16-1 Cost Volume - Profit Relationships
Objectives 16-2 1. Determine the After number studying of units this that must be sold to break chapter, even or you earn should a target profit. 2. Calculate the amount be able of to: 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 costvolume-profit graph, and explain the meaning of each.
Objectives 16-3 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) $400,000 Less: Variable expenses 325,000 Contribution margin $ 75,000 Less: Fixed expenses 45,000 Operating income $ 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) $240,000 Less: Variable exp. 195,000 Contribution margin $ 45,000 Less: Fixed expenses 45,000 Operating income $ 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) $560,000 Less: Variable exp. 455,000 Contribution margin $105,000 Less: Fixed expenses 45,000 Operating income $ 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 Units = 1,600 Proof Sales (1,600 units) $640,000 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
Break-Even Point in Sales Dollars 16-13 First, the contribution margin ratio must be calculated. Sales $400,000 100.00% Less: Variable expenses 325,000 81.25% Contribution margin $ 75,000 18.75% Less: Fixed exp. 45,000 Operating income $ 30,000
Break-Even Point in Sales Dollars 16-14 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 Profit Contribution Margin Revenue Total Variable Cost
16-17 Relationships Among Contribution Margin, Fixed Cost, and Profit Fixed Cost > Contribution Margin Fixed Cost Loss Contribution Margin Revenue Total Variable Cost
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 Mulching Riding Mower Mower Total Sales $480,000 $640,000 $1,120,000 Less: Variable expenses 390,000 480,000 870,000 Contribution margin $ 90,000 $160,000 $ 250,000 Less: Direct fixed expenses 30,000 40,000 70,000 Product margin $ 60,000 $120,000 $ 180,000 Less: Common fixed expenses 26,250 Operating income $ 153,750
16-20 Income Statement: B/E Solution Mulching Riding Mower Mower Total Sales $184,800 $246,400 $431,200 Less: Variable expenses 150,150 184,800 334,950 Contribution margin $ 34,650 $ 61,600 $ 96,250 Less: Direct fixed expenses 30,000 40,000 70,000 Segment margin $ 4,650 $ 23,600 $ 26,250 Less: Common fixed expenses 26,250 Operating income $ 0
The profit-volume graph portrays the relationship between profits and sales volume. 16-21
16-22 Example The Tyson Company produces a single product with the following cost and price data: Total fixed costs $100 Variable costs per unit 5 Selling price per unit 10
Profit-Volume Graph 16-23 Profit or Loss $100 80 60 40 20 0-20 - 40-60 -80-100 Break-Even Point (20, $0) (40, $100) I = $5X - $100 5 10 15 20 25 30 35 40 45 50 Units Sold Loss (0, -$100)
The cost-volume-profit graph depicts the relationship among costs, volume, and profits. 16-24
Cost-Volume-Profit Graph 16-25 Revenue $500 -- 450 -- 400 -- 350 -- 300 -- 250 -- 200 -- 150 -- 100 -- 50 -- 0 -- Loss Break-Even Point (20, $200) Total Revenue Total Cost Variable Expenses ($5 per unit) Fixed Expenses ($100) 5 10 15 20 25 30 35 40 45 50 55 60 Units Sold
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.
Relevant Range 16-27 $ Total Revenue Total Cost Relevant Range Units
Alternative 1: If advertising expenditures increase by $8,000, sales will increase from 1,600 units to 1,725 units. BEFORE THE INCREASED ADVERTISING WITH THE INCREASED ADVERTISING Units sold 1,600 1,725 Unit contribution margin x $75 x $75 Total contribution margin $120,000 $129,375 Less: Fixed expenses 45,000 53,000 Profit $ 75,000 $ 76,375 DIFFERENCE IN PROFIT Change in sales volume 125 Unit contribution margin x $75 Change in contribution margin $9,375 Less: Change in fixed expenses 8,000 Increase in profits $1,375 16-28
Alternative 2: A price decrease from $400 to $375 per lawn mower will increase sales from 1,600 units to 1,900 units. BEFORE THE PROPOSED CHANGES WITH THE PROPOSED CHANGES Units sold 1,600 1,900 Unit contribution margin x $75 x $50 Total contribution margin $120,000 $95,000 Less: Fixed expenses 45,000 45,000 Profit $ 75,000 $50,000 16-29 DIFFERENCE IN PROFIT Change in contribution margin $ -25,000 Less: Change in fixed expenses -------- Decrease in profits $ -25,000
Alternative 3: Decreasing price to $375and increasing advertising expenditures by $8,000 will increase sales from 1,600 units to 2,600 units. BEFORE THE PROPOSED CHANGES WITH THE PROPOSED CHANGES Units sold 1,600 2,600 Unit contribution margin x $75 x $50 Total contribution margin $120,000 $130,000 Less: Fixed expenses 45,000 53,000 Profit $ 75,000 $ 77,000 16-30 DIFFERENCE IN PROFIT Change in contribution margin $10,000 Less: Change in fixed expenses 8,000 Increase in profit $ 2,000
Margin of Safety 16-31 Assume that a company has the following projected income statement: Sales $100,000 Less: Variable expenses 60,000 Contribution margin $ 40,000 Less: Fixed expenses 30,000 Income before taxes $ 10,000 Break-even point in dollars (R): 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 $125,000 Less: Variable expenses 75,000 Contribution margin $ 50,000 Less: Fixed expenses 30,000 Income before taxes $ 20,000
CVP and ABC 16-34 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 fixed Activity Activity Driver Costs Driver Setups $500 100 Inspections 50 600
CVP and ABC 16-35 1. What is the BEP under conventional analysis? BEP = $180,000 $10 = 18,000 units
CVP and ABC 16-36 2. What is the BEP under ABC analysis? BEP = [$100,000 + (100 x $500) + (600 x $50)]/$10 = 18,000 units
CVP and ABC 16-37 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
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