Chapter Cost-Volume-Profit Relationships Learning Objectives LO1.Explain how changes in activity affect contribution margin and net operating income LO2.Prepare and interpret a cost-volume-profit (CVP) graph LO3.Use the contribution margin ratio (CM ratio) to compute changes in contribution margin and net operating income resulting from changes in sales volume LO4.Show the effects on contribution margin of changes in variable costs, fixed costs, selling price, and volume LO5.Compute the break-even point in unit sales and sales dollars LO6.Determine the level of sales needed to achieve a desired target profit LO7.Compute the margin of safety and explain its significance LO8.Compute the degree of operating leverage at a particular level of sales, and explain how the degree of operating leverage can be used to predict changes in net operating income LO9.Compute the break-even point for a multiple product company and explain the effects of shifts in the sales mix on contribution margin and the break-even point New in this Edition • Several new In Business boxes have been added • A number of new exercises have been added, each of which focuses on a single learning objective Chapter Overview A The Basics of Cost-Volume-Profit (CVP) Analysis (Exercises 6-1, 6-10, 6-14, and 6-15.) Cost-volume-profit (CVP) analysis is a key step in many decisions CVP analysis involves specifying a model of the relations among the prices of products, the volume or level of activity, unit variable costs, total fixed costs, and the sales mix This model is used to predict the impact on profits of changes in those parameters Contribution Margin Contribution margin is the amount remaining from sales revenue after variable expenses have been deducted It contributes towards covering fixed costs and then towards profit Unit Contribution Margin The unit contribution margin can be used to predict changes in total contribution margin as a result of changes in the unit sales of a product To this, the unit contribution margin is simply multiplied by the change in unit sales Assuming no change in fixed costs, the change in total contribution margin falls directly to the bottom line as a change in profits 333 Contribution Margin Ratio The contribution margin (CM) ratio is the ratio of the contribution margin to total sales It shows how the contribution margin is affected by a given dollar change in total sales The contribution margin ratio is often easier to work with than the unit contribution margin, particularly when a company has many products This is because the contribution margin ratio is denominated in sales dollars, which is a convenient way to express activity in multi-product firms B Some Applications of CVP Concepts (Exercises 6-4, 6-10, 6-11, 6-12, 6-13, and 616.) CVP analysis is typically used to estimate the impact on profits of changes in selling price, variable cost per unit, sales volume, and total fixed costs CVP analysis can be used to estimate the effect on profit of a change in any one (or any combination) of these parameters A variety of examples of applications of CVP are provided in the text C CVP Relationships in Graphic Form (Exercises 6-2 and 6-11.) CVP graphs can be used to gain insight into the behavior of expenses and profits The basic CVP graph is drawn with dollars on the vertical axis and unit sales on the horizontal axis Total fixed expense is drawn first and then variable expense is added to the fixed expense to draw the total expense line Finally, the total revenue line is drawn The total profit (or loss) is the vertical difference between the total revenue and total expense lines The break-even occurs at the point where the total revenue and total expenses lines cross D Break-Even Analysis and Target Profit Analysis (Exercises 6-5, 6-6, 6-11, 6-12, and 6-15.) Target profit analysis is concerned with estimating the level of sales required to attain a specified target profit Break-even analysis is a special case of target profit analysis in which the target profit is zero Basic CVP equations Both the equation and contribution (formula) methods of breakeven and target profit analysis are based on the contribution approach to the income statement The format of this