Cost Behavior And Costvolume-profit Analysis

Chapter 20 Cost Behavior and CostVolume-Profit Analysis Accounting, 21st Edition Warren Reeve Fess

PowerPoint Presentation by Douglas Cloud Professor Emeritus of Accounting Pepperdine University

© Copyright 2004 South-Western, a division of Thomson Learning. All rights reserved. Task Force Image Gallery clip art included in this electronic presentation is used with the permission of NVTech Inc.

Some Some of of the the action action has has been been automated, automated, so so click click the themouse mouse when when you you see see this this lightning lightning bolt bolt in in the thelower lower right-hand right-hand corner corner of of the the screen. screen. You You can can point point and and click click anywhere anywhere on on the the screen. screen.

Objectives Objectives 1. Classify costs by their behavior as variable After studying this Afteror studying this costs, fixed costs, mixed costs. you should 2. Compute thechapter, contribution chapter, youmargin, should the contribution margin ratio, and the unit be able to: be able to: contribution margin, and explain how they may be useful to management. 3. Using the unit contribution margin, determine the break-even point and the volume necessary to achieve a target profit.

Objectives Objectives 4. Using a cost-volume profit chart and a profit-volume chart, determine the break-even point and the volume necessary to achieve a target profit.

5. Calculate the break-even point for a business selling more than one product. 6. Compute the margin of safety and the operating leverage, and explain how managers use this concept. 7. List the assumptions underlying cost-volumeprofit analysis.

Cost Cost Behavior Behavior

Variable Variable Cost Cost Jason Inc. produces stereo sound systems under the brand name of J-Sound. The parts for the stereo are purchased from an outside supplier for $10 per unit (a variable cost).

Variable Variable Cost Cost Total Variable Cost Graph

Total Costs

$300,000 $250,000 $200,000 $150,000 $100,000 $50,000

0 10 20 30 Units Produced (in thousands)

Variable Variable Cost Cost

Cost per Unit

Unit Variable Cost Graph $20 $15 $10 $5 0

10 20 30 Units Produced (000)

$300,000 $250,000 $200,000 $150,000 $100,000 $50,000 0 10 20 30 Units Produced (000) Number of Units Produced

5,000 units 10,000 15,000 20,000 25,000 30,000

Cost per Unit

Total Costs

Variable Variable Cost Cost $20 $15 $10 $5 0

10 20 30 Units Produced (000)

Direct Materials Cost per Unit

Total Direct Materials Cost

$10 10 10 10 10 10

$ 50,000 l00,000 150,000 200,000 250,000 300,000

Fixed Fixed Costs Costs The production supervisor for Minton Inc.’s Los Angeles plant is Jane Sovissi. She is paid $75,000 per year. The plant produces from 50,000 to 300,000 bottles of perfume.

La Fleur

Fixed Fixed Costs Costs Number of Bottles Produced

Total Salary for Jane Sovissi

50,000 bottles 100,000 15,000 20,000 25,000 30,000

$75,000 75,000 75,000 75,000 75,000 75,000

Salary per Bottle Produced $1.500 0.750 0.500 0.375 0.300 0.250

Fixed Costs Unit Fixed Cost Graph

$150,000 $125,000 $100,000 $75,000 $50,000 $25,000 0 100 200 300 Bottles Produced (000) Number of Bottles Produced

50,000 bottles 100,000 15,000 20,000 25,000 30,000

Cost per Unit

Total Costs

Total Fixed Cost Graph

$1.50 $1.25 $1.00 $.75 $.50 $.25 0

100 200 300 Units Produced (000)

Total Salary for Jane Sovissi

Salary per Bottle Produced

$75,000 75,000 75,000 75,000 75,000 75,000

$1.500 0.750 0.500 0.375 0.300 0.250

Simpson Inc. manufactures sails using rented equipment. The rental charges are $15,000 per year, plus $1 for each machine hour used over 10,000 hours.

Mixed Mixed Costs Costs

Total Costs

Total Mixed Cost Graph $45,000 $40,000 $35,000 $30,000 $25,000 $20,000 $15,000 $10,000 $5,000 0

10 20 30 40 Total Machine Hours (000)

Mixed Mixed costs costs are are sometimes sometimes called called semivariable semivariable or or semifixed semifixed costs. costs. Mixed Mixed costs costs are are usually usually separated separated into into their their fixed fixed and and variable variable components components for for management management analysis. analysis.

