Questions Addressed by Cost-Volume-Profit Analysis CVP analysis is used to answer questions such as: How many coffees must Starbucks sell in a store to break even? How many coffees must Starbucks sell in order to make $10,000 at a store? What is the change in income if selling prices decline and sales volume increases? How much does income increase if we install a new machine to reduce labor costs? What is the income effect if we change the sales mix of our products or services? 18-1

C1 Cost Behavior Summary 18-2

C1 Mixed Costs Mixed costs contain a fixed portion that is incurred even when the facility is unused, and a variable portion that increases with usage. Example: monthly electric utility charge Fixed service fee Variable charge per kilowatt hour used 18-3

Step-Wise Costs Cost Activity C1 Total cost remains constant within a narrow range of activity. Example: Adding a supervisor for each 10 new workers. Another type of cost is referred to as a step cost. Step costs remain constant in total within a relatively narrow range of activity. Cost Activity

Curvilinear Costs Also called a nonlinear cost, it increases at a NON-constant rate as volume increases. A linear cost increases at a constant rate (variable costs) Example: adding hourly workers. The first few increase output because they can specialize more, but too many starts to slow communications and crowd a work space.

Total Variable Cost Graph Unit Variable Cost Graph Variable Costs Total Variable Cost Graph Unit Variable Cost Graph $300,000 $250,000 $200,000 $150,000 $100,000 $50,000 $20 $15 $10 $5 Total Costs Cost per Unit 10 20 30 Units Produced (000) 10 20 30 Units Produced (000) Units Total Cost Produced Cost per Unit 5,000 $ 50,000 $10 10,000 100,000 10 15,000 150,000 10 20,000 200,000 10 25,000 250,000 10 30,000 300,000 10

Total Variable Cost Graph Unit Variable Cost Graph Variable Costs Total Variable Cost Graph Unit Variable Cost Graph $300,000 $250,000 $200,000 $150,000 $100,000 $50,000 $20 $15 $10 $5 Total Costs Cost per Unit 10 20 30 Units Produced (000) 10 20 30 Units Produced (000) Units Total Cost Produced Cost per Unit 5,000 $ 50,000 $10 10,000 100,000 10 15,000 150,000 10 20,000 200,000 10 25,000 250,000 10 30,000 300,000 10

Total Variable Cost Graph Unit Variable Cost Graph Variable Costs Total Variable Cost Graph Unit Variable Cost Graph $300,000 $250,000 $200,000 $150,000 $100,000 $50,000 $20 $15 $10 $5 Total Costs Cost per Unit 10 20 30 Units Produced (000) 10 20 30 Units Produced (000) Units Total Cost Produced Cost per Unit 5,000 $ 50,000 $10 10,000 100,000 10 15,000 150,000 10 20,000 200,000 10 25,000 250,000 10 30,000 300,000 10

Fixed Costs Total Fixed Cost Graph Unit Fixed Cost Graph $150,000 $125,000 $100,000 $75,000 $50,000 $25,000 $1.50 $1.25 $1.00 $.75 $.50 $.25 Total Costs Cost per Unit 100 200 300 100 200 300 Units Produced (000) Units Produced (000) Units Total Cost Produced Cost per Unit 50,000 $75,000 $1.500 100,000 75,000 .750 150,000 75,000 .500 200,000 75,000 .375 250,000 75,000 .300 300,000 75,000 .250

Fixed Costs Total Fixed Cost Graph Unit Fixed Cost Graph $150,000 $125,000 $100,000 $75,000 $50,000 $25,000 $1.50 $1.25 $1.00 $.75 $.50 $.25 Total Costs Cost per Unit 100 200 300 100 200 300 Units Produced (000) Units Produced (000) Units Total Cost Produced Cost per Unit 50,000 $75,000 $1.500 100,000 75,000 .750 150,000 75,000 .500 200,000 75,000 .375 250,000 75,000 .300 300,000 75,000 .250

