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COSTVOLUMEPROFITANALYSIS

This section is going to dealwith sales, expenses and profits of an enterprise.

Profitsofanenterpriseareaffectedbymanyfactors.ThepurposeofCostvolume

profitanalysis (CVP) is tostudyall the factorsandhelp inmakingdecisions to

improveprofitsforthecompany.

Keyfactorsinfluencingprofitsare:

1. Sellingprices

2. Volumeofsales

3. Variablecost

4. Fixedcost

The purpose of this chapter is to analyze relationship among the above-

mentioned factors in such a way that we can estimate change in profits with

changeinanyoftheabovefactors.

CVPanalysisfindsouttherelationshipbetweensales,expensesandprofits.

Letusfirstunderstandthebasicstructuretoanalyzefinancialinformation.Then

wewillmovetowardstechniquesofCVPanalysis.

HYPOTHETICALEXAMPLE:

SALES 100,000

LESS:VARIABLECOST 40,000

CONTRIBUTION 60,000

LESS:FIXEDCOST 20,000

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EARNINGBEFOREINTERESTANDTAXES(EBIT) 40,000

LESS:INTEREST 3000

EARNINGAFTERINTERESTBEFORETAXES 37,000

LESS:TAXES 3700

EARNINGAFTERTAX/PROFITAFTERTAX 33,300

DIVIDENDS 33,300

Theaboveexampleshowstheentirestructure,whichisusedtocalculateoverall

financial performance of a company from different dimensions.Wewill break

downtheentirechain intodifferentpartsandanalyzeeachpart tounderstand

micro-performanceoftheenterprise.

A total of 3 techniques are used for makingmanagement decisions regarding

performanceofthecompany:

1. Contributionmarginconcept

2. Breakevenanalysis

3. Profitvolumeanalysis

In 2016 RBI PHASE 2, one question was asked from break-even analysis. We

expectRBI toget into furtherdetails in this topicnextyear.This is the reason

thatwearegoingtocoverall3techniquesrelatedtoCVPanalysis.

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CONTRIBUTIONMARGINCONCEPT:

Contributionmargin shows the relationshipbetween sales and contributionof

theenterprise.Contributionmarginhelpsusunderstandtwoimportantthings:

1. Theratioofvariable cost to sales-There isalwaysadirect relationand

constant ratio between sales and variable cost. For example, a question

may say that variable costs are 40% of sales. Thismeans that as sales

increase, variable costwill also increaseproportionatelydue toadirect

relation between the two. So if sales are 1 lakh, variable cost will be

40,000 and if sales are increased to 2 lakh, variable cost will increase

proportionately to 80,000. Contributionmargin helps us to understand

thisratioanddecidewhetherthecompanyhasveryhighvariablecostsor

not.

2. The level of fixed costs- fixed costs are costs which remain fixed, no

matter what is the level of sales. Contribution margin to fixed cost

comparisonhelpsus tounderstandwhether contributionprovidedbya

company isenoughtocover fixedcostsornot. Ifnot, thenwhat levelof

saleswillberequiredtocoveratleastfixedcosts.

The formula for contribution margin ratio (or PV Ratio) is:

(SALES–VARIABLECOST)/SALES

Forexample,

PRODUCTIONOF10000UNITS PRODUCTIONOF14000UNITS

SALES 10,00,000 SALES 14,00,000

LESS:VC(60%) 600,000 LESS:VC(60%) 840,000

CONTRIBUTION 400,000 CONTRIBUTION 5,60,000

LESS:FC 200,000 LESS:FC 200,000

EBIT 200,000 EBIT 360,000

Ascanbeseen,EBITincreasedfrom200,000to3,60,000assalesincreasedfrom

10,000to14,000units.Withanincreaseinsalesof40%,profitsshouldalsohave

increasedby40%buttheyincreasedmoreduetoconstantfixedcost.

