复习一节补课

RevisiononCorporateFinance

PartII&PartIII26Oct,2014byHuangJialiang12SomethingtosaybeforethissectionOutlineTimevalueofmoneyValuationofBondValuationofStockBasicinvestmentevaluationtoolsCapitalbudgetingPartIIPartIII3OutlineTimevalueofmoneyConceptsCalculation(usingtableoffactors)ValuationofbondConceptsCalculation(YTM,Bondvalue,EAIR)PreferredstockandperpetuitybondInterestrateriskofbondValuationofstockConceptsCalculation(DGM)BasicinvestmentevaluationtoolsConceptsProsandconsCapitalbudgetingDeterminerelevantcashflowEstimateprojectfreecashflow(Baldwincase)4TimeValueofMoney5TimeValueofMoney

Concepts资金时间价值一定量资金在不同时点上的价值量的差额（from百度文库）当前所持有的一定量货币比未来获得的等量货币具有更高的价值（from百度百科）理解今天的100元和1年后的100元在同一时点的价值相等吗？不，今天的100元可以存一年期银行定期存款，一年后可得103.25元（年利率3.25%)所以，今天的100元等值于一年后的103.25元。（终值）同样的，一年后的103.25元等值于今天的100元。（现值）R=3.25%?6现值：PresentValue(“P”)指资金折算至基准年的数值，也称折现值、也称在用价值，是指对未来现金流量以恰当的折现率进行折现后的价值(from百度百科）一年后的100元在今天价值多少？终值FutureValue(“F”)又称将来值或本利和，是指现在一定量的资金在未来某一时点上的价值。(from百度百科）今天的100元在1年后价值多少？TimeValueofMoney

Concepts7利率/折现率(“R”)Discountrate基准：无风险无通胀的社会平均利润率(e.g.长期国债利率)与债券的Couponrate(“I”)区分在不同环境中以及为不同目的，使用不同的R–(slides2.4)在评估债券和股票价值时,R为依据标的公司的风险而定的折现率（基准利率+风险溢价)在衡量一个投资项目时(PartIII)作为investor,R为期望回报率作为investee,R为资本成本(WACC)TimeValueofMoney

Concepts8年金Annuity，是定期或不定期的时间内一系列的现金流入或流出。(from百度百科)定额不一定按年例：按揭贷款，寿险永续年金Perpetuity(e.g.Consol,preferredstock)恒定增长永续年金(Dividendgrowthmodel/DGM)TimeValueofMoney

Concepts年金的特殊形式9类型TypeFormula(notrequired)终值(复利)FuturevalueFn=P(1+r)n现值(复利)PresentvalueP=Fn(1+r)-n末付年金终值FuturevalueannuityinarrearsF=A[((1+r)n–1)/r]预付年金终值FuturevalueannuityinadvanceF=A[((1+r)n+1–1)/r-1]末付年金现值PresentvalueannuityinarrearsP=A[(1-(1+r)-n)/r]预付年金现值PresentvalueannuityinadvanceP=A[(1-(1+r)-(n-1))/r+1]永续年金现值(末付)PerpetuityP=A/r恒定增长永续年金现值(末付)GrowingperpetuityP=A/(r-g)TimeValueofMoney

Calculation10确定现值/终值种类三步骤现值or终值？计算价值时点在现金流的未来（右侧）还是过去（左侧）是否是年金？是否存在定期的相等的现金流不必定是每年如果是年金末付还是预付？计算价值时点上是否有现金流发生？价值时点有现金流价值时点无现金流年金现值预付InAdvance末付InArrears年金终值末付InArrears预付InAdvanceCashflowValuepointTimeValueofMoney

Calculation11价值时点有现金流价值时点无现金流年金现值预付InAdvance末付InArrears年金终值末付InArrears预付InAdvance直接根据n和r查table4(“末付不变”)直接根据n和r查table3(“末付不变”)根据n-1和r查table4相应系数后+1(“现值减加”)根据n+1和r查table3相应系数后-1(“终值加减”)末付不变预付要变,现值减加终值加减TimeValueofMoney

