16 -1 CHAPTER Cost-VolumeProfit Analysis: A Managerial Planning Tool 16 -2 Objectives 1. Determine the number of units After studying this that must be sold to breakchapter, even oryou earnshould a target profit. 2. Calculate the amount of to: revenue required to be able 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 costvolume-profit graph, and explain the meaning of each. 16 -3 Objectives 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 16 -4 Using Operating Income in CVP Analysis Narrative Equation Sales revenue – Variable expenses – Fixed expenses = Operating income 16 -5 Using Operating Income in CVP Analysis Sales (1,000 units @ $400) Less: Variable expenses Contribution margin Less: Fixed expenses Operating income $400,000 325,000 $ 75,000 45,000 $ 30,000 16 -6 Using Operating Income in CVP Analysis Break Even in Units 0 = ($400 x Units) – ($325 x Units) – $45,000 $400,000 ÷ 1,000 $325,000 ÷ 1,000 16 -7 Using Operating Income in CVP Analysis Break Even in Units 0 = ($400 x Units) – ($325 x Units) – $45,000 0 = ($75 x Units) – $45,000 $75 x Units = $45,000 Units = 600 Proof Sales (600 units) Less: Variable exp. Contribution margin Less: Fixed expenses Operating income $240,000 195,000 $ 45,000 45,000 $ 0 16 -8 Achieving a Targeted Profit Desired Operating Income of $60,000 $60,000 = ($400 x Units) – ($325 x Units) – $45,000 $105,000 = $75 x Units Units = 1,400 Proof Sales (1,400 units) Less: Variable exp. Contribution margin Less: Fixed expenses Operating income $560,000 455,000 $105,000 45,000 $ 60,000 16 -9 Targeted Income as a Percent of Sales Revenue Desired Operating Income of 15% of Sales Revenue 0.15($400)(Units) = ($400 x Units) – ($325 x Units) – $45,000 $60 x Units = ($400 x Units) – $325 x Units) – $45,000 $60 x Units = ($75 x Units) – $45,000 $15 x Units = $45,000 Units = 3,000 16 -10 After-Tax Profit Targets Net income = Operating income – Income taxes = Operating income – (Tax rate x Operating income) = Operating income (1 – Tax rate) Or Operating income = Net income (1 – Tax rate) 16 -11 After-Tax Profit Targets If the tax rate is 35 percent and a firm wants to achieve a profit of $48,750. How much is the necessary operating income? $48,750 = Operating income – (0.35 x Operating income) $48,750 = 0.65 (Operating income) $75,000 = Operating income 16 -12 After-Tax Profit Targets How many units would have to be sold to earn an operating income of $48,750? Units = ($45,000 + $75,000)/$75 Units = $120,000/$75 Proof Sales (1,600 units) $640,000 Units = 1,600 Less: Variable exp. 520,000 Contribution margin $120,000 Less: Fixed expenses 45,000 Operating income $ 75,000 Less: Income tax (35%) 26,250 Net income $ 48,750 16 -13 Break-Even Point in Sales Dollars First, the contribution margin ratio must be calculated. Sales Less: Variable expenses Contribution margin Less: Fixed exp. Operating income $400,000 100.00% 325,000 81.25% $ 75,000 18.75% 45,000 $ 30,000 16 -14 Break-Even Point in Sales Dollars Given a contribution margin ratio of 18.75%, how much sales revenue is required to break even? Operating income = Sales – Variable costs – Fixed costs $0 = Sales – (Variable costs ratio x Sales) – $45,000 $0 = Sales (1 – 0.8125) – $45,000 Sales (0.1875) = $45,000 Sales = $240,000 16 -15 Relationships Among Contribution Margin, Fixed Cost, and Profit Fixed Cost = Contribution Margin Fixed Cost Contribution Margin Revenue Total Variable Cost 16 -16 Relationships Among Contribution Margin, Fixed Cost, and Profit Fixed Cost < Contribution Margin Fixed Cost Contribution Margin Revenue Total Variable Cost Profit 16 -17 Relationships Among Contribution Margin, Fixed Cost, and Profit Fixed Cost > Contribution Margin Fixed Cost Contribution Margin Revenue Total Variable Cost Loss 16 -18 Profit Targets and Sales Revenue How much sales revenue must a firm generate to earn a before-tax profit of $60,000. Recall that fixed costs total $45,000 and the contribution margin ratio is .1875. Sales = ($45,000 + $60,000)/0.1875 = $105,000/0.1875 = $560,000 16 -19 Multiple-Product Analysis Sales Less: Variable expenses Contribution margin Less: Direct fixed expenses Product margin Less: Common fixed expenses Operating income Mulching Mower $480,000 390,000 $ 90,000 30,000 $ 60,000 Riding Mower Total $640,000 $1,120,000 480,000 870,000 $160,000 $ 250,000 40,000 70,000 $120,000 $ 180,000 26,250 $ 153,750 16 -20 Income Statement: B/E Solution Mulching Mower Sales Less: Variable expenses Contribution margin Less: Direct fixed expenses Segment margin Less: Common fixed expenses Operating income $184,800 150,150 $ 34,650 30,000 $ 4,650 Riding Mower $246,400 184,800 $ 61,600 40,000 $ 23,600 Total $431,200 334,950 $ 96,250 70,000 $ 26,250 26,250 $ 0 16 -21 The profit-volume graph portrays the relationship between profits and sales volume. 