Chapter Three

Cost-volume-profit (CVP) analysis Cost-volume-profit (CVP) analysis examines the behavior of total revenues, total costs, and operating income as changes occur in the units sold, the selling price, the variable cost per unit, or the fixed costs of a product

A Five-Step Decision Making Process in Planning & Control RevisitedIdentify the problem and uncertaintiesObtain informationMake predictions about the futureMake decisions by choosing between alternatives, using Cost-Volume-Profit (CVP) analysisImplement the decision, evaluate performance, and learn

Assumptions of Cost-Volume-Profit Analysis1.Total sales and total costs can be represented by straight lines.2.Within the relevant range of operating activity, the efficiency of operations does not change.3.Costs can be accurately divided into fixed and variable components.4.The sales mix is constant.5.There is no change in the inventory quantities during the period.The reliability of cost-volume-profit analysis depends upon several assumptions.

Assumptions UnderlyingCVP AnalysisSelling price is constant throughout the entire relevant range.Costs are linear over the relevant range.In multi-product companies, the sales mix is constant.In manufacturing firms, inventories do not change (units produced = units sold).

2009 Pearson Prentice Hall. All rights reserved.

Foundational Assumptions in CVPChanges in production/sales volume are the sole cause for cost and revenue changesTotal costs consist of fixed costs and variable costsRevenue and costs behave and can be graphed as a linear function (a straight line)Selling price, variable cost per unit and fixed costs are all known and constantIn many cases only a single product will be analyzed. If multiple products are studied, their relative sales proportions are known and constantThe time value of money (interest) is ignored


Basic Formulae


CVP: Contribution MarginManipulation of the basic equations yields an extremely important and powerful tool extensively used in Cost Accounting: the Contribution MarginContribution Margin equals sales less variable costs CM = S VCContribution Margin per Unit equals unit selling price less variable cost per unit CMu = SP VCu


Contribution Margin, continuedContribution Margin also equals contribution margin per unit multiplied by the number of units sold (Q)CM = CMu x QContribution Margin Ratio (percentage) equals contribution margin per unit divided by Selling PriceCMR = CMu SPInterpretation: how many cents out of every sales dollar are represented by Contribution Margin


Basic Formula DerivationsThe Basic Formula may be further rearranged and decomposed as follows: Sales VC FC = Operating Income (OI) (SP x Q) (VCu x Q) FC = OI Q (SP VCu) FC = OI Q (CMu) FC = OI

Remember this last equation, it will be used again in a moment


Breakeven PointRecall the last equation in an earlier slide:Q (CMu) FC = OIA simple manipulation of this formula, and setting OI to zero will result in the Breakeven Point (quantity):BEQ = FC CMu At this point, a firm has no profit or loss at the given sales levelIf per-unit values are not available, the Breakeven Point may be restated in its alternate format:BE Sales = FC CMR


Breakeven Point, extended: Profit PlanningWith a simple adjustment, the Breakeven Point formula can be modified to become a Profit Planning tool.Profit is now reinstated to the BE formula, changing it to a simple sales volume equationQ = (FC + OI) CM


Sales (50,000 units) $1,000,000Variable costs 600,000Contribution margin $400,000 Fixed costs 300,000Income from operations$100,000Contribution Margin Income StatementTotal The contribution margin is available to cover the fixed costs and income from operations.SalesVariable costsFixed costsIncome from operations


Contribution Margin Income StatementSales (50,000 units) $1,000,000 $20 100%Variable costs 600,000 12 60%Contribution margin $400,000 $ 8 40%Fixed costs 300,000Income from operations $100,000Total Per Unit Percent

The statement can be extended to include per unit dollars and percentage numbers.


Sales (50,000 units) $1,000,000 $20 100%Variable costs 600,000 12 60%Contribution margin $400,000 $ 8 40%Fixed costs 300,000Income from operations $100,000Contribution Margin Income StatementTotal Per Unit Percent Sales Variablecosts Fixedcosts Income from operations =++ Sales Variablecosts Contributionmargin=


Contribution Margin Income Statement Total Per Unit PercentUnit Contribution MarginContribution Margin RatioSales (50,000 units) $1,000,000 $20 100%Variable costs 600,000 12 60%Contribution margin $400,000$ 8 40%Fixed costs 300,000Income from operations $100,000The contribution margin can be expressed three ways:1. Total contribution margin in dollars.2. Unit contribution margin (dollars per unit).3. Contribution margin ratio (percentage).


Sales (50,000 units) ? $20 100%Variable costs ? 12 60%Contribution margin $300,000 $ 8 40%Fixed costs 300,000Income from operations $ 0Calculating the Break-Even Point Total Per Unit PercentAt the break-even point, fixed costs and the contribution margin are equal.


Calculating the Break-Even Point Total Per Unit Percent Break-evensales Fixedcosts =/ContributionmarginSales (50,000 units) ? $20 100%Variable costs ? 12 60%Contribution margin $ 300,000 $ 8 40%Fixed costs 300,000Income from operations $ 0/or Divide by either: $8 per unit or 40%


Calculating the Break-Even Point Total Per Unit Percent Break-evensales Fixedcosts = /ContributionmarginSales (50,000 units) ? $20 100%Variable costs ? 12 60%Contribution margin $ 300,000 $ 8 40%Fixed costs 300,000Income from operations $ 0orWhat is the break-even sales in units?


