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© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Accounting Systems For Measuring Costs
Chapter
17
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Planning andcontrol
functions.
Providingproducts or services tocustomers.
Assessing theefficiency andeffectivenessof operations.
Determining unitmanufacturing
costs.
Cost accounting systems provide information supporting decisions making the business successful.
Cost Accounting Systems
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Discloseinventoriesand cost ofgoods sold.
Track resourcesconsumed byproducts and
services.
Manage activitiesthat consume
resources.
Evaluate andreward
employeeperformance.
Cost accounting systems are the proceduresand techniques used by management.
Cost Accounting Systems
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ProcessCosting
Job OrderCosting
Used for production of large, unique, high-cost items. Built to order rather than mass produced. Many costs can be directly traced to each job.
Basic Cost Accounting Procedures
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Typical job order cost applications:
Special-order printing Building construction
Also used in service industry Hospitals Law firms
Basic Cost Accounting Procedures
ProcessCosting
Job OrderCosting
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Used for production of small, identical, low-cost items. Mass produced in automated continuous production process. Costs cannot be directly traced to each unit of product.
Basic Cost Accounting Procedures
ProcessCosting
Job OrderCosting
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Typical process cost applications: Petrochemical refinery Paint manufacturer Paper mill
Basic Cost Accounting Procedures
ProcessCosting
Job OrderCosting
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THE JOB
Directmaterials
Direct labor
Traced directly to each job
Traced directly
to each job
Manufacturingoverhead (OH)
Applied to eachjob using a
predeterminedrate (POHR)
Job Order Costing
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The primary document for tracking the costs
associated with a given job is the job
cost sheet.
Let’s investigate
Job Order Costing
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The Job Cost SheetRoseCo Job Cost Sheet
Job Number A - 143 Date Initiated 3-4-X9Date Completed
Department B3 Units CompletedItem Wooden cargo crate
Direct Materials Direct Labor Manufacturing OverheadReq. No. Amount Ticket Hours Amount Hours Rate Amount
Cost Summary Units ShippedDirect Materials Date Number BalanceDirect LaborManufacturing OverheadTotal CostUnit Cost
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The Job Cost SheetRoseCo Job Cost Sheet
Job Number A - 143 Date Initiated 3-4-X9Date Completed
Department B3 Units CompletedItem Wooden cargo crate
Direct Materials Direct Labor Manufacturing OverheadReq. No. Amount Ticket Hours Amount Hours Rate AmountX7-6890 116$
Cost Summary Units ShippedDirect Materials 116$ Date Number BalanceDirect LaborManufacturing OverheadTotal CostUnit Cost
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The Job Cost SheetRoseCo Job Cost Sheet
Job Number A - 143 Date Initiated 3-4-X9Date Completed
Department B3 Units CompletedItem Wooden cargo crate
Direct Materials Direct Labor Manufacturing OverheadReq. No. Amount Ticket Hours Amount Hours Rate AmountX7-6890 116$ 36 8 88$
Cost Summary Units ShippedDirect Materials 116$ Date Number BalanceDirect Labor 88$ Manufacturing OverheadTotal CostUnit Cost
Accumulate direct labor
costs by means of a
work record, such as a time ticket, for each
employee.
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The Job Cost SheetRoseCo Job Cost Sheet
Job Number A - 143 Date Initiated 3-4-X9Date Completed 3-5-X9
Department B3 Units Completed 2Item Wooden cargo crate
Direct Materials Direct Labor Manufacturing OverheadReq. No. Amount Ticket Hours Amount Hours Rate AmountX7-6890 116$ 36 8 88$ 8 4$ 32$
Cost Summary Units ShippedDirect Materials 116$ Date Number BalanceDirect Labor 88$ Manufacturing Overhead 32$ Total Cost 236$ Unit Cost 118$
Apply manufacturing overhead to jobs using a predetermined overhead rate (POHR) based on
direct labor hours (DLH).
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Let’s summarize the document flow we have
been discussing in a job order
costing system.
Job Order CostingDocument Flow Summary
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Materials Ledger CardsMaterials
Ledger CardsMaterials Ledger CardsMaterialsRequisition
Direct materials
The materials requisition
indicates the cost of direct
materialto charge to
jobsand the cost of
indirect material to charge to overhead.
