Three conventions for dividing the cost of one process between its products, and the decision none of them can make.
Joint costs are allocated to the products that come out of one process on a base chosen by policy: physical quantity, sales value at the split-off point, net realisable value (NRV), or a constant gross margin. On an illustrative 600,000 joint cost shared by three products, the physical method charges 15.00 a kilogram and shows product B breaking even, while the NRV method gives it a 31.8 per cent margin. Total gross margin is 280,000 under every method, and none of them tells you whether to make B.
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A joint process produces several products at once from the same input: a refinery, a dairy, a sawmill, a chemical cracker, or a metals process that yields a main alloy and saleable by-streams. Up to the split-off point the products are inseparable, and so is their cost. Inventory and product margins still need a figure for each, so the cost must be divided, and the division is a convention, not a measurement.
| Product | Output, kg | Final price per kg | Revenue | Further processing | NRV |
|---|---|---|---|---|---|
| A | 10,000 | 40.00 | 400,000 | 0 | 400,000 |
| B | 20,000 | 15.00 | 300,000 | 0 | 300,000 |
| C | 10,000 | 30.00 | 300,000 | 120,000 | 180,000 |
| Total | 40,000 | 1,000,000 | 120,000 | 880,000 |
The joint cost to the split-off point is 600,000. A and B are sold as they come out; C has no market at split-off and needs 120,000 of further processing before it can be sold.
Rate = joint cost ÷ total physical output
600,000 ÷ 40,000 kg = 15.00 a kilogram. A takes 150,000, B 300,000 and C 150,000.
The method is simple and ignores what the kilograms are worth. B, the heaviest and cheapest stream, carries half the joint cost and shows a gross margin of exactly zero. A shows 62.5 per cent and C, after its further processing, 10.0 per cent.
Allocation = joint cost × product NRV ÷ total NRV
NRV is final sales value less further processing cost. Joint cost is 68.18 per cent of the 880,000 of total NRV, so A takes 272,727, B 204,545 and C 122,727.
In Excel, with NRV in column F: =600000*F2/SUM($F$2:$F$4).
Where every product has a market at split-off, the sales value at split-off replaces NRV and the calculation is the same. NRV allocation gives A and B the same 31.8 per cent margin, because neither has costs after split-off; C shows 19.1 per cent, lower because its own further processing earns no share of the joint margin.
The last method makes every product earn the same overall margin. Total revenue is 1,000,000 and total cost 720,000, so the margin is 28 per cent. Each product's cost of sales is 72 per cent of its revenue, and its joint cost is that figure less its own further processing: A 288,000, B 216,000, C 216,000 less 120,000, or 96,000.
| Product | Physical | Margin | NRV | Margin | Constant margin | Margin |
|---|---|---|---|---|---|---|
| A | 150,000 | 62.5% | 272,727 | 31.8% | 288,000 | 28.0% |
| B | 300,000 | 0.0% | 204,545 | 31.8% | 216,000 | 28.0% |
| C | 150,000 | 10.0% | 122,727 | 19.1% | 96,000 | 28.0% |
| Total gross margin | 280,000 | 280,000 | 280,000 |
The total never moves. The allocation only decides where the 280,000 is reported, and therefore which product a margin report flatters and which it condemns.
| B price per kg | B revenue | Physical margin | NRV allocation | NRV margin |
|---|---|---|---|---|
| 12.00 | 240,000 | −60,000 | 175,610 | 64,390 |
| 15.00 | 300,000 | 0 | 204,545 | 95,455 |
| 18.00 | 360,000 | 60,000 | 229,787 | 130,213 |
At 12.00 a kilogram the physical method reports B as losing 60,000. The NRV method moves part of the joint cost onto A and C as B's value falls, so B stays profitable at 26.8 per cent. Neither figure is the economic answer, because the joint cost does not depend on B at all.
If B is dropped because the physical method shows it at zero or below, the process still runs for A and C, the 600,000 is still spent, and the business loses B's 300,000 of revenue for no saving. The joint cost is unavoidable for every product taken one at a time. The only valid decisions are about what happens after split-off: if a buyer offered 8.00 a kilogram for C as it comes out, worth 80,000, processing further adds 220,000 of revenue for 120,000 of cost, a gain of 100,000, whatever joint cost C has been allocated. The same logic of avoidable cost runs through accepting a special order below full cost.
Allocate joint costs on NRV or sales value at split-off for inventory and reporting, because it keeps margins in line with what each product is worth; physical units can make a valuable stream look worthless. Here the same 600,000 shows B at 0.0, 31.8 or 28.0 per cent, while the business earns 280,000 in every case. How an allocation base moves cost between products without creating or destroying any is the argument of the free workbooks for Cost Accounting.
Each product takes joint cost in proportion to its final sales value less the cost of processing it after split-off. With NRVs of 400,000, 300,000 and 180,000, a 600,000 joint cost is 68.18 per cent of the 880,000 total, so the products take 272,727, 204,545 and 122,727.
No. The joint cost is incurred whatever happens to any single product. Dropping a product shown at zero margin here would lose 300,000 of revenue and save nothing. The relevant test is after split-off: processing C further adds 220,000 of revenue for 120,000 of cost against a hypothetical 8.00 a kg split-off price.
For reporting, a value-based method: sales value at split-off where markets exist, otherwise NRV. Physical units can show a valuable product at a loss and a low-value one as highly profitable. All methods give the same total, here 280,000 of gross margin; they differ only in where it is reported.
This article is one calculation from Cost Accounting. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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