Cost-Benefit Analysis for Investment Decisions Chapter 4 PDF

COST-BENEFIT ANALYSIS FOR INVESTMENT DECISIONS, CHAPTER 4: DISCOUNTING AND ALTERNATIVE INVESTMENT CRITERIA Glenn P. Jenkins Queen’s University,...

COST-BENEFIT ANALYSIS FOR INVESTMENT DECISIONS, CHAPTER 4: DISCOUNTING AND ALTERNATIVE INVESTMENT CRITERIA Glenn P. Jenkins Queen’s University, Kingston, Canada and Eastern Mediterranean University, North Cyprus Chun-Yan Kuo Queen’s University, Kingston, Canada Arnold C. Harberger University of California, Los Angeles, USA Development Discussion Paper: 2011-4 ABSTRACT This chapter discusses the alternative investment criteria commonly used in the appraisal of investment projects. The net present value (NPV) of a project criterion is widely accepted by accountants, financial analysts, and economists as the one that yields the correct project choices in all circumstances. However, some decision makers have frequently relied upon other criteria such as the internal rate of return, the benefit-cost ratio, the pay-back period and the debt service capacity ratio. The strengths and weaknesses of these criteria are examined in this chapter in order to demonstrate why the NPV criterion is the most reliable. To be Published as: Jenkins G. P, C. Y. K Kuo and A.C. Harberger, “Discounting And Alternative Investment Criteria ” Chapter 4, Cost-Benefit Analysis for Investment Decisions. (2011 Manuscript) JEL code(s): H43 Keywords: Investment Appraisal, Discount Rate, Project Appraisal CHAPTER 4: CHAPTER 4 DISCOUNTING AND ALTERNATIVE INVESTMENT CRITERIA 4.1 Introduction This chapter discusses the alternative investment criteria commonly used in the appraisal of investment projects. The net present value (NPV) of a project criterion is widely accepted by accountants, financial analysts, and economists as the one that yields the correct project choices in all circumstances. However, some decision makers have frequently relied upon other criteria such as the internal rate of return, the benefit-cost ratio, the pay-back period and the debt service capacity ratio. The strengths and weaknesses of these criteria are examined in this chapter in order to demonstrate why the NPV criterion is the most reliable. Section 4.2 explains the concept of discounting and discusses the choice of discount rate. Section 4.3 elaborates and compares alternative investment criteria for the appraisal investment projects. Conclusions are made in the last section. 4.2 Time Dimension of a Project Investment decisions are fundamentally different from consumption decisions. For example, fixed assets such as land and capital equipment are purchased at one point in time, and they are expected to generate net cash flows, or net economic benefits, over a number of subsequent years. To determine whether the investment is worthwhile, it is necessary to compare its benefits and costs with alternative projects, which may occur at different time periods. A dollar spent or received today is worth more than a dollar spent or received in a later time period. It is not possible just to add up the benefits and the costs of a project to see which is larger without taking account of the fact that amounts spent on investment today are worth more today than the same amount received as a benefit in the future. 1 CHAPTER 4: The time dimension of a project’s net cash flows and net economic benefits can be captured by expressing the values in terms of either future or present values. When moving forward in time to compute future values, analysts must allow for the compounding of interest rates. On the other hand, when bringing future values back to the present for comparison purposes, it is necessary to discount them. Discounting is just the inverse of compounding. 4.2.1 Time Value of Money Time enhances the value of a dollar today and erodes the value of a dollar spent or received in the future. It is necessary to compensate individuals for forgoing their consumption today or lending their funds to a bank. In turn, banks and other financial institutions have to offer lenders interest in order to induce them to part temporarily with their funds. If the annual market interest rate is 5%, then 1 dollar today would be worth 1.05 dollars that are received one year in the future. This means that in equilibrium lenders value 1.05 dollars in one year’s time, the same as 1 dollar today. 4.2.2 Compounding There are two main ways that interest can be included in future values, simple interest and compound interest. Simple interest is paid on only the principal amount that is invested while compound interest is paid on both the principal and the interest as it accumulates. Compound interest, which is the most commonly used way of charging interest, can cause the future value of 1 dollar invested today to increase by substantially more than simple interest over time. The difference is caused by the interest on the cumulative interest. The formula for compound interest payment is Vt = (1+r)t where Vt stands for the value in year t with 1 dollar received in year zero and r denotes the rate of interest. Interest may be compounded annually. It is common, however, for interest to be compounded more frequently, e.g., semi-annually, quarterly, monthly or even daily. The number of compounding intervals will also affect the future value of an amount of cash 2 CHAPTER 4: invested today. Thus the two factors affecting the future value of a dollar invested today are the time period of the investment and the interest rate. Furthermore, when comparing two debt contracts it is essential that they be judged on the basis of equivalent rates -- e.g., annual rates in the case of loan agreements, semi-annual rates in the case of bonds. The magnitude of the interest rate is certainly a major determinant of the future value of series of a cash flow item. 4.2.3 Discounting The discount factor allows us to compute the present value of a dollar received or paid in the future. Since we are moving backward, rather than forward in time, the discount factor is the inverse of the compound interest factor. For example, an amount of 1 dollar now will, if invested, grow to (1+r) a year later. It follows that an amount B to be received in n years in the future will have a present value of B/(1+r)n. The greater the rate of discount used, the smaller is its present value. The nature of investment projects is such that their benefits and costs usually occur in different periods over time. The NPV of a future stream of net benefits, (B0 - C0), (B1 – C1), (B2 - C2),..., (Bn - Cn), can be expressed algebraically as follows: B0 − C 0 B1 − C1 B − Cn NPV 0 = +...... + n (1 + r ) 0 (1 + r ) 1 (1 + r ) n n ( Bt − C t ) = ∑ t =0 (1 + r ) t (4.1) where “n” denotes the length of life of the project. The expression 1/(1+r)t is commonly referred to as the discount factor for year t. For purposes of illustration, the present value of the stream of net benefits over the life of an investment is calculated in Table 4.1 by multiplying the discount factors, given in row 4, by 3 CHAPTER 