《技术经济学英文版演示文稿C(4)课件》由会员分享，可在线阅读，更多相关《技术经济学英文版演示文稿C(4)课件（91页珍藏版）》请在金锄头文库上搜索。
1、Example:P=$500 A=$140 n=10 NPV=? i() 0 10 20 25 30 40 NPV 900 360 87 0 -67 -162 -500技术经济学英文版演示文稿C(4)课件 ROR的意义：的意义：从收益的观点看，从收益的观点看，ROR就是项目所能达到的最高收益水平。就是项目所能达到的最高收益水平。技术经济学英文版演示文稿C(4)课件ROR的意义：的意义：从收益的观点看，从收益的观点看，ROR就是项目所能达到的最高收益水平。就是项目所能达到的最高收益水平。技术经济学英文版演示文稿C(4)课件NPV是折现率是折现率ic的函数，的函数，ic连续，则连续，则NPV可导。
2、可导。一阶导数：一阶导数：NPV函数曲线单调递减。函数曲线单调递减。二阶导数：二阶导数：NPV函数曲线凸向原点。函数曲线凸向原点。技术经济学英文版演示文稿C(4)课件当当ic=0，当当ic趋向于无穷大，趋向于无穷大，NPV=NCF0技术经济学英文版演示文稿C(4)课件3.4 Rate of Return AnalysisThe rate of return analysis is probably the most popular criterion in economic analysis. Its popularity stems from the ease with which a co
3、mmon person can understand the meaning of rate of return. Most of the investment brochures will use rate of return on your investment as a criterion to show how good a given investment opportunity is. It is much easier to understand that a project will provide 20% return on your investment than the
4、project will result in a NPV of $5,000. Unfortunately, although simple to understand, the technique has some major drawbacks. In this section, in addition to explaining how to calculate the rate of return (ROR), we will discuss the advantages and disadvantages of this technique .技术经济学英文版演示文稿C(4)课件Ra
5、te of return has two definitions. One definition can be stated as “the interest rate earned on the unpaid balance of a loan such that the payment schedule makes the unpaid balance equal to zero when the final payment is made.” Consider a simple example to illustrate this definition. 1001,000$1,00010
6、0 1001 2n-1 nFigure 3.9: A Loan of $1,000 with a Uniform Payment of Interest技术经济学英文版演示文稿C(4)课件Assume that you take a loan of $1,000 from a bank at an interest rate of 10% for a period of four years. Every year, including last year, you pay an interest of $100 to the bank. At the end of four years, y
7、ou pay the principal amount of $l,000. Therefore, at the end of four years the unpaid balance is zero. The rate of return for the bank is (l,00/1000=)10%. Schematically, the cash flow is shown in Fig. 3.9.技术经济学英文版演示文稿C(4)课件This definition can be turned around to state that the rate of return is the
8、interest rate earned on the unrecovered investment such that the payment schedule makes the unrecovered investment equal to zero at the end of the life of the investment. Using a similar example as before, let us assume that you have invested $10,000 in the bank at an interest rate of 6% for five ye
9、ars. At the end of each year, you withdraw $600 in interest and at the end of five years, you withdraw $10,000. The investment in the bank at the end of five years is, therefore, zero. You can consider that the rate of return on the investment is (600/10,000=) 6%. Schematically, the cash flow pro sh
10、own in Fig. 3.10技术经济学英文版演示文稿C(4)课件Figure 3.10: Investment of $10,000 with a Uniform Payment of Interest1 2n-1 n60010,000$10,000600 600技术经济学英文版演示文稿C(4)课件Mathematically, the rate of return (ROR) is defined as the rate at which net present worth (NPV) for a given investment is equal to zero. In equatio
11、n form, the rate at which, (3.4)is the rate of return.In other words, the rate at which NPV = 0 3.5)If we assume that the cash flow for a particular project is given by Aj where Aj represents the cash flow in year j, we can write the equation for NPV as, (3.6)If we define the rate iR corresponding t
12、o the rate at which NPV is zero, we can write the equation for iR as, (3.7)技术经济学英文版演示文稿C(4)课件Observing Eq.3.7, we notice that the equation represents a polynomial(多多项项式式) in iR which may result in n possible solutions for iR which will satisfy Eq.3.7. In economic analysis, we are only interested in
