Chapter Five. Scale, Timing, Length, and Interdependencies in Project Selection

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1 Chapter Five Scale, Timing, Length, and nterdependencies in Project Selection 5.1 ntroduction n the previous chapter, it was concluded that a project s net present value (NPV) is the most important criterion for financial and economic evaluation. The NPV criterion requires that only projects with a positive NPV are approved. The next step is to endeavour to maximize the NPV in order to extract as much value from the project as possible. The aim should be to maximize the NPV of incremental net cash flows or net economic benefits. Of course, such optimization should not be pursued blindly, as it may have repercussions for other stakeholders that need to be considered in the final decision-making. Project analysts often encounter a range of other important considerations. These include changes in project parameters, such as the scale of investment, the date of initiation of a project, the length of project life, or interdependencies of project components. Each of these is addressed in this chapter using the criterion of a project s NPV. 5.2 Determination of Scale in Project Selection Projects are rarely, if ever, constrained by technological factors to a unique capacity or scale. Thus, one of the most important decisions to be made in the design of a project is the selection of the scale to which a facility should be built. n too many cases, scale selection has been treated as if it were a purely technical decision, neglecting its financial or economic aspects. When financial or economic considerations have been neglected at the design stage, the scale to which the project is built is not likely to be the one that would maximize the NPV. Thus, in addition to Chapter Five 123

2 technological factors, the size of the market, the availability of project inputs, and the quality of manpower, etc. will also have a role to play. The most important principle for selecting the best scale of a project (e.g., height of an irrigation dam or size of a factory) is to treat each incremental change in its size as a project in itself. An increase in the scale of a project will require additional expenditures and is likely to generate additional expected benefits over and above those that would have been produced by the project at its previous size. Using the present value of the incremental benefits and the present value of the incremental costs, the change in NPV stemming from changing scales of the project can be derived. n Figure 5.1, the cash flow profiles of a project are shown for three alternative scales. C 1 and B 1 denote the expected costs and benefits if the project is built at the smallest scale relevant for this evaluation. f the project is built at one size larger, it will require additional expenditure of C 2. Therefore, the total investment cost of the project at its expanded scale is (C 1 + C 2 ). t is also anticipated that the benefits of the project will be increased by an amount of B 2, implying that the total benefits from this scale of investment will now be (B 1 + B 2 ). A similar relationship holds for the largest scale of the project. n this case, additional expenditures of C 3 are required, and extra benefits of B 3 are expected. The total investment costs for this scale are (C 1 + C 2 + C 3 ), and the total benefits (B 1 + B 2 + B 3 ). Figure 5.1: Net Benefit Profiles for Alternative Scales of a Facility The goal is to choose the scale that has the highest NPV. f the present value of (B 1 C 1 ) is positive, it is a viable project. The next step 124 Scale, Timing, Length, and nterdependencies

3 is to determine whether the present value of (B 2 C 2 ) is positive. f the incremental NPV is positive, then this project at scale 2 is preferable to scale 1. This procedure is repeated until a scale is reached where the NPV of the incremental benefits and costs associated with a change in scale is negative. This incremental NPV approach helps in the choice of a scale that has maximum NPV for the entire investment. The NPV is the maximum because the incremental NPV for any addition to the scale of the project would be negative. f the initial scale of the project had a negative NPV but all the subsequent incremental NPVs for changes of scale were positive, it would still be possible for the overall project to have a negative NPV. Therefore, in order to select the optimum scale for a project, it is necessary to first ensure that the NPV of the overall project is positive, and that the NPV of the last addition to the investment to increase the project s scale is non-negative. This is illustrated in Figure 5.2, in which all project sizes between scale C and scale M yield a positive NPV. However, the NPV of the entire investment is maximized at scale H. After scale H, the incremental NPV of any expansion of the facility becomes negative. Therefore, the optimum scale for the project is H, even though the NPV for the entire project is still positive until scale M. Figure 5.2: Relationship between NPV and Scale The optimal scale of a project can also be determined by the use of the internal rate of return (RR), assuming that each successive increment Chapter Five 125

