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2 Product Costing Systems: Concepts and Design Issues
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2-2
Learning Objective 1
McGraw-Hill/Irwin
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2-3
The Meaning of Cost
Product Costs • Related to the purchase or manufacture of goods for resale. • Assigned to inventory and cost of goods sold. McGraw-Hill/Irwin
The use of valuable resources, in order to achieve a stated purpose. In ing, cost is reported in monetary .
Period Costs • Related to selling and istrative operations. • Recognized as expenses in the same time period.
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2-4
Learning Objective 3
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Comparing Service, Retail and Manufacturing Companies Service firms . . . Provide a service that is consumed when produced.
Retailers . . . Buy finished goods. Sell finished goods.
Have no inventories. MegaLoMart
Manufacturers . . . Buy raw materials. Produce and sell finished goods.
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Manufacturing Companies The 3 major categories of manufacturing costs:
Direct Materials Raw materials, components, and other parts that can be traced to a specific product. McGraw-Hill/Irwin
Direct Labor Payments and benefits for those employees who convert direct materials into finished product.
Manufacturing Overhead Indirect material Indirect labor Other overhead
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Manufacturing Companies Prime Costs include:
Direct Materials
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Direct Labor
Manufacturing Overhead
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Manufacturing Companies Conversion Costs include:
Direct Materials
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Direct Labor
Manufacturing Overhead
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Stages of Production and the Flow of Costs Add: =
Less:
=
Raw Materials Beg. Inventory Purchases Raw Materials Available for Production Raw Materials Transferred to Production Ending Inventory
Add:
= Less:
=
McGraw-Hill/Irwin
Work-In-Process Beg. WIP Inventory Raw Materials Transferred In Direct Labor Manufacturing Overhead Total Manufacturing Costs Incurred Cost of Goods Completed and Transferred to Finished Goods Ending WIP Inventory
Add:
= Less: =
Finished Goods Beg. Inventory Cost of Goods Completed and Transferred from WIP Goods Available for Sale Cost of Goods Sold Ending Inventory
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2-10
Stages of Production and the Flow of Costs - Example
Add: =
Less:
=
Raw Materials Beg. Inventory Purchases Raw Materials Available for Production Raw Materials Transferred to Production Ending Inventory
What is Ending Inventory in February? McGraw-Hill/Irwin
Axel Electronics makes toasters. On February 1, Axel has $15,000 of raw material on hand. Axel’s purchase and transfers to the production floor are indicated below. Date Feb 3 Feb 10 Feb 15 Feb 20 Feb 22 Feb 27
Cost of Purchases $ 8,000 12,000 14,000
Cost of Transfers $ 5,000 11,000 7,000 6,000
9,000 16,000 Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
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Stages of Production and the Flow of Costs - Example
Add: = Less: =
Raw Materials $15,000 43,000 $58,000 45,000 $13,000
Now let’s look at Work-in-Process. McGraw-Hill/Irwin
Axel Electronics makes toasters. On February 1, Axel has $15,000 of raw material on hand. Axel’s purchase and transfers to the production floor are indicated below. Date Feb 3 Feb 10 Feb 15 Feb 20 Feb 22 Feb 27
Cost of Purchases $ 8,000 12,000 14,000
Cost of Transfers $ 5,000 11,000 7,000 6,000
9,000 16,000 Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-12
Stages of Production and the Flow of Costs - Example
Add: = Less: =
Raw Materials $15,000 43,000 $58,000 45,000 $13,000
Add:
=
What is the amount of cost transferred to Finished Goods in February? McGraw-Hill/Irwin
Less:
=
Work-In-Process Beg. WIP Inventory Raw Materials Transferred In Direct Labor Manufacturing Overhead Total Manufacturing Costs Incurred Cost of Goods Completed and Transferred to Finished Goods Ending WIP Inventory
On February 1, Axel had WIP of $30,000 on the factory floor. During February, Axel paid $92,000 in direct labor wages. Overhead is applied at 150% of direct labor. On 2/28, $22,000 is still in WIP.
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Stages of Production and the Flow of Costs - Example 150 % of $92,000 Add: = Less: =
Raw Materials $15,000 43,000 $58,000 45,000 $13,000
Now let’s look at Finished Goods. McGraw-Hill/Irwin
Add:
= Less: =
Work-In-Process $30,000 45,000 92,000 138,000 $305,000 283,000 $22,000
Transferred to Finished Goods
On February 1, Axel had WIP of $30,000 on the factory floor. During February, Axel paid $92,000 in direct labor wages. Overhead is applied at 150% of direct labor. On 2/28, $22,000 is still in WIP.
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2-14
Stages of Production and the Flow of Costs - Example
Add: = Less: =
Raw Materials $15,000 43,000 $58,000 45,000 $13,000
Add:
= Less: =
Work-In-Process $30,000 45,000 92,000 138,000 $305,000 283,000 $22,000
Add:
= Less: =
Finished Goods Beg. Inventory Cost of Goods Completed and Transferred from WIP Goods Available for Sale Cost of Goods Sold Ending Inventory
On February 1, Axel had Finished Goods of $125,000 on hand. At the end of February, a physical inventory count revealed $96,000 in Finished Goods still on hand. What was Cost of Goods Sold for February? McGraw-Hill/Irwin
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Stages of Production and the Flow of Costs - Example Cost of goods sold Add: = Less: =
Raw Materials $15,000 43,000 $58,000 45,000 $13,000
Add:
= Less: =
Work-In-Process $30,000 45,000 92,000 138,000 $305,000 283,000 $22,000
Add: = Less: =
Finished Goods $125,000 283,000 $408,000 312,000 $96,000
On February 1, Axel had Finished Goods of $125,000 on hand. At the end of February, a physical inventory count revealed $96,000 in Finished Goods still on hand. What was Cost of Goods Sold for February? McGraw-Hill/Irwin
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Learning Objective 2
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Schedule of Cost of Goods Manufactured
Let’s look at a Schedule of Cost of Goods Manufactured for CollegePak Company.
