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Chapter 9Break-Even Point andCost-Volume-Profit AnalysisCost AccountingFoundations and EvolutionsKinney, Prather, Raiborn

Cost-Volume-Profit (CVP) AnalysisRelationship ofRevenueCostsVolume changesTaxesProfitsApplies toManufacturersWholesalersRetailersService industriesVariable Costing and CVPVariable costingSeparates costs into fixed and variable componentsShows fixed costs in lump-sum amounts, not on a per-unit basisDoes not allow for deferral/release of fixed costs to/from inventory when production and sales volumes differUse CVP Analysis toCompute the break-even pointStudy interrelationships of pricesvolumesfixed and variable costscontribution marginsprofitsUse CVP Analysis toCalculate the level of sales necessary to achieve a target profitSet sales priceAnswer what-if questions to influence current operations and predict future operationsCost-Volume-Profit AssumptionsCompany is operating within the relevant rangeRevenue per unit remains constantVariable costs per unit remain constantTotal fixed costs remain constantMixed costs are separated into variable and fixed elementsEquationsBreak-even point Total Revenues = Total CostsTotal Revenues - Total Costs = Zero Profit

EquationsContribution Margin (CM)Sales Price - Variable Cost = CM per unitRevenue - Total Variable Costs = CM in total

Contribution Margin Ratio (CM%)Sales Price Variable Cost Sales PriceBreak-Even Formula - UnitsTotal Fixed CostsSales Price (per unit) - Variable Cost (per unit)

$100,000 12 - 4 = 12,500 unitsIf fixed costs are $100,000, unit sales price is $12, and unit variable cost is $4, the break-even point is 12,500 unitsContributionMarginBreak-Even Formula - DollarsTotal Fixed CostsSales Price (per unit) - Variable Cost (per unit)Sales Price (per unit)

If fixed costs are $100,000, unit sales price is $12, and unit variable cost is $4, the break-even point is $150,000$100,000 12 - 4 = $150,000 12ContributionMargin RatioIncome Statement ProofSalesLessTotal variable costsContribution MarginLessTotal fixed costsProfit before taxes$ 150,000 (12,500 * 12) (50,000) (12,500 * 4)$ 100,000 (100,000) -0-If fixed costs are $100,000, unit sales price is $12, and unit variable cost is $4, the break-even point is 12,500 unitsUsing Cost-Volume-Profit AnalysisSetting a target profitEnter before-tax profit in numerator

$100,000 + $30,000 12 - 4 = $195,000 12If fixed costs are $100,000, unit sales price is $12, unit variable cost is $4, and the desired before-tax profit is $30,000, the required sales are $195,000Using Cost-Volume-Profit AnalysisSetting a target profitConvert after-tax profit to before-tax profit

Before-tax profit = After-tax profit 1 - tax rate $48,000 = 1 - 20%$60,000At a 20% tax rate, an after-tax profit of $48,000 equals a before-tax profit of $60,000 Setting a target profitConvert after-tax profit to before-tax profit Enter before-tax profit in numeratorIf fixed costs are $100,000, unit sales price is $12, unit variable cost is $4, and the desired after-tax profit is $48,000, the required sales are $240,000$100,000 + $60,000 12 - 4 = $240,000 12Using Cost-Volume-Profit AnalysisIncome Statement ProofSalesLessTotal variable costsContribution MarginLessTotal fixed costsProfit before taxesIncome taxesProfit after taxes$ 240,000 (20,000 * 12) (80,000) (20,000 * 4)$ 160,000 (100,000)$ 60,000 (12,000) (60,000 * 20%)$ 48,000If fixed costs are $100,000, unit sales price is $12, unit variable cost is $4, and the desired after-tax profit is $48,000, the required sales are $240,000Using Cost-Volume-Profit AnalysisSet profit per unit

X = FC / (CMu - PuBT)Sales VolumeTotalFixedCostContributionMargin

Profit per Unit Before TaxGraph Approach to BreakevenBreak-even chart illustrates relationships amongRevenueVolumeCosts

Traditional CVP GraphTotal$Activity LevelFixed CostsTraditional CVP GraphTotal$Activity LevelFixed CostsTotal CostsTraditional CVP GraphTotal$Activity LevelTotal CostsVariable CostsTraditional CVP GraphTotal$Activity LevelTotal CostsTotal RevenuesTraditional CVP GraphTotal$Activity LevelTotal CostsTotal RevenuesBEPLossProfitProfit-Volume Graph

