Draft/PGarg:gms November 1, 1982 COST-BENEFIT ANALYSIS: AN INTRODUCTION 1/ I. General 1. This note has two main purposes: (a) to describe the main features of cost-benefit analysis (CBA); and (b) to discuss its uses and limitations for making decisions about development projects and programs. 2. The exposition is aimed primarily at non-economists. The object is to give such non-specialists an appreciation of the key concepts, without trying to produce proficient practitioners of the technique. The use of economic jargon has been kept to a minimum even at the cost of some rigor and precision. Conceptual and analytical refinements have also been kept to a minimum. In essence, the note tries to exploit the highly developed economic intuition usually found among experienced public administrators even though they may have little or no formal training in economics. What is CBA? 3. CBA is a quantitative technique for rational decision making. Based on a comparison of the costs and benefits of a particular program or project, CBA tries to answer the practical question of whether on balance, the program or project is worthwhile ("profitable") and whether its worth ("profitability") could be increased by changes in its composition, scale, timing and the method of implementation. The basic rationale for using CBA rests on the fact that resources available to an individual or an economy 1.are scarce in relation to the needs, and therefore it is imperative that they be used in a manner so as to produce the largest possible benefits. 4. Conceptually, the CBA methodology is deceptively simple, involving no-more than: (i) identification of the various costs and benefits associated with a decision; (ii) quantification of the costs and benefits identified in step (i); (iii) valuation of the quantities estimated in step (ii); and (iv) comparison of cost and benefit values in step (iii) to determine "profitability." This note draws heavily upon several EDI course notes, including (i) EN-201: Cost-Benefit Analysis: Techniques, Uses and Limitations by I.S. Sirken; and CN-32: Economic Analysis of Agricultural Projects by J. Price Gittinger. -2- In principle, the CBA technique is applicable to any personal, commercial or social decision. In practice, however, the usefulness of CBA greatly depends upon the ease and reliability with which we can identify, quantify and value the costs and benefits associated with a particular decision. 5. The organization of the remainder of this note is as follows. In section II, we clarify some of the key concepts associated with CBA, including: Decision-Maker and Objectives, Time Value of Money, Shadow Prices, Indices of Economic Profitability, and Uncertainty and Sensitivity Analysis. In section III, we provide a summary view of the CBA'techniques to draw out some of the main uses and limitations in a practical context. 6. As noted earlier, the principles underlying CBA have applicability to a broad range of policy and/or project decisions; for presentational simplicity and convenience, however, the discussion in the rest of this note will only be in the context of investment projects. II. Key Concepts in CBA Decision-Maker and Objectives 7. Central to the measurement of costs and benefits of an investment project are the questions of who is the decision-maker and what are his objectives. Thus, the costs and benefits associated with a particular decision will often differ materially depending upon whether they are viewed from the standpoint of the individual concerned or the economy as a whole. For example, an education project for the expansion of an engineering faculty may be clearly very profitable to the students enrolling in that faculty if they do not have to pay for their education and can count on getting jobs at high salaries after graduation. But looking at the project from the standpoint of the national economy, we would have to take into account the costs incurred by the government for providing the engineering training. (There may also be, of course, some additional benefits that might accrue to the economy but not to the students who receive the training. An example of such benefits to the economy would be lower costs and foreign exchange savings that might result from training nationals to replace foreign technicians). -This illustrates the essential difference between financial and economic CBA--the former deals with costs and benefits measured from the viewpoint of an individual (or an'enterprise), the latter with "profitability" for the economy as a whole. 