Calculating the Break-Even Point Total Per Unit Percent Break-evensales Fixedcosts =/ContributionmarginBreak-even sales = $300,000 / $8 = 37,500 unitsSales (50,000 units) ? $20 100%Variable costs ? 12 60%Contribution margin $ 300,000 $ 8 40%Fixed costs 300,000Income from operations $ 0What is the break-even sales in dollars?/or


Calculating the Break-Even Point Total Per Unit Percent Break-evensales Fixedcosts =/ContributionmarginBreak-even sales = $300,000 / $8 = 37,500 unitsBreak-even sales = $300,000 / 40% = $750,000Sales (50,000 units) ? $20 100%Variable costs ? 12 60%Contribution margin $ 300,000 $ 8 40%Fixed costs 300,000Income from operations $ 0/or

The Break-Even PointThe break-even point is the point in the volume of activity where the organizations revenues and expenses are equal.

Sheet1

Sales$250,000

Less: variable expenses150,000

Contribution margin100,000

Less: fixed expenses100,000

Net income0.0

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Equation ApproachSales revenue Variable expenses Fixed expenses = ProfitX = 400 surf boards

Contribution-Margin Approach Consider the following information developed by the accountant at Curl, Inc.:

Sheet1

TotalPer UnitPercent

Sales (500 surf boards)$250,000$500100%

Less: variable expenses150,00030060%

Contribution margin$100,000$20040%


Net income$20,000

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Contribution-Margin Approach For each additional surf board sold, Curl generates $200 in contribution margin.

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Net income$20,000

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Contribution-Margin Approach Fixed expenses Unit contribution margin =Break-even point(in units)

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Net income$20,000

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Contribution Margin RatioCalculate the break-even point in sales dollars rather than units by using the contribution margin ratio. Contribution margin Sales= CM Ratio

Contribution Margin Ratio

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Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

Learning Objective2


Learning Objective3

Cost-Volume-Profit ChartSales and Costs ($000)0Units of Sales (000)$500$450$400$350$300$250$200$150$100$ 50Unit selling price$ 50Unit variable cost30Unit contribution margin$ 20

Total fixed costs$100,000Total Sales12345678910


Total fixed costs$100,000Total SalesVariable Costs60%

100% 60% 40%Cost-Volume-Profit ChartSales and Costs ($000)0Units of Sales (000)$500$450$400$350$300$250$200$150$100$ 5012345678910Unit selling price$ 50Unit variable cost30Unit contribution margin$ 20

Total fixed costs$100,000Total SalesVariable CostsContribution Margin40%60%


Total fixed costs$100,000Total CostsTotal SalesFixed CostsVariable Costs


Total fixed costs$100,000Total CostsTotal Sales


Total fixed costs$100,000Operating Loss AreaOperating Profit AreaTotal CostsTotal Sales

Cost-Volume-Profit ChartSales and Costs ($000)0Units of Sales (000)Break-Even PointUnit selling price$ 50Unit variable cost30Unit contribution margin$ 20

Total fixed costs $100,000Total CostsTotal Sales12345678910$500$450$400$350$300$250$200$150$100$ 50

Cost-Volume-Profit ChartSales and Costs ($000)0Units of Sales (000)Break-Even PointUnit selling price$ 50Unit variable cost30Unit contribution margin$20

Total fixed costs$100,000Total CostsTotal Sales$100,000$20= 5,000 units12345678910$500$450$400$350$300$250$200$150$100$ 50

Cost-Volume-Profit Chart (Break-Even)Sales and Costs ($000)0Units of Sales (000)Break-Even PointUnit selling price$ 50Unit variable cost30Unit contribution margin$ 20

Total fixed costs $100,000Operating Loss AreaOperating Profit AreaTotal CostsTotal Sales$100,000$20= 5,000 units12345678910$500$450$400$350$300$250$200$150$100$ 50


CVP: Graphically

Revised Cost-Volume-Profit ChartSales and Costs ($000)0Units of Sales (000)Revised Break-Even PointUnit selling price$ 50Unit variable cost30Unit contribution margin$ 20

Total fixed costs$80,000Operating Loss AreaOperating Profit AreaTotal CostsTotal Sales$80,000$20= 4,000 units12345678910$500$450$400$350$300$250$200$150$100$ 50

Profit-Volume ChartOperating Profit(Loss) $000s

$100$75$50$25$ 0$(25)$(50)$(75)$(100) Sales (10,000 units x $50) $500,000 Variable costs (10,000 units x $30) 300,000

Contribution margin (10,000 units x $20) $200,000 Fixed costs 100,000

Operating profit $100,000

Units of Sales (000s)12345678910Relevant range is 10,000 units.





Units of Sales (000s)12345678910Maximum profit within the relevant range.Maximum loss is equal to the total fixed costs.





