Benefit Cost Ratio - Definition, Formula, How to Calculate?

The benefit-cost ratio indicates the relationship between the cost and benefit of project or investment for analysis as it is shown by the present value of ... SkiptoprimarynavigationSkiptomaincontentSkiptoprimarysidebarSkiptofooter Home»FinancialModelingGuides»ExcelModeling»BenefitCostRatioArticlebyHarshKataraReviewedbyDheerajVaidya,CFA,FRM Benefit-CostRatioDefinition Thebenefit-costratioindicatestherelationshipbetweenthecostandbenefitofprojectorinvestmentforanalysisasitisshownbythepresentvalueofbenefitexpecteddividedbypresentvalueofcostwhichhelpstodeterminetheviabilityandvaluethatcanbederivedfrominvestmentorproject. Formula Benefit-CostRatioFormula=PVofBenefitExpectedfromtheProject/PVoftheCostoftheProject Youarefreetousethisimageonyourwebsite,templatesetc,PleaseprovideuswithanattributionlinkHowtoProvideAttribution?ArticleLinktobeHyperlinkedForeg:Source:BenefitCostRatio(wallstreetmojo.com) IfthatinvestmentortheprojecthasaBCRvaluethatisgreaterthanone,thantheprojectcanbeexpectedtoreturnordeliverapositiveNPV,i.e., netpresentvalueNetPresentValueNetPresentValue(NPV)estimatestheprofitabilityofaprojectandisthedifferencebetweenthepresentvalueofcashinflowsandthepresentvalueofcashoutflowsovertheproject’stimeperiod.Ifthedifferenceispositive,theprojectisprofitable;otherwise,itisnot.readmore tothebusinessorthefirmandtheirinvestors.IfBCRvalueislessthan1,thentheprojectcostcanbeexpectedtohigherthanthereturns,andtherefore,itshouldbediscarded. StepstoCalculateBenefit-CostRatio(BCR) TocalculatetheBCRformula,usethefollowingsteps: Step1: Calculatethepresentvalueofthebenefitexpectedfromtheproject.Theproceduretodeterminethepresentvalueis: Theamountforeachyear=CashInflows*PVfactorAggregatetheamountsforalltheyears. Step2: Calculatethepresentvalueofcosts.Ifthecostsareincurredupfront,thecostincurredisthepresentvaluePresentValuePresentValue(PV)isthetoday's valueofmoneyyouexpecttogetfromfutureincome.Itiscomputedasthesumoffutureinvestmentreturnsdiscountedatacertainrateofreturnexpectation.readmoreoftheexpensesasthereisnoPVfactor. Step3: Calculatethebenefit-costratiousingtheformula: BCRformula=PVofBenefitExpectedfromtheProject/PVoftheCostoftheProject Examples YoucandownloadthisBenefitCostRatioExcelTemplatehere– BenefitCostRatioExcelTemplate Example#1 EFGltdisworkingupontherenovationofitsfactoryintheupcomingyear,andfortheyexpectanoutflowof$50,000immediately,andtheyexpectthebenefitsoutofthesamefor$25,000forthenextthreeyears.Theinflationratethatiscurrentlyprevailingis3%.YouarerequiredtoassesswhetherthedecisiontorenovatewillbeprofitablebyusingaBCR. Solution Todothecost-benefitanalysisCost-benefitAnalysisCost-benefitanalysisisthetechniqueusedbythecompaniestoarriveatacriticaldecisionafterworkingoutthepotentialreturnsofaparticularactionandconsideringitsoverallcosts.SomeofthesemodelsincludeNetPresentValue,Benefit-CostRatioetc.readmorefirst,weneedtobringbothcostsandbenefitintoday’svalue.Sincetheoutflowof$50,000isimmediateandhencethatwouldremainthesame. Sincethegainsareinfuturevalue,weneedtodiscountthembackbyusingadiscountrateof3%. Therefore,theBenefit-CostRatiocanbecalculatedasusingthebelowformulaas,  