8. The objectives provide the standards against which we define costs and benefits--anything that reduces an objective is a cost, while anything that adds to an objective is a benefit. In reality, a decision-maker may have a multiplicity of (sometimes) conflicting objectives. A business firm, for example, may want to: maximize net profits; minimize risks; be generous to its employees; and to earn a favorable "public image". Similarly, an economy as a whole may want to increase its national income, reduce income inequalities, reduce unemployment, and strengthen national security. In principle, the CBA methodology can accomodate (of course, with increasing complexity) as many of the objectives as are seen necessary. In practice, however, the difficulties in making trade-offs among the various objectives makes it almost obligatory that the analyst focus on at most two or three of the -3- main objectives. Much of the traditional CBA, for example, takes profit maximization as the sole objective for individuals and private business firms. Similarly, for the economy as a whole, the objective is generally taken to be the maximization of national income.2/ 9. The importance of having a clear understanding of the objectives can hardly be over-emphasized. If one looks close enough, one will notice that most raging controversies in public policy are in the final analysis often a reflection of the disagreements on the appropriate national objectives. . Time Value of Money 10. This -is a simple concept whose clear understanding is absolutely imperative for a sound grasp of the CBA methodology. For most investment projects, the benefits (and often the costs) are spread over a fairly long period. How should one compare costs and benefits in such a situation? A simple numerical example should help clarify the problem. Let us assume two projects whose costs have different time distribution patterns. Project I consists of a group of vocational schools and Project II is a group of primary schools with a much larger total enrollment. If we add up the total costs of each project without paying any attention to their distribution over time, the total costs of the two projects are $13 million and $14 million, respectively. If we assume that the benefits of the two projects are approximately equal, Project.I would be a bit better than Project II because its costs are slightly lower. But if we look at the time distribution of the costs, we find that in Project I, $9 million of the $13 million of costs would be incurred during the first 3 years of the 10-year period compared with $2 million in Project II. This is not surprising because in Project I (vocational schools), capital costs, notably equipment, incurred in the early years of the project would account Table 1 Project I Project II Year Costs Costs (million US$) (million US$) 0 1.0 0.5 1 2.0 0.5 2 3.0 0.5 3 3.0 0.5 4 1.0 0.5 5 0.5 1.5 6 0.5 2.0 7 0.5 2.0 8 0.5 2.0 9 0.5 2.0 10 0.5 2.0 Total 13.0 14.0 2/ The main innovation of the so-called "Social CBA", which has generated considerable controversy during the past decade, is the inclusion in the national objective of considerations of income inequality and of the national savings rate. for a larger proportion of total costs than in the primary schools project; and recurrent costs, mostly teacher salaries, for a smaller proportion. Given the choice, a politician would very-likely choose Project II because most of its costs would be incurred in the later years. By choosing Project II, rather than Project I, he would "save" $7 million that he could use for other purposes. (The political pressures for making this type of choice would be irresistible if his government's term of office ended within three years!) 11. Attaching more weight to $1 million of costs incurred in the early years than to the same amount of costs incurred in later years is not only good politics, but also good economics. Why? The simple answer is that $100 spent.today involves a greater economic cost or sacrifice to an individual or an economy than $100 spent a year from now. Let us be sure that we understand the economic logic of it. Spending or investing $100 today involves giving up or sacrificing $100 worth of resources today. Let us compare the magnitude of this sacrifice or economic cost with the cost of spending or investing $100 a year from now. An easy way to make this comparison is to determine how much would have to be given up today in order to have $100 to invest a year from now. The answer is that we need to give up less than $100 today because the money can be invested elsewhere and earn a return in the form of interest or profits. How much less depends on the earning power of money. In any economy, there are always alternative ways of investing resources to yield an annual return. This return is called the opportunity cost of capital. (We shall see later that it serves as a convenient standard for judging the economic merits of investment projects.) 12. Now that we understand the need to adjust costs that are distributed over time before we can add them up, how do we do it? Let us return to our two hypothetical' projects. We have seen that if we simply added up the annual costs of each project without taking account of the time distribution of these costs, we would get a distorted picture of the relative economic costs of the two projects. We would be adding apples and watermelons, because in Project I $0.5 million of costs in year 9 is not equivalent to $0.5 million of costs in year 5. We have to convert the annual cost estimates into common units that can be added up. This means expressing them in terms of a single year which is the common denominator. Since these cost estimates are intended to assist current decision making, the most straightforward approach is to convert the annual cost estimates to the present or year 0. The process of converting future value to the present is called discounting. 