Indirect materials
Job Cost SheetsJob Cost SheetsJob Cost SheetsJob Cost Sheets
Manufacturing Overhead Account
Job Order CostingDocument Flow Summary
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Employee time tickets indicate
the cost of direct labor
to charge tojobs
and the cost of indirect labor
to charge to overhead.
Job Cost Sheets
Manufacturing Overhead Account
Job Cost SheetsJob Cost SheetsJob Cost Sheets
Direct Labor
Indirect Labor
Employee Time TicketEmployee Time
TicketEmployee Time TicketEmployee Time
Ticket
Job Order CostingDocument Flow Summary
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EmployeeTime Ticket
MaterialsRequisition
OtherActual OHCharges
IndirectMaterial
IndirectLabor
OverheadApplied
withPOHR
Manufacturing Overhead Account
Job Cost Sheets
Job Order CostingDocument Flow Summary
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Let’s examine the cost flows in a
job order costing system. We will use T-accounts and start with
materials.
Flow of Costs in Job CostingFlow of Costs in Job Costing
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•MaterialPurchases
•Direct Material
•Direct Material
Mfg. Overhead•Indirect Material
Work in Process(Job Cost Sheet)
•Indirect Material
Materials Inventory
Flow of Costs in Job Costing
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Next let’s add labor costs and
applied manufacturing overhead to the job order cost flows. Are you
with me?
Flow of Costs in Job Costing
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•Direct Labor
Mfg. Overhead
Work in Process(Job Cost Sheet)
•Indirect Material
•Direct Material
•OverheadApplied to
Work inProcess
•IndirectLabor
•Direct Labor
•Overhead Applied
•IndirectLabor
the difference is closed to cost of goods sold.
When Actual Applied factory factoryoverhead overhead
=/
Labor
Flow of Costs in Job Costing
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If Manufacturing Effect of Closing toOverhead is . . . Cost of Goods Sold
UNDERAPPLIED INCREASE(Applied OH is less Cost of Goods Sold
than actual OH)
OVERAPPLIED DECREASE(Applied OH is greater Cost of Goods Sold
than actual OH)
Closing Under- or OverappliedManufacturing Overhead
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Now let’s complete the
goods and sell them. Still with
me?
Flow of Costs in Job Costing
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•Cost ofGoodsMfd.
Finished Goods
•Cost ofGoodsSold
•Cost ofGoodsMfd.
Cost of Goods Sold
•Cost ofGoodsSold
Work in Process(Job Cost Sheet)•Direct
Material•Direct Labor
•Overhead Applied
Flow of Costs in Job Costing
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Used for production of small, identical, low-cost items. Mass produced in automated continuous production process. Costs cannot be directly traced to each unit of product.
Process Costing
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Job Costing
Custom orders
Heterogeneous products
Low production volume
High product flexibility
Low to medium standardization
Process Costing
Repetitive production
Homogeneous products
High production volume
Low product flexibility
High standardization
Comparing Job and Process Costing
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DirectMaterials
FinishedGoods
Cost per unit for
each job
DirectLabor
FactoryOverhead
Jobs
The Work in Process account consists of
individual jobs in job costing.
Job and Process Costing
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DirectMaterials
FinishedGoods
DirectLabor
FactoryOverhead
Processes
The Work in Process account consists of specific processes in
process costing.
Cost per unit
processed
Job and Process Costing
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Same objective: to determine the cost of products
Same inventory accounts: raw materials, work in process, and finished goods
Same overhead assignment method:predetermined rate times actual activity
Job and ProcessCosting Similarities
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Work in ProcessAssembly
Labor
Materials
Indi
rect
Indi
rect
FinishedGoods
FactoryOverhead
Direct
Direct
Deliveredto
Customers
AppliedOverhead
Work in Process
Packaging
Work in Process Accounts — The Key to Process Costing
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Costs are accumulated for a period of time by process or department.
Unit cost is computed by dividing the accumulated costs by the number of
units produced in the period.
Computing Unit Cost
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Unit cost is computed by dividing the accumulated costs by the number of
units produced in the period.
If partially complete units remain in process, we must use equivalent units
as the divisor to obtain unit costs.
Computing Unit Cost
Costs are accumulated for a period of time by process or department.
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Equivalent units is a concept expressing a number of partially completed units as a smaller number of fully completed units.
