Process Costing, Joint Products and By-Products — Practice

Question 1

A process has no opening WIP. During the period, 10,000 units were introduced, of which 8,000 were completed and transferred out, and 2,000 remain in closing WIP, 100% complete for material and 40% complete for conversion cost. Material cost incurred was Rs.4,00,000 and conversion cost was Rs.2,64,000. Compute equivalent units and cost per equivalent unit for material and conversion cost separately.

Accepted Answer

Since there is no opening WIP, the weighted average and FIFO methods coincide and give the same result, simplifying the computation. Equivalent units for material: the 8,000 completed and transferred units are 100% complete for material, contributing 8,000 equivalent units; the 2,000 closing WIP units are also 100% complete for material, since material is added fully at the start of this process, contributing a further 2,000 equivalent units; total equivalent units for material are 8,000 plus 2,000, giving 10,000. Equivalent units for conversion cost: the 8,000 completed and transferred units are fully complete, contributing 8,000 equivalent units; the 2,000 closing WIP units are only 40% complete for conversion cost, contributing 2,000 times 40%, that is 800 equivalent units; total equivalent units for conversion cost are 8,000 plus 800, giving 8,800. Cost per equivalent unit for material is 4,00,000 divided by 10,000, giving 40 per equivalent unit. Cost per equivalent unit for conversion cost is 2,64,000 divided by 8,800, giving 30 per equivalent unit. This illustrates why material and conversion cost must be computed separately whenever their completion percentages differ: using a single blended completion percentage, or applying the conversion cost completion percentage to material as well, would materially misstate the cost per equivalent unit for material, since material here is fully complete for all units including closing WIP while conversion cost is not.

Question 2

A process has opening WIP of 1,000 units, 100% complete for material and 50% complete for conversion cost, brought forward at a cost of Rs.36,000 (material) and Rs.11,000 (conversion). During the period, 9,000 units are introduced, 8,500 units are completed and transferred out (including the opening WIP), and 1,500 units remain in closing WIP, 100% complete for material and 30% complete for conversion cost. Current period costs are Rs.3,80,000 (material) and Rs.2,50,800 (conversion). Using the FIFO method, compute equivalent units for material and conversion cost.

Accepted Answer

The FIFO method separates the work needed to complete opening WIP, the work on units started and completed entirely within the period, and the work in closing WIP, rather than blending opening WIP's prior-period work into the current period's figures. Units started and completed entirely this period are total units transferred out less opening WIP units, since opening WIP is completed first under FIFO's logical flow assumption: 8,500 less 1,000, giving 7,500 units, fully complete for both material and conversion cost in the current period's figures. For material: opening WIP was already 100% complete for material brought forward, so no further material equivalent units are needed to complete it in this period, contributing 0 equivalent units for that portion; units started and completed contribute 7,500 equivalent units, being 100% complete; closing WIP, 100% complete for material, contributes 1,500 equivalent units. Total equivalent units for material under FIFO: 0 plus 7,500 plus 1,500, giving 9,000. For conversion cost: opening WIP was only 50% complete for conversion cost brought forward, so the remaining 50% must be completed this period, contributing 1,000 times 50%, that is 500 equivalent units; units started and completed contribute 7,500 equivalent units, being fully complete; closing WIP, 30% complete for conversion cost, contributes 1,500 times 30%, that is 450 equivalent units. Total equivalent units for conversion cost under FIFO: 500 plus 7,500 plus 450, giving 8,450. Cost per equivalent unit for material, using only the current period's cost of 3,80,000 divided by 9,000, gives approximately 42.22; cost per equivalent unit for conversion cost, using only current period's cost of 2,50,800 divided by 8,450, gives 29.68, both figures reflecting the FIFO method's characteristic of keeping current period cost separate from the cost already embedded in opening WIP from the prior period.

Question 3

A process introduces 5,000 units at a total cost of Rs.4,50,000. Normal loss is expected at 5% of input, with scrap value of Rs.10 per unit. Actual output is 4,600 good units. Compute the normal loss quantity, the cost per good unit, and identify and value any abnormal loss or gain.