Calculation12如何确定n?对于现值或终值n是valuepoint和F或P(已知)之间的时间段的数量对于年金现值或年金终值n是等额现金流的笔数

解题黄金法则！分解现金流确定各现金流种类（三部曲）确定n和r，以及P,F,A查表（口诀！）代入，搞定！TimeValueofMoney

Calculation13Amortizedloanwithfixedpayment(等额本息按揭贷款）Principle=$5,0004yearswithannualpaymentsateachyearendInterestrate=8%p.a.Question:Whatistheamountofeachpayment?Whatistheamountoftotalpayment?Whatistheamountoftotalinterestpayment?TimeValueofMoney

Calculation–Sample(Slide2.7)14Answer:AmountofeachpaymentDrawthetimeline:FigureoutthetypeofcashflowPresentvalueannuityinarrears(A,R,PV,n)R=8%,PV=5000,n=4,A=?PV=k*ALookforkintable2k=3.312A=5000/3.312=1509.6ATimeValueofMoney

Calculation–Sample(Slide2.7)15Answer:AmountoftotalpaymentTotalpayment=1509.6*4=6038.4AmountoftotalinterestpaymentYearBeginningbalanceTotalpaymentInterestpaidPrinciplepaidEndingbalance150001509.64001109.63890.423890.41509.6311.231198.372692.0332692.031509.6215.361294.241397.7941397.791509.111.821397.780.01Total6038.41038.414999.99TimeValueofMoney

Calculation–Sample(Slide2.7)16UnderstandthemeaningofPV,FV,Annuity,Perpetuity,A,R,I,nKnowhowtodivideupthecashflowintostandardonesKnowhowtousethetableTimeValueofMoney

Takeaways–317ValuationofBond18ValueofBondandStock=Presentvalueofexpectedfuturecashflowsfrominvestinginthesecurities(e.g.Bondandstock)3stepstovaluebondsandstocks:Estimatefuturecashflows(size&timing)Decide“R”(therateshouldreflecttheriskassociatedwiththesecurity)DiscountthefuturecashflowwithRValuationofBondandStock

KeyconceptCashisKing19BondtypesLevelcouponbondZerocouponbondConsolsParvalueCouponMaturitydateAdditionaltermsCallprovisionSinkingfundYieldtomaturity(YTM)---R!!!BondValue(price)Couponrate&CurrentYieldEAIRValuationofBond

Concepts20BondtypesLevelcouponbondZerocouponbondConsolsParvalueCouponMaturitydateAdditionaltermsCallprovisionSinkingfundYieldtomaturity(YTM)---R!!!BondValue(price)Couponrate&

CurrentYieldEAIRValuationofBond

Concepts21

ValuationofBond

Concepts22ValuationofBond

CalculationBondtypesLevelcouponbondZerocouponbondConsolsParvalueCouponMaturitydateAdditionaltermsCallprovisionSinkingfundYieldtomaturity(YTM)---R!!!BondValue(price)Couponrate&

CurrentYieldEAIRBondtermsCalculation23Yieldtomaturity(YTM)=Discountrate(annualized)=R!!!changing,permarketbenchmarkrateandcreditrisk/ratingoftheissuerValuationofBond

Calculation-YTM24Yieldtomaturity(YTM)Roughway,applicabletoLevelcouponbondDiscountrate=YTM=Discountrate*KWhereCoup=couponinterestperperiodPar=facevalueP0=currentbondpriceN=totalnumberofperiodsofinterestpaymentbeforematurityK=numberofcouponseachyearValuationofBond

Calculation-YTM25Supposeabondwitha10%couponandsemiannualcoupons,hasafacevalueof$1000,20yearstomaturity,issellingfor$1197.93.WhatistheYTM?(Inpractice,couponratealwaysmeansannualcouponrate)ValuationofBond

Calculation–YTM–Sample(Slide2.32)26Answer:(byusingtheroughway)Discountrate(semi-annual)===3.98%YTM=2*3.98%=7.96%ValuationofBond

Calculation–YTM–Sample(Slide2.32)27BondValue(price)=PVofcoupons+PVofparCouponrate=annualinterestpayment/parCurrentYield=annualinterestpayment/bondpriceValuationofBond

Calculation–BondValue,CouponRate,CouponYield28APR–AnnualPercentageRateBylaw,returnofinvestmentisquotedinAPREAIR–EffectiveAnnualInterestRateIfyoucanearn1%permonthon$1investedtodayAPR=1%*12=12%EAIR=1*(1.01)12-1=12.68%ValuationofBond