statement can be expressed in equation form as: Profits = Sales − Variable expenses − Fixed expenses In CVP analysis this equation is commonly rearranged and expressed as: Sales = Variable expenses + Fixed expenses + Profits a The above equation can be expressed in terms of unit sales as follows: Price × Unit sales = Unit variable cost × Unit sales + Fixed expenses + Profits ⇓ Unit contribution margin × Unit sales = Fixed expenses + Profits ⇓ Fixed expenses +Profits Unit sales = Unit contribution margin b The basic equation can also be expressed in terms of sales dollars using the variable expense ratio: Sales = Variable expense ratio × Sales + Fixed expenses + Profits ⇓ 334 (1 − Variable expense ratio) × Sales = Fixed expenses + Profits ⇓ Contribution margin ratio* × Sales = Fixed expenses + Profits ⇓ Fixed expenses +Profits Sales = Contribution margin ratio Variable expenses Sales Sales-Variable expenses = Sales Contribution margin = Sales = Contribution margin ratio * − Variable expense ratio = 1− Break-even point using the equation method The break-even point is the level of sales at which profit is zero It can also be defined as the point where total sales equals total expenses or as the point where total contribution margin equals total fixed expenses Breakeven analysis can be approached either by the equation method or by the contribution margin method The two methods are logically equivalent a The Equation Method—Solving for the Break-Even Unit Sales This method involves following the steps in section (1a) above Substitute the selling price, unit variable cost and fixed expense in the first equation and set profits equal to zero Then solve for the unit sales b The Equation Method—Solving for the Break-Even Sales in Dollars This method involves following the steps in section (1b) above Substitute the variable expense ratio and fixed expenses in the first equation and set profits equal to zero Then solve for the sales Break-even point using the contribution method This is a short-cut method that jumps directly to the solution, bypassing the intermediate algebraic steps a The Contribution Method—Solving for the Break-Even Unit Sales This method involves using the final formula for unit sales in section (1a) above Set profits equal to zero in the formula Break-even unit sales = Fixed expenses +$0 Fixed expenses = Unit contribution margin Unit contribution margin b The Contribution Method—Solving for the Break-Even Sales in Dollars This method involves using the final formula for sales in section (1b) above Set profits equal to zero in the formula Break-even sales = Fixed expenses +$0 Fixed expenses = Contribution margin ratio Contribution margin ratio 335 Target profit analysis Either the equation method or the contribution margin method can be used to find the number of units that must be sold to attain a target profit In the case of the contribution margin method, the formulas are: Unit sales to attain target profits = Dollar sales to attain target profits = Fixed expenses +Target profits Unit contribution margin Fixed expenses +Target profits Contribution margin ratio Note that these formulas are the same as the break-even formulas if the target profit is zero E Margin of Safety (Exercises 6-7 and 6-15.) The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales It is the amount by which sales can drop before losses begin to be incurred The margin of safety can be computed in terms of dollars: Margin of safety in dollars = Total sales – Break-even sales or in percentage form: Margin of safety percentage = Margin of safety in dollars Total sales F Cost Structure Cost structure refers to the relative proportion of fixed and variable costs in an organization Understanding a company’s cost structure is important for decision-making as well as for analysis of performance G Operating Leverage (Exercises 6-8 and 6-16.) Operating leverage is a measure of how sensitive net operating income is to a given percentage change in sales Degree of operating leverage The degree of operating leverage at a given level of sales is computed as follows: Contribution margin Degree of operating leverage = Net operating income The math underlying the degree of operating leverage The