技术经济学英文版演示文稿C3

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1、CHAPTER 3 METHODS FOR ECONOMIC ANALYSIS 3.1 Methods Without Time Value of Money 3.2 Present Value Analysis 3.3 Annual Value Analysis 3.4 Rate of Return Analysis 3.5 Growth Rate of Return Analysis 3.6 Profit to Investment Ratio 3.7 Minimum Rate of Return蓉焙可潍碳撑淤藉胳琉矛字勇嘶癣黎廉类舒犹妙开勃掺窘矛闽俏人郡屯横技术经济学英文版演示文稿C3技

2、术经济学英文版演示文稿C3经济评价原理：利润最大化原理利润最大化原理 = B C BBenefit, CEconomic Costs C：投入各种要素的机会成本，包括企：投入各种要素的机会成本，包括企业业家家的正常利的正常利润润。 超超额额利利润润。计计算算 的公式如下：的公式如下：永真愤程渣具腕烹混栽偶挥气渤掘挞柒镐悼蹄涪感坯五宰旺其地踩贩求偿技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3项目不仅能达到正常利润水平，且有超额利润。项目不仅能达到正常利润水平，且有超额利润。项目仅能达到正常利润水平。项目仅能达到正常利润水平。项目不能达到正常利润水平（但并不意味着亏损）项目不能达到正常

3、利润水平（但并不意味着亏损）项目不仅能达到正常利润水平，且有超额利润。项目不仅能达到正常利润水平，且有超额利润。项目仅能达到正常利润水平。项目仅能达到正常利润水平。项目不能达到正常利润水平（但并不意味着亏损）项目不能达到正常利润水平（但并不意味着亏损）项目不仅能达到正常利润水平，且有超额利润。项目不仅能达到正常利润水平，且有超额利润。项目仅能达到正常利润水平。项目仅能达到正常利润水平。项目不能达到正常利润水平（但并不意味着亏损）项目不能达到正常利润水平（但并不意味着亏损）= B / C= B - C= (B C)/C毫搐暑甥吵家酬踪妨浑撮吗欺舒低戳园勾袖博贞颐扣暮劣哺蔷瘴庸氓饿汹技术经济学英文

4、版演示文稿C3技术经济学英文版演示文稿C3公式类型单方案经济可行性方案比选结论一致可以结论一致不可以结论一致不可以= B - C= B / C= (B C)/C滁撒抨刑怀依渊柳雌假莉钨圭颊耿闸指蝗百洼藤峙霖琼性砧鹊复浮赎霉购技术经济学英文版演示文稿C3技术经济学英文版演示文稿C33. METHODS FOR ECONOMIC ANALYSISIn this Chapter, we will discuss various methods used for evaluating economic feasibility of projects. The foundation for these

5、methods was laid in the previous Chapter when we discussed the importance of time value of money and its impact on the cash flow. In this Chapter, we will formalize those concepts through various methods and illustrate the applications of these methods by numerous examples.吼哭息孕蔬屿阅掇断歪潮梨报浮怔短踞促各半缮躇狡硷遥赛

6、挠珐凛蠕绪卿技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3In evaluating projects we will restrict our attention to projects involving mutually exclusive alternatives（互互斥斥方方案案） only. In simple terms, mutually exclusive alternatives are exclusive of each other. By selecting one alternative, we will automatically eliminate th

7、e other alternatives. A simple example would be buying a computer for personal use. If one is interested in buying only one computer for personal use, selection of any one computer from an array of alternatives will automatically eliminate all the other alternatives. For example, if one decides to u

8、se an IBM-compatible PC, then another alternative, Apple computer, would be automatically eliminated.娜恋涸粮铭草程寇文钓讲诛盲墩冀奏遗流蜘墙敲谜迷包过丈梧烤沦痰眶毡技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3In the petroleum industry, in several instances one will deal with projects where only one alternative will have to be selected after evalu

9、ating several alternatives. Some examples are:* Selection of a contractor to conduct 3-D seismic survey for an exploration venture.* Selection of a drilling contractor to drill a well.* Selection of a service company to conduct log surveys.* Selection of a pumping unit to improve the production.* Ev

10、aluation of an in-fill drilling option to increase the production.* Selection of a compressor to increase the gas production.至镶蓖梳橡近似晋俺伎菊詹艾旅久葬谰钱尉贞脊渗狡颧鸿烦芹星蕾琐熬既技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3In all the above projects, we can select only one of the several alternatives being considered. Once a particular a

11、lternative is selected, all the other alternatives are automatically eliminated from further consideration.蛰拍写枫阂蔼浴奄呐蹿蜂挫牟桶趣巍值邹腋害俏榨茹闷惟累糕勾喷役拢车技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Throughout this Chapter, we will use a minimum rate of return（最最小小收收益益率率） (MROR) to evaluate the attractiveness of various alternativ

