Chapter 18 Cost Behavior and CostVolumeProfit Analysis Objectives

Chapter 18 Cost Behavior and Cost-Volume-Profit Analysis Objectives 1. Classify costs by their behavior as variable costs, fixed costs, or mixed costs. 2. Compute the contribution margin, the contribution margin ratio, and the unit 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 4. Using a cost-volume profit chart and a profit-volume chart, determine the breakeven 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 costvolume-profit analysis.

Cost Behavior Variable 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 Cost $300, 000 $250, 000 $200, 000 $150, 000 $100, 000 $50, 000 0 10 20 30 Units Produced (in thousands) Unit Variable Cost Graph $20 Cost per Unit Total Costs Total Variable Cost Graph $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 Cost $20 $15 $10 $5 0 10 20 30 Units Produced (000) Direct Materials Cost per Unit Total Direct Materials Cost $10 10 10 $ 50, 000 l 00, 000 150, 000 200, 000 250, 000 300, 000

Fixed 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 Costs Number of Bottles Produced Total Salary for Jane Sovissi 50, 000 bottles 100, 000 150, 000 200, 000 250, 000 300, 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 $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 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 costs are sometimes called semivariable or semifixed costs. Mixed costs are usually separated into their fixed and variable components for management analysis.

Mixed 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 Production. Total (Units) Cost $ June July August September October Activity relates 1, 000 $45, 550 to units of 1, 500 production 52, 000 2, 100 61, 500 1, 800 57, 500 Highest level of activity ($) minus 750 41, 250 lowest level of activity ($) ariable cost per unit = Highest level of activity (units) minus lowest level of activity (units)

High-Low Method Actual costs incurred Production. Total (Units) Cost June 1, 000 $45, 550 July 1, 500 52, 000 August 2, 100 61, 500 September 1, 800 $61, 500 – $41, 250 57, 500 Variable cost per unit = October 750 41, 250 2, 100 – 750 = $15 $20, 250 = 1, 350

High-Low Method Actual costs incurred Production. Total (Units) Cost Variable cost per unit = $15 What is the total 1, 000 $45, 550 fixed cost (using the July 1, 500 highest level)? 52, 000 August 2, 100 61, 500 September 1, 800 cost per unit x Units of production) Total cost = (Variable 57, 500 cost + Fixed October 750 41, 250 June $61, 500 = ($15 x 2, 100) + Fixed cost = ($15 x 2, 100) + $30, 000

High-Low Method Actual costs incurred Production. Total (Units) Cost June Variable cost per unit = $15 The fixed cost is the same at the lowest level. 1, 000 $45, 550 July 1, 500 52, 000 August 2, 100 61, 500 September 1, 800 cost per unit x Units of production) Total cost = (Variable 57, 500 cost + Fixed October 750 41, 250 $41, 250 = ($15 x 750) + Fixed cost = ($15 x 750) + $30, 000

Variable Costs Fixed Costs Unit costs remain the same. Total 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 level. Produced activity Unitcosts Fixedremain Costs the same regardless of activity. Per Unit Cost Total Costs Total Variable Costs Total Units Produced

Contribution Margin Income Statement Sales (50, 000 units) Variable costs Contribution margin Fixed costs Income from operations The contribution margin is available to cover the fixed costs and income from operations. Contribution $1, 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 – Variable costs = $1, 000 600, 000 $ 400, 000 300, 000 $ 100, 000 Contribution margin

Contribution Margin Ratio Sales (50, 000 units) Variable costs Contribution margin Fixed costs Income from operations $1, 000 600, 000 $ 400, 000 300, 000 $ 100, 000 100% 60% 40% 30% 10% Sales – Variable costs Contribution margin ratio = Sales $1, 000 – $600, 000 Contribution margin ratio = $1, 000 Contribution margin ratio = 40%

Contribution Margin Ratio Sales (50, 000 units) Variable costs Contribution margin Fixed costs Income from operations $1, 000 600, 000 $ 400, 000 300, 000 $ 100, 000 100% 60% 40% 30% 10% $20 12 $ 8 The contribution margin can be expressed three ways: 1. Total contribution margin in dollars. 3. Contribution margin ratio (percentage). 3. Unit contribution margin (dollars per unit).

What is the break-even point? Revenues = Break-even Costs

Calculating the Break-Even Point Sales (? units) Variable costs Contribution margin Fixed costs Income from operations $ $ $ ? ? 90, 000 0 $25 15 $10 At the break-even point, fixed costs and the contribution margin are equal.