Accepted Answer

Normal loss is 5% of 5,000 units introduced, that is 250 units, expected to be lost as an inherent, unavoidable feature of the process. Expected good output, after removing normal loss, is 5,000 less 250, that is 4,750 units. Actual good output is given as 4,600 units, which is less than the 4,750 expected, so an abnormal loss has occurred: actual loss is 5,000 less 4,600, that is 400 units, of which 250 is normal and the excess, 400 less 250, that is 150 units, is abnormal loss. Net cost to be absorbed by good units is total process cost less the scrap value recoverable from the normal loss units, since scrap value of normal loss is credited to the process account, reducing the net cost: 4,50,000 less (250 times 10), that is 4,50,000 less 2,500, giving 4,47,500. This net cost is divided by the expected good output of 4,750 units, not the actual 4,600, since the cost per unit rate is based on what a normal, expected outcome would have produced: 4,47,500 divided by 4,750, giving 94.21 per unit approximately. The abnormal loss of 150 units is valued at this same rate, 150 times 94.21, giving approximately 14,132, debited to a separate Abnormal Loss Account and subsequently transferred to the costing profit and loss account, kept entirely apart from the cost of the 4,600 good units actually produced, which are valued at 4,600 times 94.21, giving approximately 4,33,368, the two figures together, 14,132 plus 4,33,368, reconciling back to the net cost of 4,47,500 absorbed across expected good output plus abnormal loss.

Question 4

Process 1's output is transferred to Process 2 at a transfer price of Rs.60 per unit, which includes a profit loading of Rs.15 per unit over Process 1's actual cost of Rs.45 per unit. At the year end, 800 units of Process 1's output remain in Process 2's closing stock, still valued at the transfer price. Compute the stock reserve required, and explain why it is necessary.

Accepted Answer

Stock reserve is computed as closing stock at transfer price multiplied by the ratio of profit loading to transfer price: closing stock at transfer price is 800 units times 60, giving 48,000; the profit loading ratio is 15 divided by 60, that is 25%; stock reserve is 48,000 times 25%, giving 12,000. This stock reserve is necessary because the transfer price from Process 1 to Process 2 includes an internal profit margin, here 15 per unit, that has not been realised by any sale to a genuine outside party, since the 800 units are still sitting in Process 2's closing stock at the year end, not yet sold onward. If the entity's overall financial statements simply valued this closing stock at the transfer price without adjustment, they would report a profit that includes 12,000 of unrealised, purely internal profit generated by one part of the business selling to another part of the same business, exactly analogous to unrealised profit embedded in intra-group stock on consolidation, or in branch stock invoiced above cost, both principles met elsewhere in the syllabus. The stock reserve reduces the reported closing stock value, and correspondingly the reported profit, by exactly this unrealised amount, ensuring the entity's overall accounts reflect only profit that has genuinely been earned from a transaction with an outside party, consistent with the broader principle that an entity cannot make a profit by trading with itself.

Question 5

A dairy processes raw milk into cream and skimmed milk, both of comparable significant value, and the process also incidentally produces a small quantity of low-value whey. Classify cream, skimmed milk and whey, and explain why the accounting treatment differs between the two categories.

Accepted Answer

Cream and skimmed milk are joint products: both are of significant, comparable value, and both are produced simultaneously from the same process and the same input, raw milk, up to the point at which they are separated. Whey is a by-product: it is a product of relatively minor value, incidentally produced alongside the main outputs from the same process, rather than being a significant, deliberately targeted output in its own right. The accounting treatment differs because of what each category needs. Cream and skimmed milk, being significant enough to each require their own cost figure for inventory valuation and profitability assessment, require the joint cost incurred up to the point of separation to be apportioned between them using one of the recognised apportionment methods, such as physical unit, sales value at split-off, or net realisable value, so that each product carries a cost figure meaningful enough to support pricing and profitability decisions about it individually. Whey, being minor, is not worth the effort of a full joint cost apportionment; instead, its net realisable value, whatever it can be sold for less any selling cost, is simply credited against the cost of the main products, reducing their joint cost without attempting to build a separate, formally apportioned cost figure for the whey itself, since the informational value of doing so would not justify the additional computational effort for a product of such minor significance.

