Chapter 6

Cost-Volume-Profit Analysis and Relevant Costing

1. How is breakeven point computed and what does it

represent?

2. How do costs, revenues, and contribution margin

interact with changes in an activity base (volume)?

Learning Objectives

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3. How does cost-volume-profit (CVP) analysis in single-

product and multiproduct firms differ?

4. What are the underlying assumptions of CVP analysis

and how do these assumptions create a short-run

managerial perspective?

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Continuing . . . Learning Objectives

5. How do quality decisions affect the components of CVP

analysis?

6. What constitutes relevance in a decision-making

situation?

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Continuing . . . Learning Objectives

7. How can management best utilize a scarce

resource?

8. What is the relationship between sales mix and

relevant costing problems?

Continuing . . . Learning Objectives

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9. How can pricing decisions be used to

maximize profit?

10. How can product margin be used to determine

whether a product line should be retained or

eliminated?

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Continuing . . . Learning Objectives

11. How are breakeven and profit-volume graphs

prepared? (Appendix 1)

12. What are the differences between absorption and

variable costing? ( Appendix 2)

13. Why is linear programming a valuable tool for

managers? (Appendix 3)

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Continuing . . . Learning Objectives

The Breakeven Point (BEP)

The level of activity, in units or dollars, at which

REVENUES = COSTS

Basic Assumption: Relevant Range

Company is operating within the relevant

range of activity specified in determining the revenue

and cost information used.

Total$

Activity Level

RelevantRange

Basic Assumption: Revenue

Total revenue fluctuates in direct proportion to level of activity or volume. On a per unit basis, the selling

price remains constant.

Total$

Activity Level

Basic Assumption: Variable Costs

Total variable costs fluctuate in direct proportion to level of activity or volume. On a per unit basis,

variable costs remain constant.

Total$

Activity Level

Basic Assumption: Fixed Costs

Total fixed costs remain constant relative to activity level changes. Per-unit fixed costs decrease as

volume increases and increase as volume decreases.

Total$

Activity Level

Basic Assumption: Mixed Costs

Mixed costs must be separated into variable and fixed elements.

Total$

Activity Level

Cost Behavior Example

Selling price per ice bucket $40

Variable production cost per ice bucket $20Variable selling cost per ice bucket 4Total variable cost per ice bucket $24

Fixed production costs $100,000Fixed selling and administrative costs 20,000

Contribution Margin Per Unit

Contribution margin per unit equals selling price per unit less variable cost per unit.

sp -vc = cm

$40 - $24 = $16

Contribution Margin Ratio

Contribution margin ratio is per-unit contribution margin divided by selling price, or total contribution margin divided by total sales dollars.

cm/sp=cm%

$16 / $40 = 40%

Breakeven Point

Breakeven point is the point at which profits are

zero because total revenues equal total costs, or

Total revenues = Total variable costs + Total fixed costs

Continuing . . . Breakeven Point

Total fixed costs In units = ---------------------

CM per unit

Total fixed costs In sales dollars = ---------------------

CM ratio

Continuing . . . Breakeven Point

$120,000 In units = ----------- = 7,500 ice buckets

$16

$120,000 In sales dollars = ----------- = $300,000

.40

CVP Analysis: Fixed Amount of

Profit Before Taxes (PBT)

Total fixed costs + PBTIn units = ------------------------------

CM per unit

Total fixed costs + PBTIn sales dollars = ------------------------------

CM ratio

CVP Analysis: Fixed Amount of

Profit Before Taxes (PBT)

