1、ROR（IRR)的优缺点：易理解；与基准点无关；在项目寿命期内任意时刻，使项目收益换算值之和等于费用换算值之和的利率称为ROR(IRR)。所以，ROR的计算，可以用NPV(i)=0,NFV(i)=0,NAV(i)=0 进行计算。NPVIRR0ic=0=ic0MROR,we consider the alternative to be feasible.If GRORMROR.Therefore,both alternatives are feasible alternatives.This brings us to the next step.The cash flow profile for
2、 the incremental analysis,along with the cash flow profile for each alternative,is reproduced below.Year0123456A030201814106B-2060406420B-A-203020-12-10-8-6 million99.36$2.0162.0182.01102.0112206543Pmillion12.116$)2.01(20)2.01(3045F6)1(99.3612.116)1(GRORGRORPFnSolving for GROR,GROR=21%YearB-ASTEPS12
3、340-20-20-20-20-2013030*1.220000220202020203-1231.231.2*1.20004-10-1027.4427.44*1.2005-8-8-824.9324.93*1.206-6-6-6-623.91 F=23.91+20(1+0.2)4=65.3856Using the equation,F=P(1+GROR)n 65.3856=20(1+GROR)nSolving,GROR=21.8%.Although in this example,we could cover the subsequent negative cash flows with ou
4、r positive cash flows,in some cases in between positive cash flows may not be able to cover all the subsequent negative cash flows.If that happens,then the net negative cash flows in a given year should be treated as out of pocket expense and should be converted to the present value in the GROR anal
5、ysis.Example 3.30 An investment in a producing property results in the following cash profile due to price fluctuations.If the MROR is 15%,calculate the GROR.Year01234567Cash Flow(in thousands)-3015-2015101086 SolutionWe have negative cash flows in year 0 and year 2.Before we consider the actual out
6、 of pocket expenses,we need to cover the negative cash flow in year 2 with the positive cash flow in year l.Investing$15,000 at a rate of 15%will result in,15,000(1+.15)=17,250Adding the positive cash flow to-$20,000,the net cash flow in year 2,-20,000+17,250=-2,750This negative cash flow cannot be
7、covered from any previously generated revenues.Therefore,it is considered out-of-pocket expenses.The new cash flow profile is presented below.Year01234567Cash Flow(in thousands)-300-2.7515101086 1.32)15.01(75.2302PF=15(1+.15)4+10(l+.15)3+10(l+.15)2+8(l+.15)1+6=69.9Therefore,to calculate the GROR,F=P
8、(l+GROR)n 69.9=32.l(l+GROR)7 GROR=11.8%To summarize the GROR method,it is a modification of the rate of return method.It requires an additional knowledge of reinvestment rate.However,if such information is known,the method eliminates the need of trial and error procedure as required for the ROR meth
9、od.Further,by using the GROR method,we eliminate the possibility of multiple rates of return.3.6 Profit to Investment Ratio Profit to investment ratio(PIR)is the ratio of the NPV at MROR to the present value of out of pocket investment.We can write it as,COSTSPVNPVPIR This number is an indication of
10、 the efficiency of the investment.In other words,PIR is the amount of money earned per dollar invested.As in the case of GROR calculations,only if the subsequent investment is not covered by prior benefits,that investment is included in the present value of investments.Since the future benefits can
11、only be received if we initiate the project,it is critical that we try to cover the subsequent costs by prior benefits before we cover them with out of pocket expenses.The out of pocket expense being an additional expense should be reflected in the denominator of Eq.3.14.For a project to be feasible
12、,the PIR has to be greater than zero.The following examples illustrate the application.Example 3.31 An oil company intends to buy a producing property for a price of$l million.It is expected to generate$280,000 net income in the first year declining at 10%per year.The property will be held for at le