$Activity LevelProfit-Volume Graph

$Activity LevelFixed CostsProfit-Volume Graph

$Activity LevelFixed CostsBEPProfit-Volume Graph$Activity LevelFixed CostsBEPProfitLossIncome Statement ApproachSalesLessTotal variable costsContribution MarginLessTotal fixed costsProfit before taxesIncome taxesProfit after taxes B/E$ 150,000 (50,000)$ 100,000 (100,000) -0-Target Profit$ 240,000 (80,000)$ 160,000 (100,000) 60,000 (24,000)$ 36,000Proof of CVP and/or graph solutionsIncremental AnalysisFocuses only on factors that change from one option to anotherChanges in revenues, costs, and/or volumeBreak-even point increases whenfixed costs increasesales price decreasesvariable costs increase

Multiproduct Cost-Volume-Profit AnalysisAssumes a constant product sales mixContribution margin is weighted on the quantities of each product included in the bag of productsContribution margin of the product making up the largest proportion of the bag has the greatest impact on the average contribution margin of the product mixMultiproduct Cost-Volume-Profit Analysis

32Sales mixContributionmargin per unit$2$1FC = $8,000The BagThree units of spray for every two units of liquidMultiproduct Cost-Volume-Profit Analysis

32Sales mixContributionmargin per unit$2$1 $80003($2) + 2($1) = 1,000 bagsBreakevenMultiproduct Cost-Volume-Profit Analysis

32Sales mixx 1,000 3,000x 1,000 2,000Breakeven bagBreakeven unitsTo break evensell 3,000 sprays and 2,000 liquidsIncome Statement ProofSales (units)*CM per unitTotal CMLessTotal fixed costsProfit before taxesSpray3,000* 2$6,000 Liquid2,000* 1$2,000 Total

$8,000(8,000) -0- Margin of SafetyHow far the company is operating from its break-even pointBudgeted (or actual) sales after the break-even pointThe amount that sales can drop before reaching the break-even pointMeasure of the amount of cushion against lossesIndication of riskMargin of SafetyUnits Actual units - break-even unitsDollarsActual sales dollars - break-even sales dollarsPercentage Margin of Safety in units or dollarsActual unit sales or dollar salesMargin of SafetyThe lower the margin of safety, the more carefully management must watch sales and control costsOperating LeverageRelationship of variable and fixed costsEffect on profits when volume changesCost structure strongly influences the impact that a change in volume has on profits

Operating LeverageHigh Operating LeverageLow variable costsHigh fixed costsHigh contribution margin High break-even pointSales after break-even have greater impact on profitsLow Operating LeverageHigh variable costsLow fixed costsLow contribution marginLow break-even pointSales after break-even have lesser impact on profitsDegree of Operating LeverageMeasures how a percentage change in sales will affect profitsDegree of Operating LeverageContribution MarginProfit Before TaxesDegree of Operating Leverage and Margin of SafetyWhen margin of safety is small, the degree of operating leverage is largeMargin of Safety% = 1/Degree of Operating Leverage

Degree of Operating Leverage = 1/Margin of Safety%Degree of Operating Leverage and Margin of SafetyActual sales200,000 unitsBreak-even sales 90,000 unitsContribution margin$408,000Profit before tax$224,400Margin of Safety % = Actual sales Break-even sales Actual sales

= 200,000 - 90,000200,00055%Degree of Operating Leverage and Margin of SafetyActual sales200,000 unitsBreak-even sales 90,000 unitsContribution margin$408,000Profit before tax$224,400Degree of Operating = Contribution margin Leverage = Profit before taxes

= 408,000224,4001.818Margin of Safety% = 1 Degree of Operating Leverage 55% = 1 1.818

Degree of Operating =1Leverage Margin of Safety% 1.818 = 1 .55Degree of Operating Leverage and Margin of SafetyCost-Volume-Profit AssumptionsCompany is operating within the relevant rangeRevenue and variable costs per unit are constantTotal contribution margin increases proportionally with increases in unit salesTotal fixed costs remain constantMixed costs are separated into variable and fixed elements

Cost-Volume-Profit AssumptionsNo change in inventory (production equals sales)No change in capacitySales mix remains constantAnticipated price level changes included in formulasLabor productivity, production technology, and market conditions remain constant

Additional ConsiderationAre fixed costs fixed or long-term variable costs?

QuestionsWhat is the difference between absorption and variable costing?How do companies use cost-volume-profit analysis?What are the underlying assumptions of cost-volume-profit analysis?