Solution manual cost accounting 12e by horngren ch 16

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CHAPTER 16
COST ALLOCATION: JOINT PRODUCTS AND BYPRODUCTS
16-1 Exhibit 16-1 presents nine examples of joint products from four different general
industries. These include:
Industry
Separable Products at the Splitoff Point
Food Processing:
• Lamb
• Lamb cuts, tripe, hides, bones, fat
• Turkey
• Breasts, wings, thighs, poultry meal
Extractive:
• Petroleum

• Crude oil, natural gas, raw LPG

16-2 A joint cost is a cost of a production process that yields multiple products simultaneously.
A separable cost is a cost incurred beyond the splitoff point that is assignable to each of the
specific products identified at the splitoff point.
16-3 The distinction between a joint product and a byproduct is based on relative sales value.
A joint product is a product from a joint production process (a process that yields two or more
products) that has a relatively high sales value. A byproduct is a product that has a relatively low
sales value compared to the sales value of the joint (or main) products.
16-4 A product is any output that has a positive sales value (or an output that enables a
company to avoid incurring costs). In some joint-cost settings, outputs can occur that do not have
a positive sales value. The offshore processing of hydrocarbons yields water that is recycled back
into the ocean as well as yielding oil and gas. The processing of mineral ore to yield gold and
silver also yields dirt as an output, which is recycled back into the ground.
16-5

1.
2.
3.
4.
5.
6.

The chapter lists the following six reasons for allocating joint costs:
Computation of inventoriable costs and cost of goods sold for financial accounting
purposes and reports for income tax authorities.
Computation of inventoriable costs and cost of goods sold for internal reporting purposes.
Cost reimbursement under contracts when only a portion of a business's products or
services is sold or delivered under cost-plus contracts.
Insurance settlement computations for damage claims made on the basis of cost
information of joint products or byproducts.
Rate regulation when one or more of the jointly-produced products or services are subject
to price regulation.
Litigation in which costs of joint products are key inputs.

16-6 The joint production process yields individual products that are either sold this period or
held as inventory to be sold in subsequent periods. Hence, the joint costs need to be allocated
between total production rather than just those sold this period.
16-7 This situation can occur when a production process yields separable outputs at the splitoff
point that do not have selling prices available until further processing. The result is that selling
prices are not available at the splitoff point to use the sales value at splitoff method. Examples
include processing in integrated pulp and paper companies and in petro-chemical operations.
16-1


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16-8 Both methods use market selling-price data in allocating joint costs, but they differ in
which sales-price data they use. The sales value at splitoff method allocates joint costs to joint
products on the basis of the relative total sales value at the splitoff point of the total production of
these products during the accounting period. The net realizable value method allocates joint costs
to joint products on the basis of the relative net realizable value (the final sales value minus the
separable costs of production and marketing) of the total production of the joint products during
the accounting period.
16-9

Limitations of the physical measure method of joint-cost allocation include:
a. The physical weights used for allocating joint costs may have no relationship to the
revenue-producing power of the individual products.
b. The joint products may not have a common physical denominator––for example, one
may be a liquid while another a solid with no readily available conversion factor.

16-10 The NRV method can be simplified by assuming (a) a standard set of post-splitoff point
processing steps, and (b) a standard set of selling prices. The use of (a) and (b) achieves the same
benefits that the use of standard costs does in costing systems.
16-11 The constant gross-margin percentage NRV method takes account of the post-splitoff
point ―profit‖ contribution earned on individual products, as well as joint costs, when making
cost assignments to joint products. In contrast, the sales value at splitoff point and the NRV
methods allocate only the joint costs to the individual products.
16-12 No. Any method used to allocate joint costs to individual products that is applicable to
the problem of joint product-cost allocation should not be used for management decisions
regarding whether a product should be sold or processed further. When a product is an inherent
result of a joint process, the decision to process further should not be influenced by either the
size of the total joint costs or by the portion of the joint costs assigned to particular products.
Joint costs are irrelevant for these decisions. The only relevant items for these decisions are the
incremental revenue and the incremental costs beyond the splitoff point.

16-13 No. The only relevant items are incremental revenues and incremental costs when
making decisions about selling products at the splitoff point or processing them further.
Separable costs are not always identical to incremental costs. Separable costs are costs incurred
beyond the splitoff point that are assignable to individual products. Some separable costs may
not be incremental costs in a specific setting (e.g., allocated manufacturing overhead for postsplitoff processing that includes depreciation).
16-14 Two methods to account for byproducts are:
a. Production method—recognizes byproducts in the financial statements at the time
production is completed.
b. Sales method—delays recognition of byproducts until the time of sale.
16-15 The sales byproduct method enables a manager to time the sale of byproducts to affect
reported operating income. A manager who was below the targeted operating income could
adopt a ―fire-sale‖ approach to selling byproducts so that the reported operating income exceeds
the target. This illustrates one dysfunctional aspect of the sales method for byproducts.