4 of investment has a unique RR. f this condition is met, the optimal scale of the facility will be the one at which the RR for the incremental benefits and costs equals the discount rate used to calculate the NPV of the project. This RR for the incremental investment required to change the scale of the project will be the marginal internal rate of return (MRR) for a given scale of facility. The relationships between the RR, the MRR, and the NPV of a project are shown in Figure 5.3. Figure 5.3: Relationships between the MRR, RR, and NPV From Figure 5.3, it can be observed that in a typical project, the MRR from incremental investments will initially rise as the scale is increased, but will soon begin to fall with further expansions. This path of the MRR will also cause the RR to rise for the initial ranges of scale and then to fall. At some point, the RR and the MRR must be equal and then change their relationship to each other. Prior to the point S 1 in Figure 5.3, the MRR of the project is greater than the RR: here, expansions of scale will cause the overall RR of the project to rise. At scales beyond S 1, the MRR is less than the RR: in this range, expansions of scale will cause the overall RR to fall. 126 Scale, Timing, Length, and nterdependencies

5 The point at which the RR equals the MRR always corresponds to the scale at which the RR is maximized. However, it is important to note that this is not the scale at which the NPV of the project is likely to be maximized. The NPV of a project obviously depends on the discount rate. Only when the relevant discount rate is precisely equal to the maximum RR will S 1 be the optimal scale. f the relevant discount rate is lower, it pays to expand the project s scale up to the point where the MRR is equal to the discount rate. As shown for the case in which the discount rate is 10 percent, this scale yields the maximum NPV at a scale of S 2 in Figure 5.3. To illustrate this procedure for determining the optimal scale of a project, consider the construction of an irrigation dam that could be built at different heights. Because of the availability of water, the expectation would be that expansions of the scale of the dam would reduce the overall level of utilization of the facilities when measured as a proportion of its total potential capacity. The information is provided in Table 5.1. Table 5.1: Determination of Optimal Scale of rrigation Dam (dollars) Time Scales Costs Benefits NPV RR S 0 3, S 1 4, S 2 5, S 3 6, S 4 7, S 5 8, Time Changes ncremental Chang in Scales Costs Benefits e in MR NPV R S 0 3, S 1 S 0 1, S 2 S 1 1, S 3 S 2 1, S 4 S 3 1, S 5 S 4 1, Notes: Discount rate (opportunity cost of funds) = 10 percent. The depreciation rate of the dam is assumed to be zero. Chapter Five 127

6 n this example, the NPV can be calculated for each scale of the dam from S 0 to S 5. Thus, the NPV for S 0 is 500; for S 1 S 0, it is 400; for S 2 S 1, 500; for S 3 S 2, 300; for S 4 S 3, 50; and for S 5 S 4, Applying the above rule for determining the optimal scale would lead to scale S 4 being chosen because beyond this point, additions to scale contribute negatively to the overall NPV of the project. At scale S 4, the NPV of the project is +750; at scale S 3, it is +700; and at S 5, it is Therefore, the NPV is maximized at S 4. f the project is expanded beyond scale 4, the NPV begins to fall, even though at scale S 5 the RR of the entire project is still (which is greater than the discount rate of 0.10). However, the MRR is only 0.09, placing the marginal return from the last addition to scale below the discount rate. 5.3 Timing of nvestments One of the most important steps in the process of project preparation and implementation is to decide on the appropriate time at which the project should start. This decision becomes particularly difficult for large indivisible projects, such as infrastructure investments in roads, water systems, and electricity generation facilities. f these projects are built too soon, a large amount of idle capacity will exist. n such cases, the forgone return (that would have been realized if these funds had been invested elsewhere) might be higher in value than the benefits gained in the first few years of the project s life. Conversely, if a project is delayed for too long, shortages of goods or services will persist and the output forgone will be greater than the alternative yield of the funds involved. Whenever a project is undertaken too early or too late, its NPV will be lower than the level it could have been if it had been developed at the right time. The NPV of a project may still be positive, but it will not be at its maximum. The determination of the correct timing of investment projects will be a function of how it is anticipated that future benefits and costs will move in relation to their present values. Situations in which the timing of investment projects becomes an important issue can be classified into four different cases. 1 For perpetuity, the RR can be calculated as the ratio of annual income to initial investment. 128 Scale, Timing, Length, and nterdependencies

