20-1 Cost-Volume Profit Analysis Prepared by Douglas Cloud Pepperdine University Prepared by Douglas Cloud Pepperdine University

Determine the number of units that must be sold to break even or to earn a targeted profit. 2.Calculate the amount of revenue required to break even or to earn a targeted profit. 3.Apply cost-volume-profit analysis in a multiple-product setting. 4.Prepare a profit-volume graph and a cost- volume-profit graph, and explain the meaning of each. ObjectivesObjectives After studying this chapter, you should be able to: ContinuedContinued

Explain the impact of the risk, uncertainty, and changing variables on cost-volume-profit analysis. 6.Discuss the impact of activity-based costing on cost-volume-profit analysis. ObjectivesObjectives

20-4 Operating-Income Approach Narrative Equation Sales revenues – Variable expenses – Fixed expenses = Operating income

20-5 Sales (72,500 $40)$2,900,000 Less: Variable expenses 1,740,000 Contribution margin$1,160,000 Less: Fixed expenses 800,000 Operating income$ 360,000 Operating-Income Approach

20-6 Operating-Income Approach 0 = ($40 x Units) – ($24 x Units) – $800,000 Break Even in Units 0 = ($16 x Units) – $800,000 ($16 x Units) = $800,000 Units = 50,000 $1,740,000 ÷ 72,500 Proof Sales (50,000 $40)$2,000,000 Less: Variable expenses 1,200,000 Contribution margin$ 800,000 Less: Fixed expenses 800,000 Operating income$ 0 Proof Sales (50,000 $40)$2,000,000 Less: Variable expenses 1,200,000 Contribution margin$ 800,000 Less: Fixed expenses 800,000 Operating income$ 0

20-7 Contribution-Margin Approach Number of units = $800,000 $40 – $24 Number of units = = 50,000 units Fixed costs Unit contribution margin

20-8 Target Income as a Dollar Amount $424,000= ($40 x Units) – ($24 x Units) – $800,000 $1,224,000= $16 x Units Units= 76,500 Proof Sales (76,500 $40)$3,060,000 Less: Variable expenses 1,836,000 Contribution margin$1,224,000 Less: Fixed expenses 800,000 Operating income$ 424,000 Proof Sales (76,500 $40)$3,060,000 Less: Variable expenses 1,836,000 Contribution margin$1,224,000 Less: Fixed expenses 800,000 Operating income$ 424,000

20-9 Target Income as a Percentage of Sales Revenue 0.15($40)(Units)= ($40 x Units) – ($24 x Units) – $800,000 $6 x Units= ($40 x Units) – ($24 x Units) – $800,000 $6 x Units= ($16 x Units) – $800,000 $10 x Units= $800,000 Units= 80,000 More-Power Company wants to know the number of sanders that must be sold in order to earn a profit equal to 15 percent of sales revenue.

20-10 Net income = Operating income – Income taxes = Operating income – (Tax rate x Operating income) After-Tax Profit Targets = Operating income (1 – Tax rate) Or Operating income = Net income (1 – Tax rate)

20-11 $487,500 = Operating income – 0.35(Operating income) $487,500 = 0.65(Operating income) After-Tax Profit Targets $750,000 = Operating income More-Power Company wants to achieve net income of $487,500 and its income tax rate is 35 percent. Units = ($800,000 + $750,000)/$16 Units = $1,550,000/$16 Units = 96,875

20-12 After-Tax Profit Targets Proof Sales (96,875 $40)$3,875,000 Less: Variable expenses 2,325,000 Contribution margin$1,550,000 Less: Fixed expenses 800,000 Income before income taxes$ 750,000 Less: Income taxes (35%) 262,500 Net income$ 487,500 Proof Sales (96,875 $40)$3,875,000 Less: Variable expenses 2,325,000 Contribution margin$1,550,000 Less: Fixed expenses 800,000 Income before income taxes$ 750,000 Less: Income taxes (35%) 262,500 Net income$ 487,500

20-13 Break-Even Point in Sales Dollars Revenue Equal to Variable Cost Plus Contribution Margin Contribution Margin $10 $6 $0 Variable Cost Revenue 10Units

20-14 Break-Even Point in Sales Dollars The following More-Power Company contribution margin income statement is shown for sales of 72,500 sanders. Sales$2,900,000100% Less: Variable expenses 1,740,000 60% Contribution margin$1,160,00040% Less: Fixed expenses 800,000 Operating income$ 360,000 Sales$2,900,000100% Less: Variable expenses 1,740,000 60% Contribution margin$1,160,00040% Less: Fixed expenses 800,000 Operating income$ 360,000 To determine the break-even in sales dollars, the contribution margin ratio must be determined ($1,160,000 ÷ $2,900,000).