Mixed Mixed Costs Costs The high-low method is a simple way to separate mixed costs into their fixed and variable components.

Low High

High-Low Method Actual costs incurred ProductionTotal (Units) Cost June July August September October

1,000 $45,550 1,500 52,000 2,100 61,500 1,800 57,500 750 41,250

What month has the highest level of activity in terms of cost?

Highest level of activity ($) minus lowest level of activity ($) Variable cost per unit = Highest level of activity (n) minus lowest level of activity (n)

High-Low Method Actual costs incurred ProductionTotal (Units) Cost June July August September October

1,000 $45,550 1,500 52,000 2,100 61,500 1,800 57,500 750 41,250

What month has the highest level of activity in terms of cost?

$61,500 minus lowest level of activity ($) Variable cost per unit = Highest level of activity (n) minus lowest level of activity (n)

High-Low Method Actual costs incurred ProductionTotal (Units) Cost June July August September October

1,000 $45,550 1,500 52,000 2,100 61,500 1,800 57,500 750 41,250

For the highest level of cost, what is the level of production?

$61,500 minus lowest level of activity ($) Variable cost per unit = Highest of lowest activitylevel (n) minus 2,100level minus of lowestactivity level of(n) activity (n)

High-Low Method Actual costs incurred ProductionTotal (Units) Cost June July August September October

1,000 $45,550 1,500 52,000 2,100 61,500 1,800 57,500 750 41,250

Variable cost per unit =

What month has the lowest level of activity in terms of cost?

$61,500 minus lowest level of $57,500 – $41,250 activity ($) 2,100 2,100 minus – lowest 750 level of activity (n)

High-Low Method Actual costs incurred ProductionTotal (Units) Cost June July August September October

1,000 $45,550 1,500 52,000 2,100 61,500 1,800 57,500 750 41,250

What is the variable cost per unit?

$20,250 $57,500 – $41,250 Variable cost per unit = $15 1,350 2,100 – 750

High-Low Method Actual costs incurred ProductionTotal (Units) Cost June July August September October

1,000 $45,550 1,500 52,000 2,100 61,500 1,800 57,500 750 41,250

Variable cost per unit = $15

What is the total fixed cost (using the highest level)?

Total cost = (Variable cost per unit x Units of production) + Fixed cost $61,500 = ($15 x 2,100) + Fixed cost $61,500 = ($15 x 2,100) + $30,000

High-Low Method Actual costs incurred ProductionTotal (Units) Cost June July August September October

1,000 $45,550 1,500 52,000 2,100 61,500 1,800 57,500 750 41,250

Variable cost per unit = $15

The fixed cost is the same at the lowest level.

Total cost = (Variable cost per unit x Units of production) + Fixed cost $41,250 = ($15 x 750) + Fixed cost $41,250 = ($15 x 750) + $30,000

Variable Costs

Fixed Costs

Unit costs remain the sameTotal per Units unit Produced regardless Review of activity. Total costs increase and Per Unit Cost

decreases proportionately Unit Variable Costs with activity level.

Total Costs

Total Fixed Costs

Total costs increase and decreases with Total Units Produced activity level. Unit Unitcosts Fixedremain Costs the same regardless of activity. Per Unit Cost

Total Costs

Total Variable Costs

Total Units Produced Total Units Produced

Contribution Margin Income Statement Sales (50,000 units) Variable costs Contribution margin Fixed costs Income from operations

The The contribution contribution margin margin isis available available to to cover cover the the fixed fixed costs costs and and income income from from operations. operations. Contribution $1,000,000 600,000 $ 400,000 300,000 $ 100,000

margin

FIXED COSTS

Income from Operations

Contribution Margin Income Statement Sales (50,000 units) Variable costs Contribution margin Fixed costs Income from operations

Sales

Sales

=

–

Variable costs Variable costs

$1,000,000 600,000 $ 400,000 300,000 $ 100,000

+

=

Fixed costs

+

Income from operations

Contributio n margin

Contribution Margin Ratio Sales (50,000 units) Variable costs Contribution margin Fixed costs Income from operations

$1,000,000 600,000 $ 400,000 300,000 $ 100,000

100% 60% 40% 30% 10%

Sales – Variable costs Contribution margin ratio = Sales $1,000,000 – $600,000 Contribution margin ratio = $1,000,000 Contribution margin ratio = 40%

