Joint and by-product costing: cost allocation methods and by-product costing

Cost allocation methods

As a quick reminder, joint costs are the shared production costs incurred before the split-off point - the stage at which joint products become separately identifiable - and separable costs are the costs incurred after that point to finish each product for sale.

Once joint products are identified at the split-off point, the total joint costs incurred up to that point must be allocated to each product using a rational and consistent method. The goal of cost allocation is to assign a fair share of joint costs to each output based on either their physical characteristics or their economic value.

The CMA exam recognizes four commonly used methods for allocating joint costs:

1. Physical measure method
2. Sales value at split-off method
3. Net realizable value (NRV) method
4. Constant gross margin percentage (gross profit) method

Each method has its own rationale, benefits, and limitations, and is chosen based on data availability, reporting objectives, and the relative importance of accuracy versus simplicity.

1. Physical measure method

The physical measure method allocates joint costs to products based on a quantifiable physical attribute at the split-off point, such as weight, volume, or units produced. This method assumes that each product shares in the joint costs proportionally to its physical output, regardless of its market value.

This method is generally less preferred for financial reporting due to its lack of linkage to revenue generation, but it may still be used in internal reporting or regulated industries where physical quantity matters.

Example: Physical measure method

A process yields the below joint products with a total joint cost of $10,000.

• Product A: 600 kg
• Product B: 400 kg

Allocation of joint costs:

• Product A: (600 / 1,000) × $10,000 = $6,000
• Product B: (400 / 1,000) × $10,000 = $4,000

Benefits:

• Simple and objective: Based on measurable output
• Useful when market values are unavailable or unstable

Limitations:

• Ignores economic value - products with very different selling prices can end up with distorted profitability, since low-value outputs get over-allocated costs and high-value outputs get under-allocated costs

2. Sales value at split-off method

The sales value at split-off method allocates joint costs based on the relative sales value of each product at the split-off point. This approach assumes that the economic value of a product at the point of separation reflects its consumption of joint resources.

This method is widely used when:

• Products are marketable immediately at the split-off point, and
• Their sales prices are known or reliably estimable

Example: Sales value at split-off method

A joint process yields:

• Product A: 600 units, selling price $5/unit → $3,000 total value
• Product B: 400 units, selling price $10/unit → $4,000 total value

Total joint cost: $10,000
Total sales value: $7,000

Proportional allocation of joint costs:

• Product A: (3,000 / 7,000) × $10,000 = $4,286
• Product B: (4,000 / 7,000) × $10,000 = $5,714

Benefits:

• Economically meaningful: Reflects revenue-generating ability of each product
• Generally accepted for inventory costing in external reporting when split-off values are available
• Common in external financial reporting

Limitations:

• Requires a reliable market price at the split-off point - the product doesn’t need to actually be sold there, but a price must exist; if no market price exists until after further processing, use the NRV method instead

3. Net realizable value (NRV) method

The net realizable value (NRV) method allocates joint costs based on the final sales value of each product minus any separable (post-split-off) costs required to make the product saleable. This approach is useful when products cannot be sold at split-off and require further processing. NRV is commonly used in industries like food processing or chemicals, where further refinement is necessary before a product becomes marketable.

The NRV method estimates each product’s contribution to revenue after further processing and uses that as the basis for allocating joint costs. The formula for the NRV is as follows:

$$\text{NRV}=\text{final sales value}-\text{separable costs}$$

Example: Net realizable value (NRV) method

Product A:

• Final sales value: $7,000
• Separable costs: $2,000
• NRV = $5,000

Product B:

• Final sales value: $9,000
• Separable costs: $4,000
• NRV = $5,000

Total NRV: $10,000
Total joint costs: $8,000

Allocation of joint costs:

• Product A: (5,000 / 10,000) × $8,000 = $4,000
• Product B: (5,000 / 10,000) × $8,000 = $4,000

Benefits:

• Appropriate when products must be further processed before sale
• Relates joint cost allocation to net economic benefit
• More flexible than sales value at split-off

Limitations:

• Requires accurate estimation of separable costs, which may vary
• For any product sold at split-off, NRV is simply its sales value at split-off (separable costs = $0), so the method still works when some products are processed further and others are not
• Complex in cases with many cost layers or uncertain selling prices

4. Constant gross margin percentage method

The constant gross margin percentage method (also called the gross profit method) allocates joint costs in a way that ensures each product earns the same gross margin percentage. Rather than basing the allocation on physical measures or market values, this method starts by determining a target gross margin for all products and then backs into the appropriate joint cost allocation. This approach is primarily used in internal performance analysis where consistent profitability metrics are desired across product lines.

