22-1 Chapter 22 McGraw-Hill/Irwin1 Cost-VolumeProfit Analysis © The McGraw-Hill Companies, Inc., 2006 22-2 Questions Addressed by Cost-Volume-Profit Analysis CVP analysis is used to answer questions such as: • How much must I sell to earn my desired income? • How will income be affected if I reduce selling prices to increase sales volume? • How will income be affected if I change the sales mix of my products? McGraw-Hill/Irwin2 © The McGraw-Hill Companies, Inc., 2006 22-3 Total Fixed Cost Monthly Basic Telephone Bill Total fixed costs remain unchanged when activity changes. Number of Local Calls McGraw-Hill/Irwin3 Your monthly basic telephone bill probably does not change when you make more local calls. © The McGraw-Hill Companies, Inc., 2006 22-4 Fixed Cost Per Unit Your average cost per local call decreases as more local calls are made. McGraw-Hill/Irwin4 Monthly Basic Telephone Bill per Local Call Fixed costs per unit decline as activity increases. Number of Local Calls © The McGraw-Hill Companies, Inc., 2006 22-5 Total Variable Cost Total Long Distance Telephone Bill Total variable costs change when activity changes. Minutes Talked McGraw-Hill/Irwin5 Your total long distance telephone bill is based on how many minutes you talk. © The McGraw-Hill Companies, Inc., 2006 22-6 Variable Cost Per Unit The cost per long distance minute talked is constant. For example, 7 cents per minute. McGraw-Hill/Irwin6 Per Minute Telephone Charge Variable costs per unit do not change as activity increases. Minutes Talked © The McGraw-Hill Companies, Inc., 2006 22-7 Cost Behavior Summary Summary of Variable and Fixed Cost Behavior Cost In Total Per Unit Variable Changes as activity level changes. Remains the same over wide ranges of activity. Fixed Remains the same even when activity level changes. Decreases as activity level increases. McGraw-Hill/Irwin7 © The McGraw-Hill Companies, Inc., 2006 22-8 Mixed Costs Mixed costs contain a fixed portion that is incurred even when facility is unused, and a variable portion that increases with usage. Example: monthly electric utility charge • Fixed service fee • Variable charge per kilowatt hour used McGraw-Hill/Irwin8 © The McGraw-Hill Companies, Inc., 2006 22-9 Total Utility Cost Mixed Costs Variable Utility Charge Fixed Monthly Utility Charge Activity (Kilowatt Hours) McGraw-Hill/Irwin9 © The McGraw-Hill Companies, Inc., 2006 22-10 Step-Wise Costs Cost Total cost remains constant within a narrow range of activity. Activity McGraw-Hill/Irwin10 © The McGraw-Hill Companies, Inc., 2006 22-11 Step-Wise Costs Cost Total cost increases to a new higher cost for the next higher range of activity. Activity McGraw-Hill/Irwin11 © The McGraw-Hill Companies, Inc., 2006 22-12 Curvilinear Costs Total Cost Costs that increase when activity increases, but in a nonlinear manner. Activity McGraw-Hill/Irwin12 © The McGraw-Hill Companies, Inc., 2006 22-13 Identifying and Measuring Cost Behavior The objective is to classify all costs as either fixed or variable. McGraw-Hill/Irwin13 © The McGraw-Hill Companies, Inc., 2006 22-14 Scatter Diagram A scatter diagram of past cost behavior may be helpful in analyzing mixed costs. McGraw-Hill/Irwin14 © The McGraw-Hill Companies, Inc., 2006 22-15 Scatter Diagram Total Cost in 1,000’s of Dollars Plot the data points on a graph (total cost vs. activity). 