16-2


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16-16

(20-30 min.) Joint-cost allocation, insurance settlement.

1.

(a)

Breasts
Wings
Thighs

Bones
Feathers

Sales value at splitoff-point method.
Pounds
of
Product
100
20
40
80
10
250

Wholesale
Selling Price
per Pound
$1.10
0.40
0.70
0.20
0.10

Sales
Value
at Splitoff
$110
8
28
16

1
$163

Weighting:
Joint
Sales Value
Costs
at Splitoff Allocated
0.675
$ 67.50
0.049
4.90
0.172
17.20
0.098
9.80
0.006
0.60
1.000
$100.00

Allocated
Costs per
Pound
0.6750
0.2450
0.4300
0.1225
0.0600

Costs of Destroyed Product
Breasts: $0.6750 per pound 20 pounds = $13.50
Wings: $0.2450 per pound 10 pounds =
2.45
$15.95
b.
Physical measures method.
Pounds
Weighting:
of
Physical
Product
Measures
Breasts
100
0.400
Wings
20
0.080
Thighs
40
0.160
Bones
80
0.320
Feathers
10
0.040
250
1.000

Costs of Destroyed Product
Breast: $0.40 per pound 20 pounds
Wings: $0.40 per pound 10 pounds

Joint
Costs
Allocated
$ 40.00
8.00
16.00
32.00
4.00
$100.00
=
=

Allocated
Costs per
Pound
$0.400
0.400
0.400
0.400
0.400

$ 8
4
$12

Note: Although not required, it is useful to highlight the individual product profitability figures:

Product
Breasts
Wings
Thighs
Bones
Feathers

Sales
Value
$110
8
28
16
1

Sales Value at
Splitoff Method
Joint Costs
Gross
Allocated
Income
$67.50
$42.50
4.90
3.10
17.20
10.80
9.80
6.20

0.60
0.40

16-3

Physical
Measures Method
Joint Costs
Gross
Allocated
Income
$40.00
$70.00
8.00
0.00
16.00
12.00
32.00
(16.00)
4.00
(3.00)


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2.
The sales-value at splitoff method captures the benefits-received criterion of cost
allocation and is the preferred method. The costs of processing a chicken are allocated to
products in proportion to the ability to contribute revenue. Chicken Little’s decision to process
chicken is heavily influenced by the revenues from breasts and thighs. The bones provide

relatively few benefits to Chicken Little despite their high physical volume.
The physical measures method shows profits on breasts and thighs and losses on bones
and feathers. Given that Chicken Little has to jointly process all the chicken products, it is nonintuitive to single out individual products that are being processed simultaneously as making
losses while the overall operations make a profit. Chicken Little is processing chicken mainly for
breasts and thighs and not for wings, bones, and feathers, while the physical measure method
allocates a disproportionate amount of costs to wings, bones and feathers.

16-17 (10 min.) Joint products and byproducts (continuation of 16-16).
1.

Ending inventory:
Breasts
10
Wings
4
Thighs
3
Bones
5
Feathers
2

$0.6750
0.2450
0.4300
0.1225
0.0600

=
=

=
=
=

$6.7500
0.9800
1.2900
0.6125
0.1200
$9.7525

2.
Joint products
Breasts
Thigh

Byproducts
Wings
Bones
Feathers

Revenues of byproducts:
Wings
$ 8
Bones
16
Feathers
1
$25

Joint costs to be allocated:
Joint costs – Revenues of byproducts
$100 – $25 = $75

Breast
Thighs

Pounds
of
Product

Wholesale
Selling Price
per Pound

Sales
Value
at Splitoff

Weighting:
Sales Value
at Splitoff

Joint
Costs
Allocated

Allocated
Costs Per
Pound

100
40

$1.10
0.70

$110
28
$138

110/138
28/138

$59.78
15.22
$75.00

$0.5978
0.3805

Ending inventory:
Breasts 10 $0.5978
Thighs 3
0.3805

$5.9780
1.1415
$7.1195

3.
Treating all products as joint products does not require judgments as to whether a product
is a joint product or a byproduct. In contrast, the approach in requirement 2 results in inventory
values being shown for only two of the five products.

16-4


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16-18 (10 min.) Net realizable value method.
A diagram of the situation is in Solution Exhibit 16-18 (all numbers are in thousands).
Cooking Oil
Final sales value of total production,
1,000 $50; 500 $25
Deduct separable costs
Net realizable value at splitoff point
Weighting, $20,000; $5,000 $25,000
Joint costs allocated, 0.8; 0.2 $24,000

$50,000
30,000
$20,000
0.8
$19,200

Soap Oil

Total

$12,500
7,500
$ 5,000
0.2
$ 4,800

$62,500
37,500
$25,000
$24,000

SOLUTION EXHIBIT 16-18 (all numbers are in thousands)

Joint Costs

Separable Costs
Processing
$30,000

Cooking Oil:
1,000 drums at
$50 per drum

Processing
$7,500

Soap Oil:
500 drums at
$25 per drum

Processing
$24 000

Splitoff
Point

16-5


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16-19 (40 min.) Alternative joint-cost-allocation methods, further-process decision.
A diagram of the situation is in Solution Exhibit 16-19.
1.
Physical measure of total production (gallons)
Weighting, 2,500; 7,500 10,000
Joint costs allocated, 0.25; 0.75 $120,000
2.
Final sales value of total production,
2,500 $21.00; 7,500 $14.00
Deduct separable costs,
2,500 $3.00; 7,500 $2.00
Net realizable value at splitoff point
Weighting, $45,000; $90,000 $135,000
Joint costs allocated, 1/3; 2/3 $120,000
3.