Calculating the Break-Even Point In Units Sales($25 xx? 9, 000) Sales units) $ Variablecosts($15 xx? 9, 000) Variable units) Contributionmargin Contribution $ Fixedcosts Fixed Incomefromoperations Income $ Break-even sales (units) = = = $225, 000 ? 135, 000 ? $90, 000 $ 00 $25 15 $10 Fixed costs Unit contribution margin $90, 000 $10 9, 000 units

Calculating the Break-Even Point In 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 the Break-Even Point In Units Sales ($25 x ? Next, units) assume$ ? variable Variable costs ($15 x ? costs units)is ? Contribution margin by $5. $ ? increased Fixed costs 840, 000 Income from operations $ 0 $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 the Break-Even Point In 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 the Break-Even Point In Units Management increases Salesthe selling price from $ Variable costs $50 to $60. Contribution margin Fixed costs Income from operations ? ? $600, 000 $ 0 $60 $50 30 $20 $600, 000 Fixed costs Break-even sales (units) = 20, 000 units $30 margin Unit contribution

Summary of Effects of Changes on Break-Even Point

Target Profit Sales (? units) Variable costs Contribution margin Fixed costs Income from operations $ ? ? $ ? 200, 000 $ 0 In 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 Profit Sales (? units) Variable costs Contribution margin Fixed costs Income from operations $ ? ? $ ? 200, 000 $ 0 In Units $75 45 $30 Fixed costs ++ target profit $200, 000 $100, 000 Sales (units) = 10, 000 units Unit contribution margin $30

Target 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 that sales of 10, 000 units will provide a profit of $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 selling price Unit variable cost Unit contribution margin Total fixed costs $100, 000 $ 50 30 $ 20 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 selling price Unit variable cost Unit contribution margin Total fixed costs $100, 000 $ 50 100% 30 60% $ 20 40% 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 selling price Unit variable cost Unit contribution margin Total fixed costs $100, 000 $ 50 100% 30 60% $ 20 40% 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 selling price Unit variable cost Unit contribution margin Total fixed costs $100, 000 $ 50 100% 30 60% $ 20 40% 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 selling price Unit variable cost Unit contribution margin Total fixed costs $100, 000 $ 50 100% 30 60% $ 20 40%

Operating Profit (Loss) $000’s $100 $75 $50 $25 $ 0 $(25) $(50) $(75) $(100) 1 2 3 4 5 6 7 Relevant range is 8 10, 000 9 10 units Units of Sales (000’s) Sales (10, 000 units x $50) Variable costs (10, 000 units x $30) Contribution margin (10, 000 units x $20) Fixed costs Operating profit $500, 000 300, 000 $200, 000 100, 000 $100, 000

Operating Profit (Loss) $000’s $100 $75 $50 $25 $ 0 $(25) Operating loss $(50) $(75) $(100) 1 2 3 Profit Line Operating profit 4 5 6 7 Units of Sales (000’s) Maximum loss is equal (10, 000 to the total Sales units x $50) fixed costs. Variable costs (10, 000 units x $30) Contribution margin (10, 000 units x $20) Fixed costs Operating profit 8 9 Maximum profit within the relevant 10 range. $500, 000 300, 000 $200, 000 100, 000 $100, 000

Operating Profit (Loss) $000’s $100 $75 $50 $25 $ 0 $(25) Operating loss $(50) $(75) $(100) 1 2 3 Operating profit Break-Even Point 4 5 6 7 8 9 10 Units of Sales (000’s) Sales (10, 000 units x $50) Variable costs (10, 000 units x $30) Contribution margin (10, 000 units x $20) Fixed costs Operating profit $500, 000 300, 000 $200, 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 Mix 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 Mix Considerations Product contribution margin Products A B $16 $ 9 $25 Break-even sales units $200, 000 $25 Fixed costs, $200, 000

Sales Mix 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 Mix 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 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 Product B Total $224, 000 $576, 000 224, 000 $800, 000 $152, 000 $ 72, 000 $448, 000 152, 000 $600, 000 $200, 000 $576, 000 $448, 000 $128, 000 Break-even point PROOF 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 Leverage

Operating 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 companies have the same contribution margin. Contribution margin Income from operations

Operating 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, 000 margin Contribution Income $20, 000 from operations Wilson Inc. $400, 000 300, 000 $100, 000 50, 000 $ 50, 000 ? = 5. 0

Operating 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 ? $100, 000 margin Contribution Income $20, 000 from operations = 5. 0

Operating 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, 000 margin Income $50, 000 from operations Labor intensive? = 2. 0

Assumptions of Cost-Volume-Profit 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 18 The End