Planning a company’s future activities and events is crucial to successful management. One of the first steps in planning is to predict the volume of activity, the costs to be incurred, sales to be made, and profit to be earned. An important tool in such planning is cost-volume-profit (CVP) analysis, which helps managers predict how changes in costs and sales levels affect profit. In its basic form, CVP analysis involves computing the sales level at which a company neither earns an income nor incurs a loss, called the break-even point. For this reason, this basic form of cost-volume-profit analysis is often called break-even analysis.
Managers use variations of CVP analysis to answer questions like:
How much does income increase if we install a new machine to reduce labor costs?
What is the change in income if selling prices decline and sales volume increases?
How will income change if we change the sales mix of our products or services?
What sales volume is needed to earn a target income?
Consequently, cost-volume-profit analysis is useful in a wide range of business decisions.

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Cost-Volume-Profit AnalysisChapter 21PowerPoint Editor: Beth Kane, MBA, CPACopyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 21-C1: Fixed Costs 2Identifying Cost Behavior Cost-volume-profit analysis is used to answer questions such as:How much does income increase if we install a new machine to reduce labor costs? What is the change in income if selling prices decline and sales volume increases? How will income change if we change the sales mix of our products or services?What sales volume is needed to earn a target income?C 13Fixed CostsC 14Variable CostsC 15Mixed CostsC 16Step-Wise CostsTotal cost increases to a new higher cost for the next higher range of activity, but remains constant within a range of activity. C 17Curvilinear Costs Costs that increase when activityincreases, but in a nonlinear manner.C 18NEED-TO-KNOWDetermine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinearcost with respect to product units.Rubber used to manufacture tennis balls $0.50 per tennis ballVariable costDepreciation (straight-line method) Electricity cost Supervisory salariesA salesperson’s commission is 7% for sales of up to $100,000, and 10% of sales for sales above $100,000$0$1,000$2,000$3,000$4,000$5,000$6,00002,0004,0006,0008,00010,000Total CostUnits Produced$0.50 per tennis ball -VariableC 19NEED-TO-KNOWDetermine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinearcost with respect to product units.Rubber used to manufacture tennis balls $0.50 per ballVariable costDepreciation (straight-line method) $2,000 per monthFixed costElectricity cost Supervisory salariesA salesperson’s commission is 7% for sales of up to $100,000, and 10% of sales for sales above $100,000$0$500$1,000$1,500$2,000$2,50002,0004,0006,0008,00010,000Total CostUnits Produced$2,000 per month -FixedC 110NEED-TO-KNOWDetermine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinearcost with respect to product units.Rubber used to manufacture tennis balls $0.50 per ballVariable costDepreciation (straight-line method) $2,000 per monthFixed costElectricity cost $500 + $0.10 per ballMixed costSupervisory salariesA salesperson’s commission is 7% for sales of up to $100,000, and 10% of sales for sales above $100,000$0$200$400$600$800$1,000$1,200$1,400$1,60002,0004,0006,0008,00010,000Total CostUnits Produced$500 + $0.10 per unit-MixedC 111NEED-TO-KNOWDetermine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinearcost with respect to product units.Rubber used to manufacture tennis balls $0.50 per ballVariable costDepreciation (straight-line method) $2,000 per monthFixed costElectricity cost $500 + $0.10 per ballMixed costSupervisory salaries 4,000 units per shift$5,000 per mo. per supervisor Step-wise costA salesperson’s commission is 7% for sales of up to $100,000, and 10% of sales for sales above $100,000$0$2,000$4,000$6,000$8,000$10,000$12,000$14,000$16,00002,0004,0006,0008,00010,000Units Produced$5,000 per supervisor per month -Step-wiseTotal CostC 112NEED-TO-KNOWDetermine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinearcost with respect to product units.Rubber used to manufacture tennis balls $0.50 per ballVariable costDepreciation (straight-line method) $2,000 per monthFixed costElectricity cost $500 + $0.10 per ballMixed costSupervisory salaries 4,000 units per shift$5,000 per mo. per supervisor Step-wise costCurvilinear costA salesperson’s commission is 7% for sales of up to $100,000, and 10% of sales for sales above $100,000$0$5,000$10,000$15,000$20,000$25,000$30,000$0$50,000$100,000$150,000$200,000$250,000$300,000Sales $Sales Commissions -CurvilinearTotal CostC 113 21-P1: Measuring Cost Behavior 14Measuring Cost Behavior The objective is to classify all costs as either fixed or variable. We will look at three methods:Scatter diagrams.The high-low method.Least–squares regression.A scatter diagram is a plot of cost data points on