公司理财精要 chapter4

Chapter4•Supposeyouhave￥10,000toinvestforalongtime,willyouinvestonagovernmentbondwhichpromisestorepay￥20,000in10years,orsaveyourmoneyinabankwithinterestrateof4%compoundedannually?KeyConceptsandSkills•Timevalueofmoney•Beabletocomputethefuturevalueofaninvestmentmadetoday•Beabletocomputethepresentvalueofcashtobereceivedatsomefuturedate•BeabletocomputethereturnonaninvestmentChapterOutlines4.1FUTUREVALUEANDCOMPOUNDING4.2PRESENTVALUEANDDISCOUNTING4.3MOREONPRESENTANDFUTUREVALUESBasicDefinitions•PresentValue(现值)–thecurrentvalueoffuturecashflowsdiscountedattheappropriatediscountrate.•FutureValue(终值)–thecashvalueofaninvestmentatsometimeinthefuture.•Interestrate–“exchangerate”betweenearliermoneyandlatermoney•◆Discountrate•◆Costofcapital•◆Opportunitycostofcapital•◆RequiredreturnFutureValuesSupposeyouinvest$1000foroneyearat5%peryear.Whatisthefuturevalueinoneyear?◆Interest=1000(.05)=50◆Valueinoneyear=principal+interest=1000+50=1050Supposeyouleavethemoneyinforanotheryear.Howmuchwillyouhavetwoyearsfromnow?◆FV=1000(1.05)(1.05)=1000(1.05)2=1102.50FUTUREVALUES:GENERALFORMULAFV=PV(1+r)t◆FV=futurevalue◆PV=presentvalue◆r=periodinterestrate,expressedasadecimal◆t=numberofperiodsFutureValueInterestFactor=(1+r)tFVIF(r,t)EFFECTSOFCOMPOUNDINGSimpleinterest（单利）Compoundinterest(复利)Considerthepreviousexample◆FVwithsimpleinterest=1000+50+50=1100◆FVwithcompoundinterest=1102.50◆Theextra2.50comesfromtheinterestof.05(50)=2.50earnedonthefirstinterestpaymentFIGURE4.1FIGURE4.3SETTINGSDecimal(2):(2ND)(FORMAT)(2OR4)(ENTER)P/Y(Paymentsperyear)=1；C/Y(Compoundingperiodsperyear)=1:(2ND)(P/Y)(1)(ENTER)(ARROWDOWN)(1)(ENTER)END-OF-PERIOD:(2ND)(BGN)(2ND)(SET)(CE/C)Howtoavoidmistakesinusingthecalculator(P94)TEXASINSTRUMENTSBA-IIPLUS◆FV=FUTUREVALUE◆PV=PRESENTVALUE◆I/Y=PERIODINTERESTRATE◆P/YMUSTEQUAL1FORTHEI/YTOBETHEPERIODRATE◆INTERESTISENTEREDASAPERCENT,NOTADECIMAL◆N=NUMBEROFPERIODS◆REMEMBERTOCLEARTHEREGISTERS(CLRTVM)AFTEREACHPROBLEM◆OTHERCALCULATORSARESIMILARINFORMATCALCULATORKEYSEXAMPLE1(ONP93)-100(keyin100andkeyin+/-)=PV5=N10(decimal)=I/YCPTFVGotFV=161.05FUTUREVALUES–EXAMPLE2Supposeyouinvestthe$1000at5%for5years.Howmuchwouldyouhaveatmaturity?◆FV=1000(1.05)5=1276.28Theeffectofcompoundingissmallforasmallnumberofperiods,butincreasesasthenumberofperiodsincreases.Simpleinterestwouldhaveafuturevalueof$1250(1000(1+0.05*5)=1250),foradifferenceof$26.28EXAMPLE4-THEVALUEOFMANHATTANThedealofforManhanttan(P92)In1626,PeterMinuitboughtManhattanIslandforUSD24ingoodsandtrinkets(小装饰品).IsitagooddealtoPeter?SupposePeterinvestedUSD24at8%,whatisthevalueat2006(total380years)?EXAMPLE4-THEVALUEOFMANHATTANFV=＄24×(1+.08)380=＄120.57trillionWorkitwithcalculator,N=380,I/Y=8,PV=-24,CPTFV:wegetthesameresult.8%istoohigh,whatabout5%？