CHAPTER 7JOINT PRODUCT AND BY-PRODUCT COSTING

QUESTIONS FOR WRITING AND DISCUSSION

1. A joint cost is a cost incurred in the simulta-neous production of two or more products.

2. The joint costing problem is determining how best to allocate joint costs to the various products. The difficulties are that all of the joint costs must be incurred to produce the products, and the allocation is arbitrary.

3. A by-product is a jointly produced product of relatively little sales value relative to the main product(s).

4. Joint costs are allocated to products for fi-nancial reporting purposes, to value invento-ries, and to determine income.

5. The sales-value-at-split-off method is neutral in that joint costs are allocated in accor-dance with the revenue-producing ability of each product. In this way, products will not show a loss due to joint cost allocation. However, other considerations may take precedence over this type of neutrality. For example, the physical units method may be easier to apply and does not have the disad-vantage of changing prices.

6. Joint cost allocation may lead managers to believe that part of a joint cost is avoidable when this is not true. Additionally, allocated joint costs may affect the pricing decisions of the individual products when it is the over-

all product package which must be evalu-ated in terms of profitability.

7. Three methods of allocating joint product costs are the physical units method, the market value method, and the net realizable method. The constant gross margin percent-age method is also used to allocate joint cost.

8. Joint costs occur only in cases of joint pro-duction. A joint cost is a common cost, but a common cost is not necessarily a joint cost. Many overhead costs are common to the products manufactured in a factory but do not signify a joint production process.

9. No. Joint costs are irrelevant. They occur re-gardless of whether the product is sold at the split-off point or processed further.

10. All sales value methods are based on price. If price is used to determine cost, then that cost cannot be used to turn around and de-termine price. The decision would be circu-lar.

11. By-products can be accounted for using cost or noncost methods. Cost methods involve assigning some cost to the by-product for in-ventory purposes. Noncost methods make no attempt to cost the by-product, but in-stead they make some credit either to in-come or to the main product.

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EXERCISES

7–1

Units Percent Joint Cost = Allocated Joint CostPhils 1,000 0.200 $72,000 $14,400Bills 1,500 0.300 72,000 21,600Gills 2,500 0.500 72,000 36,000

Total 5,000 $ 72,000

7–2

Price at Sales Value Joint AllocatedUnits Split-off at Split-off Percent Cost Joint Cost

Phils 1,000 $18.75 $ 18,750 0.0625 $72,000 $ 4,500Bills 1,500 75.00 112,500 0.3750 72,000 27,000Gills 2,500 67.50 168,750 0.5625 72,000 40,500

Total 5,000 $300,000 $ 72,000

7–3

Eventual Separable HypotheticalUnits Price Market Value Costs Market Value Percent

Ups 39,000 $2.00 $78,000 $18,000 $ 60,000 0.60Downs 21,000 2.18 45,780 5,780 40,000 0.40

Total $100,000 Ups Downs

Joint cost $42,000 $42,000 Percent of hypothetical market value 0.60 0.40 Allocated joint cost $ 25,200 $ 16,800

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7–4

Units Percent Joint Cost = Allocated Joint CostUps 39,000 0.65 $42,000 $27,300Downs 21,000 0.35 42,000 14,700

Total 60,000 $ 42,000

7–5

Value of ups at split-off (39,000 $1.80) $ 70,200 Value of ups when processed further $78,000Less: Further processing cost 18,000 Incremental value of further processing $ 60,000 Ups should NOT be processed further as there will $10,200 more profit if sold at split-off.

7–6

1. Units Percent Joint Cost = Allocated Joint CostGrade A 3,000 0.200 $200,000 $ 40,000Grade B 4,500 0.300 200,000 60,000Grade C 7,500 0.500 200,000 100,000

Total 15,000 $200,000

2. Weighting Weighted Joint AllocatedUnits Factor Units Percent Cost Joint Cost

Grade A 3,000 4.5 13,500 0.3750 $200,000 $ 75,000Grade B 4,500 2.5 11,250 0.3125 200,000 62,500Grade C 7,500 1.5 11,250 0.3125 200,000 62,500 Total 15,000 $ 36,000 $200,000