Profit LineUnits of Sales (000s)OperatingProfitOperatingLoss12345678910

Graphing Cost-Volume-Profit RelationshipsViewing CVP relationships in a graph gives managers a perspective that can be obtained in no other way.Consider the following information for Curl, Inc.:

Sheet1

300 units400 units500 units

Sales$150,000$200,000$250,000

Less: variable expenses90,000120,000150,000

Contribution margin$60,000$80,000$100,000

Less: fixed expenses80,00080,00080,000

Net income (loss)$(20,000)0.0$20,000

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Cost-Volume-Profit Graph

Sheet1

FCTCTR

0.080,00080,0000.0

10080,000110,00050,000

20080,000140,000100,000

30080,000170,000150,000

40080,000200,000200,000

50080,000230,000250,000

60080,000260,000300,000

70080,000290,000350,000

80080,000320,000400,000

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450,000

Dollars

400,000

350,000

300,000

250,000

200,000

150,000

100,000

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100200300400500600700800

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Cost-Volume-Profit GraphFixed expenses

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FCTCTR

0.080,00080,0000.0

10080,000110,00050,000

20080,000140,000100,000

30080,000170,000150,000

40080,000200,000200,000

50080,000230,000250,000

60080,000260,000300,000

70080,000290,000350,000

80080,000320,000400,000

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450,000

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400,000

350,000

300,000

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Cost-Volume-Profit GraphFixed expensesTotal expenses

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0.080,00080,0000.0

10080,000110,00050,000

20080,000140,000100,000

30080,000170,000150,000

40080,000200,000200,000

50080,000230,000250,000

60080,000260,000300,000

70080,000290,000350,000

80080,000320,000400,000

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450,000

Dollars

400,000

350,000

300,000

250,000

200,000

150,000

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Cost-Volume-Profit GraphFixed expensesTotal expensesTotal sales

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FCTCTR

0.080,00080,0000.0

10080,000110,00050,000

20080,000140,000100,000

30080,000170,000150,000

40080,000200,000200,000

50080,000230,000250,000

60080,000260,000300,000

70080,000290,000350,000

80080,000320,000400,000

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350,000

300,000

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Cost-Volume-Profit GraphFixed expensesTotal expensesTotal salesBreak-evenpointProfit areaLoss area

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FCTCTR

0.080,00080,0000.0

10080,000110,00050,000

20080,000140,000100,000

30080,000170,000150,000

40080,000200,000200,000

50080,000230,000250,000

60080,000260,000300,000

70080,000290,000350,000

80080,000320,000400,000

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350,000

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Profit-Volume GraphSome managers like the profit-volumegraph because it focuses on profits and volume.Loss areaProfit areaBreak-evenpoint

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0.080,00080,0000.0

10080,000110,00050,000

20080,000140,000100,000

30080,000170,000150,000

40080,000200,000200,000

50080,000230,000250,000

60080,000260,000300,000

70080,000290,000350,000

80080,000320,000400,000

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0.080,00080,0000.0

10080,000110,00050,000100,000

20080,000140,000100,000Profit

30080,000170,000150,00080,000

40080,000200,000200,000

50080,000230,000250,00060,000

60080,000260,000300,000

70080,000290,000350,00040,000

80080,000320,000400,000

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Profit Planning, Illustrated


Learning Objective4


Calculating a Planned Sales Level Total Per Unit PercentPlannedsales Fixed Target costs profit =/ContributionmarginSales (50,000 units) ? $20 100%Variable costs ? 12 60%Contribution margin $ 400,000 $ 8 40%Fixed costs 300,000Income from operations $ 100,000+/orFixed costs plus the target profit equals the required total contribution margin.


Calculating a Planned Sales Level Total Per Unit PercentPlannedsales Fixed Targetcosts profit =/ContributionmarginSales (50,000 units) ? $20 100%Variable costs ? 12 60%Contribution margin $ 400,000 $ 8 40%Fixed costs 300,000Income from operations $ 100,000+/or $8 per unit or 40%


Calculating a Planned Sales Level Total Per Unit PercentPlannedsales Fixed Targetcosts profit =/Contributionmargin+/orWhat is the planned sales level in units?


Calculating a Planned Sales LevelPlannedsales Fixed Targetcosts profit =/ContributionmarginPlanned sales = ($300,000 + $100,000) / $8 = 50,000 units+What is the planned sales level in dollars? Total Per Unit Percent/or


Calculating a Planned Sales Level Total Per Unit PercentPlannedsales Fixed Targetcosts profit =/ContributionmarginPlanned sales = ($300,000 + $100,000) / $8 = 50,000 units+Planned sales = ($300,000 + $100,000) / 40% = $1,000,000/or$1,000,000Sales (50,000 units) $1,000,000 $20 100%Variable costs 600,000 12 60%Contribution margin $ 400,000 $ 8 40%Fixed costs 300,000Income from operations $ 100,000

Contribution Margin Ratio

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Target Net Profit We can determine the number of surfboards that Curl must sell to earn a profit of $100,000 using the contribution margin approach.

Target Net Profit We can determine the total revenue that Curl must make to earn a profit of $100,000 using the contribution margin approach.

Equation ApproachSales revenue Variable expenses Fixed expenses = ProfitX = 900 surf boards or $450,000

Sensitivity AnalysisCVP Provides structure to answer a variety of what-if scenariosWhat happens to profit if:Cost structure changesVariable cost per unit changesFixed cost changesSelling price changesVolume changes

Curl Data

Sheet1

Current Sales (500 Boards)

Sales$250,000

Less: variable expenses150,000

Contribution margin$100,000


Net income$20,000

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Changes in Variable CostsCurl is currently selling 500 surfboards per year.The owner believes that the Variable Cost would Increase by 15 % during the current year.The owner believes that the Variable Cost would decrease by 10 % during the current year.