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Schedule of Cost of Goods Manufactured CollegePak Company Schedule of Cost of Goods Manufactured Raw material used
$
Direct labor Total manufacturing overhead
850,000 700,000 1,850,000
Total manufacturing costs Add: Work-in-process inventory, January 1
$ 3,400,000 350,000
Subtotal Deduct: Work-in-process inventory, December 31
$ 3,750,000 400,000
Cost of goods manufactured
$ 3,350,000
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Schedule of Cost Goods Computation of Costof of Raw Material Used Raw-material inventory, January 1 $ Manufactured Add: Purchases of raw materials Raw material available for use Deduct: Raw material inventory, December 31 Raw material used
200,000 800,000 1,000,000 150,000
$ 850,000
CollegePak Company Schedule of Cost of Goods Manufactured Raw material used
$
Direct labor Total manufacturing overhead
850,000 700,000 1,850,000
Total manufacturing costs Add: Work-in-process inventory, January 1
$ 3,400,000 350,000
Subtotal Deduct: Work-in-process inventory, December 31
$ 3,750,000 400,000
Cost of goods manufactured
$ 3,350,000
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Schedule of Cost of Goods Manufactured Include all direct labor costs incurred during the CollegePak Company current period. Schedule of Cost of Goods Manufactured Raw material used
$
Direct labor Total manufacturing overhead
850,000 700,000 1,850,000
Total manufacturing costs Add: Work-in-process inventory, January 1
$ 3,400,000 350,000
Subtotal Deduct: Work-in-process inventory, December 31
$ 3,750,000 400,000
Cost of goods manufactured
$ 3,350,000
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Schedule of Cost of Goods Manufactured Beginning work-inprocess inventory is carried over from the CollegePak Company prior period. Schedule of Cost of Goods Manufactured Raw material used
$
Direct labor Total manufacturing overhead
850,000 700,000 1,850,000
Total manufacturing costs Add: Work-in-process inventory, January 1
$ 3,400,000 350,000
Subtotal Deduct: Work-in-process inventory, December 31
$ 3,750,000 400,000
Cost of goods manufactured
$ 3,350,000
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Schedule of Cost of Goods Manufactured Ending work-in-process inventory contains the cost of unfinished goods, CollegePak Company and is reported in the current assets section of the balance sheet. Schedule of Cost of Goods Manufactured Raw material used
$
Direct labor Total manufacturing overhead
850,000 700,000 1,850,000
Total manufacturing costs Add: Work-in-process inventory, January 1
$ 3,400,000 350,000
Subtotal Deduct: Work-in-process inventory, December 31
$ 3,750,000 400,000
Cost of goods manufactured
$ 3,350,000
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Income Statement for a Manufacturer
Now let’s look at an income statement for CollegePak.
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Income Statement for a Manufacturer
CollegePak Company Income Statement For the Year Ended December 31, 20X2 Sales revenue Less: Cost of goods sold
$ 4,500,000 2,810,000
Gross margin Selling and istrative expenses
$ 1,690,000 1,440,000
Operating profit before taxes
$
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250,000
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Income Statement for a Manufacturer CollegePak Company Schedule of Cost of Goods Sold For the Year Ended December 31, 20X2 Finished-goods inventory, Jan. 1 Add: Cost of goods manufactured
$
Cost of goods availableCollegePak for sale Company Deduct Finished-goods inventory, Dec. 31
920,000 3,350,000 4,270,000 1,460,000
Income Statement Cost of goods sold $ 2,810,000 For the Year Ended December 31, 20X2 Sales revenue Less: Cost of goods sold
$ 4,500,000 2,810,000
Gross margin Selling and istrative expenses
$ 1,690,000 1,440,000
Operating profit before taxes
$
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250,000
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Production Costs in the Service Sector
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A service provider cannot “inventory” its services. The costs of providing the service can be identified and measured, just as occurs in manufacturing industries. Managing and tracking the costs associated with valuechain activities can point to opportunities for improvement.
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Cost Drivers An “activity” is any discrete task that an organization undertakes to make or deliver a good or service. A “cost driver” is some characteristic of the activity that causes costs to be incurred. McGraw-Hill/Irwin
Number of computers made by Dell in a day
Number of flights by Southwest Airlines in a given market
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Learning Objective 4
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Cost Behavior Cost behavior means how a cost will react to changes in the level of business activity.
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Total variable costs change when activity level changes.
Total fixed costs remain unchanged when activity level changes.
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Total Variable Cost Example
Total Long Distance Telephone Bill
Your total long distance telephone bill is based on how many minutes you talk.
Minutes Talked McGraw-Hill/Irwin
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Variable Cost Per Unit Example
Per Minute Telephone Charge
The cost per long distance minute talked is constant. For example, 5 cents per minute.
Minutes Talked McGraw-Hill/Irwin
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Total Fixed Cost Example
Monthly Basic Telephone Bill
Your monthly basic telephone bill probably does not change when you make more local calls.
