Chapter 7: Joint Product and By-Product Costing



CHAPTER 7

joint product and by-product costing

1 questions for writing and discussion

1. A joint cost is a cost incurred in the simultaneous 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 financial reporting purposes, to value inventories, and to determine income.

5. The sales-value-at-split-off method is neutral in that joint costs are allocated in accordance 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 disadvantage 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 overall product package which must be evaluated 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 percentage method is also used to allocate joint cost.

8. Joint costs occur only in cases of joint production. 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 regardless 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 determine price. The decision would be circular.

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

2

3 Exercises

7–1

Units Percent ( Joint Cost = Allocated Joint Cost

Phils 1,000 0.200 $72,000 $ 14,400

Bills 1,500 0.300 72,000 21,600

Gills 2,500 0.500 72,000 36,000

Total 5,000 $ 72,000

1 7–2

Price at Sales Value Joint Allocated

Units Split-off at Split-off Percent Cost Joint Cost

Phils 1,000 $18.75 $ 18,750 0.0625 $72,000 $ 4,500

Bills 1,500 75.00 112,500 0.3750 72,000 27,000

Gills 2,500 67.50 168,750 0.5625 72,000 40,500

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

2 7–3

Eventual Separable Hypothetical

Units Price Market Value Costs Market Value Percent

Ups 39,000 $2.00 $78,000 $18,000 $ 60,000 0.60

Downs 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

7–4

Units Percent ( Joint Cost = Allocated Joint Cost

Ups 39,000 0.65 $42,000 $ 27,300

Downs 21,000 0.35 42,000 14,700

Total 60,000 $ 42,000

3 7–5

Value of ups at split-off (39,000 ( $1.80) $ 70,200

Value of ups when processed further $ 78,000

Less: 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.

4 7–6

1. Units Percent ( Joint Cost = Allocated Joint Cost

Grade A 3,000 0.200 $200,000 $ 40,000

Grade B 4,500 0.300 200,000 60,000

Grade C 7,500 0.500 200,000 100,000

Total 15,000 $200,000

2. Weighting Weighted Joint Allocated

Units Factor Units Percent Cost Joint Cost

Grade A 3,000 4.5 13,500 0.3750 $200,000 $ 75,000

Grade B 4,500 2.5 11,250 0.3125 200,000 62,500

Grade C 7,500 1.5 11,250 0.3125 200,000 62,500

Total 15,000 $ 36,000 $200,000

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 $ 60,000

Less: Gross margin at 14.5% of market value 6,960 8,700

Cost of goods sold $ 41,040 $ 51,300

Less: 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 Percent

High 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

5 7–8

Percent Percent of Sales to Allocated

of Sales Production Production Percent Joint Cost

High 0.40 0.25 1.60 0.6667 $ 53,336

Low 0.60 0.75 0.80 0.3333 26,664

Total 2.40 $ 80,000

7–9

Number Price at Total Revenue

of Units Split-Off at Split-Off

Alpha 1,000 $ 2.00 $ 2,000

Beta 2,000 4.50 9,000

Gamma 2,500 3.75 9,375

Delta 6,000 8.00 48,000

Rho 3,000 0.50 1,500

Chi 150 0.20 30

Psi 1,000 0.04 40

Omega 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 produced.)

Beta, Gamma, and Delta are joint or main products due to their considerable revenue.

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.

6 7–10

1. High-Density Low-Density

Income Percent Income Percent

Sales $5,250 100.0% $9,000 100.0%

Less: Joint cost 2,000a 38.1% 6,000b 66.7%

Gross margin $3,250 61.9% $3,000 33.3%

a[375/(375 + 1,125)] ( $8,000

b[1,125/(375 + 1,125)] ( $8,000

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 1,500a 28.6% 4,500b 50.0% 2,000c —

Gross margin $3,750 71.4% $4,500 50.0% $(1,975) —

a(375/2,000) ( $8,000

b(1,125/2,000) ( $8,000

c(500/2,000) ( $8,000

Previously, defective chips were thrown out and never appeared on the income 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 imply 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 reduction 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 1,994a 38.0% 5,981b 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.

7–11

1. Net realizable value of by-product = $2 ( 60,000 = $120,000

Joint 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 $ 900,000

Second main product 150,000 0.625 2,400,000 1,500,000

Total 240,000 $ 2,400,000

7 7–12

1. Allocated

Units Percent ( Joint Cost = Joint Cost

Two Oil 300,000 0.4546* $10,000,000 $ 4,546,000

Six Oil 240,000 0.3636 10,000,000 3,636,000

Distillates 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 $ 4,000,000

Six Oil 240,000 30 7,200,000 0.4800 10,000,000 4,800,000

Distillates 120,000 15 1,800,000 0.1200 10,000,000 1,200,000

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

4 problems

7–13

1. Liquid Skin Silken Skin Total

Revenue $432,000 $468,000 $900,000

Variable expenses 252,000 108,000 360,000

Contribution margin $180,000 $360,000 $540,000

Joint 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 Order

Liquid Skin Silken Skin Total

Revenue $576,000a $876,000 $ 1,452,000

Variable expenses 504,000b 204,000 708,000

Contribution margin $ 72,000 $672,000 $ 744,000

Joint 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.

