公司理财第九版-第5章.ppt

Chapter5FormulasIntroductiontoValuation:TheTimeValueofMoney,McGraw-Hill/Irwin,Copyright2010byTheMcGraw-HillCompanies,Inc.Allrightsreserved.,KeyConceptsandSkills,BeabletocomputethefuturevalueofaninvestmentmadetodayBeabletocomputethepresentvalueofcashtobereceivedatsomefuturedateBeabletocomputethereturnonaninvestmentBeabletocomputethenumberofperiodsthatequatesapresentvalueandafuturevaluegivenaninterestrateBeabletouseafinancialcalculatorand/oraspreadsheettosolvetimevalueofmoneyproblems,5F-2,ChapterOutline,FutureValueandCompoundingPresentValueandDiscountingMoreaboutPresentandFutureValues,5F-3,什么是货币的时间价值,货币时间价值：是指货币随着时间的推移而发生的增值，也称为资金时间价值。是不是货币在任何状态下都可以产生时间价值呢？是不是货币作为资本投入到经营活动中所获得的增值额都是时间价值呢？,利率的构成,利率=时间价值+风险报酬+通货膨胀贴水利率在经济生活中的表现形式银行存款利息率银行贷款利率债券利息率股息率时间价值是扣除风险报酬和通货膨胀贴水后的真实收益率（社会平均资金收益率）。,BasicDefinitions,PresentValue现值（PV），是指未来某一时点上的一定量现金折合到现在的价值，又称本金。FutureValue终值（FV），是现在一定量现金在未来某一时点上的价值，即本利和，又称将来值。Interestrate“exchangerate”betweenearliermoneyandlatermoneyDiscountrateCostofcapitalOpportunitycostofcapitalRequiredreturn,5F-6,FutureValues,Supposeyouinvest$1,000foroneyearat5%peryear.Whatisthefuturevalueinoneyear?Interest=1,000(.05)=50Valueinoneyear=principal+interest=1,000+50=1,050FutureValue(FV)=1,000(1+.05)=1,050Supposeyouleavethemoneyinforanotheryear.Howmuchwillyouhavetwoyearsfromnow?FV=1,000(1.05)(1.05)=1,000(1.05)2=1,102.50,5F-7,FutureValues:GeneralFormula,FV=PV(1+r)tFV=futurevaluePV=presentvaluer=periodinterestrate,expressedasadecimalt=numberofperiodsFuturevalueinterestfactor=(1+r)t复利终值系数，可查表，中文教材表现为（F/P，i,n),5F-8,EffectsofCompounding,SimpleinterestCompoundinterestConsiderthepreviousexampleFVwithsimpleinterest=1,000+50+50=1,100两年期单利FVwithcompoundinterest=1,102.50两年期复利Theextra2.50comesfromtheinterestof.05(50)=2.50earnedonthefirstinterestpayment,5F-9,CalculatorKeys计算器,TexasInstrumentsBA-IIPlusFV=futurevaluePV=presentvalueI/Y=periodinterestrateP/Ymustequal1fortheI/YtobetheperiodrateInterestisenteredasapercent,notadecimalN=numberofperiodsRemembertocleartheregisters(CLRTVM)aftereachproblemOthercalculatorsaresimilarinformat了解即可,5F-10,FutureValuesExample2,Supposeyouinvestthe$1,000fromthepreviousexamplefor5years.Howmuchwouldyouhave?FV=1,000(1.05)5=1,276.28Theeffectofcompoundingissmallforasmallnumberofperiods,butincreasesasthenumberofperiodsincreases.(Simpleinterestwouldhaveafuturevalueof$1,250,foradifferenceof$26.28.),5F-11,FutureValuesExample3,Supposeyouhadarelativedeposit$10at5.5%interest200yearsago.Howmuchwouldtheinvestmentbeworthtoday?FV=10(1.055)200=447,189.84Whatistheeffectofcompounding?Simpleinterest=10+200(10)(.055)=120.00Compoundingadded$447,069.84tothevalueoftheinvestment,5F-12,FutureValueasaGeneralGrowthFormula,Supposeyourcompanyexpectstoincreaseunitsalesofwidgets（小部件）by15%peryearforthenext5years.Ifyoucurrentlysell3millionwidgetsinoneyear,howmanywidgetsdoyouexpecttosellin5years?FV=3,000,000(1.15)5=6,034,072,5F-13,QuickQuizPartI,Whatisthedifferencebetweensimpleinterestandcompoundinterest?Supposeyouhave$500toinvestandyoubelievethatyoucanearn8%peryearoverthenext15years.Howmuchwouldyouhaveattheendof15yearsusingcompoundinterest?Howmuchwouldyouhaveusingsimpleinterest?,5F-14,PresentValues现值,HowmuchdoIhavetoinvesttodaytohavesomeamountinthefuture?FV=PV(1+r)tRearrangetosolveforPV=FV/(1+r)tWhenwetalkaboutdiscounting,wemeanfindingthepresentvalueofsomefutureamount.Whenwetalkaboutthe“value”ofsomething,wearetalkingaboutthepresentvalueunlesswespecificallyindicatethatwewantthefuturevalue.,5F-15,PresentValueOnePeriodExample,Supposeyouneed$10,000inoneyearforthedownpaymentonanewcar.Ifyoucanearn7%annually,howmuchdoyouneedtoinvesttoday?PV=10,000/(1.07)1=9,345.79Calculator1N7I/Y10,000FVCPTPV=-9,345.79,5F-16,PresentValuesExample2,Youwanttobeginsavingforyourdaughterscollegeeducationandyouestimatethatshewillneed$150,000in17years.Ifyoufeelconfidentthatyoucanearn8%peryear,howmuchdoyouneedtoinvesttoday?PV=150,000/(1.08)17=40,540.34,5F-17,PresentValuesExample3,Yourparentssetupatrustfund（托管基金）foryou10yearsagothatisnowworth$19,671.51.Ifthefundearned7%peryear,howmuchdidyourparentsinvest?PV=19,671.51/(1.07)10=10,000,5F-18,PresentValueImportantRelationshipI,Foragiveninterestratethelongerthetimeperiod,thelowerthepresentvalueWhatisthepresentvalueof$500tobereceivedin5years?10years?Thediscountrateis10%.