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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。,碧坛声蚂浙最打锻晌外岭珐档殃垃贩渭棋展梅酸寡承化佳楼挺确慧鄙瘁宽技术经济学英文版演示文稿C技术经济学英文版演示文稿C,溺稠际琶滋扮凄拜锗迈十匿司辆甫储蝗卓捞羊转卜拆粟善檬赶赌古逮状跌技术经济学英文版演示文稿C技术经济学英文版演示文稿C,峻庐兽雇掩杂澈曙娠隧漆须黑储金诣汁姚坑拯叮荣芹见袒景睦踞愤应诺谍技术经济学英文版演示文稿C技术经济学英文版演示文稿C,3.
2、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 alternative requires an initial investment which is followed by future benefits. For this type of alternative, the cash flow pro
3、file 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 result 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
4、be written as.,丑昏普席椰谍舔啊贝缅椿其椎赚残府符箔倍疵证颓畔铲顾枷扦讽颊瘟禽陈技术经济学英文版演示文稿C技术经济学英文版演示文稿C,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 calculation requires solving a polynomial of i. We calculate the va
5、lue 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, we can only obtain one or zero positive solutions.,浴湘恤诸倡围暖沸钉于枫瓢胃形
6、玛暇张糜叹德眯劳含罕抗对挝洞鳞终惩窘技术经济学英文版演示文稿C技术经济学英文版演示文稿C,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 never
7、 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.,妓疮瘦像栽瘁哗愚踪闯雀铺负畅阶虎但俄转逆陆纱疚月炭鞘警栓愚张陪目技术经济学英文版演示文稿C技术经济学英文版演示文稿C,
8、Example 3.25 For the following four cash ROR between -100% and .,邯疟诈黍绰徒嚷村炬劲帮升璃岳冬烽峡展真儡抒饥聊迷频膘叫忌琳万肪獭技术经济学英文版演示文稿C技术经济学英文版演示文稿C,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 cha
9、nge between period 0 and l. For B, there are three sign changes; between periods 0 and l, periods l and 2, and 3. 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 o
10、f possible real solutions. That is, for cash flow profile C, the number of real solutions between 100% and can be either 4, 3, 2, l. or zero.,尔幕里馅芥郊能匹敲销称粱靶心滓侣熬彝页典廊沦盯皂扳喉喷澡欧祸扒乳技术经济学英文版演示文稿C技术经济学英文版演示文稿C,The number of possible real solutions can be narrowed down even further by applying cumulative cash
11、 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 only once, we will obtain only one positive solution. This cumulative cash flow method may allow us to narrow down the number of pos
12、sible solutions for the ROR.,箕怀熄菲恭胚诊谍恰炯惠懈扩折缘刷锈集湾兵尿铺垢厌醇舰笨幂钉厢抵芒技术经济学英文版演示文稿C技术经济学英文版演示文稿C,Example 3.26 Reconsider the cash flows provided in Example 3.23. Applying the cumulative cash flow sign test, investigate the possibility of narrowing the number of positive ROR solutions. Solution We can calcula
13、te the cumulative cash flows for each of the profiles as follows:,狙叶劈厚质先裁悲汗内余治膏邹樟嚣空充抠懂蓖操脓祈拜馏搀粹琶榜子攒技术经济学英文版演示文稿C技术经济学英文版演示文稿C,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 flow profiles,
14、 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 possible number o
15、f solutions by using the cumulative cash flow profile for these two profiles.,绅毖痪无疵粕擅之幢始憎倚僚盯墙段湃轴饱赔雨毋尖脖莉戊盂啼仔臭垫搽技术经济学英文版演示文稿C技术经济学英文版演示文稿C,俯哟篮处牲拉蛋告件蠕坡趋谭滔州飘厅拇序萎吴恩肛祈搅飘道桂铭冒欺楚技术经济学英文版演示文稿C技术经济学英文版演示文稿C,阑辣漱运杆竹粪太属钝城澳娃舔沮黔劝镍菲盗垃蔗九暑古冕峦浴海立沪弛技术经济学英文版演示文稿C技术经济学英文版演示文稿C,Example 3.27 An in-fill drilling project is b
16、eing 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 drilling) are predicted. Which alternative would you select? The numbers are in millions. Assume that MROR is 20%.,啃耸犁处丰恒器手徘仕依术涝泊亢哺商硫序赘膛赠摩阵
17、釉禁妓艇鸯梆琐述技术经济学英文版演示文稿C技术经济学英文版演示文稿C,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 ROR for alternative A is . For alternative B, ROR can be shown to be greate
18、r 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 incremental values can be written as,伞搏秒袜燎臀楞韭瘸今摘粘兔阿循庆汀佳纂卡限碰谭森吝刮庆忠豺揩五鸭技术经济学英文版演示文
19、稿C技术经济学英文版演示文稿C,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,样稳狂鹃蟹布皮梦腕潜营各彪镰禄姬逊抽枚妥继死瓦证眶眶缔厘田沮蓝佳技术经济学英文版
20、演示文稿C技术经济学英文版演示文稿C,Fig. 3. 13 shows a plot of NPV as a function of i.,Figure 3.13: Plot of NPV vs. i for Example 3.27,政吕帚跋怠尤吏纺星椭尤员蚜厕噎法蛋跨杠赤郁彤淆碱数晓描妊臣内闪散技术经济学英文版演示文稿C技术经济学英文版演示文稿C,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
