Problem for Self-Study

Inorganic Chemicals (IC) processes salt into various industrial products. In July 2020, IC incurred joint costs of $100,000 to purchase salt and convert it into two products: caustic soda and chlorine. Although there is an active outside market for chlorine, IC processes all 800 tons of chlorine into 500 tons of PVC (polyvinyl chloride), which is then sold. There were no beginning or ending inventories of salt, caustic soda, chlorine, or PVC in July. Information for July 2020 production and sales follows:

Spreadsheet screenshot shows the manufacturing details of various products of Inorganic chemicals (IC).

Details of the spreadsheet are as follows:

  1. Joint costs (which is the costs of salt and processing to splitoff point): $100,000

  2. Separable cost of processing 800 tons of chlorine into 500 tons of PVC: $20,000

  3. Beginning inventory in tons

    • Caustic Soda: 0

    • Chlorine: 0

    • PVC: 0

  4. Production in tons

    • Caustic Soda: 1,200

    • Chlorine: 800

    • PVC: 500

  5. Transfer for further processing in tons

    • Chlorine: 800

  6. Sales in tons

    • Caustic Soda: 1,200

    • PVC: 500

  7. Ending inventory in tons

    • Caustic Soda: 0

    • Chlorine: 0

    • PVC: 0

  8. Selling price per ton in active outside market (for products not actually sold)

    • Chlorine: $75

  9. Selling price per ton for products sold

    • Caustic Soda: $50

    • PVC: $200

Required

  1. Allocate the joint costs of $100,000 between caustic soda and PVC under (a) the sales value at splitoff method and (b) the physical-measure method.
  2. Allocate the joint costs of $100,000 between caustic soda and PVC under the NRV method.
  3. Under the three allocation methods in requirements 1 and 2, what is the gross-margin percentage of (a) caustic soda and (b) PVC?
  4. Lifetime Swimming Pool Products offers to purchase 800 tons of chlorine in August 2020 at $75 per ton. Assume all other production and sales data are the same for August as they were for July. This sale of chlorine to Lifetime would mean that no PVC would be produced by IC in August. How would accepting this offer affect IC’s August 2020 operating income?

Solution

The following picture provides a visual illustration of the main facts in this problem.

Flow-chart shows Inorganic chemicals manufacturing details depicting the joint and separable costs of the company.

The details are as follows:

  • Salt is processed at joint processing costs of $100,000 before reaching splitoff point.

  • After reaching splitoff point the salt is separated into 1,200 tons of main or joint product caustic soda at $50 per ton and 800 tons of chlorine at $75 per ton.

  • The chlorine obtained from the first process is further processes at $20,000 to obtain 500 tons of main or joint product PVC at $200 per ton

Note that caustic soda is sold as is, while chlorine, despite having a market value at splitoff, is sold in processed form as PVC. The goal is to allocate the joint costs of $100,000 to the final products—caustic soda and PVC. However, because PVC exists only in the form of chlorine at the splitoff point, we use chlorine’s sales value and physical measure to allocate joint costs to PVC under the sales value at splitoff and physical measure at splitoff methods.

1a. Sales value at splitoff method

Spreadsheet screenshot shows the allocation of joint costs using sales value at splitoff method of IC.

Details of the spreadsheet are as follows:

  1. Sales value of total production at splitoff point

    • Caustic Soda (1,200 tons times $50 per ton): $60,000

    • Chlorine/PVC (800 times $75 per ton): $60,000

    • Total: $120,000

  2. Weighting

    • Caustic Soda (($60,000 divided by $120,000): 0.50

    • Chlorine/PVC ($60,000 divided by $120,000): 0.50

  3. Joint costs allocated

    • Caustic Soda (0.50 times $100,000): $50,000

    • Chlorine/PVC (0.50 times $100,000): $50,000

    • Total: $100,000

1b. Physical-measure method

Spreadsheet screenshot shows the allocation of joint costs using physical-measure method of IC.