210210

7–7

1. Constant gross margin percentage method:

Total revenue ($12 4,000) + ($5 12,000) $108,000 100.0%Less costs: $80,000 + $4,000 + $8,340 92,340 85.5 %Gross margin $ 15,660 14.5 %

High Low Eventual market value $48,000 $60,000Less: Gross margin at 14.5% of market value 6,960 8,700 Cost of goods sold $41,040 $51,300Less: Separable costs 4,000 8,340 Allocated joint costs $ 37,040 $ 42,960

2. Net realizable value method:Eventual Separable Hypothetical

Units Price Market Value Costs Market Value PercentHigh 4,000 $12 $48,000 $4,000 $44,000 46%Low 12,000 5 60,000 8,340 51,660 54 %

Total $95,660 100 %

High Low Joint cost $80,000 $80,000 Percent of hypothetical market value 0.46 0.54 Allocated joint cost $ 36,800 $ 43,200

7–8

Percent Percent of Sales to Allocatedof Sales Production Production Percent Joint Cost

High 0.40 0.25 1.60 0.6667 $53,336Low 0.60 0.75 0.80 0.3333 26,664

Total 2.40 $ 80,000

211211

7–9

Number Price at Total Revenueof Units Split-Off at Split-Off

Alpha 1,000 $ 2.00 $ 2,000Beta 2,000 4.50 9,000Gamma 2,500 3.75 9,375Delta 6,000 8.00 48,000Rho 3,000 0.50 1,500Chi 150 0.20 30Psi 1,000 0.04 40Omega 10 10.00 100

$ 70,045

Chi, Psi, and Omega are, at best, by-products. Arguably, Chi and Psi could be considered scrap. The amount of revenue they produce is not worth a great deal of effort in handling or in accounting. Note that Omega has the highest price per unit of any of the eight. Still, it is a by-product for this company unless and until they can figure out a way to produce more of it.

(Note: A similar situation exists in copper mining. Copper ore may contain gold. While the gold refined from copper ore is very valuable per ounce compared to copper, the gold is accounted for as a by-product since so little of it is pro-duced.)

Beta, Gamma, and Delta are joint or main products due to their considerable rev-enue.

Alpha and Rho are probably by-products. Together, they account for just under 5 percent of the total revenue. Still, the company may choose to consider them main products based on future revenue estimates or their importance to the overall product line.

7–10

1. High-Density Low-Density Income Percent Income Percent

Sales $5,250 100.0% $9,000 100.0%Less: Joint cost 2,000 a 38 .1 % 6,000 b 66 .7 %Gross margin $3,250 61 .9 % $3,000 33 .3 %a[375/(375 + 1,125)] $8,000b[1,125/(375 + 1,125)] $8,000

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7–10 Concluded

2. High-Density Low-Density Defective Income Percent Income Percent Income Percent

Sales $5,250 100.0% $9,000 100.0% $ 25 100.0%Less: Joint cost 1,500 a 28 .6 % 4,500 b 50 .0 % 2,000 c — Gross margin $3,750 71 .4 % $4,500 50 .0 % $(1,975) — a(375/2,000) $8,000b(1,125/2,000) $8,000c(500/2,000) $8,000Previously, defective chips were thrown out and never appeared on the in-come statement. The entire joint cost was absorbed by the high-density and low-density chips. These product lines maintained gross margins well above the 25 percent limit.

Clearly, the gross margin for the defective chips is negative and doesn’t come close to meeting the Ultratech requirements. Yet, this result would im-ply that LaTonya should throw away the chips instead of selling them for $25. This is a counterintuitive result.

3. A preferred method is to recognize that the defective chips are a by-product. One possibility is to treat the $25 revenue from by-product sales as a reduc-tion in joint cost; then, allocate the remaining joint cost to the main products as follows:

High-Density Low-Density Income Percent Income Percent

Sales $5,250 100.0% $9,000 100.0%Less: Allocated

joint cost 1,994 a 38 .0 % 5,981 b 66 .5 %Gross profit $3,256 62 .0 % $3,019 33 .5 %a(375/1,500) ($8,000 – $25)b(1,125/1,500) ($8,000 –$25)An alternative approach is to account for the by-product revenue as “Other income” or “Revenue from sales of the by-product” which would leave the gross margins for the main products as calculated in Requirement 1.