Two one-half full pitchers are equivalent to one full pitcher.
+ =
Computing and Using Equivalent Units of Production
1
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Question For the current period, PencilCo started
15,000 units and completed 10,000 units, leaving 5,000 units in process 30 percent complete. How many equivalent units of
production did PencilCo have for the period?
a. 10,000b. 11,500c. 1,500d. 15,000
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For the current period, PencilCo started 15,000 units and completed 10,000 units, leaving 5,000 units in process 30 percent complete. How many equivalent units of
production did PencilCo have for the period?
a. 10,000b. 11,500c. 1,500d. 15,000
10,000 units + (5,000 units × .30) = 11,500 equivalent units
Question
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Cost perequivalent
unit
= Product costs for the periodEquivalent units for the period
Cost Per Equivalent Unit
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Now assume that PencilCo incurred $27,600 in production costs. What was PencilCo’s cost per unit for the period?
a. $1.84b. $2.40c. $2.76d. $2.90
Question
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Now assume that PencilCo incurred $27,600 in production costs. What was PencilCo’s cost per unit for the period?
a. $1.84b. $2.40c. $2.76d. $2.90
$27,600 ÷ 11,500 equivalent units
= $2.40 per equivalent unit
Question
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Equivalent units may be different for material and labor
and overhead at different stages of a process.
At completion of Stage 1 of the process, materialis 40% complete, but labor and overhead are only
25% complete.
Stage 1
40% ofMaterial
25% ofLabor andOverhead
Equivalent Units
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Stage 2
25% ofLabor andOverhead
60% ofMaterial
Stage 1
40% ofMaterial
25% ofLabor andOverhead
+
+
=
=
100%
50%
Equivalent Units
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Stage 3
50% ofLabor andOverhead
The process is now complete.
Stage 2
25% ofLabor andOverhead
60% ofMaterial
Stage 1
40% ofMaterial
25% ofLabor andOverhead
Equivalent Units
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Owl Inc uses FIFO process costing in its Fabrication
Department where a product called Strata is made.
Process Costing andEquivalent Units
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Process Costing andEquivalent Units
Owl Inc Fabrication Department Data For April 2002Beginning Inventory: Units of product 30,000
Percentage of completion - direct material 100%Percentage of completion - direct labor 40%Percentage of completion - overhead 40%
Units started in April 90,000 Units transferred from grinding to mixing 100,000 Ending Inventory:
Units of product 20,000 Percentage of completion - direct material 100%Percentage of completion - direct labor 25%Percentage of completion - overhead 25%
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Owl Inc Fabrication Department Data For April 2002Beginning Inventory: Units of product 30,000
Percentage of completion - direct material 100%Percentage of completion - direct labor 40%Percentage of completion - overhead 40%
Units started in April 90,000 Units transferred from grinding to mixing 100,000 Ending Inventory:
Units of product 20,000 Percentage of completion - direct material 100%Percentage of completion - direct labor 25%Percentage of completion - overhead 25%
Material is added at thebeginning of the process soit is always 100% complete.
Process Costing andEquivalent Units
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Owl Inc Fabrication Department Data For April 2002Beginning Inventory: Units of product 30,000
Percentage of completion - direct material 100%Percentage of completion - direct labor 40%Percentage of completion - overhead 40%
Units started in April 90,000 Units transferred from grinding to mixing 100,000 Ending Inventory:
Units of product 20,000 Percentage of completion - direct material 100%Percentage of completion - direct labor 25%Percentage of completion - overhead 25%
Overhead is applied on the basis of labor, so both are at the
same percentage of completion.
Process Costing andEquivalent Units
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April Fabrication Department Physical Flow
Units to account for:Beginning inventory 30,000 Units started during April 90,000 Total number of units 120,000
Units accounted for as:Units transferred from Fabrication to Mixing 100,000 Ending inventory 20,000 Total number of units 120,000
Physical Flow of Units
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Fabrication DepartmentDirect Material Equivalent Units of Production - April 2002
Units of Percent Added EquivalentProduct This Period Units
Beginning goods in process 30,000 0% 0Goods started and completed 70,000 100% 70,000 Ending work in process 20,000 100% 20,000 Total units 120,000 90,000
Computing EquivalentUnits of Production
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Fabrication DepartmentDirect Material Equivalent Units of Production - April 2002
Units of Percent Added EquivalentProduct This Period Units
Beginning goods in process 30,000 0% 0Goods started and completed 70,000 100% 70,000 Ending work in process 20,000 100% 20,000 Total units 120,000 90,000
Since materials are added at the beginning of the process, no additional materials are necessary to complete the
beginning inventory.