4: the values of the net benefits for the corresponding periods shown in row 3. The NPV of $1,000 is the simple sum of the present values of net benefits arising each period throughout the life of the project. Table 4.1 Calculating the Present Value of Net Benefits from an Investment Project (Dollars) Items 0 1 2 3 4 5 1. Benefits 3,247 4,571 3,525 2,339 2. Costs 5,000 2,121 1,000 1,000 1,000 1,000 3. Net Benefits (=1-2) -5,000 -2,121 +2,247 +3,571 +2,525 +1,339 4. Discount Factor at 6% (=1/(1+r)t) 1.000 0.943 0.890 0.840 0.792 0.747 5. Present values (=4*3) -5,000 -2,000 +2,000 +3,000 +2,000 +1,000 6. Net Present Value 1,000 Equation (4.1) shows that the net benefits arising during the project's life are discounted to period zero. Instead of discounting all the net benefit flows to the initial year of a project, we could evaluate the project's stream of net benefits as of a year k, which does not even need to fall within the project's expected life. In this case all the net benefits arising from year zero to year k must be cumulated forward at a rate of r to period k. Likewise, all net benefits associated with years k+1 to n are discounted back to year k at the same rate r. The expression for the NPV as of period k becomes: n NPV k = ∑ [(Bt - Ct) · (1+r)k-t] t=0 n = ∑ [(Bt - Ct) / (1+r)t] · (1+r)k t=0 (4.2) The terms, (1+r)k, is a constant value as it is a function of the discount rate and the date to which the present values are calculated. The rankings of alternative projects will not be altered if the project’s net benefits are discounted to year k instead of year zero. The present values of their respective net benefits discounted at period zero are all multiplied by the same constant term. Hence the ranking of the net present values of the net benefits of the alternative projects will not be affected. 4 CHAPTER 4: 4.2.4 Variable Discount Rates To this point we have assumed that the discount rate remains constant throughout the life of a project. This need not be the case. Suppose that funds are very scarce at present relative to the historical experience of the country. In such circumstances, we would expect to find that the cost of funds will currently be abnormally high and the discount rate will most likely fall over time as the supply and demand for funds return to normal. On the other hand, if funds are abundant at present, we would expect the cost of funds and the discount rate to be below their long-term average. In this case we would expect the discount rate to rise as the demand and supply of funds return to their long-term trend over time. This process is illustrated in Figure 4.1. Figure 4.1 Adjustment of Cost of Funds through Time If funds currently are abnormally scarce Discount Rate Normal or historical (percent) average cost of funds If funds currently are abnormally abundant Years from present period 0 1 2 3 4 5 Suppose that the discount rates will vary from period to period over the life of a four-year project. The discount rate r1 is the cost of capital or the rate of discount extending from period zero to period one. The NPV of the project should be calculated as: 0 B1 −C1 B2 − C 2 B3 − C 3 NPV = ( B0 − C 0 ) + + + (1+ r1 ) (1+ r1 )(1+ r2 ) (1+ r1 )(1+ r2 )(1+ r3 ) 5 CHAPTER 4: where r1, r2 and r3 are the discount rates for period 1, period 2 and period 3, respectively. Each discount factor after period two will be made up of more than one discount rate. For example, the discount factor for year three’s net benefits is 1/[(1+r1)(1+r2)(1+r3)]. The general expression for the NPV of the project with a life of n years, evaluated as of year zero, becomes: n Bi − C i NPV0 = (B0 - C0) + ∑ (4.3) i =1 ∏(1 + ri ) i As in the case of the constant rate of discount, when comparing two or more projects the period to which the net benefits of the projects are discounted does not matter provided that the present values of the net benefits of each of the projects being compared are discounted to the same date. 4.2.5 Choice of Discount Rate The discount rate is a key variable in applying investment criteria for project selection. Its correct choice is critical given the fact that a small variation in its value may significantly alter the results of the analysis and affect the final choice of a project. The discount rate, stated in simple terms, is the opportunity cost of funds that are invested in the project. In financial analysis, the discount rate depends upon the viewpoints of analysis. For instance, when a project is being appraised from the point of view of the equity holders, the relevant cost of funds is the return to equity that is being earned in its alternative use. Thus if the equity holders are earning a return of 15% on their current investments and decide to invest in a new project, the cost of funds or the discount rate from their perspective for the new project is 15%. 6 CHAPTER 4: When we conduct the economic analysis of a project, the relevant discount rate is the economic opportunity cost of capital for the country. To estimate this cost we start with the capital market as the marginal source of funds we need to determine the ultimate sources of funds obtained via the capital market and estimate the respective cost of each source. The funds are generally drawn from three sources. First, funds that would have been invested in other investment activities have now been displaced by the project. The cost of these funds is the gross of tax return that would have been earned by the alternative investments, which are now foregone. Second, funds come from different categories of savers in the economy who postpone some of their consumption in the expectation of getting a return on their savings. The cost of this part of the funds is the cost of postponing this consumption. Third, some funds may be coming from abroad, that is from foreign savers. The cost of these funds is the marginal cost of foreign borrowing. Thus, the economic opportunity cost of capital will simply be a weighted average of the costs of funds from three alternative sources. The detailed methodology for measuring the economic opportunity cost of capital will be discussed later. 4.3 Alternative Investment Criteria Different criteria have been used in the past to evaluate if an investment project is financially and economically viable. In this section, we review six of these criteria including the net present value, the internal rate of return, the benefit-cost ratio, the pay-out or pay-back period, the debt service coverage ratio, and cost-effectiveness. 4.3.1 Net Present Value Criterion The NPV is the algebraic sum of the present values of the expected incremental net cash flows for a project over the project’s anticipated lifetime. It measures the change in wealth created by the project. 