$120,000 + $64,000In units = ------------------------ = 11,500 buckets

$16

$120,000 + $64,000In sales dollars = ------------------------ = $460,000

.40

CVP Analysis: Variable Amount

of Profit Before Taxes

Assume PUBT desired is 25% on sales

Therefore, PUBT = .25 ($40) = $10

Total fixed costsSales in units = ---------------------------

CM per unit - PUBT

$120,000Sales in units = --------------- = 20,000 ice buckets

$16 - $6

CVP Analysis: Variable Amount

of Profit Before Taxes

Assume PUBT desired is 25% on sales

Therefore, PUBT = .25 ($40) = $10

Total fixed costsSales in $ = ---------------------

CM% - PUBT%

$120,000Sales in $ = --------------- = $800,000 .40 - .25

Income Statement

Dollars Percentages

Sales $800,000 100%

Variable costs 480,000 60%

Contribution margin $320,000 40%

Fixed costs 120,000 15%

Income $200,000 25%======= ==

CVP Analysis - Multiple Products

Ice ServingBuckets Sets

Selling price $40 $24Variable cost 24 12Contribution margin $16 $12

Contribution margin ratio 40.0% 50.0%Sales mix* 80.6% 19.4%

*5:2 ratio

Continuing . . . CVP Analysis -

Multiple Products

Ice ServingBuckets Sets

Contribution margin ratio 40.0% 50.0%

Sales mix* 80.6% 19.4%

Weighted contribution margin 32.2% 9.7%

Contribution margin ratio per bag 41.9%

*5:2 ratio

Continuing . . . CVP Analysis -

Multiple Products

Total fixed costs BEP in sales dollars = -----------------------

CM ratio per bag

($120,000 + $30,000*) BEP in sales dollars = ----------------------------

.419

= $357,995

*$30,000 of additional fixed cost is incurred to produce both units

Scarce Resource -- Machine Hours

Ice Juice Crushers Extractors

Selling price per unit $15 $12Variable production cost per unit: Direct materials $3 $3 Direct labor 4 2 Variable overhead 3 1Total variable cost 10 6Unit contribution margin $5 $6Units of output per machine hour 30 20Contribution margin per machine hour $150 $120

Sales Mix Decisions

How many of each product?

Relevant Costs in

Product Line Decisions

• Revenues associated with product• Variable costs associated with product• Avoidable fixed costs • Consider product margin

Revenues - Variable costs - Avoidable fixed costs

Exhibit 6-12: Partial Product Line

Income Statement

ElectricSkillet

Sales $75,000Total direct variable expenses 43,750Total contribution margin $31,250Total fixed expenses* 39,500Net loss ($8,250)

*Fixed expenses:Avoidable fixed expenses $25,000Unavoidable fixed expenses 4,500Allocated common costs 10,000 Total $39,500

Exhibit 6-13: Product Margin for

the Electric Skillet Product Line

Electric

Skillet

Sales $75,000

Total direct variable expenses 43,750

Total contribution margin $31,250

Avoidable fixed expenses 25,000

Product margin $6,250

CVP Graph

Total$

Volume

Total Costs

Total RevenuesBEP

Profit-Volume Graph

BEP

Fixed Costs

Volume

Profit or Loss

Total$

Absorption Costing

• Also known as full costing• Treats costs of all manufacturing components as

inventoriable, or product, costs– Direct materials

– Direct labor

– Variable factory overhead

– Fixed factory overhead

• Presents expenses on income statement according to functional classifications

– Cost of goods sold

– Selling expenses

– Administrative expenses

Variable Costing

• Also known as direct costing

• Includes only variable production costs as inventoriable, or product, costs

– Direct materials

– Direct labor

– Variable factory overhead

• Fixed factory overhead costs treated as period expenses

• Income statement separates costs by cost behavior– May also present expenses by functional classifications within

behavioral categories

Absorption Costing

Income Statement

Sales XXXCost of Goods Sold:

Beginning inventory XXXCost of goods manufactured XXX Cost of goods available XXXEnding inventory XXX

Cost of goods sold XXXGross Margin XXXOperating Expenses:

Selling XXXAdministrative XXX XXX

Income before Taxes XXX

Variable Costing

Income StatementSales XXXCost of Goods Sold:

Beginning inventory XXXCost of goods manufactured XXX Cost of goods available XXXEnding inventory XXX

Variable cost of goods sold XXXProduct Contribution Margin XXXVariable Selling Expense XXXTotal Contribution Margin XXXFixed Expenses:

Factory XXXSelling XXXAdministrative XXX XXX

Income before Taxes XXX

Absorption Costing vs. Variable

Costing Income Statements

Absorption Costing Variable Costing:

Sales $60,000 Sales $60,000

Cost of sales 30,000 Variable costs:

Gross profit $30,000 Cost of sales 30,000

Operating expenses: Operating expenses 6,000

Variable $6,000 Total variable costs $36,000

Fixed 20,000 Contribution margin: $24,000

Total operating expenses $26,000 Fixed costs 20,000

Income $4,000 Income $4,000

Linear Programming

• Used to solve problems with one objective and multiple limiting factors

• Objective

• Constraints

– Resource

– Demand

– Technical product requirements

– Non-negativity

• Optimal solution

• Simplex