Methanol

Turpentine

Total

2,500
0.25
$ 30,000

7,500
0.75
$ 90,000

10,000

Methanol

Turpentine

$ 52,500

$105,000

$157,500

7,500
$ 45,000

15,000
$ 90,000

22,500

$135,000

1/3
$ 40,000

2/3
$ 80,000

$120,000

$120,000
Total

a. Physical-measure (gallons) method:
Revenues
Cost of goods sold:
Joint costs
Separable costs
Total cost of goods sold
Gross margin

Methanol
$52,500

Turpentine
$105,000

Total
$157,500

30,000
7,500
37,500
$15,000

90,000
15,000
105,000
0

120,000
22,500
142,500
$ 15,000

Methanol
$52,500

Turpentine
$105,000

Total
$157,500

40,000
7,500
47,500
$ 5,000

80,000

15,000
95,000
$ 10,000

120,000
22,500
142,500
$ 15,000

$

b. Estimated net realizable value method:
Revenues
Cost of goods sold:
Joint costs
Separable costs
Total cost of goods sold
Gross margin

16-6


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4.

Alcohol Bev.
Final sales value of total production,
2,500 $60.00; 7,500 $14.00
Deduct separable costs,

(2,500 $12.00) + (0.20 $150,000);
7,500 $2.00
Net realizable value at splitoff point
Weighting, $90,000; $90,000 $180,000
Joint costs allocated, 0.5; 0.5 $120,000

Turpentine

$150,000

$105,000

60,000
$ 90,000
0.50
$ 60,000

15,000
$ 90,000
0.50
$ 60,000

An incremental approach demonstrates that the company should use the new process:
Incremental revenue,
($60.00 – $21.00) 2,500
Incremental costs:
Added processing, $9.00 2,500
Taxes, (0.20 $60.00) 2,500
Incremental operating income from
further processing

Proof:

Total sales of both products
Joint costs
Separable costs
Cost of goods sold
New gross margin
Old gross margin
Difference in gross margin

16-7

$ 97,500
$22,500
30,000

(52,500)
$ 45,000
$255,000
120,000
75,000
195,000
60,000
15,000
$ 45,000

Total
$255,000

75,000

$180,000
$120,000


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SOLUTION EXHIBIT 16-19

Joint Costs

Separable Costs
2 500
gallons

Processing
$3 per gallon

Methanol:
2 500 gallons
at $21 per gallon

7 500
gallons

Processing
$2 per gallon

Turpentine:
7 500 gallons
at $14 per gallon

Processing
$120 000
for 10 000
gallons

Splitoff
Point

16-8


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16-20 (40 min.) Alternative methods of joint-cost allocation, ending inventories.
Total production for the year was:

X
Y
Z

Ending
Inventories
180
60
25

Sold
120
340

475

Total
Production
300
400
500

A diagram of the situation is in Solution Exhibit 16-20.
1.

a. Net realizable value (NRV) method:
X

Final sales value of total production,
300 $1,500; 400 $1,000; 500 $700
Deduct separable costs
Net realizable value at splitoff point
Weighting, $450; $400; $150

$1,000

Joint costs allocated,
0.45, 0.40, 0.15 $400,000

Y

Z

Total

$450,000
––
$450,000

$400,000
––
$400,000

$350,000
200,000
$150,000

$1,200,000
200,000
$1,000,000

0.45

0.40

0.15

$180,000

$160,000

$ 60,000

X

180
300
60%

Y
60
400
15%

$ 400,000

Ending Inventory Percentages:
Ending inventory
Total production
Ending inventory percentage

Z
25
500
5%

Income Statement
X
Revenues,
120 $1,500; 340 $1,000; 475 $700
Cost of goods sold:
Joint costs allocated
Separable costs
Production costs
Deduct ending inventory,

60%; 15%; 5% of production costs
Cost of goods sold
Gross margin
Gross-margin percentage

Y

Z

Total

$180,000

$340,000

$332,500

$852,500

180,000
––
180,000

160,000
––
160,000

60,000
200,000
260,000

400,000
200,000
600,000

108,000
72,000
$108,000

24,000
136,000
$204,000

13,000
247,000
$ 85,500

145,000
455,000
$397,500

60%

60%

25.71%

16-9

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b.

