復(fù)習(xí)一節(jié)補(bǔ)課

RevisiononCorporateFinance

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

Concepts資金時(shí)間價(jià)值一定量資金在不同時(shí)點(diǎn)上的價(jià)值量的差額（from百度文庫）當(dāng)前所持有的一定量貨幣比未來獲得的等量貨幣具有更高的價(jià)值（from百度百科）理解今天的100元和1年后的100元在同一時(shí)點(diǎn)的價(jià)值相等嗎？不，今天的100元可以存一年期銀行定期存款，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。（終值）同樣的，一年后的103.25元等值于今天的100元。（現(xiàn)值）R=3.25%?6現(xiàn)值：PresentValue(“P”)指資金折算至基準(zhǔn)年的數(shù)值，也稱折現(xiàn)值、也稱在用價(jià)值，是指對(duì)未來現(xiàn)金流量以恰當(dāng)?shù)恼郜F(xiàn)率進(jìn)行折現(xiàn)后的價(jià)值(from百度百科）一年后的100元在今天價(jià)值多少？終值FutureValue(“F”)又稱將來值或本利和，是指現(xiàn)在一定量的資金在未來某一時(shí)點(diǎn)上的價(jià)值。(from百度百科）今天的100元在1年后價(jià)值多少？TimeValueofMoney

Concepts7利率/折現(xiàn)率(“R”)Discountrate基準(zhǔn)：無風(fēng)險(xiǎn)無通脹的社會(huì)平均利潤(rùn)率(e.g.長(zhǎng)期國(guó)債利率)與債券的Couponrate(“I”)區(qū)分在不同環(huán)境中以及為不同目的，使用不同的R–(slides2.4)在評(píng)估債券和股票價(jià)值時(shí),R為依據(jù)標(biāo)的公司的風(fēng)險(xiǎn)而定的折現(xiàn)率（基準(zhǔn)利率+風(fēng)險(xiǎn)溢價(jià))在衡量一個(gè)投資項(xiàng)目時(shí)(PartIII)作為investor,R為期望回報(bào)率作為investee,R為資本成本(WACC)TimeValueofMoney

Concepts8年金Annuity，是定期或不定期的時(shí)間內(nèi)一系列的現(xiàn)金流入或流出。(from百度百科)定額不一定按年例：按揭貸款，壽險(xiǎn)永續(xù)年金Perpetuity(e.g.Consol,preferredstock)恒定增長(zhǎng)永續(xù)年金(Dividendgrowthmodel/DGM)TimeValueofMoney

Concepts年金的特殊形式9類型TypeFormula(notrequired)終值(復(fù)利)FuturevalueFn=P(1+r)n現(xiàn)值(復(fù)利)PresentvalueP=Fn(1+r)-n末付年金終值FuturevalueannuityinarrearsF=A[((1+r)n–1)/r]預(yù)付年金終值FuturevalueannuityinadvanceF=A[((1+r)n+1–1)/r-1]末付年金現(xiàn)值PresentvalueannuityinarrearsP=A[(1-(1+r)-n)/r]預(yù)付年金現(xiàn)值PresentvalueannuityinadvanceP=A[(1-(1+r)-(n-1))/r+1]永續(xù)年金現(xiàn)值(末付)PerpetuityP=A/r恒定增長(zhǎng)永續(xù)年金現(xiàn)值(末付)GrowingperpetuityP=A/(r-g)TimeValueofMoney

Calculation10確定現(xiàn)值/終值種類三步驟現(xiàn)值or終值？計(jì)算價(jià)值時(shí)點(diǎn)在現(xiàn)金流的未來（右側(cè)）還是過去（左側(cè)）是否是年金？是否存在定期的相等的現(xiàn)金流不必定是每年如果是年金末付還是預(yù)付？計(jì)算價(jià)值時(shí)點(diǎn)上是否有現(xiàn)金流發(fā)生？?jī)r(jià)值時(shí)點(diǎn)有現(xiàn)金流價(jià)值時(shí)點(diǎn)無現(xiàn)金流年金現(xiàn)值預(yù)付InAdvance末付InArrears年金終值末付InArrears預(yù)付InAdvanceCashflowValuepointTimeValueofMoney

Calculation11價(jià)值時(shí)點(diǎn)有現(xiàn)金流價(jià)值時(shí)點(diǎn)無現(xiàn)金流年金現(xiàn)值預(yù)付InAdvance末付InArrears年金終值末付InArrears預(yù)付InAdvance直接根據(jù)n和r查table4(“末付不變”)直接根據(jù)n和r查table3(“末付不變”)根據(jù)n-1和r查table4相應(yīng)系數(shù)后+1(“現(xiàn)值減加”)根據(jù)n+1和r查table3相應(yīng)系數(shù)后-1(“終值加減”)末付不變預(yù)付要變,現(xiàn)值減加終值加減TimeValueofMoney

Calculation12如何確定n?對(duì)于現(xiàn)值或終值n是valuepoint和F或P(已知)之間的時(shí)間段的數(shù)量對(duì)于年金現(xiàn)值或年金終值n是等額現(xiàn)金流的筆數(shù)

解題黃金法則！分解現(xiàn)金流確定各現(xiàn)金流種類（三部曲）確定n和r，以及P,F,A查表（口訣?。┐?，搞定！TimeValueofMoney

Calculation13Amortizedloanwithfixedpayment(等額本息按揭貸款）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:分解現(xiàn)金流PVannuityinarrearsn=20，A=4%*1000=40,r=3%查表得系數(shù)=14.877PV1=40*14.877=595.08PVn=20,FV=1000,r=3%查表得系數(shù)=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:分解現(xiàn)金流ValuationofStock

Calculation–Differentialdividendgrowthmodel40

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

Calculation–Differentialdividendgrowthmodel41Answer畫圖分解現(xiàn)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(互斥項(xiàng)目“MEPs”)OnlyoneofseveralpotentialprojectscanbechosenCannotbetakenatthesametimeTochoosethebestoneIndependentprojects(獨(dú)立項(xiàng)目“IPs”)Accepting/rejectingaprojectdoesnotaffectthedecisionontheotherprojectsCanbetakenatthesametimeMustexceedaminimumacceptancecriteria52Basicinvestmentevaluationtools

ProsandCons–NPVvs.IRRNPV

絕對(duì)指標(biāo)vs.IRR相對(duì)指標(biāo)在互斥項(xiàng)目中用單純IRR來選擇，可能會(huì)選到IRR很高的但NPV很小的項(xiàng)目（由于項(xiàng)目規(guī)模的原因），在資金規(guī)模足夠的前提下不是最優(yōu)選擇因此互斥項(xiàng)目不用IRR作為參考指標(biāo)(SampleNPV,IIRR,INPV-Slide3.30)非常規(guī)現(xiàn)金流的項(xiàng)目計(jì)算后會(huì)得不止一個(gè)IRRIRR優(yōu)勢(shì)：可以在沒有貼現(xiàn)率時(shí)計(jì)算得出53Basicinvestmentevaluationtools

ProsandCons–PIPros容易理解在資金量有限時(shí)較有用Cons在比較互斥項(xiàng)目并資金量不受限時(shí)可能做出錯(cuò)誤決策（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+