13、real solutions. Although negative rate of return is a real value, we may not be interested in an investment of negative rate of return. As a practical matter, we are searching for positive, real solutions of this equation. In most instances, we will obtain only one positive, real solution which repr
14、esents the rate of return. This is shown in the following examples.技术经济学英文版演示文稿C(4)课件Example 3.17 Calculate the rate of return for the following cash flow. Year 0 1 2 3 4 Cash Flow -4,000 2,500 1,800 1,300 900SolutionUsing the cash flows, we can write the equation for NPV as,Since this is a polynomi
15、al equation in i , we will have to solve it by trial and error, 技术经济学英文版演示文稿C(4)课件Since the value of NPV changes a sign between i = 15% and i = 35%, the rate of return should fall in between the two values. By linear interpolation(线形内插法线形内插法), we can write an approximate equation for the rate of ret
16、urn (ROR) as, (3.8)where i+ and i- respectively represent the vial values which resulted in positive and negative NPV values, and NPV+ and NPV _ represent the positive and the negative NPV values respectively. In our example,技术经济学英文版演示文稿C(4)课件Therefore,We can calculate the NPV at 29.3%. NPV=-66.5Alt
17、hough close to zero, we can try one more interpolation between 15% and 29.3%. NPV at 28.3% = -10.2We would assume this value to be close enough to zero. You may note that higher is the difference between the i+ and i-, bigger will be the deviation(背背离离) between the true ROR and the interpolated valu
18、e. Therefore, the interpolation may have to be carried out more than once to obtain a correct value of the ROR.技术经济学英文版演示文稿C(4)课件Example 3.18 By investing $10,000 in a project, you are promised that you will earn $2,700 per year for a period of six years. What is the ROR for this investment?Solution
19、 For i = 10%, For i =20%, Using Eq.3.8, For 16.3%, NPV = -129 At i = 15.8% NPV=1.70Therefore, the rate of return is 15.8%.技术经济学英文版演示文稿C(4)课件From the above examples, one can see that the ROR calculation has to be done by trial and error. Many times, it is very difficult to assume the initial value of
20、 interest rate. One way to overcome this problem is to use a ratio of periodic payment to initial investment. We can show that if the initial investment is equal to the salvage value, the ROR can be calculated as,技术经济学英文版演示文稿C(4)课件Using Eq.3.9, if the salvage value is less than the initial investmen
21、t, On the other hand, if the salvage value is greater than the initial investment, Eq.3.9 through Eq.3. 11 are applicable only if the investment is made at the beginning of the project and the periodic payments are equal to each other.技术经济学英文版演示文稿C(4)课件Example 3.19 As an investment, you bought a hou
22、se for $50,000. If you can rent the house for $800 per month, and can sell the house for $70,000 at the end of ten years, what is the ROR on your investment?SolutionLet us assume the ROR to be .017/month. where 120 is the number of months in which the rent is collected. Therefore, the ROR is l.7%/mo
23、nth. or 20.4%/year.技术经济学英文版演示文稿C(4)课件As can be seen from the above example, by using the correct initial guess. we did not have to use too many trial and errors. A similar equation can be developed for geometric series as explained in the example below.Example 3.20 A proposal calls for an investment
24、 of $25,000 in an oil property which will result in an initial income of $6,000 per year declining at a rate of 8% per year over the next twenty years. What is the rate of return? Assume the salvage value to be zero.SolutionIn this example we have a geometric series.Given: A = $6,000, n = 20 years,
25、g = -0.08Using the equation for geometric series,技术经济学英文版演示文稿C(4)课件技术经济学英文版演示文稿C(4)课件After one additional trial and error, the ROR = 15.7%.The ROR can also be calculated using a graphical procedure. For a typical investment scenario, we call assume different interest rates and calculate the NPV as a
