Author CollinsQian Reviewer BrianBilello bc BainMath March1998 Copyright 1998Bain Company Inc BainMath Agenda Basicmath Financialmath Statisticalmath BainMath Agenda Basicmathratioproportionpercentinflationforeignexchangegraphing Financialmath Statisticalmath BainMath Ratio Definition Application Note TheratioofAtoBiswrittenorA B AB Aratiocanbeusedtocalculatepriceperunit giventhetotalrevenueandtotalunits PriceUnit totalrevenue Given Answer PriceUnit 9MM1 5MM Themathforratiosissimple Identifyingarelevantunitcanbechallenging totalunits price unit 9 0MM 1 5MM 6 0 BainMath Proportion Definition IftheratioofAtoBisequaltotheratioofCtoD thenAandBareproportionaltoCandD Application ItfollowsthatAxD BxC AB CD Revenue SG A Given 135MM 83MM 270MM 1996 1999 Answer 135MM 270MM 83MM 135MMx 83MMx270MM 83MMx270MM135MM TheconceptofproportioncanbeusedtoprojectSG Acostsin1999 givenrevenuein1996 SG Acostsin1996 andrevenuein1999 assumingSG Aandrevenuein1999areproportionaltoSG Aandrevenuein1996 166MM BainMath Percent Definition Apercentage abbreviated percent isaconvenientwaytoexpressaratio Literally percentagemeans per100 Application Inpercentageterms 0 25 25per100or25 InherfirstyearatBain anAClogged7 000frequentfliermilesbyflyingtoherclient Inhersecondyear shelogged25 000miles Whatisthepercentageincreaseinmiles Given Apercentagecanbeusedtoexpressthechangeinanumberfromonetimeperiodtothenext change 1 newvalue originalvalueoriginalvalue newvalueoriginalvalue Theratioof5to20isor0 25 BainMath Inflation Definitions Ifanitemcost 1 00in1997andcost 1 03in1998 inflationwas3 from1997to1998 Theitemisnotintrinsicallymorevaluablein1998 thedollarislessvaluableWhencalculatingthe real growthofadollarfigureovertime e g revenuegrowth unitcostgrowth itisnecessarytosubtractouttheeffectsofinflation Inflationarygrowthisnot real growthbecauseinflationdoesnotcreateintrinsicvalue Definition Apricedeflatorisameasureofinflationovertime RelatedTerminology 1 Real constant dollars 2 Nominal current dollars 3 Pricedeflator Pricedeflator currentyear Pricedeflator baseyear Inflationbetweencurrentyearandbaseyear Dollarfigure currentyear Dollarfigure baseyear Dollarfiguresforanumberofyearsthatarestatedinachosen base year sdollarterms i e inflationhasbeentakenout Anyyearcanbechosenasthebaseyear butalldollarfiguresmustbestatedinthesamebaseyear Dollarfiguresforanumberofyearsthatarestatedineachindividualyear sdollarterms i e inflationhasnotbeentakenout Inflationisdefinedastheyear over yeardecreaseinthevalueofaunitofcurrency BainMath Inflation U S PriceDeflators 1996isthebaseyearNote ThesearetheU S PriceDeflatorswhichWEFAGrouphasforecastedthroughtheyear2020 ThelibraryhaspurchasedthistimeseriesforallBainemployeestouse Adeflatortablelistspricedeflatorsforanumberofyears BainMath Inflation Realvs NominalFigures Tounderstandhowacompanyhasperformedovertime e g intermsofrevenue costs orprofit itisnecessarytoremoveinflation i e userealfigures Sincemostcompaniesusenominalfiguresintheirannualreports ifyouareshowingtheclient srevenueovertime itispreferabletousenominalfigures Foranexperiencecurve whereyouwanttounderstandhowpriceorcosthaschangedovertimeduetoaccumulatedexperience youmustuserealfigures Note Whentouserealvs Nominalfigures Whetheryoushouldusereal constant figuresornominal current figuresdependsonthesituationandtheclient spreference Itisimportanttospecifyonslidesandspreadsheetswhetheryouareusingrealornominalfigures Ifyouareusingrealfigures youshouldalsonotewhatyouhavechosenasthebaseyear BainMath Inflation Example 1 1970 1992 Adjustingforinflationiscriticalforanyanalysislookingatpricesovertime Innominaldollars GE swasherpriceshaveincreasedbyanaverageof4 5 since1970 Whenyouusenominaldollars itisimpossibletotellhowmuchofthepriceincreasewasduetoinflation CAGR BainMath Inflation Example 2 PriceofaGEWasher CAGR 1970 1992 Ifyouuserealdollars youcanseewhathashappenedtoinflation adjustedprices Theyhavefallenanaverageof1 0 peryear BainMath Inflation Exercise 1 Considerthefollowingrevenuestreaminnominaldollars Revenue million 199020 5 199125 3 199227 4 199331 2 199436 8 199545 5 199651 0 Howdowecalculatetherevenuestreaminrealdollars BainMath Inflation Exercise 2 Answer Step1 Chooseabaseyear Forthisexample wewilluse1990Step2 Finddeflatorsforallyears fromthedeflatortable 1990 85 34 1991 88 72 1992 91 16 1993 93 54 1994 95 67 1995 98 08 Step3 Usetheformulatocalculaterealdollars Pricedeflator currentyear Dollarfigure currentyear Pricedeflator baseyear Dollarfigure baseyear Step4 Calculatetherevenuestreaminreal 1990 dollarsterms 1990 1991 1992 1993 X 20 5 85 3485 34 1994 1995 1996 20 5X X 24 3 88 7285 34 25 3X X 25 7 91 1685 34 27 4X X 28 5 93 5485 34 31 2X X 32 8 95 6785 34 36 8X X 39 6 98 0885 34 45 5X X 43 5 100 0085 34 51 0X Revenue Million 199020 5 199124 3 199225 7 199328 5 199432 8 199539 6 199643 5 1996 100 00 BainMath ForeignExchange Definitions Investmentsemployedinmakingpaymentsbetweencountries e g papercurrency notes checks billsofexchange andelectronicnotificationsofinter