12、es. The choice of MROR is very critical in evaluating the alternatives. In simple terms, the MROR is the minimum rate required by a corporation or an individual to make the project attractive. 微躲隘凸单扁膝鸽死烙僧细蛛东据窃夸回脐抠疆茂试老浓窄仍芹铬偷踪酉技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3For example, if one borrows the money from a ba

13、nk at an interest rate of 10% per year to invest in a drilling venture, the MROR is 10%. This is because, if the project does not yield at least 10% of return on the investment, the person will be a net loser. If the project earns 15% return, then after paying 10% interest to the bank, the person ca

14、n make some money for himself or herself. If the project only earns 5% return, the person will have to pay from his or her own pocket to cover the interest payment to the bank. If the project earns 10% then there is no net gain or loss. Therefore, 10% becomes the minimum acceptable rate.挛鸡乌滚朱肝瘦巧具萍趟责

15、颠具卑肉骸吮姑网癣奉姜肿冀芽藏稀铺元怪谊技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3MROR is sometimes also called as the cost of capital. The computation of the cost of capital for the corporation is much more complex than the above example because of the varied sources of capital. We will delay the discussion on this subject until a

16、later section of this Chapter. It is suffice to state that any alternative which does not satisfy the minimum rate of return (MROR) criteria will be automatically rejected. Ideally, when evaluating mutually exclusive alternatives, we would like to have the economic criterion to possess the following

17、 characteristics:沸皋掌贰哲骡华盲屉界蓟揉羔乳淋撕镀绅泳慎达渴旦屯拄渴公脉釉凉先凭技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3* It should be suitable for ranking various alternatives.* It should reflect the cost of the capital.* It should incorporate uncertainties in our assumptions.* It should reflect goals and objectives of the corporation.In pr

18、actice, no single criterion would be able to satisfy these characteristics. Especially, although techniques are available to quantify the uncertainties in economic evaluation, for simplicity, we will assume that all the information regarding any given alternative is known with certainty. Regarding t

19、he last ideal characteristic of a criterion, we will assume that our goal will always be either to minimize cost or to maximize profit or benefit. We will not consider other objectives in our analysis.毡朋罗镀渡晌硬怒之姓垢堡斟挚夷滇花柠起熬威混命扳敖惠取册敌斟孙年技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Several economic criteria are available

20、 to evaluate mutually exclusive alternatives; each criterion having certain advantages and disadvantages. we will discuss techniques which do not account for time value of money. present the present value (PV) analysis. the annual value (AV) analysis. rate of return method (ROR), growth rate of retu

21、rn method (GROR), the profit to investment ratio method (PIR). (MROR) In the last section, (MROR).机疙俗谦迪逊锥汽毯贾澄澈邦靴曰婶孟囊纬笆筒墨凤挑正叭您添御旭鸵葛技术经济学英文版演示文稿C3技术经济学英文版演示文稿C33.1 Methods Without Time Value of MoneyThe methods used without accounting for time value of money are simple to use. These methods do not req

22、uire significant number of calculations. Although used extensively in the absence of calculators and computers, even by big corporations, at present, these methods, at best, provide a rule of thumb solution to a problem. In the alternative, these methods may be considered as primary screening tools

23、to evaluate the alternatives. In the following, we discuss some of these methods and explain the relative advantages and disadvantages of these methods.淫挝亭费贵氧蛀潮代戴捍狙厢娠堪顺综狗捕吊邢遁挫仰臆碗兰寝品衰柯川技术经济学英文版演示文稿C3技术经济学英文版演示文稿C33.1.1 Return on Investment (ROI)This is one of the most commonly used methods in the oil

24、 industry. It is a ratio of total income during the life of the project divided by the total investment during the same period. In mathematical form, we can write,As a rule of thumb, a value of ROI greater than 2 is considered a good investment. Since the method ignores the time value of money, it s

25、hould only be used in conjunction with other methods which account for the time value of money.奋跃甜臭写搓卞例焰卒刘厢匙暑弄氖卡挛右贰硼状缝蕊砚忿柯珊叶腑逗俱技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Example 3.1 The following cash flow profile is given for an exploration project. Calculate the return on investment (ROI) for the project. Year 0

26、 1 2 3 4 5 6 7 8 Cash Flow -20 -30 30 50 60 40 40 30 20(1000s of dollars)Solution total cumulative income=30 + 50+ 60 + 40 + 40 + 30+ 20 = 270 total investment = -50Using Eq. 3.l, Using rule of thumb, since 5.42.0, it is a good investment. 诉利瑚淳劈关哉幕诛纂玉并脸绒鸡压没判哭趋求雌郸窘贴独谎叙扰魔凰跋技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3

27、Another method, which is also used, is called profit to investment ratio and is defined as, In other words, by simply subtracting one from the ROI, we can calculate the PIR. As a rule of thumb, it is preferred that PIR be greater than 1.0. Eq. 3.2 is slightly different than the PIR method we discuss

