IntroductionAlthough materials inventory is essential to keep production running and meet sales demand, it comes at a cost. That cost has several components, and depending on which ones they focus on, different departments may want opposite things. After the cost of the goods themselves, logistics costs are often among a company's largest expenses. Managing them well can be critical to its survival.From a financial perspective, inventory is capital tied up in materials: money that has left the company's cash reserves and will not come back until the product is sold or used. In some circumstances, holding inventory can be advantageous. During periods of high inflation, retailers may hold onto products in anticipation of further price increases, while buyers of exchange-traded commodities may stock up to protect themselves against price swings. In these cases, inventory serves a speculative purpose. At the other end of the chain, inventory is justified by demand: without it, companies lose sales and customers.From a warehousing perspective, inventory brings costs for space, special conditions (refrigeration, temperature control), internal handling, tracking, losses, missing goods and obsolescence.This lesson divides those costs into four groups, shows how to estimate each one and explains how they add up to the total cost. It lays the groundwork for the next lesson, on economic order quantity, which uses these same figures.Why each department wants a different inventory levelBefore looking at the numbers, it helps to understand the conflict. Each department sees the part of the cost that affects it:DepartmentWants inventory levelsBecauseSalesHigh (finished goods)To fill orders quickly, in the quantities customers want, without losing salesWarehousingLowLess space occupied, less handling and lower storage costsPurchasingHigh (large orders)Greater bargaining power and volume discounts from suppliersFinanceLowInventory ties up capital; large purchases strain cash flow and may force the company to borrowProductionHigh (raw materials)To avoid production stoppages and support large-scale productionFinancial controlLowLarge inventories mean a greater risk of loss, higher storage costs and congestionNo department is wrong: each is concerned with a real cost. Inventory management puts all those costs into the same calculation to find the right balance.The main cost categoriesInventory costs fall into four broad categories:Acquisition cost: the price paid for the materials.Ordering cost (also called replenishment or procurement cost): the cost of placing each order.Holding cost (also called carrying or storage cost): the cost of keeping materials in inventory.Stockout cost: the cost of not having an item when it is needed.A note on terminology: textbooks use different abbreviations. In this series, we use Cp for the cost per order and Cm for the holding cost per unit per year. In Paulo Gonçalves's book, for example, cr means replenishment cost (ordering cost), while cp means holding cost. Before using a formula from another source, check what each letter stands for.Acquisition costThis is the amount paid for the materials: unit price multiplied by the quantity purchased during the year (D × P), including shipping and taxes the company cannot recover. It may seem unrelated to inventory levels, but it matters when a supplier offers volume discounts: order size then affects the price. We will look at this in the lesson on economic order quantity.Ordering costOrdering cost is the expense a company incurs each time it places a replenishment order with a supplier. It covers the entire process: the purchase requisition, price comparisons, negotiations, issuing the purchase order, tracking delivery, receiving, checking and inspecting the materials, and paying the invoice.In manufacturing, when an item is made in-house, the equivalent is the setup cost (setup): machine downtime and the work needed to switch a production line from one product to another.The key point is that ordering cost is largely fixed per order, whether the order is for 10 or 10,000 units. Annual ordering cost therefore depends on how many orders are placed during the year:Annual ordering cost = (D ÷ Q) × Cpwhere D is annual demand, Q is the quantity per order (D ÷ Q is the number of orders per year), and Cp is the cost per order. Buying in small batches means placing many orders and paying more in ordering costs.How to estimate the cost per orderA practical approach is to divide the annual cost of the purchasing process by the number of orders placed. Suppose the purchasing department, including two buyers, its systems and communication expenses, costs R$ 18,000 a month (R$ 216,000 a year) and places 1,200 orders a year:216,000 ÷ 1,200 = R$ 180 per orderIf receiving each delivery also requires R$ 20 for checking and inspection, the cost per order is R$ 200.There is an important