Managerial/Cost Accounting | Horngren/Datar/Rajan, 14e | Objectives 16.3–16.4
Difficulty: Intermediate to Advanced | Prerequisites: Part 1 of these notes (joint cost fundamentals, Obj 16.1 and 16.2).
Once you accept that joint costs must be allocated, the next question is how. There is no cause-and-effect relationship between a product's value and its share of joint costs, so every method is ultimately arbitrary. The textbook covers four methods: three market-based approaches (sales value at splitoff, estimated NRV, constant gross-margin percentage NRV) and one physical-measure approach. This section walks through each method's mechanics, strengths and weaknesses, and shows when each is appropriate.
Four methods allocate joint costs: sales value at splitoff (uses market prices at the split), estimated NRV (final sales value minus separable costs), constant gross-margin percentage NRV (forces every product to the same gross-margin %), and physical measures (weight, volume, etc.). Market-based methods are preferred because revenues best reflect the benefits received. Sales value at splitoff is the simplest and the preferred method when splitoff-point prices exist.
Sales value at splitoff method
Allocates joint costs to joint products based on the relative total sales value of each product at the splitoff point. A market-based method.
In simple terms, the product that is worth more at the split picks up a bigger share of the bill.
Estimated net realisable value (NRV) method
Allocates joint costs based on relative NRV, calculated as final sales value minus separable costs for each product. Used when market selling prices at the splitoff point are not available.
Think of it as backing into a splitoff value by starting with what the finished product sells for and stripping out the costs to get it there.
Constant gross-margin percentage NRV method
Allocates joint costs so that every individual product achieves an identical gross-margin percentage. This is the only method under which a product can receive a negative allocation of joint costs.
Think of it as treating all the joint products as though they were one combined product and spreading the overall margin evenly.
Physical-measure method
Allocates joint costs based on a comparable physical measure at the splitoff point, such as weight, volume or units. This is not a market-based method.
In simple terms, the product that takes up more physical space (or weight) picks up more cost, regardless of what it sells for.
Calculate the total sales value at the splitoff point for each product: units produced multiplied by the selling price at splitoff.
Compute each product's percentage of the total sales value.
Multiply the total joint costs by each product's percentage to get its allocated share.
Yakima Manufacturing processes 100 trees into 60,000 sheets of paper (selling at $0.04/sheet) and 60,000 pencil casings (selling at $0.10/casing). Joint costs are $3,000.
Paper sales value at splitoff: 60,000 x $0.04 = $2,400
Pencil casings sales value at splitoff: 60,000 x $0.10 = $6,000
Total sales value: $8,400
Paper's share: $2,400 / $8,400 = 28.57%, so allocated joint cost = 28.57% x $3,000 = $857
Pencil casings' share: $6,000 / $8,400 = 71.43%, so allocated joint cost = 71.43% x $3,000 = $2,143
Simplest market-based method to implement.
Does not require information about processing steps after splitoff.
Costs are allocated in proportion to revenue-generating ability (benefits-received criterion).
Enables the accountant to obtain individual product costs and gross margins.
Both products end up with the same gross-margin percentage when sold at splitoff.
Preferred whenever selling-price data exists at the splitoff point. It is the recommended method in the textbook.
Identify a comparable physical measure for all products (e.g., gallons, pounds, board feet).
Calculate each product's proportion of total physical output.
Multiply the total joint costs by each product's proportion.
Oxnard Corporation produces 147,500 gallons of Mr. DirtOut and 95,000 gallons of Mr. SinkClean (242,500 total good gallons). Joint costs are $760,000.
Mr. DirtOut: 147,500 / 242,500 = 60.82%, allocated = $760,000 x 60.82% = $462,232
Mr. SinkClean: 95,000 / 242,500 = 39.18%, allocated = $760,000 x 39.18% = $297,768
The measurement basis may differ across products (one measured in litres, another in kilograms), requiring a common denominator.
Physical volume usually has little relationship to the revenue-producing power of products.
The heaviest or bulkiest product absorbs the most cost, regardless of its market value.
For some products (e.g., gas), obtaining physical measures is difficult.
Used when selling prices at the splitoff point are unavailable and an NRV calculation is impractical. It is the fallback method.
How it works:
For each product, calculate NRV = (final selling price x units produced) minus separable costs after splitoff.
Compute each product's NRV as a percentage of total NRV.
Multiply total joint costs by each product's NRV percentage.
When to use it: when market selling prices at the splitoff point are not available, but you do know the final selling price and the separable processing costs.
Criticism: carrying inventory at estimated NRV recognises income before sales are made. Some accountants find this objectionable.
How it works (three steps):
Step 1: Calculate the overall gross-margin percentage for all products combined. Overall GM% = (Total revenues minus Total costs) / Total revenues.
Step 2: For each product, calculate total production cost = final sales value minus gross margin (i.e., final sales value x (1 minus GM%)).