20 10 * * * * * ** * ** 0 0 1 2 3 4 Activity, 1,000’s of Units Produced McGraw-Hill/Irwin15 © The McGraw-Hill Companies, Inc., 2006 22-16 Scatter Diagram Total Cost in 1,000’s of Dollars Draw a line through the plotted data points so that about equal numbers of points fall above and below the line. 20 10 * * * * * ** * ** Estimated fixed cost = 10,000 0 0 1 2 3 4 Activity, 1,000’s of Units Produced McGraw-Hill/Irwin16 © The McGraw-Hill Companies, Inc., 2006 22-17 Scatter Diagram Total Cost in 1,000’s of Dollars in cost Unit Variable Cost = Slope = in units 20 10 * * * * * ** * ** Vertical distance is the change in cost. Horizontal distance is the change in activity. 0 0 1 2 3 4 Activity, 1,000’s of Units Produced McGraw-Hill/Irwin17 © The McGraw-Hill Companies, Inc., 2006 22-18 The High-Low Method Exh. 22-6 The following relationships between sales and costs are observed: High activity level Low activity level Change Sales $ 67,500 17,500 $ 50,000 Cost $ 29,000 20,500 $ 8,500 Using these two levels of activity, compute: the variable cost per unit. the total fixed cost. McGraw-Hill/Irwin18 © The McGraw-Hill Companies, Inc., 2006 22-19 The High-Low Method High activity level Low activity level Change Sales $ 67,500 17,500 $ 50,000 Exh. 22-6 Cost $ 29,000 20,500 $ 8,500 $8,500 in cost Unit variable cost = = = $0.17 per $ in units $50,000 McGraw-Hill/Irwin19 © The McGraw-Hill Companies, Inc., 2006 22-20 The High-Low Method High activity level Low activity level Change Exh. 22-6 Sales $ 67,500 17,500 $ 50,000 Cost $ 29,000 20,500 $ 8,500 $8,500 in cost Unit variable cost = = = $0.17 per $ in units $50,000 Fixed cost = Total cost – Total variable McGraw-Hill/Irwin20 © The McGraw-Hill Companies, Inc., 2006 22-21 The High-Low Method High activity level Low activity level Change Exh. 22-6 Sales $ 67,500 17,500 $ 50,000 Cost $ 29,000 20,500 $ 8,500 $8,500 in cost Unit variable cost = = = $0.17 per $ in units $50,000 Fixed cost = Total cost – Total variable cost Fixed cost = $29,000 – ($0.17 per sales $ × $67,500) Fixed cost = $29,000 – $11,475 = $17,525 McGraw-Hill/Irwin21 © The McGraw-Hill Companies, Inc., 2006 22-22 Least-Squares Regression Least-squares regression is usually covered in advanced cost accounting courses. It is commonly used with computer software because of the large number of calculations required. The objective of the cost analysis remains the same: determination of total fixed cost and the variable unit cost. McGraw-Hill/Irwin22 © The McGraw-Hill Companies, Inc., 2006 22-23 Break-Even Analysis Let’s extend our knowledge of cost behavior to break-even analysis. McGraw-Hill/Irwin23 © The McGraw-Hill Companies, Inc., 2006 22-24 Computing Break-Even Point The break-even point (expressed in units of product or dollars of sales) is the unique sales level at which a company earns neither a profit nor incurs a loss. McGraw-Hill/Irwin24 © The McGraw-Hill Companies, Inc., 2006 22-25 Computing Break-Even Point Sales Revenue (2,000 units) Less: Variable costs Contribution margin Less: Fixed costs Net income Total $ 100,000 60,000 $ 40,000 30,000 $ 10,000 Unit $ 50 30 $ 20 Contribution margin is amount by which revenue exceeds the variable costs of producing the revenue. McGraw-Hill/Irwin25 © The McGraw-Hill Companies, Inc., 2006 22-26 Computing Break-Even Point Sales Revenue (2,000 units) Less: Variable costs Contribution margin Less: Fixed costs Net income Total $ 100,000 60,000 $ 40,000 30,000 $ 10,000 Unit $ 50 30 $ 20 How much contribution margin must this company have to cover its fixed costs (break even)? Answer: $30,000 McGraw-Hill/Irwin26 © The McGraw-Hill Companies, Inc., 2006 22-27 Computing Break-Even Point Sales Revenue (2,000 units) Less: Variable costs Contribution margin Less: Fixed