CHAPTER 16
COST ALLOCATION: JOINT PRODUCTS AND BYPRODUCTS
16-16
(20-30 min.) Joint-cost allocation, insurance settlement.
1.
(a)
Breasts
Wings
Thighs
Bones
Feathers
Sales value at splitoff method:
Pounds
of
Product
100
20
40
80
10
250
Wholesale
Selling Price
per Pound
$0.55
0.20
0.35
0.10
0.05
Sales
Value
at Splitoff
$55.00
4.00
14.00
8.00
0.50
$81.50
Weighting:
Sales Value
at Splitoff
0.675
0.049
0.172
0.098
0.006
1.000
Joint
Costs
Allocated
$33.75
2.45
8.60
4.90
0.30
$50.00
Allocated
Costs per
Pound
0.3375
0.1225
0.2150
0.0613
0.0300
Costs of Destroyed Product
Breasts: $0.3375 per pound  40 pounds = $13.50
Wings: $0.1225 per pound  15 pounds =
1.84
$15.34
b.
Physical measure method:
Breasts
Wings
Thighs
Bones
Feathers
Pounds
of
Product
100
20
40
80
10
250
Weighting:
Physical
Measures
0.400
0.080
0.160
0.320
0.040
1.000
Costs of Destroyed Product
Breast: $0.20 per pound  40 pounds
Wings: $0.20 per pound  15 pounds
Joint
Costs
Allocated
$20.00
4.00
8.00
16.00
2.00
$50.00
=
=
Allocated
Costs per
Pound
$0.200
0.200
0.200
0.200
0.200
$ 8
3
$11
Note: Although not required, it is useful to highlight the individual product profitability figures:
Product
Breasts
Wings
Thighs
Bones
Feathers
Sales
Value
$55.00
4.00
14.00
8.00
0.50
Sales Value at
Splitoff Method
Joint Costs
Gross
Allocated
Income
$33.75
$21.25
2.45
1.55
8.60
5.40
4.90
3.10
0.30
0.20
16-1
Physical
Measures Method
Joint Costs
Gross
Allocated
Income
$20.00
$35.00
4.00
0.00
8.00
6.00
16.00
(8.00)
2.00
(1.50)
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. Quality Chicken’s decision to process
chicken is heavily influenced by the revenues from breasts and thighs. The bones provide
relatively few benefits to Quality Chicken despite their high physical volume.
The physical measures method shows profits on breasts and thighs and losses on bones
and feathers. Given that Quality Chicken 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. Quality Chicken 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
15
Wings
4
Thighs
6
Bones
5
Feathers
2
 $0.3375 =
 0.1225 =
 0.2150 =
 0.0613 =
 0.0300 =
$5.06
0.49
1.29
0.31
0.06
$7.21
2.
Joint products
Breasts
Thighs
Net Realizable Values of
byproducts:
Wings
$ 4.00
Bones
8.00
Feathers
0.50
$12.50
Byproducts
Wings
Bones
Feathers
Joint costs to be allocated:
Joint costs – Net Realizable Values of byproducts = $50 – $12.50 = $37.50
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
$0.55
0.35
$55
14
$69
55 ÷ 69
14 ÷ 69
$29.89
7.61
$37.50
$0.2989
0.1903
Ending inventory:
Breasts 15  $0.2989
Thighs 6  0.1903
$4.48
1.14
$5.62
3.
Treating all products as joint products does not require judgments as to whether a product
is a joint product or a byproduct. Joint costs are allocated in a consistent manner to all products
for the purpose of costing and inventory valuation. In contrast, the approach in requirement 2
lowers the joint cost by the amount of byproduct net realizable values and results in inventory
values being shown for only two of the five products, the ones (perhaps arbitrarily) designated as
being joint products.
16-2
16-18 (10 min.) Net realizable value method.
A diagram of the situation is in Solution Exhibit 16-18.
