贝恩公司战略分析方法(英文版)(ppt 53页).ppt

Author:CollinsQian,Reviewer:BrianBilello,bc,BainMath,March1998,Copyright1998Bainsemi-logpaperislogarithmicononeaxisandlinearontheother,LogScale,LinearScale,23,CU7112997ECA,BainMath,Graphing-Logarithmic(3),Themostusefulfeatureofaloggraphisthatequalmultiplicativechangesindataarerepresentedbyequaldistancesontheaxesthedistancebetween10and100isequaltothedistancebetween1,000,000and10,000,000becausethemultiplicativechangeinbothsetsofnumbersisthesame,10Itisconvenienttouselogscalestoexaminetherateofchangebetweendatapointsinaseries,Logscalesareoftenusedfor:Experiencecurve(alog/logscaleismandatory-naturallogs(lnorloge)aretypicallyusedpricesandcostsovertimeGrowthSharematricesROS/RMSgraphs,LineShapeofDataPlots,Explanation,Astraightline,Thedatapointsarechangingatthesameratefromonepointtothenext,Curvingupward,Therateofchangeisincreasing,Curvingdownward,Therateofchangeisdecreasing,Inmanysituations,itisconvenienttouselogarithms.,24,CU7112997ECA,BainMath,Agenda,Basicmath,FinancialmathsimpleinterestcompoundinterestpresentvalueriskandreturnnetpresentvalueinternalrateofreturnbondandstockvaluationStatisticalmath,25,CU7112997ECA,BainMath,SimpleInterest,Definition:,SimpleinterestiscomputedonaprincipalamountforaspecifiedtimeperiodTheformulaforsimpleinterestis:i=prtwhere,p=theprincipalr=theannualinterestratet=thenumberofyears,Application:,SimpleinterestisusedtocalculatethereturnoncertaintypesofinvestmentsGiven:Apersoninvests$5,000inasavingsaccountfortwomonthsatanannualinterestrateof6%.Howmuchinterestwillshereceiveattheendoftwomonths?Answer:i=prti=$5,000 x0.06xi=$50,212,26,CU7112997ECA,BainMath,CompoundInterest,“Moneymakesmoney.Andthemoneythatmoneymakes,makesmoremoney.”-BenjaminFranklin,Definition:,Compoundinterestiscomputedonaprincipalamountandanyaccumulatedinterest.Abankthatpayscompoundinterestonasavingsaccountcomputesinterestperiodically(e.g.,dailyorquarterly)andaddsthisinteresttotheoriginalprincipal.Theinterestforthefollowingperiodiscomputedbyusingthenewprincipal(i.e.,theoriginalprincipalplusinterest).Theformulafortheamount,A,youwillreceiveattheendofperiodnis:A=p(1+)ntwhere,p=theprincipalr=theannualinterestraten=thenumberoftimescompoundingisdoneinayeart=thenumberofyears,rn,Notes:,Asthenumberoftimescompoundingisdoneperyearapproachesinfinity(asincontinuouscompounding),theamount,A,youwillreceiveattheendofperiodniscalculatedusingtheformula:A=pertTheeffectiveannualinterestrate(oryield)isthesimpleinterestratethatwouldgeneratethesameamountofinterestaswouldthecompoundrate,27,CU7112997ECA,BainMath,CompoundInterest-Application,$1,000.00,$30.00,$1,030.00,$30.90,$1,060.90,$31.83,$1,092.73,$32.78,$1,125.51,$0,$250,$500,$750,$1,000,$1,250,Dollars,i1,i2,i3,i4,A1,A2,A3,A4,1stQuarter,2ndQuarter,3rdQuarter,4thQuarter,Given:,Whatamountwillyoureceiveattheendofoneyearifyouinvest$1,000atanannualrateof12%compoundedquarterly?,Answer:,A=p(1+)nt=$1,000(1+)4=$1,125.51,rn,0.124,DetailedAnswer:,Attheendofeachquarter,interestiscomputed,andthenaddedtotheprincipal.Thisbecomesthenewprincipalonwhichthenextperiodsinterestiscalculated.,Interestearned(i=prt):i1=$1,000 x0.12x0.25i2=$1,030 x0.12x0.25i3=$1,060.90 