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It is also important to remember that fixed cost remain constant till the time

productioniswithin100%capacityofthecompany.Themomentitgoesabove

itsfullcapacity,additionalfixedassetshavetobepurchasedforproduction.

Intheabovequestion,contributionmarginratioiscalculatedas:

Sales–VC/sales=10,00,000–600,000/10,00,000=40%

PV Ratio helps us to decide whether to increase sales or not. In the above

example, an increase in sales turned profitable for the company as it was

operatingatbelow100%capacityandhadthepotentialtoproducemoreprofits

forthecompany.

AlowPVratio(lesscontributionmargin)isasignthatvariablecostsaretoohigh

andneedtobereducedinordertoincreaseprofits. It isawarningsignofvery

highcostsofproduction.

BREAKEVENANALYSIS:

Break-even analysis aims to tell us the level atwhich cost and revenue are in

equilibrium.

Break-evenpoint is thepointofproductionorsalesatwhich there isnoprofit

andnoloss.Atapointabovebreak-evenpoint,theenterpriseexperiencesprofit

andifthecompanyproduceslessthanbreak-evensales,itexperiencesloss.

Atthebreak-evenpoint,profitbeingzero,contribution(sales–variablecost)is

equaltofixedcost.Inotherwords,thebreak-evenpointisthatpointwherethe

companyisabletocoveritsfixedcostscompletely.

Forexample,

Sellingpriceperunit=Rs.20

Variablecostperunit=Rs.10

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Totalfixedcost=Rs.100,000

Letusmakethechartfortheabove:

SALES(20*X) 200,000

LESS:VC(10*X) 100,000

CONTRIBUTION(10*X) 100,000

LESS:FIXEDCOST 100,000

EBIT NIL

Since,itisbreak-evenpoint,soEBIToroperatingprofitswillbeZERO.

Wehavetofindthelevelofsaleswherebreak-evenpointisachieved.Byusing

theabovechart,wefindoutthelevelofsalesasRs.200,000with10,000unitsof

Rs.20each.

Ifthecompanysellsmorethan10,000units,itwillmakeprofits.Youcanjustify

thisbykeepingafigureof11000unitsinsales.

BREAKEVENPOINT/SALESFORMULA:

• Breakevenpoint=fixedcosts/contributionmarginperunit

• Breakevensales=fixedcosts/PVratio

Youcanverifytheaboveanswerof10,000unitsandRs200,000salesbyusing

theabove-mentionedformulas.

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MARGINOFSAFETY:

Thedifferencebetweensalesandbreak-evenpointiscalledasmarginofsafety.

Themargindeterminessafetyfortheenterprise.Acompanywithfewermargins

is on the verge of going into losses, if its production or sales reduces. On the

otherhand,acompanywithhighermarginsissafeagainstrunningintolosses.

Themarginofsafetycanbefoundoutbyusingthefollowingformula:

1. Marginofsafety=Profit/PVratio

2. Marginofsafety=profit*sales/sales–VC

ANGLEOFINCIDENCE:

Theangleatwhichsalesareequal to totalcosts iscalledangleof incidence. In

the above CHART, it is clear that the break-even point is at 10,000 units. The

anglemadebyincomelineandtotalcostlineatthebreak-evenpointiswhatis

calledasangleofincidence.

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Alargeangleofincidenceispreferablebytheenterpriseasitshowsthatprofits

increasefasterafterreachingbreakevenpoint.Asmallangleofincidenceshows

that variable cost forms a larger part of total cost, reducing the gap between

incomeandcostline.

The third concept, PROFIT VOLUME ANALYSIS has been studied partially

throughprofit-volumeratio/contributionmarginratio.Adetailedstudyofthis

conceptisnotrequired.

