8: Economic Criteria

Transcription

1 8.1 Economic Criteria Capital Budgeting 1 8: Economic Criteria The preceding chapters show how to discount and compound a variety of different types of cash flows. This chapter explains the use of those computations in selecting projects on an economic basis. It first provides an overview of capital budgeting in which a firm seeks to select projects today that will maximize its capital at the end of the planning horizon, its future total worth or FTW. This introduces concepts that allow developing models that identify which alternative from a mutually exclusive set of projects should be selected today. These models recognize that industrial projects reinvest returns in new projects, and each new project is like a savings account paying its own rate of return. This extends the material presented in the preceding chapters where all reinvestment occurred in a single account. 8.1 Capital Budgeting There are two basic categories of industrial projects. Mutually exclusive projects typically are different ways of accomplishing the same task, such as the best way to remove waste from a site. Only one alternative can be selected. Independent projects have nothing to do with each other. For example, one project might be to remove waste and another might be to install a new computer system. The only limit to the number of independent projects selected is the amount of capital available. The capital budgeting problem is to select independent projects subject to a budget constraint that maximize a firm s FTW. Example 8.1 Simple Capital Budgeting Problem Suppose that a company has five sets of mutually exclusive projects, and Table 8.1 shows the clear choices from each set. Project A is the best alternative from the first set, B the best from the second one, and so forth. These one-year projects are independent of each other, but they all are competing for inclusion in a capital budget of $10 (millions). It can be seen by inspection that selecting projects B and C provides the most money at the end of the planning horizon of one year. No other combination of projects satisfies the budget constraint and provides a larger FTW than $13.0. If there are 20, 30, or even hundreds of independent projects and a longer planning horizon, then there can be millions of combinations of projects that must be examined. Additionally, there is the question of how the returns from each project will grow when they are reinvested. This is a very complex optimization problem, so heuristics that produce good solutions with relatively little computational effort commonly are used. The following section discusses the popular internal rate of return heuristic. Internal Rate of Return Table 8.1 Independent Projects Prj. c 0 c 1 A B C D E Recall that the internal rate of return (IRR) of a project is defined to be the interest rate that would be paid by a savings account receiving c 0 dollars and returning yearly flows of

2 8.1 Economic Criteria Capital Budgeting 2 c j dollars, with the last flow emptying the account. It is computed by setting the compound amount of the cash flows equal to $0.00, 0 = c 0 (1+i) n + c 1 (1+i) n c n-1 (1+i) + c n, (8-1) and solving by trial and error for the unknown interest rate. The IRR heuristic selects independent projects in decreasing order of IRR until funds are exhausted. For example, suppose that the IRRs are 30%, 23%, 18%, Then the project with the IRR of 30% is the first selected, followed in turn by the others until there is no more money. Example 8.2 Internal Rate of Return Consider projects A and B in Figure The IRR of A can be obtained by setting the compound amount at either year 2 or 10 Project A 9 Project B year 3 to $0. If the balance is $0 at year 2, then it must also be $0 at year 3. The Figure 8.1 Cash Flows equation for time 2 is 0 = -10(1+i A ) 2 + 7(1+i A ) (8-2) Note that multiplying both sides of (8-2) by (1+i A ) yields the equation for time 3, 0 = -10(1+i A ) 3 + 7(1+i A ) 2 + 5(1+i A ) 1 + 0, (8-3) so both have the same solution, 13.9%. If project A were a savings account, then it would be paying interest at a rate of 13.9% per year. The IRR of project B must be evaluated no earlier than year 3, since that is when its last cash flow occurs. Its IRR of 14.5% is the solution to 0 = -9(1+i B ) 3 + 3(1+i B ) 2 + 4(1+i B ) (8-4) or 14.5%. If projects A and B should be independent projects, then B would be more highly ranked than A based on the IRR heuristic. Average Marginal and High Rates of Return Thuesen [1] simulated the growth of industrial firms on the computer to examine methods for selecting projects. The IRR heuristic worked very well, but an optimization procedure provided slightly better results. The procedure was computationally expensive, so a heuristic designed for that type of optimization problem also was examined. It ranks each project based on a number known as its benefit to cost (B/C) ratio. This ratio equals the discounted amount of all cash flows after time 0 divided by the initial cost at time 0. As with the IRR heuristic, projects with the largest B/C ratios were selected first. The B/C heuristic yielded results comparable to the IRR heuristic. Ristroph [2] noted that a project s IRR and its B/C ratio tend to be proportional to each other, exhibiting a correlation coefficient of roughly 97%. Figure 8.2 shows a sample plot for 50 projects in which each project s B/C ratio is plotted against its IRR. The correspondence between the two measures is clear, particularly for lower values of IRR and B/C. Thus a project s desirability tends to be proportional to its IRR, regardless of whether B/C or IRR is used to rank projects.