degree of operating leverage can be used to estimate how a given percentage change in sales volume will affect net income at a given level of sales, assuming there is no change in fixed expenses To verify this, consider the following: Degree of operating × Percentage change = ⎛ Contribution margin ⎞ × ⎛ New sales-Sales ⎞ ⎜ ⎟ ⎜ ⎟ leverage in sales Sales ⎠ ⎝ Net operating income ⎠ ⎝ = ⎛ Contribution margin ⎞ ⎛ New sales-Sales ⎞ ⎟ ⎜ ⎟×⎜ Sales ⎝ ⎠ ⎝ Net operating income ⎠ 336 ⎛ New sales-Sales ⎞ = CM ratio × ⎜ ⎟ ⎝ Net operating income ⎠ ⎛ CM ratio × New sales-CM ratio × Sales ⎞ =⎜ ⎟ Net operating income ⎝ ⎠ = ⎛ New contribution margin-Contribution margin ⎞ ⎜ ⎟ Net operating income ⎝ ⎠ ⎛ Change in net operating income ⎞ =⎜ ⎟ Net operating income ⎝ ⎠ = Percentage change in net operating income Thus, providing that fixed expenses are not affected and the other assumptions of CVP analysis are valid, the degree of operating leverage provides a quick way to predict the percentage effect on profits of a given percentage increase in sales The higher the degree of operating leverage, the larger the increase in net operating income Degree of operating leverage is not constant The degree of operating leverage is not constant as the level of sales changes For example, at the break-even point the degree of operating leverage is infinite since the denominator of the ratio is zero Therefore, the degree of operating leverage should be used with some caution and should be recomputed for each level of starting sales Operating leverage and cost structure Richard Lord, “Interpreting and Measuring Operating Leverage,” Issues in Accounting Education, Fall 1995, pp 31xx-229, points out that the relation between operating leverage and the cost structure of the company is contingent It is difficult, for example, to infer the relative proportions of fixed and variable costs in the cost structures of any two companies just by comparing their operating leverages We can, however, say that if two single-product companies have the same profit, the same selling price, the same unit sales, and the same total expenses, then the company with the higher operating leverage will have a higher proportion of fixed costs in its cost structure If they not have the same profit, the same unit sales, the same selling price, and the same total expenses, we cannot safely make this inference about their cost structure All of the statements in the text about operating leverage and cost structure assume that the companies being compared are identical except for the proportions of fixed and variable costs in their cost structures H Structuring Sales Commissions Students may have a tendency to overlook the importance of this section due to its brevity You may want to discuss with your students how salespeople are ordinarily compensated (salary plus commissions based on sales) and how this can lead to dysfunctional behavior For example, would a company make more money if its salespeople steered customers toward Model A or Model B as described below? 337 Price Variable cost Unit CM Model A $100 75 $ 25 Model B $150 130 $ 20 Which model will salespeople push hardest if they are paid a commission of 10% of sales revenue? I Sales Mix (Exercises 6-9, 6-14, and 6-17.) Sales mix is the relative proportions in which a company’s products are sold Most companies have a number of products with differing contribution margins Thus, changes in the sales mix can cause variations in a company’s profits As a result, the break-even point in a multi-product company is dependent on the sales mix Constant sales mix assumption In CVP analysis, it is usually assumed that the sales mix will not change Under this assumption, the break-even level of sales dollars can be computed using the overall contribution margin (CM) ratio In essence, it is assumed that the company has only one product that consists of a basket of its various products in a specified proportion The contribution margin ratio of this basket can be easily computed by dividing the total contribution margin of all products by total sales Total contribution margin Overall CM ratio = Total sales Use of the overall CM ratio The overall contribution margin ratio can be used in CVP