Relationships
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TheBenefitsofCostVolumeProfit Chapter7
CostVolumeProfit (CVP)Analysis
CVPanalysisaidsmanagementin:
settingpricesforproductsandservices; introducinganewproductorservice; replacingapieceofequipment; decidingwhetheragivenproductorservice shouldbemadewithinthefirmor purchasedoutsidethefirm;or performingstrategicwhatif?analyses.
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TheBasicsofCostVolumeProfit(CVP) Analysis
Profit = Revenues - Total Costs
or
Revenues = Fixed Costs + Variable Costs + Profits
or
(Units sold x Price) = Fixed Cost + (Units sold x Unit Variable Cost) + Profit
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TheBasicsofCostVolumeProfit(CVP) Analysis
WIND BICYCLE CO. Contribution Income Statement For the Month of June Total Sales (500 bikes) $ 250,000 Less: variable expenses 150,000 Contribution margin 100,000 Less: fixed expenses 80,000 Net income $ 20,000
Per Unit $ 500 300 $ 200
ContributionMargin(CM)istheamountremaining fromsalesrevenueaftervariableexpenseshavebeen deducted.
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TheBasicsofCostVolumeProfit(CVP) Analysis
WIND BICYCLE CO. Contribution Income Statement For the Month of June Total Sales (500 bikes) $ 250,000 Less: variable expenses 150,000 Contribution margin 100,000 Less: fixed expenses 80,000 Net CMisusedtocoverfixedexpenses. income $ 20,000
Per Unit $ 500 300 $ 200
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TheBasicsofCostVolumeProfit(CVP) Analysis
WIND BICYCLE CO. Contribution Income Statement For the Month of June Total Sales (500 bikes) $ 250,000 Less: variable expenses 150,000 Contribution margin 100,000 Less: fixed expenses 80,000 Net income $ 20,000
Per Unit $ 500 300 $ 200
Aftercoveringfixedcosts,anyremainingCM contributestoincome.
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TheAssumptionsofCVPAnalysis
Sellingpriceisconstantthroughoutthe entirerelevantrange. Costsarelinearthroughouttheentire relevantrange. Inmultiproductcompanies,thesalesmix isconstant. Inmanufacturingcompanies,inventories donotchange(unitsproduced=units sold).
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TheContributionApproach
ForeachadditionalunitWindsells,$200 moreincontributionmarginwillhelptocover moreincontributionmargin fixedexpensesandprofit.
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TheContributionApproach
EachmonthWindmustgenerateatleast $80,000intotalCMtobreakeven.
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TheContributionApproach
IfWindsells400unitsamonth,itwillbe amonth, operatingatthebreakevenpoint.
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TheContributionApproach
IfWindsellsoneadditionalunit,i.e.,401bikes, IfWindsellsoneadditionalunit,i.e.,401bikes, netincomewillincreaseby$200.
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StrategicusesofCVP
Whatistheexpectedlevelofprofitata givesalesvolume? Whatadditionalamountofsalesisneeded toachieveadesiredlevelofprofit? Whatwillbetheeffectonprofitsofagiven increaseinsales? Whatistherequiredfundinglevelfora governmentalagency,givendesired servicelevel?
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StrategicusesofCVP
Istheforecastforsalesconsistentwith forecastedprofits? Whatadditionalprofitwouldbeobtained fromagivenpercentageofreductionin unitvariablecosts?
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Breakevenanalysis
Thebreakevenpointcanbedefined eitheras:
1. thepointwheretotalsalesrevenueequals totalexpenses(variableplusfixed)or 2. thepointwheretotalcontributionmargin equalstotalfixedexpenses.
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TheContributionMarginRatio
Thecontributionmarginratiois: Contributionmargin Sales ForWindBicycleCo.theratiois:
$200 $500 =40%
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TheContributionMarginRatio
Inotherwords,each$1.00increaseinsales revenueresultsinatotalcontributionmargin increaseof40. SoforWind,ifsalesincreaseby$50,000, whatwillbetheincreaseintotalcontribution margin?
