Opening and ending inventory: formulas and example
Opening and ending inventory: formulas and example
The result of a period is not explained by sales or by the cash that came in: it is explained by two photographs of the same warehouse. The first is taken on the opening day and shows how much you started with; the second is taken on the closing day and shows how much you ended with. Everything else, the purchases, the issues, the cost of what was sold and the profit that remains, comes from comparing those two photographs against the movement in between.
That is why opening inventory and ending inventory sit at the center of the close. If the opening figure is wrong, the error travels through the whole period and contaminates every report; if the ending figure is guessed or copied from last month without a count, profit becomes an opinion instead of a data point. The two formulas that connect them are short, and in practice the work is not in the arithmetic but in deciding which one to use, in what order, and what to do when the physical count does not match the number the system produced.
The two photographs of the warehouse and what joins them
Both concepts already have their own article on this blog, so they are not introduced from scratch here: what matters is the exact point where they meet. Opening inventory is the quantity on hand and its value at the start of the period, and in a well-run business it equals the ending inventory the previous period closed with. That continuity is what turns a series of months into a coherent story: the balance left in December is the balance that opens January, with no changes other than the adjustments that were documented and approved.
Ending inventory is the quantity on hand and its value at the close of the period. It can be obtained by formula at any time, and it must always be confirmed with the physical count. The reason is simple: the formula says what should be there according to the records, while the count says what is there. When the two numbers agree, the period is healthy; when they do not, the gap is the most useful clue available for finding the error.
What joins them is a single equation. Ending inventory is the opening point plus the entries of the period minus what left through sales; cost of goods sold comes out of that same addition and that same subtraction. Put another way, cost of goods sold and ending inventory are the two unknowns of the same system: if the business knows two of the three middle figures it can solve for the third, and the physical count is what validates that the number holds together.
So anyone looking at opening and ending inventory is looking at the same calculation from both ends. The order in which it is solved depends on the information the business has at hand: if it knows how much it sold, it computes what was left; if it knows what was left, it computes how much it sold. On both paths the physical count is the referee, and on both paths one poorly recorded figure in the middle ruins the result without anyone noticing at first glance.
The five figures of the system
Before the formulas it helps to have the five figures that combine clearly in mind. They are not five loose numbers: they are two photographs, one inflow, one outflow and one verification. If any of the five is measured badly, the period result is wrong no matter how well the subtraction is done.
| Figure | What it represents | Where it comes from | What happens if it is wrong |
|---|---|---|---|
| Opening inventory | The value of goods on hand when the period opens | From the previous close or from the initial count record | The whole period carries the error and the profit for the month is distorted |
| Purchases for the period | Every receipt of goods during the period, already valued | From supplier invoices and receiving notes | Cost of goods sold and the ending balance move the wrong way together |
| Cost of goods sold | The cost of the goods that left through sales, not the price they were sold at | From the solved formula or from the moving-record stock ledger | Gross profit is inflated or punished with no visible explanation |
| Ending inventory by formula | The balance that should exist according to the records | From the formula: opening plus purchases minus cost of goods sold | It becomes a convenient estimate that nobody ever verifies |
| Physical count at close | The balance that actually exists in the warehouse | From the count, valued on the same basis used during the period | Without it there is no way to know whether the formula worked |
The first two figures come from the previous period and from purchasing; the last two are the result of the calculation and its verification. Cost of goods sold is the figure that moves between the two ends, which is why most of the closing work consists of making sure it is complete.
