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1、成本收益分析Cost-Benefit AnalysisPublic FinanceMcGraw-Hill/Irwin 2005 The McGraw-Hill Companies,Inc.,All Rights Reserved.IntroductionCost-benefit analysis is a set of practical procedures for guiding public expenditure decisions.Future Value（终值）：Present Dollars into the FutureSuppose you invest$100 today
2、in the bank.At the end of year 1,it is worth(1+.05)x$100,or$105At the end of year 2,it is worth(1+.05)x$105,or$110.25The interest compounds over time,that is,the interest is also earning interest.Future Value:Present Dollars into the FutureDefineR=initial investment amountr =rate of return on invest
3、mentT=years of investmentThe future value(FV，终值)of the investment is:Present Value（现值）:Future Dollars into the PresentSuppose someone promises to pay you$100 one year from now.What is the maximum amount you should be willing to pay today for such a promise?Present Value:Future Dollars into the Prese
4、ntThe present value of a future amount of money is the maximum amount you would be willing to pay today for the right to receive the money in the future.Present Value:Future Dollars into the PresentDefineR=amount to be received in futurer =rate of return on investmentT=years of investmentThe present
5、 value(PV)of the investment is:Present Value:Future Dollars into the PresentIn previous equation,r is often referred to as the discount rate（贴现率）,and(1+r)-T is the discount factor（贴现因子）.Finally,consider a promise to pay a stream of money,$R0 today,$R1 one year from now,and so on,for T years.Present
6、Value:Future Dollars into the PresentPresent value is an enormously important conceptA$1,000,000 payment 20 years from now is only worth today:$376,889 if r=.05$148,644 if r=.10Private Sector Project Evaluation私人部门的项目评估Suppose there are two projects,X and Y.Each entails certain benefits and costs,de
7、noted as BX,CX,BY,and CY.Need to ask:Is the project admissible（可行）?Is the project preferable（最好）?Private Sector Project EvaluationAdmissible:Are the benefits greater than the costs?Preferable:Are the net benefits the highest?Most projects involve a stream of benefits and costs over time.Private Sect
8、or Project EvaluationDefine:Benefits from project i at time tCosts from project i at time tThen the present value of project i is:Private Sector Project EvaluationThe present value criteria（现值标准）for project evaluation are that:A project is admissible only if its present value is positive.When two pr
9、ojects are mutually exclusive（二选一的）,the preferred project is the one with the highest present value.Private Sector Project EvaluationTable 1 shows two different projects(R&D or Advertising).The discount rate plays a key role in deciding what project to choose,because the cash inflows occur at differ
10、ent times.The lower the discount rate,the more valuable the back-loaded project.Private Sector Project EvaluationSeveral other criteria are often used for project evaluation,but can give misleading answersInternal rate of return（内部收益率）Benefit-cost ratio（收益成本比率）Private Sector Project EvaluationThe in
11、ternal rate of return,is defined as the that solves the equation:The IRR is the discount rate that would make the present value of the project equal to zero.Admissible if r.The flawed analysis would choose an admissible project with the higher internal rate of return,ignoring scale.X项目项目现在投入现在投入100，
12、一年后收入，一年后收入110Y项目项目现在投入现在投入1000，一年后收入，一年后收入1080假定企业按假定企业按6的利率借贷的利率借贷X项目赚了项目赚了4美元，美元，Y项目赚了项目赚了20美元美元Private Sector Project EvaluationThe benefit-cost ratio divides the discounted stream of benefits by the discounted stream of costs.In this case:B=stream of benefits and C=stream of costs:Private Secto
13、r Project EvaluationAdmissibility using the benefit-cost ratio requires:This ratio is virtually useless for comparing across admissible projects,however.Ratio can be manipulated by counting benefits as“negative costs”and vice-versa.案例分析方案方案1：建造垃圾场：建造垃圾场B=2.5亿美元亿美元 C=1亿美元亿美元 收益成本比率收益成本比率2.5方案方案2：将垃圾送到土星上：将垃圾送到土星上B=2亿美元亿美元 C=1亿美元亿美元 收益成本比率收益成本比率2若方案若方案1忽略了垃圾泄漏对农作物造成价值忽略了垃圾泄漏对农作物造成价值4000万美元的危害万美元的危害将将4000万美元作为收益的减项：收益成本比率万美元作为收益的减项：收益成本比率2.4将将4000万美元作为成本的增项：收益成本比率万美元作为成本的增项：收益成本比率1.79