Cost-Volume-Profit Analysis: A Managerial Planning Tool CHAPTER

After studying this chapter, you should be able to: Objectives 1. Determine the number of units that must be sold to break even or earn a target 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. After studying this chapter, you should be able to:

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

Using Operating Income in CVP Analysis Narrative Equation Sales revenue – Variable expenses – Fixed expenses = Operating income

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

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

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

Desired Operating Income of $60,000 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

Desired Operating Income of 15% of Sales Revenue 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

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)

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

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 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 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

Fixed Cost = Contribution Margin Relationships Among Contribution Margin, Fixed Cost, and Profit Fixed Cost = Contribution Margin Fixed Cost Contribution Margin Total Variable Cost Revenue

Fixed Cost < Contribution Margin Relationships Among Contribution Margin, Fixed Cost, and Profit Fixed Cost < Contribution Margin Fixed Cost Profit Contribution Margin Total Variable Cost Revenue

Fixed Cost > Contribution Margin Relationships Among Contribution Margin, Fixed Cost, and Profit Fixed Cost > Contribution Margin Fixed Cost Loss Contribution Margin Total Variable Cost Revenue

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

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

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.

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 (40, $100) I = $5X - $100 $100— 80— 60— 40— 20— 0— - 20— - 40— -60— 100— Profit or Loss Break-Even Point (20, $0) | | | | | | | | | | 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.

Cost-Volume-Profit Graph Revenue Units Sold $500 -- -- 250 -- 200 -- 150 -- 50 -- 0 -- 5 10 15 20 25 30 35 40 45 50 55 60 | | | | | | | | | | | | Total Revenue Profit ($100) Total Cost Variable Expenses ($5 per unit) Loss Break-Even Point (20, $200) Fixed Expenses ($100)

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 $ 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 WITH THE INCREASED INCREASED ADVERTISING 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

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 WITH THE PROPOSED PROPOSED CHANGES 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 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 WITH THE PROPOSED PROPOSED CHANGES 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 DIFFERENCE IN PROFIT Change in contribution margin $10,000 Less: Change in fixed expenses 8,000 Increase in profit $ 2,000

Margin of Safety 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

Degree of Operating Leverage (DOL) 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%

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 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 18

CVP and ABC 1. What is the BEP under conventional analysis? = 18,000 units 19

CVP and ABC 2. What is the BEP under ABC analysis? BEP = [$100,000 + (100 x $500) + (600 x $50)]/$10 = 18,000 units

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

Chapter Sixteen The End