UPI Study › Courses › Quantitative Analysis › Free lessons › Lesson 4.2 Free with a free account
The True Cost of Keeping Stock
Quantitative Analysis · Chapter 4: Inventory Management and QueuingSection 4.2 · lesson 13 of 5512 min · free with a free account
Free preview
Create a free account to keep watching
It takes a minute and costs nothing. Your free account unlocks all of Chapter 1 and 3 more lessons of Quantitative Analysis.
Lesson complete
Earn the 3 college credits for Quantitative Analysis
Enrolling adds a quiz after each lesson, the graded work and the official transcript. Recommended for credit by NCCRS.
Next lesson: Supply Meets Demand: Inventory Optimization →← Components of Merchandise InventoryNext lesson: Supply Meets Demand: Inventory Optimization →
In this lesson
Definitions, methods, and types of inventory costs.
- Break total inventory cost into its four components
- Compute holding cost from an annual rate and a unit cost
- Explain the trade-off the EOQ model is built to solve
- Value COGS and ending inventory under FIFO, LIFO and WAC
Transcript
Everything said in the video, section by section (1,770 words). Read along, or search it.
Inventory Management and Queuing · Section 4.2
The True Cost of Keeping Stock
Inventory is one of the largest line items on a typical company's balance sheet. It is also one of the easiest things in the whole business to mismanage. Order too little, and the firm pays in lost sales and frantic emergency purchases. Order too much, and capital sits idle on a warehouse shelf. Idle stock quietly loses value to insurance premiums, depreciation, and obsolescence. So the central problem of inventory management is cost minimization. How much to order, and how often, so total cost is as low as it reasonably can be. This section splits that total into four components, and shows how each is measured. Then we turn to the accounting side of the same stock.
The Central Problem
Order Too Little, Order Too Much
Start with the shape of the problem, because it is genuinely two sided. Understocking has a cost, overstocking has a cost, and the two pull in opposite directions. A manager who only fears stockouts will carry far too much inventory. A manager who only fears carrying charges will run out at the worst possible moment. Neither instinct is wrong. Both are incomplete. The goal is not the lowest holding cost, nor the smallest number of orders. It is the lowest total cost, added up across every category. Three things follow. First, the four components of inventory cost, and how each one is measured. Second, the trade-off that the Economic Order Quantity model is built to solve. Third, the conventions that decide which unit's cost becomes cost of goods sold.
Four Components
What Total Inventory Cost Is Made Of
Total inventory cost is conventionally decomposed into four categories. Ordering cost, holding cost, stockout cost, and purchase cost. Each one behaves differently as order size and order frequency change. That is exactly why the best policy is rarely obvious. If all four moved together you could minimize any one of them and be done, but they do not. The decomposition is not academic bookkeeping. It lets a manager see which cost a proposed change actually moves. A bulk discount offer cuts purchase cost, but it raises holding cost. A faster supplier cuts stockout cost, but it may raise ordering cost. One confusing number becomes four levers you can analyze one at a time.
Ordering Cost
The Price of Placing an Order at All
Ordering cost is what you pay each time you place an order at all. The load-bearing phrase there is regardless of order size. It is written as capital S, or as C sub o, in most texts. For a retailer or a distributor it covers purchase order processing and administrative time. It also covers fixed delivery fees, and the back and forth with the supplier. A manufacturer producing in house has an equivalent, called setup cost. That is the time and labor to reconfigure machines for the next production run. Plus the initial scrap that always comes with a new setup, before the line settles. Now notice what fixed per order implies: the larger the order, the smaller the ordering cost per unit. That single fact is the force pushing managers toward bulk buying.
Holding Cost
What It Costs to Keep a Unit on the Shelf
Holding cost, also called carrying cost, is the cost of keeping a unit in stock. It is really five separate expenses bundled into one number. Storage covers warehouse rent, utilities, refrigeration, shelving, and material handling. Insurance and taxes cover premiums on stored goods, and in some places property tax. Capital cost is the return the firm could have earned investing that money elsewhere. That opportunity cost is often the single largest piece, and the one people forget. Obsolescence and spoilage cover markdowns, write offs, and physical deterioration. Shrinkage covers theft, damage, and plain counting errors. In practice holding cost is expressed per unit per year, and it equals the annual holding rate times the unit cost. A rate of twenty-five percent a year is a common rule of thumb. It rolls capital, storage and obsolescence together into one figure. So a unit costing forty dollars carries ten dollars of holding cost every year.
