Joint Products and By Products: formula sheet

Key formulas

Joint cost

Joint cost = All costs incurred up to the split-off point

Includes material, labour and overheads of the common process. Costs after split-off are not joint costs.

Separable (further processing) cost

Separable cost = Cost incurred after split-off for a specific product

Charge it directly to that product. Do not share it among other products.

Test for classification

Significant sales value → Joint product; Small sales value → By-product

The judgement is on relative value, not on the order of production or on quantity.

Cost to be shared among joint products

Joint cost to share = Total joint cost − Net realisable value of by-product (when by-product credit is allowed)

This is one common treatment. The by-product treatment can differ by method and question wording.

Physical unit method

Share of joint cost = (Units of the product ÷ Total units of all joint products) × Joint cost

Use the same unit (kg, litres) for all products. Convert if units differ.

Average unit cost method

Average cost per unit = Total joint cost ÷ Total units of all joint products; Product cost = Units × Average cost per unit

Gives the same result as the physical unit method when units are comparable. Profits per unit differ widely.

Sales value at split-off point method

Share of joint cost = (Sales value of the product at split-off ÷ Total sales value at split-off) × Joint cost

Sales value = Units produced × Selling price at split-off. Use units produced, not units sold, unless told.

Net realisable value (NRV) method

NRV = Final sales value − Further processing cost − Selling and distribution cost (if given); Share = (NRV ÷ Total NRV) × Joint cost

Use when products are processed further after split-off and there is no selling price at split-off. The NRV so found is the hypothetical NRV at split-off: final sales value less post-split-off processing and selling costs.

Contribution margin method

Step 1: Apportion joint variable cost on a suitable basis (physical units or sales value). Step 2: Contribution = Sales value − joint variable cost share − separable variable cost. Step 3: Apportion joint fixed cost in the ratio of contribution.

Joint variable cost goes on physical units or sales value, as the question states. Joint fixed cost goes on each product's contribution. Follow the question's wording.

Weighted average (weighting factor) method

Weighted units = Units × Weight; Share = (Weighted units of product ÷ Total weighted units) × Joint cost

Weights reflect size, effort or market value as given. Use when physical units are not directly comparable.

Estimated NRV at split-off

NRV = Final sales value − Further processing cost − Selling and distribution cost (after split-off)

Use total value for the quantity sold, not per-unit price, unless the question gives units.

NRV at split-off (no further processing)

NRV = Sales value at split-off − Selling and distribution cost, if any

Here NRV is just the market value at the split-off point, net of selling costs.

Joint cost apportioned

Joint cost share of a product = (NRV of the product ÷ Total NRV of all joint products) × Total joint cost

Use only joint cost to be apportioned. Reduce it by by-product credit if the question says so.

Further processing decision

Incremental profit = (Sales value after processing − Sales value at split-off) − Further processing cost

Process further if incremental profit is positive. Joint cost is ignored.

Decision rule

Process further if incremental revenue > incremental cost; sell at split-off if incremental revenue < incremental cost

If both are equal, you are indifferent on money grounds.

By-product credit when sold as it is

Credit = Sales value of by-product − Selling and distribution cost of by-product (if separately incurred)

If no separate cost is given, credit the full sales value.

Reversal cost (NRV) method

Credit to main product = Sales value of by-product − Post-split-off processing cost − Selling and distribution cost − Normal profit (if given)

This is the NRV-based method. Deduct profit only when the question gives a profit margin.

Net realisable value (NRV) when no profit is given

NRV = Sales value of by-product − Post-split-off processing cost − Selling and distribution cost

This is the same reversal cost working. When the question gives no normal profit, there is no profit to deduct.

Cost of main product after by-product credit

Net cost of main product = Total joint cost − By-product credit

Use this when the question asks for the by-product to be adjusted against main product cost.

Cost per unit of main product

Cost per unit = Net cost of main product ÷ Units of main product

Divide by main product units only, never by the by-product units.

By-product credited to Profit and Loss

Profit = Sales of main product − Full cost of main product + By-product income

The by-product income is shown below the cost sheet as other income, so it does not change the main product cost.

Quick revision

• Joint cost is the cost of a common process up to the split-off point.
• Joint products are all major products of value; by-products are minor outputs of low value.
• Costs after split-off are separable costs and are charged directly to the product.
• Physical unit method shares joint cost in the ratio of quantities produced.
• Sales value at split-off method shares joint cost in the ratio of sales value at that point.
• NRV method uses final sales value less further processing and selling costs.
• Joint cost already incurred is sunk, so ignore it in further processing decisions.
• Process further only if incremental revenue is more than incremental cost.
• Check that apportioned shares add up to the total joint cost.
• By-product income may be credited to profit and loss or deducted from joint cost, as stated.
• Read units carefully: use output units, and watch for losses and opening or closing stock.

Common mistakes

• Treating all outputs of a process as joint products. Fix: Check sales value. Low-value outputs are by-products. Only significant ones are joint products.
• Including post split-off processing cost in joint cost. Fix: Joint cost stops at the split-off point. Later costs belong to the specific product.
• Apportioning separable costs along with joint cost. Fix: Split only costs up to the split-off point. Add each product's post-split-off cost directly to that product.
• Using final selling price instead of NRV in the NRV method. Fix: Always compute NRV = final sales value − further processing cost − selling cost before taking the ratio.
• Including the joint cost in the further processing decision. Fix: Joint cost is sunk at the split-off point. Compare only extra revenue and extra processing cost.
• Using final sales value instead of NRV to apportion joint cost. Fix: Deduct further processing and post-split-off selling costs from the final value first. Then apportion.
• Crediting the full selling price of a by-product that needs further processing. Fix: Deduct post-split-off processing cost, selling cost and any profit margin before crediting.
• Dividing the net cost by total units, including by-product units. Fix: Divide only by main product units, because the by-product value is already deducted.

Exam tips

• Theory questions often ask for the difference between joint products and by-products. Give at least four points: value, objective of production, importance, and costing treatment.
• In numericals, mark the split-off point first. This prevents the wrong costs from entering the joint cost pool.
• In MCQs, watch for the words 'significant value' and 'incidental'. They usually decide the answer.
• Give one clear example for each term. Use sugar and molasses for a by-product, and petrol and diesel for joint products.
• Keep working neat. Even a short, labelled answer earns step marks, since MCQs need no working but the 70 marks of written answers do.
• Look for the method name in the question. Many questions ask for two or three methods, so build one table and extend it for each method.
• Check whether the question gives selling price at split-off or only final price. That tells you whether to use sales value or NRV.
• Show the ratio and the check total in every answer. Examiners award marks for each step even if the final figure has a small error.