Constant gross-margin percentage NRV method:

Step 1:
Final sales value of prodn., (300 $1,500) + (400 $1,000) + (500
Deduct joint and separable costs, $400,000 + $200,000
Gross margin
Gross-margin percentage, $600,000 ÷ $1,200,000

$700)

$1,200,000
600,000
$ 600,000
50%

Step 2:
X
Final sales value of total production,
300 $1,500; 400 $1,000; 500 $700
Deduct gross margin, using overall
gross-margin percentage of sales, 50%
Total production costs
Step 3: Deduct separable costs
Joint costs allocated

Y

Z

$450,000

$400,000

$350,000

$1,200,000

225,000
225,000

200,000
200,000

175,000
175,000

600,000
600,000

$225,000

$200,000

Total

200,000

200,000
$(25,000) $ 400,000

The negative joint-cost allocation to Product Z illustrates one ―unusual‖ feature of the
constant gross-margin percentage NRV method: some products may receive negative cost
allocations so that all individual products have the same gross-margin percentage.
Income Statement
Revenues, 120 $1,500;
340 $1,000; 475 $700
Cost of goods sold:
Joint costs allocated
Separable costs
Production costs
Deduct ending inventory,
60%; 15%; 5% of production costs
Cost of goods sold
Gross margin
Gross-margin percentage

X

Y

Z

Total

$180,000

$340,000

$332,500

$852,500

225,000
225,000

200,000
200,000

(25,000)
200,000
175,000

400,000
200,000
600,000

135,000
90,000
$ 90,000
50%

30,000
170,000
$170,000
50%

8,750

166,250
$166,250
50%

173,750
426,250
$426,250
50%

16-10


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Summary
a.
NRV method:
Inventories on balance sheet
Cost of goods sold on income statement

b.

Y

Z

Total

$108,000
72,000

$ 24,000
136,000

$ 13,000
247,000

$145,000
455,000
$600,000

$135,000
90,000

$ 30,000
170,000

$

$173,750
426,250
$600,000

Constant gross-margin
percentage NRV method

Inventories on balance sheet
Cost of goods sold on income statement

2.

X

8,750
166,250

Gross-margin percentages:
X
60%
50%

NRV method
Constant gross-margin percentage NRV

Y
60%
50%

Z
25.71%
50.00%

SOLUTION EXHIBIT 16-20

Joint Costs

Separable Costs
Product X:
300 tons at
$1,500 per ton

Joint
Processing
Costs
$400,000

Product Y:
400 tons at
$1,000 per ton

Processing
$200 000
Splitoff
Point

16-11

Product Z:
500 tons at
$700 per ton


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16-21 (30 min.) Joint-cost allocation, process further.

Joint Costs =
$1 800

Processing

$175

ING4
(Non-Salable)

Processing
$105

NGL
50bbls X $15 / bbl =
$750

XGE3
(Non-Salable)

Processing
$210

Gas
800 eqvt bbls X
$1.30 / eqvt bbl =
$1 040

Splitoff
Point
1a.

Physical Measure Method

1. Physical measure of total prodn.

2. Weighting (150; 50; 800 ÷ 1,000)
3. Joint costs allocated (Weights $1,800)
1b.
1.
2.
3.
4.
5.

Crude Oil
150 bbls X $18/bbl =
$2 700

ICR8
(Non-Salable)

Crude Oil
150
0.15
$270

NGL
50
0.05
$90

Crude Oil
$2,700
175
$2,525

0.63125
$1,136.25

NGL
$750
105
$645
0.16125
$290.25

Gas
800
0.80
$1,440

Total
1,000
1.00
$1,800

NRV Method
Final sales value of total production
Deduct separable costs
NRV at splitoff
Weighting (2,525; 645; 830 ÷ 4,000)
Joint costs allocated (Weights $1,800)

16-12

Gas

$1,040
210
$ 830
0.20750
$373.50

Total
$4,490
490
$4,000
$1,800


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2.
(a)

The operating-income amounts for each product using each method is:
Physical Measures Method
Crude Oil
NGL
Gas
Revenues
$2,700
$750
$1,040
Cost of goods sold
Joint costs
270

90
1,440
Separable costs
175
105
210
Total cost of goods sold
445
195
1,650
Gross margin
$2,255
$555
$ (610)
(b)

Total
$4,490
1,800
490
2,290
$2,200

NRV Method

Revenues
Cost of goods sold
Joint costs
Separable costs
Total cost of goods sold

Gross margin

Crude Oil
NGL
$2,700.00 $750.00
1,136.25 290.25
175.00
105.00
1,311.25 395.25
$1,388.75 $354.75

Gas
$1,040.00
373.50
210.00
583.50
$ 456.50

Total
$4,490.00
1,800.00
490.00
2,290.00
$2,200.00

3.
Neither method should be used for product emphasis decisions. It is inappropriate to use
joint-cost-allocated data to decide dropping individual products, or pushing individual products,
as they are joint by definition. Product-emphasis decisions should be made based on relevant
revenues and relevant costs. Each method can lead to product emphasis decisions that do not lead

to maximization of operating income.
4.
A letter to the taxation authorities would stress the conceptual superiority of the NRV
method. Chapter 16 argues that, using a benefits-received cost allocation criterion, market-based
joint cost allocation methods are preferable to physical-measure methods. A meaningful common
denominator (revenues) is available when the sales value at splitoff point method or NRV
method is used. The physical-measures method requires nonhomogeneous products (liquids and
gases) to be converted to a common denominator.