costs Net income Total $ 100,000 60,000 $ 40,000 30,000 $ 10,000 Unit $ 50 30 $ 20 How many units must this company sell to cover its fixed costs (break even)? Answer: $30,000 ÷ $20 per unit = 1,500 units McGraw-Hill/Irwin27 © The McGraw-Hill Companies, Inc., 2006 22-28 Computing Break-Even Point Exh. 22-8 We have just seen one of the basic CVP relationships – the break-even computation. Break-even point in units = Fixed costs Contribution margin per unit Unit sales price less unit variable cost ($20 in previous example) McGraw-Hill/Irwin28 © The McGraw-Hill Companies, Inc., 2006 22-29 Computing Break-Even Point Exh. 22-9 The break-even formula may also be expressed in sales dollars. Break-even point in dollars = Fixed costs Contribution margin ratio Unit contribution margin Unit sales price McGraw-Hill/Irwin29 © The McGraw-Hill Companies, Inc., 2006 22-30 Computing Break-Even Point ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even? a. 100,000 units b. 40,000 units c. 200,000 units d. 66,667 units McGraw-Hill/Irwin30 © The McGraw-Hill Companies, Inc., 2006 22-31 Computing Break-Even Point ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even? a. 100,000 units Unit contribution = $5.00 - $3.00 = $2.00 b. 40,000 units $200,000 Fixed costs c. 200,000 units = $2.00 per unit Unit contribution d. 66,667 units = 100,000 units McGraw-Hill/Irwin31 © The McGraw-Hill Companies, Inc., 2006 22-32 Computing Break-Even Point Use the contribution margin ratio formula to determine the amount of sales revenue ABC must have to break even. All information remains unchanged: fixed costs are $200,000; unit sales price is $5.00; and unit variable cost is $3.00. a. b. c. d. $200,000 $300,000 $400,000 $500,000 McGraw-Hill/Irwin32 © The McGraw-Hill Companies, Inc., 2006 22-33 Computing Break-Even Point Use the contribution margin ratio formula to determine the amount of sales revenue ABC must have to break even. All information remains unchanged: fixed costs are $200,000; unit sales price is $5.00; and unit variable cost is $3.00. Unit contribution = $5.00 - $3.00 = $2.00 a. b. c. d. $200,000 Contribution margin ratio = $2.00 ÷ $5.00 = .40 $300,000 Break-even revenue = $200,000 ÷ .4 = $500,000 $400,000 $500,000 McGraw-Hill/Irwin33 © The McGraw-Hill Companies, Inc., 2006 22-34 Preparing a CVP Chart Costs and Revenue in Dollars Plot total fixed costs on the vertical axis. Total fixed costs Total costs Draw the total cost line with a slope equal to the unit variable cost. Volume in Units McGraw-Hill/Irwin34 © The McGraw-Hill Companies, Inc., 2006 22-35 Preparing a CVP Chart Starting at the origin, draw the sales line Sales Costs and Revenue in Dollars with a slope equal to the unit sales price. Total fixed costs Total costs Breakeven Point Volume in Units McGraw-Hill/Irwin35 © The McGraw-Hill Companies, Inc., 2006 22-36 Assumptions of CVP Analysis A limited range of activity called the relevant range, where CVP relationships are linear. Unit selling price remains constant. Unit variable costs remain constant. Total fixed costs remain constant. Production = sales (no inventory changes). McGraw-Hill/Irwin36 © The McGraw-Hill Companies, Inc., 2006 22-37 Computing Income from Expected Sales Exh. 22-12 Income (pretax) = Sales – Variable costs – Fixed costs McGraw-Hill/Irwin37 © The McGraw-Hill Companies, Inc., 2006 22-38 Computing Income from Expected Sales Exh. 22-13 Rydell expects to sell 1,500 units at $100 each next month. Fixed costs are $24,000 per month and the unit variable cost is $70. What amount of income should