Computing EquivalentUnits of Production
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Fabrication DepartmentDirect Material Equivalent Units of Production - April 2002
Units of Percent Added EquivalentProduct This Period Units
Beginning goods in process 30,000 0% 0Goods started and completed 70,000 100% 70,000 Ending work in process 20,000 100% 20,000 Total units 120,000 90,000
} 100,000
100,000 units completed and transferred.
Computing EquivalentUnits of Production
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Fabrication Department Direct Labor and FactoryOverhead Equivalent Units of Production - April 2002
Units of Percent Added EquivalentProduct This Period Units
Beginning goods in process 30,000 60% 18,000 Goods started and completed 70,000 100% 70,000 Ending work in process 20,000 25% 5,000 Total units 120,000 93,000
Computing EquivalentUnits of Production
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Fabrication Department Direct Labor and FactoryOverhead Equivalent Units of Production - April 2002
Units of Percent Added EquivalentProduct This Period Units
Beginning goods in process 30,000 60% 18,000 Goods started and completed 70,000 100% 70,000 Ending work in process 20,000 25% 5,000 Total units 120,000 93,000
Since labor and overhead were 40 percent complete in the beginning
inventory, 60 percent of the work must be completed in April.
Computing EquivalentUnits of Production
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Fabrication Department Direct Labor and FactoryOverhead Equivalent Units of Production - April 2002
Units of Percent Added EquivalentProduct This Period Units
Beginning goods in process 30,000 60% 18,000 Goods started and completed 70,000 100% 70,000 Ending work in process 20,000 25% 5,000 Total units 120,000 93,000
} 100,000Transferred
Computing EquivalentUnits of Production
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Summary of Fabrication DepartmentEquivalent Units of Production - April 2002
Direct Direct FactoryActivities during April 2002 Material Labor OverheadUnits from beginning inventory
processed in current period 0 18,000 18,000
Units started and completedin current period 70,000 70,000 70,000
Units in ending inventory at end of current period 20,000 5,000 5,000
Equivalent units of productionfor period 90,000 93,000 93,000
Computing EquivalentUnits of Production
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Fabrication DepartmentApril Work in Process Costs
Beginning work in process 22,380$ Costs added in April: Direct material 45,000 Direct labor 11,160 Overhead 44,640 Total costs to account for 123,180$
Process Costing andEquivalent Units
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Fabrication DepartmentCost Per Equivalent Unit - April 2002
Direct Direct FactoryMaterials Labor Overhead
Total cost of resource for April 45,000$ 11,160$ 44,640$
Equivalent units of productionin April ÷ 90,000 ÷ 93,000 ÷ 93,000
Cost per equivalent unit forApril = 0.50$ = 0.12$ = 0.48$
Cost per Equivalent Unit
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We will account for all costs incurred
by assigning unit costs to the: A. 100,000 units completed and
transferred. B. 20,000 units remaining in ending
work in process inventory.