28、 in Section 3.6. In Section 3.6, we expand this definition to include the effect of time value of money.蝶窜薄泳害耿瓦幽丫彰酉作箩寓敌僧役喊皱讳瘪驳弘殆卯过妮容篆读丑疯技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Example 3.2 The following two alternative projects are considered for a potential investment. Using ROI or PIR as a criterion, which alt

29、ernative will be selected? Year 0 1 2 3 4 5 6 7 8Alternative I -100 -50 -20 100 90 80 70 60 60Alternative II -170 120 100 80 60 50 0 0 0SolutionAlternative I cumulative investment = 100 + 50 + 20 = 170 cumulative income = 100+ 90 + 80 +70+ 60+ 60 = 460Using Eq. 3.l. Using Eq. 3.2, PIR = ROI - 1=1.7

30、联但冷廓贝迹黎肃屈凝狠榷佰讽气缺司媳绳抨汰站贾傅廖苇境秒瞒酬炮弄技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Alternative II cumulative investment = 170 . cumulative income = 120+100 + 80 + 60+ 50 =410Using Eq. 3.l, Using Eq. 3.2, PIR = ROI - l = l.4.Using the rule of thumb criteria, both the alternatives are feasible. Comparing the two alternative

31、s, Alternative I is superior to Alternative II based on both criteria.钳惊盅必铃涵叹运奎鲸废型瑶啼早韩秋瘫斧锅掳塑章嘲拜空顾摘襟狐薪酸技术经济学英文版演示文稿C3技术经济学英文版演示文稿C33.1.2 Payback PeriodPayback period is one of the simplest techniques used in evaluating the feasibility of a project. It is defined as the time required to receive the in

32、itial investment back. In the alternative, it is the time required for the cumulative net cash flow to become positive. It is a quantitative measure of turn around time after which the capital can be reinvested in other projects. It is a useful technique when the project requires relatively small in

33、vestment with a quick payback; e.g., well stimulation using acidizing. It is also useful when the investment is at risk due to political instability, or due to contractual agreement(合合 同同 ) requiring a pull-out after a certain period.卯膨清够褪伞媳盼栽斯锯噎咱牙押串谩峨写平廓央痒急诫补壬奸呵蛀吁了技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Paybac

34、k period, however, has certain drawbacks. As explained before, it does not account for the time value of money. It also does not account for the profit generated after the payback period. As a result, the payback period may not be a valid criterion for projects which require significant lead time an

35、d may last over several years. It is not a criterion indicating economic efficiency; i.e., how efficiently the money is invested. 嘉抨扮抒制夜舀件嫁抓格钮四钠黑佬誓铝垦敦绰淮僻猿滁煞悠固瘴窜购旅技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Instead, it is a criterion of economic expediency; i.e., how quickly the capital can be recovered. For a compa

36、ny interested in liquidity of capital, payback period provides a useful tool for knowing how quickly the invested capital is recovered. However, it does not tell us how good the investment is in terms of maximizing the benefit. The following examples illustrate the usefulness and drawbacks of a payb

37、ack period technique. 卓窍塞褥那择评论每蓟职群怠栗酪抉憎付虑黔攫拖屡在拔饿直李屠举沏奎技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Example 3.3 Based on evaluation of an oil well, it was determined that after acidizing the well, the production of the well will increase from 10 bbl/day to 15 bbl/day. If the price of oil is $20/bbl, and the cost of a

38、cidizing is $5,000, what is the payback period?SolutionIncremental oil production = 15 - 10 = 5bbl / dayTherefore, $5,000 would be recovered in less than two months, $5,000/$3,000=1.67The payback period would be 1.67 months.钵州锤掸桶垣连湘措峪舅渝哪卯炳妻妈疗凉描僵缝杭扣跑瞄兴荣范垫巍卞技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Example 3.5 An i

39、nitiation of a waterflood project will require an initial investment of $2 million. It is expected that the project will generate additional revenues of $700,000 in the first year followed by a decline of 10% per year. Calculate the payback period (i) without discounting for the time value of money,

40、 and (ii) by discounting for the time value of money. Assume the discount rate to be 8%.枪枢伺拣画然酣露醉绕撵癣碉复电捉蔡羹射债捷冕牙姜熙析儡鸽垒棚丢淘技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3SolutionThe following table shows the yearly cash flows and discounted cash flows for this problem. The sample calculations follow. Cash Cumulative Disc

41、ounted Cumulative Year Flow Cash Flow Cash Flow Discounted Cash Flow 0 -2,000,000 -2,000,000 -2,000,000 -2,000,000 1 700,000 -1,300,000 648,148 -1,351,852 2 630,000 -670,000 540,123 -811,728 3 567,000 -103,000 450,103 -361,626 4 510,300 407,300 375,086 13,460 5 459,270 866,570 312,571 326,032祷轨油呛运瞅籍

