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1、成本收益分析Cost-Benefit Analysis,Public Finance,Introduction,Cost-benefit analysis is a set of practical procedures for guiding public expenditure decisions.,Future Value（终值）：Present Dollars into the Future,Suppose you invest$100 today in the bank.At the end of year 1,it is worth(1+.05)x$100,or$105At the
2、 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 Future,DefineR=initial investment amountr=rate of return on investmentT=years of investmentThe future value(FV，终值)of the investment is
3、:,Present Value（现值）:Future Dollars into the Present,Suppose someone promises to pay you$100 one year from now.What is the maximum amount you should be willing to pay today for such a promise?,Present Value:Future Dollars into the Present,The present value of a future amount of money is the maximum a
4、mount you would be willing to pay today for the right to receive the money in the future.,Present Value:Future Dollars into the Present,DefineR=amount to be received in futurer=rate of return on investmentT=years of investmentThe present value(PV)of the investment is:,Present Value:Future Dollars in
5、to the Present,In previous equation,r is often referred to as the discount rate（贴现率）,and(1+r)-T is the discount factor（贴现因子）.Finally,consider a promise to pay a stream of money,$R0 today,$R1 one year from now,and so on,for T years.,Present Value:Future Dollars into the Present,Present value is an en
6、ormously important conceptA$1,000,000 payment 20 years from now is only worth today:$376,889 if r=.05$148,644 if r=.10,Private 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,denoted as BX,CX,BY,and CY.Need to ask:Is the project admis
7、sible（可行）?Is the project preferable（最好）?,Private Sector Project Evaluation,Admissible: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 Sector Project Evaluation,Define:,Benefits from project i
8、at time t,Costs from project i at time t,Then the present value of project i is:,Private Sector Project Evaluation,The 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 projects are mutually exclusive（二选一的）,the preferre
9、d project is the one with the highest present value.,Private Sector Project Evaluation,Table 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 different times.The lower the discount rate,the more
10、 valuable the back-loaded project.,Private Sector Project Evaluation,Several 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 Evaluation,The internal rate of return,is defined as the th
11、at 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项目现在投入100，一年后收入110Y项目现在投入1000，一年后收入1080假定企业按6的利率借贷X项目赚了4
12、美元，Y项目赚了20美元,Private Sector Project Evaluation,The 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 Sector Project Evaluation,Admissibility using the benefit-cost ratio requires:,This ratio
13、 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1：建造垃圾场B=2.5亿美元 C=1亿美元 收益成本比率2.5方案2：将垃圾送到土星上B=2亿美元 C=1亿美元 收益成本比率2若方案1忽略了垃圾泄漏对农作物造成价值4000万美元的危害将4000万美元作为收益的减项：收益成本比率2.4将4000万美元作为成本的增项：收益成本比率1.79,