Details of the spreadsheet are as follows:

  1. Physical measure of total production in tons

    • Caustic Soda: 1,200

    • Chlorine/PVC: 800

    • Total: 2,000

  2. Weighting

    • Caustic Soda (1,200 tons divided by 2000 tons): 0.60

    • Chlorine/PVC (800 tons divided by 2000 tons): 0.40

  3. Joint costs allocated

    • Caustic Soda (0.60 times $100,000): $60,000

    • Chlorine/PVC (0.40 times $100,000): $40,000

    • Total: $100,000

2. Net realizable value (NRV) method

Spreadsheet screenshot shows the allocation of joint costs using net realizable value method of IC.

Details of the spreadsheet are as follows:

  1. Final sales value of total production during accounting period

    • Caustic Soda (1,200 tons multiplied by $50 per ton): $60,000

    • PVC (500 tons multiplied by $200 per ton): $100,000

    • Total: $160,000

  2. Deduct separable costs to complete and sell

    • Caustic Soda (1,200 tons divided by 2000 tons): 0

    • PVC (800 tons divided by 2000 tons): $20,000

    • Total: $20,000

  3. Net realizable value at splitoff point

    • Caustic Soda: $60,000

    • PVC: $80,000

    • Total: $140,000

  4. Weighting

    • Caustic Soda ($60,000 divided by $140,000): fraction 3 by 7

    • PVC ($80,000 divided by $140,000): fraction 4 by 7

  5. Joint costs allocated

    • Caustic Soda (fraction 3 by 7 multiplied by $100,000): $42,857

    • PVC (fraction 4 by 7 multiplied by $100,000): $57,143

    • Total: $100,000

3a. Gross-margin percentage of caustic soda

Spreadsheet screenshot shows gross margin and gross margin percentage of IC’s caustic soda.

Details of various costs incurred on caustic soda for various methods of allocation used are as follows:

  1. Revenues (1,200 tons multiplied by $50 per ton)

    • Sales value at splitoff point: $60,000

    • Physical measure: $60,000

    • NRV method: $60,000

  2. Cost of goods sold (joint costs)

    • Sales value at splitoff point: $50,000

    • Physical measure: $60,000

    • NRV method: $42,857

  3. Gross margin

    • Sales value at splitoff point: $10,000

    • Physical measure: $0

    • NRV method: $17,143

  4. Gross margin percentage

    • Sales value at splitoff point ($100,000 divided by $60,000): 16.67%

    • Physical measure ($0 divided by $60,000): 0.00%

    • NRV method ($17,143 divided by $60,000): 28.57%

3b. Gross-margin percentage of PVC

Spreadsheet screenshot shows gross margin and gross margin percentage of IC’s PVC.

Details of various costs incurred on PVC for various methods of allocation used are as follows:

  1. Revenues (500 tons multiplied by $200 per ton)

    • Sales value at splitoff point: $100,000

    • Physical measure: $100,000

    • NRV method: $100,000

  2. Cost of goods sold (joint costs)

    • Sales value at splitoff point: $50,000

    • Physical measure: $40,000

    • NRV method: $57,143

  3. Cost of goods sold (separable costs)

    • Sales value at splitoff point: $20,000

    • Physical measure: $20,000

    • NRV method: $20,000

  4. Total cost of goods sold

    • Sales value at splitoff point: $70,000

    • Physical measure: $60,000

    • NRV method: $77,143

  5. Gross margin

    • Sales value at splitoff point: $30,000

    • Physical measure: $40,000

    • NRV method: $22,857

Gross margin percentage

  • Sales value at splitoff point ($30,000 divided by $100,000): 30.00%

  • Physical measure ($40,000 divided by $100,000): 40.00%

  • NRV method ($22,857 divided by $100,000): 22.86%

4. Sale of chlorine versus processing into PVC

Spreadsheet screenshot shows the effect of sale of chlorine versus processing it into PVC.

Details are as follows:

  1. Incremental revenue from processing 800 tons of chlorine into 500 tons of PVC, which is the difference of (500 tons multiplied by $200 per ton) and (800 tons multiplied by $75 per ton): $40,000

  2. Incremental cost of processing 800 tons of chlorine into 500 tons of PVC: $20,000

  3. Incremental operating income from further processing: $20,000

If IC sells 800 tons of chlorine to Lifetime Swimming Pool Products instead of further processing it into PVC, its August 2020 operating income will reduce by $20,000.