analysis exactly like the contribution margin ratio for a single product company For a multi-product company the formulas for break-even sales dollars and the sales required to attain a target profit are: Break-even sales = Sales to achieve target profits = Fixed expenses Overall CM ratio Fixed expenses +Target profits Overall CM ratio Note that these formulas are really the same as for the single product case The constant sales mix assumption allows us to use the same simple formulas Changes in sales mix If the proportions in which products are sold change, then the overall contribution margin ratio will change Since the sales mix is not in reality constant, the results of CVP analysis should be viewed with more caution in multi-product companies than in single product companies J Assumptions in CVP Analysis Simple CVP analysis relies on simplifying assumptions However, if a manager knows that one of the assumptions is violated, the CVP analysis can often be easily modified to make it more realistic Selling price is constant The assumption is that the selling price of a product will not change as the unit volume changes This is not wholly realistic since unit sales and the selling price are usually inversely related In order to increase volume it is often necessary to drop the price However, CVP analysis can easily accommodate more realistic 338 assumptions A number of examples and problems in the text show how to use CVP analysis to investigate situations in which prices are changed Costs are linear and can be accurately divided into variable and fixed elements It is assumed that the variable element is constant per unit and the fixed element is constant in total This implies that operating conditions are stable It also implies that the fixed costs are really fixed When volume changes dramatically, this assumption becomes tenuous Nevertheless, if the effects of a decision on fixed costs can be estimated, this can be explicitly taken into account in CVP analysis A number of examples and problems in the text show how to use CVP analysis when fixed costs are affected The sales mix is constant in multi-product companies This assumption is invoked so as to use the simple break-even and target profit formulas in multi-product companies If unit contribution margins are fairly uniform across products, violations of this assumption will not be important However, if unit contribution margins differ a great deal, then changes in the sales mix can have a big impact on the overall contribution margin ratio and hence on the results of CVP analysis If a manager can predict how the sales mix will change, then a more refined CVP analysis can be performed in which the individual contribution margins of products are computed In manufacturing companies, inventories not change It is assumed that everything the company produces is sold in the same period Violations of this assumption result in discrepancies between financial accounting net operating income and the profits calculated using the contribution approach This topic is covered in detail in the chapter on variable costing 339 Assignment Materials Assignment Exercise 6-1 Exercise 6-2 Exercise 6-3 Exercise 6-4 Exercise 6-5 Exercise 6-6 Exercise 6-7 Exercise 6-8 Exercise 6-9 Exercise 6-10 Exercise 6-11 Exercise 6-12 Exercise 6-13 Exercise 6-14 Exercise 6-15 Exercise 6-16 Exercise 6-17 Problem 6-18 Problem 6-19 Problem 6-20 Problem 6-21 Problem 6-22 Problem 6-23 Problem 6-24 Problem 6-25 Problem 6-26 Problem 6-27 Problem 6-28 Problem 6-29 Problem 6-30 Case 6-31 Case 6-32 Case 6-33 Case 6-34 Case 6-35 Level of Topic Difficulty Preparing a contribution margin format income statement Basic Prepare a cost-volume-profit (CVP) graph Basic Computing and using the CM ratio Basic Changes in variable costs, fixed costs, selling price, and volume Basic Compute the break-even point Basic Compute the level of sales required to attain a target profit Basic Compute the margin of safety Basic Compute and use the degree of operating leverage Basic Compute the break-even point for a multi-product company Basic Using a contribution format income statement Basic Break-even analysis and CVP graphing Basic Break-even and target profit analysis Basic