3 B/C 8.1 Economic Criteria Capital Budgeting 3 This leads to the concept of a marginal project. 1.5 Such projects are affected by 1.4 small changes in capital availability. If there is slightly more capital, then more marginal projects can be selected. If 1.1 there is slightly less capital, 1 then fewer marginal projects 0.9 can be accepted. For example, 0.8 suppose that projects affected by small changes in capital have IRRs between 9% and IRR 11%, averaging 10%. Then the Figure 8.2 Sample Plot of B/C Versus IRR average marginal rate of return (AMRR) is 10%. The better projects that definitely will be accepted tend to have higher IRRs with an average value referred to as the average high rate of return (AHRR). 8.2 Future Total Worth Model The foregoing overview of capital budgeting serves to explain the concepts of the AMRR and AHRR that are used in this section. A complete treatment of the capital budgeting problem recognizes that there can be several sets of mutually exclusive projects that can be independent of each other to varying degrees. Understanding the basics of analyzing a single set of mutually exclusive projects is necessary before examining capital budgeting in more detail. The primary concern now and in the following chapters is selecting the best project from a mutually exclusive set. The IRR is a good heuristic for this purpose, but this section develops a model that produces better results. This model also has the benefit of explaining the dynamics of industrial growth and other practical applications. The alternative yielding the largest FTW based on this model will be considered the best project in the set until later in the text when capital budgeting is considered in detail. At that time, it will be possible to revisit some of the assumptions of the FTW model to obtain slightly improved results. The following subsections first use an example to illustrate the basic assumptions and logic of industrial investments, and then generalize it into the FTW model for mutually exclusive projects. Assumptions Table 8.2 contains the cash flows depicted in Figure 8.1. Suppose that projects A and B are mutually exclusive so that at the most only one can be chosen. Let the investment capital at time 0 be $100. All amounts can be thousands or millions of dollars, depending on the size of a company. The objective is to choose the alternative that maximizes the FTW or capital at the end of the planning horizon, time 3 in this case. Table 8.2 Cash Flows Time A B Null

4 8.2 Economic Criteria Future Total Worth Model 4 Alternative A initially requires $10, leaving $90 available for other investments, Table 8.3 Investment Capital as shown in Table 8.3. Time A B Null Common Similarly, alternative B allows $91 for other investments. The null alternative consists of rejecting all of the alternatives under consideration, so its cash flows are all $0.00. It results in the entire $100 remaining available. All alternatives have at least $90 available for other currently unknown investments. It is assumed that the more highly rated projects with an AHRR of 15% will consume this common funding base of $90. It also is assumed that there are a limited number of good investments, and that any funds above the common base will be used by projects of marginal quality. For example, selecting A results in $0 for marginal projects at time 0, whereas B and Null provide $1 and $10, respectively. It is estimated that marginal projects will provide an AMRR of 10%. The reinvestment assumption is that common funds are reinvested at the AHRR and that funds in excess of the common funds are reinvested at the AMRR. The project size assumption is that the better projects have costs that total to exactly the common amount (e.g., $90) and that marginal projects costing exactly the excess amount (e.g., $1 or $10) are available. The single-year assumption is that any amount of funds can be invested and that returns are available after one year. These assumptions are necessary for mathematical tractability in an area where the development of exact mathematical models does not seem to be possible. They generally will not be true in practice, but they are accurate enough to produce economic criteria of demonstrated effectiveness. The importance of the FTW model is that it captures the essentials of capital growth, explains which interest rate to use in computations involving industrial projects, and leads to the development of criteria for selecting industrial projects. Thuesen [1] used similar assumptions to develop a related model leading to the same criteria. He validated the model with computer-based simulation experiments that empirically verified that using these criteria maximizes a company s economic growth. The following section explains the development of the FTW model. Logic The foregoing assumptions allow computing the investment capital corresponding to each alternative at time 1. Choosing alternative A implies that the remaining $90.00 of investment funds available at time 0 will be invested in non-marginal projects, grow at an AHRR of 15%, and then be augmented by the first return of $7. Thus the capital funds for project A at time 1 is F A,1 = 90.00(1.15) + 7 (8-5) or $ Choosing alternative B results in the first $90.00 of investment funds growing at 15%, the marginal amount of $1.00 ( ) increasing at 10%, and then augmentation by the return of $3, so