x0.12x0.2514=$1,092.73x0.12x0.25=$30.00=$30.90=$31.83=$32.78NewprincipleA1=$1,000+$30A2=$1,030+30.90A3=$1,060.90+31.83A4=$1,092.73+32.78=$1,030=$1,060.90=$1,092.73=$1,125.51,28,CU7112997ECA,BainMath,PresentValue-Definitions(1),TimeValueofMoney:,Atdifferentpointsintime,agivendollaramountofmoneyhasdifferentvalues.Onedollarreceivedtodayisworthmorethanonedollarreceivedtomorrow,becausemoneycanbeinvestedwithsomereturn.,PresentValue:,PresentvalueallowsyoutodeterminehowmuchmoneythatwillbereceivedinthefutureisworthtodayTheformulaforpresentvalueis:PV=Where,C=theamountofmoneyreceivedinthefuturer=theannualrateofreturnn=thenumberofyearsiscalledthediscountfactorThepresentvaluePVofastreamofcashisthen:PV=C0+WhereC0isthecashexpectedtoday,C1isthecashexpectedinoneyear,etc.,1(1+r)n,C11+r,C2(1+r)2,Cn(1+r)n,29,CU7112997ECA,BainMath,PresentValue-Definitions(2),Thepresentvalueofaperpetuity(i.e.,aninfinitecashstream)ofis:PV=,Aperpetuitygrowingatrateofghaspresentvalueof:PV=,ThepresentvaluePVofanannuity,aninvestmentwhichpaysafixedsum,eachyearforaspecificnumberofyearsfromyear1toyearnis:,Perpetuity:,Growingperpetuity:,Annuity:,30,CU7112997ECA,BainMath,PresentValue-Exercise(1),1)$10.00today2)$20.00fiveyearsfromtoday3)Aperpetuityof$1.504)Aperpetuityof$1.00,growingat5%5)Asixyearannuityof$2.00Assumeyoucaninvestat16%peryear,Whichofthefollowingwouldyouprefertoreceive?,31,CU7112997ECA,BainMath,PresentValue-Exercise(2),*Thepresentvalueisnegativebecausethisisthecashoutflowrequiredtodayreceiveacashinflowatalatertime,1)$10.00today,PV=$10.002)$20.00fiveyearsfromtoday,ForHP12C:5163)Aperpetuityof$1.50,PV=$9.384)Aperpetuityof$1.00,growingat5%,PV=$9.095)Asixyearannuityof$2.00,PV=-=$7.37,$1.500.16,$1.000.16-0.05,Theoptionwiththehighestpresentvalueis#1,receiving$10.00today,$2.000.16,1(1+0.16)5,$2.000.16,FV,i,PV,N,=(9.52)*,20,(),(),Answer:,32,CU7112997ECA,BainMath,RiskandReturn,NotallinvestmentshavethesameriskinvestingintheU.S.stockmarketismoreriskythaninvestinginaU.S.governmenttreasurybill,butlessriskythaninvestinginthestockmarketofadevelopingcountryMostinvestorsareriskaverse-theyavoidriskwhentheycandosowithoutsacrificingreturnRiskaverseinvestorsdemandahigherreturnonhigherriskinvestments,Asafedollarisworthmorethanariskyone.,33,CU7112997ECA,BainMath,NetPresentValue,Netpresentvalue(NPV)isthemethodusedinevaluatinginvestmentswherebythepresentvalueofallcaseoutflowsrequiredfortheinvestmentareaddedtothepresentvalueofallcashinflowsgeneratedbytheinvestmentCashoutflowshavenegativepresentvalues;cashinflowshavepositivepresentvaluesTherateusedtocalculatethepresentvaluesisthediscountrate.Thediscountrateistherequiredrateofreturn,ortheopportunitycostofcapital(i.e.,thereturnyouaregivinguptopursuethisproject)AninvestmentisacceptableiftheNPVispositiveIncapitalbudgeting,thediscountrateusediscalledthehurdlerate,Definition:,34,CU7112997ECA,BainMath,InternalRateofReturn,Theinternalrateofreturn(IRR)isthediscountrateforwhichthenetpresentvalueiszero(i.e.,thecostoftheinvestmentequalsthefuturecashflowsgeneratedbytheinvestment)TheinvestmentisacceptablewhentheIRRisgreaterthantherequiredrateofreturn,orhurdlerateUnfortunately,comparingIRRsandchoosingthehighestonesometimesdoesnotleadtothecorrectanswer.Therefore,IRRjectAcanhaveahigherIRRbutlowerNPVthanprojectB;thatis,IRRsdoNOTindicatethemagnitudeofanopportunityprojectswithcashflowsthatfluctuatebetweennegativeandpositivemorethanoncehavemultipleIRRsIRRscannotbecalculatedforallnegativecashflows,Definition:,35,CU7112997ECA,BainMath,NPVandIRR-Exercise,*Youcanusethisabbreviatedformatsincetheotherdatahasnotchangedfromparta,Given:,Aninvestmentcosting$2MMwillproducecashflowsof$700,000inYear1,$700,000inYear2,and$900,000inYear3.Calculateitsnetpresentvalueatdiscountratesof(a)5%,(b)10%,and(c)15%.Also,(d)calculatetheprojectsIRR.,Answer:,Usinga5%discountrate,NPV=-$2MM+=$79,041,$700,000(1.05),$700,000