26、 function of the interest rate. As shown in Fig.3.ll, by connecting the points, we can calculate the ROR corresponding to a point on the curve where NPV is equal to zero. 技术经济学英文版演示文稿C(4)课件Figure 3.11: ROR Determination技术经济学英文版演示文稿C(4)课件3.4.l Economic CriteriaAs stated before, the ROR technique is p
27、robably the most used technique in economic analysis. It is easy to understand. Since every one understands the interest rate, rate of return is equated to return on investment in terms of an interest rate that would be earned. Intuitively(直直 观观 地地 讲讲 ), when comparing two investments, one fetching
28、a higher ROR is always more attractive.In a corporate structure, to evaluate the feasibility of a project, we need to compare the ROR to the minimum rate of return (MROR). If the RORMROR, the project is selected; if the ROR MROR and RORb MROR, both alternatives satisfy the feasibility criterion.技术经济
29、学英文版演示文稿C(4)课件Intuitively, since RORa RORb, one may be inclined to select (a) over (b), but notice that the initial investment for both alternatives is not the same. One of the drawbacks of the ROR analysis is its inability(无无能能) to account for the investment amount. To properly(完完全全) account for th
30、e investment, we need to conduct incremental analysis. That is, to find out by investing additional (incremental) $450,000 in alternative (b), what incremental benefit are received? Subtracting values related to alternative (a) from alternative (b), we obtain,技术经济学英文版演示文稿C(4)课件For incremental invest
31、ment, we can calculate the ROR by Eq. 3.9 (since the investment = the salvage value),a - bInitial Investment$450,000Annual Benefit$10,000Life, Years5Salvage Value$450,000技术经济学英文版演示文稿C(4)课件This number indicates that the ROR on incremental investment is 22.2% which is greater than the MROR. In other w
32、ords, by investing an additional $450,000, we will earn a ROR of 22.2%. On the other hand, if we do not invest an additional $450,000 in alternative b, we will earn only MROR on that additional amount. Therefore, it is more attractive to invest the additional $450,000 in alternative b. That is, to s
33、elect alternative b over a.This analysis can be easily confirmed by calculating the NPV for both the alternatives at MROR.技术经济学英文版演示文稿C(4)课件For alternative a,For alternative b,ince (NPV)b (NPV)a, alternative b should be chosen. This is consistent with the answer we obtained from the incremental anal
34、ysis.技术经济学英文版演示文稿C(4)课件To generalize, if two alternatives requiring different amounts of investment need to be compared, we should carry out an incremental analysis. If RORMROR, we should select an alternative requiring a larger investment. If RORMROR, assume that the alternative is feasible and ret
35、ain it for further incremental analysis. If the RORMROR, remove the alternative from further analysis.技术经济学英文版演示文稿C(4)课件b. Take two alternatives requiring the smallest investments. Calculate the ROR on the incremental investment by subtracting the smaller investment from the larger investment. We de
36、note the ROR on incremental analysis as ROR. If RORMROR, select the alternative requiring the larger investment; if RORMROR, select the alternative requiring the smaller investment. Remove the rejected alternative from further analysis.c. Take the remaining alternative and compare it with the altern
37、ative requiring the next largest investment. Calculate the incremental ROR. If RORMROR, select the alternative requiring the larger investment; if RORMROR, select (b) over (a). Eliminate alternative (a) from further analysis.In the next step (step c), compare (b) with the remaining alternative (c).
