starting, or convert C to a monthly figure, but never mix the two.
Leaving out purchase cost when comparing totals. Fix: With discounts the price changes between options, so always include A × price in every total.
Using the EOQ of a band even though it falls outside that band's quantity range. Fix: After every EOQ calculation, compare it with the band limits. If it is too low, use the lower limit of the band instead.
Using normal usage × normal lead time as the reorder level. Fix: That product is only lead-time consumption. Add safety stock, or use maximum usage × maximum lead time.
Using maximum usage and maximum lead time inside the maximum level formula's deduction. Fix: Deduct minimum usage × minimum lead time. The maximum level assumes the order arrives early while usage is low.
Ranking items by unit price or by quantity instead of annual consumption value. Fix: Always multiply units by unit cost first. Rank only on that product.
Calculating cumulative percentages without sorting first. Fix: Sort in descending order of value before adding. A cumulative total is meaningless otherwise.

Exam tips

In MCQs, first decide whether a cost varies with the number of orders or with the quantity held. That settles classification.
For 'discuss' questions, list motives and objectives as short numbered points, each with a one-line reason.
Show the number of orders, ordering cost, carrying cost and total cost as separate lines in numericals to earn step marks.
If carrying cost is given as a %, convert it to rupees per unit before using it.
Link this topic to EOQ in your answer when asked why firms balance costs, since total cost is lowest where the two cost types balance.
In the MCQ section, questions are short: a direct EOQ, a number of orders, or a total cost. Do the 2AO ÷ C step mentally and test your answer by squaring.
In written answers, show the formula, the substitution and the check that ordering cost equals carrying cost. These are separate step marks.
Read the carrying cost line twice. It may be a percentage of price, a rupee amount per unit, or a monthly figure.