Question 6

A process yields two joint products, X and Y, from a joint cost of Rs.6,00,000. Neither product is saleable at split-off; both require further processing. Product X: 4,000 units, further processing cost Rs.80,000, final sales value Rs.4,20,000. Product Y: 3,000 units, further processing cost Rs.50,000, final sales value Rs.3,30,000. Apportion the joint cost using the net realisable value method.

Accepted Answer

Since neither product is saleable at split-off, the sales value at split-off method cannot be applied directly, and the net realisable value method is used instead, working backward from each product's final sales value to an imputed value at the split-off point. NRV at split-off for Product X is its final sales value less its further processing cost: 4,20,000 less 80,000, giving 3,40,000. NRV at split-off for Product Y is 3,30,000 less 50,000, giving 2,80,000. Total NRV at split-off across both products is 3,40,000 plus 2,80,000, giving 6,20,000. Joint cost is apportioned in proportion to each product's share of this total NRV: Product X's share is 3,40,000 divided by 6,20,000, that is approximately 54.84%, giving joint cost apportioned to X of 54.84% times 6,00,000, that is approximately 3,29,032. Product Y's share is 2,80,000 divided by 6,20,000, that is approximately 45.16%, giving joint cost apportioned to Y of approximately 2,70,968. The two apportioned figures sum back to the total joint cost of 6,00,000, as they must. Total cost of Product X is joint cost apportioned plus its own further processing cost: 3,29,032 plus 80,000, giving approximately 4,09,032, against a final sales value of 4,20,000, leaving a modest profit; total cost of Product Y is 2,70,968 plus 50,000, giving approximately 3,20,968, against a final sales value of 3,30,000, also leaving a modest profit, illustrating that the NRV method by construction tends to leave each product with a broadly comparable margin relative to its own final sales value, since the apportionment is built directly from each product's own net realisable contribution.

Question 7

A sawmill's main product is timber. The process also produces sawdust as a by-product, which can either be sold as is for Rs.8 per bag with negligible selling cost, or, if processed further at a cost of Rs.3 per bag, sold as compressed fuel pellets for Rs.14 per bag with selling cost of Rs.1 per bag. If 500 bags of sawdust are produced, compute the credit to the main product's cost under each option, and advise which option yields the higher net benefit.

Accepted Answer

If sold as is, the by-product's net realisable value credited against the main product's cost is sale value less selling cost: 8 per bag less negligible selling cost, effectively 8 per bag, giving a total credit of 500 times 8, that is 4,000. If processed further into compressed fuel pellets, the credit is final sales value less both selling cost and further processing cost: 14 per bag less selling cost of 1, less further processing cost of 3, giving a net figure of 14 less 1 less 3, that is 10 per bag, giving a total credit of 500 times 10, that is 5,000. Comparing the two options, processing the sawdust further into pellets yields a higher net credit to the main product's cost, 5,000 against 4,000 for selling as is, a difference of 1,000 in favour of further processing. The advice, based purely on this comparison, is that the sawmill should process the sawdust into pellets rather than selling it as is, since doing so increases the net benefit credited against the cost of the main product, timber, by 1,000, effectively reducing timber's reported cost, and by extension improving timber's reported margin, by that additional amount; this is the same working-backward NRV logic applied to joint product apportionment, here used instead to decide the best disposal option for a single by-product and to determine the correct figure to credit whichever option is chosen.

Question 8

A process has opening WIP of 1,000 units, 100% complete for material and 60% for conversion, brought forward at Rs.28,000 (material) and Rs.9,600 (conversion). During the period 9,000 units are introduced. 8,500 units are completed and transferred out. Closing WIP is 1,500 units, 100% complete for material and 40% for conversion. Current period costs: material Rs.4,05,000, conversion Rs.2,88,000. Using the weighted average method, compute equivalent units and cost per equivalent unit for material and conversion cost.