Curl Data

Sheet1

Current Sales (500 Boards)Proposed Sales (500 Boards)

Sales$250,000$250,000

Less: variable expenses150,000172,500

Contribution margin$100,000$77,500

Less: fixed expenses80,00080,000

Net income$20,000$(2,500)

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Admin:Proposed Sales(500 Boards)

Admin:$ 250,000

Admin:

Curl Data

Sheet1


Sales$250,000$250,000




Net income$20,000$35,000

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Admin:Proposed Sales(500 Boards)

Admin:$ 250,000

Admin:

Changes in Fixed CostsCurl is currently selling 500 surfboards per year.The owner believes that an increase of $10,000 in the annual advertising budget, would increase sales to 540 units. Should the company increase the advertising budget?

Curl Data

Sheet1


Sales$250,000$270,000




Net income$20,000$18,000

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Changes in Fixed CostsSales will increase by $20,000, but net incomedecreased by $2,000.

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Sales$250,000$270,000




Net income$20,000$18,000

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Changes in Fixed Costs$80,000 + $10,000 advertising = $90,000540 units $500 per unit = $270,000

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Sales$250,000$270,000




Net income$20,000$18,000

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Changes in UnitContribution MarginBecause of increases in cost of raw materials, Curls variable cost per unit has increased from $300 to $310 per surfboard. With no change in selling price per unit, what will be the new break-even point?X = 422 units (rounded)

Changes in UnitContribution MarginSuppose Curl, Inc. increases the price of each surfboard to $550. With no change in variable cost per unit, what will be the new break-even point?X = 320 units

Applying CVP AnalysisSafety MarginThe difference between budgeted sales revenue and break-even sales revenue.The amount by which sales can drop before losses begin to be incurred.

Safety MarginCurl, Inc. has a break-even point of $200,000. If actual sales are $250,000, the safety margin is $50,000 or 100 surf boards.

Sheet1


Sales (500 bikes)$250,000$500100%




Net income$20,000

Break-even sales 400 unitsActual sales 500 units

Sales$200,000$250,000


Contribution margin80,000100,000


Net income0.0$20,000

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Margin of SafetySales Sales at break-even pointSalesDollars UnitsSales $250,000 500Break-even sales 200,000 400Excess $ 50,000 100

Margin of SafetySales Sales at break-even pointSalesDollars UnitsASales $250,000 500Break-even sales 200,000 400Excess $ 50,000 100 Actual sales level.

Margin of SafetySales Sales at break-even pointSalesDollars UnitsABSales $250,000 500Break-even sales 200,000 400Excess $ 50,000 100Margin of safety (B/A) 20%Excess of actual sales over the break-even sales.What is the margin of safety as a percentage?

Margin of SafetySales Sales at break-even pointSalesDollars UnitsSales $250,00010,000Break-even sales 200,000 8,000Excess $ 50,000 2,000

Margin of SafetySales Sales at break-even pointSalesDollars UnitsASales $250,00010,000Break-even sales 200,000 8,000Excess $ 50,000 2,000 Actual sales level.

Margin of SafetySales Sales at break-even pointSalesDollars UnitsABSales $250,00010,000Break-even sales 200,000 8,000Excess $ 50,000 2,000Margin of safety (B/A) = 20%Excess of actual sales over the break-even sales.What is the margin of safety as a percentage?

Predicting Profit Given Expected Volume

Predicting Profit GivenExpected VolumeIn the coming year, Curls owner expects to sell 525 surfboards. The unit contribution margin is expected to be $190, and fixed costs are expected to increase to $90,000.X = $9,750 profitX = $99,750 $90,000Total contribution - Fixed cost = Profit


Learning Objective5

Effects of Sales-Mix on CVPThe formulae presented to this point have assumed a single product is produced and soldA more realistic scenario involves multiple products sold, in different volumes, with different costsThe same formulae are used, but instead use average contribution margins for bundles of products.

Sales Mix ConsiderationsSales $ 90 $140 Variable costs 70 95 Contribution margin $ 20 $ 45 Sales mix 80% 20% Contribution margin Products A BWhat is the average contribution for each product?

Sales Mix ConsiderationsSales $ 90 $140Variable costs 70 95Contribution margin $ 20 $ 45Sales mix x 80% x 20%Product contribution $ 16 $ 9Total product contribution$ 25

Contribution margin Break-even sales units Products ABTotal fixed costs $200,000

Product contribution $25What is the break-even sales units?

Sales Mix ConsiderationsSales $ 90 $140Variable costs 70 95Contribution margin $ 20 $ 45Sales mix x 80% x 20%Product contribution $ 16 $ 9

Total product contribution $ 25


Product contribution $25

Break-even sales units 8,000Product A units (80%) 6,400Product B units (20%) 1,600= 8,000 units

Sales Mix ConsiderationsSales $ 90 $ 140 Variable costs 70 95 Contribution margin $ 20 $ 45 Sales mix 60% 40%

Contribution margin Products ABIf the sales mix is 60% for product A and 40% for product B, what is the break-even sales units?