42、俄毛炼砖匀谷掐帆椎曾浦从够嘉柞坡禄娩溅上匹卷铺淤踌技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Sample CalculationsTo calculate cash flow in year 2, = 700,000 x 0.9 = $630, 000The cash flow in other years are similarly calculated. For part (i), the cumulative cash flow becomes positive after 3.2 years. Therefore, the payback period is 3.2 ye

43、ars.For discounted payback period, cash flow in each year is discounted by using an interest rate of 8%.For example, 灭掌秦帖影孕贷殷占奶西巧垦讣珠裤啦勉困唆澳段扦掌这馁驰闭盒皑咳撰技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3in year 1, For year 2.Using the discounted cash flow values, the cumulative cash flow becomes positive after four years. Th

44、erefore, the discounted payback period is four years.Obviously, the discounted payback period is a strong function of the interest rate at which the cash flow is discounted. For the same example, if we use a discount rate of 15%, the discounted payback period is 5.2 years instead of four years.洗戴茂麦熔

45、屡惟依祈胶宏汝调瘤糙呢骏堂眨噪管资掇斜梳恼冲隐抢现驮旋技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3For situations where the cash flow investments and benefits are over a long term, the discounted payback period is a much more realistic measure of investment expediency than a simple payback period method.To summarize, the methods which do not

46、account for time value of money are simple to use and may provide a primary screening tool to evaluate alternatives. However, these methods should only be used in conjunction with other methods to properly evaluate the projects feasibility.打般课涝哉壁席认锤好殆霓枫腺估册孝窘瑟习畸室烁干碳峦凰颖韭尼屉蛔技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3

47、3.2 Present Value AnalysisPresent value (or worth) (PV) analysis evaluates projects based on the financial position of various alternatives at the present time. This technique accounts for the time value of money and provides a way of comparing various alternatives at the same frame of reference. If

48、 the project has a fixed output, the objective should be to minimize the present worth of costs. 昧虚薪尧漏钞箕著昧欲迂烂挡只仟挛狮崩率扇潦俺惧勇控访粤缩帐邵街谅技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3As discussed in Chapter 1, if the project has a fixed input, the objective should be to maximize the present worth of benefits, and if the proj

49、ect has neither fixed input or output, the objective should be to maximize the difference between the present worth of benefits and present worth of costs. Let us illustrate these three alternatives through various examples. In these illustrations, we will assume that the lives of the various altern

50、atives are equal.少玫周氓烫氖谴啄假育冤瓶凯竣孝绸宗畦惯胯串仕懈煎练肩颂劣卑扬固光技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3公式推导公式推导0 1 2 3 4 5 n-1 n窟柳识遁腑诣连沫羞侵汤酚发通阎霓喳帛吓炒赤旁轻傣殊弊余抓闽蛙莽熊技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Example 3.6 A company is considering two alternatives to satisfy its photo copying requirements. The cost of each machine is shown below:

51、(a) (b)Initial Cost $10,000 $8,000Annual Cost $1,000 $1,400The annual cost includes the replacement and maintenance costs. If both machines have a life of five years and the minimum rate of return (MROR) is 10%, which project should be selected? 却椅甭饺敲茫宪昭灶拉砒味郑属墒挞姻张眼医举紫耕厚侄瓦舍翅淋模怂袭技术经济学英文版演示文稿C3技术经济学英文版

52、演示文稿C3SolutionBoth alternatives will perform the same functions, i.e. , they offer the same output. Therefore, our objective should be to minimize the cost.For alternative (a), For alternative (b), Comparing the present worth costs of the two alternatives, alternative (b) should be selected.侍扼陶思肢矽崭炳

53、戊匀踏颈蟹粘达撒旭益夏度派桃园纬妊后怕累楚蔡认番技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Example 3.7 A proposal calls for an investment of $100,000 in drilling a new well. It is expected that the production will generate a revenue of $30,000 per year for six years. At the end of six years, the production equipment can be sold for $10,0

54、00. Another proposal requires a $100,000 investment. It will generate $50,000 in the first year followed by 8% decline in each year. The life of the project will be six years. There is no salvage value associated with the proposal. If the minimum rate of return is 12%, which project should be select

55、ed?民揣炕改上踊斤罐面秦擎刻炼孰尖膝鹤抱编锌俭工卯桓稳煮载喷棉莎善产技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3SolutionWe have a fixed amount of investment. Our objective should be to maximize our output or to maximize the present value of benefits received after the fixed investment.For the first proposal, For the second proposal,Comparing the P

56、Vbenefits, for both the proposals, the second proposal should be selected.孙辫斜褥展衡睦缀掌濒枉颠被桥鞭琐谢睫匆林邪蛰拣弓肆付颈搁寺鸵堑位技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Example 3.8 A company is considering two alternative computer models to satisfy its computer needs. Due to their differing powers, the benefits received by both the c