Cost Reconciliation
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Fabrication Department Work in ProcessCost Summary for April 2002
Cost of completed unitsFrom beginning work in process
April 1 balance 22,380$ Costs to complete April 1 inventory
Direct materialDirect labor Overhead
Started and completed Total completed and transferred
Cost of ending work in processDirect material Direct labor Overhead
Total cost accounted for
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Fabrication Department Work in ProcessCost Summary for April 2002
Cost of completed unitsFrom beginning work in process
April 1 balance 22,380$ Costs to complete April 1 inventory
Direct material 0$ Direct labor (18,000 × $0.12) 2,160 Overhead (18,000 × $0.48) 8,640 10,800
Started and completed Total completed and transferred
Cost of ending work in processDirect material Direct labor Overhead
Total cost accounted for
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Fabrication Department Work in ProcessCost Summary for April 2002
Cost of completed unitsFrom beginning work in process
April 1 balance 22,380$ Costs to complete April 1 inventory
Direct material 0$ Direct labor (18,000 × $0.12) 2,160 Overhead (18,000 × $0.48) 8,640 10,800
Started and completed (70,000 × $1.10) 77,000 Total completed and transferred (100,000 units) 110,180$
Cost of ending work in processDirect material Direct labor Overhead
Total cost accounted for
$0.12 + $0.48 + $0.50 = $1.10
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Fabrication Department Work in ProcessCost Summary for April 2002
Cost of completed unitsFrom beginning work in process
April 1 balance 22,380$ Costs to complete April 1 inventory
Direct material 0$ Direct labor (18,000 × $0.12) 2,160 Overhead (18,000 × $0.48) 8,640 10,800
Started and completed (70,000 × $1.10) 77,000 Total completed and transferred (100,000 units) 110,180$
Cost of ending work in processDirect material (20,000 × $0.50) 10,000$ Direct labor (5,000 × $0.12) 600 Overhead (5,000 × $0.48) 2,400 13,000
Total cost accounted for 123,180$
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AB C
ACB
Activity-Based Costing (ABC)
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One of the most difficult tasks in
computing accurate unit costs lies in determining the
proper amount of overhead cost to
assign to each job.
Assigningoverhead is
difficult. I agree!
Activity-Based Costing (ABC)
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Level of C
omplexity
Overhead Allocation
Plantwide Overhead
Rate
DepartmentalOverhead
Rates
Activity-BasedCosting
Activity-Based Costing (ABC)
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In the ABC method, we recognize that many
activities within a department drive overhead costs.A
B CA
CB
Activity-Based Costing (ABC)
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Identify activities and assign indirect costs to those activities.
Central idea . . . Products require activities. Activities consume resources. A
B CA
CB
Activity-Based Costing (ABC)
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More detailed measures of costs.Better understanding of activities.More accurate product costs for . . .
Pricing decisions. Product elimination decisions. Managing activities that cause costs.
Benefits should always be compared tocosts of implementation.
The Benefits of ABC
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Most cost drivers are related to either volume or complexity of production. Examples: machine time, machine setups,
purchase orders, production orders.
Three factors are considered in choosing a cost driver: Causal relationship. Benefits received. Reasonableness.
Identifying Cost Drivers
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Overhead Actual Rate Activity×
Rate = Estimated overhead costs in activity cost pool Estimated number of activity units
Identify activities that consume resources. Assign costs to a cost pool for each activity. Identify cost drivers associated with each activity. Compute overhead rate for each cost pool:
Assign costs to products:
Activity-Based CostingProcedures
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Let’s look at anexample comparingtraditional costing
with ABC. We will start with
traditional costing.
Activity-Based Costing
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Pear Company manufactures a product in regular and deluxe models. Overhead is assigned on the basis of direct labor hours. Budgeted overhead for the current
year is $2,000,000. Other information:
Deluxe RegularModel Model
Direct Material 150$ 112$ Direct Labor Cost 16 8 Direct Labor Time 1.6 hours 0.8 hoursExpected Volume (units) 5,000 40,000
First, determine the unit cost of each model using traditional costing methods.
Traditional Costing vs. ABCExample
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DirectLabor Hours
Deluxe Model 5,000 units @ 1.6 hours 8,000 Regular Model 40,000 units @ 0.8 hours 32,000 Total Direct Labor Hours (DLH) 40,000
Overhead Estimated overhead costs Rate Estimated activity
=
Overhead $2,000,000 Rate 40,000 DLH
= = $50 per DLH
Traditional Costing
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Deluxe RegularModel Model
Direct Material 150$ 112$ Direct Labor 16 8 Manufacturing Overhead$50 per hour × 1.6 hours 80 $50 per hour × 0.8 hours 40 Total Unit Cost 246$ 160$
ABC will have differentoverhead per unit.
Traditional Costing
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Pear Company plans to adopt activity-based costing. Using the following activity center data, determine the unit cost of the two products using
activity-based costing.