Break-even and target profit analysis Basic Missing data; basic CVP concepts Basic Break-even analysis; target profit; margin of safety; CM ratio Basic Operating leverage Basic Multi-product break-even analysis Basic Basic CVP analysis; graphing Basic Basics of CVP analysis; cost structure Basic Basics of CVP analysis Basic Sales mix; multi-product break-even analysis Basic Break-even analysis; pricing Medium Interpretive questions on the CVP graph Medium Various CVP questions; break-even point; cost structure; target sales Medium Graphing; incremental analysis; operating leverage Medium Changes in fixed and variable costs; break-even and target profit analysis Medium Break-even and target profit analysis Medium Changes in cost structure; break-even analysis; operating leverage; margin of safety Medium Sales mix; break-even analysis; margin of safety Medium Sales mix; multi-product break-even analysis Medium Detailed income statement; CVP analysis Difficult Missing data; break-even analysis; target profit; margin of safety; operating leverage Difficult Cost structure; break-even; target profits Difficult Break-even analysis with step fixed costs Difficult Break-evens for individual products in a multi-product company Difficult 340 Suggested Time 20 30 10 20 20 10 10 20 20 20 30 30 30 20 30 15 30 60 60 60 30 45 30 75 60 30 30 60 45 60 60 90 75 75 60 Essential Problems: Problem 6-18 or Problem 6-25, Problem 6-19 or Problem 6-20, Problem 621, Problem 6-24 Supplementary Problems: Problem 6-22, Problem 6-23, Problem 6-26, Problem 6-27, Problem 6-28, Problem 6-29, Problem 6-30, Case 6-31, Case 6-32, Case 6-33, Case 6-34, Case 6-35 341 342 TM 6-2 THE CONTRIBUTION APPROACH A contribution format income statement is very useful in CVP analysis since it highlights cost behavior EXAMPLE: Last month’s contribution income statement for Nord Corporation, a manufacturer of exercise bicycles, follows: Total Sales (500 bikes) $250,000 Less variable expenses 150,000 Contribution margin 100,000 Less fixed expenses 80,000 Net operating income $ 20,000 Per Unit Percent $500 300 $200 100% 60 40% CONTRIBUTION MARGIN: • The amount that sales (net of variable expenses) contributes toward covering fixed expenses and then toward profits • The unit contribution margin remains constant so long as the selling price and the unit variable cost not change © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 6-3 VOLUME CHANGES AND NET OPERATING INCOME Contribution income statements are given on this and the following page for monthly sales of 1, 2, 400, and 401 bikes Sales (1 bike) Less variable expenses Contribution margin Less fixed expenses Net operating income (loss) Sales (2 bikes) Less variable expenses Contribution margin Less fixed expenses Net operating income (loss) $ Total Per Unit Percent Total Per Unit Percent 500 300 200 80,000 $(79,800) $ 1,000 600 400 80,000 $(79,600) $500 300 $200 $500 300 $200 100% 60 40% 100% 60 40% Note the following points: The contribution margin must first cover the fixed expenses If it doesn’t, there is a loss As additional units are sold, fixed expenses are whittled down until they have all been covered © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 6-4 VOLUME CHANGES AND NET OPERATING INCOME (cont’d) Sales (400 bikes) Less variable expenses Contribution margin Less fixed expenses Net operating income (loss) Sales (401 bikes) Less variable expenses Contribution margin Less fixed expenses Net operating income (loss) Total Per Unit Percent Total Per Unit Percent $200,000 120,000 80,000 80,000 $ $200,500 120,300 80,200 80,000 $ 200 $500 300 $200 $500 300 $200 100% 60 40% 100% 60 40% Note the following points: If the company sells exactly 400 bikes a month, it will just break even (no profit or loss) The break-even point is: • The point where total sales revenue equals total expenses (variable and fixed) • The point where total contribution margin equals total fixed expenses Each additional unit sold increases net operating income by the amount of the unit contribution margin © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 6-5 PREPARING A CVP GRAPH Dollars (000) $300 Step (Total Sales) 250 230 Step (Total Expenses) $200 Step (Fixed Expenses) $100 