某咨詢公司戰(zhàn)略方法英文

Author:CollinsQianReviewer:BrianBilello

bcBainMathMarch1998Copyright?1998Bain&Company,Inc.1CU7112997ECABainMathAgenda

BasicmathFinancialmathStatisticalmath2CU7112997ECABainMathAgenda

BasicmathratioproportionpercentinflationforeignexchangegraphingFinancialmathStatisticalmath3CU7112997ECABainMathRatio

Definition:Application:Note:TheratioofAtoBiswrittenorA:BABAratiocanbeusedtocalculatepriceperunit(),giventhetotalrevenueandtotalunitsPriceUnittotalrevenue=

Given:

==Answer:PriceUnit$9MM1.5MMThemathforratiosissimple.Identifyingarelevantunitcanbechallengingtotalunits=

price/unit=

$9.0MM1.5MM$?$6.04CU7112997ECABainMathProportion

Definition: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)?==$166MM5CU7112997ECABainMathPercent

Definition: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==-1

newvalue-originalvalueoriginalvaluenewvalueoriginalvalueTheratioof5to20isor0.255206CU7112997ECABainMathInflation-DefinitionsIfanitemcost$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.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.7CU7112997ECABainMath

Inflation-U.S.PriceDeflators*1996isthebaseyearNote:ThesearetheU.S.PriceDeflatorswhichWEFAGrouphasforecastedthroughtheyear2020.ThelibraryhaspurchasedthistimeseriesforallBainemployeestouse.Adeflatortablelistspricedeflatorsforanumberofyears.8CU7112997ECABainMathInflation-Realvs.NominalFigures

Tounderstandhowacompanyhasperformedovertime(e.g.,intermsofrevenue,costs,orprofit),itisnecessarytoremoveinflation,(i.e.userealfigures).Sincemostcompaniesusenominalfiguresintheirannualreports,ifyouareshowingtheclient’srevenueovertime,itispreferabletousenominalfigures.Foranexperiencecurve,whereyouwanttounderstandhowpriceorcosthaschangedovertimeduetoaccumulatedexperience,youmustuserealfiguresNote:Whentouserealvs.Nominalfigures:Whetheryoushouldusereal(constant)figuresornominal(current)figuresdependsonthesituationandtheclient’spreference.Itisimportanttospecifyonslidesandspreadsheetswhetheryouareusingrealornominalfigures.Ifyouareusingrealfigures,youshouldalsonotewhatyouhavechosenasthebaseyear.9CU7112997ECABainMathInflation-Example(1)

(1970-1992)Adjustingforinflationiscriticalforanyanalysislookingatpricesovertime.Innominaldollars,GE’swasherpriceshaveincreasedbyanaverageof4.5%since1970.Whenyouusenominaldollars,itisimpossibletotellhowmuchofthepriceincreasewasduetoinflation.$2,00072Nominaldollars4.5%PriceofaGEWasher1970717374757677787980818283848586878889909192$0$500$1,000$1,500CAGR10CU7112997ECABainMathInflation-Example(2)

PriceofaGEWasherCAGR(1970-1992)(1.0%)4.5%197071727374757677787980818283848586878889909192$0$500$1,000$1,500$2,000$2,500$3,000NominaldollarsReal(1992)dollarsIfyouuserealdollars,youcanseewhathashappenedtoinflation-adjustedprices.Theyhavefallenanaverageof1.0%peryear.11CU7112997ECABainMathInflation-Exercise(1)

Considerthefollowingrevenuestreaminnominaldollars:Revenue($million)199020.5199125.3199227.4199331.2199436.8199545.5199651.0Howdowecalculatetherevenuestreaminrealdollars?12CU7112997ECABainMathInflation-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)=98.08Step3:Usetheformulatocalculaterealdollars:Pricedeflator(currentyear)

Dollarfigure(currentyear)Pricedeflator(baseyear)Dollarfigure(baseyear)Step4:Calculatetherevenuestreaminreal(1990)dollarsterms:1990:1991:1992:1993:

=,X=20.585.3485.341994:1995:1996:=20.5X

=,X=24.388.7285.3425.3X

=,X=25.791.1685.3427.4X

=,X=28.593.5485.3431.2X

=,X=32.895.6785.3436.8X

=,X=39.698.0885.3445.5X

=,X=43.5100.0085.3451.0XRevenue($Million)199020.5199124.3199225.7199328.5199432.8199539.6199643.5

(1996)=100.0013CU7112997ECABainMathForeignExchange-Definitions

Investmentsemployedinmakingpaymentsbetweencountries(e.g.,papercurrency,notes,checks,billsofexchange,andelectronicnotificationsofinternationaldebitsandcredits)Priceatwhichonecountry’scurrencycanbeconvertedintoanother’sTheinterestandinflationratesofagivencurrencydeterminethevalueofholdingmoneyinthatcurrencyrelativetoinothercurrencies.Inefficientinternationalmarkets,exchangerateswilladjusttocompensatefordifferencesininterestandinflationratesbetweencurrencies

ForeignExchange:ExchangeRate:14CU7112997ECABainMathForeignExchangeRates1)US$equivalent=USdollarsper1selectedforeigncurrencyunit2)CurrencyperUS$=selectedforeigncurrencyunitsper1USdollarTheWallStreetJournalTuesday,November25,1997CurrencyTradingMonday,November24,1997ExchangeRatesCountryArgentina(Peso)Britain(Pound)US$Equiv.11.00011.6910Currency

perUS$20.99990.5914CountryFrance(Franc)Germany(Mark)US$Equiv.0.17190.5752CurrencyperUS$5.81851.7384CountrySingapore(dollar)US$Equiv.0.6289CurrencyperUS$1.5900Financialpublications,suchastheWallStreetJournal,provideexchangerates.15CU7112997ECABainMathForeignExchange-Exercises

Question1:Answer:Question2:Answer:Question3:Answer:

650.28USdollars=?Britishpoundsfromtable:0.5914￡=US$1.00 $650.28x=384.58￡1490.50Francs=?US$

fromtable:$0.1719=1Franc 1490.50Francx=$256.221,000GermanMarks=?Singaporedollars

fromtable:$0.5752=1Mark 1.59Singaporedollar=US$1 1,000GermanMarksxx=914.57Singaporedollars0.5914￡US$1$0.17191Franc$0.57521Mark1.59SingaporedollarUS$116CU7112997ECABainMathGraphing-Linear

X0Y(X1,Y1)(X2,Y2)bXYTheformulaforalineis:y=mx+bWhere,m=slope==y2-y1x2-x1b=theyintercept=theycoordinatewhenthexcoordinateis“0”y

x17CU7112997ECABainMathGraphing-LinearExercise#1

Formulaforline:y=mx+bInthisexercise,y=15x+400,where,02004006008001,0001,2001,4001,6001,800$2,000Dollarschanging050100People(100,1900)(50,1150)Thecatererwouldcharge$1900fora100personparty.yxXaxis=peopleYaxis=dollarschargedm=slope==15b=Yintercept=400dollarscharged(whenpeople=0)Acaterercharges$400.00forsettingupaparty,plus$15.00foreachperson.Howmuchwouldthecatererchargefora100personparty?Usingthisformula,youcansolvefordollarscharged(y),givenpeople(x),andvice-versa18CU7112997ECABainMathGraphing-LinearExercise#2(1)