The two formulas are one equation
The formula for ending inventory and the formula for cost of goods sold look different because they answer different questions, but they are the same equality read from opposite sides. This table puts them side by side with the meaning of each term.
| Question it answers | Formula | What each term means |
|---|---|---|
| How much should still be on hand at the close? | Ending inventory = opening inventory + purchases for the period minus cost of goods sold | Opening inventory: goods on hand at the start. Purchases: valued receipts of the period. Cost of goods sold: cost of what left through sales. Ending inventory: goods on hand at the close |
| What did the goods that were sold actually cost? | Cost of goods sold = opening inventory + purchases for the period minus ending inventory | The same terms, now solved: the unknown is the cost of what was sold and the known figure is the balance the period closed with |
Solve the first formula for cost of goods sold and the second appears; solve the second for ending inventory and the first comes back. That has a practical consequence many businesses overlook: there is no main formula and no backup formula. There is one equation with two unknowns, and the business chooses which one to compute based on what it already knows for sure.
The detail that decides whether the calculation is useful is valuation. Purchases must be complete and must include the freight that is capitalized into cost; cost of goods sold must be cost and not selling price; ending inventory must be valued on the same basis used during the period. If the basis changes halfway through, the formula is still correct and the result is still useless.
And there is one element no formula replaces: the physical count. The formula may say twelve and a half million while the warehouse holds twelve million four hundred eighty thousand; algebra does not close that gap, investigation explains it.
When each formula is the right one
Choosing between them is not a matter of taste, it is a matter of control method. A business that keeps perpetual inventory, meaning a stock ledger with every receipt and every issue valued movement by movement, already has ending inventory inside the system: it reads the figure and is done. In that case the formula is not there to discover the balance but to reconcile it: if the system balance and the balance the equation produces do not agree, there is a misrecorded movement or a misapplied cost, and it can be tracked down.
A business that keeps periodic inventory works the other way around. It does not record the cost of each issue, because doing so would mean valuing every sale, so it counts at the end of the period, once a month or once a year, and with that valued count it computes cost of goods sold using the solved formula. For this method the formula is not support, it is the only path, and the count is not an extra control but the source of the figure itself.
Between the two extremes there are mixed situations: businesses with a stock ledger only for the most expensive items, or with cycle counts by section. The practical rule does not change: where movements are valued, the formula reconciles; where they are not, the formula calculates and the count has the final word.
| Point of comparison | Perpetual inventory with stock ledger | Periodic inventory with count |
|---|---|---|
| How each issue is recorded | Valued at cost at the moment of the movement | The cost of each issue is not recorded |
| Where ending inventory comes from | From the system, item by item | From the physical count valued at the close |
| What the formula is for | To reconcile the system against the equation | To compute cost of goods sold for the period |
| Role of the physical count | Confirms and detects misrecorded movements | Mandatory: without a count there is no figure |
| Main risk | Trusting the system and never counting | Depending on an incomplete or badly valued count |
A full example reconciled against the count
Take a one-month period in a small business. It opened with goods on hand worth 12,000,000, received purchases of 45,000,000 and had sales whose cost adds up to 44,500,000. With those three figures the ending inventory formula is direct.
12,000,000 plus 45,000,000 minus 44,500,000 gives 12,500,000. That is the balance that should exist. The physical count, taken on the last afternoon of the period with movement already cut off, came to 12,480,000. The difference is 20,000 and against a balance of twelve and a half million it looks like very little; yet a gap of twenty thousand is exactly the kind of difference that grows when nobody looks at it.
| Item | Amount | How it is obtained |
|---|---|---|
| Opening inventory | 12,000,000 | Previous period close, already adjusted |
| Purchases for the period | 45,000,000 | Invoices and receipts of the period, with freight capitalized into cost |
| Goods available | 57,000,000 | Opening inventory plus purchases for the period |
| Cost of goods sold for the period | 44,500,000 | Taken from the stock ledger or found with the solved formula |
| Ending inventory by formula | 12,500,000 | Goods available minus cost of goods sold |
| Physical count at the close | 12,480,000 | Count valued on the same basis used during the period |
| Difference to be explained | 20,000 | Inventory by formula minus the physical count |
| Average unit cost from the count | 1,066.67 | Count value divided by the 11,700 units counted |
| Difference expressed in units | 18.75 | The 20,000 restated at the average unit cost |
With the table in front of you, the difference of 20,000 is worth eighteen and three-quarter units at average cost, a figure someone can actually go and look for in the warehouse. If an issue without paperwork turns up, or a return applied to the wrong period, or a purchase that arrived on the last day and was never recorded, the balance is corrected at the source and the period is clean. If after reviewing there is no reasonable explanation, the adjustment is recorded and written into the count record: a documented adjustment teaches something once, and a silent adjustment repeated every month hides the underlying problem.