Number of Local Calls McGraw-Hill/Irwin
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Fixed Cost Per Unit Example
Monthly Basic Telephone Bill per Local Call
The average cost per local call decreases as more local calls are made.
Number of Local Calls McGraw-Hill/Irwin
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Cost Behavior Summary
Summary of Variable and Fixed Cost Behavior Cost
In Total
Per Unit
Variable
Changes proportionately with changes in activity within the relevant range.
Remains constant for each additional unit as long as activity is in the relevant range.
Fixed
Remains the same even when activity changes within the relevant range.
The per unit amount changes each time the level of activity changes due to the fixed nature of the related costs.
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Cost Hierarchy Unit-level Costs
Directly traceable to the decision to produce the level of output
Costs that are incurred for every unit of product manufactured or service produced.
Includes direct material, direct labor, utilities to run equipment, other overhead directly related to the production process. All unit level costs are variable, but not all variable costs are unit level costs. McGraw-Hill/Irwin
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Cost Hierarchy Batch-level Costs Costs that are incurred for batch of product manufactured or service produced.
Includes setup costs, material-handling costs related to delivering raw material to the production line, etc.
McGraw-Hill/Irwin
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Cost Hierarchy Product-level Costs Costs that are incurred for each line of product or service.
Includes design costs for product lines and marketing costs for each product line.
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Cost Hierarchy Facility-level Costs Costs that are incurred to maintain the organization’s overall facility and infrastructure.
Includes production manager’s salary, plant depreciation, and insurance on the facility and equipment.
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Learning Objective 5
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Committed and Discretionary Costs Committed
Discretionary
Long-term obligations, difficult to change in the short term.
Easier to alter in the short term by current managerial decisions.
Rental and/or Lease Financing of Buildings and equipment McGraw-Hill/Irwin
Advertising and Research and Development Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-41
Opportunity Costs The potential benefit that is given up when one alternative is selected over another.
If you were not attending college, you could be earning $20,000 per year. Your opportunity cost of attending college for one year is $20,000.
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Sunk Costs Past payments for resources that cannot be changed by any current or future decision.
Sunk costs should not be considered in decisions. Example: You bought an automobile for $12,000 two years ago. Whatever you do with the automobile in the future, you cannot nullify the original transaction. If it has a trade-in value, that value would become an opportunity cost in your future decisions.
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Traceability of Resources Direct Costs
Indirect Costs
Costs that can be traced easily and conveniently to a product or department.
Costs that need to be allocated, before they can be assigned to a product or department.
Example: Cost of paint in the paint department of an automobile assembly plant.
Example: Cost of national advertising for an airline is indirect to a given flight or route.
McGraw-Hill/Irwin
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Learning Objective 6
McGraw-Hill/Irwin
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Absorption (Full) Costing A system of ing for costs in which both fixed and variable production costs are included in product costs.
Fixed Costs Product Variable Costs McGraw-Hill/Irwin
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2-46
Variable Costing A system of cost ing that assigns only the variable cost of production to products.
Fixed Costs Product Variable Costs McGraw-Hill/Irwin
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2-47
Learning Objective 7
McGraw-Hill/Irwin
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2-48
Absorption Costing vs. Variable Costing Absorption Costing
Product costs
Variable Costing Direct materials Direct labor Variable mfg. overhead
Product costs
Fixed mfg. overhead Period costs Period costs
McGraw-Hill/Irwin
Selling & . exp.
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Absorption and Variable Costing Let’s see what we can learn about the differences between absorption and variable costing by looking at a numerical example.
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Absorption Costing vs. Variable Costing - Example Howell, Inc. produces a single product with a sales price of $40 and the following cost information:
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Absorption Costing vs. Variable Costing - Example Unit product cost is determined as follows:
Selling and istrative expenses are always treated as period expenses and deducted from revenue as they are incurred. McGraw-Hill/Irwin
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2-52
Absorption Costing vs. Variable Costing - Example Howell, Inc. had no beginning inventory, produced 30,000 units and sold 28,000 units this year. Absorption Costing Sales (28,000 × $40) Less cost of goods sold: Beginning inventory $ Add COGM (30,000 × $19) 570,000 Goods available for sale 570,000 Ending inventory (2,000 × $19) 38,000 Gross margin Less selling & . exp. Variable (28,000 x $4) $ 112,000 Fixed 250,000 Net income McGraw-Hill/Irwin
$ 1,120,000
532,000 588,000
$
362,000 226,000
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2-53
Absorption Costing vs. Variable Costing - Example Variable costs only.
Variable Costing
Sales (28,000 × $40) Less variable expenses: Beginning inventory $ Add COGM (30,000 × $12) 360,000 Goods available for sale 360,000 Ending inventory (2,000 × $12) 24,000 Variable cost of goods sold 336,000 Variable selling & istrative expenses (28,000 × $4) 112,000 Contribution margin Less fixed expenses: Manufacturing overhead $ 210,000 Selling & istrative expenses 250,000 Net income McGraw-Hill/Irwin
$ 1,120,000
All fixed manufacturing overhead is expensed. 448,000 672,000
$
460,000 212,000
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2-54
Comparing Absorption and Variable Costing Let’s compare the methods. Cost of Goods Sold
Ending Inventory
Period Expense
Absorption costing Variable mfg. costs $ 336,000 Fixed mfg. costs 196,000 $ 532,000
$ 24,000 14,000 $ 38,000
$
Variable costing Variable mfg. costs $ 336,000 Fixed mfg. costs $ 336,000
$ 24,000 $ 24,000
$
McGraw-Hill/Irwin
$
-
210,000 $ 210,000
Total $ 360,000 210,000 $ 570,000
$ 360,000 210,000 $ 570,000
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2-55
Reconciling Income We can reconcile the difference between absorption and variable net income as follows:
Variable costing net income Add: Fixed mfg. overhead costs deferred in inventory (2,000 units × $7 per unit) Absorption costing net income
Fixed mfg. overhead $210,000 = Units produced 30,000 McGraw-Hill/Irwin
$ 212,000
14,000 $ 226,000
= $7.00 per unit
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2-56
Extending the Example
Let’s look at the second year of operations for Howell, Inc.
