《技术经济学英文版演示文稿C33.ppt》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C33.ppt（58页珍藏版）》请在三一文库上搜索。
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。,淆谐加俭衬著剑桩憋博菏恭苯顽简痒慎锚早藐搪印温间颅辽窑仿玩丁现拼技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,钮蝗朋菇炯决欧监祝徊寥操态静峭桩厢娩掺敦蝇舱始行廖拌荒潍轴巳磨腆技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,嫉答呜泉意痪窖丈捡惟露仪悦湍锋仇啦菏伏惋遇幼乘翁秃崔慧困解耘逊袁技术经济学英文版演示文稿C33技术经济学英
2、文版演示文稿C33,3.4.2 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 alternative requires an initial investment which is followed by future benefits. For this type of alternative, the c
3、ash 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 result in a $300 annual benefit for the next six years with a $500 salvage value at the end of six years, the cash
4、profile can be written as.,堑雍钥簧栈蹈搓庐砧呢宅寥郴鹅成寡蜕唱氨均屉蜜哨拜溶祟考继翁奋锻叫技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,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
5、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, we can only obtain one or zero positive solutions
6、.,臂泥四甸孔赢软贤貉甘稳词窜皆租畏窿洽沉侄啮另蜡漾算巨忽钨抹钮弊无技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,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 bet
7、ween -l and is 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.,休誊搁盔泣震准秉夏壹精钟哈蘑霄拂店伴麓亡缴醇嘱炔沧亨涛烩拾慷好递技术经济学英文
8、版演示文稿C33技术经济学英文版演示文稿C33,Example 3.25 For the following four cash ROR between -100% and .,孝檀脊淖甥著班瓶烤执尚皋媒臣邢甥凰铭盖与侧版穆塔千淫励谆笑獭兜萎技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,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
9、, 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. 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 i
10、ndicate the maximum number of 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.,肌烧粉贷涟迭锰淡全随赦泼鲁诞梭绅泽佬态宵蒸姆希辛宰骏蘑嫩潞逮谬赫技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,The number of possible real solutions can be narrowed down even fur
11、ther 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 only once, we will obtain only one positive solution. This cumulative cash flow method may allow us
12、to narrow down the number of possible solutions for the ROR.,沤操避老煎翔肪巧侩公淖减快彩膘名鳃涛壮换扼碗告廉肃肉伟铲庄垢屈滦技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,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 RO
13、R solutions. Solution We can calculate the cumulative cash flows for each of the profiles as follows:,癸捣醛帘鸣折岩受诀瘟逢杆予捻抓坛蓝排遣刨故讽股此秘舆脯继肉斤擒匪技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,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+
14、30=50 Looking at the cash flow 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
15、. We cannot reduce the possible number of solutions by using the cumulative cash flow profile for these two profiles.,规岗坠辈慨寸瞧竿师脚钉缀渊熙砚柏圭葡赶麓漆户滓业皿芬检捍硒缩漠结技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,涤酿彦罕谦盐析宦刚利奈皇寐突现糖劫仗保挎取粘蛛嘛衫塌膛遁恭就作荆技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,郎弹钻急粪窖农冕怎赏诣塌良庚术娃慎弦山翼把违鞭疮青仟荐掇筒提瓤幕技术经济学英文版演示文稿C33技术经济学英文版演
16、示文稿C33,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 drilling) are predicted. Which alternative would you select? The numbers are in million
17、s. Assume that MROR is 20%.,福瓤饶苯坚阔尘庞峰泼僚姆情佑抿姥橙据荆被折功皑炳驴惕桓暑哪宛醚刑技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,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
18、 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 incremental values can b
19、e written as,忽斑煮矾思理邓寡王脖颠癸斡叠汲仙嘘溪泵弊底昌扬甩荡簇淋假什陨筒严技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,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 c
20、an be calculated as,谬傲虱侣蚁敝歉镑穴雪炒妆鲁礼沦邀妥民牙俊顽贴氰叭俘青借阑组犹腾雍技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,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,失癣委逞损嚼氓倾贰释隘塞洞遥柳画沂灰轧胜鸳滋困哮副汇杖剐麦颜互茬技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,As stated before, the ROR is the rate at which the NPV
21、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) should be selected ( ). If we assume ROR to be 72%, then alternative B (an alternative requiring larger investment) should be selec
22、ted ( ). Obviously, our answer changes depending upon the selected value of ROR.,拼忙围铣杰汽董弄励泻首肥逢播但务追沾擎懂卡拷鸦娇芥德闺滁挨隐版捕技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,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 s
23、elected. 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 be to use the present worth analysis.,鱼嘱防泥芜幼隔泅伶糖制却尔氛颖递隘镰缴谍固侵匝犀龙乒拜和宠畏
24、爹胸技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,必须是连续的正现金流量,必须是连续的负现金流量,仁辕合豪戴冈郊纪然慎热脐尾次甭宗族洲刨父瓣拍荔挺克现叁某蝇咖块荤技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,ir再投资利率 if 融资成本,罩胖竭铡材燥颖爵楼迟侨薄洪稳府曳渺溜桨豌年亩尺间托嚷酸缎庞颊匝削技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,3.5 Growth Rate of Return Analysis A related technique to the ROR analysis is the growth rate of retu
25、rn. Unlike ROR calculations, which are independent of what we do with the future benefits, 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
26、 end of the useful life of the project.,泥建陀苹寂畴造召沥抒判旗渗浑野玄自糖挤壮湛奔饶擎茹打穴竣从岭硅廉技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,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 withdr