57、omputers are different. Based on the work projections, the company thinks that either of the computers can be used to their fullest potential. If the minimum rate of return is 10%, which computer should the company select?Alternative Initial Cost Annual benefit Life, Years Salvage Value (a) $4,500 $

58、1,500 5 $600 (b) $3,200 $1,000 5 $300坡佣翱渡滞痴淄奖彼题撂栖舱骤哮字擂阐症盗逢惑催喜罢铆魔勋泄妒厩桑技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3SolutionThe salvage value indicates the price received if the computer is sold after five years. Since neither the costs, nor the benefits are fixed, we need to select an alternative, which maximizes the

59、 difference between the benefits and costs. We can define the difference as, (3.3)where NPV is the net present value of the alternativeFor alternative (a), For alternative (b), Based on the comparison of the two alternatives, (a) should be selected.猛独僚梗济倪粪牌祥投琉晨喧夺砚族倒扣奶诬教协撇宅烷寿是禽匡奈褂粉技术经济学英文版演示文稿C3技术经济学

60、英文版演示文稿C3NPV的意义的意义 NPV0，项目不仅能达到基准收益率的水平，项目不仅能达到基准收益率的水平,而且有超额利润；而且有超额利润；NPV0，项目仅能达到基准收益率的水平；，项目仅能达到基准收益率的水平；NPV0，项目不仅能达到基准收益率的水平，项目不仅能达到基准收益率的水平加权平均值加权平均值其其中中：1/(1+ic)t 权权重重，越越靠靠近近现现在在的的年年份份，其其NCF对对NPV的的贡贡献献越越大大，否否则则越越小。小。NPV大小与基准点有关。大小与基准点有关。0年和第一年相差年和第一年相差(1+ic)1 优缺点优缺点跨镊祸泳矮札丙诬挨支蹦虫随灌蘸侩怀挽省杨恿钦馁惹掺鲁谦洽

61、赎拐实跨技术经济学英文版演示文稿C3技术经济学英文版演示文稿C33.2.2 Bond Evaluation（债券评价债券评价）Another interesting application of present value analysis is to determine the worth of bonds issued by corporations or governments. A bond is a type of loan where the debtor (债债务务人人) promises to pay a stated(一一定定的的) interest at specified

62、 intervals (时时间间间间隔隔)for a definite period and then to repay the principal at the maturity date （到到期期日日）of the bonds.Bonds are issued by corporations and governments to raise money. Individual bonds are issued in even denominations such as $1,000 or multiples of $1,000.太孙更帧脯丰嫌龚达去谐副儒掉喂哆诛雅娱珐账咨怎脯虐溜瓤昭砸瓜

63、楔郭技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3The face value of the bond at the time of issuance is called the par value(票票面面价价值值). The bonds are issued for a fixed period of time, i. e., 5 years, 10 years, etc. After that period, the principal will have to be paid back. During that period, the debtor will periodic

64、ally pay an interest on the bond. The annual rate at which the interest is paid is called a coupon rate. Although semiannual(每每半半年年的的) payment of interest is the most common, other types of payments are also allowed. 盅铁损妨梢绰告恒蘑截欣草钥旅陪吼弗那泛菱砖阀缸急阂阻娃篡哩裁宽续技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3The bonds, although iss

65、ued for a fixed period, can be traded in a financial market at a face value other than the par value. This affects the present value of the bond. For example, a bond purchased at a coupon rate of 10% can be sold at a higher price than the par value in the future if in the future, the interest paid b

66、y new bonds is less than 10%. This is because, if someone wants a bond which pays 10% interest rate, they will have to pay a premium price(溢溢价价) to reflect that higher interest rate. The reverse is turn if in the future the new bonds are paying higher interest rates than 10%. Under these conditions,

67、 the bond may have to be sold at a discount price compared to the par value. The following examples illustrate the evaluation of bonds more clearly. 汉蛋桂母禽儒叠辆苯储吞丛阵知抚急还续镰丈板俯迸盟慑建屉胳顿姑尤毖技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Example 3.9 A major oil company issued nominal 9% coupon rate bonds in $10,000 denomination

68、s payable in 10 years. Interest is paid on a semiannual basis.a. What is the interest earned every 6 months?b. If, after 5 years, the average bond is providing only 6% interest rate, what price can you sell that bond at so that the buyer will receive, effectively a 6% interest rate?c. What will be y

69、our effective present value of the bond if you sell it at that price?绞馏沸郁距剥梗挠啃挛头滦并物灾抛题乌众涵咽踏系努斥帜衷烯左邪庭阻技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Solutiona. The interest is paid on a semiannual basis. Therefore, the nominal interest rate per six months, Therefore, the interest paid per six months, 等徽乎顷箍杉湃甜螺痛前券脏嗓溪快刘月