Step by step to close the period properly
Sequence matters as much as the figures. These are the steps that keep you from doing the close twice:
- Cut off movement on the last day at the established hour, and never close in the middle of a dispatch. An issue left half recorded lands in the wrong period and contaminates both.
- No receipt or issue after the cutoff enters the period without the period being reprocessed from scratch. It is better to open the next period with the correct date than to dress up the previous one.
- Count before the statements are issued, never after. If the statement is issued first and the count comes later, the adjustment shows up as a correction nobody understands.
- Count blind: the person counting does not see the system balance. Seeing the expected number first makes the count confirm rather than measure.
- Value the count on the basis used during the period, the same cost applied in the stock ledger or in the purchases. Switching basis at the end creates differences that look like shortages and are not.
- Leave the count record signed by the person who counted and the person who supervised, with date, time and remarks. It is the backing for the entire close.
- Reconcile against the system or against the formula before accepting the number. The difference is investigated movement by movement, not averaged away into next month.
- Only once the difference is explained or adjusted, compute the final cost of goods sold and close the period with the profit that actually belongs to it.
The five enemies of the calculation
Most closes that fail to balance do not fail because of bad arithmetic, they fail because of incomplete data. These five problems explain almost every discrepancy that comes back month after month:
- Unrecorded purchases: goods that arrived in the warehouse and whose invoice has not been entered yet. The formula believes the balance is lower than it really is and cost of goods sold comes out understated.
- Sales without relieving the cost: the customer was invoiced but the stock ledger never took the goods out. The system shows stock that has already left and the error piles up period after period.
- Undocumented shrinkage: product broken, expired or consumed internally that nobody reported. It is a real shortage the formula cannot guess and only the count record brings to light.
- Freight costs left out: the transport that belongs in the cost of the goods was booked as an expense of the period. Ending inventory ends up understated and the profit for the month is distorted.
- Comparing weights with different packaging: one period was valued by the kilo and the next by the sack, or the unit changed presentation halfway through the year. Both numbers exist, but they are not comparable and the subtraction means nothing.
Common mistakes when comparing the two inventories
Beyond those five enemies there is a set of method mistakes that show up again and again at closing time:
- Using last period's ending inventory as the opening figure without checking whether approved adjustments exist. The continuity is correct, but only if those adjustments are included.
- Computing cost of goods sold with the selling price instead of the cost. Gross profit becomes a mirror: it reflects the margin you expected, not the margin you earned.
- Valuing the count at a cost different from the one used during the period, which produces differences that do not exist in the warehouse.
- Counting with movements still open: a receipt half entered means the count and the system can never agree.
- Accepting the system figure when the count does not match, on the grounds that the difference is small. Small differences are the ones that repeat.
- Mixing periods: recording in the wrong month a purchase that arrived on the last day or a sale dated the first of the following month.
Closing thought: two numbers, one system
Opening and ending inventory are not two separate chores: they are the two banks of the same equation. The opening figure arrives from the previous close, the ending figure comes from the formula or from the stock ledger and is confirmed by the count, and cost of goods sold is the bridge between them. When that circuit is in order, profit stops being a surprise and becomes a figure you can explain.
With Kardex Tauro every receipt and every issue is recorded and valued in a moving-record stock ledger, so ending inventory is read from the system and the formula is used to reconcile, which is the fastest way to find the movement that is missing. Kardex Tauro does not replace the physical count and does not try to: what it does is give the count something to compare against and give the difference a meaning.