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TheContributionMarginRatio
Sales Less: variable expenses Contribution margin Less: fixed expenses Net income 400 Bikes $ 200,000 120,000 80,000 80,000 $ 500 Bikes $ 250,000 150,000 100,000 80,000 $ 20,000
A$50,000increaseinsalesrevenue
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TheContributionMarginRatio
Sales Less: variable expenses Contribution margin Less: fixed expenses Net income 400 Bikes $ 200,000 120,000 80,000 80,000 $ 500 Bikes $ 250,000 150,000 100,000 80,000 $ 20,000
A $50,000 increase in sales revenue results in a $20,000 increase in CM or ($50,000 x 40% = $20,000)
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ChangesinFixedCosts andSalesVolume
Windiscurrentlyselling500bikesper month.Thecompanyssalesmanager believesthatanincreaseof$10,000inthe monthlyadvertisingbudgetwouldincrease bikesalesto540units. Shouldweauthorizetherequestedincrease intheadvertisingbudget?
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ChangesinFixedCosts andSalesVolume
$80,000+$10,000advertising=$90,000
Current Sales (500 bikes) $ 250,000 150,000 100,000 80,000 $ 20,000 Projected Sales (540 bikes) $ 270,000 162,000 108,000 90,000 $ 18,000
Sales Less: variable expenses Contribution margin Less: fixed expenses Net income
Salesincreasedby$20,000,butnetincome decreasedby$2,000.
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ChangesinFixedCosts andSalesVolume
TheShortcutSolution TheShortcutSolution
Increase in CM (40 units x $200) Increase in advertising expenses Decrease in net income
$ 8,000 10,000 $ (2,000)
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ApplicationsofCVPanalysis
Considerthefollowingbasicdata: SalesPrice Less:Variablecost Contributionmargin PerunitPercent $250 100 150 60 100 40
Fixedcoststotal$35,000
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ApplicationsofCVPanalysis
Currentsalesare$100,000.Thesalesmanager feels$10,000increaseinsalesbudgetwill provide$30,000increaseinsales.Shouldthe budgetbechanged?
Incremental CM approach: $30,000 x 40% CM ratio Additional advertising expense Increase in net income
YES
12,000 10,000 2,000
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ApplicationsofCVPanalysis
Managementisconsideringincreasingthe qualityofitsproductatanadditionalcostof$10 perunit.Theyexpecttosell80moreunits. Shouldmanagementincreasequality?
Expected total CM = (480 units x $90) = Present total CM = (400 units x $100) = Increase in total contribution margin and net income $43,200 40,000 3,200
YES
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ApplicationsofCVPanalysis
Managementistoldthatifthesellingprice dropped$20perunitandadvertisingincreased by$15,000/month,saleswouldincrease50%. Goodidea?
NO
Expected total CM = (400 x $80 x 150%) = Present total CM = (400 units x $100) = Increase in contribution margin Increase in advertising Decrease in net income $48,000 40,000 8,000 15,000 7,000
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ApplicationsofCVPanalysis
Aplantoswitchsalespeoplefromflatsalary ($6,000permonth)toasalescommissionof$15 perspeakercouldincreasesalesby15%.Good idea?
YES
Expected total CM = (400 x 85 x 115%) = Present total CM = (400 units x $100) = Decrease in contribution margin Salaries avoided if commissions paid Increase in net income Line 1: 85 because variable has increased.
$39,100 40,000 900 6,000 5,100
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ApplicationsofCVPanalysis
Awholesaleriswillingtobuy150unitsifwewill givehimadiscountedprice.Thesalewillnotaffect regularsalesnorwillitchangefixedcosts.We wanttomake$3,000onthissale.Whatprice shouldwequote?
Variable cost per speaker Desired profit on order (3,000/150) Quoted price per speaker $150 20 $170
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Thebreakevenpoint
Thebreakevenpointcanbeapproached intwoways:
1. theEquationmethodor 2. theContributionmarginmethod.
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Equationmethod
Profits=Sales(Variableexpenses+ Fixedexpenses) Sales=Variableexpenses+Fixed expenses+Profits Atthebreakevenpoint,profitsequal zero
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Equationmethod
HereistheinformationfromWindBicycle Co.
Sales (500 bikes) Less: variable expenses Contribution margin Less: fixed expenses Net income Total $ 250,000 150,000 $ 100,000 80,000 $ 20,000 Per Unit $ 500 300 $ 200 Percent 100% 60% 40%
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Equationmethod
Wecalculatethebreakevenpointas follows:
Sales=Variableexpenses+Fixedexpenses+ Profits $500Q=$300Q+$80,000+$0 Where: Q $500 $300 $80,000 =Unitsalesprice =Numberofbikessold =Unitvariableexpenses =Totalfixedexpenses
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Equationmethod
Wecalculatethebreakevenpointas follows:
Sales=Variableexpenses+Fixedexpenses+ Profits $500Q=$300Q+$80,000+$0 $200Q=$80,000 Q=400bikes
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Equationmethod
Wecanalsousethefollowingequationto computethebreakevenpointinsales dollars.