Accepted Answer

Under weighted average, opening WIP's prior-period work is blended together with current period work rather than separated out, so equivalent units are simply units completed and transferred out plus equivalent units in closing WIP, with no separate accounting for what portion of opening WIP's completion happened in a prior period. Equivalent units for material: 8,500 completed and transferred, fully complete, contributing 8,500; plus 1,500 closing WIP units, 100% complete for material, contributing 1,500; total 10,000. Equivalent units for conversion cost: 8,500 completed and transferred, fully complete, contributing 8,500; plus 1,500 closing WIP units, 40% complete for conversion, contributing 600; total 9,100. Cost per equivalent unit for material under weighted average uses the combined cost, opening WIP's brought-forward material cost plus current period material cost: 28,000 plus 4,05,000, that is 4,33,000, divided by 10,000 equivalent units, giving 43.30 per unit. Cost per equivalent unit for conversion cost similarly combines opening WIP's brought-forward conversion cost with current period conversion cost: 9,600 plus 2,88,000, that is 2,97,600, divided by 9,100 equivalent units, giving 32.70 per unit approximately. This illustrates the defining feature of the weighted average method relative to FIFO: prior period cost embedded in opening WIP is blended into a single average with current period cost, rather than kept separately identifiable, which is simpler to compute but less precise about which period's cost applies to which portion of output.

Question 9

A process yields two joint products, P and Q, saleable at split-off. Joint cost is Rs.4,50,000. Product P: 3,000 kg. Product Q: 6,000 kg. Apportion joint cost using the physical unit method, and comment on a situation where this method would be inappropriate.

Accepted Answer

Under the physical unit method, joint cost is apportioned in proportion to the physical quantity, here weight, of each joint product. Total physical output is 3,000 plus 6,000, giving 9,000 kg. Product P's share is 3,000 divided by 9,000, that is one-third, giving joint cost apportioned to P of one-third of 4,50,000, that is 1,50,000. Product Q's share is 6,000 divided by 9,000, that is two-thirds, giving joint cost apportioned to Q of two-thirds of 4,50,000, that is 3,00,000. This method is simple to apply, requiring only the physical measure of each product's output rather than any market or valuation data, but it would be inappropriate, and can produce genuinely misleading results, where the joint products differ greatly in value per physical unit; if, for instance, Product P were a high-value specialty chemical selling at a substantial premium per kilogram while Product Q were a low-value bulk commodity selling for very little per kilogram, the physical unit method would still apportion joint cost purely by weight, potentially assigning a large share of joint cost to the low-value bulk product simply because it happens to weigh more, and correspondingly leaving the high-value product carrying too little cost relative to its actual economic contribution; in such a situation, the sales value at split-off method, or the net realisable value method if no split-off market exists, would generally produce a more economically meaningful apportionment, since both anchor the cost split to each product's actual value rather than to a physical measure that may bear little relationship to value at all.

Question 10

A process yields three joint products, all saleable at split-off. Joint cost is Rs.9,00,000. Product X: 2,000 units at Rs.150 per unit. Product Y: 3,000 units at Rs.100 per unit. Product Z: 1,000 units at Rs.300 per unit. Apportion the joint cost using the sales value at split-off method.

Accepted Answer

Sales value at split-off for each product is its units multiplied by its per-unit sales value at that point. Product X: 2,000 times 150, giving 3,00,000. Product Y: 3,000 times 100, giving 3,00,000. Product Z: 1,000 times 300, giving 3,00,000. Total sales value at split-off across all three products is 3,00,000 plus 3,00,000 plus 3,00,000, giving 9,00,000. Each product's share of total sales value is therefore exactly one-third, and joint cost is apportioned equally: one-third of 9,00,000, that is 3,00,000, to each of Product X, Product Y and Product Z. This result, though the underlying physical volumes differ substantially between the three products, 2,000, 3,000 and 1,000 units respectively, reflects that the sales value at split-off method apportions based on each product's economic contribution rather than its physical quantity; here, despite very different unit counts and very different per-unit prices, each product happens to generate an identical total sales value at split-off, and the method accordingly apportions joint cost identically across all three, illustrating that this method would produce a materially different, and generally considered more economically meaningful, apportionment than the physical unit method would on the same underlying data, since a physical unit method here would instead have apportioned cost heavily towards Product Y purely because of its larger physical volume, despite all three products contributing equally to total sales value.