13. We saw that the difference between the economic value of costs incurred in year 1 and the same amount of costs incurred in year 0 depends -on the earning power of money which we have called the opportunity cost of capital. Let us assume that the opportunity cost of capital is 8%, i.e., the going yield on investments is 8%, and let us discount the stream of annual costs of the two Projects to determine their present value (p.v.). Fortunately, we can use discount tables. to avoid a lot of tedious arithmetic. -5- Table 2 .Project I Project II Year Costs p.v. p.v. Costs p.v. p.v. (million US$) (8%) (12%) (million US$) (8%) (12%) 0 1.0 1.00 1.00 0.5 0.50 0.50 1 2.0 1.85 1.79 0.5 0.46 0.45 2 3.0 2.58 2.40 0.5 0.43 0.40 3 3.0 2.40 2.14 0.5 0.37 0 36 4 1.0 0.74 0.64 0.5 1.02 0.32 5 0.5 0.34 0.28 1.5 1.28 0.84 6 0.5 0.32 0.25 2.0 1.16 1.00 7 0.5 0.29 0.23 2.0 1.08 0.92 8 0.5 0.27 0.20 2.0 1.00 0.80 9 0.5 0.25 0.18 2.0 1.00 0.72 10 0.5 0.23 0.16 2.0 0.64 0.64 Total 13.0 10.17 9.27 14.0 8.62 6.95 14. The costs in year 0, i.e., the present, do not have to be discounted because they are present value.' The costs in year 1 do have to be discounted, and the discount tables tell us what discount factor to apply to year 1 if the earning power of money is 8%. We find that the present value of $1 in year I at 8% is $0.926. This means that if we invest $0.926 today and the investment earns 8% per annum, the investment will have a value of $1 in year 1 which includes $0.926 of the original investment and $0.074 of earnings. Thus $2 million in year 1 has a present value of $1.85 million. To get the present value of $3 million in year 2, -we apply a .discount factor of 0.857 and we get $2.57 million. The further we go into he future, the less is the present value of a given amount. For example, the present value of $0.5 million of costs in year 5 is $0.34 million, while the present value of $0.5 million of costs in year 10 is $0.23 million. 15. After discounting each of the annual cost estimates in Project I and II to their present values, we can add them up because they are all expressed in terms of the same point in time, i.e., year 0. We find that the present value of the total costs of Project I is 19% higher than Project I, while the undiscounted total cost of Project I is 8% lower. Taking account of the time distribution of costs would make a significant difference in the relative economic merits of the two projects--assuming the benefits are approximately equal. 16. What would be the effect of a higher discount rate, say 12% rather than 8%? Intuition and logic tell us that the higher the discount rate, the lower the present value of total costs. From Table 2, we see that the costs of Project II would be affected more by the higher discount rate than Projedt I because much higher proportion of Project II costs are incurred in the more distant future. We find that the present value of the total costs of Project I is $9.27 milliori, compared with $10.27 million with a discount rate of 8%; the comparable totals for project II are $6.95 -6- million and $8.62 million. With a discount rate of 8%, Project II looks better than Project I on the basis of the present value of their total costs. With a discount rate of 12%, Project II looks still better. 17. Thus, the importance of time discounting depends on how the costs and benefits are distributed over time and also on the level of the discount rate. The level of the discount rate can be regarded as a measure of the strength of the decision-maker's preference for late rather than early costs--a high discount rate meaning a high opportunity cost of capital, i.e., the yield -f alternative investments is high. The discount rate can help decision-m.kers to apply their time preferences in choosing among projects in which the streams of costs and benefits are such that the preferred choices are not obvious. 18. It is reasonable to ask at this stage: how does one get the discount rate, i.e., the opportunity cost of capital. The short answer is that it is not easy. Indeed, a review of the vast Uiterature on this subject suggest that the opportunity cost of capital or the proper discount rate is a notional concept rather than a precise one. We may have a pretty good idea of the range of yields on alternative investments (and therefore of discount rates) in a particular country, e.g., 10-15%, but yields are bound to vary depending on the characteristics of the investment. Thus, we can be reasonably sure that certain discount rates would be too low, e.g., 3% in.most developing countries, and others would be too high, e.g., 25%. The application ,of the former rate would overestimate and the latter underEStimate the economic costs of a project. 3/ Shadow Prices -19. With profit maximization as the objective, measuring the costs and benefits of a project to an individual or an enterprise is in most cases simple and straightforward. The costs are the amount of money that has to be paid, i.e., the costs of acquiring the goods and services that are needed to establish and operate the project. The benefits, in turn, are the monetary receipts for the goods and services produced by the project. In most cases, the prevailing market prices for the goods and services involved may be taken as the appropriate unit values for estimating the costs and benefits to the enterprise. 