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Howell Inc., Year 2 In its second year of operations, Howell started with an inventory of 2,000 units, produced 30,000 units and sold 32,000 units at $40 each.
McGraw-Hill/Irwin
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Howell Inc., Year 2 Unit product cost is determined as follows:
There has been no change in Howell’s cost structure. McGraw-Hill/Irwin
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2-59
Howell Inc., Year 2 Units in ending inventory from the previous period. Absorption Costing Sales (32,000 × $40) Less cost of goods sold: Beg. inventory (2,000 x $19) Add COGM (30,000 × $19) Goods available for sale Ending inventory Gross margin Less selling & . exp. Variable (32,000 × $4) Fixed Net income
$ 1,280,000 $ 38,000 570,000 $ 608,000 $
608,000 672,000
$
378,000 294,000
$ 128,000 250,000
30,000 units produced in the current period. McGraw-Hill/Irwin
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2-60
Howell Inc., Year 2 Variable Costing Sales (32,000 × $40) Less variable expenses: Beg. inventory (2,000 × $12) Add COGM (30,000 × $12) Goods available for sale Ending inventory Variable cost of goods sold Variable selling & istrative expenses (32,000 × $4) Contribution margin Less fixed expenses: Manufacturing overhead Selling & istrative expenses Net income
McGraw-Hill/Irwin
$ 1,280,000 $
24,000 360,000 $ 384,000 $ 384,000 128,000 $
512,000 768,000
$
460,000 308,000
$ 210,000 250,000
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2-61
Summary Income Comparison Costing Method Absorption Variable
1st Period $ 226,000 212,000
2nd Period $ 294,000 308,000
Total $ 520,000 520,000
In the first period, production (30,000 units) was greater than sales (28,000). In the second period, production (30,000 units) was less than sales (32,000). For the two-year period, total absorption income and total variable income are the same. McGraw-Hill/Irwin
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Summary
McGraw-Hill/Irwin
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2-63
Learning Objective 8
McGraw-Hill/Irwin
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2-64
Variable versus Absorption Costing All manufacturing costs must be assigned to products to properly match revenues and costs.
Absorption Costing McGraw-Hill/Irwin
Fixed costs are not really the costs of any particular product.
Variable Costing Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-65
Variable versus Absorption Costing Depreciation, taxes, insurance and salaries are just as essential to products as variable costs.
Absorption Costing McGraw-Hill/Irwin
These are capacity costs and will be incurred even if nothing is produced.
Variable Costing Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-66
Variable versus Absorption Costing Absorption costing product costs are misleading for decision making.
Variable Costing McGraw-Hill/Irwin
They are the numbers that appear on our external reports.
Absorption Costing Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-67
Variable versus Absorption Absorption CostingCosting Cost of goods sold decreases because production exceeds sales, leaving a portion of fixed manufacturing costs in inventory. Variable cost Fixed manufacturing overhead Units sold
Units Total Variable Produced Cost 10,000 $100,000 12,000 $120,000 14,000 $140,000 16,000 $160,000 18,000 $180,000 20,000 $200,000 McGraw-Hill/Irwin
$10 $100,000 10,000
Fixed Total Average Manufacturing Manufacturing Manufacturing Overhead Cost Cost $100,000 $200,000 $ 20.00 $100,000 $220,000 $ 18.33 $100,000 $240,000 $ 17.14 $100,000 $260,000 $ 16.25 $100,000 $280,000 $ 15.56 $100,000 $300,000 $ 15.00
Cost of Goods Sold $ 200,000 $ 183,333 $ 171,429 $ 162,500 $ 155,556 $ 150,000
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
Absorption Costing Cost of goods sold decreases because production exceeds sales, leaving a portion of fixed manufacturing costs in inventory.
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Variable versus Absorption Costing COGS for 10,000 units
COGS
$200,000
$150,000
0 ,0 0
34
0
30 ,0 0
0
26 ,0 0
0
22 ,0 0
0
18 ,0 0
0
14 ,0 0
10 ,0 0
0
$100,000
Number of units produced McGraw-Hill/Irwin
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2-69
Throughput Costing Unit-level spending for direct costs
Product cost
Indirect, past or committed costs Unit-level costs are incurred every time a unit of product is manufactured and will not be incurred again until the next unit is manufactured. McGraw-Hill/Irwin
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2-70
Throughput Costing Example In an automated process direct material may be the only unit-level cost and so is the only product cost. All other manufacturing costs are expensed as period costs. Incentive to overproduce is reduced
Average unit cost does not vary with changes in production levels.
Advantages McGraw-Hill/Irwin
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2-71
Learning Objective 9
McGraw-Hill/Irwin
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2-72
Intentional Overproduction of Inventory
Absorption costing: Excess inventory would include more fixed production costs, so that gross income for the period would be artificially higher. An unethical manager would have an incentive to “produce for inventory” at the end of a period, in order to obtain a better looking bottom line. Throughput costing: No such incentive would exist, since fixed production costs would be charged against operating income for the period.