7 Case A The benefits of the project are a continuously rising function of calendar time, but investment costs are independent of calendar time. Case B The benefits and investment costs of the project are rising with calendar time. Case C The benefits are rising and then falling with calendar time, while the investment costs are a function of calendar time. Case D The benefits and investment costs do not change systematically with calendar time. Case A: Potential Benefits Are a Rising Function of Calendar Time This is the case in which the benefits net of operating costs are continuously rising through time, and costs do not depend on calendar time. For example, the benefits of a road improvement project rise because of the growth in demand for transportation between two or more places. t can thus be expected that as population and income grow, the demand for the road will also increase through time. f the project s investment period ends in Period t, it can be assumed that its net benefit stream will start the year after construction and will rise continuously thereafter. This potential benefit stream is illustrated by the curve B(t) in Figure 5.4. f construction were postponed from t 1 to t 2, lost benefits amount to B 1, but the same capital in alternative uses yields rk, where K denotes the initial capital expenditure and r denotes the opportunity cost of capital for one period. Postponing construction from t 1 to t 2 thus yields a net gain of ADC. Similarly, postponing construction from t 2 to t 3 yields a net benefit of CDE. n this situation, the criterion for ensuring that investments are undertaken at the correct time is quite straightforward. f the present value of the benefits that are lost by postponing the start of the project from Period t to Period t+1 is less than the opportunity cost of capital multiplied by the present value of capital costs as of Period t, the project should be postponed because the funds would earn more in the capital market than if they were used to start the project. On the other hand, if the forgone benefits are greater than the opportunity cost of the investment, the project should proceed. n short, if rk t > B t+1, the decision should be to postpone the project; and if rk t < B t+1, the project should go ahead. Here t is the period in which the project is to begin, K t is the present value of the investment costs of the project as of Period t, Chapter Five 129

8 and B t+1 is the present value of the benefits lost by postponing the project for one period from t to t 1. Figure 5.4: Timing of Projects: Benefits Are Rising, but nvestment Costs Are ndependent of Calendar Time Rules: rk t > B t+1 Postpone rk t < B t+1 Start Case B: Both nvestment Costs and Benefits Are a Function of Calendar Time n this case, as illustrated in Figure 5.5, the investment costs and benefits of a project will grow continuously with calendar time. Suppose the capital cost is K 0 when the project is started in Period t 0 and the costs will become K 1 if it is started in Period t 1. The change in investment costs must be included in the calculations of optimum timing. When the costs of constructing a project are greater in Period 1 than in Period 0, there is an additional loss caused by postponement of (K 1 K 0 ), as shown by the area FGH in Figure Scale, Timing, Length, and nterdependencies

9 Figure 5.5: Timing of Projects: Both Benefits and nvestment Costs Are a Function of Calendar Time Rules: rk t > B t+1 + (K t+1 K t ) Postpone rk t < B t+1 + (K t+1 K t ) Start n Case A, when benefits are a positive function of calendar time, the decision rule for the timing of investments is to postpone if rk 0 > B 1 and to proceed as soon as B t+1 > rk t. Now, when the present value of the investment costs changes with the timing of the starting date, the rule is slightly modified: if rk 0 > [B 1 + (K 1 K 0 )], postpone the project; otherwise, undertake the project. The term (K 1 K 0 ) represents the savings of the increase in capital costs by commencing the project in Period t 0 instead of t 1. The rule shows a comparison of the area t 1 DEt 2 with (t 1 ACt 2 + FGH). Hence, if investment costs are expected to rise in the future, the optimal option would be for the project to be undertaken earlier than if investment costs remained constant over time. Case C: Potential Benefits Rise and Fall According to Calendar Time n the case in which the potential benefits of the project are also a function of calendar time, but are not expected to grow continuously Chapter Five 131

10 through time, at some date in the future they are expected to decline. For example, the growth in demand for a given type of electricity generation plant in a country is expected to continue until it can be replaced by a cheaper technology. As the alternative form of technology becomes cheaper and more easily available, it is expected that the demand faced by the initial plant will decline through time. f the net benefits from an electricity generation plant are directly related to the volume of production it generates, it would be expected that the pattern of benefits would appear similar to B(t) in Figure 5.6. Figure 5.6: Timing of Projects: Potential Benefits Rise and Decline with Calendar Time Rules: Start if rk ti < B ti+1 Stop if rsv tn B tn+1 SV tn+1 > 0 Do project if: NPV t i = t nå B i SV - K ti + tn > 0 i=t i+1 Do not do project if: NPV t i = (1+ r) i-t i (1+ r) t n -t i t nå B i SV - K ti + tn < 0 i=t i+1 (1+ r) i-t i (1+ r) t n -t i 132 Scale, Timing, Length, and nterdependencies

