Author:CollinsQianReviewer:BrianBilellobcBainMathMarch1998Copyright©1998Bain&Company,Inc.2CU7112997ECABOSCopyright©1998Bain&Company,Inc.BainMathAgenda•Basicmath•Financialmath•Statisticalmath3CU7112997ECABOSCopyright©1998Bain&Company,Inc.BainMathAgenda•Basicmath–ratio–proportion–percent–inflation–foreignexchange–graphing•Financialmath•Statisticalmath4CU7112997ECABOSCopyright©1998Bain&Company,Inc.BainMathRatioDefinition:Application:Note:TheratioofAtoBiswrittenorA:BABAratiocanbeusedtocalculatepriceperunit(),giventhetotalrevenueandtotalunitsPriceUnittotalrevenue=Given:==Answer:PriceUnit$9MM1.5MMThemathforratiosissimple.Identifyingarelevantunitcanbechallengingtotalunits=price/unit=$9.0MM1.5MM$?$6.05CU7112997ECABOSCopyright©1998Bain&Company,Inc.BainMathProportionDefinition:IftheratioofAtoBisequaltotheratioofCtoD,thenAandBareproportionaltoCandD.Application:=ItfollowsthatAxD=BxCABCDRevenue=SG&A=Given:$135MM$83MM$270MM$?19961999Answer:$135MM$270MM$83MM$?135MMx?=83MMx270MM83MMx270MM135MM=TheconceptofproportioncanbeusedtoprojectSG&Acostsin1999,givenrevenuein1996,SG&Acostsin1996,andrevenuein1999(assumingSG&Aandrevenuein1999areproportionaltoSG&Aandrevenuein1996)?==$166MM6CU7112997ECABOSCopyright©1998Bain&Company,Inc.BainMathPercentDefinition:Apercentage(abbreviated“percent”)isaconvenientwaytoexpressaratio.Literally,percentagemeans“per100.”Application:Inpercentageterms,0.25=25per100or25%InherfirstyearatBain,anAClogged7,000frequentfliermilesbyflyingtoherclient.Inhersecondyear,shelogged25,000miles.Whatisthepercentageincreaseinmiles?Given:ApercentagecanbeusedtoexpressthechangeinanumberfromonetimeperiodtothenextAnswer:-1=3.57-1=2.57=257%25,0007,000%change==-1newvalue-originalvalueoriginalvaluenewvalueoriginalvalueTheratioof5to20isor0.255207CU7112997ECABOSCopyright©1998Bain&Company,Inc.BainMathInflation-Definitions•Ifanitemcost$1.00in1997andcost$1.03in1998,inflationwas3%from1997to1998.Theitemisnotintrinsicallymorevaluablein1998-thedollarislessvaluable•Whencalculatingthe“real”growthofadollarfigureovertime(e.g.,revenuegrowth,unitcostgrowth),itisnecessarytosubtractouttheeffectsofinflation.Inflationarygrowthisnot“real”growthbecauseinflationdoesnotcreateintrinsicvalue.Definition:Apricedeflatorisameasureofinflationovertime.RelatedTerminology:1.Real(constant)dollars:2.Nominal(current)dollars:3.PricedeflatorPricedeflator(currentyear)Pricedeflator(baseyear)Inflationbetweencurrentyearandbaseyear=Dollarfigure(currentyear)Dollarfigure(baseyear)=Dollarfiguresforanumberofyearsthatarestatedinachosen“base”year’sdollarterms(i.e.,inflationhasbeentakenout).Anyyearcanbechosenasthebaseyear,butalldollarfiguresmustbestatedinthesamebaseyearDollarfiguresforanumberofyearsthatarestatedineachindividualyear’sdollarterms(i.e.,inflationhasnotbeentakenout).Inflationisdefinedastheyear-over-yeardecreaseinthevalueofaunitofcurrency.8CU7112997ECABOSCopyright©1998Bain&Company,Inc.BainMathInflation-U.S.PriceDeflators*1996isthebaseyearNote:ThesearetheU.S.PriceDeflatorswhichWEFAGrouphasforecastedthroughtheyear2020.ThelibraryhaspurchasedthistimeseriesforallBainemployeestouse.Year1996=100*%ChangeYear1996=100*%Change197027.795.321996100.001.95197129.235.181997101.971.97197230.464.231998104.482.46197332.185.641999107.102.51197435.078.992000109.802.52197538.369.372001112.512.47197640.615.862002115.41...