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End of Chapter 2
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2-2
Learning Objective 1
McGraw-Hill/Irwin
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2-3
The Meaning of Cost
Product Costs • Related to the purchase or manufacture of goods for resale. • Assigned to inventory and cost of goods sold. McGraw-Hill/Irwin
The use of valuable resources, in order to achieve a stated purpose. In ing, cost is reported in monetary .
Period Costs • Related to selling and istrative operations. • Recognized as expenses in the same time period.
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2-4
Learning Objective 3
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Comparing Service, Retail and Manufacturing Companies Service firms . . . Provide a service that is consumed when produced.
Retailers . . . Buy finished goods. Sell finished goods.
Have no inventories. MegaLoMart
Manufacturers . . . Buy raw materials. Produce and sell finished goods.
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-6
Manufacturing Companies The 3 major categories of manufacturing costs:
Direct Materials Raw materials, components, and other parts that can be traced to a specific product. McGraw-Hill/Irwin
Direct Labor Payments and benefits for those employees who convert direct materials into finished product.
Manufacturing Overhead Indirect material Indirect labor Other overhead
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-7
Manufacturing Companies Prime Costs include:
Direct Materials
McGraw-Hill/Irwin
Direct Labor
Manufacturing Overhead
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-8
Manufacturing Companies Conversion Costs include:
Direct Materials
McGraw-Hill/Irwin
Direct Labor
Manufacturing Overhead
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2-9
Stages of Production and the Flow of Costs Add: =
Less:
=
Raw Materials Beg. Inventory Purchases Raw Materials Available for Production Raw Materials Transferred to Production Ending Inventory
Add:
= Less:
=
McGraw-Hill/Irwin
Work-In-Process Beg. WIP Inventory Raw Materials Transferred In Direct Labor Manufacturing Overhead Total Manufacturing Costs Incurred Cost of Goods Completed and Transferred to Finished Goods Ending WIP Inventory
Add:
= Less: =
Finished Goods Beg. Inventory Cost of Goods Completed and Transferred from WIP Goods Available for Sale Cost of Goods Sold Ending Inventory
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-10
Stages of Production and the Flow of Costs - Example
Add: =
Less:
=
Raw Materials Beg. Inventory Purchases Raw Materials Available for Production Raw Materials Transferred to Production Ending Inventory
What is Ending Inventory in February? McGraw-Hill/Irwin
Axel Electronics makes toasters. On February 1, Axel has $15,000 of raw material on hand. Axel’s purchase and transfers to the production floor are indicated below. Date Feb 3 Feb 10 Feb 15 Feb 20 Feb 22 Feb 27
Cost of Purchases $ 8,000 12,000 14,000
Cost of Transfers $ 5,000 11,000 7,000 6,000
9,000 16,000 Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-11
Stages of Production and the Flow of Costs - Example
Add: = Less: =
Raw Materials $15,000 43,000 $58,000 45,000 $13,000
Now let’s look at Work-in-Process. McGraw-Hill/Irwin
Axel Electronics makes toasters. On February 1, Axel has $15,000 of raw material on hand. Axel’s purchase and transfers to the production floor are indicated below. Date Feb 3 Feb 10 Feb 15 Feb 20 Feb 22 Feb 27
Cost of Purchases $ 8,000 12,000 14,000
Cost of Transfers $ 5,000 11,000 7,000 6,000
9,000 16,000 Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-12
Stages of Production and the Flow of Costs - Example
Add: = Less: =
Raw Materials $15,000 43,000 $58,000 45,000 $13,000
Add:
=
What is the amount of cost transferred to Finished Goods in February? McGraw-Hill/Irwin
Less:
=
Work-In-Process Beg. WIP Inventory Raw Materials Transferred In Direct Labor Manufacturing Overhead Total Manufacturing Costs Incurred Cost of Goods Completed and Transferred to Finished Goods Ending WIP Inventory
On February 1, Axel had WIP of $30,000 on the factory floor. During February, Axel paid $92,000 in direct labor wages. Overhead is applied at 150% of direct labor. On 2/28, $22,000 is still in WIP.
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-13
Stages of Production and the Flow of Costs - Example 150 % of $92,000 Add: = Less: =
Raw Materials $15,000 43,000 $58,000 45,000 $13,000
Now let’s look at Finished Goods. McGraw-Hill/Irwin
Add:
= Less: =
Work-In-Process $30,000 45,000 92,000 138,000 $305,000 283,000 $22,000
Transferred to Finished Goods
On February 1, Axel had WIP of $30,000 on the factory floor. During February, Axel paid $92,000 in direct labor wages. Overhead is applied at 150% of direct labor. On 2/28, $22,000 is still in WIP.
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-14
Stages of Production and the Flow of Costs - Example
Add: = Less: =
Raw Materials $15,000 43,000 $58,000 45,000 $13,000
Add:
= Less: =
Work-In-Process $30,000 45,000 92,000 138,000 $305,000 283,000 $22,000
Add:
= Less: =
Finished Goods Beg. Inventory Cost of Goods Completed and Transferred from WIP Goods Available for Sale Cost of Goods Sold Ending Inventory
On February 1, Axel had Finished Goods of $125,000 on hand. At the end of February, a physical inventory count revealed $96,000 in Finished Goods still on hand. What was Cost of Goods Sold for February? McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-15
Stages of Production and the Flow of Costs - Example Cost of goods sold Add: = Less: =
Raw Materials $15,000 43,000 $58,000 45,000 $13,000
Add:
= Less: =
Work-In-Process $30,000 45,000 92,000 138,000 $305,000 283,000 $22,000
Add: = Less: =
Finished Goods $125,000 283,000 $408,000 312,000 $96,000
On February 1, Axel had Finished Goods of $125,000 on hand. At the end of February, a physical inventory count revealed $96,000 in Finished Goods still on hand. What was Cost of Goods Sold for February? McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-16
Learning Objective 2
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-17
Schedule of Cost of Goods Manufactured
Let’s look at a Schedule of Cost of Goods Manufactured for CollegePak Company.