Corn Syrup
Corn Starch
$625,000
375,000
$250,000
0.8
$260,000
$156,250
93,750
$ 62,500
0.2
$ 65,000
Final sales value of total production,
12,500  $50; 6,250  $25
Deduct separable costs
Net realizable value at splitoff point
Weighting, $250,000; $62,500  $312,500
Joint costs allocated, 0.8; 0.2  $325,000
Total
$781,250
468,750
$312,500
$325,000
SOLUTION EXHIBIT 16-18 (all numbers are in thousands)
Joint Costs
Separable Costs
Processing
$375,000
Corn Syrup:
12,500 cases at
$50 per case
Processing
$93,750
Corn Starch:
6,250 cases at
$25 per case
Processing
$325000
Splitoff
Point
16-20 (40 min.) Alternative methods of joint-cost allocation, ending inventories.
Total production for the year was:
Ending
Inventories
175
75
70
Sold
X
Y
Z
75
225
280
Total
Production
250
300
350
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,
250  $1,800; 300  $1,300; 350  $800
Deduct separable costs
Net realizable value at splitoff point
16-3
$450,000
––
$450,000
Y
Z
Total
$390,000
––
$390,000
$280,000
120,000
$160,000
$1,120,000
120,000
$1,000,000
Weighting, $450; $390; $160  $1,000
Joint costs allocated,
0.45, 0.39, 0.16  $328,000
0.45
0.39
0.16
$147,600
$127,920
$ 52,480
X
175
250
70%
Y
75
300
25%
$ 328,000
Ending Inventory Percentages:
Ending inventory
Total production
Ending inventory percentage
Income Statement
X
Z
70
350
20%
Y
Z
Total
$135,000
$292,500
$224,000
$651,500
147,600
––
147,600
127,920
––
127,920
52,480
120,000
172,480
328,000
120,000
448,000
103,320
44,280
$ 90,720
31,980
95,940
$196,560
34,496
137,984
$ 86,016
169,796
278,204
$373,296
Gross-margin percentage
67.2%
b. Constant gross-margin percentage NRV method:
67.2%
38.4%
Revenues,
75  $1,800; 225  $1,300; 280  $800
Cost of goods sold:
Joint costs allocated
Separable costs
Production costs
Deduct ending inventory,
70%; 25%; 20% of production costs
Cost of goods sold
Gross margin
Step 1:
Final sales value of prodn., (250  $1,800) + (300  $1,300) + (350  $800)
$1,120,000
Deduct joint and separable costs, $328,000 + $120,000
448,000
Gross margin
$ 672,000
Gross-margin percentage, $672,000 ÷ $1,120,000
60%
Step 2:
X
Y
Z
Total
Final sales value of total production,
250  $1,800; 300  $1,300; 350  $800
$450,000
$390,000
$280,000 $1,120,000
Deduct gross margin, using overall
Gross-margin percentage of sales, 60%
270,000
234,000
168,000
672,000
Total production costs
180,000
156,000
112,000
448,000
Step 3: Deduct separable costs
—
—
120,000
120,000
Joint costs allocated
$180,000
$156,000
$ (8,000) $ 328,000
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 grossmargin percentage.
16-4
Income Statement
X
Y
Z
Total
$135,000
$292,500
$224,000
$651,500
180,000
180,000
156,000
156,000
(8,000)
120,000
112,000
328,000
120,000
448,000
126,000
54,000
$ 81,000
60%
39,000
117,000
$175,500
60%
22,400
89,600
$134,400
60%
187,400
260,600
$390,900
60%
X
Y
Z
Total
$103,320
44,280
$ 31,980
95,940
$ 34,496
137,984
$169,796
278,204
$448,000
b. Constant gross-margin
percentage NRV method
Inventories on balance sheet
$126,000
Cost of goods sold on income statement
54,000
$ 39,000
117,000
Revenues, 75  $1,800;
225  $1,300; 280  $800
Cost of goods sold:
Joint costs allocated
Separable costs
Production costs
Deduct ending inventory,
70%; 25%; 20% of production costs
Cost of goods sold
Gross margin
Gross-margin percentage
Summary
a.
NRV method:
Inventories on balance sheet
Cost of goods sold on income statement
2.
