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经济评价原理：利润最大化原理利润最大化原理 =B C BBenefit,CEconomic C
2、osts C：投入各种要素的机会成本，包括企业家：投入各种要素的机会成本，包括企业家的正常利润。的正常利润。超额利润。超额利润。计算计算 的公式如下：的公式如下：000111000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
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）=B/C=B-C=(B C)/C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)/C3.METHODS FOR ECONOMIC ANALYSISIn this Chapter,we will discuss various methods used for evaluating economi
4、c feasibility of projects.The foundation for these 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 method
5、s by numerous examples.In evaluating projects we will restrict our attention to projects involving mutually exclusive alternatives（互斥方互斥方案案）only.In simple terms,mutually exclusive alternatives are exclusive of each other.By selecting one alternative,we will automatically eliminate the other alternat
6、ives.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 use an IBM-compatible
7、PC,then another alternative,Apple computer,would be automatically eliminated.In the petroleum industry,in several instances one will deal with projects where only one alternative will have to be selected after evaluating several alternatives.Some examples are:*Selection of a contractor to conduct 3-
8、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.*Evaluation of an in-fill drilling option to increase the production.*Selection of a compresso
9、r to increase the gas production.In all the above projects,we can select only one of the several alternatives being considered.Once a particular alternative is selected,all the other alternatives are automatically eliminated from further consideration.Throughout this Chapter,we will use a minimum ra
10、te of return（最小收益率最小收益率）(MROR)to evaluate the attractiveness of various alternatives.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.For example,if one borrows th
11、e money from a bank 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 per
12、son can 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.MROR is someti
13、mes 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 later section of this Chapter.It is suffice to state that any al
14、ternative 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 characteristics:*It should be suitable for ranking various alternativ
15、es.*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 practice,no single criterion would be able to satisfy these characteristics.Especially,although techniques are available to quantify the
16、 uncertainties in economic evaluation,for simplicity,we will assume that all the information regarding any given alternative is known with certainty.Regarding the last ideal characteristic of a criterion,we will assume that our goal will always be either to minimize cost or to maximize profit or ben
17、efit.We will not consider other objectives in our analysis.Several economic criteria are available 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(
18、PV)analysis.the annual value(AV)analysis.rate of return method(ROR),growth rate of return method(GROR),the profit to investment ratio method(PIR).(MROR)In the last section,(MROR).3.1 Methods Without Time Value of MoneyThe methods used without accounting for time value of money are simple to use.Thes
19、e methods do not require 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 scre
20、ening tools to evaluate the alternatives.In the following,we discuss some of these methods and explain the relative advantages and disadvantages of these methods.3.1.1 Return on Investment (ROI)This is one of the most commonly used methods in the oil industry.It is a ratio of total income during the
21、 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 should only be used in conjunction with other methods whi
22、ch account for the time value of money.investmenttotalincomecumulativetotalROI Example 3.1 The following cash flow profile is given for an exploration project.Calculate the return on investment(ROI)for the project.Year 0 1 2 3 4 5 6 7 8 Cash Flow -20 -30 30 50 60 40 40 30 20(1000s of dollars)Solutio
23、n 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.4.550270ROIAnother 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 c
24、an 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 in Section 3.6.In Section 3.6,we expand this definition to include the effect of time value of money.0.1ROIinvestmenttotalinvestmenttotal-incomecumulative(
25、PIR)ratioinvestmenttoprofitExample 3.2 The following two alternative projects are considered for a potential investment.Using ROI or PIR as a criterion,which alternative 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 0Solu
26、tionAlternative 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 7.2170460ROIAlternative 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,bo
27、th the alternatives are feasible.Comparing the two alternatives,Alternative I is superior to Alternative II based on both criteria.4.2170410ROI3.1.2 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 re
28、ceive the initial 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
29、small investment 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(合同合同)requiring a pull-out after a certain period.Payback period,however,has certain drawbacks.As explained before,
30、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 and may last over several years.It is not a criterion indicating eco
31、nomic efficiency;i.e.,how efficiently the money is invested.Instead,it is a criterion of economic expediency;i.e.,how quickly the capital can be recovered.For a company interested in liquidity of capital,payback period provides a useful tool for knowing how quickly the invested capital is recovered.
32、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 payback period technique.Example 3.3 Based on evaluation of an oil well,it was determined that after acidizing the well,the production of the
33、well will increase from 10 bbl/day to 15 bbl/day.If the price of oil is$20/bbl,and the cost of acidizing 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/$3,000=1.67The payback period would be 1.67
34、 months.000,3$bbl20$mod30dbbl5month per revenue lIncrementaExample 3.5 An initiation 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 t
35、he payback period(i)without discounting for the time value of money,and(ii)by discounting for the time value of money.Assume the discount rate to be 8%.SolutionThe following table shows the yearly cash flows and discounted cash flows for this problem.The sample calculations follow.Cash Cumulative Di
36、scounted 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 5 459,270 866,570 312,571 326,032Sampl
37、e CalculationsTo calculate cash flow in year 2,=700,000 x 0.9=$630,000The cash flow in other years are similarly calculated.For part(i),the cumulative cash flow becomes positive after 3.2 years.Therefore,the payback period is 3.2 years.For discounted payback period,cash flow in each year is discount
38、ed by using an interest rate of 8%.For example,in year 1,For year 2.Using the discounted cash flow values,the cumulative cash flow becomes positive after four years.Therefore,the discounted payback period is four years.Obviously,the discounted payback period is a strong function of the interest rate
39、 at which the cash flow is discounted.For the same example,if we use a discount rate of 15%,the discounted payback period is 5.2 years instead of four years.148,648$.08)(1700,000flowcash discounted123,540$.08)(1630,000flowcash discounted2For situations where the cash flow investments and benefits ar
40、e 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 account for time value of money are simple to use and may provide a primary screening tool to evaluate alternatives.How
41、ever,these methods should only be used in conjunction with other methods to properly evaluate the projects feasibility.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
42、for the time value of money and provides a way of comparing various alternatives at the same frame of reference.If the project has a fixed output,the objective should be to minimize the present worth of costs.As discussed in Chapter 1,if the project has a fixed input,the objective should be to maxim
43、ize the present worth of benefits,and if the project 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 wil
44、l assume that the lives of the various alternatives are equal.公式推导公式推导0 1 2 3 4 5 n-1 nExample 3.6 A company is considering two alternatives to satisfy its photo copying requirements.The cost of each machine is shown below:(a)(b)Initial Cost$10,000$8,000Annual Cost$1,000$1,400The annual cost include
45、s 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?SolutionBoth alternatives will perform the same functions,i.e.,they offer the same output.Therefore,our objective should be to minimize the c
46、ost.For alternative(a),For alternative(b),Comparing the present worth costs of the two alternatives,alternative(b)should be selected.791,13$1.011.011.01000,1$000,10$PV55costs307,13$1.011.011.01400,1$000,8$PV55costsExample 3.7 A proposal calls for an investment of$100,000 in drilling a new well.It is
47、 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$10,000.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 p
48、roject 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 selected?SolutionWe have a fixed amount of investment.Our objective should be to maximize our output or to maximize the present value of benefits received afte
49、r the fixed investment.For the first proposal,For the second proposal,Comparing the PVbenefits,for both the proposals,the second proposal should be selected.408,128$12.01000,1012.0112.0112.01000,30PV666benefits200,173$12.0108.01108.012.0000,50PV66benefitsExample 3.8 A company is considering two alte
50、rnative computer models to satisfy its computer needs.Due to their differing powers,the benefits received by both the computers 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%,whic