refinement: strictly speaking, only costs that change with the number of orders should be included. The purchasing department's rent, for example, will not fall if the company places half as many orders. Many companies use the simpler calculation above, but it tends to overestimate Cp.Shipping needs separate consideration: if the supplier charges a fixed amount per delivery, it behaves like an ordering cost. If the charge is per kilogram or per unit, it is part of the acquisition cost because the charge per item does not change with order size.A company's purchasing department costs R$ 300,000 a year and places 1,500 orders annually. If the company starts buying in batches twice as large, what happens to its annual ordering cost, assuming all of that cost is variable?Answer: It falls by half, from R$ 300,000 to R$ 150,000, because the company will place 750 orders at R$ 200 each — the cost per order is 300,000 ÷ 1,500 = R$ 200. With batches twice as large, the same demand can be met with half as many orders. Ordering cost depends on the number of orders, not the size of each one.Holding costHolding cost concerns inventory sitting in storage: rather than measuring the flow of goods, it adds up what a company spends to keep materials on hand. It is proportional to average inventory and is usually expressed as an annual percentage of inventory value (for example, 25% a year) or as an amount in reais per unit per year. It has four components.Cost of capitalThis is the cost of the money tied up in inventory. That money could be earning a return elsewhere or paying down debt, so inventory costs at least the return the money could have earned (the opportunity cost) or the interest on the loan used to finance it. This is often the largest component of holding cost.Which rate should be used? Textbooks offer three approaches: the return on a typical financial investment; the return the company earns on its own capital; or the weighted average cost of its sources of financing. In Brazil, a natural minimum benchmark is the benchmark interest rate, Selic, which was around 14% to 15% a year in 2025 and 2026. That is roughly what the money could earn with very little risk if it were not sitting on a shelf. Companies that finance inventory with bank loans pay considerably more. That is why expensive inventory weighs more heavily in high-interest-rate countries than in low-interest-rate ones, and why examples in foreign textbooks that assume a 5% cost of capital do not apply here.Storage costThis is the cost of space: warehouse rent (or depreciation if the property is owned), electricity, water, property taxes such as IPTU, and refrigeration when needed. If inventory shares a building with the office, the company allocates a share of those costs based on the space inventory uses.One effect deserves attention: space saturation. Up to a point, storing more goods raises costs proportionally. But when a warehouse fills up, moving goods becomes harder, operations slow down, and extra costs rise disproportionately: overtime, emergency rental of additional space and damage caused by cramped handling conditions.Inventory service costsThese include warehouse staff, security, insurance for stored materials, inventory management systems (IT) and periodic stocktakes.Inventory risk costsThese cover the loss of value while materials are stored: obsolescence (a model is discontinued or fashions change), expiry, deterioration, theft and missing goods. They are especially important for perishables, electronics and fashion products.Example: calculating the holding-cost rateA company holds average inventory worth R$ 500,000 and has calculated the following costs for the past year:ComponentAnnual cost% of average inventoryCapital (company's chosen rate: 14% a year)R$ 70,00014%Storage (rent, electricity, proportional share of IPTU)R$ 40,0008%Services (staff, insurance, systems)R$ 25,0005%Risks (losses, expiry, obsolescence)R$ 15,0003%TotalR$ 150,00030% a yearBreakdown of holding costs in the example: the cost of capital accounts for almost halfTo use this rate in formulas, we convert it into reais per unit: an item costing R$ 40 has a holding cost of Cm = 30% × R$ 40 = R$ 12 per unit per year.Because inventory fluctuates between full (just after an order of Q arrives) and nearly empty, average inventory is approximately Q ÷ 2. Thus:Annual holding cost = (Q ÷ 2) × CmBuying in large batches means holding more inventory on average and paying more in holding costs: the exact opposite of ordering costs.An item costs R$ 80, and the company estimates its holding cost at 25% a year. If average inventory of this item is 300 units, how much does the company spend each year to hold it?Answer: R$ 6,000 — the cost per unit is 25% × 80 = R$ 20 a year; with 300 units on average, 300 × 20 = R$ 6,000. R$ 24,000 is the value of average inventory (300 × 80), not the cost of holding it.The