$
22,400
89,600
$187,400
260,600
$448,000
Gross-margin percentages:
X
67.2%
60.0%
NRV method
Constant gross-margin percentage NRV
SOLUTION EXHIBIT 16-20
Joint Costs
Y
67.2%
60.0%
Z
38.4%
60.0%
Separable Costs
Product X:
250 tons at
$1,800 per ton
Joint
Processing
Costs
$328,000
Product Y:
300 tons at
$1,300 per ton
Processing
$120000
Splitoff
Point
16-5
Product Z:
350 tons at
$800 per ton
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 Method
Sales value of total production at splitoff point
(10,000 tons  $10 per ton; 20,000  $15 per ton)
Weighting ($100,000; $300,000 ÷ $400,000)
Joint costs allocated (0.25; 0.75  $240,000)
PANEL B: Product-Line Income Statement for June 2012
Revenues
(12,000 tons  $18 per ton; 24,000  $25 per ton)
Deduct joint costs allocated (from Panel A)
Deduct separable costs
Gross margin
Gross margin percentage
Special B/
Beef
Ramen
Special S/
Shrimp
Ramen
$100,000
0.25
$60,000
$300,000
0.75
$180,000
Special B
Special S
$216,000
60,000
48,000
$108,000
50%
$600,000
180,000
168,000
$252,000
42%
$816,000
240,000
216,000
$360,000
44%
Special B/
Beef
Ramen
10,000
33%
$80,000
Special S/
Shrimp
Ramen
20,000
67%
$160,000
Total
30,000
$240,000
Special B
Special S
Total
Total
$400,000
$240,000
Total
1b.
PANEL A: Allocation of Joint Costs using Physical-Measure
Method
Physical measure of total production (tons)
Weighting (10,000 tons; 20,000 tons ÷ 30,000 tons)
Joint costs allocated (0.33; 0.67  $240,000)
PANEL B: Product-Line Income Statement for June 2012
Revenues
(12,000 tons  $18 per ton; 24,000  $25 per ton)
Deduct joint costs allocated (from Panel A)
Deduct separable costs
Gross margin
Gross margin percentage
$216,000
80,000
48,000
$ 88,000
41%
$600,000
160,000
168,000
$272,000
45%
$816,000
240,000
216,000
$360,000
44%
Special B
Special S
Total
1c.
PANEL A: Allocation of Joint Costs using Net Realizable
Value Method
Final sales value of total production during accounting period
(12,000 tons  $18 per ton; 24,000 tons  $25 per ton)
Deduct separable costs
Net realizable value at splitoff point
Weighting ($168,000; $432,000 ÷ $600,000)
Joint costs allocated (0.28; 0.72  $240,000)
PANEL B: Product-Line Income Statement for June 2012
Revenues (12,000 tons  $18 per ton; 24,000 tons  $25 per ton)
Deduct joint costs allocated (from Panel A)
Deduct separable costs
Gross margin
Gross margin percentage
16-6
$216,000
48,000
$168,000
28%
$67,200
$600,000
168,000
$432,000
72%
$172,800
$816,000
216,000
$600,000
Special B
$216,000
67,200
48,000
$100,800
46.7%
Special S
$600,000
172,800
168,000
$259,200
43.2%
Total
$816,000
240,000
216,000
$360,000
44.1%
$240,000
2.
Sherrie Dong probably performed the analysis shown below to arrive at the net
loss of $2,228 from marketing the stock:
PANEL A: Allocation of Joint Costs using
Sales Value at Splitoff
Sales value of total production at splitoff point
(10,000 tons  $10 per ton; 20,000  $15 per
ton; 4,000  $5 per ton)
Weighting
($100,000; $300,000; $20,000 ÷ $420,000)
Joint costs allocated
(0.238095; 0.714286; 0.047619  $240,000)
PANEL B: Product-Line Income Statement
for June 2012
Revenues
(12,000 tons  $18 per ton; 24,000  $25 per ton;
4,000  $5 per ton)
Separable processing costs
Joint costs allocated (from Panel A)
Gross margin
Deduct marketing costs
Operating income
Special B/
Beef
Ramen
Special S/
Shrimp
Ramen
Stock
$100,000
$300,000
$20,000
$420,000
23.8095%
71.4286%
4.7619%
100%
$57,143
$171,429
$11,428
$240,000
Special S
Stock
$600,000
168,000
171,429
$260,571
$20,000
0
11,428
8,572
10,800
$ (2,228)
Special B
$216,000
48,000
57,143
$110,857
Total
Total
$836,000
216,000
240,000
380,000
10,800
$369,200
In this (misleading) analysis, the $240,000 of joint costs are re-allocated between
Special B, Special S, and the stock. 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 stock are
$20,000, and the incremental costs are the marketing costs of $10,800. So, Instant
Foods should sell the stock—this will increase its operating income by $9,200
($20,000 – $10,800).