80 200 400 Number of bikes 500 © The McGraw-Hill Companies, Inc., 2006 All rights reserved 600 TM 6-6 THE COMPLETED CVP GRAPH Total Sales Dollars (000) $300 Break-even point: 400 bikes or $200,000 in sales $200 $100 ss o L a re a fit o Pr Total Expenses ea ar 80 200 400 Number of bikes © The McGraw-Hill Companies, Inc., 2006 All rights reserved 600 TM 6-7 CONTRIBUTION MARGIN RATIO The contribution margin (CM) ratio is the ratio of contribution margin to total sales: CM ratio= Contribution margin Total sales If the company has only one product, the CM ratio can also be computed using per unit data: CM ratio= Unit contribution margin Unit selling price EXAMPLE: For Nord Corporation, the CM ratio is 40%, computed as follows: CM ratio= Contribution margin $100,000 = =40% Total sales $250,000 or CM ratio= Unit contribution margin $200 per unit = =40% Unit selling price $500 per unit © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 6-8 CONTRIBUTION MARGIN RATIO (cont’d) The CM ratio shows how the contribution margin will be affected by a given change in total sales EXAMPLE: Assume that Nord Corporation’s sales increase by $150,000 next month What will be the effect on (1) the contribution margin and (2) net operating income? (1) Effect on contribution margin: Increase in sales Multiply by the CM ratio Increase in contribution margin (2) $150,000 × 40% $ 60,000 Effect on net operating income: If fixed expenses not change, the net operating income for the month will also increase by $60,000 Sales (in units) Sales (in dollars) Less variable expenses Contribution margin Less fixed expenses Net operating income Present 500 $250,000 150,000 100,000 80,000 $ 20,000 Expected 800 $400,000 240,000 160,000 80,000 $ 80,000 Change 300 $150,000 90,000 60,000 $ 60,000 © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 6-9 BREAK-EVEN ANALYSIS Summary of Nord Corporation Data: Per Bike Percent Selling price Variable expenses Contribution margin Fixed expenses $500 300 $200 100% 60 40% Per Month $80,000 EQUATION METHOD Q = Break-even quantity in bikes Profits = Sales – (Variable expenses + Fixed expenses) Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 + $0 $200Q = $80,000 Q = $80,000 ÷ $200 per bike Q = 400 bikes X = Break-even point in sales dollars Sales = Variable expenses + Fixed expenses + Profits X = 0.60X + $80,000 + $0 0.40X = $80,000 X = $80,000 ÷ 0.40 X = $200,000 CONTRIBUTION MARGIN METHOD Fixed expenses $80,000 Breakeven = = =400 bikes in units Unit contribution margin $200 per bike Breakeven = Fixed expenses = $80,000 =$200,000 in sales dollars CM ratio 0.40 © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 6-10 TARGET PROFIT ANALYSIS EXAMPLE: Assume that Nord Corporation’s target profit is $70,000 per month How many exercise bikes must it sell each month to reach this goal? EQUATION METHOD Q = Number of bikes to attain the target profit Sales = Variable Expenses + Fixed Expenses + Profits $500Q = $300Q + $80,000 + $70,000 $200Q = $150,000 Q = $150,000 ÷ $200 bikes Q = 750 Bikes (or, in sales dollars, 750 bikes × $500 per bike = $375,000) X = Dollar sales to reach the target profit figure Sales = Variable Expenses + Fixed Expenses + Profits X = 0.60X + $80,000 + $70,000 0.40X = $150,000 X = $150,000 ÷ 0.40 X = $375,000 CONTRIBUTION MARGIN METHOD Unit sales to attain = Fixed expenses + Target profit target profit Unit contribution margin = $80,00+$70,000 =750 bikes $200 per bike Dollar sales to attain = Fixed expenses + Target profit target profit CM ratio = $80,00+$70,000 =$375,000 0.40 © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 6-11 MARGIN OF SAFETY The margin of safety is the excess of budgeted (or actual) sales over the break-even sales The margin of safety can be expressed either in dollar or percentage form The formulas are: Margin of safety =Total sales-Breakeven sales in dollars Margin of safety = Margin of safety in dollars percentage Total sales Company X Sales $500,000 Less variable expenses 350,000 Contribution margin 150,000 Less fixed expenses 90,000 Net operating income $ 60,000 Break-even point: $90,000 ÷ 0.30 $300,000 $340,000 ÷ 0.80 Margin of safety in dollars: $500,000 – $300,000 $200,000 $500,000 – $425,000 Margin of