Calculation–EAIR&APR–Slide2.5729Whatisthepriceofabondwithcouponrate8%,paidtwiceayear,10-yrtomaturity,currentmarketinterestrate6%p.a.?Whyisthebondpriceover$1000?ValuationofBond

Calculation–Bondprice–Sample(Slide2.30)30Answer:分解现金流PVannuityinarrearsn=20，A=4%*1000=40,r=3%查表得系数=14.877PV1=40*14.877=595.08PVn=20,FV=1000,r=3%查表得系数=0.554PV2=1000*0.554=554Bondprice=PV=PV1+PV2=595.08+554=1149.08ValuationofBond

Calculation–Bondprice–Sample(Slide2.30)31PreferredstockandConsols(perpetual

bond)Valueofpreferredstock/perpetualbond=PVofaperpetuity=

A/rAmeansdividendinpreferredstock,andcouponinperpetualbondRememberAandrhavethesameperiodCostofpreferredstock/perpetualbond=A/P0(needtobeannualized)P0isthecurrentmarketpriceValuationofBond

Calculation–PreferredstockandConsols32InterestrateriskofbondRincreasesbondpricedecreases(ViceVersa)Priceoflong-termandlow-couponbondsaremoresensitivetointerestratechangesValuationofBond

Calculation–InterestrateriskofBond33CashisKing!(securityvalueisdeterminedbycashflows)UnderstandthebondtermsKnowhowtocomputetheYTM(byusingtheformula)InterestrateriskofBondValuationofBond

Takeaways-434ValuationofStock35RelevantcashflowstoastockholderDividendeProceedsfromsellingthesharesThereforethefairvalueofastockisthesumofthepresentvalueoftheabovementioned2cashflowsHowtodetermineR?expectedreturn–(riskassociated,higherrisk,higherreturn)ValuationofStock

Concepts36ValuationofStock

Calculation–3dividendmodels37ConstantdividendmodelDividendsarepaidatthesamelevelconstantlyDividendgrowthmodelDividendsareexpectedtogrowataconstantrateperperiodDifferentialdividendgrowthmodelDividendaregrowingatahigherrateinthefirstseveralyearsandthenthegrowthsettlesdowntoalower&morestablelevelConstantdividendmodelLikepreferredstockP0=D/RSample:Slide2.39Supposeastockisexpectedtopaya$0.5dividendeveryquarterandtherequiredreturnis10%.Whatistheprice?Answer:P0=D/R=0.5/(10%/4)=20Returnalwaysindicatesannualreturn,andthetenorofDandRmustbematchedAssumingthestockiskeptforever,thereforenocashinflowforsellingstockValuationofStock

Calculation–Constantdividendmodel38DividendgrowthmodelDividendsareexpectedtogrowataconstantrate(“g”)perperiod

priceisPVofagrowingperpetuityP0==(R=

)Consideration:DGMcanonlybeusedifR>gD0isnotincludedinthevaluecalculationNotworkablewhenthereisnodividendRcanalsobeestimatedfromCAPM(PartIV)…….D1D2D3D4D5D6P0ValuationofStock

Calculation–Dividendgrowthmodel39DifferentialdividendgrowthmodelAllowingforahigherdividendgrowthrateinthefirstseveralyearsandthenthegrowthsettlesdowntoalower&morestablelevelNormally2or3stagesKeytocalculation:分解现金流ValuationofStock

Calculation–Differentialdividendgrowthmodel40

Sample(Slide2.43)Supposeafirmisexpectedtoincreasedividendsby20%inoneyearandby15%intwoyears.Afteryear2,dividendswillincreaseat5%peryearindefinitely.Ifthepreviousdividendwas$1andtherequiredreturnis20%,whatisthefarestockprice?ValuationofStock

Calculation–Differentialdividendgrowthmodel41Answer画图分解现金流CashflowA=D1(PV)P0-A=D1/(1+R)=1*1.2/1.2=1CashflowB=D2~Dn(Growingperpetuity/DGM)P1-B=D2/(R-g)=1.2*1.15/(0.2–0.05)=9.2P0-B=P1-B/(1+R)=1.23/1.2=7.67P0=P0-A+P0-B=8.67…….15%5%5%5%5%D1D2D3D4D5D6P0ValuationofStock

