16-1
SOLUTION EXHIBIT 16-19
Joint Costs
Separable Costs
Processing
$120000
for 10000
gallons
Processing
$2 per gallon
Processing
$3 per gallon
7500
gallons
2500
gallons
Turpentine:
7500 gallons
at $14 per gallon
Splitoff
Point
16-2
16-20 (40 min.) Alternative methods of joint-cost allocation, ending inventories.
The Cook Company operates a simple chemical process to convert a single material into three
separate items, referred to here as X, Y, and Z. All three end products are separated simultaneously
at a single splitoff point.
Products X and Y are ready for sale immediately upon splitoff without further processing or
any other additional costs. Product Z, however, is processed further before being sold. There is no
available market price for Z at the splitoff point.
The selling prices quoted here are expected to remain the same in the coming year. During
2014, the selling prices of the items and the total amounts sold were as follows:
▪ X—68 tons sold for $1,200 per ton
▪ Y—480 tons sold for $900 per ton
▪ Z—672 tons sold for $600 per ton
The total joint manufacturing costs for the year were $580,000. Cook spent an additional $200,000
to finish product Z.
There were no beginning inventories of X, Y, or Z. At the end of the year, the following
inventories of completed units were on hand: X, 132 tons; Y, 120 tons; Z, 28 tons. There was no
beginning or ending work in process.
Required:
1. Compute the cost of inventories of X, Y, and Z for balance sheet purposes and the cost of
goods sold for income statement purposes as of December 31, 2014, using the following joint
cost allocation methods:
a. NRV method
b. Constant gross-margin percentage NRV method
2. Compare the gross-margin percentages for X, Y, and Z using the two methods given in
requirement 1.
SOLUTION
Total production for the year was:
Ending
Total
Sold
Inventories
Production
X 68 132 200
Y 480 120 600
Z 672 28 700
A diagram of the situation is in Solution Exhibit 16-20.
1. a. Net realizable value (NRV) method:
X Y Z Total
Final sales value of total production,
200 $1,200; 600 $900; 700 $600 $240,000 $540,000 $420,000 $1,200,000
Deduct separable costs –– –– 200,000 200,000
16-3
Net realizable value at splitoff point $240,000 $540,000 $220,000 $1,000,000
Weighting, $240; $540; $220
$1,000 0.24 0.54 0.22
Joint costs allocated,
0.24, 0.54, 0.22 $580,000 $139,200 $313,200 $ 127,600 $ 580,000
Ending Inventory Percentages:
X Y Z
Ending inventory 132 120 28
Total production 200 600 700
Ending inventory percentage 66% 20% 4%
Income Statement
X Y Z Total
Revenues,
68 $1,200; 480 $900; 672 $600 $81,600 $432,000 $403,200 $916,800
Cost of goods sold:
Joint costs allocated 139,200 313,200 127,600 580,000
Separable costs –– –– 200,000 200,000
Production costs 139,200 313,200 327,600 780,000
Deduct ending inventory,
66%; 20%; 4% of production costs 91,872 62,640 13,104 167,616
Cost of goods sold 47,328 250,560 314,496 612,384
Gross margin $ 34,272 $181,440 $ 88,704 $304,416
Gross-margin percentage 42% 42% 22%
b. Constant gross-margin percentage NRV method:
Step 1:
Final sales value of prodn., (200 $1,200) + (600 $900) + (700 $600) $1,200,000
Deduct joint and separable costs, $580,000 + $200,000 780,000
Gross margin $ 420,000
Gross-margin percentage, $420,000 ÷ $1,200,000 35%
Step 2:
X Y Z Total
Final sales value of total production,
250 $1,800; 300 $1,300; 350 $800 $240,000 $540,000 $420,000 $1,200,000
Deduct gross margin, using overall
Gross-margin percentage of sales, 35% 84,000 189,000 147,000 420,000
Total production costs 156,000 351,000 273,000 780,000
Step 3: Deduct separable costs — — 200,000
200,000
Joint costs allocated $156,000 $351,000 $ 73,000 $ 580,000
16-4
Income Statement
X Y Z Total
Revenues, 68 $1,200;
480 $900; 672 $600 $81,600 $432,000 $403,200 $916,800
Cost of goods sold:
Joint costs allocated 156,000 351,000 73,000 580,000
Separable costs — — 200,000 200,000
Production costs 156,000 351,000 273,000 780,000
Deduct ending inventory,
66%; 20%; 4% of production costs 102,960 70,200 10,920 184,080
Cost of goods sold 53,040 280,800 262,080 595,920
Gross margin $ 28,560 $151,200 $141,200 $320,880
Gross-margin percentage 35% 35% 35% 35%
Summary
X Y Z Total
a. NRV method:
Inventories on balance sheet $91,872 $ 62,640 $ 13,104 $167,616
Cost of goods sold on income statement 47,328 250,560 314,496 612,384
$780,000
b. Constant gross-margin
percentage NRV method
Inventories on balance sheet $102,960 $ 70,200 $ 10,920 $184,080
Cost of goods sold on income statement 53,040 280,800 262,080 595,920
$780,000
2. Gross-margin percentages:
X Y Z
NRV method 42% 42% 22%
Constant gross-margin percentage NRV 35.0% 35.0% 35.0%
16-5
SOLUTION EXHIBIT 16-20
Splitoff
Point
Processing
$200000
Product Y:
600 tons at
$900 per ton
Product X:
200 tons at
$1,200 per ton
Joint
Processing
Costs
$580,000
Product Z:
700 tons at
$600 per ton
Joint Costs
Separable Costs
16-21 (30 min.) Joint-cost allocation, process further.