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-18
Schedule of Cost of Goods Manufactured CollegePak Company Schedule of Cost of Goods Manufactured Raw material used
$
Direct labor Total manufacturing overhead
850,000 700,000 1,850,000
Total manufacturing costs Add: Work-in-process inventory, January 1
$ 3,400,000 350,000
Subtotal Deduct: Work-in-process inventory, December 31
$ 3,750,000 400,000
Cost of goods manufactured
$ 3,350,000
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-19
Schedule of Cost Goods Computation of Costof of Raw Material Used Raw-material inventory, January 1 $ Manufactured Add: Purchases of raw materials Raw material available for use Deduct: Raw material inventory, December 31 Raw material used
200,000 800,000 1,000,000 150,000
$ 850,000
CollegePak Company Schedule of Cost of Goods Manufactured Raw material used
$
Direct labor Total manufacturing overhead
850,000 700,000 1,850,000
Total manufacturing costs Add: Work-in-process inventory, January 1
$ 3,400,000 350,000
Subtotal Deduct: Work-in-process inventory, December 31
$ 3,750,000 400,000
Cost of goods manufactured
$ 3,350,000
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-20
Schedule of Cost of Goods Manufactured Include all direct labor costs incurred during the CollegePak Company current period. Schedule of Cost of Goods Manufactured Raw material used
$
Direct labor Total manufacturing overhead
850,000 700,000 1,850,000
Total manufacturing costs Add: Work-in-process inventory, January 1
$ 3,400,000 350,000
Subtotal Deduct: Work-in-process inventory, December 31
$ 3,750,000 400,000
Cost of goods manufactured
$ 3,350,000
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-21
Schedule of Cost of Goods Manufactured Beginning work-inprocess inventory is carried over from the CollegePak Company prior period. Schedule of Cost of Goods Manufactured Raw material used
$
Direct labor Total manufacturing overhead
850,000 700,000 1,850,000
Total manufacturing costs Add: Work-in-process inventory, January 1
$ 3,400,000 350,000
Subtotal Deduct: Work-in-process inventory, December 31
$ 3,750,000 400,000
Cost of goods manufactured
$ 3,350,000
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-22
Schedule of Cost of Goods Manufactured Ending work-in-process inventory contains the cost of unfinished goods, CollegePak Company and is reported in the current assets section of the balance sheet. Schedule of Cost of Goods Manufactured Raw material used
$
Direct labor Total manufacturing overhead
850,000 700,000 1,850,000
Total manufacturing costs Add: Work-in-process inventory, January 1
$ 3,400,000 350,000
Subtotal Deduct: Work-in-process inventory, December 31
$ 3,750,000 400,000
Cost of goods manufactured
$ 3,350,000
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-23
Income Statement for a Manufacturer
Now let’s look at an income statement for CollegePak.
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-24
Income Statement for a Manufacturer
CollegePak Company Income Statement For the Year Ended December 31, 20X2 Sales revenue Less: Cost of goods sold
$ 4,500,000 2,810,000
Gross margin Selling and istrative expenses
$ 1,690,000 1,440,000
Operating profit before taxes
$
McGraw-Hill/Irwin
250,000
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-25
Income Statement for a Manufacturer CollegePak Company Schedule of Cost of Goods Sold For the Year Ended December 31, 20X2 Finished-goods inventory, Jan. 1 Add: Cost of goods manufactured
$
Cost of goods availableCollegePak for sale Company Deduct Finished-goods inventory, Dec. 31
920,000 3,350,000 4,270,000 1,460,000
Income Statement Cost of goods sold $ 2,810,000 For the Year Ended December 31, 20X2 Sales revenue Less: Cost of goods sold
$ 4,500,000 2,810,000
Gross margin Selling and istrative expenses
$ 1,690,000 1,440,000
Operating profit before taxes
$
McGraw-Hill/Irwin
250,000
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-26
Production Costs in the Service Sector
McGraw-Hill/Irwin
A service provider cannot “inventory” its services. The costs of providing the service can be identified and measured, just as occurs in manufacturing industries. Managing and tracking the costs associated with valuechain activities can point to opportunities for improvement.
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-27
Cost Drivers An “activity” is any discrete task that an organization undertakes to make or deliver a good or service. A “cost driver” is some characteristic of the activity that causes costs to be incurred. McGraw-Hill/Irwin
Number of computers made by Dell in a day
Number of flights by Southwest Airlines in a given market
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-28
Learning Objective 4
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-29
Cost Behavior Cost behavior means how a cost will react to changes in the level of business activity.
McGraw-Hill/Irwin
Total variable costs change when activity level changes.
Total fixed costs remain unchanged when activity level changes.
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-30
Total Variable Cost Example
Total Long Distance Telephone Bill
Your total long distance telephone bill is based on how many minutes you talk.
Minutes Talked McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-31
Variable Cost Per Unit Example
Per Minute Telephone Charge
The cost per long distance minute talked is constant. For example, 5 cents per minute.