38、For incremental analysis,(b)- (a)Initial Investment$2,000Annual Benefit$700Life, Years10Salvage Value$2,000技术经济学英文版演示文稿C(4)课件Therefore, Since ROR.c-b MROR, select (c) over (b). After eliminating (b), we are left with only alternative (c). This will be our choice.(c)- (b)Initial Investment$3,000Annua
39、l Benefit$800Life, Years10Salvage Value$3,000技术经济学英文版演示文稿C(4)课件To summarize, the economic criterion applied for the rate of return analysis for a single project: if the RORMROR, the project is selected; if the ROR0ic=0=ic0MROR, we consider the alternative to be feasible. If GRORMROR. Therefore, both
40、 alternatives are feasible alternatives. This brings us to the next step. The cash flow pro the incremental analysis, along with the cash flow pro each alternative, is reproduced below.Year0123456A030201814106B-2060406420B-A-203020-12-10-8-6技术经济学英文版演示文稿C(4)课件 技术经济学英文版演示文稿C(4)课件 Solving for GROR, GRO
41、R=21%技术经济学英文版演示文稿C(4)课件 YearB-ASTEPS12340-20-20-20-20-2013030*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技术经济学英文版演示文稿C(4)课件 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 examp
42、le, we could cover the subsequent negative cash flows with our 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 expen
43、se and should be converted to the present value in the GROR analysis.技术经济学英文版演示文稿C(4)课件 Example 3.30 An investment in a producing property results in the following cash pro to price fluctuations. If the MROR is 15%, calculate the GROR.Year01234567Cash Flow(in thousands)-3015-2015101086技术经济学英文版演示文稿C(
44、4)课件 SolutionWe have negative cash flows in year 0 and year 2. Before we consider the actual out 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
45、cash flow to -$20,000, the net cash flow in year 2, -20,000 + 17,250 = -2,750This negative cash flow cannot be covered from any previously generated revenues. Therefore, it is considered out-of-pocket expenses. The new cash flow pro presented below.Year01234567Cash Flow(in thousands)-300-2.751510108
46、6技术经济学英文版演示文稿C(4)课件 F= 15(1+.15)4+10(l+.15)3+10(l+.15)2+8(l+.15) + 6 =69.9Therefore, to calculate the GROR, F = P(l +GROR)n 69.9 = 32.l(l + GROR)7 GROR = 11.8%技术经济学英文版演示文稿C(4)课件 To summarize the GROR method, it is a modification of the rate of return method. It requires an additional knowledge of re
47、investment rate. However, if such information is known, the method eliminates the need of trial and error procedure as required for the ROR method. Further, by using the GROR method, we eliminate the possibility of multiple rates of return.技术经济学英文版演示文稿C(4)课件 3.6 Profit to Investment Ratio Profit to
48、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, 技术经济学英文版演示文稿C(4)课件 This number is an indication of the efficiency of the investment. In other words, PIR is the amount of money earned per dollar invested. As in the case of G
49、ROR 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 only be received if we initiate the project, it is critical that we try to cover the subsequent costs by prior benefits
50、 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, the PIR has to be greater than zero. The following examples illustrate the application.技术经济学英文版演示文稿C(4)课件 Example
51、 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 least 10 years with an expected salvage value of $200,000. If the MROR is 15%, should the p
52、roperty be b o u g h t ? U s e P I R a n a l y s i s .技术经济学英文版演示文稿C(4)课件 Example 3.32 The following cash flow pro expected for an investment. If the MROR is 10%, check the feasibility of the project using PIR criterion.Period0123456Cash flow-10080-100200100503080(l+0.l) = 88 -100+88 = -12技术经济学英文版演示文
53、稿C(4)课件 Total out of pocket expenses are calculated as,Since this value is greater than 0, the project is feasible.技术经济学英文版演示文稿C(4)课件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)Initi
54、al Investment$10,000$20,000Annual Benefit$3,000$7,000Life, Years55Salvage Value$8,000$3,000技术经济学英文版演示文稿C(4)课件 技术经济学英文版演示文稿C(4)课件Although PIRa PIRb , we need not select (a) unless we carry out one additional calculation. Since projects (a) and (b) require different amounts of investment, we will have
55、 to calculate the PIR for incremental investment, Since 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 been selected.技术经济学英文版演示文稿C(4)课件 a. Calculate the PIR for all the alternati
56、ves. 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 requiring a bigger investment. Reject the remaining a
57、lternative 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 step (c) until only one alternative rema
58、ins. The following example illustrates the application.技术经济学英文版演示文稿C(4)课件 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 Annual Benefit
59、$6,000$9,000$16,000Life, Years777Salvage Value$4,000$4,000$8,000技术经济学英文版演示文稿C(4)课件 技术经济学英文版演示文稿C(4)课件 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,PIR=B/C-1 技术经济学英文版演示文稿C(4)课件 Example 3.35 Informati
60、on for two mutually exclusive alternatives is given as follows.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.技术经济学英文版演示文稿C(4)课件 SolutionAlternative AAlternative B技术经济学英文版演示文稿C(4)课件We can confirm this analysis by PIR method.Alternative ANPV=PVbenefits PVcosts = 29,724 12,000=17,724 Alternative BNPV= 37,180 18,000=19,180技术经济学英文版演示文稿C(4)课件 技术经济学英文版演示文稿C(4)课件