16-13


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16-22 (30 min.) Joint-cost allocation, sales value, physical measure, NRV methods.
1a.
PANEL A: Allocation of Joint Costs using Sales Value at
Splitoff
Sales value of total production at splitoff point
(25,000 tons $10 per ton; 50,000 $15 per ton)
Weighting ($250,000; $750,000 ÷ $1,000,000)
Joint costs allocated (0.25; 0.75 $600,000)
PANEL B: Product-Line Income Statement for June 2006
Revenues
(25,000 tons $10 per ton; 50,000 $15 per ton)
Joint costs allocated (from Panel A)
Gross margin
Gross margin percentage

Ricito

$250,000
0.25
$150,000
Ricito

Pancito

Total

$750,000 $1,000,000
0.75
$450,000
$600,000
Pancito

Total

$250,000
150,000
$100,000
40%

$750,000 $1,000,000
450,000
600,000
$300,000 $ 400,000
40%
40%

Ricito

25,000
33%
$200,000

Pancito
50,000
67%
$400,000

Ricito

Pancito

1b.
PANEL A: Allocation of Joint Costs using Physical Measure
Method
Physical measure of total production (tons)
Weighting (25,000 tons; 50,000 tons ÷ 75,000 tons)
Joint costs allocated (0.33; 0.67 $600,000)
PANEL B: Product-Line Income Statement for June 2006
Revenues
(25,000 tons $10 per ton; 50,000 $15 per ton)
Joint costs allocated (from Panel A)
Gross margin
Gross margin percentage

$250,000
200,000
$50,000
20%

Total
75,000
$600,000
Total

$750,000 $1,000,000
400,000
600,000
$350,000 $ 400,000
47%
40%

1c.
PANEL A: Allocation of Joint Costs using Net Realizable
Value
Final sales value of total production during accounting period
(30,000 tons $18 per ton; 60,000 tons $25 per ton)
Deduct separable costs
Net realizable value at splitoff point
Weighting ($420,000; $1,080,000 ÷ $1,500,000)
Joint costs allocated (0.28; 0.72 $600,000)

$540,000 $1,500,000 $2,040,000
120,000
420,000
540,000
$420,000 $1,080,000 $1,500,000
28%
72%

$168,000
$432,000
$600,000

PANEL B: Product-Line Income Statement for June 2006
Revenues (30,000 tons $18 per ton; 60,000 tons $25 per ton)
Joint costs allocated (from Panel A)
Separable costs
Gross margin
Gross margin percentage

Rilaf
Pilaf
Total
$540,000 $1,500,000 $2,040,000
168,000
432,000
600,000
120,000
420,000
540,000
$252,000 $ 648,000 $ 900,000
46.7%
43.2%
44.1%

16-14

Rilaf

Pilaf

Total


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2.
Shel Brown probably performed the analysis shown below to arrive at the net loss of
$5,571 from marketing the sludge:
PANEL A: Allocation of Joint Costs using
Sales Value at Splitoff
Sales value of total production at splitoff point
(25,000 tons $10 per ton; 50,000 $15 per
ton; 10,000 $5 per ton)
Weighting
($250,000; $750,000; $50,000 ÷ $1,050,000)
Joint costs allocated
(0.238095; 0.714286; 0.047619 $600,000)

Ricito

Pancito

Sludge

Total

$250,000

$750,000

$50,000

$1,050,000

23.8095%

71.4286%

4.7619%

100%

$142,857

$428,571

$28,571

$600,000

Ricito

Pancito

Sludge

Total

$250,000
142,857
$107,143

$750,000
428,572
$321,428

$50,000
28,571
$21,429
27,000
($5,571)

$1,050,000
600,000
$ 450,000
27,000
$ 423,000

PANEL B: Product-Line Income Statement
for June 2006
Revenues
(25,000 tons $10 per ton; 50,000 $15 per ton;
10,000 $5 per ton)
Joint costs allocated (from Panel A)
Gross margin
Deduct marketing costs
Operating income

In this (misleading) analysis, the $600,000 of joint costs are re-allocated between Ricito, Pancito
and the sludge. Irrespective of the method of allocation, this analysis is wrong. Joint costs are
always irrelevant in a process-further decision. Only incremental costs and revenues past the
splitoff point are relevant. In this case, the correct analysis is much simpler: the incremental
revenues from selling the sludge are $50,000, and the incremental costs are the marketing costs
of $27,000. So, Armstrong Foods should sell the sludge—this will increase its operating income
by $23,000 ($50,000 – $27,000).