7 CHAPTER 4: (a) When to Accept and Reject Projects If the NPV of the project is equal to zero, investors can expect to recover their incremental investment and also earn a rate of return on their capital that would have been earned elsewhere and is equal to the private discount rate used to compute the present values. This implies that investors would be neither worse off nor better off than they would have been if they had left the funds in the capital market. A positive NPV project means that investors can expect not only to recover their capital investment, but also to receive a rate of return on capital higher than the discount rate. However, if the NPV is less than zero, then investors cannot expect to earn a rate of return equal to the discount rate, nor can they recover their invested capital, and hence, their real net worth is expected to decrease. Only projects with positive NPV are attractive to private investors. They are unlikely to pursue a project with a negative NPV unless there are strategic reasons to do so. Many of these strategic reasons can also be evaluated in terms of their net present values through the valuation of the real options made possible by the strategic project. This leads to Decision Rule 1 of the net present value criterion that holds under all circumstances. Rule 1: Do not accept any project unless it generates a positive NPV when discounted by the opportunity cost of funds. (b) Budget Constraints Often investors cannot obtain sufficient funds to undertake all the available projects having a positive NPV. Similarly, it is the case for governments. When such a situation arises, a choice must be made among the projects to determine the subset that will maximize the NPV produced by the investment package while fitting within the budget constraint. Thus, Decision Rule 2 is: Rule 2: Within the limit of a fixed budget, choose the subset of the available projects that maximizes the NPV. Since a budget constraint does not require that all the money be spent, the rule will prevent 8 CHAPTER 4: any project that has a negative present value from being undertaken. Even if not all the funds in the budget are spent, the NPV generated by the funds in the budget will be increased if a project with a negative NPV is dropped from consideration. Keeping in mind that the funds assigned by the budget allocation but are not spent will simply remain in the capital market and continue to generate a rate of return equal to the economic opportunity cost of capital. Suppose the following set of projects describes the investment opportunities faced by an investor with a fixed budget for capital expenditures of $4.0 million: Project A Project B Project C Project D PV investment costs $1.0 million $3.0 million $2.0 million $2.0 million NPV of net benefits +$60,000 +$400,000 +$150,000 +$225,000 With a budget constraint of $4 million we would explore all possible combinations that fit within this constraint. Combinations BC and BD are impossible, as they cost too much. AC and AD are within the budget, but are dominated by the combination AB which has a total NPV of $460,000. The only other feasible combination is CD, but its NPV of $375,000 is not as high as that of AB. If the budget constraint were expanded to $5 million, then project A should be dropped and project D undertaken in conjunction with project B. In this case, the NPV from this package of projects (D and B) is expected to be $625,000 which is greater than the NPV of the next best alternative (B and C) of $550,000. Suppose that project A, instead of having an NPV of +$60,000, had an NPV of -$60,000. If the budget constraint were still $4.0 million, then the best strategy would be to undertake only project B which would yield a NPV of $400,000. In this case, $1 million of the budget would remain in the capital market, even though it is the budget constraint which is preventing us from undertaking the potentially good projects, C and D. (c) No Budget Constraints In evaluating investment projects, we often come across a situation where we have to make a choice between mutually exclusive projects. It may not be possible for all projects to be 9 CHAPTER 4: undertaken for technical reasons. For example, in building a road between two towns, there are several different qualities of road that can be built, given that only one road will be built. The problem facing the investment analyst is to choose from among the mutually exclusive alternatives such that the project will yield the maximum net present value. This can be expressed in Decision Rule 3: Rule 3: When there is no budget constraint but a project must be chosen from mutually exclusive alternatives, investors should always choose the alternative that generates the largest net present value. Consider three projects, E, F and G that are mutually exclusive for technical reasons and have the following characteristics: Project E Project F Project G PV investment costs $1.0 million $4.0 million $1.5 million NPV of net benefits +$300,000 +$700,000 +$600,000 In this situation, all three are good potential projects that would yield a positive net present value. However, only one can be undertaken. Project F involves the biggest expenditure; it also has the largest NPV of $700,000. Thus, project F should be chosen. Although project G has the biggest NPV per dollar of investment, this is not relevant if the discount rate reflects the economic opportunity cost of the funds. If we undertake project F rather than G, there is an incremental gain in NPV of $100,000 over and above the opportunity cost of the additional investment of $2.5 million. Therefore, project F is preferred. It is worth pointing out that NPV of a project measures the value or surplus generated by a project over and above what would be gained or generated by these funds if they were not used in the project in question. (d) Projects with Different Lifetime In some situations, an investment in a facility such as a road can be carried out in a number 10 CHAPTER 4: of mutually exclusive ways. For example, the road services could be provided by a series of projects with short lives such as gravel surface, or by ones with longer lives such as paved surface. If the return on the expansion of the facility over its lifetime is such as to be an investment opportunity that would yield a significantly positive NPV, it would not be meaningful to compare the NPV of a project that produced road services for the full duration, to the NPV of a project that produced road services for only part of the period. The same issue arises when alternative investment strategies are evaluated for power generation. It is not correct to compare the NPV of a gas turbine plant with a life of ten years to a coal generation station having a life of 30 years. In such a case, we must compare investment strategies that have approximately the same length of life. This may involve the comparison of a series of gas turbine projects followed by other types of generation which in total have the same lengths of life as the coal plant. When projects of short lives lead to further projects which yield supra-marginal returns, the comparison of alternative projects of different lives which will provide the same services at a point in time will require us to make adjustments to our investment strategies so