Fixed Costs Total Fixed Cost Graph Unit Fixed Cost Graph $150,000 $125,000 $100,000 $75,000 $50,000 $25,000 $1.50 $1.25 $1.00 $.75 $.50 $.25 Total Costs Cost per Unit 100 200 300 100 200 300 Units Produced (000) Units Produced (000) Units Total Cost Produced Cost per Unit 50,000 $75,000 $1.500 100,000 75,000 .750 150,000 75,000 .500 200,000 75,000 .375 250,000 75,000 .300 300,000 75,000 .250

Mixed Costs Total Mixed Cost Graph $40,000 $35,000 $30,000 $25,000 $20,000 $15,000 $10,000 $5,000 Mixed costs are sometimes called semivariable or semifixed costs. Total Costs Mixed costs are usually separated into their fixed and variable components for management analysis. 10 20 30 40 Total Machine Hours (000)

Variable Costs Fixed Costs Total Variable Costs Total Fixed Costs Total Costs Total Costs Total Units Produced Total Units Produced Unit Fixed Costs Unit Variable Costs Per Unit Cost Per Unit Cost Total Units Produced Total Units Produced

regardless of activity level. Variable Costs Fixed Costs Total Variable Costs Total Fixed Costs Used for planning. Remains the same regardless of activity level. Total Costs Total Costs $75,000 total Total Units Produced Total Units Produced Unit Fixed Costs Unit Variable Costs Per Unit Cost Per Unit Cost $10 per unit Total Units Produced Total Units Produced

Step-Wise Costs Cost Activity C1 Total cost remains constant within a narrow range of activity. Example: Adding a supervisor for each 10 new workers. Another type of cost is referred to as a step cost. Step costs remain constant in total within a relatively narrow range of activity. Cost Activity

Curvilinear Costs Also called a nonlinear cost, it increases at a NON-constant rate as volume increases. A linear cost increases at a constant rate (variable costs) Example: adding hourly workers. The first few increase output because they can specialize more, but too many starts to slow communications and crowd a work space.

Contribution Margin helps us figure out: How many coffees must Starbucks sell in a store to break even? How many coffees must Starbucks sell in order to make $10,000 at a store? What is the change in income if selling prices decline and sales volume increases? How much does income increase if we install a new machine to reduce labor costs? What is the income effect if we change the sales mix of our products or services? 18-17

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

Contribution Margin Income Statement Total Per Unit Percent/Ratio Sales (50,000 units) $1,000,000 $ % Variable costs 600,000 % Contribution margin $400,000 $ % Fixed costs 300,000 Income from operations $100,000 The statement can be extended to include per unit dollars and percentage numbers.

Contribution Margin Income Statement Total Per Unit Percent/Ratio Sales (50,000 units) $1,000,000 $20 100% Variable costs 600,000 12 60% Contribution margin $400,000 $ 8 40% Fixed costs 300,000 Income from operations $100,000 The statement can be extended to include per unit dollars and percentage numbers.

Contribution Margin Income Statement Total Per Unit Percent/Ratio Sales (50,000 units) $1,000,000 $20 100% Variable costs 600,000 12 60% Contribution margin $400,000 $ 8 40% Fixed costs 300,000 Income from operations $100,000 Income from operations Variable costs Fixed costs Sales = + + Variable costs Contribution margin Sales – =

Contribution Margin Income Statement Total Per Unit Percent/Ratio Sales (50,000 units) $1,000,000 $20 100% Variable costs 600,000 12 60% Contribution margin $400,000 $ 8 40% Fixed costs 300,000 Income from operations $100,000 Unit Contribution Margin Contribution Margin Ratio The contribution margin can be expressed three ways: 1. Total contribution margin in dollars. 2. Unit contribution margin (dollars per unit). 3. Contribution margin ratio (percentage).

Calculating the Break-Even Point Total Per Unit Percent Sales (???? units) ? $20 100% Variable costs ? 12 60% Contribution margin $300,000 $ 8 40% Fixed costs 300,000 Income from operations $ 0 At the break-even point, fixed costs and the contribution margin are equal.