Minutes Talked McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-32
Total Fixed Cost Example
Monthly Basic Telephone Bill
Your monthly basic telephone bill probably does not change when you make more local calls.
Number of Local Calls McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-33
Fixed Cost Per Unit Example
Monthly Basic Telephone Bill per Local Call
The average cost per local call decreases as more local calls are made.
Number of Local Calls McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-34
Cost Behavior Summary
Summary of Variable and Fixed Cost Behavior Cost
In Total
Per Unit
Variable
Changes proportionately with changes in activity within the relevant range.
Remains constant for each additional unit as long as activity is in the relevant range.
Fixed
Remains the same even when activity changes within the relevant range.
The per unit amount changes each time the level of activity changes due to the fixed nature of the related costs.
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-35
Cost Hierarchy Unit-level Costs
Directly traceable to the decision to produce the level of output
Costs that are incurred for every unit of product manufactured or service produced.
Includes direct material, direct labor, utilities to run equipment, other overhead directly related to the production process. All unit level costs are variable, but not all variable costs are unit level costs. McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-36
Cost Hierarchy Batch-level Costs Costs that are incurred for batch of product manufactured or service produced.
Includes setup costs, material-handling costs related to delivering raw material to the production line, etc.
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-37
Cost Hierarchy Product-level Costs Costs that are incurred for each line of product or service.
Includes design costs for product lines and marketing costs for each product line.
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-38
Cost Hierarchy Facility-level Costs Costs that are incurred to maintain the organization’s overall facility and infrastructure.
Includes production manager’s salary, plant depreciation, and insurance on the facility and equipment.
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-39
Learning Objective 5
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-40
Committed and Discretionary Costs Committed
Discretionary
Long-term obligations, difficult to change in the short term.
Easier to alter in the short term by current managerial decisions.
Rental and/or Lease Financing of Buildings and equipment McGraw-Hill/Irwin
Advertising and Research and Development Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-41
Opportunity Costs The potential benefit that is given up when one alternative is selected over another.
If you were not attending college, you could be earning $20,000 per year. Your opportunity cost of attending college for one year is $20,000.
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-42
Sunk Costs Past payments for resources that cannot be changed by any current or future decision.
Sunk costs should not be considered in decisions. Example: You bought an automobile for $12,000 two years ago. Whatever you do with the automobile in the future, you cannot nullify the original transaction. If it has a trade-in value, that value would become an opportunity cost in your future decisions.
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-43
Traceability of Resources Direct Costs
Indirect Costs
Costs that can be traced easily and conveniently to a product or department.
Costs that need to be allocated, before they can be assigned to a product or department.
Example: Cost of paint in the paint department of an automobile assembly plant.
Example: Cost of national advertising for an airline is indirect to a given flight or route.
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-44
Learning Objective 6
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-45
Absorption (Full) Costing A system of ing for costs in which both fixed and variable production costs are included in product costs.
Fixed Costs Product Variable Costs McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-46
Variable Costing A system of cost ing that assigns only the variable cost of production to products.
Fixed Costs Product Variable Costs McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-47
Learning Objective 7
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-48
Absorption Costing vs. Variable Costing Absorption Costing
Product costs
Variable Costing Direct materials Direct labor Variable mfg. overhead
Product costs
Fixed mfg. overhead Period costs Period costs
McGraw-Hill/Irwin
Selling & . exp.
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-49
Absorption and Variable Costing Let’s see what we can learn about the differences between absorption and variable costing by looking at a numerical example.
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-50
Absorption Costing vs. Variable Costing - Example Howell, Inc. produces a single product with a sales price of $40 and the following cost information:
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-51
Absorption Costing vs. Variable Costing - Example Unit product cost is determined as follows:
Selling and istrative expenses are always treated as period expenses and deducted from revenue as they are incurred. McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-52
Absorption Costing vs. Variable Costing - Example Howell, Inc. had no beginning inventory, produced 30,000 units and sold 28,000 units this year. Absorption Costing Sales (28,000 × $40) Less cost of goods sold: Beginning inventory $ Add COGM (30,000 × $19) 570,000 Goods available for sale 570,000 Ending inventory (2,000 × $19) 38,000 Gross margin Less selling & . exp. Variable (28,000 x $4) $ 112,000 Fixed 250,000 Net income McGraw-Hill/Irwin
$ 1,120,000
532,000 588,000
$
362,000 226,000
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-53
Absorption Costing vs. Variable Costing - Example Variable costs only.
Variable Costing
Sales (28,000 × $40) Less variable expenses: Beginning inventory $ Add COGM (30,000 × $12) 360,000 Goods available for sale 360,000 Ending inventory (2,000 × $12) 24,000 Variable cost of goods sold 336,000 Variable selling & istrative expenses (28,000 × $4) 112,000 Contribution margin Less fixed expenses: Manufacturing overhead $ 210,000 Selling & istrative expenses 250,000 Net income McGraw-Hill/Irwin
$ 1,120,000
All fixed manufacturing overhead is expensed. 448,000 672,000
$
460,000 212,000
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-54
Comparing Absorption and Variable Costing Let’s compare the methods. Cost of Goods Sold
Ending Inventory
Period Expense
Absorption costing Variable mfg. costs $ 336,000 Fixed mfg. costs 196,000 $ 532,000
$ 24,000 14,000 $ 38,000
$
Variable costing Variable mfg. costs $ 336,000 Fixed mfg. costs $ 336,000
$ 24,000 $ 24,000
$
McGraw-Hill/Irwin
$
-
210,000 $ 210,000
Total $ 360,000 210,000 $ 570,000
$ 360,000 210,000 $ 570,000
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-55
Reconciling Income We can reconcile the difference between absorption and variable net income as follows:
Variable costing net income Add: Fixed mfg. overhead costs deferred in inventory (2,000 units × $7 per unit) Absorption costing net income
Fixed mfg. overhead $210,000 = Units produced 30,000 McGraw-Hill/Irwin
$ 212,000
14,000 $ 226,000
= $7.00 per unit
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-56
Extending the Example
Let’s look at the second year of operations for Howell, Inc.