they span approximately the same period of time. One such form of adjustment is to consider the same project being repeated through time until the alternative investment strategies have the same lengths of life. Consider the following three types of road surfaces. Alternative Investment Projects: Duration of Road A: Gravel surfaced road 3 years B: Gravel-Tar surfaced road 5 years C: Asphalt surface road 15 years If we compare the NPV of these three alternatives with lives of 3, 5 and 15 years, the results could be misleading. However, a correct comparison of these projects can be made if we construct an investment strategy which consists of five gravel road projects, each one undertaken at a date in the future when the previous one is worn out. We would then compare five gravel road projects, extending fifteen years into the future with three tar surface roads and one asphalt road of fifteen-year duration. This comparison can be written 11 CHAPTER 4: as follows: Alternative Strategies Duration of Road (i) (A + A + A + A + A) 15 years (i.e., 1-3, 4-6, 7-9, 10-12, 13-15) (ii) (B + B + B) 15 years (i.e., 1-5, 6-10, 11-15) (iii) (C) 15 years (i.e., 1-15) Alternatively, it might be preferable to consider investment strategies made up of a mix of different types of road surfaces through time such as: Duration of Road (iv) (A + A + A + B + C) 29 years (i.e., 1-3, 4-6, 7-9, 10-14, 15-29) (v) (A + B + B + C) 28 years (i.e., 1-3, 4-8, 9-13, 14-28) In this situation it is a further adjustment should be made to the 29-year strategy (iv) to make it comparable to strategy (v) that is expected to last for only 28 years. This can be done by calculating the NPV of the project after dropping the benefits accruing in year 29 from the NPV calculation while at the same time multiplying the present value of its costs by the fraction PVB 1-28/PVB, where PVB denotes the present value of the benefits of the entire strategy, including year 29 and PVB 1-28 is the present value of the benefits that arise in the first 28 years of the project’s life. In this way the present value of the costs of the project are reduced by the same fraction as the present value of its benefits so that it will be comparable in terms of both costs and benefits to the strategy with the shorter life. Although the NPV criterion is widely used in making investment decisions there are also alternative criteria that frequently used. Some of these alternatives has serious drawbacks compared to the NPV criterion and are therefore judged not only less reliable, but potentially misleading. When two or more criteria are used to appraise a project, there is a chance that they will point to different conclusions, and a wrong decision could be made.1 This creates unnecessary confusion and possibly mistakes. 1 See, e.g., Ley, E., “Cost-benefit Analysis: Evaluation Criteria (Or: “Stay away from the IRR”)”, paper prepared for the World Bank, (November 2007). 12 CHAPTER 4: 4.3.2 Internal Rate of Return Criterion The internal rate of return (IRR) for a project is the discount rate (ρ) that is obtained by the solution of the following equation: n ∑ [(Bj – Cj) / (1+ρ)j] = 0 j=0 (4.4) where Bj and Cj are the respective cash inflow and outflow in year t to capital. This definition is consistent with the meaning of a zero NPV that investors recover their invested capital and earn a rate of return equal to the IRR. Thus, the IRR and the NPV criteria are related in the way they are derived. To calculate the NPV the discount rate is given and used to find the present value of benefits and costs. In contrast, when finding the IRR of a project the procedure is reversed by setting the NPV of the net benefit stream at zero. The IRR criterion has seen considerable use by both private and public sector investors as a way of describing the attractiveness of a particular project. However, it is not a reliable investment criterion as there are several problems associated with it. We shall discuss these problems in turn. Problem No. 1: The IRR may not be unique. The IRR is, strictly speaking, the root of a mathematical equation. The equation is based on the time profile of the incremental net cash flows like those in Figure 4.2. If the time profile crosses the horizontal axis from negative to positive only once as in Figure 4.2 (a), then the root, or IRR, will exist. However, if the time profile crosses the axis more than once as in Figure 4.2 (b) and (c), it may not be possible to determine a unique internal rate of return. Projects whose major items of equipment must be replaced from time to time will give rise to periodic negative net cash flows in the years of reinvestment. Road projects have this characteristic as major expenditures on resurfacing must be undertaken periodically for them to remain serviceable. 13 CHAPTER 4: Figure 4.2 Time Profiles of the Incremental Net Cash Flows for Various Types of Projects a) Incremental b) Incremental c) Incremental Net Cash Net Cash Net Cash Flow Flow Flow + + + 0 Time Time Time - - - There are also cases where the termination of a project entails substantial costs. Examples of such situations are the land reclamation costs required at the closing down of a mine to meet environmental standards or the agreement to restore rented facilities to their former state. These cases are illustrated by Figure 4.2(c). These project files may yield multiple solutions for the internal rate of return; these multiple solutions, when present, face us with a problem of proper choice of the rate of return. Let us consider the simple case of an investment of $100 in year 0, a net benefit of $300 in year 1, and a net cost of $200 in year 2. The solutions for the internal rate of return are zero and 100 percent. Even when the internal rate of return can be unambiguously calculated for each project under consideration, its use as an investment criterion poses difficulties when some of the projects in question are strict alternatives. This can come about in three ways: projects require different sizes of investment, projects have different lengths of life, and projects represent different timing for a project. In each of these three cases, the internal rate of return can lead to the incorrect choice of project. 