TheformulaforCalculatingBCR=PVofBenefitexpectedfromtheProject/PVofthecostoftheProject =70715.28/-50,000.00 BCR=1.41 SincetheBenefit-Costratioisgreaterthan1,therenovationdecisionappearstobebeneficial. Example#2 Sunshineprivatelimitedhasrecentlyreceivedanorderwheretheywillsell50tvsetsof32inchesfor$200eachinthefirstyearofthecontract,100airconditionof1tonneeachfor$320eachinthesecondyearofthecontract,andthethirdyeartheywillsell1,000smartphonesvaluingat$500each.Buttofulfillthisrequirement,theyneedtoincreasetheproduction,andforthat,theyarelookingforacashflowof$35,000tohirepeopleoncontract.AllthiswillbedepositedinaseparateescrowaccountEscrowAccountTheescrowaccountisatemporaryaccountheldbyathirdpartyonbehalfoftwopartiesinatransaction.Itreducestheriskoffailingtoobligethetransactionbyeitheroftheparties.Itoperatesuntilatransactioniscompletedandalltheconditionsaremet.readmoreexplicitlycreatedforthispurposeandcannotbewithdrawnforanyotherpurpose.Still,thecompanywillearna2%rateonthesameforthenextthreeyearsasthesamewillbepaidattheendof3rdyeartothecontractemployees. Further,thecostofproductionthatwillbeincurredinthe1styearwillbe$6,500.Inthe2ndyear,itwillbe75%ofthegrossrevenueearned,andinthelastyearwillbe83%ofthegrossincomeaspertheestimates.Youarerequiredtocalculatethebenefit-costratioandadvisewhethertheorderisworthful?Assumethecostoftheprojectis9.83%. Solution Todothecost-benefitanalysisfirst,weneedtobringbothcostsandbenefitintoday’svalue.Sinceherethecostsarealsoincurredindifferentyears,weneedtodiscountthemaswell. Beforediscounting,weneedtocomputetotalcashflowsfortheentireprojectlife. Thereisnocashoutfloworinflowinthe0yearsasthecompanyismakingadepositanditsearninginterestonthesameattherateof3%,andinthefinalyear,thecompanywillmakeapaymentof$35,000,whichhasbeenincludedinthecashoutflow. YearCashOutflowCashInflowInterestEarnedTotalCashFlows0––––1-6500.0010000.00700.004200.002-24000.0032000.00700.008700.003-450000.00500000.00700.0050700.00 Nowwecandiscountthecashflowsat9.83%andarriveatthediscountedbenefitanddiscountedcostperbelow: Therefore,theBenefit-CostRatiocanbecalculatedasusingthebelowformulaas, Benefit-costratio=PVofBenefitexpectedfromtheProject/PVofthecostoftheProject =414783.70/-365478.43 Benefit-CostRatio=1.13 Sinceitisgreaterthan1,themegaorderappearstobebeneficial. Example#3 TheMayorofacityisevaluatingtwotransportationprojects–ProjectAandProjectB. ProjectA–Thepresentvalueofthebenefitsexpectedfromtheprojectis$40,00,000.Thepresentvalueofcostsis$20,00,000. ProjectB–Thepresentvalueofbenefitexpectedfromtheprojectis$60,00,000.Thepresent valueofcostsis$20,00,000. Calculatethebenefit-costratioandevaluatewhichprojectshouldbeundertaken. Solution ProjectA Usethefollowingdataforcalculationofthebenefit-costratio. ParticularsAmountPresentValueofBenefitExpectedfromProject4000000PresentValueofCostoftheProject2000000 =4000000/2000000 ProjectB Usethefollowingdataforcalculationofthebenefit-costratio. =6000000/2000000 BCR=3 SincetheBCRofProjectBishigher,ProjectBshouldbeundertaken. Example#4 Acompanywillhavetoincuracostof$1,00,000ifnewmachineryispurchased.Itwillleadtothefollowingextraprofitsinthefollowingyears: YearProfit2016$40,0002017$50,0002018$50,000 Assumingadiscountingrateof3%,calculateabenefit-costratiooftheproposedinvestment. Solution: Step1:CalculatethePresentValueFactorPresentValueFactorPresentvaluefactorisfactorwhichisusedtoindicatethepresentvalueofcashtobereceivedinfutureandisbasedontimevalueofmoney.ThisPVfactorisanumberwhichisalwayslessthanoneandiscalculatedbyonedividedbyoneplustherateofinteresttothepower,i.e.numberofperiodsoverwhichpaymentsaretobemade.readmore.Inserttheformula=1/((1+0.03))^1incellC9. Step2:InserttherelevantformulaincellsC10andC11. Step3:Insertformula=B9*C9incellD9. Step4:DragtheformulafromcellD9uptoD11. Step5:Inserttheformula=SUM(D9:D11)incellD12 Step6:Inserttheformula=-D12/B8incellD13. Step7:PressEntertogettheResult Advantages  Thebenefitofusingthebenefit-costratio(BCR)isthatithelpstocomparevariousprojectsinasingletermandhelpstodecidefasterwhichprojectsshouldbepreferredandwhichprojectsshouldberejected.Itcomparesbenefitandcostatthesamelevelthatisitconsidersthetimevalueofmoneybeforegivinganyoutcomebasedonabsolutefiguresastherecouldbeascenariothattheprojectappearstobelucrativewithoutconsideringtimevalueandwhenweconsidertimevalue,thebenefit-costratiogoeslessthan1. Disadvantages ThemajorlimitationoftheBCRisthatsinceitreducestheprojecttomereanumberwhenthefailureorsuccessoftheprojectorofexpansionorinvestmentetc.reliesuponvariousvariablesandotherfactors,andthosecanbeweakenedbyeventswhichareunforeseen. ImportantPoints ThefollowingpointsmustbenotedbeforemakingadecisionbasedupontheBenefit-CostRatio. SimplyfollowingarulethatsuccessmeansaboveoneandfailureorrejectdecisionwouldmeanBCRbelowonecanbemisleadingandleadtoamisfitwiththeprojectinwhichheavyinvestmentismade.  Hence,theBCRshouldbeusedasaconjunctivetoolwithdifferenttypesofanalysisastheuseofNPV,IRRIRRInternalrateofreturn(IRR)isthediscountratethatsetsthenetpresentvalueofallfuturecashflowfromaprojecttozero.Itcomparesandselectsthebestproject,whereinaprojectwithanIRRoverandabovetheminimumacceptablereturn(hurdlerate)isselected.readmore,otherqualitativefactors,andthenmakeagooddecision. Conclusion WecanconcludethatiftheinvestmenthasaBCRwhichisgreaterthanone,theinvestmentproposalwilldeliverapositiveNPVandontheotherhand,itshallhaveanIRRthatwouldbeabovethediscountrateorthecostofprojectrate,whichwillsuggestthattheNetPresentValueoftheinvestment’scashflowswilloutweightheNetPresentValueoftheinvestment’soutflowsandtheprojectcanbeconsidered. IftheBenefit-CostRatio(BCR)isequaltoone,theratiowillindicatethattheNPVofinvestmentinflowswillequalinvestment’soutflows. Lastly,iftheinvestment’sBCRisnotmorethanone,theinvestment’soutflowshalloutweightheinflowsorthebenefits,andtheprojectshouldnotbetakenintoconsideration. RecommendedArticles ThisarticlehasbeenaguidetoBenefit-CostRatioanditsdefinition.HerewediscusstheformulatocalculateBenefit-CostRatio(BCR)alongwithexamples.Advantagesandlimitations.Youcanlearnmoreaboutexcelmodelingfromthefollowingarticles– AdvantagesofNetPresentValueCost-BenefitAnalysisExamplesMutualFundExpenseRatioCalculateBenefit-CostRatio PrimarySidebar GetFREEAccessto500+VideoTutorials SubscribetoYoutubeNow! 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