16-15


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16-23 (30 min.) Process further or sell.
A diagram of the situation is in Solution Exhibit 16-23.
1. Product A (5,000 units disposed of at splitoff point)
Incremental revenues, 5,000 × $0
Incremental costs, 5,000 × $0.20
Incremental operating income
Product A (5,000 units processed further)
Incremental revenues, 5,000 × $1.50
Incremental processing costs
Fixed
Variable, 5,000 × $0.90
Incremental operating income

$6,000
4,500

Product B (15,000 units processed further)

Incremental revenues, 15,000 × $1.50
Incremental processing costs
Fixed
Variable, 15,000 × $1
Incremental operating income

Product C (10,000 units processed further)
Incremental revenues, 10,000 × $5.40
Incremental processing costs
Fixed
Variable, 10,000 × $1.10
Incremental operating income
Summary of the alternatives is:

Product
A
B
C
Total

10,500
$(3,000)

$ 7,500
0
$ 7,500

$22,500
$ 1,000
15,000

Product C (10,000 units disposed of at splitoff point)
Incremental revenues, 10,000 × $0
Incremental costs, 10,000 × $0.90
Incremental operating income

Process
Further
$(3,000)
6,500
33,000
$36,500

0
1,000
$(1,000)

$ 7,500

Product B (15,000 units sold at splitoff point)
Incremental revenues, 15,000 × $0.50
Incremental processing costs, 15,000 × $0
Incremental operating income

Dispose
at Splitoff
$(1,000)
7,500
(9,000)
$(2,500)

$

16,000
$ 6,500

$

0
9,000
($ 9,000)

$54,000
$10,000
11,000

21,000
$33,000

Preferred
Alternative
Decision
$(1,000)
Dispose at splitoff
7,500
Sell at splitoff
33,000
Process further
$39,500

16-16

Preferred
Alternative
Better By
$ 2,000
1,000
42,000
$45,000


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2. Revenues
Product B, 15,000 × $0.50
Product C, 10,000 × $5.40
Costs
Joint costs, $5,000 + (5,000 × $2)
Disposal costs, A: 5,000 × $0.20
Processing costs, C: $10,000 + $11,000

$ 7,500
54,000

$61,500

$15,000
1,000
21,000

37,000

Gross margin

$24,500

SOLUTION EXHIBIT 16-23

Joint Costs

Separable Costs

Processing
$6,000 +
$0.90 per unit
$5,000 +
$2.00 per unit

B
$0.50 per unit

A
$1.50 per unit

Processing
$1,000 +
$1.00 per unit

B
$1.50 per unit

Processing
$10,000 +
$1.10 per unit

C
$5.40 per unit

Splitoff
Point

16-17


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16-24 (30 min.) Accounting for a main product and a byproduct.
Production
Method
1.

a
b

c

2.
a

Sales

Method

Revenues
Main product
Byproduct
Total revenues

$160,000a
—
160,000

$160,000
2,800d
162,800

Cost of goods sold
Total manufacturing costs
Deduct byproduct revenue
Net manufacturing costs
Deduct main product inventory
Cost of goods sold
Gross margin

120,000
4,000b
116,000
23,200c
92,800
$ 67,200

120,000
0
120,000
24,000e
96,000
$ 66,800

8,000 $20.00
2,000 $2.00

2,000
10,000

Rainbow Dew
Resi-Dew

d

e

$116 ,000

$23,200

Production
Method
$23,200
1,200a

1,400

2,000
10,000

Sales
Method
$24,000
0

Ending inventory shown at unrealized selling price.
BI + Production – Sales = EI
0 + 2,000 – 1,400 = 600 gallons
Ending inventory = 600 gallons $2 per gallon = $1,200

16-18

$2.00

$120 ,000

$24,000


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16-25 (35-45 min.) Joint costs and byproducts.
Joint Costs
$800,000

Se p a r a bl e Co st s

Dept. 2

50,000 p o u n d s

L
50,000
pound s
$10/ lb.

P r oce ssi n g
$100,000

Dept. 1
W
300,000 pound s
$2/ lb.

Pr oce ssi n g
o f 600,000 lb s.

Dept. 3

100,000 p o u n d s

Pr oce ssi n g
$50,000

X
100,000 pound s
$3/ lb.

Splitoff
Point

1.