The Other Two
Stockout Cost and Purchase Cost
Stockout cost is the cost of not having enough inventory when demand arrives. It has a tangible side and an intangible side. Tangible means the lost gross margin on the sale you could not make. It also means backorder fees, and the premium you pay to resupply in a hurry. Overnight shipping, or buying on the spot market at full list price. The intangible side is damaged goodwill, and a customer who could not get the item may go elsewhere. This is the hardest of the four costs to measure precisely. So firms often estimate it implicitly, by setting a target service level instead. Fill ninety-eight percent of orders from stock, rather than pricing every missed sale. Purchase cost is the simplest of the four, just unit cost times quantity ordered. In the basic Economic Order Quantity model, unit cost does not depend on order size, so purchase cost drops out of the optimization. That changes the moment quantity discounts appear, and purchase cost becomes a decision variable.
The Total Cost Function
Four Costs Pulling in Two Directions
Total cost for a year is simply the sum of the four components. Purchase cost, plus ordering cost, plus holding cost, plus stockout cost. The interesting part is a tug of war between just two of them. Place larger, less frequent orders and ordering cost falls, but average inventory climbs, and holding cost climbs with it. Place smaller, more frequent orders, and average inventory shrinks. Holding cost falls, but now ordering cost piles up. Plot both against order quantity, and one curve falls while the other rises. The order size at the bottom of the total curve is the Economic Order Quantity. Chapter four point three derives that formula properly, so here the point is conceptual. Because the four components do not move in the same direction, minimizing one is a trap. Cheapest unit price, fewest orders, smallest warehouse. Each, chased alone, raises total cost.
Valuation Methods
Which Unit's Cost Becomes COGS?
Now the second half of the story, which is accounting rather than operations. The stock is in the warehouse, a unit sells, and which unit's cost becomes cost of goods sold? If every unit had been bought at the same price, the question would be trivial. But prices drift, so the firm has to choose a convention. Four are in common use. First in, first out assumes the oldest stock is sold first. That matches the real flow of perishable goods, like food or pharmaceuticals. When prices rise it charges older, cheaper costs to cost of goods sold, so profit and ending inventory both look higher. Last in, first out assumes the newest stock is sold first. When prices rise, it charges the most recent and highest costs against revenue. That reduces reported profit and, where it is permitted, reduces taxable income. Note the qualifier. It is allowed under United States accounting rules, but not under IFRS. Weighted average smooths the swings by averaging every unit available for sale, and usually lands between the other two. Specific identification tracks each unit individually, from purchase all the way to sale.
Worked Example
Hartwell Hardware: One Quarter of Drills
Time to put real numbers on this, with Hartwell Hardware, a regional retailer of mid range power tools. We follow one cordless drill product code through a single quarter. It opened April with two hundred units, carried at thirty dollars each. That is six thousand dollars of opening inventory. On April eighteenth it bought a hundred and fifty more, at thirty-two dollars. Another four thousand eight hundred dollars. On May tenth it sold two hundred and fifty units. Then on May thirtieth it bought a hundred more, at thirty-six dollars. So four hundred and fifty units were available for sale across the quarter. They cost fourteen thousand four hundred dollars in total, with two hundred and fifty sold and two hundred left. Now hold on to one detail, because it decides two of the three answers. The May tenth sale happened before the May thirtieth purchase.
Method 1 - FIFO
Oldest Layers Leave First
Take first in, first out first. The two hundred and fifty units sold come from the oldest layers available. The whole opening layer goes first, two hundred units at thirty dollars, or six thousand dollars. We still need fifty more units, so we dip into the April eighteenth purchase. Fifty units at thirty-two dollars is one thousand six hundred dollars. Add the two layers, and cost of goods sold is seven thousand six hundred dollars. What remains is a hundred units at thirty-two, and a hundred at thirty-six. Three thousand two hundred, plus three thousand six hundred, gives ending inventory of six thousand eight hundred dollars. Notice that the two figures add to fourteen thousand four hundred. That is exactly the total cost of goods available for sale. The identity holds under every method, and it is your fastest arithmetic check.