COSTINDIFFERENCEPOINT:

Cost indifferencepointreferstothat levelofoutputwherethetotalcostorthe

profit of two alternatives is equal.When two or more alternative methods of

productionareconsidered,andtheuseofonemachineinvolveshigherfixedcost

andlowervariablecostwhileuseofanothermachineinvolveslowerfixedcost

and higher variable cost, cost indifference point will help in identifying the

alternativewhichismoreprofitableforagivenoutput.Whensalesarebelowthe

point of cost indifference, the machine with lower fixed cost will be more

profitable.

CostIndifferencepoint=differenceinfixedcost/differenceincontributionper

unit

Or,

Costindifferencepoint=differenceinfixedcost/differenceinPVratio

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Letussolvesomequestionstounderstandwhatkindofquestionsmaybeasked

intheexamination:

1. ThesellingpriceperTelevisionisRs.100.VariablecostperTVisRs50.

Themaximumcapacityoftheplantis2000TVs.Fixedcostisprovideto

usasRs.50,000.Findoutthebreakeventsalesforthecompany.Also,find

outthenumberofTVs,whichneedtobesoldtogetaprofitofRs.50,000

Answer:

BES=Fixedcost/PVratio;

BES=50,000/0.5=100,000rupees

Salesfordesiredprofit=fixedcost+profit/contributionperunit

100,000/50=2000unitsorsalesofRs200,000

NOTEthat thisquestioncanalsobesolvedby takinghelpof thestructure that

wehavecreatedonfirstpage.Evenifyoufailtoremembertheformulas,it’snot

impossibletosolvethesekindofquestions.

2. Break even point of a machine is given as 5000 units. Fixed cost is

providedtousasRs.60,000.ThevariablecostisgivenasRs12.Findout

theprofitforthecompanyataproductionandsaleof10,000units.

Answer:

At 5000 units production, there is no profit no loss. Therefore, at this level of

production,contributionisequaltofixedcosti.e.60,000rupees.Variablecostis

also Rs 60,000 (12 * 5000). Therefore, sales at break even point is 1,20,000

rupeeswithperunitsalepricebeingRs24(1,20,000/5000).

Atsaleunitsof10,000units, totalsales isequal to240,000rupees.Now,using

the structure created to solve such questions,we get contribution as 1,20,000

andfixedcostislimitedat60,000.TheprofitatthislevelisRs.60,000.

IMPORTANTFORMULAS:

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• P/VRATIO=ChangeinProfit/ChangeinSales

• CONTRIBUTION=sales*P/Vratio

• Contribution=(salesatBreakevenpointinRs*PVratio)+Profit

• Contribution=(salesatBreakevenpointinunits*contributionperunit)

+Profit

• Contribution=(marginofsafety*PVratio)+Fixedcost

• Contribution=Profit/marginofsafetyin%

• Salesforadesiredprofit=(FixedCost+desiredprofit)/PVRatio

• MarginofSafety=ActualSales–breakevenpoint

• Profit=MarginofSafety*PVratio

• Profit=actualsales*M/Sratio*PVratio

• FixedCost=salesatBreakEvenPointinRs.*PVratio

• PVRatio=changeinprofit*100/changeinsales

PracticeQuestions:

1. Calculatebreakevenpointfromthefollowinginformation:

SellingpriceperunitofaproductisgivenasRs.10.Variablecostofthe

productisRs.7.50perunit.ThefixedcostisgivenasRs10,000.

Answer:

Contributionperunit=Rs2.50

Fixedcost=Rs10,000

Break even point = fixed cost / contribution per unit = 10,000/2.50 =

4000units

2. ThesellingpriceofaproductisgivenasRs.20perunit.Thevariablecost

is Rs 14 per unit. The fixed costs are Rs. 792000. Find out Break even

salesandnumberofunitsthatmustbesoldtoearnaprofitofRs60,000.

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Answer:

Contributionperunit=20-14=6perunit.

PVratio=contribution/sales=6/20=30%

Breakevensales=fixedcost/PVratio=792000/30%=2640,000.