Computing byproduct deduction to joint costs:
Revenues from X, 100,000 $3
Deduct:
Gross margin, 10% of revenues
Marketing costs, 25% of revenues
Department 3 separable costs
Net realizable value (less gross margin) of X

$300,000

Joint costs
Deduct byproduct contribution
Net joint costs to be allocated

$800,000
145,000
$655,000

16-19

30,000
75,000
50,000
$145,000

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Quantity
L
50,000
W
300,000
Totals

L
W
Totals

Deduct
Unit
Final
Separable
Sales
Sales
Processing
Price
Value
Cost
$10
$ 500,000 $100,000
2
600,000
––

$1,100,000 $100,000

Joint Costs
Allocation
$262,000
393,000
$655,000

Add Separable
Processing
Costs
$100,000
––
$100,000

Net
Realizable
Value at
Splitoff
$ 400,000
600,000
$1,000,000

Total Costs
$362,000
393,000
$755,000

Weighting
40%

60%

Units
50,000
300,000
350,000

Allocation of
$655,000
Joint Costs
$262,000
393,000
$655,000

Unit Cost
$7.24
1.31

Unit cost for X: $1.45 ($145,000 ÷ 100,000) + $0.50 ($50,000 ÷ 100,000) = $1.95,
or
$3.00 – $0.30 (10% $3) – $0.75 (25% $3) = $1.95.
2.

If all three products are treated as joint products:

Quantity
L
50,000
W
300,000

X
100,000
Totals

L
W
X
Totals

Unit
Final
Sales
Sales
Price
Value
$10
$ 500,000
2
600,000
3
300,000
$1,400,000

Joint Costs
Allocation
$272,340
408,511
119,149
$800,000

Deduct
Separable
Processing
Cost
$100,000
125,000
$225,000

Add Separable
Processing
Costs
$100,000
––
50,000
$150,000

Net
Realizable
Value at
Splitoff
$ 400,000
600,000
175,000
$1,175,000

Total Costs
$372,340
408,511
169,149
$950,000

Allocation of
$800,000
Weighting Joint Costs
400/1,175
$272,340
600/1,175
408,511
175/1,175
119,149
$800,000

Units
50,000
300,000
100,000
450,000

Unit Cost
$7.45
1.36
1.69

Call the attention of students to the different unit ―costs‖ resulting from the two assumptions
about the relative importance of Product X. The point is that costs of individual products depend
heavily on which assumptions are made and which accounting methods and techniques are used.

16-20

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16-26 (40 min.) Alternative methods of joint-cost allocation, product-mix decision.
1.
a.

Joint costs = $300,000
Sales value at splitoff method

1.

Sales value of total prodn. at splitoff
(30,000 $8, 50,000 $4, 20,000 $3)
Weighting
(240/500, 200/500, 60/500)
Joint costs allocated
(0.48, 0.40, 0.12 $300,000)
Total cost computation
Joint costs
Separable processing costs
Total costs
Total board feet
Total cost per board foot

2.
3.
4.

b.

Physical-measures method

1.

Physical measure of total production
(board feet)
Weighting
(30/100, 50/100, 20/100)
Joint costs allocated
(0.30, 0.50, 0.20 $300,000)
Total cost computation
Joint costs
Separable processing
Total costs
Total board feet
Total cost per board foot

2.
3.
4.

Select

White

Knotty

Total

$240,000

$200,000

$60,000

$500,000

0.48

0.40

0.12

$144,000

$120,000

$36,000

$300,000

$144,000
60,000
$204,000
25,000
$8.16

$120,000
90,000
$210,000

40,000
$5.25

$36,000
15,000
$51,000
15,000
$3.40

$300,000
165,000
$465,000

Select

White

Knotty

Total

30,000

50,000

20,000

0.30

0.50

0.20

$90,000

$150,000

$60,000

$300,000

$90,000
60,000
$150,000
25,000
$6.00

$150,000
90,000
$240,000
40,000
$6.00

$60,000
15,000
$75,000
15,000
$5.00

$300,000

165,000
$465,000

16-21

100,000


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c.

Net realizable value method

1.

Final sales value of total production
(25,000 $16, 40,000 $9, 15,000 $7)
Deduct separable costs
NRV at splitoff
Weighting (340 700, 270 700, 90 700)
Joint costs allocated
(0.4857, 0.3857, 0.1286 $300,000)
Total cost computation
Joint costs
Separable processing
Total costs
Total units
Unit cost

2.
3.
4.
5.

2.

Ending Inventory Values

a.

Sales value at splitoff method
($8.16 1,000, $5.25 2,000, $3.40
Physical measures method
($6.00 1,000, $6.00 2,000, $5.00
NRV method
($8.23 1,000, $5.14 2,000, $3.57

b.
c.

3.

Select

White

Knotty

Total

$400,000
60,000
$340,000
0.4857

$360,000
90,000
$270,000
0.3857

$105,000
15,000
$ 90,000
0.1286

$865,000
165,000
$700,000

$145,710

$115,710

$38,580

$300,000

$145,710
60,000

$205,710
25,000
$8.23

$115,710
90,000
$205,710
40,000
$5.14

$38,580
15,000
$53,580
15,000
$3.57

$300,000
165,000
$465,000

Select

White

Knotty

Total

500)

$8,160

$10,500

$1,700

$20,360

500)

6,000

12,000

2,500

20,500

500)

8,230

10,280

1,785

20,295

Raw to Select Oak
Incremental revenues: $400,000 – $240,000

Deduct incremental processing costs
Increase in operating income

$160,000
60,000
$100,000

Raw to White Oak
Incremental revenues: $360,000 – $200,000
Deduct incremental processing costs
Increase in operating income

$160,000
90,000
$ 70,000

Raw to Knotty Oak
Incremental revenues: $105,000 – $60,000
Deduct incremental processing costs
Increase in operating income

$ 45,000
15,000
$ 30,000

Since the processing of each raw-oak product into finished-product form increases operating
income, Pacific Lumber is indeed maximizing operating income by processing all products fully.