Central Bank raises interest rates, increasing the company's cost of capital. If everything else stays the same, what is likely to happen to the ideal order size?Answer: It will decrease because holding inventory has become more expensive — the cost of capital is part of holding cost. When it rises, placing more, smaller orders becomes worthwhile because it reduces average inventory. Ordering cost does not depend on interest rates.Stockout costThe final piece of the picture is the cost of not having inventory. These costs arise when an item is unavailable when needed. Some can be measured:the profit margin on a lost sale;emergency shipping and purchases, which are usually more expensive;contractual penalties for delays;production stopped while waiting for a component (idle workers and machinery);substituting a more expensive or less profitable product or raw material.Others are difficult to measure but may be the most costly: customers who never return, lost market share and damage to the company's reputation.For example, a store ran out of a product for a week and missed out on 50 sales, each with a margin of R$ 20 (R$ 1,000). It paid R$ 400 for express shipping to restock quickly. The measurable stockout cost was R$ 1,400, not counting customers who switched to a competitor and never came back.Because stockout costs are hard to estimate, they rarely go directly into a formula. Instead, companies set a target service level (for example, avoiding stockouts in 95% of cycles) and hold enough safety stock to meet it. That is the subject of the lesson on lead times and safety stock.Putting it all together: total costAdding up the components gives the annual total cost for an inventory item:CT = D × P + (D ÷ Q) × Cp + (Q ÷ 2) × Cm(plus stockout costs, when they can be estimated). The key is that the two terms in the middle move in opposite directions:larger order quantities → fewer orders (lower ordering costs), but more inventory on average (higher holding costs);smaller order quantities → less inventory on average (lower holding costs), but more orders (higher ordering costs).Example. An item has annual demand of 6,000 units, a price of R$ 40, an ordering cost of R$ 200 and a holding cost of R$ 12 per unit per year. Compare two approaches:Order quantityPurchase cost (D × P)Ordering cost (D ÷ Q × Cp)Holding cost (Q ÷ 2 × Cm)Total1,000 unitsR$ 240,0006 × 200 = R$ 1,200500 × 12 = R$ 6,000R$ 247,200500 unitsR$ 240,00012 × 200 = R$ 2,400250 × 12 = R$ 3,000R$ 245,400Ordering 500 units at a time costs R$ 1,800 less per year. But is 500 the best order quantity? What about 400 or 450? Finding the quantity that minimizes total cost is the economic order quantity problem, the subject of the next lesson.Poor cost estimates lead to poor decisions. Paulo Gonçalves’s book sums up the likely outcomes:If a company estimates...It is likely to...Ordering costs too lowPlace too many orders, risking stockouts and worse pricesOrdering costs too highBuy large quantities, tying up capital and filling its warehouseHolding costs too lowBuy large quantities that require more storage spaceHolding costs too highIncrease the number of orders, deliveries, inspections and goods receiptsIn the example above (D = 6,000, Cp = R$ 200, Cm = R$ 12), what would the combined ordering and holding costs be for orders of 2,000 units?Answer: R$ 12,600 — ordering: 6,000 ÷ 2,000 = 3 orders × 200 = R$ 600; holding: 2,000 ÷ 2 = 1,000 units on average × 12 = R$ 12,000; total R$ 12,600, far higher than the R$ 5,400 for orders of 500. The trap is forgetting to divide the order quantity by 2 to get average inventory, which would give R$ 24,000 in holding costs alone.ReferencesCHIAVENATO, Idalberto. Iniciação à administração da produção. São Paulo: McGraw-Hill, 1991.GONÇALVES, Paulo Sérgio. Administração de materiais. Rio de Janeiro: Elsevier, 2010 (chapter 3, Custo dos estoques).RICARTE, Marcos António Chaves. A importância dos custos logísticos na cadeia de suprimentos. São Paulo: Widesoft Sistemas, 2002.ExercisesEasy1) A distributor spends R$ 96,000 a year on its purchasing department and issues 800 orders a year. Each delivery received also costs R$ 30 to check. What is the cost of each order?2) Classify each expense as an acquisition, ordering, holding or stockout cost:a) inventory insurance;b) a fixed freight charge of R$ 150 per delivery;c) a penalty for delivering late to a customer;d) a buyer's salary;e) an expired product that is discarded;f) the unit price of the goods.3) A company estimates its holding cost at 32% a year. What is Cm for an item that costs R$ 25?4) An item has demand of 12,000 units a year and is bought in batches of 1,500 units. Each order costs R$ 90. What is the annual ordering cost?5) When estimating the cost of each order, why, strictly speaking, should the rent on the purchasing department's office not be included in the calculation?Hard6) A company's