11 f the project with present value of costs of K 0 is undertaken in Period t 0, its first-year benefits will fall short of the opportunity cost of the funds shown by the area ABC. The correct point to start the project is t 1, when rk t1 < B t2, and if the following project s NPV (measured by the present value of the area under the B(t) curve minus K 1 ) is positive: NPV K /(1 r) n t2 [ B t /(1 r) ] t is obviously essential that this NPV be positive in order for the project to be worthwhile. The above formula assumes that the life of the project is infinite, or that after some time, its annual benefit flows fall to zero. nstead of lasting for its anticipated lifetime, the project could be abandoned at some point in time, with the result that a one-time benefit is generated, equal to its scrap value, SV. n this case, it pays to keep the project in operation only so long as B tn+1 > rsv tn SV tn+1, so it would make sense to stay in business during t n+1. f B tn+1 < rsv tn SV tn+1, it would make more sense to shut down operations at the end of t n. n practice, there are five special cases in relation to scrap value and change in scrap value of a project: t SV > 0 and ΔSV < 0, e.g., machinery SV > 0 but ΔSV > 0, e.g., land SV < 0 but ΔSV = 0, e.g., a nuclear power plant SV < 0 but ΔSV > 0, e.g., severance pay for workers SV < 0 and ΔSV < 0, e.g., clean-up costs n general, a project should be undertaken if the following condition is met: NPV t i = t nå B i SV tn > 0 (5.1) i=t i+1 - K (1+ r) i-t ti + i (1+ r) t n -t i f this condition cannot be met, and if NPV t i = t nå B i SV - K ti + tn < 0 i=t i+1 (1+ r) i-t i the project should not be undertaken. (1+ r) t n -t i Chapter Five 133

12 Case D: The Costs and Benefits Do Not Change Systematically with Calendar Time This is perhaps the most common situation, in which there is no systematic movement in either costs or benefits with respect to calendar time. As illustrated in Figure 5.7, if a project is undertaken in Period t 0, its profile begins with investment costs of K 0, followed by a stream of benefits shown as the area t 1 ABt n. Alternatively, if it is postponed for one period, investment costs will be K 1, and benefits will be t 2 CDt n+1. n this case, the optimal date to start the project is determined by estimating the NPV of the project in each instance and choosing the time to start the project that yields the highest NPV. t is important to note that in determining the timing of the project, the date to which the NPVs are calculated must be the same for all cases, even though the period in which the projects are to be initiated varies. Figure 5.7: Timing of Projects: Benefits and Costs Do Not Change Systematically with Calendar Time 134 Scale, Timing, Length, and nterdependencies

13 5.4 Adjusting for Different Lengths of Life f there is no budget constraint, and if a choice must be made between two or more mutually exclusive projects, investors seeking to maximize net worth should select the project with the highest NPV. f the mutually exclusive projects are expected to have continuously high returns over time, it is necessary to consider the lengths of life of the two or more projects. The reason for wanting to ensure that mutually exclusive projects are compared over the same span of time is to give them the same opportunity to accumulate value over time. One way to think about the NPV is as an economic rent that is earned by a fixed factor of production. n the case of two mutually exclusive projects, for example, the fixed factor could be the building site, a right-of-way, or a licence. That fixed factor should have the same amount of time to generate economic rents, regardless of which project is chosen. What is required is a reasonable method of equalizing lengths of life that can be applied. This is elaborated with the help of the following two examples. Example 1 Consider two mutually exclusive projects, Project A (three years) and Project B (four years), with the same scale of investment, and the net cash flows as shown in Table 5.2. All the net cash flows are expressed in thousands of dollars, and the cost of capital is 10 percent. Table 5.2: Net Cash Flows for Projects with Different Lengths of Life (thousand dollars) Time Period t 0 t 1 t 2 t 3 NPV@10% Net cash flows of Project A 10,000 6,000 6, Net cash flows of Project B 10,000 4,000 4,000 4, f the differences in the lengths of life were overlooked, Project B would be selected because it has the higher NPV. However, this would run the risk of rejecting the potentially better Project A with the shorter life. One approach to addressing this problem is to determine whether the projects could be repeated a number of times (not necessarily the same Chapter Five 135