Rydell expect? Income (pretax) = Sales – Variable costs – Fixed costs = [1,500 units × $100] – [1,500 units × $70] – $24,000 = $21,000 McGraw-Hill/Irwin38 © The McGraw-Hill Companies, Inc., 2006 22-39 Computing Sales for a Target Income Break-even formulas may be adjusted to show the sales volume needed to earn any amount of income. Unit sales = Fixed costs + Target income Contribution margin per unit Fixed costs + Target income Dollar sales = Contribution margin ratio McGraw-Hill/Irwin39 © The McGraw-Hill Companies, Inc., 2006 22-40 Computing Sales for a Target Income ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn income of $40,000? a. 100,000 units b. 120,000 units c. 80,000 units d. 200,000 units McGraw-Hill/Irwin40 © The McGraw-Hill Companies, Inc., 2006 22-41 Computing Sales for a Target Income ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn income of $40,000? Unit contribution = $5.00 - $3.00 = $2.00 a. 100,000 units Fixed costs + Target income b. 120,000 units Unit contribution c. 80,000 units$200,000 + $40,000 = 120,000 units d. 200,000 units $2.00 per unit McGraw-Hill/Irwin41 © The McGraw-Hill Companies, Inc., 2006 22-42 Computing Sales (Dollars) for a Target Net Income Exh. 22-14 Target net income is income after income tax. Dollar sales = McGraw-Hill/Irwin42 Fixed Target net Income + + costs income taxes Contribution margin ratio © The McGraw-Hill Companies, Inc., 2006 22-43 Computing Sales (Dollars) for a Target Net Income To convert target net income to before-tax income, use the following formula: Target net income Before-tax income = 1 - tax rate McGraw-Hill/Irwin43 © The McGraw-Hill Companies, Inc., 2006 22-44 Computing Sales (Dollars) for a Target Net Income Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent. What is Rydell’s before-tax income and income tax expense? McGraw-Hill/Irwin44 © The McGraw-Hill Companies, Inc., 2006 22-45 Computing Sales (Dollars) for a Target Net Income Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent. What is Rydell’s before-tax income and income tax expense? Target net income Before-tax income = 1 - tax rate $18,000 Before-tax income = 1 - .25 = $24,000 Income tax = .25 × $24,000 = $6,000 McGraw-Hill/Irwin45 © The McGraw-Hill Companies, Inc., 2006 22-46 Computing Sales (Dollars) for a Target Net Income Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent. What monthly sales revenue will Rydell need to earn the target net income? McGraw-Hill/Irwin46 © The McGraw-Hill Companies, Inc., 2006 22-47 Computing Sales (Dollars) for a Target Net Income Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent. What monthly sales revenue will Rydell need to earn the target net income? Dollar sales = Dollar sales = McGraw-Hill/Irwin47 Fixed + Target net + Income costs income taxes Contribution margin ratio $24,000 + $18,000 + $6,000 = $160,000 30% © The McGraw-Hill Companies, Inc., 2006 22-48 Formula for Computing Sales (Units) for a Target Net Income Exh. 22-16 The formula for computing dollar sales may be used to compute unit sales by substituting contribution per unit in the denominator. Unit sales = Fixed + Target net + Income costs income taxes Contribution margin per unit $24,000 + $18,000 + $6,000 Unit sales = $30 per unit McGraw-Hill/Irwin48 = 1,600 units © The McGraw-Hill Companies, Inc., 2006 22-49 Computing the Margin of Safety Exh. 22-17 Margin of safety is the amount by which sales may decline before reaching breakeven sales. Margin of safety may be expressed as a percentage of expected sales. Margin of safety percentage