Contribution Margin Ratio Sales (50,000 units) Variable costs Contribution margin Fixed costs Income from operations

$1,000,000 600,000 $ 400,000 300,000 $ 100,000

100% 60% 40% 30% 10%

$20 12 $ 8

The Thecontribution contributionmargin margincan canbe beexpressed expressedthree threeways: ways: 1.1.Total Totalcontribution contributionmargin marginin indollars. dollars. 2.2.Contribution Contributionmargin marginratio ratio(percentage). (percentage). 3.3.Unit Unitcontribution contributionmargin margin(dollars (dollarsper perunit). unit).

What What is is the the break-even break-even point? point?

Revenues

=

Break-even

Costs

Calculating Calculating the the Break-Even Break-Even Point Point Sales (? units) Variable costs Contribution margin Fixed costs Income from operations

$ $ $

? ? 90,000 90,000 0

$25 15 $10

At At the the break-even break-even point, point, fixed fixed costs costs and and the the contribution contribution margin margin are are equal. equal.

Calculating Calculating the the Break-Even Break-Even Point Point

In InUnits Units

Sales($25 ($25xx?9,000) Sales units) $ Variablecosts costs($15 ($15xx?9,000) Variable units) Contributionmargin margin Contribution $ Fixedcosts costs Fixed Incomefrom fromoperations operations Income $

$225,000 ? 135,000 ? $90,000 90,000 90,000 90,000 $ 00

$25 15 $10

$90,000 Fixed costs Break-even sales (units) = 9,000 units $10 margin Unit contribution

PROOF! PROOF!

Calculating Calculating the the Break-Even Break-Even Point Point

In InUnits Units

Sales ($250 x ? units) $ ? Variable costs ($145 x ? units) ? Contribution margin $ ? Fixed costs 840,000 Income from operations $ 0

$250 145 $105

$840,000 Fixed costs Break-even sales (units) = 8,000 units $105 margin Unit contribution The unit selling price is $250 and unit variable cost is $145. Fixed costs are $840,000.

Calculating Calculating the the Break-Even Break-Even Point Point

In InUnits Units

Next, assume$ Sales ($25 x ?Next, units) assume ? Variable costs ($15 x ?costs units)is ? variable variable costs is Contribution margin by $5. $ ? increased increased by $5. Fixed costs 840,000 Income from operations $ 0

$250 $250 145 150 $105 $100

$840,000 Fixed costs Break-even sales (units) = 8,400 units $100 margin Unit contribution The unit selling price is $250 and unit variable cost is $145. Fixed costs are $840,000.

Calculating Calculating the the Break-Even Break-Even Point Point

In InUnits Units

Sales Variable costs Contribution margin Fixed costs Income from operations

$

? ? $ ? $600,000 $ 0

$50 30 $20

$600,000 Fixed costs Break-even sales (units) = 30,000 units $20 margin Unit contribution A firm currently sells their product at $50 per unit and it has a related unit variable cost of $30. The fixed costs are $600,000.

Calculating Calculating the the Break-Even Break-Even Point Point

In InUnits Units

Management Management increases increases Salesthe $ the selling selling price price from from Variable costs $50 to $60. $50 to Contribution margin$60. $ Fixed costs Income from operations

? ? ? $600,000 $ 0

$60 $50 30 30 $30 $20

$600,000 Fixed costs Break-even sales (units) = 20,000 units $30 margin Unit contribution

Summary Summary of of Effects Effects of of Changes Changes on on Break-Even Break-Even Point Point

Target Target Profit Profit Sales (? units) Variable costs Contribution margin Fixed costs Income from operations

$

? ? $ ? 200,000 $ 0

In In Units Units $75 45 $35

Fixed costs are estimated at $200,000, and the desired profit is $100,000. The unit selling price is $75 and the unit variable cost is $45. The firm wishes to make a $100,000 profit.

Target Target Profit Profit Sales (? units) Variable costs Contribution margin Fixed costs Income from operations

$

? ? $ ? 200,000 $ 0

In In Units Units

Target Target profit profit isis $75 here used used here to to refer refer 45 to to “Income “Income from from $35 operations.” operations.”