a graph. It is almost always helpful to plot cost data to be able to observe a visual picture of the relationship between cost and activity.P 115Scatter DiagramsP 116The High-Low MethodThe following relationships between unitsproduced and total cost are observed: Using these two levels of activity, compute: the variable cost per unit. the total fixed cost. P 117The High-Low MethodTotal cost = $17,525 + $0.17 per unit producedP 118The objective of the cost analysis remains the same: determination of total fixed cost and the variable unit cost.Least-Squares RegressionLeast-squares regression is usually covered in advanced cost accounting courses. It is commonly used with spreadsheet programs or calculators.P 119Comparison of Cost Estimation MethodsP 120NEED-TO-KNOWUsing the information below, use the high-low method to determine the cost equation (total fixed costs plus variable costs per unit).Activity Level Units Produced Total CostLowest1,600$9,800Highest4,00017,000Variable Cost = $7,2002,400$3per unit producedFixed Costs (at high point)Total cost = Fixed costs + $3 per unit$17,000 = Fixed costs + ($3 x 4,000)$5,000 = Fixed costsFixed Costs (at low point)Total cost = Fixed costs + $3 per unit$9,800 = Fixed costs + ($3 x 1,600)$5,000 = Fixed costsCost at high point - Cost at low pointUnits at high point - Units at low point($17,000 - $9,800)(4,000 - 1,600)Total costs = $5,000 + $3 per unitP 121NEED-TO-KNOW$0$2,000$4,000$6,000$8,000$10,000$12,000$14,000$16,000$18,00005001,0001,5002,0002,5003,0003,5004,0004,500Total Cost Units ProducedTotal CostSlope = Variable Cost $3 per unity-intercept = Fixed Costs $5,000(1,600 units, $9,800)(4,000 units, $17,000)(0 units, $5,000)= $5,000 + $3 per unitP 122 21-A1: Contribution Margin and Its Measures 23Contribution Margin and Its MeasuresA 124 21-P2: Computing the Break-Even Point 25Using Break-Even AnalysisThe 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.P 226Computing the Break-Even PointP 227 P 2Computing the Margin of Safety28NEED-TO-KNOWA manufacturer predicts fixed costs of $400,000 for the next year. Its one product sells for $170 per unit,and it incurs variable costs of $150 per unit. The company predicts total sales of 25,000 units for the nextyear.1. Compute the contribution margin per unit.2. Compute the break-even point (in units).3. Compute the margin of safety (in dollars).Contribution margin per unit, or unit contribution margin, is the amount by which a product’s unit selling price exceeds its total variable cost per unit. Sales $170 per unit Variable costs 150 per unit Contribution margin $ 20 per unit$20 per unitP 229NEED-TO-KNOWA manufacturer predicts fixed costs of $400,000 for the next year. Its one product sells for $170 per unit,and it incurs variable costs of $150 per unit. The company predicts total sales of 25,000 units for the nextyear.1. Compute the contribution margin per unit.2. Compute the break-even point (in units).3. Compute the margin of safety (in dollars).Break-even point in units = Fixed costs Contribution margin per unit $400,000 $20 per unit 20,000 units to break-evenUnitsper unitTotalSales20,000$170$3,400,000Variable costs20,000$1503,000,000Contribution margin$20400,000Fixed costs400,000Net income$0$20 per unit20,000 unitsP 230NEED-TO-KNOWA manufacturer predicts fixed costs of $400,000 for the next year. Its one product sells for $170 per unit,and it incurs variable costs of $150 per unit. The company predicts total sales of 25,000 units for the nextyear.1. Compute the contribution margin per unit.2. Compute the break-even point (in units).3. Compute the margin of safety (in dollars).The excess of expected sales over the break-even sales level is called a company’s margin of safety$20 per unit20,000 unitsUnitsper unitTotalExpected sales25,000$170$4,250,000Break-even sales20,000$1703,400,000Margin of safety$850,000$850,000P 231 21-P3: Preparing a Cost-Volume-Profit Chart 32Preparing a CVP ChartP 333Working with Changesin EstimatesP 334 21-C2: Applying Cost-Volume-Profit Analysis 35Computing Income from Sales and CostsC 236Computing Salesfor a Target IncomeC 237Computing Salesfor a Target IncomeC 238Computing Salesfor a Target IncomeC 239NEED-TO-KNOWA manufacturer predicts fixed costs of $502,000 for the next year. Its one product sells for $180 per unit,and it incurs variable costs of $126 per unit. Its target income (pretax) is $200,000.1. Compute the contribution margin ratio.2. Compute the dollar sales needed to yield the target income.3. Compute the unit sales needed to yield the target income.The contribution margin ratio is the percent of a unit’s selling price that exceeds total unit variable cost.Contribution margin ratio = Contribution margin per unit Selling price per unit $180 - $126 $54 $180 $180 30% 30%per unitRatioSales$180100%Variable costs 12670%Contribution margin$5430%C 240NEED-TO-KNOWDollar sales to achieve target income = Fixed costs + Pretax Income Contribution margin ratio $502,000 + $200,000 .30 $2,340,000A manufacturer predicts fixed