McGraw-Hill/Irwin49 = Expected sales - Break-even sales Expected sales © The McGraw-Hill Companies, Inc., 2006 22-50 Computing the Margin of Safety Exh. 22-17 If Rydell’s sales are $100,000 and breakeven sales are $80,000, what is the margin of safety in dollars and as a percentage? Margin of safety percentage McGraw-Hill/Irwin50 = Expected sales - Break-even sales Expected sales © The McGraw-Hill Companies, Inc., 2006 22-51 Computing the Margin of Safety Exh. 22-17 If Rydell’s sales are $100,000 and breakeven sales are $80,000, what is the margin of safety in dollars and as a percentage? Margin of safety = $100,000 - $80,000 = $20,000 Margin of safety percentage = Expected sales - Break-even sales Expected sales Margin of safety percentage = $100,000 - $80,000 $100,000 McGraw-Hill/Irwin51 = 20% © The McGraw-Hill Companies, Inc., 2006 22-52 Sensitivity Analysis The basic CVP relationships may be used to analyze a number of situations such as changing sales price, changing variable cost, or changing fixed cost. Consider the following example. Continue McGraw-Hill/Irwin52 © The McGraw-Hill Companies, Inc., 2006 22-53 Sensitivity Analysis Example Rydell Company is considering buying a new machine that would increase monthly fixed costs from $24,000 to $30,000, but decrease unit variable costs from $70 to $60. The $100 per unit selling price would remain unchanged. What is the new break-even point in dollars? McGraw-Hill/Irwin53 © The McGraw-Hill Companies, Inc., 2006 22-54 Sensitivity Analysis Example Exh. 22-18 Rydell Company is considering buying a new machine that would increase monthly fixed costs from $24,000 to $30,000, but decrease unit variable costs from $70 to $60. The $100 per unit selling price would remain unchanged. Revised Break-even point in dollars = Revised fixed costs Revised contribution margin ratio Revised Break-even point in dollars = $30,000 40% McGraw-Hill/Irwin54 = $75,000 © The McGraw-Hill Companies, Inc., 2006 22-55 Computing Multiproduct Break-Even Point The CVP formulas may be modified for use when a company sells more than one product. • The unit contribution margin is replaced with the contribution margin for a composite unit. • A composite unit is composed of specific numbers of each product in proportion to the product sales mix. • Sales mix is the ratio of the volumes of the various products. McGraw-Hill/Irwin55 © The McGraw-Hill Companies, Inc., 2006 22-56 Computing Multiproduct Break-Even Point Exh. 22-19 The resulting break-even formula for composite unit sales is: Break-even point in composite units = Fixed costs Contribution margin per composite unit Consider the following example: Continue McGraw-Hill/Irwin56 © The McGraw-Hill Companies, Inc., 2006 22-57 Computing Multiproduct Break-Even Point Hair-Today offers three cuts as shown below. Annual fixed costs are $96,000. Compute the break-even point in composite units and in number of units for each haircut at the given sales mix. Selling Price Variable Cost Unit Contribution Sales Mix Ratio McGraw-Hill/Irwin57 Haircuts Basic Ultra Budget $ 10.00 $ 16.00 $ 8.00 6.50 9.00 4.00 $ 3.50 $ 7.00 $ 4.00 4 2 1 © The McGraw-Hill Companies, Inc., 2006 22-58 Computing Multiproduct Break-Even Point Hair-Today offers three cuts as shown below. Annual fixed costs are $96,000. Compute the break-even point in composite units and in number of units for A 4:2:1 mix thatsales if there are eachsales haircut atmeans the given mix. 500 budget cuts, then there will be 1,000 ultra cuts, and 2,000 basic cuts. Selling Price Variable Cost