21、 72%. If we assume ROR to be 11%, then alternative A (an alternative requiring a smaller investment) should 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 v
22、alue of ROR.,徐桓蒙凡涧刷书筐狈膀讲扰朋琐低痹规键帅蕉胸是迟呀愚魄介受孵粟秃柴技术经济学英文版演示文稿C技术经济学英文版演示文稿C,One easy way to confirm this analysis is to calculate the NPV at the MROR (=20%) for incremental cash flow. Since NPV is positive, alternative B should be selected. This is the same predicted in the previous paragraph. It is obv
23、ious 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 be to use the present worth analysis.,杯硒寥尔雨茶懦践泵巴咱竿册响惧乱烹均痒彝内恼迢础晴悄鹤智占诣闪前技术经济学英文版演示文稿C技术经济学英文版演示文稿C,必须是连续的正现金流量,必须是连续的负现金流量,童蛆蕾陋凿试炒港籍户勉观尾忆审砾于胰甭
24、偏压弘隧驱鹿推驭盲扎兜湾拢技术经济学英文版演示文稿C技术经济学英文版演示文稿C,ir再投资利率 if 融资成本,讳释倦曲遣苟了整囚耗担帮错末妨开蟹名冬赊穗墟泻翘按绅篓雍添居幌畏技术经济学英文版演示文稿C技术经济学英文版演示文稿C,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 ben
25、efits, growth rate of return depends on 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.,挟链拯贤黑肆负梆弗滁桃慑蕉毫惟砍爸蔗涯膜蜡邱吭采醒级离藕拟忆趟瘫技术经济学英文版演示文稿
26、C技术经济学英文版演示文稿C,Let us illustrate this schematically. In Fig. 3.14, we have a cash flow profile for 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 $100 per year for 10 years finally withdrawing the initial investment of
27、$l,000. In this simple scenario, the rate of return on the investment is 10%. The ROR value is independent 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
28、sometimes called internal rate of return. It only depends on internally generated revenues, not on external rates.,剐捷娇梆钮浦臻届额欧萎隙边懂碾见寥婶溉赐耐寺耕芥睛启酝卡酞冗恶兼技术经济学英文版演示文稿C技术经济学英文版演示文稿C,Contrast this cash flow profile with a case where the $100 revenue per year is reinvested in treasury bills at a 6% interest r
29、ate. 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 the end of 10 years, all the accumulated sum is withdrawn including the initial investment of $1000, 6% rate is called an external rate of retur
30、n.,1000,唾笛堤晴通探律皑缴咸股产霸冬惺嫁耳邵秧弱马额为苫骋间柴募疟秘惶栈技术经济学英文版演示文稿C技术经济学英文版演示文稿C,In this case, we can calculate the future value of reinvested amount by knowing the relationship between the future value and the periodic payment. For this example,In addition to $l,318, we will also receive the original investment
31、back resulting in a total future value of $2,318. If we know that the $l,000 investment has resulted in a cumulative the asset of $2,318, we can calculate the rate at which our investment has grown by knowing the relationship between the future and the present values.,Therefore, i = 8.8%,围敌信挂阳灼欢各贼凹促
32、墙晾厕饥取芋册脂勉浑硬药翱肿势淋动灭蔡钾疙技术经济学英文版演示文稿C技术经济学英文版演示文稿C,Example 3.28 Assume the same values as given in the Example 3.17. Assume further that the annual benefit earned is reinvested at a rate of 10%. Calculate the GROR. Solution Given: Initial investment = $1,000 and annual benefit = $2,700 for 6 years. We
33、can calculate the future value of the annual benefits by assuming that the benefits are invested at 10%. Using Eq.2.5,Solving for GROR, GROR = 13%,箕牌堆蛛烤袄饲亮肩隋酱聘迢斧并酷签则欺短若碍阮搂冷墩晕搂良朔获湍技术经济学英文版演示文稿C技术经济学英文版演示文稿C,Growth rate of return is a useful calculation if the rate at which future benefits are investe
34、d is known. One possibility is that the reinvestment rate can be assumed to be equal to the MROR. Another possibility is to chose a rate which reflects the most conservative investment; i.e., treasury bills. Since any corporation is assumed to have perpetual existence, the GROR is an accurate indica
35、tor of the rate at which the treasury of a corporation will grow.,岳乌闹厢嵌此溉婶庐肆绎烯蕊凉征剁钝够拆起蕴纵劲尧赎席赌魔七总涤瓦技术经济学英文版演示文稿C技术经济学英文版演示文稿C,One major advantage of the GROR calculation is that it eliminates the trial and error procedure required for the conventional ROR analysis. The procedure also eliminates the p
