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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