COST MANAGEMENT Accounting & Control Hansen▪Mowen▪Guan COPYRIGHT © 2009 South-Western Publishing, a division of Cengage Learning. Cengage Learning and South-Western are trademarks used herein under license. 1 Chapter 17 Cost-Volume-Profit Analysis

2 Study Objectives 1.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. 5.Explain the impact of risk, uncertainty, and changing variables on cost-volume-profit analysis. 6.Discuss the impact of activity-based costing on cost- volume-profit analysis.

3 The Break-Even Point in Units The controller of More-Power Company has prepared the following projected income statement: 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

4 0 = ($40 x Units) – ($24 x Units) – $800,000 Operating Income Approach 0 = ($16 x Units) – $800,000 ($16 x Units) = $800,000 Units = 50,000 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 The Break-Even Point in Units $1,740,000 ÷ 72,500

5 Number of units Contribution Margin Approach = $800,000 ÷ $16 contribution margin per unit = 50,000 = $800,000 ÷ ($40 - $24) The Break-Even Point in Units

6 Target Income as a Dollar Amount $424,000= ($40 x Units) – ($24 x Units) – $800,000 $1,224,000= $16 x Units Units= $1,224,000 ÷ $16 = 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 The Break-Even Point in Units

7 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. Target Income as a Percentage of Sales Revenue The Break-Even Point in Units

8 Net income = Operating income – (Tax rate × Operating income) = Operating income × (1 – Tax rate) After-Tax Profit Targets = Operating income – Income taxes The Break-Even Point in Units Or

9 $487,500 = Operating income – 0.35(Operating income) $487,500 = 0.65(Operating income) $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 = $1,550,000 ÷ $16 = $96,875 The Break-Even Point in Units After-Tax Profit Targets

10 Break-Even Point in Sales Dollars

11 Sales$2,900,000 Less: Variable expenses 1,740,000 Contribution margin$1,160,000 Less: Fixed expenses 800,000 Operating income$ 360,000 The following More-Power Company contribution margin income statement is shown for sales of 72,500 sanders. Break-Even Point in Sales Dollars

12 Break-Even Point in Sales Dollars To determine the break-even in sales dollars, the contribution margin ratio must be determined ($1,160,000 ÷ $2,900,000) Sales$2,900,000 Less: Variable expenses 1,740,000 Contribution margin$1,160,000 Less: Fixed expenses 800,000 Operating income$ 360,000 Sales$2,900,000100% Less: Variable expenses 1,740,000 60% Contribution margin$1,160,000 40% Less: Fixed expenses 800,000 Operating income$ 360,000

13 Operating income =Sales – Variable costs – Fixed Costs 0 =Sales – (Variable cost ratio × 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 Break-Even Point in Sales Dollars

14 Break-Even Point in Sales Dollars

15 Break-Even Point in Sales Dollars

16 Break-Even Point in Sales Dollars

17 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 Profit Targets Break-Even Point in Sales Dollars

18 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 Multiple-Product Analysis More-Power plans on selling 75,000 regular sanders and 30,000 mini-sanders. The sales mix is 5:2

19 Regular sander break-even units = Fixed costs ÷ (Price – Unit variable) = $250,000 ÷ $16 = 15,625 units Mini-sander break-even units = Fixed costs ÷ (Price – Unit variable) = $450,000 ÷ $30 = 15,000 units Multiple-Product Analysis Break-Even Point in Units

20 Multiple-Product Analysis Package break-even units = Fixed costs ÷ Package contribution margin = $1,300,000 ÷ $140 = 9, units Sales volume for break-even Regular sander: 46,429 units Mini sander: 18,571 units Sales Mix and CVP Analysis

21 Multiple-Product Analysis

22 Multiple-Product Analysis Sales Dollar Approach Projected Income: Sales$4,800,000 Less: Variable expenses 2,700,000 Contribution margin$2,100, Less: Fixed expenses 1,300,000 Operating income$ 800,000 Break-even sales= Fixed costs ÷ contribution margin ratio = 1,300,000 ÷ = $2,971,429

23 Graphical Representation of CVP Relationships

24 Graphical Representation of CVP Relationships

25 Assumptions of C-V-P Analysis Graphical Representation of CVP Relationships 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.

26 Changes in the CVP Variables Alternative 1: If advertising expenditures increase by $48,000, sales will increase from 72,500 units to 75,000 units.

27 Changes in the CVP Variables Alternative 2: A price decrease from $40 per sander to $38 would increase sales from 72,500 units to 80,000 units.

28 Alternative 3: Decreasing price to $38 and increasing advertising expenditures by $48,000 will increase sales from 72,500 units to 90,000 units. Changes in the CVP Variables

29 Changes in the CVP Variables Margin of safety –The excess of units sold over break-even units –The excess of revenue earned over break- even sales Current sales500 Break-even volume200 Margin of safety (in units)300 Current revenue$350,000 Break-even volume200,000 Margin of safety (in dollars)$150,000

30 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 Changes in the CVP Variables DOL of 4 $500,000 ÷ $125,000 DOL of 2 $200,000 ÷ $100,000

31 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 Changes in the CVP Variables Assume a 40% increase in sales Increase in sales40%40% Degree of operating leverage × 4 × 2 Increase in operating income160%80% AutomatedManualSystem Operating Leverage

32 Fixed costs +Unit variable cost × number of units +Setup cost × number of setups +Engineering cost × number of engineering hours =Total cost The ABC Cost Equation: CVP Analysis and Activity-Based Costing Break-Even in Units: Total revenue – Total Cost =Operating income Operating Income:

33 CVP Analysis and Activity-Based Costing Differences between ABC break-even and conventional break-even –Fixed costs differ Costs by vary with non-unit cost drivers –The numerator of the ABC break-even equation has two nonunit-variable cost terms Batch-related activities Product-sustaining activities

34 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 Example Comparing Conventional and ABC Analysis CVP Analysis and Activity-Based Costing

35 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 Same data using the ABC Units= ($20,000 + $50,000 + $20,000 + $30,000) ÷ ($20 – $10) = $120,000 ÷ $10 = 12,000 CVP Analysis and Activity-Based Costing Example Comparing Conventional and ABC Analysis

36 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 : Units= Fixed costs ÷ (Price – Unit variable cost) = $100,000 ÷ ($20 – $8) = 8,333 CVP Analysis and Activity-Based Costing Example Comparing Conventional and ABC Analysis

37 Projected income if 10,000 units are sold: Sales ($20 × 10,000)$200,000 Less: Variable expenses ($8 × 10,000) 80,000 Contribution margin$120,000 Less: Fixed expenses 100,000 Operating income$ 20,000 CVP Analysis and Activity-Based Costing Example Comparing Conventional and ABC Analysis

38 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. New cost equation: $50,000 (fixed costs) + ($8 × units) + ($1,600 × setups) + ($30 × engineering hours) CVP Analysis and Activity-Based Costing Example Comparing Conventional and ABC Analysis

39 Break-even point using the ABC equation: This exceeds the firm’s sales capacity! CVP Analysis and Activity-Based Costing Example Comparing Conventional and ABC Analysis

COST MANAGEMENT Accounting & Control Hansen▪Mowen▪Guan COPYRIGHT © 2009 South-Western Publishing, a division of Cengage Learning. Cengage Learning and South-Western are trademarks used herein under license. 40 End Chapter 17