Sales=Variableexpenses+Fixedexpenses+ Profits X=0.60X+$80,000+$0 Where: X =Totalsalesdollars 0.60 =Variableexpensesasa percentageofsales $80,000 = Totalfixedexpenses
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Equationmethod
Wecanalsousethefollowingequationto computethebreakevenpointinsales dollars.
Sales=Variableexpenses+Fixedexpenses+ Profits X=0.60X+$80,000+$0 0.40X =$80,000 X=$200,000
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Contributionmarginmethod
Thecontributionmarginmethodisa variationoftheequationmethod.
Breakevenpoint inunitssold Breakevenpointin totalsalesdollars = Fixedexpenses Unitcontributionmargin
=
Fixedexpenses CMratio
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CVPRelationshipsinGraphicForm
ViewingCVPrelationshipsinagraphgives managersaperspectivethatcanbeobtainedinno otherway.Considerthefollowinginformationfor WindCo.
Income 300 units $ 150,000 90,000 $ 60,000 80,000 $ (20,000) Income 400 units $ 200,000 120,000 $ 80,000 80,000 $ Income 500 units $ 250,000 150,000 $ 100,000 80,000 $ 20,000
Sales Less: variable expenses Contribution margin Less: fixed expenses Net income (loss)
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CVPGraph
450,000 400,000 350,000 300,000
TotalExpenses Fixedexpenses
Dollars
250,000 200,000 150,000 100,000 50,000 100 200 300 400 500 600 700 800
Units
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CVPGraph
450,000 400,000 350,000 300,000
TotalSales
Dollars
250,000 200,000 150,000 100,000 50,000 100 200 300 400 500 600 700 800
Units
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CVPGraph
450,000 400,000 350,000 300,000
Break-even dollar sales
Break-even point
re a tA ofi Pr
Dollars
250,000 200,000 150,000 100,000 50,000 -
Break-even units
s Lo a Are s
100 200 300 400 500 600 700 800
Units
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Targetprofitanalysis
SupposeWindCo.wantstoknowhow manybikesmustbesoldtoearnaprofitof $100,000. WecanuseourCVPformulatodetermine thesalesvolumeneededtoachievea targetnetprofitfigure.
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Equationmethod
Wecalculatethebreakevenpointas follows:
Sales=Variableexpenses+Fixedexpenses+ Profits $500Q=$300Q+$80,000+$100,000 $200Q=$180,000 Q=900bikes
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Contributionmarginmethod
Wecandeterminethenumberofbikesthatmust besoldtoearnaprofitof$100,000usingthe contributionmarginapproach.
Breakevenpoint inunitssold 900units
= =
Fixedexpenses+Profit Unitcontributionmargin $80,000+$100,000 $200
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Themarginofsafety
Excessofbudgeted(oractual)salesover thebreakevenvolumeofsales.Inother words,theamountbywhichsalescan dropbeforelossesareincurred. Marginofsafety=Totalsales Breakevensales
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Themarginofsafety
Windhasabreakevenpointof$200,000.If Windhasabreakevenpointof$200,000. actualsalesare$250,000,themarginofsafety is$50,000or100bikes.
500 Bikes $ 250,000 150,000 100,000 80,000 $ 20,000
400 Bikes Sales $ 200,000 Less: variable expenses 120,000 Contribution margin 80,000 Less: fixed expenses 80,000 Net income $ -
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Themarginofsafety
Themarginofsafetycanbeexpressedas20%of sales>$50,000$250,000
500 Bikes $ 250,000 150,000 100,000 80,000 $ 20,000
400 Bikes Sales $ 200,000 Less: variable expenses 120,000 Contribution margin 80,000 Less: fixed expenses 80,000 Net income $ -
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OperatingLeverage
Operatingleverageisameasureofhow sensitivenetincomeistopercentage changesinsales. Withhighleverage,asmallpercentage increaseinsalescanproduceamuch largerpercentageincreaseinnetincome.
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OperatingLeverage
Theproblemis,asmallpercentage decreaseinsalescanproducea significantdecreaseinnetincome.