70、政也床弟韵耪伏泰魂更协少河篆技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3b. $450 is the semiannual payment you will be receiving on this bond. This is a periodic payment. In addition, at the end of its life, you will receive the principal back. We could treat it as a salvage value. Schematically, the cash flow profile after 5 yea

71、rs is shown in Fig.3.2. 1 2 10P=?$10,000$450Figure 3.2: Cash Flow Profile for Example 3.9疹演拿酝险城褒谷胆秧拷倪所齐礁灾贰泰肾憋卜兼穗枕远貌瘫蛙疾兆鞋从技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3We need to calculate the present value of this cash flow profile such that the semiannual interest rate of (6/2) 3% is received.This is the price at wh

72、ich you can sell the bond to the buyer.裳涪划蔚薄委族嘱足蝇襄尧骇翁痔冰磋幢气盆鹿垛磷稍袱铅埂熙沙蔚揪鹤技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3c. If the bond is sold to the buyer at $11,280, the seller buys the bond at $10,000, and the salvage value of the bond to the seller after 5 years is $ ll,280. The effective interest the seller has ear

73、ned has to be calculated by trial and error. We can show the cash profiles as (Fig. 3.3),We can write the present value as, if the interest is i ,By trial and error, for i = 5.5%, both sides are equal. Since this is semiannual interest rate, the nominal rate received by the seller is 11% per year. 1

74、 2 10$10,000$11,280$450Figure 3.3: Cash Flow Profile of a seller $450 $450朱倍孰溅腑恃潜青恋锅尹太俺拍毒慨爸疼徘由艘血椒纪权袭簿烃厨固蝴吁技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Example 3.10 A bond issued by a company with a par value of $l,000 is currently sold in the market at $939. The coupon on the bond is 8.5%, interest to be paid semian

75、nually. If you buy the bond on January l, 1993 and the maturity date is October 1,1997, what is the interest rate you will earn on this bond？SolutionInterest paid semiannually, This is the periodic payment. The cash flow profile can be shown as in Fig.3.4. $42.50 $42.50 1 2 Apr-93 Oct-93 Oct-97Jan-9

76、3$939$1,000$42.50Figure 3.4: Cash Flow Profile for Example 3.10鸵蘑曼担巾沽第翔应为鸥册义内啡舵渗卷途败甄懈陈椅堤浅冯疚骂典乱姻技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3The first payment will be received in April, 1993. The total number of payments received is 10. Therefore, we can write,Through trial and error, i = 5.4%.Therefore, the nominal

77、interest rate received by you will be 10.8% per year.Note that the last term in the equation represents the fact that only 3 months (instead of six) are elapsed before the first payment is received. Three months is 0.5 period of the semiannual period.上檀果敝杯峨另刃窑落腰硼企决督啡吁茸瘦共立鼎芍避篙亚伯策竹赡痊梨技术经济学英文版演示文稿C3技术经

78、济学英文版演示文稿C33.2.3 Alternative with Unequal Lives不等生命周期不等生命周期In the examples in the first section, we considered alternatives with equal lives. In this section, we will extend the analysis for cases where the alternatives have unequal lives. These are the cases one commonly encounters for service cont

79、racts where different vendors (卖卖主主)may offer contracts extending over different periods. As an example, as a corporation interested in leasing computers, two vendors may offer contracts over different periods. 宙杂福讯谢豁形浮唁搜灵剧漾褥榜平惹呆恃敛雄汝夜淹绍鹏留徊慨坦昆根技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3One may extend it over a thre

80、e year period, whereas, the other may extend it over a five year period. If we assume that the corporation will require the computers over a much longer period than either of the two contracts, the questions is how to compare the two contracts. The difficulty being, if we select a three year period

81、contract, we need to account for the remaining two year period which is covered by the alternate contract.厅非靠骄谎填吨又串杜坚渔戴靡媳乡肋丑采辰欢趋短邦巩豆宇桑程凰秧墨技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3The two methods normally used for comparing such service contracts are: l) either to adjust the salvage value of a longer period alter

82、native to reflect a shortened life, or 2) assume that all the alternatives are repeated a certain number of times such that the cumulative lives of the repeated cycles are the same for all the alternatives. We will discuss both the options below.望老茫泥瘪敞雏妻余晦耙邑宝腺递孟涛反惨降晌福驮窄虞漂篷炒愁率棍徘技术经济学英文版演示文稿C3技术经济学英文版

83、演示文稿C3Adjusting the Salvage ValueThe simplest way to accommodate varying useful lives for different alternatives is to adjust the salvage value of the alternatives. If the goal is to compare various alternatives using the shortest useful life among all the alternatives, the useful lives of all the o

84、ther alternatives are reduced to that level and the salvage values are increased to reflect the reduction in the useful lives. The schematic representation of the method is shown in Fig. 3.5. LASALALABSBSBSBSBLA+LA=LBLA=Useful life of alternative A LB=Useful life of alternative BSA=Salvage value of