20. In measuring the "profitability" of a project from the standpoint of the whole economy, however, the market prices for inputs and outputs may not generally be an acceptable measures of the true costs and benefits to the economy. This may happen because the market prices of the different inputs and outputs may be seriously distorted due to the prevalence of various taxes, subsidies, quotas and regulatory measures. Let us illustrate with a few examples. / For operational purposes in the World Bank, the cost of capital is typically taken to be 10% per annum. This is in "real" terms, i.e. net of inflation. With inflation at (say) 8% per annum, the nominal rate would amount to about 18%. -7- 21. Assume that a ministry of irrigation has to buy $100,000 worth of imported equipment subject to a duty of 40%. Thus, the total cost of the equipment to the ministry will be $140,000. What is the cost of this equipment to the economy? The $100,000 of foreign exchange that is spent on the equipment is clearly a cost to the economy because this foreign exchange could have been spent on other imported goods. But the $40,000 of import duty is nothing more than a transfer payment from the ministry of irrigation to the ministry of finance. Exempting the ministry of irrigation from paying the tax or removing it would not reduce the cost of the equipment to the economy, and would not release any economic resources for other uses. Provided there are no quantitative restrictions (i.e. import/export quotas), adjusting for tax-related distortions is generally quite straightforward. 22. In countries with heavy unemployment and underemployment, the wage rates paid to workers on, say, a road construction project would exaggerate the cost of their labor to the economy because the alternative to using the labor in the road project would be unemployment or partial employment. Hence, the employment of the workers in building the road would not deprive the economy of any production, or would deprive it of less production than these workers would contribute to the road project. For example, let us assume that the workers are fully employed about three months of the year and earn the equivalent of $150 from this employment and another $150 in odd jobs. If they are paid'$600 a year to work on the road project at the prevailing wage, the rest of the economy would be deprived of $300 worth of production and not $600 worth. Hence, the wages actually paid to the workers on the road project would exaggerate the cost of their labor to the economy. Thus, in calculating the economic costs of the ,road construction project, we would assume wage rates below the actual wages that would be paid to the workers. We would assign what economists call shadow wage rates that would come closer to measuring the cost of labor to the economy than would the actual wage rates. How much lower the shadow wage rates would be depends on estimates of what the workers would earn, i.e., contribute to the economy's total production, if they were not employed in the road project. In practice, it is quite difficult to determine shadow wage rates accurately because a fair amount of guesswork is needed as to what the workers would earn if they were not employed on the road project. The most extreme assutmption would be a shadow wage rate of zero which would mean that the employment of the workers in the project would involve no cost to the economy, i.e., they would otherwise be totally unemployed and contribute nothing to the economy's total production of goods and services. In most cases, the assumption of a shadow wage rate of zero would probably understate the economic cost of labor. The appropriate shadow wage rate in most cases is somewhere between the actual wage rate and zero. 23. In many developing countries, the official exchange rate,i.e., the price of foreign exchange, understates the economic or scarcity value of foreign exchange so that the financial cost of imported equipment and materials is below the economic cost. For example, if the.dollar exchange rate is 10 rupees to the dollar, a shadow foreign exchange rate might be applied if the amount of goods and services that can be acquired with one dollar of foreign exchange is greater than that acquired for 10 rupees in -8- the national economy. Or putting it another way, the official rate understates the economic contribution that a dollar of foreign exchange can make to the economy. What is the evidence for the belief that the official exchange rate understates the economic cost of foreign exchange? The most common evidence is the existence of a market for foreign exchange, whether legal or illegal, where it is being purchased at prices that are substantially above the official rate. Where there is no unofficial market for foreign exchange, the control of the sup)ly and price of foreign exchange by the financial authorities suggests that without this control, the price of foreign exchange would rise above the official rate because of the willingness of buyers of foreign exchange to pay more for it than the official price. As in the case of shadow wage rates, it is much easier to make the case for applying a shadow exchange rate than to decide precisely what it should be; the determination of this rate, like the determination of shadow wage rates, involves much guesswork. 