Sales Mix ConsiderationsSales $ 90 $140Variable costs 70 95Contribution margin $ 20 $ 45Sales mix x 60% x 40%Product contribution $ 12 $ 18

Total product contribution $ 30


Product contribution $30

Break-even sales units 6,667Product A units (60%) 4,000Product B units (40%) 2,667= 6,667 units

CVP Analysis with Multiple ProductsFor a company with more than one product, sales mix is the relative combination in which a companys products are sold.Different products have different selling prices, cost structures, and contribution margins. Lets assume Curl sells surfboards and sail boards and see how we deal with break-even analysis.

CVP Analysis with Multiple ProductsCurl provides us with the following information:

Sheet1

DescriptionSelling PriceUnit Variable CostUnit Contribution MarginNumber of Boards

Surfboards$500$300$200500

Sailboards1,000450550300

Total sold800

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DescriptionNumber of Boards% of Total

Surfboards50062.5%(500 800)

Sailboards30037.5%(300 800)

Total sold800100.0%

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CVP Analysis with Multiple ProductsWeighted-average unit contribution margin$200 62.5%$550 37.5%

Sheet1

DescriptionContribution Margin% of TotalWeighted Contribution

Surfboards$20062.5%$125.00

Sailboards55037.5%206.25

Weighted-average contribution margin$331.25

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CVP Analysis with Multiple ProductsBreak-even pointBreak-evenpoint= Fixed expenses Weighted-average unit contribution marginBreak-evenpoint= $170,000 $331.25 Break-evenpoint=514 combined unit sales

CVP Analysis with Multiple ProductsBreak-even pointBreak-evenpoint=514 combined unit sales

Sheet1

DescriptionBreakeven Sales% of TotalIndividual Sales

Surfboards51462.5%321

Sailboards51437.5%193

Total units514

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Learning Objective6


Learning Objective7

CVP Relationships and the Income Statement

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FCTCTR

0.080,00080,0000.0

10080,000110,00050,000

20080,000140,000100,000

30080,000170,000150,000

40080,000200,000200,000

50080,000230,000250,000

60080,000260,000300,000

70080,000290,000350,000

80080,000320,000400,000

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FCTCTR

0.080,00080,0000.0

10080,000110,00050,000100,000

20080,000140,000100,000Profit

30080,000170,000150,00080,000

40080,000200,000200,000

50080,000230,000250,00060,000

60080,000260,000300,000

70080,000290,000350,00040,000

80080,000320,000400,000

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A. Traditional Format

ACCUTIME COMPANY

Income Statement

For the Year Ended December 31, 20x1

Sales$500,000

Less:380,000

Gross margin$120,000

Less: Operating expenses:

Selling expenses$35,000

Administrative expenses35,00070,000

Net income$50,000

B. Contribution Format

ACCUTIME COMPANY

Income Statement

For the Year Ended December 31, 20x1

Sales$500,000

Less: Variable expenses:

Variable manufacturing$280,000

Variable selling15,000

Variable administrative5,000300,000

Contribution margin$200,000

Less: Fixed expenses:

Fixed manufacturing$100,000

Fixed selling20,000

Fixed administrative30,000150,000

Net income$50,000

Alternative Income Statement Formats


Learning Objective8

Cost Structure and Operating LeverageThe cost structure of an organization is the relative proportion of its fixed and variable costs.Operating leverage is . . .the extent to which an organization uses fixed costs in its cost structure.greatest in companies that have a high proportion of fixed costs in relation to variable costs.

Operating LeverageOperating Leverage (OL) is the effect that fixed costs have on changes in operating income as changes occur in units sold, expressed as changes in contribution marginOL = Contribution Margin Operating Income

Notice these two items are identical, except for fixed costs

Operating LeverageContribution marginOperating incomeSales $400,000 $400,000Variable costs 300,000 300,000Contribution margin $100,000 $100,000Fixed costs 80,000 50,000Income from operations $20,000$ 50,000Operating leverage (A/B)

ABOperating leverage is a measure of the relative mix of variable costs and fixed costs.What is the operating leverage?

Operating LeverageContribution marginOperating incomeSales $400,000 $400,000Variable costs 300,000 300,000Contribution margin $100,000 $100,000Fixed costs 80,000 50,000Income from operations $20,000$ 50,000Operating leverage (A/B)

ABOperating leverage is a measure of the relative mix of variable costs and fixed costs.What do these numbers mean? 5 2

Operating LeverageContribution marginOperating incomeSales $400,000 $400,000Variable costs 300,000 300,000Contribution margin $100,000 $100,000Fixed costs 80,000 50,000Income from operations $20,000$ 50,000Operating leverage (A/B) Jones Inc. Wilson Inc.ABOperating leverage is a measure of the relative mix of variable costs and fixed costs.Capitalintensive?Laborintensive? 5 2

Measuring Operating Leverage Contribution margin Net incomeOperating leveragefactor=

Sheet1


Sales (500 bikes)$250,000$500100%




Net income$20,000

Actual sales 500 BoardActual sales 500 units

Sales$250,000$250,000


Contribution margin100,000100,000


Net income$20,000$20,000

&A

Page &P

Measuring Operating LeverageA measure of how a percentage change in sales will affect profits. If Curl increases its sales by 10%, what will be the percentage increase in net income?