5 8.2 Economic Criteria Future Total Worth Model 5 F B,1 = 90.00(1.15) + ( )(1.10) + 3 (8-6) or $ The null alternative results in the first $90.00 growing at 15% and the marginal amount of $10.00 ( ) increasing at 10%, so or $ F O,1 = 90.00(1.15) + ( )(1.10) (8-7) The assumptions made at time 0 also are used at time 1 to compute the investment capital for time 2. At time 1, there will be investment capital of at least $ It is assumed that the first $ of investments will grow at the AHRR of 15%. Any funds above $ are assumed to be used by less attractive investments that provide an AMRR of 10%. Then the computation of the investment capital for time 2 proceeds much as before. For example, the investment capital of $ if A is chosen is computed as F A,2 = (1.15) + ( )(1.10) + 5. (8-8) This process is repeated at time 3. Investments up to the common level of $ grow at the AHRR, and investments beyond that amount increase at the AMRR. For example, the investment capital of $ at time 3 if A is chosen is computed as F A,3 = (1.15) + ( )(1.10) + 0. (8-9) Similarly, the capital amounts at time 3 corresponding to Project B and the null alternative $ and $ Project B has the largest FTW, so it is the preferred alternative, although all alternatives are close in this case. Model If all costs and benefits of alternatives are known and reinvestment occurs as described above, then it seems reasonable to use the FTW procedure [2]: 1. Set the length of the planning horizon to the life of the longest alternative. 2. Assume that future benefits and costs increase or decrease capital that is reinvested, common amounts earn the AHRR, and amounts beyond that earn the AMRR. 3. Choose the alternative producing the largest FTW. Developing a formula for FTW requires assigning symbols to the parameters of the investment problem demonstrated above, writing the expressions using those symbols instead of numbers until a pattern emerges, and then algebraically rearranging the result. The use of the following symbols is illustrated with values from the preceding example: K j Common capital at time j, e.g., K 0 equals and K 1 equals c j Value of a cash flow at time j, e.g., c 0 for alternative B equals -9. A Initial investment capital at time 0, e.g., $100. a Average non-marginal rate of return or AHRR, e.g., 15%. m Average marginal rate of return or AMRR, e.g., 10%. n Length of planning horizon, e.g., 3. Then the equation for future total worth can be shown to be: FTW = A (1+m) n + (a-m) [ K 0 (1+m) n-1 + K 1 (1+m) n K n-2 (1+m) + K n-1 ] + c 0 (1+m) n + c 1 (1+m) n c n-1 (1+m) + c n (8-10)

6 8.2 Economic Criteria Future Total Worth Model 6 The top line in equation (8-10) is the FTW of the null alternative for which the cash flows equal $0: FTW O = A (1+m) n + (a-m) [ K 0 (1+m) n-1 + K 1 (1+m) n K n-2 (1+m) + K n-1 ] (8-11) This allows the FTW of any project to be written as: FTW = FTW O + c 0 (1+m) n + c 1 (1+m) n c n-1 (1+m) + c n (8-12) Only the terms involving a project s cash flows in equation (8-12) vary among the alternatives of a mutually exclusive set, and this leads to the concept of future worth and other economic criteria for the industrial environment. Example 8.3 Future Total Worth Model Equations (8-11) and (8-12) can be used to compute the values determined in a step-by-step manner in the preceding section on the logic of the FTW model. The FTW of the null alternative is FTW O = 100 (1.10) 3 + ( ) [ 90.00(1.10) (1.1) ] (8-13) or $ The FTWs of the two alternatives are or $ and or $151.90, as before. Observations FTW A = FTW O 10(1.10) 3 + 7(1.10) 2 + 5(1.10) (8-14) FTW B = FTW O 9(1.10) 3 + 3(1.10) 2 + 4(1.10) (8-15) The FTW model uses assumptions that do not exactly correspond to reality to obtain mathematical tractability. Some of their flaws are obvious, and others are subtle. For instance, in the preceding example, $90 grows at 15% during year one. However, if another set of mutually exclusive projects should be considered for the same company, then perhaps $85 would grow at 15% during the first year. Thus the amount of funds growing at different rates is consistent only for projects in the same mutually exclusive set. The importance of the modeling process is the insight that it provides into the nature of industrial growth, rather than exact forecasts of FTW. Equation (8-12) indicates that the differences in FTW among alternatives within one mutually exclusive set are due to the compound amounts of each project s cash flows evaluated at the AMRR. This occurs because the cash flows of each alternative result in different amounts of investment capital available for marginal projects. These differences compound at the marginal rate rather than the average rate. The FTW model leads to economic criteria of demonstrated effectiveness. Thuesen s [1] modeling process also lead to the criteria presented below. He then demonstrated the superiority of the criteria to other measures with computer simulations based on much more realistic assumptions than possible for a mathematical model.