Calculation–DifferentialdividendgrowthmodelAB42KnowhowtocalculatethestockvalueConstantdividendmodelDividendgrowthmodelDifferentialdividendgrowthmodelValuationofStock

Takeaways-1Allinall,it’sjustPVofcashflows43BasicInvestmentEvaluationTools44NPV&IRRPaybackperiod&discountedpaybackperiodPIAllaboutcashflowBasicinvestmentevaluationtools123456045NPVNetpresentvaluePresentvalueofallcashflows(incanout)AccepttheprojectifNPV>0Basicinvestmentevaluationtools

Concept-NPV46IRRThediscountratethatmakestheNPV=0AccepttheprojectiftheIRRisgreaterthantherequiredrateofreturn(orcostofcapital)Basicinvestmentevaluationtools

Concept-IRR47Paybackperiod:timetorecovertheinitialcostEstimatethecashflowsSubtractthefuturecashinflowfromtheinitialcostuntiltheinitialcosthasbeenrecoveredAccepttheprojectifthepaybackperiodislessthanatargetpaybackperiodBasicinvestmentevaluationtools

Concept–Paybackperiod48DiscountedpaybackperiodUsePVofeachcashflowratherthantherawcashflowincalculationonthepaybackperiodAccepttheprojectifthediscountedpaybackperiodislessthanatargetpaybackperiodBasicinvestmentevaluationtools

Concept–Discountedpaybackperiod49PI(ProfitabilityIndex)DefinedasthePVofaninvestment’sfuturecashflows除以thePVofitsinitialcostAcceptaprojectwithPI>1Basicinvestmentevaluationtools

Concept–PI50Basicinvestmentevaluationtools

ProsandCons–PPvs.DPPSampleSlide3.1751Basicinvestmentevaluationtools

Concepts–MutuallyExclusivevs.IndependentMutuallyexclusiveprojects(互斥项目“MEPs”)OnlyoneofseveralpotentialprojectscanbechosenCannotbetakenatthesametimeTochoosethebestoneIndependentprojects(独立项目“IPs”)Accepting/rejectingaprojectdoesnotaffectthedecisionontheotherprojectsCanbetakenatthesametimeMustexceedaminimumacceptancecriteria52Basicinvestmentevaluationtools

ProsandCons–NPVvs.IRRNPV

绝对指标vs.IRR相对指标在互斥项目中用单纯IRR来选择，可能会选到IRR很高的但NPV很小的项目（由于项目规模的原因），在资金规模足够的前提下不是最优选择因此互斥项目不用IRR作为参考指标(SampleNPV,IIRR,INPV-Slide3.30)非常规现金流的项目计算后会得不止一个IRRIRR优势：可以在没有贴现率时计算得出53Basicinvestmentevaluationtools

ProsandCons–PIPros容易理解在资金量有限时较有用Cons在比较互斥项目并资金量不受限时可能做出错误决策（同IRR)54Knowhowtocalculatetheindexes(exceptIRR)Knowthepros&consoftheindexesBasicinvestmentevaluationtools

Takeaways-255CapitalBudgeting56CapitalBudgeting

RelevantcashflowToevaluateaproject,weneedtocalculatetheNPV/IRR/PP/DPP/PITocalculatetheabove,weneedprojectedcashflow,andonlyrelevantcashflowRelevantcashflow=IncrementalcashflowCashflowsthatwilloccuronlyiftheprojectisadopted57CapitalBudgeting

RelevantcashflowTypeofcashflowsRelevant/IrrelevantOperatingCashflow(“OCF”)RelevantChangeinnetworkingcapitalRelevantFixedassetsinvestmentandSalvagevalueRelevantTaxesRelevantOpportunitycostsRelevantSideeffectsRelevantSunkcostsIrrelevantFinancingcostIrrelevant58CapitalBudgeting

EstimateProjectFreecashflowOperatingcashflow“OCF”=EBIT(1-Tc)+annualdepreciationFreecashflow“FCF”(tocomputetheNPV,IRR,etc.)=OCF+