Sheet1

Percent increase in sales10%

Operating leverage factor5

Percent increase in profits50%

&A

Page &P

Measuring Operating LeverageA firm with proportionately high fixed costs has relatively high operating leverage On the other hand, a firm with high operating leverage has a relatively high break-even point.


Learning Objective9

CVP Analysis, Activity-Based Costing, and Advanced Manufacturing SystemsAn activity-based costing system can provide a much more complete picture of cost-volume-profit relationships and thus provide better information to managers.


Learning Objective10

Overhead costs like setup, inspection, and material handling are fixed with respect to sales volume, but they are not fixed with respect to other cost drivers. This is the fundamental distinction between a traditional CVP analysis and an activity-based costing CVP analysis.A Move Toward JIT andFlexible Manufacturing


Learning Objective11

Effect of Income TaxesIncome taxes affect a companys CVP relationships. To earn a particular after-tax net income, a greater before-tax income will be required.

CVP and Income TaxesFrom time to time it is necessary to move back and forth between pre-tax profit (OI) and after-tax profit (NI), depending on the facts presentedAfter-tax profit can be calculated by:OI x (1-Tax Rate) = NINI can substitute into the profit planning equation through this form:OI = I I NI I (1-Tax Rate)

Multiple Cost DriversVariable costs may arise from multiple cost drivers or activities. A separate variable cost needs to be calculated for each driver. Examples include:Customer or patient countPassenger milesPatient daysStudent credit-hours

End of Chapter 8We madeit!

*For any cost-volume-profit analysis to be valid, the following important assumptions must be reasonably satisfied within the relevant range. 1. The behavior of total revenue is linear (straight-line). This implies that the price of the product or service will not change as sales volume varies within the relevant range.2. The behavior of total expenses is linear (straight-line) over the relevant range. This implies the following more specific assumptions.a. Expenses can be categorized as fixed, variable, or semivariable. Total fixed expenses remain constant as activity changes, and the unit variableexpense remains unchanged as activity varies.b. The efficiency and productivity of the production process and workers remain constant.3. In multiproduct organizations, the sales mix remains constant over the relevant range.4. In manufacturing firms, the inventory levels at the beginning and end of the period are the same. This implies that the number of units produced during the period equals the number of units sold. (LO6)*******The break-even point is the volume of activity where the organizations revenues and expenses are equal. At this amount of sales, the organization has no profit or loss; it breaks even. This chapter will introduce an income statement highlighting the distinction between variable and fixed expenses. The statement also shows the total contribution margin, which is total sales revenue minus total variable expenses. Total contribution margin is the amount of revenue that is available to contribute to covering fixed expenses after all variable expenses have been covered. (LO1)The equation approach can be used to find the break-even point. This approach is based on the profit equation. Income (or profit) is equal to sales revenue minus expenses. Expenses can be separated in variable and fixed expenses. At the break-even point, income is $0. (LO1)

Curl, Inc. manufactures surf boards. Each surf board sells for $500 and has variable costs of $300. (LO2)

Therefore, the contribution margin per unit is $200. When enough surf boards are sold so that the total contribution margin is $80,000, Curl Inc. will break even for the period. (LO2)To compute the break-even volume of surf boards, divide the total fixed expenses by the unit contribution margin. For Curl, Inc., $80,000 is divided by $200, which is 400 surf boards. That means that the break-even point is 400 surf boards. (LO2)

Sometimes management prefers that the break-even point be expressed in sales dollars rather than units. This can be accomplished by using the contribution margin ratio. The formula for the contribution margin ratio is contribution margin divided by sales. Then divide fixed expenses by the contribution margin ratio to determine the total sales dollars at the break-even point. (LO2)

For Curl, Inc., the fixed costs of $80,000 are divided by the contribution margin ratio of 40% to determine the break-even sales of $200,000. (LO2)*While the break-even point conveys useful information to management, it does not show how profit changes as activity changes. Managers will often use a cost-volume-profit (CVP) graph to show the relationship between profit and volume of activity. Consider Curl, Inc. At sales of 300 unit, Curl Inc. incurs a net loss of $20,000. The break-even point occurs at 400 units and a $20,000 profit occurs when sales are at 500 units. (LO3)

In step 1, the horizontal and vertical axes are drawn. The vertical axis of the graph is dollars and the horizontal axis is units of sales. (LO3)In step 2, the fixed-expense line is drawn. It is parallel to the horizontal axis, since fixed expenses do not change with activity. (LO3)In step 3, compute the total expenses at any volume. Plot that point. For Curl, Inc., look at 400 units. Multiply the unit variable expenses of $300 per unit times 400 units for total variable expenses of $120,000. Add the variable expense to the fixed expenses of $80,000. So at the 500 unit level, total expenses are $200,000. (LO3)In step 4, the total expense line is drawn. Since the total expenses at zero units sold is only the fixed costs, the total expense line crosses the vertical axis at the amount of fixed costs. This line then passes through the point plotted in step 3. (LO3)