7 8.3 Economic Criteria Industrial Criteria Industrial Criteria The development of decision criteria for the industrial environment results in measures that are proportional to FTW, so they produce the same selections as FTW. They are surrogate criteria that are easier to compute than the more fundamental measure of FTW. The following subsections show that the surrogate criteria are equivalents of the original cash flows. Within an industrial context, two sets of cash flows are equivalent if they produce the same FTW. This is similar to banking equivalents that produce the same final balance. Following chapters examine the application of surrogate criteria in greater detail. Future Worth The future worth of an industrial project is defined as the difference between the project's FTW and that of the null alternative. Equation (8-12) indicates that this equals. FW = c 0 (1+m) n + c 1 (1+m) n c n-1 (1+m) + c n. (8-16) The definition of FW implies that the FW of the null alternative is $0, so non-mandatory projects should have a FW that is at least $0; otherwise the null alternative should be chosen. The formula for FW is identical to that of a compound amount or equivalent at time n computed using the AMRR. It is the bottom line of equation (8-10), so whichever project has the largest FW has the largest FTW and FW is a surrogate criterion for FTW. Equation (8-10) also makes it clear that a single cash flow of FW dollars at time n is equivalent to the cash flows of the original project. Figure 8.3 helps to interpret FW. Suppose that projects 1, 2,, 19, 20 currently are selected. Let projects 21, 22, and 23 be marginal projects, of which projects 21 and 22 currently are selected. Now suppose that project X is considered. If the null alternative is selected, then X is rejected, and the selections remain in their initial state. If X is selected, then it will displace one or more marginal projects due to capital limitations. In this case, project 20 is bumped down to the marginal level, and project 22 is no longer selected. In essence, selecting the null alternative ultimately results in choosing some marginal alternative (project 22, in this case) instead of the alternative under consideration. 1, 2,..., 19, 20 High 1, 2,..., 19, 20 High 1, 2,..., 19, X 21, 22, 23 Marginal 21, 22, 23 Marginal 20, 21, 22 24, 25, 26,... Rejected X, 24, 25, 26,... Rejected 23, 24, 25, 26,... a) Initial Status b) Null Selected Figure 8.3 Project Selections c) Project X Selected Equation (8-1) indicates that the compound amount of a project s cash flows equals $0 at the project s IRR. By definition, marginal projects have an IRR equal to m, so they have a FW of $0. Selecting a project with a FW of $1 produces a FTW of $1 more than displaced marginal projects, and a FW of $1, implies a FTW of $1 less. This

8 8.3 Economic Criteria Industrial Criteria 8 allows FW to be interpreted as the change in FTW caused by accepting a project under consideration rather than a marginal project. Example 8.4 Future Worth The future worths of alternatives A and B are and FW A = 0.66 = - 10(1.1) 3 + 7(1.1) 2 + 5(1.1) (8-17) FW B = 1.05 = - 9(1.1) 3 + 3(1.1) 2 + 4(1.1) (8-18) The FW of the null alternative is $0. Alternatives A and B will produce FTWs that are $0.66 and $1.05 larger than a marginal project. Alternative B is the preferred alternative. Present Worth The more popular present worth measure is defined as the single cash flow at time 0 that produces the same FTW as the original project. Hence a project s PW equals its equivalent at time 0. The formula for PW is derived by setting the FTW of a project equal to the FTW of a single cash flow of amount PW at time 0, and obtaining: PW = c 0 + c 1 (1+m) 1 + c 2 (1+m) c n-1 (1+m) (n-1) + c n (1+m) n. (8-19) Equation (8-19) shows that PW is the discounted amount of a project s cash flows at time 0, using the AMRR as PW c c 1 n the discount rate, as illustrated in Figure 8.4. c 2 = 0 Equation (8-19) implies that PW = FW(1+m) n, (8-20) so PW is proportional to FW. Thus PW results in the Figure 8.4 Present Worth same ranking of projects as FW and FTW, and it is another surrogate measure. Either equation (8-19) or (8-20) indicates that the PW of the null alternative is $0, so non-mandatory projects should have a PW of at least $0 or the null alternative should be chosen. Solving equation (8-20) for FW results in FW = PW(1+m) n. (8-21) Thus selecting a project changes the FTW by PW(1+m) n from what the null alternative would have produced, so FTW = FTW O + PW(1+m) n. (8-22) The value of FTW O is what the company would have if the project never existed, with a marginal project selected in its place. The value of PW(1+m) n equals the savings (or debt) caused by a totally separate deposit of PW in (or loan from) an account with rate m, the AMRR. This leads to the following interpretation of PW. A project with a present worth of PW dollars produces the same FTW as selecting a marginal project in its place, plus having PW extra (or fewer) dollars to invest today in a marginal project. Example 8.5 Present Worth The present worths of alternatives A and B are 0 c n