costs of $502,000 for the next year. Its one product sells for $180 per unit,and it incurs variable costs of $126 per unit. Its target income (pretax) is $200,000.1. Compute the contribution margin ratio.2. Compute the dollar sales needed to yield the target income.3. Compute the unit sales needed to yield the target income.30%per unitRatioTotalSales$180100%$2,340,000Variable costs$12670%1,638,000Contribution margin$5430%702,000Fixed costs502,000Net income$200,000$2,340,000C 241NEED-TO-KNOWBreak-even point in units = Fixed costs Contribution margin per unit A manufacturer predicts fixed costs of $502,000 for the next year. Its one product sells for $180 per unit,and it incurs variable costs of $126 per unit. Its target income (pretax) is $200,000.1. Compute the contribution margin ratio.2. Compute the dollar sales needed to yield the target income.3. Compute the unit sales needed to yield the target income.30%$2,340,000Units to yield target income = Fixed costs + target (pretax) income Contribution margin per unit $502,000 + $200,000 $702,000 $180 - $126 $54 13,000 unitsUnitsper unitTotalSales13,000$180$2,340,000Variable costs13,000$1261,638,000Contribution margin$54702,000Fixed costs502,000Net income$200,00013,000 units (or $2,340,000 / $180)C 242Using Sensitivity AnalysisC 243 21-P4: Computing a Multiproduct Break-Even Point 44Computing a MultiproductBreak-Even Point The CVP formulas can 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.P 445Computing a MultiproductBreak-Even PointThe resulting break-even formulafor composite unit sales is:Break-even pointin composite unitsFixed costsContribution marginper composite unit=ContinueP 446Hair-Today offers three cuts as shown below. Annual fixed costs are $192,000. Compute the break-even point in composite units and in number of units for each haircut at the given sales mix. Computing a MultiproductBreak-Even PointP 447Computing a MultiproductBreak-Even PointP 448Computing a MultiproductBreak-Even PointP 449Break-even pointin composite unitsFixed costsContribution marginper composite unit=Break-even pointin composite units$192,000$64.00 per composite unit=Break-even pointin composite units= 3,000 composite unitsComputing a MultiproductBreak-Even PointP 450Computing a MultiproductBreak-Even PointP 451Multiproduct Break-EvenIncome StatementP 452NEED-TO-KNOWThe sales mix of a company’s two products, X and Y, is 2:1. Unit variable costs for both productsare $2, and unit selling prices are $5 for X and $4 for Y. The company has $640,000 of fixed costs.1. What is the contribution margin per composite unit?2. What is the break-even point in composite units?3. How many units of X and how many units of Y will be sold at the break-even point?Selling price per composite unitUnitsper unitTotalProduct X2$5$10Product Y1$44Total3$14Variable cost per composite unitUnitsper unitTotalProduct X2$2$4Product Y1$22Total3$6Contribution margin per composite unit ($14 - $6)$8$8P 453NEED-TO-KNOWThe sales mix of a company’s two products, X and Y, is 2:1. Unit variable costs for both productsare $2, and unit selling prices are $5 for X and $4 for Y. The company has $640,000 of fixed costs.1. What is the contribution margin per composite unit?2. What is the break-even point in composite units?3. How many units of X and how many units of Y will be sold at the break-even point?$8Break-even point in composite units = Fixed costs Contribution margin per composite unit $640,000 $8 per composite unit 80,000 composite units to break even80,000 composite unitsP 454NEED-TO-KNOWThe sales mix of a company’s two products, X and Y, is 2:1. Unit variable costs for both productsare $2, and unit selling prices are $5 for X and $4 for Y. The company has $640,000 of fixed costs.1. What is the contribution margin per composite unit?2. What is the break-even point in composite units?3. How many units of X and how many units of Y will be sold at the break-even point?$880,000 composite unitsUnits of each product at break-evenTotalProduct X80,000 composite units x 2 units per composite unit160,000Product Y80,000 composite units x 1 unit per composite unit80,000240,000Total SalesUnitsper unitTotalProduct X160,000$5$800,000Product Y80,000$4320,000Total240,000$1,120,000Total Variable CostsUnitsper unitTotalProduct X160,000$2$320,000Product Y80,000$2160,000Total240,000$480,000Composite unitsper unitTotalSales$14$1,120,000Variable costs$6480,000Contribution margin$8640,000Fixed costs640,000Net income$080,00080,000P 455Global ViewOver 90 percent of German companies surveyed report their cost accounting systems focus on contribution margin. This focus helps German companies like Volkswagen control costs and plan their production levels. 56 21-A2: Degree of Operating Leverage 57Degree of Operating LeverageA 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.A 258If Rydell increases sales by 10 percent, what will the percentage increase in income be?Operating LeverageA 259Appendix 21A: Using Excel toEstimate Least-Squares Regression60End of Chapter 2161