14 number of times for each project) in order to equalize their lives. To qualify for this approach, both projects must be supra-marginal (i.e., have positive NPVs) and should be repeatable at least a finite number of times. Assume that Projects A and B above meet these requirements. f Project A was repeated three times and Project B twice, both projects would have a total operating life of six years, as shown in Table5.3. n year t 6, both projects can start up again, but there is no need to repeat this procedure. The construction of the repeated projects is initiated so as to maintain a level of service. For example, construction for the second Project B begins in year t 3 so that it is ready to begin operations when the first Project B stops providing a service. Given the equal lengths of life for the repeated projects, they can now be compared on the basis of their NPV: NPV of NPV of 410 Project A s repeats 410 (1.1) 410 (1.1) ' Project B' s repeats (1.1) 1,029 Given an equal opportunity to earn economic rents, Project A has a higher overall NPV and should be considered the more attractive project. Table 5.3: Net Present Value for Repeating Projects Time t 0 t 1 t 2 t 3 t 4 t 5 t 6 Project A s NPV for each repeat Project B s NPV for each repeat Example 2 This example refers to the case in which a choice is to be made between mutually exclusive projects representing different types of technology with different lengths of life. 136 Scale, Timing, Length, and nterdependencies

15 How can a decision be made between the two technologies using the NPV criterion? Suppose that the present value of the costs of Project [PV 0 ( C 0 )] is $100 and the present value of its benefits [PV 0 ( B 1 5 )] is $122. Similarly, the present value of the costs of Project [PV 0 ( C 0 )] is $200 and that of its benefits [PV 0 ( B 1 8 )] $225. A comparison of the NPVs of the two projects suggests that Project is preferred to Project because the NPV of Project is $25, whereas that of Project is only $22. However, since these two projects represent two different types of technology with different lengths of life, the NPV of Project is biased upward. n order to make a correct judgment, it is necessary to make the projects comparable by either adjusting the lengths of life or calculating the annualization of net benefits. One option is to adjust Project to make it comparable to Project. The benefits for only the first five years of Project should be included, and its costs should be reduced by the ratio of the present value of benefits from Years 1 5 to Years 1 8. This is expressed as follows: NPV 0 = PV 0 ( B 5 1 ) PV 0 ( C 0 ) Chapter Five 137

16 Adj NPV 0 = PV 0 ( PV 1 ) PV 0 ( C 0 ) 0( B PV0 ( B B 5 Substituting in the values of costs and benefits of the two projects in the example gives: ) ) PV ( B 8) = $225, PV C ) = $200, PV B ) = $180 Hence, 0 0 ( 0 NPV 0 = $122 $100 = $22 NPV 0 Adj 0( 1 5 = $180 $200(180/225) = $180 $160 = $20 After the adjustment, the NPV of Project is greater than that of Project ; this means that Project is better. The second way of making the two projects comparable is to adjust the length of Project. t is necessary to calculate the NPVs of Project (adjusted) and Project. The NPV of Project can be adjusted by doubling its length of life. The benefits of Years 6 8 are then added to the benefits of Years 1 5. The costs are increased by the value of the costs to lengthen the project to Year 8, which is the present value of the costs in Year 5, reduced by the ratio of the benefits of Years 6 8 to the benefits of Years This adjustment can be expressed as follows: 138 Scale, Timing, Length, and nterdependencies

17 Adj NPV 0 = PV 0 ( B 5 1 ) PV 0 ( C 0 ) + PV 0 ( B 8 6 ) PV 0 ( C 5 ) PV 0( B6 PV0 ( B6 Substituting in the present values of costs and benefits of the two projects in our example gives: 8 10 ) ) Adj NPV 0 = $122 $100 + $60 $80(60/110) = $38.36 NPV 0 = $225 $200 = $25 Using this method, the NPV of Project is still greater than that of Project. Therefore, Project is preferred to Project. The third way is to compare the annualization of the net benefits of the two projects. For Project, the NPV is $22 over a five-year period. The annualized value of the benefits can be calculated as follows (European Commission, 2005): Annualized value = [$ ] / [1 ( ) 5 ] = $5.80 For Project, the NPV is $25 over an eight-year period. The annualized value of the benefits is: Annualized value = [$ ] / [1 ( ) 8 ] = $4.69 Again, the higher NPV of Project than those of Project is due to a longer time horizon. When they are normalized for time period, it is shown that Project is in fact preferred. 5.5 Projects with nterdependent and Separable Components An investment program will often contain several interrelated investments within a single project. t has sometimes been suggested that in such integrated projects, it is correct to evaluate the project as a whole and to bypass the examination of each of the sub-components. This argument is generally not correct. The analyst should attempt to break the project down into its various components and examine the incremental costs and benefits associated with each of the components in Chapter Five 139