Question 11

Two joint products, A and B, together generate final sales value of Rs.10,00,000 (A: Rs.6,00,000; B: Rs.4,00,000) after further processing costs of Rs.1,20,000 (A) and Rs.80,000 (B). Total joint cost is Rs.3,00,000. Using the constant gross margin percentage method, compute the joint cost apportioned to each product.

Accepted Answer

The constant gross margin percentage method apportions joint cost so that every joint product earns the same gross profit percentage on its final sales value, rather than apportioning based on physical units, split-off values or net realisable value directly. First, compute the overall gross margin percentage for the combined products: total final sales value is 6,00,000 plus 4,00,000, giving 10,00,000; total cost is joint cost plus total further processing cost, that is 3,00,000 plus (1,20,000 plus 80,000), that is 3,00,000 plus 2,00,000, giving 5,00,000; total gross profit is total sales value less total cost, 10,00,000 less 5,00,000, giving 5,00,000; overall gross margin percentage is 5,00,000 divided by 10,00,000, giving 50%. This 50% margin is then imposed on each product individually. For Product A, desired gross profit is 50% of its sales value of 6,00,000, giving 3,00,000, so its total allowed cost is sales value less desired profit, 6,00,000 less 3,00,000, giving 3,00,000; since Product A's further processing cost is 1,20,000, the joint cost apportioned to it is total allowed cost less further processing cost, 3,00,000 less 1,20,000, giving 1,80,000. For Product B, desired gross profit is 50% of its sales value of 4,00,000, giving 2,00,000, so its total allowed cost is 4,00,000 less 2,00,000, giving 2,00,000; joint cost apportioned to it is 2,00,000 less its further processing cost of 80,000, giving 1,20,000. Checking the total: 1,80,000 plus 1,20,000 equals 3,00,000, matching the total joint cost, confirming the apportionment is correct; both products now show an identical 50% gross margin on their respective final sales values, which is the deliberate outcome this method is designed to produce, sometimes preferred by management for a uniform profitability presentation across products regardless of the underlying differences in their cost structures.

Question 12

A process introduces 2,000 units of raw material costing Rs.1,60,000. Direct labour is Rs.60,000 and overhead is Rs.40,000. Normal loss is 5% of input, with no scrap value. Actual output is 1,850 good units. Compute the cost per unit and identify any abnormal loss or gain.

Accepted Answer

Total process cost is material plus labour plus overhead: 1,60,000 plus 60,000 plus 40,000, giving 2,60,000. Normal loss is 5% of the 2,000 units introduced, that is 100 units, with no scrap value to credit against the process cost in this case. Expected good output after normal loss is 2,000 less 100, giving 1,900 units. Actual good output is 1,850, which is less than the 1,900 expected, indicating an abnormal loss of 1,900 less 1,850, that is 50 units. Since there is no scrap value to net off, cost per unit is simply total process cost divided by expected good output: 2,60,000 divided by 1,900, giving approximately 136.84 per unit. The abnormal loss of 50 units is valued at this same rate, 50 times 136.84, giving approximately 6,842, debited to a separate Abnormal Loss Account and subsequently transferred to the costing profit and loss account, entirely separate from the cost of the 1,850 good units actually produced, which are valued at 1,850 times 136.84, giving approximately 2,53,158; the two figures together, 6,842 plus 2,53,158, reconcile to the total process cost of 2,60,000, confirming the whole of the cost has been correctly accounted for between good output and the separately identified abnormal loss.

Question 13

A process introduces 3,000 units at total cost of Rs.5,10,000, with normal loss of 4% and scrap value of Rs.15 per unit. Actual output is 2,900 good units. Compute cost per unit, and identify and value the abnormal gain.