24. Now that we have established the need for adjusting the financial cash flows to obtain better measures of their economic costs and benefits, what are the consequences of these adjustments for decision making? We shall try to bring out the consequences by using a simple hypothetical example involving "shadow" prices for labor and foreign exchange. Let us assume two road construction projects with approximately the aame benefits and operating costs, and with construction costs as shown below. The official foreign exchange rate is 10 rupees per U.S. dollar while the shadow rate is assumed to be 14 rupees per U.S. dollar. Assume further that the workers who would be employed in the construction of the projects would otherwise be productively employed during half the year so that the shadow wage rate would be 50% of the actual rate. Table 3 Project I Project II (rupees) Local Raw Materials 15 million 15 million Wage Costs 10 million 30 million Imported Equipment 20 million 5 million Total Costs 45 million 50 million 25. On the basis of financial costs, Project I would be better than Project II because it would cost less to build. Both projects would use the same amount of local raw materials. But Project II would use much more labor and much less foreign exchange than Project I. Let us apply the shadow prices that have been assumed above to wages and foreign exchange in order to convert financial costs into economic costs. 26. For raw materials, financial and economic costs would be the same. The economic cost of wages would be 5 million rupees for Project I and 15 million rupees for Project II (i.e., 50% of their financial cost). If we apply the shadow exchange rate to the financial cost of the imported equipment, its economic cost would be 28 million rupees for Project I and 7 million rupees for Project II. The total economic cost of Project I would -.9- be 48 million rupees and 37 million rupees for Project II. Here we have a case in which Project I would be preferable to Project II on the basis of financial costs, but Project II is considerably more attractive in terms of economic costs. 27. In our hypothetical illustration, let us assume now that Project II required imported equipment with a total cost of 15 million rupees rather than 5 million. The total financial costs of Project II would then be 60 million rupees instead of 50 million, compared with 45 million rupees for Project I, and the economic costs of Project II would be 51 million rupees rather than 37 million. This compares with the economic cost of 48 million rupees for Project I. Thus, the economic costs of Project II would be higher though it would still provide more jobs and use less foreign exchange than Project I. The financial costs would also be higher. Hence, Project I would be more attractive on the basis of both financial and economic costs and the tasks of the technicians and decision-makers would be easier than in our earlier example. 28. Our two illustrations are intended to bring out the ralationship between the use of shadow prices and the application of a governmental policy that aims, say, to give priority to creating jobs and saving foreign exchange in choosing capital projects. The use of shadow prices helps to apply the policy in a systematic way. It sets limits on how far the government should go in choosing projects that create more jobs and use less foreign exchange. In our second example, Project II was less attrative than Project I in terms of economic costs because the savings in foreign exchange and the additional jobs did not justify the additional outlay of 15 million rupees. In our first example, the foreign exchange savings and the additional jobs that would result from Project II as compared with Project I did justify the 5 million rupees of additional financial outlay. These conclusion depends, of course, on our assumptions about the shadow prices for labor and foreign exchange. Different values for the shadow prices could produce different conclusions concerning the relative merits of the projects. It is because of this and the uncertainty about the appropriate values to use for shadow prices that alternative values are applied to determine if and how they affect the relative merits of different projects (See the discussion of Uncertainty and Sensitivity Analysis, para. 38 et seq. for an explanation of this practice). Indices of Economic Profitability 29. Once the economic costs and benefits of a project have been identified and measured, the next step is to compare them in order to determine the profitability, i.e., the excess of benefits over costs, from the standpoint of the economy. Techniques have been developd for expressing profitability in terms of a single number or index. The index can be used a a basis for judging whether a project is profitable enough to be acceptable and also to compare one project with another. We will limit our discussion to-two of the most commonly used indices of profitability or investment worth--the benefit-cost ratio and the Internal Rate of Return. 30. To compare costs and benefits, they have to be expressed in the same monetary units and in terms of the same point in time. We have seen, for example, that costs incurred in year 2 cannot be compared with benefits - 10 - to be realized in year 7. We have also seen that a comparison of costs and benefits distributed over a number of years must be discounted to a common year which is usually the present or year 0. The discount rate to be applied is the opportunity cost of capital. 