Unit Contribution Sales Mix Ratio McGraw-Hill/Irwin58 Haircuts Basic Ultra Budget $ 10.00 $ 16.00 $ 8.00 6.50 9.00 4.00 $ 3.50 $ 7.00 $ 4.00 4 2 1 © The McGraw-Hill Companies, Inc., 2006 22-59 Computing Multiproduct Break-Even Point Step 1: Compute contribution margin per composite unit. Selling Price Variable Cost Unit Contribution Sales Mix Ratio McGraw-Hill/Irwin59 Basic $10.00 6.50 $3.50 ×4 $ 14.00 Haircuts Ultra $16.00 9.00 $7.00 ×2 $ 14.00 Budget $8.00 4.00 $4.00 ×1 $ 4.00 © The McGraw-Hill Companies, Inc., 2006 22-60 Computing Multiproduct Break-Even Point Step 1: Compute contribution margin per composite unit. Basic Selling Price $10.00 Variable Cost 6.50 Unit Contribution $3.50 Sales Mix Ratio ×4 Weighted Contribution $ 14.00 Haircuts Ultra Budget $16.00 $8.00 9.00 4.00 $7.00 $4.00 ×2 ×1 + $ 14.00 + $ 4.00 = $ 32.00 Contribution margin per composite unit McGraw-Hill/Irwin60 © The McGraw-Hill Companies, Inc., 2006 22-61 Computing Multiproduct Break-Even Point Exh. 22-19 Step 2: Compute break-even point in composite units. Break-even point in composite units McGraw-Hill/Irwin61 = Fixed costs Contribution margin per composite unit © The McGraw-Hill Companies, Inc., 2006 22-62 Computing Multiproduct Break-Even Point Exh. 22-19 Step 2: Compute break-even point in composite units. = Fixed costs Contribution margin per composite unit Break-even point in composite units = $96,000 $32.00 per composite unit Break-even point in composite units = 3,000 composite units Break-even point in composite units McGraw-Hill/Irwin62 © The McGraw-Hill Companies, Inc., 2006 22-63 Computing Multiproduct Break-Even Point Step 3: Determine the number of each haircut that must be sold to break even. Sales Composite Product Mix Cuts Haircuts Basic 4 × 3,000 = 12,000 Ultra 2 × 3,000 = 6,000 Budget 1 × 3,000 = 3,000 McGraw-Hill/Irwin63 © The McGraw-Hill Companies, Inc., 2006 22-64 Multiproduct Break-Even Income Statement Exh. 22-20 Step 4: Verify the results. Basic Selling Price $ 10.00 Variable Cost 6.50 Unit Contribution $ 3.50 Sales Volume × 12,000 Total Contribution $ 42,000 Fixed Costs Income McGraw-Hill/Irwin64 Haircuts Ultra $ 16.00 9.00 $ 7.00 × 6,000 $ 42,000 Budget $ 8.00 4.00 $ 4.00 × 3,000 $ 12,000 Combined $ 96,000 96,000 $ 0 © The McGraw-Hill Companies, Inc., 2006 22-65 Operating Leverage A measure of the extent to which fixed costs are being used in an organization. A measure of how a percentage change in sales will affect profits. Contribution margin Net income McGraw-Hill/Irwin65 = Degree of operating leverage © The McGraw-Hill Companies, Inc., 2006 22-66 Operating Leverage Rydell Company Sales (1,600 units) Less: variable expenses Contribution margin Less: fixed expenses Net income Contribution margin Net income $48,000 $24,000 McGraw-Hill/Irwin66 = 2.0 $160,000 112,000 48,000 24,000 $ 24,000 = Degree of operating leverage If Rydell increases sales by 10 percent, what will the percentage increase in income be? © The McGraw-Hill Companies, Inc., 2006 22-67 Operating Leverage Rydell Company Sales (1,600 units) Less: variable expenses Contribution margin Less: fixed expenses Net income $160,000 112,000 48,000 24,000 $ 24,000 Percent increase in sales Degree of operating leverage Percent increase in income McGraw-Hill/Irwin67 10% × 2 20% © The McGraw-Hill Companies, Inc., 2006 22-68 Homework for Chapter 22 Ex 22-6, 22-9, 22-11, 22-13, 22-14 Problem 22-3A, 22-5A, 22-6A McGraw-Hill/Irwin68 © The McGraw-Hill Companies, Inc., 2006 22-69 End of Chapter 22 McGraw-Hill/Irwin69 © The McGraw-Hill Companies, Inc., 2006