safety percentage: $200,000 ÷ $500,000 40% $75,000 ÷ $500,000 100% 70 30% Company Y $500,000 100,000 400,000 340,000 $ 60,000 $425,000 $75,000 15% © The McGraw-Hill Companies, Inc., 2006 All rights reserved 100% 20 80% TM 6-12 OPERATING LEVERAGE Operating leverage measures how a given percentage change in sales affects net operating income Contribution margin Degree of = operating leverage Net operating income Sales Less variable expenses Contribution margin Less fixed expenses Net operating income Degree of operating leverage Company X $500,000 100% 350,000 70 150,000 30% 90,000 $ 60,000 Company Y $500,000 100% 100,000 20 400,000 80% 340,000 $ 60,000 2.5 6.7 If the degree of operating leverage is 2.5, then a 10% increase in sales should result in a 25% (= 2.5 × 10%) increase in net operating income EXAMPLE: Assume that both company X and company Y experience a 10% increase in sales: Sales Less variable expenses Contribution margin Less fixed expenses Net operating income Increase in net operating income Company X $550,000 100% 385,000 70 165,000 30% 90,000 $ 75,000 25% Company Y $550,000 100% 110,000 20 440,000 80% 340,000 $100,000 67% © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 6-13 OPERATING LEVERAGE (cont’d) The degree of operating leverage is not constant—it changes with the level of sales EXAMPLE: At the higher level of sales, the degree of operating leverage for Company X decreases from 2.5 to 2.2 and for Company Y from 6.7 to 4.4 Sales Less variable expenses Contribution margin Less fixed expenses Net operating income Degree of operating leverage Company X (000s) Company Y (000s) $500 $550 350 385 150 165 90 90 $ 60 $ 75 $500 $550 100 110 400 440 340 340 $ 60 $100 2.5 2.2 6.7 4.4 Ordinarily, the degree of operating leverage declines as sales increase © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 6-14 MULTI-PRODUCT BREAK-EVEN ANALYSIS When a company has multiple products, the overall contribution margin (CM) ratio is used in breakeven analysis Total contribution margin Total sales dollars Overall CM ratio= Sales Less variable expenses Contribution margin Less fixed expenses Net operating income Product A Product B $100,000 100% 70,000 70 $ 30,000 30% $300,000 100% 120,000 40 $180,000 60% Total $400,000 190,000 210,000 141,750 $ 68,250 Overall CM ratio= Total contribution margin $210,000 = =52.5% Total sales dollars $400,000 Breakeven sales= Fixed expenses $141,750 = =$270,000 Oveall CM ratio 0.525 © The McGraw-Hill Companies, Inc., 2006 All rights reserved 100.0% 47.5 52.5% TM 6-15 MULTI-PRODUCT BREAK-EVEN ANALYSIS (cont’d) The relative proportions in which the products are sold is called the sales mix If the sales mix changes, the overall contribution margin ratio will change Example: Assume that total sales remain unchanged at $400,000 However, the sales mix shifts so that more of Product A is sold than of Product B Sales Less variable expenses Contribution margin Less fixed expenses Net operating income Product A Product B $300,000 100% 210,000 70 $ 90,000 30% $100,000 100% 40,000 40 $ 60,000 60% Total $400,000 250,000 150,000 141,750 $ 8,250 Overall CM ratio= Total contribution margin $150,000 = =37.5% Total sales dollars $400,000 Breakeven sales= Fixed expenses $141,750 = =$378,000 Oveall CM ratio 0.375 © The McGraw-Hill Companies, Inc., 2006 All rights reserved 100.0% 62.5 37.5% TM 6-16 MAJOR ASSUMPTIONS OF CVP ANALYSIS Selling price is constant The price does not change as volume changes Costs are linear and can be accurately split into fixed and variable elements The total fixed cost is constant and the variable cost per unit is constant The sales mix is constant in multi-product companies In manufacturing companies, inventories not change The number of units produced equals the number of units sold © The McGraw-Hill Companies, Inc., 2006 All rights reserved [...].. .Chapter 6 Lecture Notes Helpful Hint: Before beginning the lecture, show students the sixth segment from the first tape of the McGraw-Hill/Irwin Managerial/ Cost Accounting video library This segment introduces students to many of the concepts discussed in chapter 6 The lecture notes reinforce the concepts introduced in the video 1 I Chapter theme: Cost-volume-profit