N=5FV=27.05亿？！FUTUREVALUEASAGENERALGROWTHFORMULASupposeyourcompanyexpectstoincreaseunitsalesofwidgetsby15%peryearforthenext5years.Ifyoucurrentlysell3millionwidgetsinoneyear,howmanywidgetsdoyouexpecttosellin5years?◆FV=3,000,000(1.15)5=6,034,072QUICKQUIZ:PART1Whatisthedifferencebetweensimpleinterestandcompoundinterest?Supposeyouhave$500toinvestandyoubelievethatyoucanearn8%peryearoverthenext15years.◆Howmuchwouldyouhaveattheendof15yearsusingcompoundinterest?◆Howmuchwouldyouhaveusingsimpleinterest?PRESENTVALUES『现值』HowmuchdoIhavetoinvesttodaytohavesomeamountinthefuture?◆FV=PV(1+r)t◆RearrangetosolveforPV=FV/(1+r)tWhenwetalkaboutdiscounting,wemeanfindingthepresentvalueofsomefutureamount.Whenwetalkaboutthe“value”ofsomething,wearetalkingaboutthepresentvalueunlesswespecificallyindicatethatwewantthefuturevalue.Discountingfactor:DFrt11()PV–ONEPERIODEXAMPLESupposeyouneed$10,000inoneyearforthedownpaymentonanewcar.Ifyoucanearn7%annually,howmuchdoyouneedtoinvesttoday?PV=10,000/(1.07)1=9345.79Calculator◆1N◆7I/Y◆10,000FV◆CPTPV=-9345.79PRESENTVALUES–EXAMPLE2Youwanttobeginsavingforyourdaughter’scollegeeducationandyouestimatethatshewillneed$150,000in17years.Ifyoufeelconfidentthatyoucanearn8%peryear,howmuchdoyouneedtoinvesttoday?◆PV=150,000/(1.08)17=40,540.34PRESENTVALUES–EXAMPLE3Yourparentssetupatrustfundforyou10yearsagothatisnowworth$19,671.51.Ifthefundearned7%peryear,howmuchdidyourparentsinvest?◆PV=19,671.51/(1.07)10=10,000PV–IMPORTANTRELATIONSHIPIForagiveninterestrate–thelongerthetimeperiod,thelowerthepresentvalue◆Whatisthepresentvalueof$500tobereceivedin5years?10years?Thediscountrateis10%◆5years:PV=500/(1.1)5=310.46◆10years:PV=500/(1.1)10=192.77PV–IMPORTANTRELATIONSHIPII•Foragiventimeperiod–thehighertheinterestrate,thesmallerthepresentvalue◆Whatisthepresentvalueof$500receivedin5yearsiftheinterestrateis10%?15%?◆Rate=10%:PV=500/(1.1)5=310.46◆Rate=15%;PV=500/(1.15)5=248.58FIGURE4.3QUICKQUIZ:PARTII•Whatistherelationshipbetweenpresentvalueandfuturevalue?•Supposeyouneed$15,000in3years.Ifyoucanearn6%annually,howmuchdoyouneedtoinvesttoday?•Ifyoucouldinvestthemoneyat8%,wouldyouhavetoinvestmoreorlessthanat6%?Howmuch?THEBASICPVEQUATION-REFRESHER•PV=FV/(1+r)t•Therearefourpartstothisequation◆PV,FV,randt◆Ifweknowanythree,wecansolveforthefourth•Ifyouareusingafinancialcalculator,besureandre