McGraw-Hill/Irwin
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2-57
Howell Inc., Year 2 In its second year of operations, Howell started with an inventory of 2,000 units, produced 30,000 units and sold 32,000 units at $40 each.
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-58
Howell Inc., Year 2 Unit product cost is determined as follows:
There has been no change in Howell’s cost structure. McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-59
Howell Inc., Year 2 Units in ending inventory from the previous period. Absorption Costing Sales (32,000 × $40) Less cost of goods sold: Beg. inventory (2,000 x $19) Add COGM (30,000 × $19) Goods available for sale Ending inventory Gross margin Less selling & . exp. Variable (32,000 × $4) Fixed Net income
$ 1,280,000 $ 38,000 570,000 $ 608,000 $
608,000 672,000
$
378,000 294,000
$ 128,000 250,000
30,000 units produced in the current period. McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-60
Howell Inc., Year 2 Variable Costing Sales (32,000 × $40) Less variable expenses: Beg. inventory (2,000 × $12) Add COGM (30,000 × $12) Goods available for sale Ending inventory Variable cost of goods sold Variable selling & istrative expenses (32,000 × $4) Contribution margin Less fixed expenses: Manufacturing overhead Selling & istrative expenses Net income
McGraw-Hill/Irwin
$ 1,280,000 $
24,000 360,000 $ 384,000 $ 384,000 128,000 $
512,000 768,000
$
460,000 308,000
$ 210,000 250,000
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-61
Summary Income Comparison Costing Method Absorption Variable
1st Period $ 226,000 212,000
2nd Period $ 294,000 308,000
Total $ 520,000 520,000
In the first period, production (30,000 units) was greater than sales (28,000). In the second period, production (30,000 units) was less than sales (32,000). For the two-year period, total absorption income and total variable income are the same. McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-62
Summary
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-63
Learning Objective 8
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-64
Variable versus Absorption Costing All manufacturing costs must be assigned to products to properly match revenues and costs.
Absorption Costing McGraw-Hill/Irwin
Fixed costs are not really the costs of any particular product.
Variable Costing Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-65
Variable versus Absorption Costing Depreciation, taxes, insurance and salaries are just as essential to products as variable costs.
Absorption Costing McGraw-Hill/Irwin
These are capacity costs and will be incurred even if nothing is produced.
Variable Costing Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-66
Variable versus Absorption Costing Absorption costing product costs are misleading for decision making.
Variable Costing McGraw-Hill/Irwin
They are the numbers that appear on our external reports.
Absorption Costing Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-67
Variable versus Absorption Absorption CostingCosting Cost of goods sold decreases because production exceeds sales, leaving a portion of fixed manufacturing costs in inventory. Variable cost Fixed manufacturing overhead Units sold
Units Total Variable Produced Cost 10,000 $100,000 12,000 $120,000 14,000 $140,000 16,000 $160,000 18,000 $180,000 20,000 $200,000 McGraw-Hill/Irwin
$10 $100,000 10,000
Fixed Total Average Manufacturing Manufacturing Manufacturing Overhead Cost Cost $100,000 $200,000 $ 20.00 $100,000 $220,000 $ 18.33 $100,000 $240,000 $ 17.14 $100,000 $260,000 $ 16.25 $100,000 $280,000 $ 15.56 $100,000 $300,000 $ 15.00
Cost of Goods Sold $ 200,000 $ 183,333 $ 171,429 $ 162,500 $ 155,556 $ 150,000
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
Absorption Costing Cost of goods sold decreases because production exceeds sales, leaving a portion of fixed manufacturing costs in inventory.
2-68
Variable versus Absorption Costing COGS for 10,000 units
COGS
$200,000
$150,000
0 ,0 0
34
0
30 ,0 0
0
26 ,0 0
0
22 ,0 0
0
18 ,0 0
0
14 ,0 0
10 ,0 0
0
$100,000
Number of units produced McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-69
Throughput Costing Unit-level spending for direct costs
Product cost
Indirect, past or committed costs Unit-level costs are incurred every time a unit of product is manufactured and will not be incurred again until the next unit is manufactured. McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-70
Throughput Costing Example In an automated process direct material may be the only unit-level cost and so is the only product cost. All other manufacturing costs are expensed as period costs. Incentive to overproduce is reduced
Average unit cost does not vary with changes in production levels.
Advantages McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-71
Learning Objective 9
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-72
Intentional Overproduction of Inventory
Absorption costing: Excess inventory would include more fixed production costs, so that gross income for the period would be artificially higher. An unethical manager would have an incentive to “produce for inventory” at the end of a period, in order to obtain a better looking bottom line. Throughput costing: No such incentive would exist, since fixed production costs would be charged against operating income for the period.
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
2-73
End of Chapter 2
McGraw-Hill/Irwin
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
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