14 CHAPTER 4: Problem No. 2: Projects of different scale The problem of having to choose between two or more mutually exclusive projects arises quite frequently. Examples may include two alternative buildings being considered for the same site, or a new highway that could run down two alternative rights of way. Whereas the NPV takes explicit account of the scale of the project by means of the investment that is required, the IRR ignores the differences in scale. Let us consider a case where project A has an investment cost of $1,000 and is expected to generate net cash flows of $300 each year in perpetuity. Project B is strictly alternative and has an investment cost of $5,000. It is expected to generate net cash flows of $1,000 each year in perpetuity. The IRR for project A is 30 percent (ρA = 300/1,000) while the IRR for project B is 20 percent (ρB = 1,000/5,000). However, the NPV of project A using a 10% discount rate is equal to $2,000 while the NPV of project B is $5,000. In this example, if a choice is made between projects A and B, the internal rate of return criterion would lead to us to choose project A because it has an IRR of 30 percent which is higher than 20 percent for project B. However, the fact that project B is larger enables it to produce a greater NPV even if its IRR is smaller. Thus the net present value criterion tells us to choose project B. From this illustration we see that when a choice has to be made among mutually exclusive projects with different sizes of investment, the use of the internal rate of return criterion can lead to the incorrect choice of investment projects. Problem No. 3: Projects with different lengths of life In this case, we have two projects C and D in which Project C calls for the planting of a species that can be harvested in five years while Project D plants a type of tree that can be harvested in ten years. The investment costs are the same for both projects at $1,000. It is also assumed that neither of the projects can be repeated. The two projects can be analysed as follows: 15 CHAPTER 4: Project C Project D Investment Costs: $1,000 in Year 0 $1,000 in Year 0 Net Benefits: $3,200 in Year 5 $5,200 in Year 10 NPV Criterion @8%: NPVC0 = $1,178 NPVD0 = $1,409 NPVC0 < NPVD0 IRR Criterion: ρC = 26.2% ρD = 17.9% ρ C> ρ D According to the NPV criterion, Project D is preferred. The IRR of Project D, however, is smaller than that of Project C. Thus, the IRR criterion is unreliable for project selection when alternative projects have different lengths of life. Problem No. 4: Projects with different timing Suppose the following two projects, E and F, are started at different times and both last for one year. Project F is started 5 years after Project E. Both projects have the investment costs of $1,000. They are summarized as follows: Project E Project F Investment Costs: $1,000 in Year 0 $1,000 in Year 5 Net Benefits: $1,500 in Year 1 $1,600 in Year 6 NPV Criterion @8%: NPVE0 = $389 NPVF0 = $328 NPVE0 > NPVF0 IRR Criterion: ρE = 50% ρF = 60% ρE< ρF Evaluating these two projects according to the net present value criterion would lead us to choose project E over project F because NPVE0 > NPVF0. However, we find that ρE< ρF leads us to choose project F if we use the internal rate of return criterion. Again, 16 CHAPTER 4: because projects E and F are strict alternatives, the IRR criterion can cause us to make the incorrect choice of project. Problem No. 5: Irregularity of cash flows In many situations the cash flows of a project may be negative in a single (investment) period but it does not occur at the beginning of the project. An example of such a situation is to look at a Build, Operate, and Transfer (BOT) arrangement from the point of view of the government. During the operating stage of this project the government is likely to receive tax benefits from the private operator. At the point when the project is turned over to the public sector the government has agreed to pay a transfer price. Such a cash flow from the government’s point of view can be illustrated as project A in Table 4.2, where the transfer price at the end of the contract is $8,000. Table 4.2 IRR for Irregular Cash Flows Year 0 1 2 3 4 IRR Project A 1,000 1,200 800 3,600 -8,000 10% Project B 1,000 1,200 800 3,600 -6,400 -2% Project C 1,000 1,200 800 3,600 -4,800 -16% Project D -1,000 1,200 800 3,600 -4,800 4% Project E -1,325 1,200 800 3,600 -4,800 20% Results: Project B is obviously better than project A, yet IRRA > IRRB. Project C is obviously better than project B, yet IRRB > IRRC. Project D is worse than project C, yet IRRD > IRRC. Project E is worse than project D, yet IRRE > IRRD. This four-year project has an internal rate of return of 10%. However, suppose the negotiators for the government were successful at obtaining a lower transfer price at the end of the private sector’s contract period. The situation when the contract price is reduced to $6,400 is shown as project B. Everything else is the same as project A except for the lower transfer payment at the end of that period. In this case, the IRR falls from 10% to -2%. It is obvious that the arrangement under project B is better for the government than project A yet it has a lower IRR. If the transfer price were reduced further to $4,800 we find that the IRR falls to a negative 16%, yet is obvious that it is a better project than either project A or B. 17 CHAPTER 4: Now consider the situation if the government were required to pay an amount of $1,000 at the start of the project in addition to a final transfer price of $4,800 at the end. It is obvious that this is an inferior arrangement (project D) for the government than the previous one (project C) where no up front payment is required. However, according to the IRR criterion it is a much improved project with an IRR of now 4%. In the final case, project E, the situation for the government is made worse by requiring an up front fee of $1,325 in year 0, in addition to the transfer price of $4,800 in year 4. Yet according to the IRR criteria the arrangement is more attractive with an IRR of 20%. None of these situations are unusual. Such patterns in the case flow are common in project finance arrangements. However, we find that the IRR is a highly unreliable measure of the financial attractiveness of such arrangement when irregular cash flows are likely to exist. 4.3.3 Benefit-Cost Ratio Criterion The benefit-cost ratio (BCR), sometimes referred to as the profitability index, is the ratio of the present value of the cash inflows (or benefits) to the present value of the cash outflows (or costs) using the opportunity cost of funds as the discount rate: PV of Cash Inflows (or Benefits) BCR = PV of Cash Outflows (or Costs ) Using this criterion, we would require that for a project to be acceptable the ratio (BCR) must have a value greater than 1. Also, for choices among mutually exclusive projects the rule would be to choose the alternative with the highest benefit-cost ratio. This criterion, however, may give us an incorrect ranking of projects if the projects differ in size. Consider the following cases of mutually exclusive Projects A, B and C: 18 CHAPTER 4: Project A Project B Project C PV investment costs $1.0 million $8.0 million $1.5 million PV benefits $1.3 million $9.4 million $2.1 million NPV of net benefits $0.3 million 1.4 million $0.6 million BCR 1.3 1.175 1.4 In this example, if the projects were ranked according to their benefit-cost ratios we would choose project C. However, since the NPV of project C is less than the NPV of project B, the ranking of the projects should lead us to choose project B and thus, the benefit-cost ratio criterion would lead to an incorrect investment decision. The second problem associated with the use of the benefit-cost ratio, and perhaps its most serious drawback, is that the benefit-cost ratio of a