Step 3: For each product, allocated joint cost = total production cost minus that product's separable costs.
Key features:
Every product ends up with the same gross-margin percentage.
This is the only method under which a product can receive a negative allocation of joint costs.
It treats all joint products as though they comprise a single product.
It takes account of profits earned before or after the splitoff point.
Criticism: assumes all products have the same ratio of cost to sales value, which is seldom true in practice.
Sales Value at Splitoff
Allocated joint cost for Product A = (Sales value of A at splitoff / Total sales value of all products at splitoff) x Total joint costs
Estimated NRV
NRV of Product A = (Units of A x Final selling price of A) minus Separable costs of A
Allocated joint cost for A = (NRV of A / Total NRV of all products) x Total joint costs
Constant Gross-Margin % NRV
Step 1: Overall GM% = (Total final revenues minus Total joint costs minus Total separable costs) / Total final revenues
Step 2: Total production cost of A = Final revenue of A x (1 minus GM%)
Step 3: Joint cost allocated to A = Total production cost of A minus Separable costs of A
Physical Measure
Allocated joint cost for A = (Physical measure of A / Total physical measure of all products) x Total joint costs
Ending Inventory Valuation
Ending inventory cost = (Allocated joint cost to product / Units produced) x Units in ending inventory
Students often think the sales value at splitoff method uses physical measures. It does not; it is a market-based method.
Students sometimes confuse the NRV formula: NRV = final sales value minus separable costs, not plus.
Students forget that the constant gross-margin percentage method is the only method that can produce negative joint-cost allocations.
Students assume the FASB specifies a single allowable method of joint cost allocation. It does not; no single method is mandated.
⚠️ Be ready to compute allocations under all four methods from the same data set. This is a common exam format.
⚠️ Know why the sales value at splitoff method is preferred: it measures benefits received, it is simple, it does not anticipate further management decisions, and it provides a common basis (revenue) for allocation.
⚠️ Understand that there is no cause-and-effect relationship between allocated joint costs and individual product values.
⚠️ The NRV method is used when splitoff selling prices are not available. The physical-measure method is the last resort when no market data is available at all.
True or false: The physical-measure method is a market-based approach. False. It uses physical units, not market data.
Fill in the blank: NRV = final sales value ________ separable costs. Minus.
True or false: The sales value at splitoff method is the simplest to implement. True.
Fill in the blank: The ________ method is the only one that can assign a negative allocation of joint costs. Constant gross-margin percentage NRV.
True or false: Revenues are a better indicator of benefits received than physical measures. True.
Q: The Arvid Corporation produces 2,000 widgets ($30 each), 3,500 gizmos ($20 each) and 4,000 turnbols ($10 each) from a joint process. Joint costs are $75,000. Using the sales value at splitoff method, how much joint cost is allocated to the widgets?
A: Total sales value = $60,000 + $70,000 + $40,000 = $170,000. Widgets' share = $60,000 / $170,000 = 35.29%. Allocated joint cost = 35.29% x $75,000 = $26,471.
Q: Product X sells for $10 at splitoff and Product Y for $8. January production: 300 units of X, 250 units of Y. Joint costs are $2,000. What is each unit's allocated joint cost under the sales value at splitoff method?
A: Total splitoff value = (300 x $10) + (250 x $8) = $5,000. Product X allocation = $3,000 / $5,000 x $2,000 = $1,200, so $1,200 / 300 = $4.00 per unit. Product Y = $2,000 / $5,000 x $2,000 = $800, so $800 / 250 = $3.20 per unit.
Q: Product Z5 can be made from Product A (1,375 litres at $25/litre) with $150 in separable costs. What is Z5's estimated NRV at the splitoff point?
A: NRV = (1,375 x $25) minus $150 = $34,375 minus $150 = $34,225.
Q: Name one positive and one negative aspect of the constant gross-margin percentage method.
A: Positive: it accounts for profits earned before or after splitoff when allocating joint costs. Negative: it assumes all products have the same ratio of cost to sales value, which is unlikely in practice.
Q: When is the physical-measure method the appropriate choice for allocating joint costs?
A: When selling prices at the splitoff point are unavailable and no market-based data can be estimated. It is the method of last resort.
The four allocation methods here build on the general cost-allocation principles from earlier chapters. The sell-or-process-further decision in Obj 16.5 (covered in Part 3 of these notes) uses the incremental revenue and cost framework from relevant costing (Chapter 11). Byproduct accounting methods (also Part 3) connect to inventory valuation and the matching principle from financial accounting.
Sales value at splitoff method, estimated net realisable value, NRV method, constant gross-margin percentage NRV, physical-measure method, joint cost allocation methods, market-based allocation, benefits-received criterion, revenue-based allocation, weight-based allocation, volume-based allocation, gross margin percentage, Horngren Chapter 16 Objective 16.3, Objective 16.4, cost allocation formulas, splitoff point valuation