Steps in applying the gross margin method:

1. Calculate the total gross margin percentage for the combined products (total costs = joint costs + all separable costs):

$$\text{Gross margin \%}=\frac{\text{Total final sales}-\text{Total costs}}{\text{Total final sales}}$$

2. Apply the same gross margin % to each product’s sales to compute cost of goods sold (COGS)
3. Subtract separable costs to derive the allocated joint cost for each product

Example: Constant gross margin percentage method

Product A:

• Sales: $10,000
• Separable costs: $2,000

Product B:

• Sales: $6,000
• Separable costs: $1,000

Other information and calculations:

• Joint costs: $10,000
• Total sales = $16,000
• Total costs = $13,000
• Gross margin = total sales less total costs = $16,000 - $13,000 = $3,000
• GM% = gross margin / total sales = 18.75%

Apply GM% to each product:

• Product A GM = 18.75% × $10,000 = $1,875 → COGS = $8,125
• Product B GM = 18.75% × $6,000 = $1,125 → COGS = $4,875

Then subtract separable costs:

• Product A: Joint cost = $8,125 – $2,000 = $6,125
• Product B: Joint cost = $4,875 – $1,000 = $3,875

Total joint cost allocated: $6,125 + $3,875 = $10,000

Benefits:

• Ensures a uniform profit margin across all products
• Useful in internal financial analysis and pricing strategy
• Reflects both sales value and separable costs

Limitations:

• Complex and not intuitive, harder to justify for external reporting
• Gross margin consistency may not reflect economic reality
• Requires reliable estimates of sales and separable costs

By-product costing

By-products are secondary outputs from a joint production process that have minimal sales value compared to the main (joint) products. While not the primary focus of production, by-products can still provide economic benefit, whether through reuse, sale, or disposal.

Accounting for by-products depends on their significance. The goal is to reflect their value in a way that’s cost-effective and not overly complex.

Other income or miscellaneous revenue method

In this simplest method, the revenue from selling a by-product is not used to reduce the joint costs of the main products. Instead, when the by-product is sold, the income is recorded separately as “other income” or “miscellaneous revenue” in the income statement. This method avoids complications in the joint cost allocation and is often used when the by-product has immaterial value.

Example: Other income method

A furniture company produces tables and chairs as joint products. In the process, it also generates wood shavings and sawdust, by-products that it sells for $500 per batch to a landscaping firm. The company does not adjust the joint product costs. When the sawdust is sold, it records:

Dr. Cash $500
Cr. Miscellaneous revenue $500

This approach is common in industries where by-products are too small in value to influence main product costing but can still generate minor income.

Net realizable value (NRV) offset method

The NRV offset method subtracts the by-product’s estimated net realizable value from total joint costs when the by-product is produced, before allocating the remaining cost to the main products. This method assumes that the by-product helps recover some production cost, so its value is used to lower the cost base of the main products.

Example: NRV offset method

A dairy produces cream and butter as main products and leftover whey as a by-product. The whey can be sold for $2,000 at the split-off point with no further processing, so its NRV (sales value minus separable processing costs of $0) is $2,000. If the total joint production cost is $20,000, then only $18,000 is allocated between the cream and butter using one of the joint cost methods (e.g., sales value at split-off). The whey is recorded as by-product inventory at $2,000. When it is sold, the entry is Dr. Cash $2,000 / Cr. By-product inventory $2,000, with no revenue recognized, because the benefit already lowered the joint cost.

This method is especially appropriate when the by-product’s value is significant enough to impact main product costing.