资产评估理论基础1007

基础概念1现值（PresentValue）2复利（CompoundInterests）利息的计算方式复利的力量图1复利本金利息和(1+i)2=12+2×i+i21Principal;2×isimpleinterest;i2interestoninterest;单利复利年度本金利率利息本息和本金利息本息和息差YearPrincipalInterestsRatesInterestsSumPrincipalInterestsSum16200003.25%20150640150620000.0020150.00640150.000106200003.25%20150821500826803.3626871.11853674.4732174.46839206200003.25%2015010230001138420.8436998.681175419.51152419.5129306200003.25%2015012245001567485.1650943.271618428.43393928.4319406200003.25%2015014260002158261.3970143.502228404.89802404.8891506200003.25%2015016275002971697.8296580.183068278.001440778606200003.25%2015018290004091713.80132980.704224694.502395694.499706200003.25%2015020305005633857.42183100.375816957.793786457.791806200003.25%2015022320007757226.20252109.858009336.055777336.048906200003.25%20150243350010680880.56347128.6211028009.188594509.1831006200003.25%20150263500014706443.61477959.4215184403.031254940312345678910110100000200000300000400000500000600000700000年度Year本金Principal利息Interests利息InterestsExample图2中国经济赶上美国需要多少时间US=1.015xChina=1.08xUS'GDPis3,China'sGDP1;项目一、城乡居民及单位存款（一）活期0.35（二）定期三个月2.85半年3.05一年3.25二年3.75三年4.25五年4.75一年2.85三年2.9五年3二、协定存款1.15三、通知存款.一天0.8七天1.35年利率（%）  1.整存整取 2.零存整取、整存零取、存本取息 3.定活两便按一年以内定期整存整取同档次利率打6折执行图3两百年以后Example2845.63Ibbotson{and}Sinquefieldcalculatedwhatthestockmarketreturnedasawholefrom1926to1999.Theyfindthatonedollarplacedinthesestocksatthebeginningof1926wouldhavebeenworth$2845.63.Annualreturnis11.346%.Example:PeterMinuit,director-generalofNewNetherlands,theDutchwestIndiaCompany'sColonyinNorthAmerica.In1626，60DutchGuilders(10.61gSliverCoin)图4DutchGuildersnativeAmericans,In1667,DucthwereforcedtoexchangeitforSurinamewiththeBritish.(1.1135)74=?;图6曼哈顿岛（ManhattanIsland）Whereistheisland?Whereis自由女神？Suriname163821squarekmJustice–Duty–Loyalty公平责任忠诚158583770.72227593806010497.3346216Question.一家餐馆的合理利润应该在多少？3永续年金（Perpetuity）PresentValue=C1+r+C(1+r)2+C(1+r)3+C(1+r)4+⋯⋯PresentValue=CrInterest=Cr×r=C24×(1+0.05)387=?4增长永续（GrowingPerpetuity）GrowingAnnuity:C[1r−g−1r−g×(1+g1+r)T]Example1Numerator2TheInterestRateandtheGrowthRate3TheTimingAssumptionRothsteinCorporationisjustabouttopayadividendof$3.00pershare.Investorsanticipatethattheannualdividendwillriseby6percentayearforever.Theapplicableinterestrateis11percent.Whatisthepriceofthestocktoday.$66.60=$3.00+$3.180.11−0.06$3.00ImminentDivedend$3.18($3.00x1.06)PresentValueofalldividendsbeginningayear¿nowAnnuity年金例子ExampleDate01234T...T+1T+2...Consol1CCCCC...CC...Consol2CC...AnnuityCCCCC...PresentValue=CrConsol2:PresentValue=Cr×[1(1+r)T]Consol2−Consol1=Cr−Cr×[1(1+r)T]Consol2−Consol1=ThepresentvalueofcashflowsforTyearsPerpetuity:PV=CrGrowingPerpetuity:PV=C(r−g)Annuity:PV=C[1r×1r×(1+r)T]GrowingAnnuity:C[1r−g−1r−g×(1+g1+r)T]ATr,Tindicatenumberofperiods,rindicateinterestrate.MarkYounghasjustwonthestatelottery,paying$50000ayearfor20years.Heistoreceivethisfirstpaymentayearformnow.ThestateadvertisesthisastheMillionDollarLotterybecause$1000000=$50000x20.Iftheinterestrateis8percent,whatisthetruevalueofthelottery?马克赢得了一笔州彩票，金额为1000000美元，但要20年分期，每期5万美元，第一笔奖金一年后收到。解答：MillionDollarLottery=50000x{1/0.08–1/[0.08(1.08)20])}MillionDollarLottery=50000x{1/0.08–1/[0.08(1.08)19])}变形1后付年金Trick1:DelayedAnnuityDanielleCaravellowillreceiveafour-yearannuityof500peryear,beginningatdata6.Iftheinterestrateis10percent,whatisthepresentvalueofherannuity?012345678910500500500500Trick2:AnnuityinAdvance先付年金Inapreviousexample,markYoungreceived50000ayearfor20years.Inthatexample,hewastoreceivethefirstpaymentayearfromthewinningdata.Letusnowassumethatthefirstpaymentoccursimmediately.Thetotalnumberofpaymentsremains20.接MarkYoung例子，如果第一期奖金立即收到，而不是一年后才能收到，维持20期的奖金，那么又如何计算呢？Trick3：TheInfrequentAnnuity不规则年金MissAnnChenreceiveanannuityof450,payableonceeverytwoyears.Theannuitystretchesoutover20years.Thefirstpaymentoccursatdate2,thatis,twoyearsfromtoday.Theannualinterestrateis6percent.AnnChen小计每次收到450，每两年一次，期限20年，第一次收到付款是在第二期，每年利息率是6%。(1.06×1.06)−1=❑450×[10.1236−10.1236×0.123610]=❑Trick4:EquatingPresentValueofTwoAnnuitiesHaroldandHelenNasharesavingforthecollegeeducationoftheirnewborndaughter,Susan.TheNashesestimatethatcollegeexpenseswillrun30000peryearwhentheirdaughterreachescollegein18years.Theannualinterestrateoverthenextfewdecadeswillbe14percent.Howmuchmoneymusttheydepositinthebankeachyearsothattheirdaughterwillbecompletelysupportedthroughfouryearsofcollege.Nash夫妇为刚出生的女儿存款。......Step1:计算学费Step2:学费折现9422.91Step3:C×A170.14=9422.91A170.14=6.3729011718192021Birth2Deposittution1tution31Depositlastdeposittution2tution4GrowingAnnuityGrowingAnnuity:C[1r−g−1r−g×(1+g1+r)T]StuartGabriel,asecond-yearMBAstudent,hasjustbeenofferedajobat$80000ayear,Heanticipateshissalaryincreasingby9percentayearuntilhisretirementin40years.Givenaninterestrateof20percent,whatisthePVofhislifetimesalary?Forperviousexample,HaroldandHelenNashplannedtomake17identicalpaymentsinordertofundthecollegeeducationoftheirdaughter,Susan.Alternatively,imaginethattheyplannedtoincreasetheirpaymentsat4percentperyear.Whatwouldtheirfirstpaymentbe?WhatIsaFirmWorth?