UnitstobesoldtoearnaprofitofRs60,000=

Fixedcost+desiredprofit/contributionperunit=852000/6=1,42000

units

3. Fillintheblanks:

Sellingpriceperunit ------

Variablecostasa%ofsales 60%

Numberofunitssold 10,000

Contribution Rs20,000

Fixedcost Rs12,000

Profit ------

Answer:

(Profit=8000;sellingpriceperunit=Rs5)

4. A company has a PV ratio of 40%. By what percentage must sales be

increasedtooffseta10%reductioninsellingprice?

Answer:

Letsalesby(100*1)=Rs100

ContributionwillbeRs40(40%PVratio)andVariablecostwillbeRs60

Whensellingpricereducesby10%,newsales=Rs90

Butvariablecostwillremainthesamei.e.Rs60

Therefore,newcontributionisRs30

Volumeofsalesrequiredtomaintainthesamesales=

Contribution*newsales/newcontribution=40*90/30=Rs120

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5. A companyhas sales ofRs140,000 andvariable cost ofRs75,000.The

fixedcostisgivenasRs50,000.Findouttherequiredsalestogetaprofit

ofRs30,000.

(Answer:Rs.160,000)

6.

Sales Profit

Year2004 Rs120,000 8000

Year2005 Rs140,000 13,000

Findoutthefollowing:

a. PVratio

b. BEpointin2004and2005

c. ProfitwhensalesareRs180,000

d. Marginofsafetyin2005

(Answer:PVRatio=changeinprofit*100/changeinsales=25%;

BEPin2004=88000rupees;BEPin2005=88000rupees;

Profit=23000;

Marginofsafety=52000)

7. Acompanysoldin2consecutiveperiods7000unitsand9000unitsand

incurredalossof10,000rupeesinyear1andprofitof10,000inyear2.

ThesellingpriceperunitisRs100.FindoutthePVratioandnumberof

unitstobreakeven

(Answer:PVratio=10%;numberofunitstobreakeven=8000units)

8. FindoutfixedcostandPVratiofromthefollowinginformation:

Totalsales Total cost (fixed +

variable)

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Year1 7000 5800

Year2 9000 6600

(Answer:PVratio=60%;fixedcost=3000)

9. FindoutfixedcostandPVratiofromthefollowinginformation:

sales Totalcost

Year1 2400,000 2180,000

Year2 30,00000 26,00,000

(Answer:PVratio=30%;fixedcost=10,00000)

10. Ifmargin of safety is Rs. 2,40,000 (40% of sales) and PV ratio is 30%.

CalculateitsbreakevensalesandamountofprofitonsalesofRs.900,000

(Answer: break even sales = 3,60,000; profit on sales of 900,000 =

162,000)

11. A company earned a profit of Rs 30,000 during a financial year. If the

variablecostandsellingpriceoftheproductareRs8andRs10perunit

respectively,findouttheamountofmarginofsafety

(Answer:MOS=Rs.150,000)

12. Fixedcost isgivenasRs4000.BreakevensalesaregivenasRs20,000.

ProfitisRs1000.CalculatesalesforearningaprofitofRs1000?

(Answer:sales=Rs25000)

13. SellingpriceperunitisgivenasRs20/unit.VariablecostisRs.12.fixed

costisgivenasRs96000.Findoutbreakevenunitsandbreakevensales.

(Answer:BEP=12000units.BES=Rs240,000)

14.

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Sales Profit

Year1 20,00,000 2,00,000

Year2 30,00,000 4,00,000

FindoutPVratioandsalesrequiredtoearnaprofitofRs500,000

(Answer:PVratio=20%;salesforprofitof5lakh=3500,000)

15. AcompanyhasafixedcostofRs20,000.Itsellstwoproducts-AandB,in

theratioof2unitsofAand1unitofB.contributionisRs1perunitofA

andRs2perunitofB.howmanyunitsofAandBwouldbesoldatbreak

evenpoint?

(Answer:A=10,000units;B=5000units)