18 order to determine whether they increase or decrease the NPV of the project. Suppose the task is to appraise a project to build a large storage dam, planned to provide hydroelectric power, irrigation water, and recreational benefits. Upon first examination of this project, it might appear that these three functions of the dam are complementary, so that it would be best to evaluate the entire project as a package. However, this is not necessarily the case. The irrigation water might be needed at a different time of the year than the peak demand for electricity. The reservoir might be empty during the tourist season if the water is used to maximize its value in generating electricity and providing irrigation. Therefore, maximizing the NPV of the whole package may mean that the efficiency of some of the individual components will be reduced. n this case, the overall project might be improved if one or more of the components were dropped from the investment package. n appraising such an integrated investment package, the first step is to evaluate each of the components as an independent project. Thus, the hydroelectric power project would be evaluated separately. The technology used in this case would be the most appropriate for this size of electricity dam without considering its potential as a facility for either irrigation or recreational use. Similarly, the uses of this water supply in an independent irrigation project and in an independent recreational development should each be appraised on their own merits. Next, the projects should be evaluated as combined facilities, such as an electricity-cum-irrigation project, an electricity-cum-recreational project, and an irrigation-cum-recreational project. n each of these combinations, the technology and operating program should be designed to maximize the net benefits from the combined facilities. Finally, the combined electricity, irrigation, and recreational projects are evaluated. Again, the technology and operating plans will have to be designed to maximize the net benefits from the combined facilities. These alternatives must then be compared to find the one that yields the maximum NPV. t is frequently the case that the project that ends up with the highest NPV is the one containing fewer components than was initially proposed by its sponsor. A common investment problem of the type that involves separable component projects arises when a decision is being made as to whether or not existing equipment should be replaced. When faced with this decision, there are three possible courses of action: (a) Keep the old asset and do not buy the new asset now. 140 Scale, Timing, Length, and nterdependencies

19 (b) Sell the old asset and purchase the new one. (c) Keep the old asset and, in addition, buy the new one. The present value of all future benefits that could be generated by the old asset (evaluated net of operating cost) will be denoted by B o and the liquidation or scrap value of the old asset, if sold, SV o. The present value of future benefits (net of operating costs) from the new asset will be expressed as B n and the present value of the investment costs for the new asset as C n. The combined benefits from the use of the old and new assets together will be denoted as B n+o. The first step is to appraise each of the three alternatives to determine which of them are feasible, i.e., which of the three generate positive NPVs. These comparisons are as follows: n order that alternative (a) be feasible, the present value of the future benefits from the old asset must exceed its liquidation value, i.e., B o SV o > 0. n order for alternative (b) to be feasible, the present value of the future benefits from the new asset must be higher than the present value of its investment costs, i.e., B n C n > 0. n order for alternative (c) to be feasible, the total benefits produced by both assets combined must be greater than the costs of the new investment plus the liquidation value of the old asset. n this case, the old asset is retained, to be used along with the new asset. This is expressed as B n+o (C n + SV o ) > 0. f each of the alternatives is feasible, a comparison must be carried out to determine which component or combination yields the greatest NPV. To determine whether or not to replace the old asset with the new one, it is necessary to calculate whether (B n B o ) (C n SV o ) is more or less than 0. f it is less than 0, the assets should not be exchanged. However, retaining the old asset while purchasing the new one would still be a viable option if (B n+o B n ) SV o > 0. This condition for retaining the two assets amounts to each one justifying itself as the marginal asset. Alternatively, if (B n B o ) (C n SV o ) < 0 and (B n+o B o ) C n < 0, the old facilities should continue to be used without any new investment. Finally, if the conditions are (B n B o ) (C n SV o ) > 0 and (B n+o B n ) SV o < 0, the old asset should be replaced with the new one. One way to describe these comparisons is to define (B n+o B o ) as B n/o and (B n+o B n ) as B o/n. n this notation, B n/o is the incremental benefit Chapter Five 141