Degreeof operatingleverage
=
Contributionmargin Netincome
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OperatingLeverage
Actual sales 500 Bikes $ 250,000 150,000 100,000 80,000 $ 20,000
Sales Less: variable expenses Contribution margin Less: fixed expenses Net income
$100,000 $20,000
=5
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OperatingLeverage
Withameasureofoperatingleverageof5,if Windincreasesitssalesby10%,netincome wouldincreaseby50%.
Percent increase in sales Degree of operating leverage Percent increase in profits
10% x5 50%
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OperatingLeverage
A10%increaseinsalesfrom$250,000to$275,000 yieldsa50%increaseinincomefrom$20,000to$30,000.
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IndifferenceAnalysis
IndifferenceanalysisusesCVPanalysis todeterminecomparativeprofitabilityof alternativeproductsormethodsof production. Themethodfocusesoncostbehaviourin relationtochangesinactivitylevels:
Productwithhighleveloffixedcostwillrequire highlevelofsalesactivity Productwithlowleveloffixedcostwillrequire lowlevelofsalesactivity
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CVPGraphforaFirmwithRelatively HighFixedCosts
$1.5
Cost or Revenue
Total Revenue Losses @ 25,000 units = 25,000 x $10 = $250,000
(in millions)
Total Cost
Fixed cost/yr. = $500,000 Variable cost/ unit = $2 Price = $12 Contribution margin = $10
$.5
25,000
50,000
75,000
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CVPGraphforaFirmwithRelatively HighFixedCosts
$1.5
Cost or Revenue
(in millions)
Profits @ 75,000 units = 25,000 x $10 = $250,000
Total Revenue
Total Cost $.5
Fixed cost/yr. = $500,000 Variable cost/ unit = $2 Price = $12 Contribution margin = $10 25,000 50,000 75,000
53 Output in Units
CVPGraphforaFirmwithRelatively LowFixedCosts
$1.5
Cost or Revenue
Total Revenue
(in millions)
$1.0
Losses @ 25,000 units = -25,000 x $3 = -$75,000
Total Cost
$.5 $ .l5
25,000 50,000
Fixed cost/yr. = $150,000 Variable cost/ unit = $9 Price = $12 Contribution margin = $3 75,000
Output in Units 54
CVPGraphforaFirmwithRelatively LowFixedCosts
$1.5
Cost or Revenue
(in millions)
Profits @ 75,000 units = 25,000 x 3 = $75,000
Total Revenue
$1.0
Total Cost
$.5 $ .l5
25,000 50,000
Fixed cost/yr. = $150,000 Variable cost/ unit = $9 Price = $12 Contribution margin = $3 75,000
Output in Units 55
CVPGraphforaFirm withStepCosts
Revenues, Total Costs
There is no breakeven below the 10,000 unit level of output.
Total Revenue
Losses
$100,000 Output in Units 10,000 20,000 25,000 30,000
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IndifferenceAnalysis
Whichisthebestalternativetoselect? Foreachalternative,calculatebreakevenunits Break evenunits
=
FixedcostOpt1FixedcostOpt2 CMOpt1CMOpt2
Breakeven=500,000150,000=50,000units 103 Whatdoesthismean? Ifproductionisexpectedtobe 50,000thenselectthe capitalintensivehighfixedcost,lowvariablecostoption
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TheSalesMix
Salesmixistherelativeproportionsin whichacompanysproductsaresold. Differentproductshavedifferentselling prices,coststructures,andcontribution margins. Thesalesmixiscomputedbyexpressing thesalesofeachproductasapercentage ofthetotalsales.
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TheSalesMix
Withchangesinthesalesmix,itis possiblefortotalsalestoincreasebut totalprofitsdecrease. LetsassumeWindsellsbikesandcarts andseehowwedealwithbreakeven analysis.
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TheSalesMix
Windsellsbikesandcarts
Sales mix for bikes 250,000/550,000 = 45% Sales mix for carts 300,000/550,000 = 55%
Break-even (Total) Fixed = 170,000 = $352,830 CM ratio .4818
CM ratio (Total) 265,000/550,000 = .4818
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TheSalesMix
Confirmbreakevensalesis$352,830 x sales mix for carts Total sales x sales mix for bikes Total sales 352, 830 x 45% 352,830 x 55%
Net Profit
Bike sales x variable rate 160,377 x .60 Cart sales x variable rate 192,453 x .45
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TheSalesMix
Sales mix for bikes 400,000/550,000 = 73% Sales mix for carts 150,000/550,000 = 27%
Net Income Same level of sales but net income
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