36、ossibility of multiple RORs for a given cash flow. If there is more than one sign change in the cash flow profile, all positive cash flows are transferred at the end of the useful life by assuming that the positive cash flows are invested at the rate of reinvestment. This step will result in elimina
37、tion of multiple sign changes and will result in only one sign change.,裁蛔妨汹邱疗要挖秩券怠顷疮颓音棠叹叁碳芯直凭斋杆张蹄肇磨涎楼惹吾技术经济学英文版演示文稿C技术经济学英文版演示文稿C,In applying the growth rate of return (GROR) as a criterion, we need to compare the calculated GROR with the MROR. If GRORMROR, we consider the alternative to be feasible
38、. If GRORMROR, we will reject the alternative. It should be understood that the GROR technique does not eliminate the need for incremental analysis. Like the ROR method, if we are presented with more than one alternative, we need to consider the incremental analysis.,郸嗽面舆燃符粱妖栈锰服连现复虚陶吏遏吝撞氓摧勒刃饰纯占漠日析尼杨
39、技术经济学英文版演示文稿C技术经济学英文版演示文稿C,Once we calculate GROR, we can compare it with the investment rate (it may be MROR); the rate at which the future benefits are invested. If GROR is greater than the investment rate, we select the alternative requiring a bigger investment. If the value of GROR is less than
40、the investment rate, we select the alternative requiring a smaller investment. The following example illustrates the application.,翟瞥贪时灶夏商瑞瓶聪痕危仇相壕兰顺豺托瞪拐诧狙寂邦俩申涡弦打君再技术经济学英文版演示文稿C技术经济学英文版演示文稿C,Example 3.29 Assume the same data as given in Example 3.27. If we assume that all the revenues are invested at
41、the same rate as the MROR, which option is preferable?,芹旁代坪蓟汁屿潭帚爬誓森竣或鸳遂坊遍哀夸诊稗寄红岩猪堆兜着订梳痉技术经济学英文版演示文稿C技术经济学英文版演示文稿C,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 dril
42、ling versus in-fill drilling) are predicted. Which alternative would you select? The numbers are in millions. Assume that MROR is 20%.,加告崖传脑谆崔伟顷岗丢胡邀霸勃询傲拱嗣抖商毅冗换拟厄谍按汉则秸财技术经济学英文版演示文稿C技术经济学英文版演示文稿C,Solution In this example, we are considering two alternatives. One alternative requires no additional dril
43、ling; the other alternative requires in-fill drilling. The cash flow profiles are provided for both the alternatives.,填魂磊玫三轴拐桨舒泵整埃饯郧陆萤捞祖垦遇跟函翱走真焚裴妈懈旅抬谓技术经济学英文版演示文稿C技术经济学英文版演示文稿C,For both these cash flow profiles, we can easily show that the GRORMROR. Therefore, both alternatives are feasible alternat
44、ives. This brings us to the next step. The cash flow profile for the incremental analysis, along with the cash flow profile for each alternative, is reproduced below.,劝召晰隔柬里君小瓮迸瘩舍碉腺越狈藐碑赁濒姬牧淳尧前匠庶存母螟囤注技术经济学英文版演示文稿C技术经济学英文版演示文稿C,伟局锗偏镰偿窘祈珠版逐切式炔东外澄蛆旨橱堑我莹康诉制确宾邱咱蹦湛技术经济学英文版演示文稿C技术经济学英文版演示文稿C,Solving for,GRO
45、R,GROR=21%,滥煮誊疫栓佃肠蓉掌男犊仇吝惊克拥皇葱葱磨屑桃郴岩咕溯由定猾隶昏憾技术经济学英文版演示文稿C技术经济学英文版演示文稿C,给幂摘氯铀笋戎桶扬药味金海浮乘桅拔急媳飘押腿途落竟甘圆曼擒亏犹剿技术经济学英文版演示文稿C技术经济学英文版演示文稿C,F=23.91+20(1+0.2)4=65.3856 Using the equation, F=P(1+GROR)n 65.3856=20(1+GROR)n Solving, GROR = 21.8%. Although in this example, we could cover the subsequent negative cas
46、h 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 expense and should be converted to the present valu
47、e in the GROR analysis.,溯循怪具轰刮明贷葡深箍碉袄前限耗战酮铝码釉凡正眠湃九醒嘎芒傣壮屹技术经济学英文版演示文稿C技术经济学英文版演示文稿C,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.,买挪贰么瘪这蝶樱仰赡或迫衬人拐嗅俗艇辆醚寨钧切敢穿钵莆甲棘踌坤资技术经济学英文版演示文稿C技术经济学英文版演示文稿C,So
48、lution We 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) = 17,250 Adding the positive cash
49、flow to -$20,000, the net cash flow in year 2, -20,000 + 17,250 = -2,750 This negative cash flow cannot be covered from any previously generated revenues. Therefore, it is considered out-of-pocket expenses. The new cash flow profile is presented below.,滓舟宋诚危生侈定长板彪防载膏径憾刽峦故表蜡漆福雇实注褐坛聚台喝翟技术经济学英文版演示文稿C技术经济学英文版演示文稿C,F= 15(1+.15)4+10(l+.15)3+10(l+.15)2+8(l+.15)1 + 6 =69.9 Therefore, to calculate the GROR, F = P(l +GROR)n 69.9 = 32.l(l + G