五年后收到500的现值5years:PV=500/(1.1)5=310.4610years:PV=500/(1.1)10=192.77,5F-19,PresentValueImportantRelationshipII,Foragiventimeperiodthehighertheinterestrate,thesmallerthepresentvalueWhatisthepresentvalueof$500receivedin5yearsiftheinterestrateis10%?15%?Rate=10%:PV=500/(1.1)5=310.46Rate=15%;PV=500/(1.15)5=248.59,5F-20,QuickQuizPartII,Whatistherelationshipbetweenpresentvalueandfuturevalue?Supposeyouneed$15,000in3years.Ifyoucanearn6%annually,howmuchdoyouneedtoinvesttoday?Ifyoucouldinvestthemoneyat8%,wouldyouhavetoinvestmoreorlessthanat6%?Howmuch?,5F-21,TheBasicPVEquation-Refresher,PV=FV/(1+r)tTherearefourpartstothisequationPV,FV,randtIfweknowanythree,wecansolveforthefourth三缺一，学会求第四个？Ifyouareusingafinancialcalculator,besuretorememberthesignconventionoryouwillreceiveanerror(oranonsenseanswer)whensolvingforrort,5F-22,DiscountRate折现率,OftenwewillwanttoknowwhattheimpliedinterestrateisinaninvestmentRearrangethebasicPVequationandsolveforrFV=PV(1+r)tr=(FV/PV)1/t1Ifyouareusingformulas,youwillwanttomakeuseofboththeyxandthe1/xkeys,5F-23,DiscountRateExample1,Youarelookingataninvestmentthatwillpay$1,200in5yearsifyouinvest$1,000today.Whatistheimpliedrateofinterest?r=(1,200/1,000)1/51=.03714=3.714%Calculatorthesignconventionmatters!N=5PV=-1,000(youpay1,000today)FV=1,200(youreceive1,200in5years)CPTI/Y=3.714%,5F-24,DiscountRateExample2,Supposeyouareofferedaninvestmentthatwillallowyoutodoubleyourmoneyin6years.Youhave$10,000toinvest.Whatistheimpliedrateofinterest?r=(20,000/10,000)1/61=.122462=12.25%用72法则，72/6=12，即12%同样，假设年利率为10%，多少年可以翻一番？72/10=7.2年,5F-25,DiscountRateExample3,Supposeyouhavea1-yearoldsonandyouwanttoprovide$75,000in17yearstowardshiscollegeeducation.Youcurrentlyhave$5,000toinvest.Whatinterestratemustyouearntohavethe$75,000whenyouneedit?r=(75,000/5,000)1/171=.172688=17.27%，可用计算器,5F-26,QuickQuizPartIII,Whataresomesituationsinwhichyoumightwanttoknowtheimpliedinterestrate?Youareofferedthefollowinginvestments:Youcaninvest$500todayandreceive$600in5years.Theinvestmentisconsideredlowrisk.Youcaninvestthe$500inabankaccountpaying4%.Whatistheimpliedinterestrateforthefirstchoiceandwhichinvestmentshouldyouchoose?,5F-27,FindingtheNumberofPeriods计算复利期数,Startwiththebasicequationandsolvefort(rememberyourlogs)FV=PV(1+r)tt=ln(FV/PV)/ln(1+r)Youcanusethefinancialkeysonthecalculatoraswell;justrememberthesignconvention.,5F-28,NumberofPeriodsExample1,Youwanttopurchaseanewcar,andyouarewillingtopay$20,000.Ifyoucaninvestat10%peryearandyoucurrentlyhave$15,000,howlongwillitbebeforeyouhaveenoughmoneytopaycashforthecar?t=ln(20,000/15,000)/ln(1.1)=3.02years,5F-29,NumberofPeriodsExample2,Supposeyouwanttobuyanewhouse.Youcurrentlyhave$15,000,andyoufigureyouneedtohavea10%downpayment（预付定金）plusanadditional5%oftheloanamountforclosingcosts（买卖房子的过户费用）.Assumethetypeofhouseyouwantwillcostabout$150,000andyoucanearn7.5%peryear,howlongwillitbebeforeyouhaveenoughmoneyforthedownpaymentandclosingcosts?,5F-30,NumberofPeriodsExample2Continued,Howmuchdoyouneedtohaveinthefuture?Downpayment=.1(150,000)=15,000Closingcosts=.05(150,00015,000)=6,750Totalneeded=15,000+6,750=21,750终值Computethenumberofperiods目前手里有15000元,7.5%回报Usingtheformulat=ln(21,750/15,000)/ln(1.075)=5.14yearsPerafinancialcalculator:PV=-15,000,FV=21,750,I/Y=7.5,CPTN=5.14years,5F-31,QuickQuizPartIV,Whenmightyouwanttocomputethenumberofperiods?Supposeyouwanttobuysomenewfurnitureforyourfamilyroom.Youcurrentlyhave$500,andthefurnitureyouwantcosts$600.Ifyoucanearn6%,howlongwillyouhavetowaitifyoudontaddanyaddition