average inventory is worth R$ 1,200,000. During the year, it spent R$ 84,000 on warehouse rent and electricity, R$ 36,000 on storeroom staff and insurance, and R$ 24,000 on losses and obsolescence. The company uses 15% a year as its cost of capital. What is the annual holding-cost rate? What is Cm for an item that costs R$ 60?7) An item has demand of 9,000 units a year and a price of R$ 50. Each order costs R$ 150, and the holding-cost rate is 24% a year. Compare the combined ordering and holding costs for batches of 300, 450 and 900 units. Which of the three policies is the cheapest? Does the acquisition cost need to be included in this comparison?8) A store uses 500 units a month of a product. Each order costs R$ 120, and holding one unit in inventory costs R$ 1.50 a month. It currently buys in batches of 1,000 units. Calculate the annual ordering-plus-holding cost of the current policy and of a policy with batches of 250 units. Which is better, and by how much?9) A manufacturer's purchasing department costs R$ 25,000 a month, of which R$ 7,000 is rent and depreciation on the office, which do not change with the number of orders. The department issues 150 orders a month, and each delivery received requires R$ 40 for checking and inspection.a) What is the cost of each order using the simple calculation (the department's entire cost divided by the number of orders)?b) What is the cost of each order counting only the costs that vary with the number of orders?c) Which of the two figures should be used in the formulas, and what happens if the company uses the other one?10) A store ran out of a product twice last year. Each time, it lost sales of 80 units, with a margin of R$ 15 per unit, and paid R$ 350 for express freight to restock. The company estimates that a permanent extra stock of 60 units would have prevented both stockouts. The product costs R$ 30, and the holding-cost rate is 30% a year. Is it worth keeping this extra stock?Answer key1) Purchasing process: 96,000 ÷ 800 = R$ 120 per order. Adding receiving: 120 + 30 = R$ 150 per order.2) a) holding (inventory services); b) ordering, because it is fixed per delivery; c) stockout; d) ordering; e) holding (inventory risk); f) acquisition.3) Cm = 32% × 25 = R$ 8 per unit per year.4) Number of orders: 12,000 ÷ 1,500 = 8 orders a year. Annual cost: 8 × 90 = R$ 720.5) Because the ordering cost that matters for the formulas is the one that changes with the number of orders. The office rent is the same with 500 or 1,000 orders a year; including it overstates Cp and leads to buying larger batches than necessary.6) Storage, services and risks: 84,000 + 36,000 + 24,000 = R$ 144,000. Relative to average inventory: 144,000 ÷ 1,200,000 = 12%. Adding the cost of capital: 15% + 12% = 27% a year. For the R$ 60 item: Cm = 27% × 60 = R$ 16.20 per unit per year.7) Cm = 24% × 50 = R$ 12 per unit per year.Batches of 300: ordering 9,000 ÷ 300 = 30 × 150 = R$ 4,500; holding 300 ÷ 2 = 150 × 12 = R$ 1,800; total R$ 6,300.Batches of 450: ordering 20 × 150 = R$ 3,000; holding 225 × 12 = R$ 2,700; total R$ 5,700.Batches of 900: ordering 10 × 150 = R$ 1,500; holding 450 × 12 = R$ 5,400; total R$ 6,900.Batches of 450 are the cheapest of the three. The acquisition cost (9,000 × 50 = R$ 450,000) does not need to be included, because it is the same under all three policies: it would only make a difference if the price changed with the batch size (quantity discount). In the next lesson, you will see that the optimal batch is close to 474 units.8) First, put everything in the same period (a year): D = 500 × 12 = 6,000 units; Cm = 1.50 × 12 = R$ 18 per unit per year.Batches of 1,000: ordering 6,000 ÷ 1,000 = 6 × 120 = R$ 720; holding 500 × 18 = R$ 9,000; total R$ 9,720.Batches of 250: ordering 24 × 120 = R$ 2,880; holding 125 × 18 = R$ 2,250; total R$ 5,130.Batches of 250 are better, saving R$ 4,590 a year. Anyone who forgets to convert the monthly Cm to an annual figure (and uses R$ 1.50) reaches the opposite conclusion.9) Orders per year: 150 × 12 = 1,800.a) 25,000 × 12 = R$ 300,000 ÷ 1,800 = R$ 166.67; plus R$ 40 for receiving: R$ 206.67 per order.b) Variable cost: 25,000 − 7,000 = R$ 18,000 a month ÷ 150 = R$ 120; plus R$ 40: R$ 160 per order.c) The R$ 160 figure, because only it changes when the company places more or fewer orders. Using R$ 206.67 overstates Cp and leads to batches larger than ideal, with more capital tied up and a fuller warehouse.10) Cost of each stockout: 80 × 15 = R$ 1,200 in lost margin + R$ 350 in freight = R$ 1,550. Two stockouts: R$ 3,100 a year, not counting lost customers.Cost of holding the extra stock: Cm = 30% × 30 = R$ 9 per unit per year; 60 × 9 = R$ 540 a year.It is worth it: spending R$ 540 to avoid R$ 3,100 in measurable costs. This is the logic of safety stock, which you will see in the lesson on lead time.
Reazioni
0
0 Commenti
Diventa il primo a commentare
Niente qui ancora.