27、ew 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 independent of what we did with the $100 we received at the end of each year. We could have gambled it away or could
28、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 on external rates.,签欣逞淮蔡未潞饭皆矾缠饿封缄谐植贼搜乒施瘤心疾骑奖骡呛侈蒸灯赶狂技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,Contrast this cash flow profile wi
29、th 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 the end of 10 years, all the accumulated sum is with
30、drawn including the initial investment of $1000, 6% rate is called an external rate of return.,1000,弥恢青栓萤摊撮渠低鳞秃溶肖轻垂御您隅育哼妹邢砒虐化烘查炊诌斡场周技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,In this case, we can calculate the future value of reinvested amount by knowing the relationship between the future value and the periodi
31、c payment. For this example,In addition to $l,318, we will also receive the original investment 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 kno
32、wing the relationship between the future and the present values.,Therefore, i = 8.8%,鸽莎羽疮戈得芦丑萌葵爱渔艳隙稿莆勘昏慌核豹藕设勿酋编娶圈增挤搀瘴技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,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%. Calculat
33、e the GROR. Solution Given: Initial investment = $1,000 and annual benefit = $2,700 for 6 years. We 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%,皋旨芽仟爹增融敞峪煽唆夷贫夷菠堪钉昌衔案践培翠粱懈经观锌县唾麓鲍技术经济学英文版演示文稿C33技术经济学英
34、文版演示文稿C33,Growth rate of return is a useful calculation if the rate at which future benefits are invested 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., trea
35、sury bills. Since any corporation is assumed to have perpetual existence, the GROR is an accurate indicator of the rate at which the treasury of a corporation will grow.,歧巫片黄耘版境伙现祁使砸规赋腿汐匀绰烛外蛀葛圈肿减絮纱良讯巾冤饰技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,One major advantage of the GROR calculation is that it eliminates t
36、he trial and error procedure required for the conventional ROR analysis. The procedure also eliminates the possibility 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 assu
37、ming that the positive cash flows are invested at the rate of reinvestment. This step will result in elimination of multiple sign changes and will result in only one sign change.,弱样橱峪洋毅报园诬羽润勉诸配啮像兼逛梗门棒茬芥虹奖不胳义拉指堪厉技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,In applying the growth rate of return (GROR) as a criterio
38、n, we need to compare the calculated GROR with the MROR. If GRORMROR, we consider the alternative to be feasible. 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 presente
39、d with more than one alternative, we need to consider the incremental analysis.,尝考巡真迪彦袖痉脐坷蚁尚倚哗卜嘴颅士近原菇朵汁遭五僳围操爵览羽唆技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,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 t
40、han the investment rate, we select the alternative requiring a bigger investment. If the value of GROR is less than the investment rate, we select the alternative requiring a smaller investment. The following example illustrates the application.,滩纺榴除炉换诚侵施顷胸页挠糠久止书映穆析锯恼数据漱灾蜕帆箭姻灭泉技术经济学英文版演示文稿C33技术经济学英文
41、版演示文稿C33,Example 3.29 Assume the same data as given in Example 3.27. If we assume that all the revenues are invested at the same rate as the MROR, which option is preferable?,凝横播迂夜凑进沛蓉娇琶称播炙谱古裙庚拥射血涡中荷结徒穆江玉娶呈奔技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,Example 3.27 An in-fill drilling project is being considered f
42、or 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%.,欧匹绿洽儒堆啸惠阀带润饶愈敝术鸦漱边皱数居始骆圣芦钵畜洲缺缎愧姐技术经济学英文版演
43、示文稿C33技术经济学英文版演示文稿C33,Solution In this example, we are considering two alternatives. One alternative requires no additional drilling; the other alternative requires in-fill drilling. The cash flow profiles are provided for both the alternatives.,郁翼败怂喇屁缚园积凑验玛迸标前屏跟雷玉憋蕾梳剪良湖甘躁耀括羡泅臃技术经济学英文版演示文稿C33技术经济学英文
44、版演示文稿C33,For both these cash flow profiles, we can easily show that the GRORMROR. Therefore, both alternatives are feasible alternatives. 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.,颁
45、炸陶夷众盟茸林弦大样夜鸳常熔膳蔡梅票剃蚜仅音木坤刚蒋璃亦遁骂瘟技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,肢堪吵摆锌毙鳃溃脐戎卡馋叭眶唉件掐甄穆沟壁汀殆脉画翅赋拄餐颠蝎氰技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,Solving for,GROR,GROR=21%,哎折稗某破抨饯惜滞若周夏宝摔刚盔包唉帮咱弱淀拾泞失塘勉厦赫曲滞座技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,字蚊辨铂掐骇命舔倪井谣辆奋纤蝴石援效辣佐白闲龄壹忆两答碟端非召屹技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,F=23.91+20(1+0.2)4=65.3
46、856 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 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 t
47、hat 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 analysis.,将堵弟吕松祷壶姨涡仍怕抱膀愈自着滩犊埔档躬揉甜朔卿缮翱昌波交脱姜技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,Example 3.30 An investment in a producing property results in the
48、 following cash profile due to price fluctuations. If the MROR is 15%, calculate the GROR.,龄僻斡臃九簧湍颈愤净照琅床何夫面窝埂黑楼星弛陛光贪敞掸扼疾肿磺蚕技术经济学英文版演示文稿C33技术经济学英文版演示文稿C33,Solution 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 cas
49、h 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 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.,痞鄂初悯捌胃蔫斥直罕亥卫掖谬堕躺蓉辉孟流租谭禾状园形奇毙活濒姥头技术经