7–14

1. @ 500 lbs. Process Further Sell Difference

Revenuesa $ 8,750 $6,000 $ 2,750

Bagsb 0 (65) 65

Shippingc (250) (300) 50

Grindingd (1,575) 0 (1,575)

Bottlese (500) 0 (500)

$ 6,425 $ 5,635 $ 790

a500 ( 5 ( $3.50; $12 ( 500

b$1.30 ( (500/10)

c[(5 ( 500)/25] ( $2.50 = $250; $0.60 ( 500

d$3.15 ( 500

e5 ( 500 ( $0.20

Pharmadon should process the chemical further.

2. $790/500 = $1.58 additional income per pound

$1.58 ( 180,000 = $284,400

1 7–15

1. Revenues $141,500

Joint costs 131,000

Gross margin $ 10,500

2. Sell Process Further Difference

Revenues $ 40,000 $ 70,000 $ 30,000

Further 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.)

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 170,000

Further processing costs 250,000 ( Price ( $3.50

Gross margin $575,000 Gross margin $595,000

Altox 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 500,000

Further processing costs 1,400,000 ( Price ( $2.25

Gross margin $1,100,000 Gross margin $1,125,000

Lorex 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 330,000

Further processing costs 75,000 ( Price ( $2.00

Gross margin $667,500 Gross margin $660,000

Hycol should be processed further.

2. a. Annual production of Dorzine 50,000

( Price offered by Dietriech ( $0.75

Revenue $ 37,500

Savings on waste disposal 1,750

Less: 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 considerations. 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 considered in those decisions.

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.

2 7–18

At first, the director would probably not view the use of the museum for weddings 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 revenue” 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.

3 7–19

1. Physical units method:

Units Percent ( Joint Cost = Allocated Joint Cost

Red 150 0.30 $5,000 $1,500

Drab 350 0.70 5,000 3,500

Total 500 $5,000

2. Market value method:

Number Price at Sales Value Joint Allocated

of Trees Split-Off at Split-Off Percent Cost Joint Cost

Red 150 $35 $5,250 60.00% $5,000 $3,000

Drab 350 10 3,500 40.00% 5,000 2,000

Total $8,750 100.00% $5,000

7–19 Concluded

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

Less:

Cost of checking seedlings ($5 ( 500) $2,500

Cost of additional labor 275

Joint 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.

4 7–20

1. a. Total Pounds Net

Product Input Proportion Pounds Lost Pounds

Slices 270,000 0.33 89,100 — 89,100

Sauce 270,000 0.30 81,000 — 81,000

Juice 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 = 72,900

Net pounds = 67,500

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

Net

Net Selling Separable Realizable

Product Pounds Price Revenue Costs Value

Slices 89,100 $0.80 $ 71,280 $ 11,280 $ 60,000

Sauce 81,000 0.55 44,550 8,550 36,000

Juice 67,500 0.40 27,000 3,000 24,000

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

7–20 Concluded

c. The net realizable value of the by-product is deducted from the production 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 Gross

Product Value Percent Costs Margin

Slices $ 60,000 50% $ 29,000 $ 31,000

Sauce 36,000 30% 17,400 18,600

Juice 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 allocation 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.

5 7–21

1. a

2. a

3. c

6 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.

7–23

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

Monthly Sales Relative Allocated

Unit Price Sales Value Percent of Joint

Output per Unit at Split-Off Sales Costs

Studs 75,000 $ 8 $ 600,000 46.15% $ 461,500

Decorative pieces 5,000 60 300,000 23.08% 230,800

Posts 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:

Allocated

Units Percent ( Joint Cost = Joint Costs

Studs 75,000 0.750 $1,000,000 $ 750,000

Decorative pieces 5,000 0.050 1,000,000 50,000

Posts 20,000 0.200 1,000,000 200,000

Total 100,000 $1,000,000

c. Estimated net realizable value method:

Fully

Processed Estimated

Monthly Sales Net Allocated

Unit Price Realizable Percent Joint

Output per Unit Value of Value Costs

Studs 75,000 $ 8 $ 600,000 44.44% $ 444,400

Decorative pieces 4,500* 100 350,000** 25.93% 259,300

Posts 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

7–23 Concluded

2. Units Dollars

Monthly unit output 5,000

Less: Normal further processing shrinkage 500

Units available for sale 4,500

Final sales value (4,500 units @ $100 per unit) $450,000

Less: Sales value at split-off 300,000

Differential revenue $150,000

Less: 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 quality

b. Reduced motivation and morale

c. 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 explanation as to the reason for the change in order to help them better understand 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 rewards with goals.

c. Provide job relocation and internal job transfers.

5 collaborative learning exercise

7–24

1. Units produced method:

Units Percent ( Joint Cost = Allocated Joint Cost

Coming 1,000 20% $6,000 $1,200

Going 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 $ 9,000

Going 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 $ 947

Going 48,000 84.211 6,000 5,053

Total $ 6,000

3. Constant gross margin percentage method:

Percent

Revenue [($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 $56,000

Less: Gross margin 9,000 42,000

Cost of goods sold $ 3,000 $14,000

Less: 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 allocate all joint costs to Going. Therefore, the least desirable method is the units produced method.

6 cyber research case

7–25

Answers will vary.

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