20-15 Break-Even Point in Sales Dollars Operating income = Sales – Variable costs – Fixed Costs 0 =Sales – (Variable cost ratio x Sales) – Fixed costs 0 =Sales (1 – Variable cost ratio) – Fixed costs 0 =Sales (1 –.60) – $800,000 Sales(0.40) =$800,000 Sales =$2,000,000

20-16 Impact of Fixed Costs on Profits Fixed Cost Fixed Costs = Contribution Margin; Profit = 0 Contribution Margin Total Variable Cost Revenue

20-17 Impact of Fixed Costs on Profits Contribution Margin Total Variable Cost Revenue Fixed Cost Fixed Costs 0 Profit

20-18 Impact of Fixed Costs on Profits Contribution Margin Total Variable Cost Revenue Fixed Cost Fixed Costs > Contribution Margin; Profit < 0 Loss

20-19 Profit Targets How much sales revenue must More-Power generate to earn a before-tax profit of $424,000? Sales = ($800,000) + $424,000/0.40 = $1,224,000/0.40 = $3,060,000

20-20 Multiple-Product Analysis Regular Mini- Sander Sander Total Sales$3,000,000$1,800,000$4,800,000 Less: Variable expenses 1,800, ,000 2,700,000 Contribution margin$1,200,000$ 900,000$2,100,000 Less: Direct fixed expenses 250, , ,000 Product margin$ 950,000$ 450,000$1,400,000 Less: Common fixed exp. 600,000 Operating income$ 800,000

20-21 Multiple-Product Analysis Regular sander break-even units = Fixed costs/(Price – Unit variable cost) = $250,000/$16 = 15,625 units Mini-sander break-even units = Fixed costs/(Price – Unit variable cost) = $450,000/$30 = 15,000 units

20-22 Multiple-Product Analysis Regular Mini- Sander Sander Total Sales$1,857,160$1,114,260$2,971,420 Less: Variable expenses 1,114, ,130 1,671,426 Contribution margin$ 742,864$ 557,130$1,299,994 Less: Direct fixed expenses 250, , ,000 Product margin$ 492,864$ 107,130$ 599,994 Less: Common fixed exp. 600,000 Operating income$ -6 Not zero due to rounding

20-23 Profit-Volume Graph Profit or Loss Loss (40, $100) I = $5X - $100 Break-Even Point (20, $0) $100— 80— 60— 40— 20— 0— - 20— - 40— -60— -80— -100— | | | | | | | | | | Units Sold (0, -$100)

20-24 Cost-Volume-Profit Graph Revenue Units Sold $ | | | | | | | | | | | | Total Revenue Total Cost Profit ($100) Loss Break-Even Point (20, $200) Fixed Expenses ($100) Variable Expenses ($5 per unit)

20-25 Assumptions of C-V-P Analysis 1.The analysis assumes a linear revenue function and a linear cost function. 2.The analysis assumes that price, total fixed costs, and unit variable costs can be accurately identified and remain constant over the relevant range. 3.The analysis assumes that what is produced is sold. 4.For multiple-product analysis, the sales mix is assumed to be known. 5.The selling price and costs are assumed to be known with certainty.

20-26 $ Units Total Cost Total Revenue Relevant Range

20-27 Alternative 1: If advertising expenditures increase by $48,000, sales will increase from 72,500 units to 75,000 units. Before theWith the IncreasedIncreased IncreasedIncreased AdvertisingAdvertising Units sold72,50075,000 Unit contribution marginx $16x $16 Total contribution margin$1,160,000$1,200,000 Less: Fixed expenses 800, ,000 Profit$ 360,000$ 352,000 Difference in Profits Difference in Profits Change in sales volume2,500 Unit contribution marginx $16 Change in contribution margin$40,000 Less: Increase in fixed expense 48,000 Decrease in profit$ -8,000

20-28 Before the With the Proposed Proposed Price IncreasePrice Increase Units sold72,50080,000 Unit contribution marginx $16x $16 Total contribution margin$1,160,000$1,120,000 Less: Fixed expenses 800, ,000 Profit$ 360,000$ 320,000 Alternative 2: A price decrease from $40 per sander to $38 would increase sales from 72,500 units to 80,000 units. Difference in Profit Change in contribution margin$-40,000 Less: Change in fixed expenses Decrease in profit $-40,000