Calculating the Break-Even Point Divide by either: $8 per unit or 40% Total Per Unit Percent Sales (???? units) ? $20 100% Variable costs ? 12 60% Contribution margin $ 300,000 $ 8 40% Fixed costs 300,000 Income from operations $ 0 / or Divide by either: $8 per unit or 40% Break-even sales Fixed costs Contribution margin = /

Calculating the Break-Even Point Total Per Unit Percent Sales (???? units) ? $20 100% Variable costs ? 12 60% Contribution margin $ 300,000 $ 8 40% Fixed costs 300,000 Income from operations $ 0  or Break-even sales Fixed costs Contribution Margin per unit = / What is the break-even sales in units?

Calculating the Break-Even Point Total Per Unit Percent Sales (????? units) ? $20 100% Variable costs ? 12 60% Contribution margin $ 300,000 $ 8 40% Fixed costs 300,000 Income from operations $ 0 / or Break-even sales Fixed costs Contribution margin = / Break-even sales = $300,000 / $8 = 37,500 units What is the break-even sales in dollars?

Calculating the Break-Even Point Total Per Unit Percent Sales (????? units) ? $20 100% Variable costs ? 12 60% Contribution margin $ 300,000 $ 8 40% Fixed costs 300,000 Income from operations $ 0 / or Break-even sales Fixed costs Contribution margin = / Break-even sales = $300,000 / $8 = 37,500 units Break-even sales = $300,000 / 40% = $750,000

Computing Sales for a Target Income Break-even formulas may be adjusted to show the sales volume needed to earn any amount of income. Fixed costs + Target income Unit sales = Contribution margin per unit Fixed costs + Target income Dollar sales = Contribution margin ratio 18-28

Calculating a Planned Sales Level Total Per Unit Percent Sales (50,000 units) ? $20 100% Variable costs ? 12 60% Contribution margin $ 400,000 $ 8 40% Fixed costs 300,000 Income from operations $ 100,000 / or Planned sales Contribution margin Fixed Target costs profit + = / Fixed costs plus the target profit equals the required total contribution margin.

Calculating a Planned Sales Level Total Per Unit Percent Sales (50,000 units) ? $20 100% Variable costs ? 12 60% Contribution margin $ 400,000 $ 8 40% Fixed costs 300,000 Income from operations $ 100,000 / or Planned sales Fixed Target costs profit Contribution margin + = / $8 per unit or 40%

Calculating a Planned Sales Level Sales (????? units) ? $20 100% Variable costs ? 12 60% Contribution margin $ 400,000 $ 8 40% Fixed costs 300,000 Income from operations $ 100,000 Total Per Unit Percent / or Planned sales Fixed Target costs profit Contribution margin + = / What is the planned sales level in units?

Calculating a Planned Sales Level Sales (????? units) ? $20 100% Variable costs ? 12 60% Contribution margin $ 400,000 $ 8 40% Fixed costs 300,000 Income from operations $ 100,000 Total Per Unit Percent / or Planned sales Fixed Target costs profit Contribution margin + = / Planned sales = ($300,000 + $100,000) / $8 = 50,000 units What is the planned sales level in dollars?

Calculating a Planned Sales Level Total Per Unit Percent Sales (50,000 units) $1,000,000 $20 100% Variable costs 600,000 12 60% Contribution margin $ 400,000 $ 8 40% Fixed costs 300,000 Income from operations $ 100,000 / or Planned sales Fixed Target costs profit Contribution margin = + / Planned sales = ($300,000 + $100,000) / $8 = 50,000 units Planned sales = ($300,000 + $100,000) / 40% = $1,000,000 $1,000,000

How do taxes impact our analysis? THINK: Taxes come out of profits, reducing our profits. Taxes are typically stated as a percent of our profits/income. Must listen carefully and read carefully, are we asked for a target income or a target “pre-tax” income or a target “after-tax” income ? Which requires higher sales: 1)a target income of $100,000 or 2) a target “pre-tax” income of $100,000 or a target “after-tax” income of $100,000? Assume a 40% tax rate. Explain, show calculations:

How do taxes impact our analysis? Which is a larger number: 1)a target income of $100,000 or 2) a target “pre-tax” income of $100,000 or a target “after-tax” income of $100,000? Assume a 40% tax rate. Explain, show calculations. A target income and “pre-tax” income are the same thing, we don’t factor in taxes. A target “after-tax” income of $100,000 means we have to earn more than $100,000 because that is what we want after we have paid our taxes. Pre-tax income = After-tax income/(100% - tax rate) Pre-tax income = $100,000 / (100% - 40%) Pre-tax income = $100,000 / 60% Pre-tax income = $166,666 Proof: = $166,666 X 40% = gives us taxes due Taxes due = $ 66,666 Income after tax = $100,000

Sales Mix – Weighted Average Contribution margin Products A B Sales $ 90 $140 Variable costs 70 95 Contribution margin $ 20 $ 45 Sales mix 80% 20% What is the average contribution for each product?