Method 2 - LIFO
Newest Available Layers Leave First
Now last in, first out, on exactly the same transactions. The units sold come from the newest layers, but only those available at the time. This is the step people get wrong, because the May thirtieth purchase happens after the May tenth sale. So it cannot supply that sale, however new it is. The newest layer actually available is the April eighteenth purchase. All hundred and fifty units, at thirty-two dollars, is four thousand eight hundred. That leaves a hundred units, which come from opening inventory at thirty dollars, another three thousand dollars. Cost of goods sold is seven thousand eight hundred dollars. Higher than under first in first out, because the pricier layer was expensed first. Ending inventory is the remainder, six thousand six hundred dollars. And again, the two add back to fourteen thousand four hundred.
Method 3 And Comparison
Weighted Average, and What Changes
The third method refuses to track layers, and divides total cost of goods available by total units available. Fourteen thousand four hundred dollars over four hundred and fifty units is exactly thirty-two dollars per unit. Both sides are then valued at that one average. Two hundred and fifty units sold gives cost of goods sold of eight thousand dollars. Two hundred units remaining gives ending inventory of six thousand four hundred. And the check still works. They sum to fourteen thousand four hundred. Now line the three methods up side by side. Cost of goods sold runs from seven thousand six hundred, up to eight thousand. Ending inventory runs the other way, from six thousand eight hundred down to six thousand four hundred. Weighted average is the outlier here, because its average includes a purchase the May tenth sale could never have used. Same drills, same warehouse, same sale. Gross profit differs by four hundred dollars between first in first out and weighted average, and only the convention changed. In a rising-price world, first in first out will systematically report the higher profit. So any comparison across companies has to normalize for the method each firm uses.
About Quantitative Analysis at UPI Study
Quantitative Analysis (Math 250) is a self-paced online course of 55 video lessons in 13 chapters, from decision analysis and simulation to inventory and queuing models, project scheduling, linear programming and transportation models. It carries a NCCRS credit recommendation for 3 semester credits.
Every lesson transcript is free on pages like this one, and the videos are free with a free UPI Study account. Enrolling adds a practice quiz after each lesson, the graded work and final exam that earn the credit, lifetime access, and an official transcript on completion. UPI Study has helped over 130,000 students with college credits. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.
Enroll now → Course details Download the syllabus All Math courses Every course with PRO →
Compare: Statistics vs Quantitative Analysis
Why take it here
Why students take Quantitative Analysis with UPI Study
Where the credit goes
Universities that work with NCCRS
Quantitative Analysis carries a NCCRS credit recommendation. These universities work with NCCRS; some are UPI Study's signed partners. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.
Thomas Edison State UniversitySigned partner
University of the PeopleSigned partner
Charter Oak State CollegeSigned partner
Strayer UniversitySigned partner
Columbia Southern UniversitySigned partner
Indiana TechSigned partner
Penn StateWorks with NCCRS
Southern New Hampshire UniversityWorks with NCCRS
SUNYWorks with NCCRS
+many more cooperating universitiesFind my college →Find my college → Not listed? Ask Athena in the corner of this page, or book a 15-minute call.
FAQ
Questions students ask us
About The True Cost of Keeping Stock
What are the four components of total inventory cost?
How do you calculate inventory holding cost?
Why does minimizing a single inventory cost usually raise total cost?
How do FIFO, LIFO, and weighted average change cost of goods sold?
About the Quantitative Analysis course
How many college credits is Quantitative Analysis?
How much does Quantitative Analysis cost and what is included?
Which universities accept UPI Study credits?
How long does Quantitative Analysis take?
How are the exams done?
How do my credits reach my college?
Ready for the full course? Earn 3 credits in Quantitative Analysis.
55 video lessons, a quiz after each one, and the graded work that earns the credit. Recommended for credit by NCCRS.
3 credits · NCCRSEnroll →