16 -22 Example The Tyson Company produces a single product with the following cost and price data: Total fixed costs Variable costs per unit Selling price per unit $100 5 10 Profit-Volume Graph (40, $100) Profit $100— or Loss 80— I = $5X - $100 60— 40— 20— Break-Even Point (20, $0) 0— | | | | | | | | | | 5 10 15 20 25 30 35 40 45 50 - 20— Units Sold - 40— Loss -60— -80— -100— (0, -$100) 16 -23 16 -24 The cost-volume-profit graph depicts the relationship among costs, volume, and profits. 16 -25 Cost-Volume-Profit Graph Revenue $500 -450 -400 -350 -300 -250 -200 -150 -100 -Loss 50 -| 0 -- | 5 10 Total Revenue Total Cost Variable Expenses ($5 per unit) Break-Even Point (20, $200) Fixed Expenses ($100) | | | | 15 20 25 30 | | 35 40 | | | 45 50 55 Units Sold | 60 16 -26 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. 16 -27 Relevant Range $ Total Revenue Total Cost Units Relevant Range Alternative 1: If advertising expenditures increase by 16 -28 $8,000, sales will increase from 1,600 units to 1,725 units. Units sold Unit contribution margin Total contribution margin Less: Fixed expenses Profit BEFORE THE INCREASED ADVERTISING WITH THE INCREASED ADVERTISING 1,600 x $75 $120,000 45,000 $ 75,000 1,725 x $75 $129,375 53,000 $ 76,375 DIFFERENCE IN PROFIT Change in sales volume Unit contribution margin Change in contribution margin Less: Change in fixed expenses Increase in profits 125 x $75 $9,375 8,000 $1,375 Alternative 2: A price decrease from $400 to $375 per 16 -29 lawn mower will increase sales from 1,600 units to 1,900 units. Units sold Unit contribution margin Total contribution margin Less: Fixed expenses Profit BEFORE THE PROPOSED CHANGES WITH THE PROPOSED CHANGES 1,600 x $75 $120,000 45,000 $ 75,000 1,900 x $50 $95,000 45,000 $50,000 DIFFERENCE IN PROFIT Change in contribution margin Less: Change in fixed expenses Decrease in profits $ -25,000 -------$ -25,000 Alternative 3: Decreasing price to $375and increasing 16 -30 advertising expenditures by $8,000 will increase sales from 1,600 units to 2,600 units. Units sold Unit contribution margin Total contribution margin Less: Fixed expenses Profit BEFORE THE PROPOSED CHANGES WITH THE PROPOSED CHANGES 1,600 x $75 $120,000 45,000 $ 75,000 2,600 x $50 $130,000 53,000 $ 77,000 DIFFERENCE IN PROFIT Change in contribution margin Less: Change in fixed expenses Increase in profit $10,000 8,000 $ 2,000 16 -31 Margin of Safety Assume that a company has the following projected income statement: Sales Less: Variable expenses Contribution margin Less: Fixed expenses Income before taxes Break-even point in dollars (R): $100,000 60,000 $ 40,000 30,000 $ 10,000 R = $30,000 ÷ .4 = $75,000 Safety margin = $100,000 - $75,000 = $25,000 16 -32 Degree of Operating Leverage (DOL) DOL = $40,000/$10,000 = 4.0 Now suppose that sales are 25% higher than projected. What is the percentage change in profits? Percentage change in profits = DOL x percentage change in sales Percentage change in profits = 4.0 x 25% = 100% 16 -33 Degree of Operating Leverage (DOL) Proof: Sales Less: Variable expenses Contribution margin Less: Fixed expenses Income before taxes $125,000 75,000 $ 50,000 30,000 $ 20,000 16 -34 CVP and ABC Assume the following: Sales price per unit $15 Variable cost 5 Fixed costs (conventional) $180,000 Fixed costs (ABC) $100,000 with $80,000 subject to ABC analysis Other Data: Unit Level of Variable Activity Activity Driver Costs Driver Setups $500 100 Inspections 50 600 16 -35 CVP and ABC 1. What is the BEP under conventional analysis? BEP = $180,000 ÷ $10 = 18,000 units 16 -36 CVP and ABC 2. What is the BEP under ABC analysis? BEP = [$100,000 + (100 x $500) + (600 x $50)]/$10 = 18,000 units 16 -37 CVP and ABC 3. What is the BEP if setup cost could be reduced to $450 and inspection cost reduced to $40? BEP = [$100,000 + (100 x $450) + (600 x $40)]/$10 = 16,900 units 16 -38 Chapter Sixteen The End 16 -39