技术经济学英文版演示文稿C.ppt
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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。,3.4.2 Multiple Rates of Return In addition to the requirement of incremental analysis, the ROR analysis method also has another drawback. This method works well when a given alte
2、rnative requires an initial investment which is followed by future benefits. For this type of alternative, the cash flow profile can be shown as negative cash flow in the first year followed by positive cash flow in the future years. For example, if we consider an investment of $1,000 which will res
3、ult in a $300 annual benefit for the next six years with a $500 salvage value at the end of six years, the cash profile can be written as.,In this profile, there is only one sign change in cash profile between Years 0 and 1. Such profile is amenable to conventional ROR analysis. Note that the ROR ca
4、lculation requires solving a polynomial of i. We calculate the value of i for which the NPV is zero. For economic analysis, we are only interested in obtaining positive, real values of i for which the NPV is equal to zero. When there is only one sign change in the cash flow profile, as shown above,
5、we can only obtain one or zero positive solutions.,In some instances, however, the sign changes more than once in a cash flow profile. Under these circumstances, we may obtain more than one real ROR. The rule of signs for polynomial solution states that the number of real solutions between -l and is
6、 never greater than the number of sign changes. That is, if we have two sign changes, we may obtain a maximum of two rates of return values between -100% and . The following example illustrates the calculation of the number of feasible solutions.,Example 3.25 For the following four cash ROR between
7、-100% and .,Solution To calculate the maximum number of possible real solutions between -100% and , we can calculate the number of sign changes. For cash flow A, there is only one sign change between period 0 and l. For B, there are three sign changes; between periods 0 and l, periods l and 2, and 3
8、. Similarly, for cash flow C, there are four sign changes, and for cash flow D, there are five sign changes. As stated before, the number of sign changes will indicate the maximum number of possible real solutions. That is, for cash flow profile C, the number of real solutions between 100% and can b
9、e either 4, 3, 2, l. or zero.,The number of possible real solutions can be narrowed down even further by applying cumulative cash flow sign test. If we assume Aj to be a cash flow in period j, then we can define the cumulative cash flow Cj as, If Cj starts with a negative number and changes sign onl
10、y once, we will obtain only one positive solution. This cumulative cash flow method may allow us to narrow down the number of possible solutions for the ROR.,Example 3.26 Reconsider the cash flows provided in Example 3.23. Applying the cumulative cash flow sign test, investigate the possibility of n
11、arrowing the number of positive ROR solutions. Solution We can calculate the cumulative cash flows for each of the profiles as follows:,As a sample calculation, for period 3 for Project A, we can calculate. C3 = -100+20+20+30 =-30 For period 6, C6 = -100+20+20 +30+20+30+30=50 Looking at the cash flo
12、w profiles, for cash flow profiles A and D, there in only one sign change in the cumulative cash flow profile. That is, we will obtain only one unique positive value of the ROR. For cash flow profiles B and C, the results of cumulative cash flow profiles are inconclusive. We cannot reduce the possib
13、le number of solutions by using the cumulative cash flow profile for these two profiles.,Example 3.27 An in-fill drilling project is being considered for an existing oil field to accelerate oil recovery. The following two scenarios, based on two alternatives (no in-fill drilling versus in-fill drill
14、ing) are predicted. Which alternative would you select? The numbers are in millions. Assume that MROR is 20%.,Solution The first step in ROR analysis is to compare individual RORs for each alternative with the MROR. For alternative A, there is no sign change in the cash flow profile. Therefore, the
15、ROR for alternative A is . For alternative B, ROR can be shown to be greater than 20% (the ROR for alternative B is 260%). Therefore, both alternatives satisfy the requirement that the ROR be greater than the MROR. The next step is to conduct the incremental analysis. The cash flow profile for incre
16、mental values can be written as,The cash flow profile shows more than one sign change. The cumulative cash flow profile also shows more than one sign change. This indicates the possibility of more than one positive ROR solution. NPV for any interest rate can be calculated as,Fig. 3. 13 shows a plot
17、of NPV as a function of i.,Figure 3.13: Plot of NPV vs. i for Example 3.27,As stated before, the ROR is the rate at which the NPV is equal to zero. Based on Fig. 3.13, two RORs are possible; 11% and 72%. If we assume ROR to be 11%, then alternative A (an alternative requiring a smaller investment) s
18、hould be selected ( ). If we assume ROR to be 72%, then alternative B (an alternative requiring larger investment) should be selected ( ). Obviously, our answer changes depending upon the selected value of ROR.,One easy way to confirm this analysis is to calculate the NPV at the MROR (=20%) for incr
19、emental cash flow. Since NPV is positive, alternative B should be selected. This is the same predicted in the previous paragraph. It is obvious that, for such problems (where more than one sign change occurs in cash flow analysis), the ROR analysis is difficult to adopt. A better alternative would b
20、e to use the present worth analysis.,必须是连续的正现金流量,必须是连续的负现金流量,ir再投资利率 if 融资成本,3.5 Growth Rate of Return Analysis A related technique to the ROR analysis is the growth rate of return. Unlike ROR calculations, which are independent of what we do with the future benefits, growth rate of return depends o
21、n the reinvestment of the future benefits. It assumes that the future benefits are reinvested at certain interest rates and calculates the future value of all the benefits at the end of the useful life of the project.,Let us illustrate this schematically. In Fig. 3.14, we have a cash flow profile fo
22、r calculation of the rate of return. We invested $l,000 in the bank at an interest rate of 10% per year, and withdrew interest of $100 per year for 10 years finally withdrawing the initial investment of $l,000. In this simple scenario, the rate of return on the investment is 10%. The ROR value is in
23、dependent of what we did with the $100 we received at the end of each year. We could have gambled it away or could have reinvested it in buying stocks. The ROR would still be 10%. This is why the ROR is sometimes called internal rate of return. It only depends on internally generated revenues, not o
24、n external rates.,Contrast this cash flow profile with a case where the $100 revenue per year is reinvested in treasury bills at a 6% interest rate. The schematic diagram is shown in Fig. 3.15. We will assume that as soon as the annual payment is received, it is reinvested at a 6% interest rate. At
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