20 of the new asset in the presence of the old, and B o/n is the incremental benefit of the old asset in the presence of the new. The condition that is required for both assets to be present in the final package is that both B n/o > C n and B o/n > SV o. This means that each component must justify itself as the marginal item in the picture. This same principle governs in all cases where one has to deal with separable components of a project. Each separable component must justify itself as a marginal or incremental part of the overall project. The careful examination of the alternative components of a potentially integrated project is thus an important task in the preparation and appraisal phase of a project. Failure to do this may mean that potentially valuable projects are not implemented because they were evaluated as part of a larger, unattractive package. On the other hand, wasteful projects might be implemented because they have been included in a larger integrated project that as a whole is worthwhile, but could be improved if the wasteful components were eliminated. Complementarity and Substitutability among Projects Once project analysts start to consider the interrelations between projects, a substantial number of possibilities emerge. t is instructive to examine these possibilities in detail. Denoting PVB as present value of benefits and PVC as present value of costs, we have the following cases: PVB + PVB = PVB + Projects and are independents on the benefit side PVB + PVB > PVB + Projects and are substitutes on the benefit side PVB + PVB < PVB + Projects and are complements on the benefit side PVC + PVC = PVC + Projects and are independents on the cost side PVC + PVC > PVC + Projects and are complements on the cost side PVC + PVC < PVC + Projects and are substitutes on the cost side ndependent projects will not be dealt with here. Examples of such projects would be a spaghetti factory in San Francisco and a highway improvement on Long sland. One project essentially has nothing to do with the other. A case in which projects are substitutes on the benefit side has already been examined. t is impossible for a multi-purpose dam to generate, as a multi-purpose project, the sum total that could be achieved 142 Scale, Timing, Length, and nterdependencies

21 if the benefits of the same project (e.g., a dam), independently maximized for each separate purpose, were added together. Thus, multipurpose dams invariably entail substitution among the separate purposes. Complementarity on the benefit side is relatively easy to deal with. An automobile will not function on three wheels, or without a carburetor. Hence, the marginal benefit of adding the fourth wheel, or the carburetor, is enormous. A more subtle case of complementarity on the benefit side, well known in the literature of economics, is that of an apiary project together with an orchard. The presence of the orchard enhances the benefits of the apiary; the presence of the bees also enhances the value of the orchard. Whereas the separate purposes of multi-purpose dams are invariable substitutes on the benefit side, they are practically always complements on the cost side. To build one dam to serve several purposes will almost always cost less than the sum total of the two or more costs of building (at least hypothetically) separate dams to serve each of the separate purposes. Cases of substitutability on the cost side are harder to find, but they clearly exist. A dam project that will produce a larger lake will clearly be competitive with a highway whose natural route would cross the area to be flooded. The total costs of the two projects together will exceed the sum of the costs of the two, considered above. Similarly, a project to urbanize an area is likely to compound the costs of a highway project going through that area. Altogether, one must be alert to the possibilities of substitution and complementarity between and among projects. The underlying principle is always the same: maximize NPV. ts corollary is precisely the principle of separable components, as previously stated. Each separable component must justify itself as the marginal one. This becomes a problem where issues of substitutability are involved, though rarely so in cases of complementarity on both sides (benefits and costs). Perhaps the most interesting cases are those (like multi-purpose dams) in which complementarity on one side (in this case, the cost side) has to fight with substitutability on the other. 5.5 Conclusion The timing and scale of projects are often important considerations in project evaluation. This chapter has discussed the issues and presented some decision rules for projects according to the NPV criterion. n Chapter Five 143

22 addition, project analysts often face an issue of choosing between highly profitable, mutually exclusive projects with different lengths of life. Alternative approaches have been presented: either adjust the costs or benefits, or annualize the benefits in making a choice among mutually exclusive projects. n reality, an investment often contains several interrelated investments, either substitute or complementary. The concept of the NPV of the project s benefits and costs can provide a powerful tool for selecting a project with single component or combination of components. References European Commission mpact Assessment Guidelines (June 15) and Annexes to mpact Assessment Guidelines (June 15). Harberger, A.C Cost-Benefit Analysis of Transportation Projects, Project Evaluation Collected Papers. London: The Macmillan Press. Pacheco-de-Almeida, G. and P. Zemsky The Effect of Time-to-Build on Strategic nvestment under Uncertainty, RAND Journal of Economics 34(1), Szymanski, S The Optimal Timing of nfrastructure nvestment, Journal of Transport Economics and Policy 25(3), Scale, Timing, Length, and nterdependencies