股息贴现模型课件

DerivingtheDividendDiscountModelintheIntermediate跨期消费模型研究不同时间人们的消费行为，涉及时间因素的的消费和储蓄。即消费者不必将每期的收入用光，他可以选择储蓄，也可以选择贷款。其预算约束线的斜率与利率有关，为-(1+R)，R是利率，然后再此预算约束现的情况下研究消费者偏好。分析的结果一般为：利率提高，人们选择少消费，更倾向于储蓄，利率降低，人们会多消费，倾向于借贷。那它的方程是什么样子的？假设只有两期,C是消费，M是收入：C2=M2+(1+R)(m1-c1)1，2都是角标。weemployedastandard

two-periodmodelwithconsumersmaximizingutility

U(C1,C2).Income(I)inbothperiods

isknown,thepriceofaunitof

consumption(C)inbothperiodsisequaltoone,andtheindividual

canborroworlendatthesamerisk-freeinterestrate(rf).Themaximizingagenthastwobudgetconstraintsoverthetwoperiods.Inthefirstperiod,

I1=C1+BwhereBisthedollarvalueofthebondspurchased.Inthesecondperiod,

I2+(1+rf)B=C2Fromthefirstbudgetconstraint,B=I1−C1andsubstitutingthatintothesecondbudget

constraint,thisgivestheequationforthebudgetconstraintlineas

C2=I2+(1+rf)(I1−C1)Theequilibriumconditionisthenstraightforwardtoderiveasfollows:Themarginalrateofsubstitution(MRS)isthetradeoffofcurrentconsumptionforfuture

consumptionthatleavestheindividualindifferent;putdifferently,theminimumamountnecessary

toreceiveinthefuturetogiveupaunitofconsumptiontoday.Aslongasthereturn(1+rf)isgreater

thantheMRSofcurrentandfutureconsumption,theindividualwillpostponeconsumptionand

increasehisutility.Theindividualwillcontinuegivingupcurrentconsumptionpreciselytothe

pointwherethereturnofthebondisjustsufficienttocompensatehimforwaiting.Theimportant

aspectistheconceptofdiminishingMRS,thatwitheachadditionalunitofpostponedcurrent

consumptiontheindividualrequiresahigherreturn(slopeofindifferencecurvegetssteeperas

onemovesfromrighttoleft).Ina

financeclass,thestudenttypicallylearnsthenetpresentvalue(NPV)criteriaforinvestment

projectsasevaluatingallprojects,rankedfromhighesttolowestrateofreturn(ROR),againstthe

opportunitycostofcapital,whichisassumedtobeconstant.Todirectlycomparetheintertemporal

consumptionmodeltoconceptsinfinancerequiresconsiderationofastandardconcaveinvestment

opportunitysetthatranksinvestmentprojectsfromrighttoleftbyhighesttolowestratesofreturn.Theslopeoftheinvestmentopportunitysetis1plustheRORofaproject.Investmentisviewed

asforegonecurrentconsumption.Assuch,thecostofcapitalistheslopeoftheindifference

curve.Thisisshowninfigure2.Theindividualwill

continuetoinvestaslongastheproject’sRORisgreaterthantheMRS(costofcapital);in

otherwords,NPV>0.UtilityismaximizedwhentheRORisjustequaltotheMRS,where

NPV=0.Inthismodel,profitmaximizationisthesameasutilitymaximization,andzero

economicprofit(NPV=0)iswherethereturnofaprojectisjustequaltothevalueofforegone

current

consumption.thetwo-periodmodelhastwoconstraintsthatarecombinedintoonetorepresentthegraph’s

budgetconstraintline.Theconstraintforperiod1is

I1=C1+P1N(whereNisthenumberofsharesofastockandP1isthepriceofashare.)Thebudgetconstraint

forperiod2is

I2+(d2+P2)N=C2(whered2istheper-sharedividendandP2isthepriceofthesh