Alampmanufacturerhascollectedasetofproductiondataasfollows:NumberoflampsProduced/DayProductionCost/Day1008509009501,000$2,000$9,500$10,000$10,500$11,000Whatisthedailyfixedcostofproduction,andwhatisthecostofmaking1,500lamps?19CU7112997ECABai悔nM三athGrap徑hing勿-L失inea暈rEx新erci寇se#僵2(2粗)08,00哭016,0晃00Prod額ucti置onC裙ost/摸Day05001,0太001,5亭00Pro民duc禽ed/鵲Day(1,梅500淺,1能6,0角00)(1,0貨00,牌11,0菜00)For矮mul榜af襯or殼lin希e:算y=特mx怪+淘bXa向xis稍=友#o顧fl蓋amp勸sp視r(shí)od墾uce題d/d廁ayYa洋xis甜=蠢pro星duc啊tio效nc黎ost瀉/da武yM=俱slop墾e=永=競(jìng)=允=貴10b=飾Yin屑terc叼ept少=pr奧oduc改tion陣cos杯t(i叔.e.,喪the爐fix屑edc君ost)圈whe搜nla楚mps定=0y=兄mx+動(dòng)bb=疤y-捏mxb=遭2,00石0-而10(件100)b=茫1,00枝0The借fi溜xed步co車st辣is林$1,糞000y=襯10賊x+牧1,脆000For蜜1,50傳0la姿mps:y=減10(柄1,50受0)+領(lǐng)1,0乓00y=糞15,0腔00+胳1,0臘00y=甲16,0泰0011,0瓣00-2里,0001,0天00撿-1奶009,00煩0900(10飽0,乒2,0揪00)X=搭900Y=御9,下000yxThe匠cost園of尸prod鋸ucin韻g1,惹500繪lamp嚴(yán)sis介$16儀,00020CU7捕112具997瓣ECABai垂nM拋athGrap器hing恒-L脅ogar扶ithm余ic(柴1)Log:A“l(fā)用og”莊orl擾ogar青ithm缸o(hù)f支give購(gòu)nnu執(zhí)mber兄is穿defi贏ned睡ast硬hep頃ower炮to逐whic漆ha劃base做num爸ber駕must甲be道rais粒edt糞oeq聞ual倦that擴(kuò)giv登enn茫umbe暮rUnl保ess訪ot慶her慰wis撓es縮慧tat室ed,澤th穗eb匠ase宋is若as遍sum肥ed蘋to敞be口10Y=屈10x,th超enl稍og10Y=招XMath困emat獲ical葛ly,截ifWhe原re,情Y吊=g翅ive健nn芹umb帽er10涌=b彎aseX=拔powe醒r(o燙rlo顫g)For正exam怕ple:譜10省0=102can余bew抹ritt弄ena猶slo蠻g10100=宴2or炮log遵100賠=221CU7最112農(nóng)997斧ECABain乏Mat傲hGrap捕hing川-L籍ogar命ithm財(cái)ic(哪2)For睜a渠log唉sc股ale屈in淺ba酬se終10,昂as窮th驚el坦ine貓ar占sca反le睬val遞ues調(diào)in尾cre虧ase佳by胞te怪nt煩ime霉s,惱the炊lo遇gv晌alu翻es尾inc開rea延se堵by岔1.98765432101,0茫00,彩000集,00霜0100吼,00臘0,0嘗0010,0巨00,0沖001,00逐0,00涌0100,心00010,0攜001,00尸0100101Log洋pa議per蹄ty芝pic葬all防yu獨(dú)ses白ba尊se魯10Log-窮log仿pape辟ris券log詢arit駕hmic棋on裂both斃axe踐s;s饒emi-助log彈pape郊ris論log是arit彼hmic庫(kù)on亭one腿axis痕and霧lin噸ear藍(lán)ont坦heo師therLog鍵Scal小eLine柱arS御cale22CU71搞1299緊7ECABai邊nM軍athGra趣phi蕉ng個(gè)-L善oga扒rit境hmi短c(槳3)The袖most訪use瓜ful驅(qū)feat歌ure淘ofa惑log碌gra釣phi繞sth農(nóng)ate條qual牲mul氣tipl腰icat戰(zhàn)ive訂chan蹲ges可ind錫ata老are寺repr寺esen忙ted去bye繭qual帖dis泄tanc寨eso上nth橋eax扁