Sales Mix – Weighted Average Contribution margin Products A B Sales $ 90 $140 Variable costs 70 95 Contribution margin $ 20 $ 45 Sales mix x 80% x 20% Product contribution $ 16 $ 9 STEP ONE: What is the total product contribution?

Sales Mix – Weighted Average Contribution margin Products A B Sales $ 90 $140 Variable costs 70 95 Contribution margin $ 20 $ 45 Sales mix x 80% x 20% Product contribution $ 16 $ 9 Total product contribution $ 25 (weighted average) The pure average is: $32.50 ($20+$45) / 2 We don’t use this because we aren’t selling products on a 1:1 basis.

Sales Mix – Weighted Average Contribution margin Products A B Sales $ 90 $140 Variable costs 70 95 Contribution margin $ 20 $ 45 Sales mix x 80% x 20% Product contribution $ 16 $ 9 Total product contribution $ 25 Step Two: Treat the “total product contribution” as if it were the CONTRIBUTION margin of a single product and CALCULATE BREAK EVEN

Sales Mix – Weighted Average Contribution margin Products A B Sales $ 90 $140 Variable costs 70 95 Contribution margin $ 20 $ 45 Sales mix x 80% x 20% Product contribution $ 16 $ 9 Total product contribution $ 25 Beak-even sales units Total fixed costs $200,000 Product contribution $25 What is the break-even sales units?

Sales Mix – Weighted Average Contribution margin Products A B Sales $ 90 $140 Variable costs 70 95 Contribution margin $ 20 $ 45 Sales mix x 80% x 20% Product contribution $ 16 $ 9 Total product contribution $ 25 Break-even sales units Total fixed costs $200,000 Product contribution $25 STEP 3: this is the total units of A and B combined. Need to calculate how many of A & B need to be sold, based on original sales mix of 80% & 20%. = 8,000 units

Sales Mix – Weighted Average Contribution margin Products A B Sales $ 90 $140 Variable costs 70 95 Contribution margin $ 20 $ 45 Sales mix x 80% x 20% Product contribution $ 16 $ 9 Total product contribution $ 25 Break-even sales units Total fixed costs $200,000 Product contribution $25 Break-even sales units 8,000 Product A units (80%) 6,400 Product B units (20%) 1,600 = 8,000 units

Operating Leverage Contribution margin Operating income Operating leverage is a measure of the relative mix of variable costs and fixed costs and tells us how sensitive operating income is to changes in sales. High leverage = higher increase in income from increased sales. Jones Inc. Wilson Inc. Sales $400,000 $400,000 Variable costs 300,000 300,000 Contribution margin $100,000 $100,000 Fixed costs 80,000 50,000 Income from operations $20,000 $ 50,000

Both companies have the same contribution margin. Operating Leverage Contribution margin Operating income Operating leverage is a measure of the relative mix of variable costs and fixed costs. Jones Inc. Wilson Inc. Sales $400,000 $400,000 Variable costs 300,000 300,000 Contribution margin $100,000 $100,000 Fixed costs 80,000 50,000 Income from operations $20,000 $ 50,000 A Both companies have the same contribution margin.

What is the operating leverage? Contribution margin Operating income Operating leverage is a measure of the relative mix of variable costs and fixed costs. Jones Inc. Wilson Inc. Sales $400,000 $400,000 Variable costs 300,000 300,000 Contribution margin $100,000 $100,000 Fixed costs 80,000 50,000 Income from operations $20,000 $ 50,000 Operating leverage (A/B) A B What is the operating leverage?