31. Let us use a simple hypothetical illustration to bring out the meaning of the benefit-cost ratio. Assume that the total costs of a project amount to $1 million and are incurred entirely in year 0 and that all of the benefits are realized in years 1 and 2, and that they amount to $540,000 in year I and $583,200 in year 2. Let us compare the present value of total costs and benefits in order to calculate the benefit-cost ratio. The present value (i.e., in year 0) of total costs is $1,000,000. To determine the present value of total benefits, we have to calculate the present value of the benefits in years 1 and 2 and add them up. Let us assume that the oportunity cost of capital, and hence the appropriate discount rate, is 8%. The present value of the $540,000 of benefits in year 1 is $500,000, and the present value of the $583,200 of benefits in year 2 is also $500,000. Therefore, the present value of the total benefits is $1,000,000 and the benefit-cost ratio is 1. What does this ratio mean? 32. At first glance, it may suggest that the project is not profitable, i.e., that it is just breaking even. But let us look at the figures more closely. If we added up the total benefits without regard to their time distribution, they would amount to $1,123,200 compared with total costs of $1,000,000 and the project would appear to be profitables How do we explain this apparent discrepancy? By the difference in the time distribution of the costs and benefits. All of the $1,000,000 of costs would be incurred this year (i.e., year 0). If this $1,000,000 of resources were not invested in this project, it could have been invested in another project that would yield 8% a year because we have assumed that the -opportunity cost of capital is 8%. To keep our illustration simple, assume that the alternative projects also have a two-year life. During the two years, these other projects would have produced total benefits with a present value equivalent to the $1,123,200 produced by our first project. For example, a project could produce total benefits of $324,000 in year 1 and $816,648 in year 2, and the sum of the present value of the two years of benefits would be $1,000,000. Thus, the fact that the present value of the benefits produced by the first project is equal to the $1,000,000 of costs means that it is profitable because the benefits have been subjected to a test which they have passed. The test is the application of the 8% discount rate. 33. If the benefit-cost ratio were less than 1, the project would fail the test and would not be acceptable in terms of economic yield because there would presumbly be alternative ways of investing the resources to produce a higher yield and a benefit-cost ratio of at least 1. If the ratio is greater than 1, the project passes the opportunity cost test with flying colors. Thus, the ratio provides a measure of the acceptability of a project; the higher the ratio, the better the project. The technique for calculating the benefit-cost ratio would be exactly the same in a more realistic situation where the costs and benefits were distributed over a period of 10 or 20 years. - 11 - 34. It should be clear that the size of the b/c ratio depends on the amount and the time distribution of costs and benefits as well as the discount rate. Suppose we applied a discount rate of 10% instead of 8% in our first example, would the b/c ratio be greater or less than 1? By applying a higher discount rate, we would be subjecing the profitability of the project to a stiffer test. In more technical terms, we would be discounting the benefits more heavily, while the costs 17uld remain the same because they are incurred entirely in year 0 and do not have to be discounted. Hence, the present value of the benefits would be less than the costs, i.e., the b/c ratio would be less than 1. The project would fail the 10% test. That is, if the opportunity cost of capital.were 10%, it would mean that there are presumably alternative projects that would pass the test and produce a b/c ratio of at least 1. But supposing we cannot find a project that passes the 10% test, i.e., they all yield a b/c ratio of less than 1? This would suggest that the opportunity cost of capital is less than 10% and that the 10% test is too stiff because the yield on alternative projects is less than 10%. The 'assumption of a 10% opportunity cost of capital means that there are projects yielding this rate. We noted earlier that the Internal Rate of Return is another commonly used index of economic profitability or invetment worth. How is it calculated and how does it differ from the b/c ratio, and does it have any advantages over the b/c ratio? 35. To answer these questions, let us.return to our simple hypothetical project in which the total costs of $1,000,000 are incurred in the year 0, and the benefits in the year 1 amount to $540,000 and $583,200 in year 2. We saw that if we apply a discount rate (i.e., opportunity cost of capital) of 8%, the present value of the total benefits is equal to the present value of the total costs and the b/c ratio is 1. The project just passes the 8% test. If the passing grade were 10%, the project would fail because the present value of the total costs would exceed the present value of total benefits. If the passing grade were.6%, the project would more 'than pass because the present value of the benefits would exceed the present value of the total costs. 