OverheadActivity Cost Cost for Units of ActivityCenter Driver Activity Deluxe Regular
Purchasing Orders 84,000$ 400 800 Scrap Rework Orders 216,000 300 600 Testing Tests 450,000 4,000 11,000 Machine Related Hours 1,250,000 20,000 30,000 Total Overhead 2,000,000$
Activity-Based Costing
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Overhead UnitsActivity Cost Cost for ofCenter Driver Activity Activity Rate
Purchasing Orders 84,000$ 1,200 Scrap Rework Orders 216,000 900 Testing Tests 450,000 15,000 Machine Related Hours 1,250,000 50,000 Total Overhead 2,000,000$
400 deluxe + 800 regular = 1,200 total
Activity-Based Costing
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Overhead UnitsActivity Cost Cost for ofCenter Driver Activity Activity Rate
Purchasing Orders 84,000$ 1,200 $ 70 per orderScrap Rework Orders 216,000 900 $240 per orderTesting Tests 450,000 15,000 $ 30 per testMachine Related Hours 1,250,000 50,000 $ 25 per hourTotal Overhead 2,000,000$
Rate = Overhead Cost for Activity ÷ Units of Activity
Activity-Based Costing
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Deluxe Model Regular ModelActual Cost Actual Cost
Units of Allocated Units of AllocatedActivity Rate Activity to Product Activity to Product
Purchasing $ 70/order 400 ? 800 ?Scrap Rework $240/order 300 ? 600 ?Testing $ 30/test 4,000 ? 11,000 ?Machine Related $ 25/hour 20,000 ? 30,000 ?Total Overhead ? ?
Activity-Based Costing
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Deluxe Model Regular ModelActual Cost Actual Cost
Units of Allocated Units of AllocatedActivity Rate Activity to Product Activity to Product
Purchasing $ 70/order 400 28,000$ 800 56,000$ Scrap Rework $240/order 300 ? 600 ? Testing $ 30/test 4,000 ? 11,000 ? Machine Related $ 25/hour 20,000 ? 30,000 ? Total Overhead ? ?
Cost Allocated to Product = Actual Units of Activity × Rate
Let’s completethe table.
Activity-Based Costing
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Deluxe Model Regular ModelActual Cost Actual Cost
Units of Allocated Units of AllocatedActivity Rate Activity to Product Activity to Product
Purchasing $ 70/order 400 28,000$ 800 56,000$ Scrap Rework $240/order 300 72,000 600 144,000 Testing $ 30/test 4,000 120,000 11,000 330,000 Machine Related $ 25/hour 20,000 500,000 30,000 750,000 Total Overhead 720,000$ 1,280,000$
Cost Allocated to Product = Actual Units of Activity × Rate
Activity-Based Costing
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Deluxe Model Regular ModelActual Cost Actual Cost
Units of Allocated Units of AllocatedActivity Rate Activity to Product Activity to Product
Purchasing $ 70/order 400 28,000$ 800 56,000$ Scrap Rework $240/order 300 72,000 600 144,000 Testing $ 30/test 4,000 120,000 11,000 330,000 Machine Related $ 25/hour 20,000 500,000 30,000 750,000 Total Overhead 720,000$ 1,280,000$
Cost Allocated to Product = Actual Units of Activity × Rate
Total overhead = $720,000 + $1,280,000 = $2,000,000Recall that $2,000,000 was the original amount of
overhead assigned to the products using traditional overhead costing.
Activity-Based Costing
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Overhead Costs Assigned to Products: Deluxe Model $720,000 ÷ 5,000 units = $144 per unit Regular Model $1,280,000 ÷ 40,000 units = $32 per unit
Deluxe RegularModel Model
Direct Materials 150$ 112$ Direct Labor 16 8 Manufacturing Overhead 144 32 Total Unit Cost 310$ 152$
Activity-Based Costing
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This result is not uncommon when activity-based costing is used. Many companies have found that low-
volume, specialized products have greater overhead costs than previously realized.
Traditional Costing ABCDeluxe Regular Deluxe RegularModel Model Model Model
Direct materials 150$ 112$ 150$ 112$ Direct labor 16 8 16 8 Overhead 80 40 144 32 Total cost 246$ 160$ 310$ 152$
Activity-Based Costing
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Cost Cost DriverMaterials purchasing Number of purchase ordersMaterials handling Number of materials
requisitionsPersonnel processing Number of employees hired
or laid offEquipment depreciation Number of products
produced or hours of useQuality inspection Number of units inspectedIndirect labor for Number of setups required equipment setupsEngineering costs for Number of modifications product modifications
Costs and Cost Drivers inActivity-Based Costing
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
End of Chapter 17