project is sensitive to the way in which costs are defined in setting out the cash flows. For example, if a good being sold is taxed at the manufacturer's level, the cash flow item for receipts could be recorded either net or gross of sales taxes. In addition, costs can also be recorded in more than one way. Suppose that a project has the recurrent costs, the benefit-cost ratio will be altered by the way these costs are accounted for. All the costs and benefits are discounted by the cost of capital at 10 percent and expressed in dollars. Project D Project E PV investment costs $1,200 $100 PV gross benefits $2,000 $2,000 PV recurrent costs $500 $1,800 If the recurrent costs are netted out cash inflows, Project E would be preferred to Project D according to the benefit-cost ratio criterion. This is because BCRD = (2,000-500)/1,200 = 1.25 and BCRE = (2,000-1,800)/100 = 2.00. However, if the recurrent costs are instead added to the present value of cash outflows, then Project D appears to be more attractive than 19 CHAPTER 4: Project E because BCRD = 2,000/(500+1,200) = 1.18 and BCRE = 2,000/(1,800+100) = 1.05. Hence, the ranking of the two projects can be reversed depending on the treatment of recurrent costs in the calculation of the benefit-cost ratio. On the other hand, the net present value of a project is not sensitive to the way the costs are treated and therefore, it is far more reliable than the benefit-cost ratio as a criterion for project selection. 4.3.4 Pay-Out or Pay-Back Period The pay-out or pay-back period measures the number of years it will take for the net cash flows to repay the capital investment. Project with the shortest pay-back period is preferred. It is easy to use in making investment decisions. The criterion puts a large premium on projects which have a quick pay-back and thus it has been a popular criterion in making business investment choices.2 Unfortunately, it may provide the wrong results especially in the cases of investments with a long life where future net benefits are known with a considerable degree of certainty. In its simplest form the pay-out period measures the number of years it will take for the undiscounted net cash flows to repay the investment. A more sophisticated version of this rule compares the discounted benefits over a number of years from the beginning of the project with the discounted investment costs. An arbitrary limit may be set on the maximum number of years allowed and only those investments having enough benefits to offset all investment costs within this period will be acceptable. The use of the pay-back period as an investment criterion by the private sector is often a reflection of a high level of risks, especially political risk. Suppose a private venture is only expected to receive a subsidy or allowed to operate only as long as the current government is in power. In such circumstances for a private investor to go ahead with this project it is critical that its pay-back period be shorter than the expected tenure of the government. 2 This criterion has similar characteristics the loan life cover ratio used by bankers. This might explain its continued use in business decision making. 20 CHAPTER 4: The implicit assumption of the pay-out period criterion is that benefits accruing beyond the time set as the pay-out period are so uncertain that they should be neglected. It also ignores any investment costs that might occur beyond that date, such as the landscaping and replanting costs arising from the closure of a strip mine. While the future is undoubtedly more uncertain than the present, it is unrealistic to assume that beyond a certain date the net benefits are zero. This is particularly true for long term investments such as bridges, roads and dams. There is no reason to expect that all quick yielding projects are superior to long- term investments. Let us consider the example of two projects illustrated in Figure 4.3. Both projects are assumed to have identical capital costs (i.e., Ca = Cb). However, the benefit profiles of the two projects are such that project A has greater benefits than project B in each period until period t*. From period t* to tb, project A yields zero net benefits, but project B yields positive benefits as shown in the shaded area. With a pay-out period of t* years, project A will be preferred to project B because for the same costs it yields larger benefits earlier. However, in terms of net present value of the overall project, it is very likely that project B, with its greater benefits in later years will be significantly superior. In such a situation, the pay-back period criterion would give the wrong recommendation for choice among investments. 21 CHAPTER 4: Figure 4.3 Comparison of Two Projects with Differing Lives using Pay-Out Period Ba Bt-Ct Bb 0 Ca=Cb t* tb Pay out Pay out period period for for Project b project a 4.3.5 Debt Service Coverage Ratios The debt service coverage ratio is a key factor in determining the ability of a project to pay its operating expenses and to meet its debt servicing obligations. This is used by bankers who want to know annual debt service coverage ratio of a project on a year-to-year basis as well as a summary ratio of the loan life cover ratio.3 The annual debt service capacity ratio (ADSCR) is the ratio of the annual net cash flow of the project over the amount of debt repayment due. It is calculated on a year to year basis as follows: ADSCRt = [ANCFt / (Annual Debt Repaymentt)] where ANCFt is annual net cash flow of the project before financing for period t, and Annual Debt Repaymentt is annual interest expenses and principal repayment due in the specific period t of the loan repayment period. 3 Yescombe, E.R., Principles of Project Finance, London: Academic Press, (2002). 22 CHAPTER 4: The overall project’s loan life cover ratio (LLCR) is calculated as the present value of net cash flows over the present value of loan repayments from the current period t to the end period of loan repayment: LLCRt = PV(ANCF t to end year of debt) / PV(Annual Debt Repayment t to end year of debt) where PV(ANCF t to end year of debt) and PV(Annual Debt Repayment t to end year of debt) are the sum of the present values of annual net cash flows and annual debt repayments, respectively, over the period of the current year t to the end of loan repayment. The discount rates used are the interest rate being paid on the loan financing. The LLCR tells the banker if there is enough cash from the project to make bridge-financing in one or more specific periods when there is inadequate cash flow to service the debt. Let us consider the example shown in Table 4.3, where an investment of $2 million is being undertaken with a proposal for financing that includes a loan of $1 million bearing a nominal interest rate of 15%, and a repayment period of 5 years (with an equal repayment) beginning in one year after the loan is given. The required rate of return on equity is assumed at 20%. Table 4.3 Calculation of Annual Debt Service Coverage Year 0 1 2 3 4 5 6 7 8 9 