16-22

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16-27 (40 min.) Alternative methods of joint-cost allocation, product-mix decisions.
A diagram of the situation is in Solution Exhibit 16-27.
1.

Computation of joint-cost allocation proportions:
a.

Sales Value of
Total Production
at Splitoff
A
$ 50,000
B
30,000
C
50,000
D
70,000
$200,000

Weighting
50/200 = 0.25
30/200 = 0.15
50/200 = 0.25
70/200 = 0.35
1.00

Allocation of $100,000
Joint Costs
$ 25,000
15,000
25,000
35,000
$100,000

Weighting
300/500 = 0.60
100/500 = 0.20
50/500 = 0.10
50/500 = 0.10
1.00

Allocation of $100,000
Joint Costs
$ 60,000
20,000
10,000
10,000
$100,000

b.

A
B
C
D

Physical Measure
of Total Production
300,000 gallons
100,000 gallons
50,000 gallons
50,000 gallons
500,000 gallons

c.

A
B
C
D

Final Sales
Value of
Total
Separable
Production
Costs
$300,000
$200,000
100,000
80,000
50,000
–
120,000
90,000

Net
Realizable
Value at
Splitoff
$100,000
20,000
50,000
30,000
$200,000

16-23

Weighting
100/200 =0.50
20/200 = 0.10
50/200 = 0.25
30/200 = 0.15
1.00

Allocation of
$100,000
Joint Costs
$ 50,000
10,000
25,000
15,000
$100,000


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Computation of gross-margin percentages:
a. Sales value at splitoff method:

Revenues
Joint costs
Separable costs
Total cost of goods sold
Gross margin
Gross-margin percentage

Super A
$300,000
25,000
200,000
225,000
$ 75,000
25%

Super B
$100,000
15,000
80,000
95,000
$ 5,000
5%

C
Super D
$50,000 $120,000

25,000
35,000
0
90,000
25,000
125,000
$25,000 $ (5,000)
50%
(4.17%)

Total
$570,000
100,000
370,000
470,000
$100,000
17.54%

b. Physical-measure method:

Revenues
Joint costs
Separable costs
Total cost of goods sold
Gross margin
Gross-margin percentage

Super A Super B
$300,000 $100,000
60,000

20,000
200,000
80,000
260,000
100,000
$ 40,000 $
0
13.33%
0%

C
Super D
$50,000 $120,000
10,000
10,000
0
90,000
10,000
100,000
$40,000 $ 20,000
80%
16.67%

Total
$570,000
100,000
370,000
470,000
$100,000
17.54%

c. Net realizable value method:

Revenues
Joint costs
Separable costs
Total cost of goods sold
Gross margin

Super A
$300,000
50,000
200,000
250,000
$ 50,000

Gross-margin percentage

16.67%

Super B
$100,000
10,000
80,000
90,000
$ 10,000

C
Super D
Total

$50,000 $120,000 $570,000
25,000
15,000 100,000
0
90,000 370,000
25,000 105,000 470,000
$25,000 $ 15,000 $100,000

10%

50%

12.5%

Super B

C

Super D

Summary of gross-margin percentages:
Joint-Cost
Allocation Method

Super A

Sales value at splitoff

25.00%

5%

50%

(4.17)%

Physical measure

13.33%

0%

80%

16.67%

10%

50%

12.50%

Net realizable value

16.67%

16-24

17.54%

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2.

Further Processing of A into Super A:
Incremental revenue, $300,000 – $50,000
Incremental costs
Incremental operating income from further processing

$250,000
200,000
$ 50,000

Further processing of B into Super B:
Incremental revenue, $100,000 – $30,000
Incremental costs
Incremental operating loss from further processing

$ 70,000
80,000
($ 10,000)

Further Processing of D into Super D:
Incremental revenue, $120,000 – $70,000
Incremental costs
Incremental operating loss from further processing

$ 50,000
90,000

$ (40,000)

Operating income can be increased by $50,000 if both B and D are sold at their splitoff point
rather than processed further into Super B and Super D.

SOLUTION EXHIBIT 16-27

Revenues at Splitoff
and Separable Costs

Joint Costs

A, 300 000 gallons
Revenue = $50 000
B, 100 000 gallons
Revenue = $30 000
Processing
$100 000

Processing
$200 000

Super A
$300 000

Processing
$80 000

Super B
$100 000

Processing
$90 000

Super D
$120 000

C, 50 000 gallons
Revenue = $50 000
D, 50 000 gallons
Revenue = $70 000

Splitoff
Point

16-25