Sinclair Oil & Gas, a large energy conglomerate, jointly processes purchased hydrocarbons to
generate three nonsalable intermediate products: ICR8, ING4, and XGE3. These intermediate
products are further processed separately to produce crude oil, natural gas liquids (NGL), and
natural gas (measured in liquid equivalents). An overview of the process and results for August
2014 are shown here. (Note: The numbers are small to keep the focus on key concepts.)
16-6
A new federal law has recently been passed that taxes crude oil at 30% of operating income. No
new tax is to be paid on natural gas liquid or natural gas. Starting August 2014, Sinclair Oil & Gas
must report a separate product-line income statement for crude oil. One challenge facing Sinclair
Oil & Gas is how to allocate the joint cost of producing the three separate salable outputs. Assume
no beginning or ending inventory.
Required:
1. Allocate the August 2014 joint cost among the three products using the following:
a. Physical-measure method
b. NRV method
2. Show the operating income for each product using the methods in requirement 1.
3. Discuss the pros and cons of the two methods to Sinclair Oil & Gas for making decisions about
product emphasis (pricing, sell-or-process-further decisions, and so on).
4. Draft a letter to the taxation authorities on behalf of Sinclair Oil & Gas that justifies the joint–
cost-allocation method you recommend Sinclair use.
SOLUTION
Joint Costs =
$1800
ICR8
(Non-Saleable)
ING4
(Non-Saleable)
XGE3
(Non-Saleable)
Processing
$175
Processing
$210
Processing
$105
Crude Oil
150 bbls × $18 / bbl =
$2700
NGL
50 bbls × $15 / bbl =
$750
Gas
800 eqvt bbls ×
$1.30 / eqvt bbl =
$1040
Splitoff
Point
16-7
1a. Physical Measure Method
Crude Oil
NGL
Gas
Total
1. Physical measure of total prodn.
2. Weighting (150; 50; 800 ÷ 1,000)
3. Joint costs allocated (Weights $1,800)
150
0.15
$270
50
0.05
$90
800
0.80
$1,440
1,000
1.00
$1,800
1b. NRV Method
Crude Oil
NGL
Gas
Total
1. Final sales value of total production
2. Deduct separable costs
3. NRV at splitoff
4. Weighting (2,525; 645; 830 ÷ 4,000)
5. Joint costs allocated (Weights $1,800)
$2,700
175
$2,525
0.63125
$1,136.25
$750
105
$645
0.16125
$290.25
$1,040
210
$ 830
0.20750
$373.50
$4,490
490
$4,000
$1,800
2. The operating-income amounts for each product using each method is:
(a) Physical Measure Method
Crude Oil
NGL
Gas
Total
Revenues
Cost of goods sold
Joint costs
Separable costs
Total cost of goods sold
Gross margin
$2,700
270
175
445
$2,255
$750
90
105
195
$555
$1,040
1,440
210
1,650
$ (610)
$4,490
1,800
490
2,290
$2,200
(b) NRV Method
Crude Oil
NGL
Gas
Total
Revenues
Cost of goods sold
Joint costs
Separable costs
Total cost of goods sold
Gross margin
$2,700.00
1,136.25
175.00
1,311.25
$1,388.75
$750.00
290.25
105.00
395.25
$354.75
$1,040.00
373.50
210.00
583.50
$ 456.50
$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 make decisions regarding 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.
16-8
4. Because crude oil is the only product subject to taxation, it is clearly in Sinclair’s best
interest to use the NRV method because it leads to a lower profit for crude oil and, consequently,
a smaller tax burden. A letter to the taxation authorities could 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.
16-22 (30 min.) Joint-cost allocation, sales value, physical measure, NRV methods.
Fancy Foods produces two types of microwavable products: beef-flavored ramen and shrimp-
flavored ramen. The two products share common inputs such as noodle and spices. The production
of ramen results in a waste product referred to as stock, which Fancy dumps at negligible costs in
a local drainage area. In June 2014, the following data were reported for the production and sales
of beef-flavored and shrimp-flavored ramen:
Due to the popularity of its microwavable products, Fancy decides to add a new line of products
that targets dieters. These new products are produced by adding a special ingredient to dilute the
original ramen and are to be sold under the names Special B and Special S, respectively. Following
are the monthly data for all the products:
16-9
Required:
1. Calculate Fancy’s gross-margin percentage for Special B and Special S when joint costs are
allocated using the following:
a. Sales value at splitoff method
b. Physical-measure method
c. Net realizable value method
2. Recently, Fancy discovered that the stock it is dumping can be sold to cattle ranchers at $4 per
ton. In a typical month with the production levels shown, 6,000 tons of stock are produced and
can be sold by incurring marketing costs of $12,400. Sandra Dashel, a management accountant,
points out that treating the stock as a joint product and using the sales value at splitoff method,
the stock product would lose about $2,435 each month, so it should not be sold. How did
Dashel arrive at that final number, and what do you think of her analysis? Should Fancy sell
the stock?