Fixed costs ++desired profit $200,000 $100,000 Sales (units) = 10,000 units Unit contribution margin $30

Target Target Profit Profit Sales (10,000 units x $75) $750,000 Variable costs (10,000 x $45) 450,000 Contribution margin $300,000 Fixed costs 200,000 Income from operations $100,000

$75 45 $30

Proof Proof that that sales sales of of 10,000 10,000 units units will will provide provide aa profit profit of of $100,000. $100,000.

Graphic Approach to Cost-Volume-Profit Analysis

Sales and Costs ($000)

Cost-Volume-Profit Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 0

Total Sales

Variable Costs

60% 1

2

3

4 5 6 7 Units of Sales (000)

Unit $$50 Unitselling sellingprice price 50 Unit 30 Unitvariable variablecost cost 30 Unit Unitcontribution contributionmargin margin $$20 20 Total $100,000 Totalfixed fixedcosts costs $100,000

8

9 10

Sales and Costs ($000)

Cost-Volume-Profit Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 0

Contribution Margin

40% 60% 1

2

3

4 5 6 7 Units of Sales (000)

Unit $$50 Unitselling sellingprice price 50 100% Unit 30 Unitvariable variablecost cost 30 60% Unit Unitcontribution contributionmargin margin $$20 20 40% Total $100,000 Totalfixed fixedcosts costs $100,000

8

9 10

Sales and Costs ($000)

Cost-Volume-Profit Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 0

Total Costs Fixed Costs

1

2

3

4 5 6 7 Units of Sales (000)

Unit $$50 Unitselling sellingprice price 50 100% Unit 30 Unitvariable variablecost cost 30 60% Unit Unitcontribution contributionmargin margin $$20 20 40% Total $100,000 Totalfixed fixedcosts costs $100,000

8

9 10

Sales and Costs ($000)

Cost-Volume-Profit Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 0

Break-Even Point

1

2

3

4 5 6 7 Units of Sales (000)

Unit $$50 Unitselling sellingprice price 50 100% Unit 30 Unitvariable variablecost cost 30 60% Unit Unitcontribution contributionmargin margin $$20 20 40% Total $100,000 Totalfixed fixedcosts costs $100,000

8

9 10

$100,000 = 5,000 units $20

Sales and Costs ($000)

Cost-Volume-Profit Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 0

Operating Profit Area

Operating Loss Area

Units of Sales (000)

Unit $$50 Unitselling sellingprice price 50 100% Unit 30 Unitvariable variablecost cost 30 60% Unit Unitcontribution contributionmargin margin $$20 20 40% Total $100,000 Totalfixed fixedcosts costs $100,000

Operating Profit (Loss) $000’s

$100 $75 $50 $25 $ 0 $(25) $(50) $(75) $(100)

1

2

3

4

5

6

7

Relevant Relevant range range isis 8 10,000 9 10 units 10,000 units

Units of Sales (000’s)

Sales Sales(10,000 (10,000units unitsxx$50) $50) Variable Variablecosts costs(10,000 (10,000units unitsxx$30) $30) Contribution Contributionmargin margin(10,000 (10,000units unitsxx$20) $20) Fixed Fixedcosts costs Operating Operatingprofit profit

$500,000 $500,000 300,000 300,000 $200,000 $200,000 100,000 100,000 $100,000 $100,000

Operating Profit (Loss) $000’s

$100 $75 $50 $25 $ 0 $(25) $(50) $(75) $(100)

Profit Line

Operating profit Operating loss 1

2

3

4

5

6

7

8

Units of Sales (000’s) Maximum loss Maximum loss isisequal to Sales (10,000 units equal tothe the Sales (10,000 unitsxx$50) $50) total costs. Variable costs (10,000 totalfixed fixed costs. Variable costs (10,000units unitsxx$30) $30) Contribution Contributionmargin margin(10,000 (10,000units unitsxx$20) $20) Fixed Fixedcosts costs Operating Operatingprofit profit

9

Maximum Maximum profit profit within within the the relevant relevant 10 range. range. $500,000 $500,000 300,000 300,000 $200,000 $200,000 100,000 100,000 $100,000 $100,000

Operating Profit (Loss) $000’s

$100 $75 $50 $25 $ 0 $(25) $(50) $(75) $(100)

Operating profit Operating loss 1

2

Break-Even Point

3

4

5

6

7

8

9 10

Units of Sales (000’s)