In step 5, compute the total sales revenue at any volume. Plot that point. For Curl, Inc., look at 500 units. Multiply the unit sales price of $500 per unit times 500 units for total sales revenue of $250,000. (LO3)In Step 6, draw the total revenue line. This line passes through the point plotted in step 5 and the origin. (LO3)In step 7 the break-even point, the profit area and the loss area are all labeled. The break-even point is the point at which total expenses and total sales are equal, which is where the two lines cross. The profit area is the area where the total sales line is above the total expenses line. This is where revenues exceed expenses. The loss area is the area where the total expenses line is above the total sales line. This is where expenses exceeds revenues. (LO3)Yet another approach to graphing cost-volume-profit relationships is called a profit-volume graph. It highlights the amount of profit or loss. The graph intercepts the vertical axis at the amount equal to fixed expenses at the zero activity level. The graph crosses the horizontal axis at the break-even point. The vertical distance between the horizontal axis and the profit line, at a particular level of sales volume, is the profit or loss at that volume. (LO3)

*For Curl, Inc., the fixed costs of $80,000 are divided by the contribution margin ratio of 40% to determine the break-even sales of $200,000. (LO2)When a company has a net profit they are trying to achieve, or a target net profit, the contribution margin approach can be used to determine the number of units that must be sold. This is very similar to finding the break-even point. The numerator is fixed expenses plus the target profit. The denominator is the contribution margin per unit. The result is the units that need to be sold to earn the target net profit. (LO4)

When a company has a net profit they are trying to achieve, or a target net profit, the contribution margin approach can be used to determine the number of units that must be sold. This is very similar to finding the break-even point. The numerator is fixed expenses plus the target profit. The denominator is the contribution margin per unit. The result is the units that need to be sold to earn the target net profit. (LO4)

The equation approach also can be used to find the units of sales required to earn a target net profit. Recall that in the profit equation, profit is equal to revenues minus variable and fixed expenses. Recall that profit was set to zero to determine the break-even point. When management has determined a target net profit greater than zero, that number becomes profit variable in the equation. (LO4)*So even though sales would increase from $250,000 to $270,000, net income would decrease by $2,000. (LO4)What would happen to a companys break-even point if fixed expenses change? Suppose the owner wanted to increase advertising by $10,000 per month in hopes that sales will increase to 540 units. (LO4)So even though sales would increase from $250,000 to $270,000, net income would decrease by $2,000. (LO4)So even though sales would increase from $250,000 to $270,000, net income would decrease by $2,000. (LO4)What would happen to a companys break-even point if fixed expenses change? Suppose the owner wanted to increase advertising by $10,000 per month in hopes that sales will increase to 540 units. (LO4)So even though sales would increase from $250,000 to $270,000, net income would decrease by $2,000. (LO4)So even though sales would increase from $250,000 to $270,000, net income would decrease by $2,000. (LO4)If the additional advertising is effective and sales increases to 540 boards, sales revenue would be $270,000, variable expenses would be $162,000 and the contribution margin would be $108,000. Fixed expenses would now be $90,000 and therefore, net income would be $18,000. Net income at the current level is $20,000. (LO4)When the variable cost per unit changes, this effects the contribution margin per unit. In turn, the break-even point would also be changed. Look at Curl, Inc. Suppose the variable cost per unit increases to $310 but there is no change in selling price. Using the equation approach, we find that the new break-even point is 422 units, instead of 400 units. (LO4)Changing the unit sales price will also alter the unit contribution margin. Suppose the price is raised from $500 to $550. This change will raise the unit contribution margin from $200 to $250. The new break-even point will be 320 units ($80,000 / $250). A $50 increase in the sales price will lower the break-even point from 400 to 320 surf boards. But is this change desirable? A lower break-even point may seem like a good thing if sales are slow. However, Curl may be more likely to at least break even with a lower sales price. Maybe sales volume would drop dramatically if the price is raised to $550. Management must try to predict the reaction of the consumers. CVP analysis provides valuable information, but it is only one of several elements that influence managements decisions. (LO4)The safety margin of an enterprise is the difference between the budgeted sales revenue and the break-even sales revenue. This is the amount by which sales can drop before losses occur. (LO4)

For example, Curl, Inc has a break-even point when sales are $200,000. If actual sales are $250,000, the margin of safety is $50,000, which is 100 surfboards. (LO4)So far, we have focused on finding the required sales volume to break even or achieve a particular target net profit. Thus, we have asked the question: if fixed expenses, unit contribution margin and the target net profit are known, we can determine the required sales volume. We can also use CVP analysis to ask: if fixed expenses, unit contribution margin and expected sales volume are known, we can determine the expected profit. (LO4)For example, Curl expects to sell 525 surfboards in the coming year. Variable costs are expected to increase which would reduce the unit contribution margin to $190. Fixed costs are also expected to increase to $90,000. The expected profit can be determined by first determining the total contribution. This is the unit contribution times the number of units sold. By deducting the fixed costs, we can see that the expected profit would be $9,750. (LO4)*If a company sells more than one product, the relative combination in which a companys products are sold is referred to as the sales mix. With different selling prices, contribution margins and fixed costs, it now becomes more difficult to determine the break-even point. Lets assume that Curl, Inc. also sells sailboard. (LO5)