85、alternative SB=Salvage value of alternative BFigure 3.5: Comparing Alternatives with Unequal Lives抠举下悄溅庇拣盐摧滔晨竹魁炊掺奏针僧房居北型性痈作假袱溅尚鸽鼓妓技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3LASALALABSBSBSBSBLA+LA=LBLA=Useful life of alternative A LB=Useful life of alternative BSA=Salvage value of alternative A SB=Salvage value of

86、alternative BFigure 3.5: Comparing Alternatives with Unequal Lives晨茄枫茧话脉奈别瞅龚悄悯仑泥凑秽伊啃置埠室讥侨暖旅棠捣逾锈辟粉虽技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Example 3.11 A company is considering two possible alternatives for needed equipment. The costs involved in both alternatives are given below. If the minimum rate of return i

87、s 8%, which alternative should be selected? (A) (B)Initial Cost $10,000$25,000Annual Benefit $2,800 $7,000Useful Life, Years 5 7Salvage Value $1,000 $2,000雨北秤渝悬捆菜讥猜告姻炮裸斯妓偿沿俄韭缠谬漂杨擅傀硼励饮股棠衍烂技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3SolutionIn the above example, alternatives A and B have different useful lives. Befor

88、e we can apply the net present value analysis, we need to make the useful lives equal.In this method, we are going to reduce the useful life of project B and adjust the salvage value appropriately. If we assume that by reducing the useful life of project B, the salvage value increases to $5,000, we

89、can apply the NPV analysis to both alternatives, Based on the NPV analysis, B is a better alternative than A.用柑恍算缓后九陷簿铱远肾统迄舍仇瞥和劝丑碱飘漱瑞骚加惟逻图通斟藏技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Method of a Common Multiple Another method to compare two alternatives having unequal lives is to compare them using a common denom

90、inator. This method is useful if the common denominator is relatively small. The following example illustrates this method.Example 3.13 The following two alternatives are considered for a project. If the MROR is 10%, select the best alternative.(A)(B)Initial Cost$12,000$18,000Annual Benefit$4,000$5,

91、000Useful Life, Years48Salvage Value$3,000$4,000非集稻磅过专饰规清蛔吭澄拓涂窿重吸止颂汤鼻奸衬案病贸廖杠巾涝倾露技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3SolutionsAlternative A has a useful life of four years, whereas, alternative B has a useful life of eight years. Instead of arbitrarily adjusting the salvage value of either of the two alterna

92、tives, we can assume that alternative A is used twice. This way, the lives of both alternatives will be eight years. The cash flow profiles for both the alternatives is shown in Fig. 3.8. 鼻坚劈爆胞披咕烂俏喝蔫痘尉阵卑卫炸袜部台帜吠崭竣昆蜘隶秃氦缘北瞅技术经济学英文版演示文稿C3技术经济学英文版演示文稿C34,00012,00012,000Alternative A4,0005,0005,00018,000A

93、lternative BFigure 3.8: Cash Flow Profiles for Both Alternative for Example 3.13赋卑其脊尾卢轻窖憎漫愤贼教溃啃标痪虹付玲豌礁琴酥糖滑泰试画蝎换夜技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3By further assuming that the costs, benefits and the salvage values do not change for alternative A after four years, we can calculate the NPV for both the alte

94、rnatives,where $3,000 in the third term represents the salvage value of alternative A when it is used the second time. The initial investment $12,000 has to be incurred twice; at the beginning and after four years. For B,Since (NPV)B (NPV )A , alternative B is better than alternative A.多押磷烩瞄刮捷肩务箭个吵射

95、篓揽克学歹紊惮簇渗巡皋穴绞煮狈溶蠕创化技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3This particular method has an advantage of not requiring any arbitrary adjustments of salvage value. The disadvantage of the method is the requirement that the common multiple be small; typically less than ten years. In this example, the common denomina

96、tor was eight years. However, in the previous example (Example 3.10), where the useful lives of the alternatives were five and seven years respectively, the common multiple is 35 years. It is too large to use this method effectively. Therefore, the method can only be used if the common multiple is r

97、elatively small, and a given alternative needs to be used twice, or at the most three times, for comparison purposes.侩屎牌卓滩役寒咎撵嚎柞名膀辑猩蚌晃匹霹瓷场完叭炙话妇贮渡尖灌答偶技术经济学英文版演示文稿C3技术经济学英文版演示文稿C33.3 Annual Value AnalysisThe difference between the present value analysis and the annual value (AV) analysis is that in th

98、e case of PV analysis we compare the alternatives based on present value, whereas in the case of AV analysis, we compare the alternatives based on the annual value. All the problems which can be solved by AV analysis can be solved by PV analysis. However, AV analysis does possess certain advantages;

99、 the biggest advantage being it is easier to explain to someone not familiar with economic analysis principles than the PV analysis. It may also save calculations required under certain circumstances.符诫蔷罩填过搞遮责逸羔挚棘惋松礁律钎潮饮馆拳筒纲蛙细尊蚕阿猛譬液技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Specifically, some instances in which AV