Sales Sales(10,000 (10,000units unitsxx$50) $50) Variable Variablecosts costs(10,000 (10,000units unitsxx$30) $30) Contribution Contributionmargin margin(10,000 (10,000units unitsxx$20) $20) Fixed Fixedcosts costs Operating Operatingprofit profit

$500,000 $500,000 300,000 300,000 $200,000 $200,000 100,000 100,000 $100,000 $100,000

Sales Mix Considerations

Cascade Company sold 8,000 units of Product A and 2,000 units of Product B during the past year. Cascade Company’s fixed costs are $200,000. Other relevant data are as follows: Products A B Sales $ 90 $140 Variable costs 70 95 Contribution margin $ 20 $ 45 Sales mix 80% 20%

Sales Sales Mix Mix Considerations Considerations

Sales Variable costs Contribution margin Sales mix Product contribution margin

Products A B $ 90 $140 70 95 $ 20 $ 45 80% 20% $16

$ 9 $25

Fixed costs, $200,000

Sales Sales Mix Mix Considerations Considerations Product contribution margin

Products A B $16 $ 9 $25

Break-even sales units

$200,000 $25

Fixed costs, $200,000

Sales Sales Mix Mix Considerations Considerations Product contribution margin

Products A B $16 $ 9 $25

Break-even sales units

$200,000 $25

= 8,000 units

Fixed costs, $200,000

Sales Sales Mix Mix Considerations Considerations Product contribution margin

Products A B $16 $ 9 $25

A: 8,000 units x Sales Mix (80%) = B: 8,000 units x Sales Mix (20%) =

6,400 1,600

Product A Product B Sales: 6,400 units x $90 1,600 units x $140 Total sales Variable costs: 6,400 x $70 1,600 x $95 Total variable costs Contribution margin Fixed costs Income from operations

$576,000 $576,000

$224,000 $224,000

$576,000 224,000 $800,000

$152,000 $152,000 $ 72,000

$448,000 152,000 $600,000 $200,000

$448,000 $448,000 $128,000

Break-even point PROOF

Total

200,000 $ 0

Margin of Safety

Margin of Safety =

Sales – Sales at break-even point

Margin of Safety =

Sales $250,000 – $200,000 $250,000

Margin of Safety = 20%

The margin of safety indicates the possible decrease in sales that may occur before an operating loss results.

Operating Operating Leverage Leverage

Operating Operating Leverage Leverage Sales Variable costs Contribution margin Fixed costs Income from operations Contribution margin

Jones Inc. $400,000 300,000 $100,000 80,000 $ 20,000 ?

Wilson Inc. $400,000 300,000 $100,000 50,000 $ 50,000 ?

Both Bothcompanies companieshave havethe thesame samecontribution contributionmargin. margin.

Contribution margin Income from operations

Operating Operating Leverage Leverage Sales Variable costs Contribution margin Fixed costs Income from operations Contribution margin

Jones Inc.:

Jones Inc. $400,000 300,000 $100,000 80,000 $ 20,000 5.0

$100,000margin Contribution

Income $20,000 from operations

Wilson Inc. $400,000 300,000 $100,000 50,000 $ 50,000 ?

= 5.0

Operating Operating Leverage Leverage Sales Variable costs Contribution margin Fixed costs Income from operations Contribution margin

Jones Inc.

Jones Inc. $400,000 300,000 $100,000 80,000 $ 20,000 5.0

$100,000margin Contribution

Income $20,000 from operations

Wilson Inc. $400,000 300,000 $100,000 50,000 $ 50,000 ?

= 5.0

Operating Operating Leverage Leverage Sales Variable costs Contribution margin Fixed costs Income from operations Contribution margin

Jones Inc. $400,000 300,000 $100,000 80,000 $ 20,000 5.0

Wilson Inc. $400,000 300,000 $100,000 50,000 $ 50,000 2.0

Capital intensive?

Wilson Inc.:

Contribution $100,000margin

Income $50,000 from operations

Labor intensive?

= 2.0

Assumptions Assumptions of of Cost-Volume-Profit Cost-Volume-Profit Analysis Analysis The reliability of cost-volume-profit analysis depends upon several assumptions. 1. Total sales and total costs can be represented by straight lines. 2. Within the relevant range of operating activity, the efficiency of operations does not change. 3. Costs can be accurately divided into fixed and variable components. 4. The sales mix is constant. 5. There is no change in the inventory quantities during the period.

Chapter 20 The The End End