The unit selling price, variable cost, and contribution margin are known for each of the two products that Curl sells. Surf boards make up 62.5% of Curls total sales and the sailboards make up the other 37.5%. (LO5)The sales mix is used to compute a weighted-average unit contribution margin. This is the average of the several products unit contribution margins, weighted by the relative sales proportion of each product. For Curl, surfboards have a unit contribution margin of $200 which is multiplied by the 62.5% sales proportion. The weighted contribution margin for the surfboards is $125. The same formula is used to calculate the weighted contribution margin for sailboards which is $206.25. The total weighted average contribution margin for Curls products is $331.25. (LO5)The break-even point can be calculated using the contribution margin approach. The total fixed costs are divided by the weighted average unit contribution margin. For Curl, the calculation is $170,000 divided by $331.25 which is 514 total units to be sold. (LO5)The total units are then multiplied by the relative sale proportion to determine the individual product sales. The number of surfboards to be sold at the break-even point is 514 units is multiplied by 62.5% which is 321 units. 514 is multiplied by 37.5% to determine that 193 sailboards must be sold to break-even. The break-even point of 514 units per year is valid only for the sales mix assumed in computing the weighted-average unit contribution margin. If units are sold in any other mix of surfboards and sailboards, the Curl will not break even. (LO5)On a traditional income statement cost of goods sold includes both variable and fixed manufacturing costs, as measured by the firms product-costing system. The gross margin is computed by subtracting cost of goods sold from sales. Selling and administrative expenses are then subtracted; each expense includes both variable and fixed costs. The traditional income statement does not disclose the breakdown of each expense into its variable and fixed components. (LO7)

Many operating managers find the traditional income-statement format difficult to use, because it does not separate variable and fixed expenses. Instead they prefer the contribution income statement. A contribution income statement The contribution format highlights the distinction between variable and fixed expenses. On the contribution income statement, all variable expenses are subtracted from sales to obtain the contribution margin. All fixed costs are then subtracted from the contribution margin to obtain net income. Operating managers frequently prefer the contribution income statement, because its separation of fixed and variable expenses highlights cost-volume-profit relationships. It is readily apparent from the contribution-format statement how income will be affected when sales volume changes by a given percentage. (LO7)

*The cost structure of an organization is the relative proportion of its fixed and variable costs. Cost structures differ widely among industries and among firms within an industry. A company using a computer-integrated manufacturing system has a large investment in plant and equipment, which results in a cost structure dominated by fixed costs. In contrast, a public accounting firms cost structure has a much higher proportion of variable costs. The highly automated manufacturing firm is capital-intensive, whereas the accounting firm is labor-intensive. An organizations cost structure has a significant effect on the sensitivity of its profit to changes in volume.

The extent to which an organization uses fixed costs in its cost structure is called operating leverage. The operating leverage is greatest in firms with a large proportion of fixed costs, low proportion of variable costs, and the resulting high contribution margin ratio. (LO8)*The managerial accountant can measure a firms operating leverage, at a particular sales volume, using the operating leverage factor. The formula is contribution margin divided by net income. For Curl, Inc., at sales of 500 surfboards, the contribution margin is $100,000 and net income is $20,000. The resulting operating leverage factor is 5. (LO8)

The operating leverage factor is a measure, at a particular level of sales, of the percentage impact on net income of a given percentage change in sales revenue. Multiplying the percentage change in sales revenue by the operating leverage factor yields the percentage change in net income. At Curl, Inc., a 10% increase in sales would be multiplied by the operating leverage of 5. Therefore, if Curl experiences a 10% increase in sales, it can expect a 50% increase in net income. (LO8)An organizations cost structure plays an important role in determining its cost-volume-profit relationships. A firm with proportionately high fixed costs has relatively high operating leverage. The result of high operating leverage is that the firm can generate a large percentage increase in net income from a relatively small percentage increase in sales revenue. On the other hand, a firm with high operating leverage has a relatively high break-even point. This entails some risk to the firm. (LO8)Traditional cost-volume-profit analysis focuses on the number of units sold as the only cost and revenue driver. Sales revenue is assumed to be linear in units sold. Moreover, costs are categorized as fixed or variable, with respect to the number of units sold, within the relevant range. This approach is consistent with traditional product-costing systems, in which cost assignment is based on a single, volume-related cost driver. In CVP analysis, as in product costing, the traditional approach can be misleading or provide less than adequate information for various management purposes. An activity based costing system can provide a much more complete picture of cost-volume-profit relationships and thus provide better information to managers. (LO9)

The important point in this section is that activity-based costing provides a richer description of a companys cost behavior. Some overhead costs may be fixed with respect to sales volume. But when analyzed, they may not be fixed with respect to other cost drivers. Just as ABC can improve an organizations product-costing system, it also can facilitate a deeper understanding of cost behavior and CVP relationships. (LO10)

The requirement that companies pay income taxes affects their cost-volume-profit relationships. To earn a particular after-tax net income, a greater before-tax income will be required. To determine what the before-tax net income is, the after-tax net income is divided by 1 minus the tax rate. The formulas presented in this chapter can now be used with the before-tax net income to provide for the effect of taxes. (LO11)**

Chapter Three

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Transcript of Chapter Three