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7–11

1. Net realizable value of by-product = $2 60,000 = $120,000Joint cost to be allocated = $2,520,000 $120,000 = $2,400,000

2. Allocated Units Percent Joint Cost = Joint Cost

First main product 90,000 0.375 $2,400,000 $ 900,000Second main product 150,000 0.625 2,400,000 1,500,000

Total 240,000 $ 2,400,000

7–12

1. Allocated Units Percent Joint Cost = Joint Cost

Two Oil 300,000 0.4546* $10,000,000 $ 4,546,000Six Oil 240,000 0.3636 10,000,000 3,636,000Distillates 120,000 0.1818 10,000,000 1,818,000

Total 660,000 $10,000,000*Rounded up

2. Price at Market Value Allocated Units Split-off at Split-off Percent Joint Cost Joint Cost

Two Oil 300,000 $20 $ 6,000,000 0.4000 $10,000,000 $ 4,000,000Six Oil 240,000 30 7,200,000 0.4800 10,000,000 4,800,000Distillates 120,000 15 1,800,000 0.1200 10,000,000 1,200,000

Total 660,000 $ 15,000,000 $10,000,000

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PROBLEMS

7–13

1. Liquid Skin Silken Skin Total Revenue $432,000 $468,000 $900,000Variable expenses 252,000 108,000 360,000 Contribution margin $180,000 $360,000 $540,000Joint costs 420,000

Operating income $120,000

2. The special order requires two additional standard production runs (2 120,000 gallons = 240,000 gallons). These two runs will also generate 360,000 gallons of Liquid Skin.

Income from Special OrderLiquid Skin Silken Skin Total

Revenue $576,000a $876,000 $ 1,452,000Variable expenses 504,000 b 204,000 708,000 Contribution margin $ 72,000 $672,000 $ 744,000Joint costs 840,000

Operating income (loss) $ (96,000 )aRevenue: (360,000 $1.60) and (240,000 $3.65)bVariable expenses: (360,000 $1.40) and (240,000 $0.85)No. The special order will result in a $96,000 loss.

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7–14

1. @ 500 lbs. Process Further Sell DifferenceRevenuesa $ 8,750 $6,000 $ 2,750Bagsb 0 (65) 65Shippingc (250) (300) 50Grindingd (1,575) 0 (1,575)Bottlese (500 ) 0 (500 )

$ 6,425 $ 5,635 $ 790 a500 5 $3.50; $12 500b$1.30 (500/10)c[(5 500)/25] $2.50 = $250; $0.60 500d$3.15 500e5 500 $0.20Pharmadon should process the chemical further.

2. $790/500 = $1.58 additional income per pound$1.58 180,000 = $284,400

7–15

1. Revenues $141,500Joint costs 131,000

Gross margin $ 10,500

2. Sell Process Further DifferenceRevenues $40,000 $70,000 $30,000Further processing costs 0 11,500 11,500

Gross margin $ 40,000 $ 58,500 $ 18,500 The company should process Inex further as gross margin would increase by $18,500.

(Note: Joint costs are irrelevant to this decision, as the company will incur them whether or not Inex is processed further.)

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7–16

1. If Altox is processed further: If Altox is sold at split-off:Revenue ($5.50 150,000) $825,000 Units at split-off 170,000Further processing costs 250,000 Price $3.50

Gross margin $575,000 Gross margin $595,000Altox should be sold at split-off.

If Lorex is processed further: If Lorex is sold at split-off:Revenue ($5 500,000) $2,500,000 Units at split-off 500,000Further processing costs 1,400,000 Price $2.25

Gross margin $1,100,000 Gross margin $1,125,000Lorex should be sold at split-off.

If Hycol is processed further: If Hycol is sold at split-off:Revenue ($1.80 412,500) $742,500 Units at split-off 330,000Further processing costs 75,000 Price $2.00

Gross margin $667,500 Gross margin $660,000Hycol should be processed further.