Accepted Answer

Normal loss is 4% of 3,000 units introduced, that is 120 units, with scrap value of 120 times 15, that is 1,800, credited to the process account, reducing net cost absorbed by good units. Expected good output after normal loss is 3,000 less 120, giving 2,880 units. Actual good output is 2,900, which exceeds the 2,880 expected, meaning fewer units were lost than the normal allowance anticipated; this is an abnormal gain of 2,900 less 2,880, that is 20 units. Net cost to be absorbed is total process cost less scrap value of normal loss: 5,10,000 less 1,800, giving 5,08,200, divided by expected good output of 2,880, giving cost per unit of approximately 176.46. The abnormal gain of 20 units is valued at this same rate, 20 times 176.46, giving approximately 3,529, credited to a separate Abnormal Gain Account and subsequently transferred to the costing profit and loss account as a gain, since fewer resources were consumed per good unit produced than the normal allowance anticipated. A further consequence of the abnormal gain worth noting is that since fewer units than expected were actually lost, the scrap value that would have been realised from those 20 additional units, which did not in fact materialise as scrap, must correspondingly be removed from the normal loss scrap value credit; the abnormal gain account is typically debited with the scrap value that would have applied to those 20 units, here 20 times 15, that is 300, alongside being credited with the full process-rate value of 3,529, netting to the actual gain the abnormal event produced.

Question 14

A chemical plant's main process yields a by-product that can be sold as is for Rs.6 per litre with no further processing or selling cost, or refined at a cost of Rs.2.50 per litre and sold as a premium grade for Rs.9.50 per litre with selling cost of Rs.0.50 per litre. 4,000 litres are produced. Determine which option the plant should choose, and compute the credit to the main product in each case.

Accepted Answer

If sold as is, the credit to the main product is net realisable value: 6 per litre with no further processing or selling cost, giving a full 6 per litre credited, that is 4,000 times 6, giving 24,000. If refined and sold as premium grade, the credit is final sales value less both selling cost and further processing cost: 9.50 less 0.50 selling cost less 2.50 further processing cost, giving 6.50 per litre, that is 4,000 times 6.50, giving 26,000. Comparing the two, refining yields a higher credit to the main product, 26,000 against 24,000, a difference of 2,000 in favour of refining. The plant should therefore choose to refine the by-product into the premium grade before sale, since doing so increases the net benefit credited against the main product's cost by 2,000, which in turn reduces the main product's reported cost, and correspondingly improves the main product's reported margin, by that additional amount; the decision rule applied here is exactly the same net-realisable-value comparison used to decide the best disposal option for any by-product, weighing the additional revenue from further processing against the additional processing and selling costs it requires, and choosing whichever option maximises the net figure available to credit back against the main product.

Question 15

A process yields two joint products, R and S, and a by-product, T. Joint cost up to split-off is Rs.5,00,000. By-product T's net realisable value is Rs.30,000, credited against the joint cost before apportioning the remainder between R and S. R and S are saleable at split-off: R at Rs.8,00,000, S at Rs.5,00,000. Apportion the cost properly to R and S using the sales value at split-off method, accounting for the by-product correctly.

Accepted Answer

The by-product's net realisable value of 30,000 is first credited against the total joint cost before any apportionment between the joint products, since by-products are handled by crediting their net realisable value against the main products' combined cost rather than by attempting a formal joint cost apportionment to them; only R and S, being the significant joint products, require the joint cost to actually be apportioned between them. Net joint cost to be apportioned between R and S is total joint cost less the by-product credit: 5,00,000 less 30,000, giving 4,70,000. Using the sales value at split-off method, total sales value of R and S combined is 8,00,000 plus 5,00,000, giving 13,00,000. R's share is 8,00,000 divided by 13,00,000, that is approximately 61.54%, giving joint cost apportioned to R of approximately 61.54% times 4,70,000, that is approximately 2,89,231. S's share is 5,00,000 divided by 13,00,000, that is approximately 38.46%, giving joint cost apportioned to S of approximately 1,80,769. The two figures sum to approximately 4,70,000, matching the net joint cost after the by-product credit, as they must. The sequence applied here, crediting the by-product first and apportioning only the residual cost between the genuine joint products, is the standard approach whenever a process yields both significant joint products and a minor by-product together, and getting the order right, by-product credit before joint product apportionment rather than after or alongside it, is what a candidate must apply correctly in any problem combining both categories in a single process.

Practice — Process Costing, Joint Products and By-Products

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