16-25 (35-45 min.) Joint costs and byproducts.
1.
A
B
Computing byproduct deduction to joint costs:
Revenues from C, 16,000  $6
$ 96,000
Deduct:
Gross margin, 10% of revenues
9,600
Marketing costs, 20% of revenues
19,200
Peanut Butter Department separable costs
12,000
Net realizable value (less gross margin) of C
$ 55,200
Joint costs
$180,000
Deduct byproduct contribution
55,200
Net joint costs to be allocated
$124,800
Deduct
Net
Unit
Final Separable
Realizable
Allocation of
Sales
Sales Processing
Value at
$124,800
Quantity Price
Value
Cost
Splitoff
Weighting Joint Costs
12,000
$12
$144,000
$27,000
$117,000
37.5%
$ 46,800
65,000
3
195,000
––
195,000
62.5%
78,000
16-7
Totals
Joint Costs
Allocation
$ 46,800
78,000
$124,800
A
B
Totals
$339,000
$27,000
$312,000
Add Separable
Processing
Costs
Total Costs
$27,000
$ 73,800
––
78,000
$27,000
$151,800
$124,800
Units
12,000
65,000
77,000
Unit Cost
$6.15
1.20
Unit cost for C: $3.45 ($55,200 ÷ 16,000) + $0.75 ($12,000 ÷ 16,000) =
$4.20,
$6.00 – $0.60 (10%  $6) – $1.20 (20%  $6) =
or
$4.20.
2.
If all three products are treated as joint products:
A
B
C
Totals
Quantity
12,000
65,000
16,000
A
B
C
Totals
Unit
Sales
Price
$12
3
6
Joint Costs
Allocation
$ 55,892
93,153
30,955
$180,000
Final
Sales
Value
$144,000
195,000
96,000
$435,000
Deduct
Separable
Processing
Cost
$27,000
─
31,200
$58,200
Add Separable
Processing
Costs
$27,000
––
12,000
$39,000
Net
Realizable
Value at
Splitoff
$117,000
195,000
64,800
$376,800
Total Costs
$ 82,892
93,153
42,955
$219,000
Weighting
117 ÷ 376.8
195 ÷ 376.8
64.8 ÷ 376.8
Allocation
of
$180,000
Joint
Costs
$ 55,892
93,153
30,955
$180,000
Units
12,000
65,000
16,000
93,000
Unit Cost
$6.91
1.43
2.68
Call the attention of students to the different unit “costs” resulting from the two
assumptions about the relative importance of Product C. The point is that costs of
individual products depend heavily on which assumptions are made and which
accounting methods and techniques are used.
16-32 (20 min.) Joint-cost allocation with a byproduct.