2. a. Annual production of Dorzine 50,000 Price offered by Dietriech $0.75 Revenue $ 37,500Savings on waste disposal 1,750Less: Processing costs (43,000 )Loss on sale of Dorzine $ (3,750 )Refining the waste product appears to be a poor decision, since it will cost Goodson an additional $3,750. However, there are other considera-tions. By converting the chemical waste to a solvent, Goodson will avoid having to locate hazardous waste disposal sites and may avoid any future litigation regarding its waste disposal.

b. Treating Dorzine as a by-product will have no effect on the decisions to process Altox, Lorex, and Hycol further, since joint costs were not con-sidered in those decisions.

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7–17

Goodson could account for the by-product in the following ways:

1. Show the $13,000 annual net revenue as “Revenue from sale of by-product” on the income statement.

2. Reduce the joint costs to be allocated to the main products by $13,000.

3. Reduce the cost of goods sold of the main products by $13,000.

7–18

At first, the director would probably not view the use of the museum for wed-dings as a joint costing problem. The first few rentals would add income to the museum and would be accounted for as “Other income” or “Miscellaneous rev-enue” on the income statement. Later, if the use of the museum for social affairs became more popular, some of the cost of the grounds and restaurant would no doubt be allocated to this use of the facilities. In effect, a by-product would turn into a main product.

7–19

1. Physical units method:

Units Percent Joint Cost = Allocated Joint CostRed 150 0.30 $5,000 $1,500Drab 350 0.70 5,000 3,500

Total 500 $5,000

2. Market value method:

Number Price at Sales Value Joint Allocatedof Trees Split-Off at Split-Off Percent Cost Joint Cost

Red 150 $35 $5,250 60.00% $5,000 $3,000Drab 350 10 3,500 40.00% 5,000 2,000

Total $8,750 100.00% $5,000

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7–19 Concluded

3. Revenue (0.7 500 $35).................................. $12,250Less:

Cost of checking seedlings ($5 500)........ $2,500Cost of additional labor................................. 275Joint costs...................................................... 5,000 7,775

Operating income................................................ $ 4,475 If Vicki undertakes the genetic testing, she will make $4,475 versus the $3,750 ($8,750 – $5,000) she would make selling both red and drab trees. She should have the trees tested.

7–20

1. a. Total Pounds NetProduct Input Proportion Pounds Lost PoundsSlices 270,000 0.33 89,100 — 89,100Sauce 270,000 0.30 81,000 — 81,000Juice 270,000 0.27 72,900 5,400 67,500*Feed 270,000 0.10 27,000 — 27,000

264,600*Net pounds = 72,900 – (0.08 Net pounds)

1.08 Net pounds = 72,900Net pounds = 67,500

b. The net realizable value for each of the three main products is calculated as follows:

NetNet Selling Separable Realizable

Product Pounds Price Revenue Costs Value Slices 89,100 $0.80 $ 71,280 $11,280 $ 60,000Sauce 81,000 0.55 44,550 8,550 36,000Juice 67,500 0.40 27,000 3,000 24,000

$142,830 $ 22,830 $120,000

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7–20 Concluded

c. The net realizable value of the by-product is deducted from the produc-tion costs prior to allocation to the main products as follows:

NRV of by-product = By-product revenue – Separable costs= $0.10(270,000 0.10) – $700= $2,000

Costs to be allocated = Joint cost – NRV of by-product= $60,000 – $2,000= $58,000

d. Gross margin for November:

Net Realizable Joint GrossProduct Value Percent Costs Margin Slices $ 60,000 50% $29,000 $31,000Sauce 36,000 30% 17,400 18,600Juice 24,000 20% 11,600 12,400

Total $120,000 100% $ 58,000 $ 62,000 The by-product is not allocated any joint costs.

2. Because the gross margin by main product is determined by the arbitrary al-location of joint product costs, these cost figures and the resulting gross margin information are of little use for planning and control. The allocation is made only for purposes of inventory valuation and income determination.

7–21

1. a2. a3. c

7–22

1. Because Product N was allocated $24,000 of the joint costs, it must account for 40 percent of the relative sales value at split-off ($24,000/$60,000 = 0.40). Therefore, Product N has a $40,000 sales value at split-off ($100,000 0.40 = $40,000).