13、ast 10 years with an expected salvage value of$200,000.If the MROR is 15%,should the property be b o u g h t?U s e P I R a n a l y s i s.906,7210115.01000,20015.011.0111.015.0000,28061010NPV073.0101906,72PVNPVPIR6COSTS Example 3.32 The following cash flow profile is expected for an investment.If the
14、 MROR is 10%,check the feasibility of the project using PIR criterion.Period0123456Cash flow-10080-100200100503080(l+0.l)=88-100+88=-126.1561.01301.01501.011001.012001.011001.0180100NPV65432 Total out of pocket expenses are calculated as,9.1091.01121002424.19.1096.156PVNPVPIRCOSTSSince this value is
15、 greater than 0,the project is feasible.Example 3.33 The following two alternatives are considered for a project.Based on the PIR analysis,select the best alternative.Assume the MROR to be 10%.(a)(b)Initial Investment$10,000$20,000Annual Benefit$3,000$7,000Life,Years55Salvage Value$8,000$3,000 339,6
16、$000,101.01000,80.110.110.11000,3NPV555a398,8$000,201.01000,30.110.110.11000,7NPV555b06339.0000,10339,6$PVNPVPIRCOSTSaaa04199.0000,20398,8$PVNPVPIRCOSTSbbbAlthough PIRa PIRb,we need not select(a)unless we carry out one additional calculation.Since projects(a)and(b)require different amounts of invest
17、ment,we will have to calculate the PIR for incremental investment,02059.0000,10000,20339,68398PVPVNPVNPVPIRainvestmentbinvestmentabSince PIR0,an alternative with a higher investment should be selected;i.e.,we should select(b)over(a).If PIR0,an alternative requiring a smaller investment would have be
18、en selected.a.Calculate the PIR for all the alternatives.If the PIR is positive,retain the alternative for future consideration;otherwise reject it from additional consideration.b.Select the two alternatives requiring the smallest investments.Calculate the PIR.If PIR0,select the alternative requirin
19、g a bigger investment.Reject the remaining alternative from further consideration.c.Select the alternative requiring the next biggest investment and compare it with the retained alternative from the previous step.Calculate PIR.If PIR0,select the alternative requiring a bigger investment.d.Repeat ste
20、p(c)until only one alternative remains.The following example illustrates the application.Example 3.34 The following three alternatives are considered for buying a workstation.Based on PIR analysis,select the appropriate alternative.Assume the MROR to be 10%.ABCInitial Cost$15,000$25,000$50,000Net An
21、nual Benefit$6,000$9,000$16,000Life,Years777Salvage Value$4,000$4,000$8,000263,16$000,151.01000,40.110.110.11000,6NPV777A008.1000,15263,16$PVNPVPIRCOSTSAAA 08347.0000,25868,20868,20NPVBBPIR064.0000,50000,32000,32NPVCCPIR04605.0000,15000,25263,16868,20PV-PVNPV-NPVPIRCOSTSCOSTSABA-BAB0445.0000,25000,5
22、0868,20000,32PV-PVNPV-NPVPIRCOSTSCOSTSBCB-CBC A method similar to the PIR method is often used in the literature to evaluate mutually exclusive alternatives.The method uses a ratio defined as,costsbenefitsPVPV/BCPIR=B/C-1 Example 3.35 Information for two mutually exclusive alternatives is given as f
23、ollows.ABInitial Cost$12,000$18,000Annual Benefit6,0007,500Life,Years77Salvage Value$1,000$1,300If the MROR is 10%,using B/C method,choose the correct alternative.Confirm the answer with PIR method.SolutionAlternative A148.2000,12724,29/724,29$1.01000,11.0111.01000,6777AbenefitsCBPVAlternative B107.
24、2000,18180,37/180,37$1.01300,11.0111.01500,7000,18PV777costsAbenefitsCBPV24.1000,12000,28724,29180,37PV-PVPV-PVB/CCOSTSCOSTSbenefitsbenefitsA-BABABWe can confirm this analysis by PIR method.Alternative ANPV=PVbenefits PVcosts=29,724 12,000=17,724 048.1000,12724,17PVNPVPIRCOSTSAlternative BNPV=37,180 18,000=19,180007.1000,18180,19PIR024.0000,12000,28724,17180,19PV-PVNPV-NPVPIRCOSTSCOSTSABA-BAB ENDEND