What do these numbers mean? Operating Leverage Contribution margin Operating income Operating leverage is a measure of the relative mix of variable costs and fixed costs. Jones Inc. Wilson Inc. Sales $400,000 $400,000 Variable costs 300,000 300,000 Contribution margin $100,000 $100,000 Fixed costs 80,000 50,000 Income from operations $20,000 $ 50,000 Operating leverage (A/B) A B 5 2 What do these numbers mean?

Operating Leverage Contribution margin Operating income Operating leverage is a measure of the relative mix of variable costs and fixed costs and tells us how sensitive operating income is to changes in sales. High leverage = higher increase in income from increased sales. Jones Inc. Wilson Inc. Sales $400,000 $400,000 Variable costs 300,000 300,000 Contribution margin $100,000 $100,000 Fixed costs 80,000 50,000 Income from operations $20,000 $ 50,000 Operating leverage (A/B) This tells us that, if sales increase 10% for both companies, we can expect a 50% and 20% increase in operating income, respectively. A B 5 2

Cost-Volume-Profit Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Total Sales Sales and Costs ($000) 1 2 3 4 5 6 7 8 9 10 Units of Sales (000) Unit selling price $ 50 Unit variable cost 30 Unit contribution margin $ 20 Total fixed costs $100,000

Cost-Volume-Profit Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Total Sales Sales and Costs ($000) 60% Variable Costs 1 2 3 4 5 6 7 8 9 10 Units of Sales (000) Unit selling price $ 50 Unit variable cost 30 Unit contribution margin $ 20 Total fixed costs $100,000

Cost-Volume-Profit Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Total Sales Contribution Margin 40% Sales and Costs ($000) 60% Variable Costs 1 2 3 4 5 6 7 8 9 10 Units of Sales (000) 100% 60% 40% Unit selling price $ 50 Unit variable cost 30 Unit contribution margin $ 20 Total fixed costs $100,000

Cost-Volume-Profit Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Total Sales Total Costs Sales and Costs ($000) Fixed Costs Variable Costs 1 2 3 4 5 6 7 8 9 10 Units of Sales (000) Unit selling price $ 50 Unit variable cost 30 Unit contribution margin $ 20 Total fixed costs $100,000

Cost-Volume-Profit Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Total Sales Total Costs Sales and Costs ($000) 1 2 3 4 5 6 7 8 9 10 Units of Sales (000) Unit selling price $ 50 Unit variable cost 30 Unit contribution margin $ 20 Total fixed costs $100,000

Cost-Volume-Profit Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Total Sales Operating Profit Area Total Costs Sales and Costs ($000) Operating Loss Area 1 2 3 4 5 6 7 8 9 10 Units of Sales (000) Unit selling price $ 50 Unit variable cost 30 Unit contribution margin $ 20 Total fixed costs $100,000

Cost-Volume-Profit Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Total Sales Total Costs Sales and Costs ($000) Break-Even Point 1 2 3 4 5 6 7 8 9 10 Units of Sales (000) Unit selling price $ 50 Unit variable cost 30 Unit contribution margin $ 20 Total fixed costs $100,000

Cost-Volume-Profit Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Total Sales Total Costs Sales and Costs ($000) Break-Even Point 1 2 3 4 5 6 7 8 9 10 Units of Sales (000) Unit selling price $ 50 Unit variable cost 30 Unit contribution margin $20 Total fixed costs $100,000 $100,000 $20 = 5,000 units

Cost-Volume-Profit Chart (Break-Even) $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Total Sales Operating Profit Area Total Costs Sales and Costs ($000) Break-Even Point Operating Loss Area 1 2 3 4 5 6 7 8 9 10 Units of Sales (000) Unit selling price $ 50 Unit variable cost 30 Unit contribution margin $ 20 Total fixed costs $100,000 $100,000 $20 = 5,000 units

Revised Cost-Volume-Profit Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Total Sales Operating Profit Area Total Costs Sales and Costs ($000) Revised Break-Even Point Operating Loss Area 1 2 3 4 5 6 7 8 9 10 Units of Sales (000) Unit selling price $ 50 Unit variable cost 30 Unit contribution margin $ 20 Total fixed costs $80,000 $80,000 $20 = 4,000 units

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

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

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

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