2. If the units produced approach is used, Product N will receive $30,000 in joint costs since it accounts for half of the total units produced.

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7–23

1. a. Relative sales value method at split-off:

Monthly Sales Relative AllocatedUnit Price Sales Value Percent of Joint

Output per Unit at Split-Off Sales Costs Studs 75,000 $ 8 $ 600,000 46.15% $ 461,500Decorative pieces 5,000 60 300,000 23.08% 230,800Posts 20,000 20 400,000 30.77% 307,700

Total $1,300,000 100.00% $1,000,000

b. Physical units method at split-off:

AllocatedUnits Percent Joint Cost = Joint Costs

Studs 75,000 0.750 $1,000,000 $ 750,000Decorative pieces 5,000 0.050 1,000,000 50,000Posts 20,000 0.200 1,000,000 200,000

Total 100,000 $1,000,000

c. Estimated net realizable value method:

FullyProcessed Estimated

Monthly Sales Net AllocatedUnit Price Realizable Percent Joint

Output per Unit Value of Value Costs Studs 75,000 $ 8 $ 600,000 44.44% $ 444,400Decorative pieces 4,500* 100 350,000** 25.93% 259,300Posts 20,000 20 400,000 29.63% 296,300

Total $1,350,000 100.00% $1,000,000*5,000 monthly units of output – 10% Normal spoilage = 4,500 good units

**4,500 good units $100 = $450,000 – Further processing cost of $100,000 = $350,000

221221

7–23 Concluded

2. Units Dollars Monthly unit output............................................................. 5,000Less: Normal further processing shrinkage..................... 500

Units available for sale.................................................. 4,500Final sales value (4,500 units @ $100 per unit)................ $450,000Less: Sales value at split-off.............................................. 300,000

Differential revenue........................................................ $150,000Less: Further processing costs......................................... 100,000

Additional contribution from further processing........ $ 50,000

3. Assuming Sonimad Sawmill, Inc., announces that in six months it will sell the rough-cut product at split-off due to increasing competitive pressure, at least three types of likely behavior will be demonstrated by the skilled labor in the planing and sizing process, including the following:

a. Poorer qualityb. Reduced motivation and moralec. Job insecurity, leading to nonproductive employee time looking for jobs

elsewhere

Management actions that could improve this behavior include the following:

a. Improve communication by giving the workers a more comprehensive ex-planation as to the reason for the change in order to help them better un-derstand the situation and bring about a plan for future operation of the rest of the plant.

b. Offer incentive bonuses to maintain quality and production and align re-wards with goals.

c. Provide job relocation and internal job transfers.

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COLLABORATIVE LEARNING EXERCISE

7–24

1. Units produced method:

Units Percent Joint Cost = Allocated Joint CostComing 1,000 20% $6,000 $1,200Going 4,000 80 6,000 4,800

Total $6,000

2. Net realizable value method:

Eventual Separable Hypothetical Number Hypothetical Price – Costs = Price of Units = Revenue

Coming $12 $3 $ 9 1,000 $ 9,000Going 14 2 12 4,000 48,000

Total $ 57,000

Hypothetical Allocated Revenue Percent Joint Cost = Joint Costs

Coming $ 9,000 15.789% $6,000 $ 947Going 48,000 84.211 6,000 5,053

Total $ 6,000

3. Constant gross margin percentage method:

PercentRevenue [($12 1,000) + ($14 4,000)] $68,000 100%Costs [$6,000 + ($3 1,000) + ($2 4,000)] 17,000 25 Gross margin $ 51,000 75 %

Coming Going Eventual market value $12,000 $56,000Less: Gross margin 9,000 42,000 Cost of goods sold $ 3,000 $14,000Less: Separable costs 3,000 8,000 Allocated joint costs $ 0 $ 6,000

4. The revenue provided by Going is so much higher than that provided by Coming that any allocation method relying on revenue will allocate much more of the joint cost to Going. At the extreme is the constant gross margin percentage method which allocates all of the joint costs to Going. Given this information, it would be preferable to treat Coming as a by-product and allo-cate all joint costs to Going. Therefore, the least desirable method is the units produced method.

223223

CYBER RESEARCH CASE

7–25

Answers will vary.

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