10 Net Cash -2,000,000 320,000 320,000 360,000 440,000 380,000 100,000 200,000 480,000 540,000 640,000 Flow Debt 0 298,316 298,316 298,316 298,316 298,316 Repayment ADSCR 1.07 1.07 1.21 1.47 1.27 Table 4.3 shows the annual cash flows net of operating expenses along with the annual debt service obligations. The project is not attractive to the banker since the ADSCRs are low. It is only 1.07 in years 1 and 2 with no single years giving a debt service ratio of more than 1.47. This means that there could be a cash shortfall and an inability to pay the lenders the principal repayment and interest that is due. 23 CHAPTER 4: The question now is how might we improve the annual debt service capacity ratios? There are fundamentally only three alternatives: – decrease the interest rate on the loan; – decrease the amount of debt financing; and – increase the duration of the loan repayment. (a) Decrease the Interest Rate on the Loan If the terms of the loan can be restructured so that the annual ratios look better, maybe it will be attractive to the banker to provide financing. Table 4.4 shows the effect of obtaining a concessional interest rate, or interest rate subsidy for the loan. In this case we assume that a 1 percent interest rate can be obtained for the full five-year period that the loan is outstanding. The ADSCRs are much larger now, never becoming less than 1.55, however, such a financing subsidy might be very difficult to obtain. Table 4.4 Decrease the Interest Rate on the loan Year 0 1 2 3 4 5 6 7 8 9 10 Net Cash -2,000,0000 320,000 320,000 360,000 440,000 380,000 100,000 200,000 480,000 540,000 640,000 Flow Debt 0 206,040 206,040 206,040 206,040 206,040 Repayment ADSCR 1.55 1.55 1.75 2.14 1.84 (b) Decrease the Amount of Debt Financing Table 4.5 shows the case where the amount of the loan is reduced from $1 million to $600 thousand. In this case we find the ADSCRs increase greatly so now they never fall below a value of 1.79. Since the amount of the annual repayment of that loan becomes smaller (equity financing is increased), the ability of the project to service the debt becomes much more certain. 24 CHAPTER 4: Table 4.5 Decrease the amount of borrowing by increasing equity to $1.4 million Year 0 1 2 3 4 5 6 7 8 9 10 Net Cash -2,000,000 320,000 320,000 360,000 440,000 380,000 100,000 200,000 480,000 540,000 640,000 Flow Debt 0 178,989 178,989 178,989 178,989 178,989 Repayment ADSCR 1.79 1.79 2.01 2.46 2.12 (c) Increase the Duration of the Loan Repayment Table 4.6 shows the case of increasing the duration of the loan from 5 to 10 years. If a financial institution is available to extend a loan for such a long period, we find that the annual debt service obligations fall greatly. The result is that except for years 6 and 7 the annual debt service obligation never falls below 1.61. In years 6 and 7 the annual debt service coverage ratios are projected to be only 0.50 and 1.00, respectively. This is due to a projected fall in the net cash flows that might arise because the need to make reinvestments or heavy maintenance expenditures in those years. Table 4.6 Increase the duration of loan repayment Year 0 1 2 3 4 5 6 7 8 9 10 Net Cash -2,000,000 320,000 320,000 360,000 440,000 380,000 100,000 200,000 480,000 540,000 640,000 Flow Debt 0 199,252 199,252 199,252 199,252 199,252 199,252 199,252 199,252 199,252 199,252 Repayment ADSCR 1.61 1.61 1.81 2.21 1.91 0.50 1.00 2.41 2.71 3.21 The question now is whether the project has sufficiently strong net cash flows in the years following years 6 and 7 to warrant the financial institution providing the project bridge financing for these two years. This additional new loan would be repaid from the surplus net cash flows in later years. To answer the question, the LLCR is the appropriate criteria to determine if the project should qualify for bridge financing. The present value of the net cash flows remaining until the end of the debt repayment period, discounted at the loan interest rate, is divided by the present value of the debt repayments for the remaining duration of the 25 CHAPTER 4: loan. It is also discounted at the loan interest rate. These estimations are presented in Table 4.7. Table 4.7 Is Bridge Financing an option? Year 0 1 2 3 4 5 6 7 8 9 10 Net Cash -2,000,000 320,000 320,000 360,000 440,000 380,000 100,000 200,000 480,000 540,000 640,000 Flow Debt 0 199,252 199,252 199,252 199,252 199,252 199,252 199,252 199,252 199,252 199,252 Repayment ADSCR 1.61 1.61 1.81 2.21 1.91 0.50 1.00 2.41 2.71 3.21 NPV of 2,052,134 1,991,954 1,922,747 1,797,159 1,560,733 1,357,843 1,446,519 1,433,497 1,096,522 640,000 NCF PV of Debt Repayments 1,150,000 1,093,360 1,028,224 953,318 867,176 768,112 654,189 523,178 372,515 199,252 LLCR 1.78 1.82 1.87 1.89 1.80 1.77 2.21 2.74 2.94 3.21 We find that the LLCRs for years 6 and 7 are 1.77 and 2.21, respectively. This indicates that there is likely to be more than adequate net cash flows from the project to safely repay the bridge financing that is needed to cover the likely shortfalls in cash during years 6 and 7. If for some reason the banks were not comfortable providing the bridge financing needed to cover the cash flow shortfalls during year 6 and 7, they might instead require the firm to build up a debt service reserve account during the first five years of the loan’s life from the cash that is over and above the requirements for servicing the debt. Alternatively, the banker may require the debt service reserve account to be immediately financed out of the proceeds of the loan and equity financing. This debt service reserve account would be invested in short-term liquid assets that could be drawn down to meet the financing requirements during years 6 and 7. It is sometimes the case that the financial institutions servicing the loan will stipulate that if the annual debt service capacity ratio ever falls below a certain benchmark, say 1.8, then it must stop paying dividends to the owners of the equity, until a certain size of sinking fund is 26 CHAPTER 4: created, or a certain amount of the loan is repaid. In this way the lenders are protected from what might become an even more precarious situation in the future. The actual benchmark requirements for the ADSCRs and the overall project’s LLCRs will depend on the business and financial risk associated with a particular sector and the specific enterprise. The sensitivity of the net cash flows from the project to movements in the economy’s business cycle will be an important determinant of what are the adequate ratios for any specific project. The existence of creditable government guarantees for the repayment of interest and principal will also serve to lower the benchmark values of the debt service coverage ratios for a project. 