esthe丙dist矩ance柏bet租ween露10狗and朗100膽ise吉qual量to炎the嫩dist吳ance缺bet恒ween書1,0礦00,0辣00a剃nd1緒0,00畢0,00紹0be壞caus勿eth褲emu召ltip低lica源tive殃cha隨nge瘦inb府oth栗sets公of鳥numb屢ers算ist各hes吼ame,糞10Iti晌sco渣nven四ient粘to保use丸log慨scal駐est寄oex焦amin摩eth愧era慌teo琴fch跌ange巖bet顯ween專dat猜apo蘋ints齡in川ase袋riesLog致sc偵ale么sa缸re與oft威en滅use別df香or:Expe拿rien贊cec哈urve哥(a播log/守log說(shuō)scal廊eis尤man抖dato乳ry-窮nat訓(xùn)ural局log謠s(l亞nor乏loge)a趨re址typ嫁ica道lly短us悶edpri紗ces速an灣dc蜻ost滅so匙ver狂ti質(zhì)meGro個(gè)wth移Sh農(nóng)are選ma桐tri懷cesROS/螺RMS愁grap辨hsLine豪Sha頌peo京fDa宜taP伸lotsExp遙lan電ati職onAst昏raig冬htl太ineThe跑data易poi折nts范are總chan捎ging素at潤(rùn)the昂same泡rat哪efr全omo什nep忌oint枕to匆the黑nextCurv宇ing理upwa帆rdThe中ra旱te稱of宋cha學(xué)nge絨is清in鍛cre模asi潛ngCur幫vin冶gd耗own飲war微dThe亮ra女te扇of元cha懇nge窄is哪de欺cre鋼asi乏ngIn具man腐ys酒itu精ati芹ons縫,i斯ti梨sc竿onv校eni腿ent持to擾us餃el額oga嚼rit本hms風(fēng).23CU71誤1299竊7ECABain刷Mat扁hAge抖ndaBas忘ic宮mat妙hFin駕anc貝ial喬ma抖thsim干ple辯in洽ter撓estcomp夾ound泥int齡eres醬tpres鈔ent嫂valu雄erisk壞and詳ret吹urnnet戰(zhàn)pres積ent逢valu孟einte局rnal疤rat松eof墳ret淹urnbon乎da嗎nd臥sto盲ck撕val枕uat脈ionSta鵝tis川tic盒al獨(dú)mat風(fēng)h24CU71詠1299筐7ECABai廊nM戚athSim繼ple色I(xiàn)n康ter脊estDefi點(diǎn)niti云on:Simp聚lei扔nter圓est境isc館ompu岡ted餅ona吃pri謀ncip焰ala匯moun址tfo丑ra焦spec秘ifie羞dti睡mep寨erio蛛dThe尖form披ula姥for扁simp錯(cuò)lei脊nter絕est見(jiàn)is:題i=容prtwhe筍re,p=打th駝ep草rin姿cip姿alr=粗the仿annu證ali黎nter閃est龜ratet=電th麻en妻umb謠er拘of檔yea越rsApp期lic喚ati陷on:Simp處lei幟nter讀est剩isu能sed泰toc號(hào)alcu粉late擊the慮ret擾urn責(zé)onc午erta弱int杯ypes兼of寸inve受stme屑ntsGive黎n:A出per教son享inve假sts賣$5,0性00i遵na譜savi覽ngs伴acco致unt劃for慶two喝mont虧hsa右tan成ann豆ual展inte位rest獅rat趁eof唯6%.泥H孟owm本uch鑰inte盼rest甩wil弄lsh店ere彼ceiv館eat幟the從end賢of遠(yuǎn)two爆mont御hs?Ans亮wer: 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Where, C= theamountofmoneyreceivedinthefuture r= theannualrateofreturn n= thenumberofyears iscalledthediscountfactorThepresentvaluePVofastreamofcashisthen:PV=C0+++WhereC0isthecashexpectedtoday,C1isthecashexpectedinoneyear,etc.1(1+捉r)nC

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