1. Sales value at splitoff method: Byproduct recognized at time of production
method
Floor Mats
Car Mats
Products manufactured
31,250a
93,750b
Products sold
25,000
85,000
Ending inventory
6,250
8,750
a
25 floor mats/100 tires = .25 floor mats per tire  125,000 tires = 31,250 floor
mats
16-8
Rubber
Shreds (lbs)
50,000c
43,000
7,000
75 car mats/100 tires = .75 car mats per tire  125,000 tires = 93,750 car mats
(125,000 tires/100)  40 lbs = 50,000 lbs rubber shreds
Joint cost to be charged to joint products = Joint Cost – NRV of Byproduct
= $600,000 – (50,000 lbs  0.70 per lb)
= $600,000 – $35,000
= $565,000
b
c
Floor Mats
Sales value of mats at splitoff,
31,250 × $12; 93,750 × $6
Weighting, $375,000; $562,500  $937,500
Joint costs allocated, 0.40; 0.60 × $565,000
Revenues, 25,000 × $12; 85,000 × $6
Cost of goods sold
Joint costs allocated, 0.40; 0.60 × $565,000
Less: Ending inventory
Cost of goods sold
Gross margin
b
c
$375,000
0.40
$226,000
Floor Mats
$300,000
226,000
(45,200)b
180,800
$119,200
Car Mats
Total
$562,500
0.60
$339,000
$937,500
Car Mats
$510,000
Total
$810,000
339,000
(31,640)c
307,360
$202,640
565,000
(76,840)
488,160
$321,840
$565,000
6,250 × $226,000/31,250 = $45,200
8,750 × $339,000/93,750 = $31,640
2. Sales value at splitoff method: Byproduct recognized at time of sale method
Joint cost to be charged to joint products = Joint Cost = $600,000
Sales value of mats at splitoff,
31,250 × $12; 93,750 × $6
Weighting, $375,000; $562,500  $937,500
Joint costs allocated, 0.40; 0.60 × $600,000
Revenues, 25,000 × $12; 85,000 × $6
Cost of goods sold
Joint costs allocated, 0.40; 0.60 × $600,000
Less: Ending inventory
Cost of goods sold
Gross margin
Floor Mats
Car Mats
Total
$375,000
0.40
$240,000
$562,500
0.60
$360,000
$937,500
Floor Mats
$300,000
Car Mats
$510,000
240,000
(48,000)e
192,000
$108,000
360,000
(33,600)f
326,400
$183,600
Rubber
Shreds
$30,100d
Total
$840,100
$30,100
600,000
(81,600)
518,400
$321,700
d
43,000 lbs × $0.70 per lb. = $30,100
6,250 × $240,000/31,250 = $48,000
f
8,750 × $360,000/93,750 = $33,600
e
3.
The production method of accounting for the byproduct is only appropriate if
The Mat Place is positive they can sell the byproduct at the expected selling price.
Moreover, The Mat Place should view the byproduct’s contribution to the firm as
material enough to find it worthwhile to record and track any inventory that may
16-9
$600,000
arise. The sales method is appropriate if either the disposition of the byproduct is
unsure or the selling price is unknown, or if the amounts involved are so negligible as
to make it economically infeasible for The Mat Place to keep track of byproduct
inventories.
16-33 (15 min.) Byproduct journal entries (continuation of 16-32).
1. Byproduct – production method journal entries
i) At time of production:
Work-in-process Inventory
Accounts Payable, etc.
600,000
600,000
For byproduct:
Finished Goods Inv – Shreds
Work-in-process Inventory
35,000
For Joint Products
Finished Goods Inv – Floor
Finished Goods Inv – Car
Work-in-process Inventory
226,000
339,000
ii) At time of sale:
For byproduct
Cash or A/R
Finished Goods Inv – Shreds
For Joint Products
Cash or A/R
Sales Revenue – Floor
Sales Revenue – Car
35,000
565,000
30,100
30,100
810,000
300,000
510,000
Cost of goods sold - Floor
Cost of goods sold – Car
Finished Goods Inv – Floor
Finished Goods Inv – Car
2. Byproduct – sales method journal entries
i) At time of production:
Work-in-process Inventory
Accounts Payable, etc.
180,800
307,360
180,800
307,360
600,000
600,000
For byproduct:
No entry
For Joint Products
Finished Goods Inv – Floor
Finished Goods Inv – Car
Work-in-process Inventory
16-10
240,000
360,000
600,000
ii) At time of sale
For byproduct
Cash or A/R
Sales Revenue – Shreds
For Joint Products
Cash or A/R
Sales Revenue – Floor
Sales Revenue – Car
Cost of goods sold - Floor
Cost of goods sold - Car
Finished Goods Inv – Floor
Finished Goods Inv – Car
16-11
30,100
30,100
810,000
300,000
510,000
192,000
326,400
192,000
326,400