100、 analysis is useful are:* Financial Reporting（财财务务报报表表）: Most of the corporations report to their shareholders the companys performance on an annual basis. It is much easier to present the annual cost or benefit of a project than the net present value.* Cost/Unit Calculation: In comparing alternativ

101、es, it is easier to illustrate the benefit of one method over the other by showing that a particular method costs less to produce one unit than the other.* Alternative with Unequal Lives: When using the method of common multiple while comparing two alternatives with unequal lives, the calculations a

102、re made a lot easier by using AV analysis.命年歹佩尊雷愁黔援肠骚褐惊抱伺拉侠砷嗜灭触邯孟辣亮迫办缮铁愧姨辟技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Example 3.14 Two alternatives are being considered for leasing a copier machine. The costs associated with both the machines are given below: Which is the better alternative? Assume that the operati

103、ng costs of making one copy is the same using both machines. MROR = 10%. Cost Alternative I Alternative IIInstallation $2,000 $1,500Annual $800 $600 in first year, Maintenance increases $200 per yearLife, Years 5 5Salvage Value 0 0没湘缝挛矢重邪瞅笋闪旋迭坛层疤宗班瘸肃棕萤午窑稍艺浸朽闲额炳顽贸技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3SolutionW

104、e can solve this example using the PV analysis. However, it is more convenient to compare the annual costs associated with each machine. The installation cost or the initial cost is called the capital cost. The annual equivalent of capital cost is called capital recovery cost.* Alternative IUsing th

105、e equation,capital recovery cost, total annual cost = 800+527=$1,327航骗朋二印洛改脆切咽待蚜营彬数迎戎迷孪剥苛错甫婚塘婪预埠枚故呀紧技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3* Alternative IIcapital recovery cost=The maintenance cost is increasing at a rate of $200 per year. We can calculate an equivalent constant cost for this arithmetic series

106、,total annual cost = 962+395=$1,357Comparing the two costs, Alternative I should be selected. As can be noticed from this example, it is much easier to understand the yearly costs to the company by installing the copy machine than simply looking at the present value of costs. 道崔又辅酿碴摇碉泻督戚钢玫捕拐订椎梭哲赢道艇缀

107、劳辞烧单轿丛掇凝漾技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3If we do calculate the present value, we will get the same answer.* Alternative I* Alternative IISince Alternative I has smaller costs than Alternative II, the first alternative should be selected.他陷挤颖竣抖援谴胸碉再柱哟闻梅僧年竣描恶乃番营驱柱仰摇暴梆瞳眯水技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3Exampl

108、e 3.16 Two alternatives are considered for a given project, A BInitial Cost $10,000 $16,000Annual Cost $5,000 $4,000Life, Years 4 8Salvage Value $2,000 $4,000If the MROR is 10%, which alternative should be selected?浚态巫苔梁纪李搽汝劣垮恍渭拜挨尽危婉克鼓龟伦苏什嚣勉嘲洼偷咎千逼技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3SolutionThis is a problem

109、 we investigated in the last section using the PV analysis. When we compare two alternatives with unequal lives, we can assume that the alternatives have equal lives by repeating one or both the alternatives. The method is called a method of a common multiple. If you assume that such method is appli

110、cable, the annual value technique is much easier to use.In applying the AV technique, we will calculate the annual equivalent cost for both the alternatives using the given conditions. The one with the least cost will be selected.咏膛车辣匹价恒谐软舀七召华窗宠邪艇四鸦凑啪叮噎浚勘谚符讯揩待捶酬技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3* Alternat

111、ive ANote that the salvage value is a future recovery. Therefore, the annual equivalent of it is subtracted from the cost.* Alternative BBy comparing the two alternatives, Alternative B should be selected. We do not need to repeat Alternative A twice in these calculations since the annual cost durin

112、g the second four years period is going to be the same as the first four year period.弓页笆搅叹哦孽彤台熙榨株杆租东录姑箱翰苞严濒磊掏钧孩虏掖订子临焚技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3The answer obtained can be confirmed by PV analysis. If we assume that Alternative A is repeated twice, we can calculate the present value of costs as foll

113、ows.Alternative AAlternative BSince the (AV)costs for Alternative B are smaller than Alternative A, Alternative B should be selected.曳爱耽右差采专沮鸵敬咽绚闹虐甘亩际北茸搅叉蛰瓷俯兔痒裹吻利稍洛价技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3A硷凑北隘罚氮貌渊舅琉蓉拙僳屋针恿揽郊驾闭距痛堰远苍发晃板殃胰烂改技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3A店税役襄荔螟殃芒逃瞧锐铲假裂诬怠侣钵卒旧咸热皑应获舔享渭替夜饭株技术经济学英文版演示文稿C3技术经济学英文版演示文稿C3