4.3.6 Cost Effectiveness Analysis4 This is an appraisal technique primarily used in social projects and programs, and sometimes in infrastructure projects, where it is difficult to quantify benefits in monetary terms. For instance, when there are two or more alternative approaches to improving the nutrition levels among children in a community, the selection criterion could simply be to select the alternative, which has the least cost. Similarly, when there are two alternatives to provide irrigation facilities to farmers in a certain region, say a canal system and a tube well network, and they cover the same area and provide the same volume of water in a year. The benefits in such cases are treated as identical and, therefore, it is not necessary to quantify them or to place a monetary value on them if the problem is to select the project that will produce these benefits at the lowest possible cost. This approach is also useful for choosing among different technologies for providing the same services, for example, when there are two alternative technologies related to supply of drinking water or generation of electricity. When the same quantity and quality of water per annum can be delivered using pipes of different diameters and the smaller pipe involves 4 See Curry, S. and Weiss, J., Project Analysis in Developing Countries, St. Martins Press, (1993) and Ginttinger J. P., Economic Analysis of Agricultural Projects, John Hopkins University Press, (1994) for discussion of Cost Effectiveness Analysis. 27 CHAPTER 4: greater pumping costs but has lower capital costs, a cost effectiveness analysis may be used for making a choice. Similarly, when there are two alternative ways to generate electricity, one with lower investment cost but higher operating expenses (single cycle versus combined cycle technologies). Again, if the decision has been made to provide this service, there is no need to calculate the benefit in monetary terms. The cost effectiveness analysis may be used in all such cases for selecting the best project or the best technology. If the amount of benefits of the alternative projects generate differ, and if the benefits cannot be measured in monetary terms but can be physically quantified, a pure cost-effectiveness of a project can be calculated by dividing the present value of total costs of the project by the present value of a non-monetary quantitative measure of the benefits it generates. The ratio is an estimate of the amount of costs incurred to achieve a unit of the benefit from a program. For example, in a health project, what is the amount of costs expressed in dollars incurred in order to save a person’s life? Presumably, there are alternative ways to save a life and what are their costs? The analysis does not evaluate benefits in monetized terms but is an attempt to find the least-cost option to achieve a desired quantitative outcome. In applying the cost effectiveness approach, the present values of costs have to be computed. While using the cost effectiveness analysis, it is important to include all external costs such as waiting time, coping costs, enforcement costs, regulatory costs, compliance costs in the case of health care, offset by the salvage values at the end of the projects and to choose the discount rate carefully. The preferred outcome will often change with a change in the discount rate. The pure cost-effectiveness analysis can be extended to more sophisticated and meaningful ways of measuring benefits. A quantitative measure can be made by constructing a composite index of two or more benefit categories, including quantity and quality. For example, the cost utility analysis (CUA) in healthcare use the “quality-adjusted life-years” (QALY) as a measure of benefits. The QALY measure integrates two dimensions of health improvement; one is the additional years of life (reduction in mortality), and the other is quality of life (morbidity) during these years. On the basis of the costs incurred, expressed in 28 CHAPTER 4: dollars, the decision-maker would still choose the option with the least cost per QALY achieved by the project or the program.5 Cost utility analysis attempts to include some of the benefits excluded from the pure cost-effective analysis, hence moving it a step closer to a full cost benefit analysis. One should be aware of some of the shortcomings inherent in the cost-effectiveness approach. It is a poor measure of consumers’ willingness to pay principle because there is no monetary value placed on the benefits. Furthermore in the calculation of cost-effectiveness, the numerator does not take into account the scale of alternative options. Nevertheless, the cost-effectiveness ratio is still a very useful criterion for selection of alternative options when the benefits cannot be monetized. 4.4 Conclusion This chapter has first described the concept of time value of money and the proper use of the discount rate in project appraisal. We have reviewed six important criteria used by various analysts for judging the expected performance of investment projects. While each one may have its own merit in specific circumstances, the net present value criterion is the most reliable and satisfactory one for both the financial and the economic evaluation. To bankers or other financial lending institutions, measurements of the annual debt service coverage ratio and loan life cover ratio are the key factors for them to determine whether the project can generate enough cash from the project to meet the debt service obligations before financing of the project should be approved. We have also discussed the criterion in which the benefits of a project or a program cannot be expressed in monetary values in a meaningful way, a cost-effectiveness analysis should be carried out to assist in making welfare improving investment decisions. 5 See, e.g., Garber, A.M. and Phelps, C.E., “Economic Foundations of Cost-effectiveness Analysis”, Journal of Health Economics, 16, (1997. 29 CHAPTER 4: REFERENCES Boardman, A.E., Greenberg, D.H., Vining, Aidan R., and Weimer, D.L., Cost-Benefit Analysis, Concepts and Practice, Third Edition, Upper Saddle River, New Jersey: Pearson Education, Inc. (2006). Curry, S. and Weiss, J., Project Analysis in Developing Countries, Second Edition, Palgrave Macmillan, (1999). Garber, A.M. and Phelps, C.E., “Economic Foundations of Cost-effectiveness Analysis”, Journal of Health Economics, Vol. 16, No. 1, (February 1997), pp. 1-31. Ginttinger J. P., Economic Analysis of Agricultural Projects, John Hopkins University Press, (1994). Gitman, L.J., Principles of Managerial Finance, Twelfth Edition, Boston: Pearson Prentice Hall, (2009). Gramlich, E.M., A Guide to Cost-Benefit Analysis, Englewood Cliffs, New Jersey: Prentice Hall, (1997). Ley, E., “Cost-benefit Analysis: Evaluation Criteria (Or: “Stay away from the IRR”)”, paper prepared for the World Bank, (November 2007). Pohl, G. and Dubravko, M., “Project Evaluation and Uncertainty in Practice: A Statistical Analysis of rate-of-Return Divergences of 1,015 World Bank Projects”, The World Bank Economic Review, Vol. 6, No. 2, (May 1992), pp. 255-277. Walker, C. and Smith, A.J., Privatized Infrastructure: the Build Operate Transfer Approach, London: Thomas Telford Publications, (1996). Yescombe, E.R., Principles of Project Finance, London: Academic Press, (2002). 30