36. But supposing that instead of asking whether a project has passed or failed in relation to a part4cular "grade," i.e., opportunity cost of capital, we wanted to know what grade the project would receive and then we could decide whether the grade was acceptable. When the project receives a passing grade, no more and no less, the b/c ratio is 1, i.e., the present value of the total benefits is equal to the present value of the total costs. We have seen that if there is a difference between their present values, the project has either a failing grade or one that is better than passing. Under these conditions, what would the passing grade, i.e , opportunity cost of capital, have to be for the project just to pass, no more and no less? To answer this question, we would have to go through a process of trial and error to find the discount rate that when applied to the stream of costs and benefits would produce equality between their present values. Applying this technique to our hypothetical project, we might begin with a discount rate of 12% and we would find that the present value of total costs exceeded the present value of total benefits, which would mean that the project has a grade of less than 12%. We would apply lower rates and we would find that 10% would still produce an excess, though a smaller one, of costs over benefits. If we applied 6% we would 12 -. find it too low because the present value of total benefits would exceed the present value of total costs. The "right" rate would therefore be somewhere between 6% and 10% and after further trials, we would find that 8% was the "right" rate, i.e., the project would just pass. Its actual grade is the discount rate that equates the present value of costs and benefits. It is this rate that is called the Internal Rate of Return (IRR) and it is defined precisely as we have derived it, as the rate that equates the present value of a stream of costs and benefits, i.e., reduces their difference to zero. 37. What is the economic meaning of our IRR of 8%? In simple terms, it means that the project is yielding an average annual economic return of 8% during its economic life after covering all of it costs including total capital costs. Many people find it easier to understand and use this index of investment worth than the b/c ratio because it is rather similar to the financial measures of investment worth that are used in the private sector. The World Bank, for example, uses the Internal Rate of Return in its project appraisal work. What about its use in the public sector as compared with the b/c ratio? Is 8% an acceptable "grade" or rate of return? It obviously would have to be compared with the rate of return on alternative projects, i.e., the opportunity cost of capital. If the rate of return on a project were 12% or higher, as is often the case in developing countries, it could be assumed that it was an acceptable project because it exceeded the opportunity cost of capital. We would not be concerned as to whether the latter was 7%, 8%, or 9%. As long as we could assume that it was below 12%, a project yielding 12% or more would be acceptable. Likewise, if the IRR were well below 8%, say 3 or 4%, we could assume that the project was unacceptable on the basis of its economic profitability. Hence, the use of the IRR avoids the need for determining and reaching agreement on the precise magnitude of the opportunity cost of capital for projects whose IRR is clearly above or below the opportunity -cost of capital. It will be recalled that the calculation of the b/c ratio requires the application of the opportunity cost of capital to discount the stream of costs and benefits to determine their present values. Where the IRR on a project appears to be close to what can be assumed to be the opportunity cost of capital, a judgment about the precise magnitude of the latter cannot be avoided. Uncertainty and Sensitivity Analysis 38. How reliable are the indices of investment worth--the benefit-cost ratio and the IRR--in measuring what they claim to measure? This will depend on the accuracy and reliability of the estimates of the costs and benefits. There are considerable possibilities for making mistakes in these estimates, especially where benefits are concerned. The uncertainty may be due to either the imperfect understanding of the input-output relationship ("production function") underlying the project, or it may arise from the fact that the project outputs are non-marketed (e.g. public health services); hence, it is difficult to place a value on the project outputs. In such a situation, the decision-makers will want to know how the economic profitability, `i.e., indices of investment worth, will be affected if their technicians are wrong in estimating certain costs or benefits. - 13 - 39. The first step in trying to determine the consequences of mistaken estimates is to decide which mistakes are likely to be most important--because some mistakes will be more important than others. The technique for identifying the factors that really matter in assessing the economic profitability of a project is