(1.05)2,$900,000(1.05)3,ForHP12c:AnothereasywaytocalculateanIRRistousetheIRRfunctioninExcel:=IRR(C1,C2,C3,Cn)whereC1isthecashflowinYear1,C2isthecashflowinYear2,etc.Inthisexample,“=IRR(-2,000,000,700,000,700,000,900,000)”=7.01%,f,CLX,f,i,CHS,CF0,2,000,000,g,700,000,CFj,g,700,000,CFj,g,900,000,CFj,g,5,NPV,=79,041,ForHP12C:,Using10%discountrate,NPV=-$2MM+=-$108,941,$700,000(1.10),$700,000(1.10)2,$900,000(1.10)3,ForHP12C:,f,i,10,NPV,=-$108941,Using15%discountrate,NPV=-$2MM+=-$270,239,$700,000(1.15),$700,000(1.15)2,$900,000(1.15)3,ForHP12C:,f,i,15,NPV,=-$270,239,f,IRR,=7.01%,*,*,*,a),b),c),d),36,CU7112997ECA,BainMath,BondandStockValuation,TheconceptofNetPresentValuecanbeappliedtovaluingbondsandstocks.,Bonds:,Themarketvalue,MV,todayofabondwithafacevalueoffandacouponrateofcmaturinginnyearswhenthemarketinterestrateisris:,Stocks:,Thepricetoday,p0ofastockthatpaysdividendsofdtinYeartandthatyousellinYearnforpnis,forsomeoneexpectingarateofreturnofr:,fc1+r,fc(1+r)2,fc(1+r)n,f(1+r)n,MV=,+,+,+,d11+r,d2(1+r)2,dn(1+r)n,pn(1+r)n,p0=+,+,+,37,CU7112997ECA,BainMath,Agenda,BasicmathFinancialmathStatisticalmathaveragesweightedaverageslinearregression,38,CU7112997ECA,BainMath,Averages,*Sometimesreferredtoasthearithmeticmean,Definition:,(Sumofdatapoints),Exercise:,Answer:,39,CU7112997ECA,BainMath,UsingAverages,(Arithmetic)Mean:,Themeanisanartificialstatisticinthatitneednotcoincidewithanypointinyourdatasetinthepreviousexample,themeanof9.3isnotintheoriginaldatasetExtremepointshavemoreeffectthanthoseclosertothemiddle,Themedianisaffectedbythenumberof,butnotthevalueof,extremepointsinthedatasetThemedianisleastusefulinsmalldatasets(e.g.,themedianof1.3and10is3,whichtellsuslittle),Themodecanbemeaninglessinadatasetwithseveralvaluesthatoccurrepeatedly,Mostusefulfordatasetsthathaveoutliers,Mostusefulwhenyouneedasimpleaveragethatweightsallofthedatapointsequally,Mostusefulfordatasetswithoneorfewvaluesthatoccurrepeatedly,Median:,Mode:,Characteristics,WhentoUse,40,CU7112997ECA,BainMath,WeightedAverages,Definition:,Weightedaverage=,(Sumofeachdatapointmultipliedbyitsweight),(Sumoftheweight),Weightedaveragesareappropriatefordatasetsinwhichthepointstobeaveragedhavedifferentlevelsofimportance.Weightedaveragesadjustfortheimportanceofdifferentdatapointsbyusingtheirweights.,Exercise:,Amattressmanufacturerproducesmattressesofallsizes(twin,queen,andkingsize).Whatistheaveragepriceofamattress?,Given:,Answer:,Application:,MattressSize,Price,MonthlyVolume,Twin,Queen,King,$99.00,$159.00,$199.00,80,120,30,Theweightedaverageofmattresspriceis:,41,CU7112997ECA,BainMath,LinearRegression-Definitions,Regressionsareusedtounderstandhowoneormoreindependentvariablesaffectadependentvariable.,Dependentvariable,Independentvariables,y=a+bx1+cx2+e,Alinearregressioncanbeexpressedasanequation:,42,CU7112997ECA,BainMath,LinearRegression-KeyStatistics,R-squared:,Tellstowhatextenttheindependentvariables“explain”thevalueofthedependentvariableGenerallyalowR-squaredmeansthatyourindependentvariablesdonotexplainthevalueofdependentvariablewell.Therefore,youmayneedtorethinkyourindependentvariables.,TellswhethertheestimatedcoefficientsaresignificantlydifferentfromzeroIfacoefficientofaparticularindependentvariableisnotsignificantlydifferentfromzero,youmaynotconcludethattheparticularindependentvariablehasaneffectonthedependentvariable,Tellstherangeofvaluesinwhichanestimatedcoefficientislikelytofall(i.e.,howmuchlargerandsmallerthetruecoefficientmaybefromtheestimatedcoefficient),T-statisticsshouldbe=2or=-2(fora