20-29 Before theWith the Proposed Proposed Price andPrice Decrease Advertising ChangeAdvertising Increase Advertising ChangeAdvertising Increase Units sold72,50090,000 Unit contribution marginx $16x $14 Total contribution margin$1,160,000$1,260,000 Less: Fixed expenses 800, ,000 Profit$ 360,000$ 412,000 Alternative 3: Decreasing price to $38 and increasing advertising expenditures by $48,000 will increase sales from 72,500 units to 90,000 units. Difference in Profit Change in contribution margin$100,000 Less: Change in fixed expenses 48,000 Increase in profit$ 52,000

20-30 Margin of Safety Assume that a company has a break-even volume of 200 units and the company is currently selling 500 units. Current sales500 Break-even volume200 Margin of safety (in units)300 Break-even point in dollars: Current revenue$350,000 Break-even volume 200,000 Margin of safety (in dollars)$150,000

20-31 Operating Leverage AutomatedManualSystem Sales (10,000 units)$1,000,000$1,000,000 Less: Variable expenses 500, ,000 Contribution margin$ 500,000$ 200,000 Less: Fixed expenses 375, ,000 Operating income$ 125,000$ 100,000 Unit selling price$100$100 Unit variable cost5080 Unit contribution margin5020 $500,000 ÷ $125,000 = DOL of 4 $200,000 ÷ $200,000 = DOL of 2

20-32 Operating Leverage What happens to profit in each system if sales increase by 40 percent?

20-33 Operating Leverage AutomatedManualSystem Sales (14,000 units)$1,400,000$1,400,000 Less: Variable expenses 700,000 1,120,000 Contribution margin$ 700,000$ 280,000 Less: Fixed expenses 375, ,000 Operating income$ 325,000$ 180,000 Automated system—40% x 4 = 160% $125,000 x 160% = $200,000 increase $125,000 + $200,000 = $325,000 Manual system—40% x 2 = 80% $100,000 x 80% = $80,000 $100,000 + $80,000 = $180,000

20-34 CVP Analysis and ABC Total cost = Fixed costs + (Unit variable cost x Number of units) + (Setup cost x Number of setups) + (Engineering cost x Number of engineering hours) The ABC Cost Equation Operating income = Total revenue – [Fixed costs + (Unit variable cost x Number of units) + (Setup cost x Number of setups) + (Engineering cost x Number of engineering hours)] Operating Income

20-35 CVP Analysis and ABC Break-even units = [Fixed costs + (Setup cost x Number of setups) + (Engineering cost x Number of engineering hours)]/(Price – Unit variable cost) Break-Even in Units Differences Between ABC Break-Even and Convention Break-Even The fixed costs differ The numerator of the ABC break-even equation has two nonunit-variable cost terms

20-36 CVP Analysis and ABC—Example Data about Variables Cost Driver Unit Variable Cost Level of Cost Driver Units sold$ 10-- Setups1,00020 Engineering hours301,000 Other data: Total fixed costs (conventional)$100,000 Total fixed costs (ABC)50,000 Unit selling price20

20-37 CVP Analysis and ABC—Example Units to be sold to earn a before-tax profit of $20,000: Units= (Targeted income + Fixed costs)/(Price – Unit variable cost) =($20,000 + $100,000)/($20 – $10) =$120,000/$10 =12,000 units

20-38 CVP Analysis and ABC—Example Same data using the ABC: Units= ($20,000 + $50,000 + $20,000 + $30,000/($20 – $10) =$120,000/$10 =12,000 units

20-39 CVP Analysis and ABC—Example Suppose that marketing indicates that only 10,000 units can be sold. A new design reduces direct labor by $2 (thus, the new variable cost is $8). The new break-even is calculated as follows: Units = Fixed costs/(Price – Unit variable cost) = $100,000/($20 – $8) = 8,333 units

20-40 CVP Analysis and ABC—Example The projected income if 10,000 units are sold is computed as follows: Sales ($20 x 10,000)$200,000 Less: Variable expenses ($8 x 10,000) 80,000 Contribution margin$120,000 Less: Fixed expenses 100,000 Operating income$ 20,000

20-41 CVP Analysis and ABC—Example Suppose that the new design requires a more complex setup, increasing the cost per setup from $1,000 to $1,600. Also, suppose that the new design requires a 40 percent increase in engineering support. The new cost equation is given below: Total cost =$50,000 + ($8 x Units) + ($1,600 x Setups) + ($30 x Engineering hours)

20-42 CVP Analysis and ABC—Example The break-even point using the ABC equation is calculated as follows: Units =[$50,000 + ($1,600 x 20) + ($30 x 1,400)]/($20 – $8) = $124,000/$12 =10,333 This is more than the firm can sell!

20-43 End of Chapter

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