called sensitivity testing. It tries to determine how and by how much the economic profitability of a project is affected by different estimates of the values that go into the computation of its profitability. We would list all the variables involved in the project's costs and benefits and by a series of simple arithmetic computations we would apply different values of each to see which of the variables really count. We can quickly eliminate a number of variables that are not importait enough to matter. For example, even if the price of electricity in the schools were two or three times as high as expected, it would have a very minor effect on the total costs of the projects and on their economic profitability. Hence we could eliminate the cost of electricity at a glance without doing any computations. On the other hand, the salaries of the teachers in the primary schools iay be important enough to make a significant difference to the total costs and economic profitability of the project. To check this, we would simply calculate the effects on the Internal Rate of Return, say, of substantially greater annual increase in these salaries than has been assumed. If the effect were significant, i.e., if the IRR were sensitive to different rates of increase in the teachers' salaries, then these salaries would be one of the key variables. The IRR could be sensitive*to certain components of costs or benefits and also to different assumptions concerning the shadow exchange rate--for example, if the costs of imported equipment and materials comprised a large enough portion of the total costs of the project. Most projects have a relatively small number of key variables. 40. After we have identified the variabl(s in which mistaken estimates can make a significant difference in the IRR, the next step is to -determine the most likely range of variation'in the values of each of these variables by consulting knowledgeable experts on each of the variables. The analyst then calculates additional IRRs replacing the most probable estimates with the most pessimistic ones for some or all of the key variables. Perhaps the most interesting of the IRRs is the one based on the most pessimistic and rather improbable estimates for all key variables, i.e., if the worst comes to the worst. If this IRR turns out to be significantly above the opportunity cost of capital, the project can be regarded as accetable in terms of its measurable economic costs and benefits and in the light of the best available judgments concerning the magnitudes of the key variables. If this pessimistic IRR turns out to be significantly below the opportuity cost of capital, the analyst would need to undertake further investigation to narrow the probable range for the key variables. III. Cost-Benefit Analysis and Decision MaKing: A Summary View 41. We have seen that cost-benefit analysis consists of the identification, measurement, and comparison of the economic costs and benefits of investment program and projects. In view of all the caveats, limitations, and technical weaknesses of cost-benefit analysis, how useful is it for decisions involving investment programs and projects? The - 14 analysis is relevant and can be useful to decision-makers only if they care about how, where, when, and for whom economic resources are used. The benefit-cost ratio and the IRR are numbers that measure the economic merits of projects entirely on the basis of measurable economic costs and benefits. If all the important costs and benefits of projects in all sectors were economic and measurable, the indices of investment worth could be used to judge the acceptability of particular projects and to compare the merits of individual projects within and between sectors. Under these conditions, public investment decisions could be based largely if not entirely on these indices, though -there would ,till be some technical problems of measurement and uncertainty. But the real world is much less tidy because many of the important benefits and some of the costs of investment projects are non-economic and, where they are economic, they cannot be measured with acceptable reliability. Since the importance of the non-economic and non-measurable benefits and costs will vary from project to project and from sector to sector, comparisons of projects on the basis of an economic index of investment worth have to be handled with considerable care. 42. We have been looking at cost-benefit analysis and its variations as a quantitative analytical technique and we have discussed its uses and limitations. But cost-benefit analysis may also be viewed as a rational approach to decision making whether the costs and benefits are measurable or not. If we accept the notion that public expenditure decisions based on rationality as opposed to whim, bias, or intuition are likely to be better decisions and to be accepted more readily by those whose acceptance is needed for the decisions to be implementd, then the identification of all the costs and benefit and the economic measurement of those that can be so measured is a major application of rationality to decision making. It does not preclude whim, bias, and intuition from playing a role in th3 decision making process. Indeed, it would be unrealistic to do so as long as the decisions are made by human beings.