95%confidencelevel),R-squaredcanonlybebetween0and1UsuallyanR-squaredabove0.7isconsideredhigh,Itistypicaltousetwostandarddeviations(ora95%confidenceinterval),T-statistics:,Standarddeviation:,Explanation,ReferencePoints,Statistics,Therearethreekeystatisticsthathelpexplainregressionoutput.,43,CU7112997ECA,BainMath,SingleVariableLinearRegression-Data,Foracommercialbankclient,aBainAChasbeenaskedtoexplaintherelationshipbetweenthenumberofdepositaccountsandthedemanddepositaccount(DDA)balance.Hehasobtainedthefollowingdatafromthirtydifferentbranchesofthebank:,Branch,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,DDABalance($000),2,240.0,2,210.2,1,368.4,1,840.0,1,884.2,2,016.2,1,890.8,1,345.0,1,448.2,1,505.0,1,525.8,1,603.4,1,884.2,1,528.2,1,384.2,NumberofAccounts,900,906,500,741,789,889,874,510,529,420,679,872,924,607,452,Branch,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,DDABalance($000),1,790.4,1,865.8,2,046.2,2,645.6,1,481.6,1,641.8,1,360.6,1,680.0,1,756.4,2,324.2,1,250.2,1,165.8,1,450.0,1,885.2,1,842.4,NumberofAccounts,729,794,844,1,005,621,703,679,718,785,938,572,508,629,801,876,44,CU7112997ECA,BainMath,LinearRegression-Steps,InputthedataintoanexcelspreadsheetEachvariableshouldbeputinitsowncolumn,Step1:,RuntheregressionChoose“dataanalysis”fromthe“tools”bar,andthenchoose“regression”Whenthe“regression”windowappears,dragthedependentvariabledata(inthiscase,the“DDAbalance”)into“InputYrange”,andtheindependentvariabledata(“numberofaccounts”)into“InputXrange)Toviewtheregressionresultsgraphically,checkofftheboxforalinefitplot,Step2:,Interprettheresults,Step3:,Thethreestepsfordoingregressionanalysisare:,45,CU7112997ECA,BainMath,SingleVariableLinearRegression-Output,SUMMARYOUTPUT,RegressionStatistics,MultipleR,0.86823719,RSquare,0.753835818,AdjustedRSquare,0.74504424,StandardError,174.6960575,Observations,30,ANOVA,df,SS,MS,F,SignificanceF,Regression,1,2616833.837,2616833.837,85.74522395,5.10952E-10,Residual,28,854523.9497,30518.71249,Total,29,3471357.787,Coefficients,StandardError,tStat,P-value,Lower95%,Upper95%,Lower95.0%,Upper95.0%,Intercept,384.9724417,148.5732885,2.591128227,0.015023879,80.63351466,689.3113687,80.63351466,689.3113687,XVariable,1.849629565,0.199746781,9.259871702,5.10952E-10,1.440466373,2.258792758,1.440466373,2.258792758,#ofaccounts,Excelgeneratesthefollowingregressionoutput:,46,CU7112997ECA,BainMath,SingleVariableLinearRegression-Actualvs.PredictedData,R=0.75,0,0,TheregressiondoesagoodjobofpredictingDDABalance.,47,CU7112997ECA,BainMath,SingleVariableLinearRegression-Answer,R-squared=0.75.Thismeansthat75%oftheDDAbalancecanbe“explainedbythenumberofaccounts.TheT-statisticsonthexvariable(i.e.,numberofaccounts)is9.3,whichissignificantlybiggerthanthereferencevalueof“2”,indicatingastrongrelationshipbetweenthenumberofaccountsandDDAbalanceThelinefitplotshowshowcloselythepredictedDDAbalancestiewiththeactualnumbersTheestimatedregressionlineis=DDAbalance=$385,000+($1,850 xnumberofaccounts)Thismeansthateveryincrementalaccountbringsin$1,850ofadditionalDDAbalances,y-intercept,Coefficientfornumberofaccounts,Usingthedatafromtheregressionanalysis,youcansummarizetherelationshipbetweenDDAbalanceandnumberofaccounts.,48,CU7112997ECA,BainMath,Multi-VariableLinearRegression-Data,Note:Thisisdifferentfromthepreviousexerciseinthatitisaregressionwithmultipleindependentvariables,(i.e.,HorsepowerandEngineDisplacement),Foranautomobileclient,aBainAChasbeenaskedtoexplainthedriversofmilespergallonforsmallautomobilemodels.Theini