9 8.3 Economic Criteria Industrial Criteria 9 and PW A = 0.50 = (1.1) 1 + 5(1.1) 2 + 0(1.1) 3 (8-23) PW B = 0.79 = (1.1) 1 + 4(1.1) 2 + 5(1.1) 3. (8-24) The present worth of the null alternative is $0. Selecting project A has the same effect on the company's FTW as having an extra $0.50 today to invest in a marginal project, and project B has the effect of an extra $0.79. The impact of project A on FTW is 0.50(1.1) 3 or $0.66 more than that of a marginal alternative, and for project B the effect is 0.79(1.1) 3 or $1.05 more. As before, B is the preferred alternative. Equivalent Annual Worth A project's equivalent annual worth is defined as equal cash flows of amount EAW occurring at times 1, 2,..., n that produce the same FTW as the project. Thus the flows of amount EAW are equivalent to the original project, as shown in Figure 8.5. Setting the FTW of equal amounts EAW at times 1, 2,..., n equal to the FTW of a project results in or EAW = PW (A P, m, n) (8-25) EAW = FW (A F, m, n). (8-26) EAW is proportional to PW and FW, and hence to FTW, so it is another surrogate criterion. The EAW must be computed over the same planning horizon for all alternatives, or the proportionality between EAW and PW is lost. Similarly, the EAW of the null alternative is $0, so select alternatives with EAWs of at least $0, if possible. The interpretation of EAW is similar to that of PW. A project having an equivalent annual worth of EAW produces the same FTW as selecting a marginal project instead of it, plus having EAW dollars more or less at years 1, 2,, n to invest in marginal projects. Example 8.6 Present Worth The equivalent annual worths of alternatives A and B are or $0.20, and EAW A = 0.50 (A P, 10%, 3) (8-27) EAW B = 0.79 (A P, 10%, 3) (8-28) or $0.32. Project A produces the same FTW having an extra $0.20 to invest at times 1, 2, and 3, and a similar interpretation can be made for project B. Notice that the number of periods used for project A is 3, even though it lasts only 2 years. The EAW of the null alternative is $0, so B is the preferred alternative, as before. The FTW equation can be used to verify that the equivalent receipts of $0.20 at times 1, 2, and 3 corresponding to alternative A will result in a FTW that is $0.66 larger than that of the null alternative. Similarly, the equivalent receipts 0 EAW 1 2 n = c 0 c 1 c Figure 8.5 Equivalent Annual Worth 0 c n n

10 8.3 Economic Criteria Industrial Criteria 10 of $0.32 at times 1, 2, and 3 corresponding to alternative B will produce a FTW $1.05 larger than that of the null alternative. 8.4 Practical Considerations All criteria are computed using the cash flows c 0, c 1,, c n and the AMRR. However, there are situations where the values of some of these cash flows might be unknown. For example consider a problem such as replacing a pump that is a small, but absolutely necessary part of a large chemical plant. How is the problem of determining the monetary benefits associated with such a pump addressed? Similarly, more thought needs to be given to determining how to compare two pumps that last 3 and 7 years, respectively. This chapter provides the fundamentals of economic criteria, and the following chapters address various practical topics such as those noted above. The criteria identify the best alternative from a single mutually exclusive set, such as the best design to do a specific job. The FTW modeling logic assumes that funds not used by each project are precisely consumed at either the AHRR or the AMRR. The capital budgeting process does not have to make such assumptions. It simultaneously examines all sets of mutually exclusive projects, so the investment possibilities for capital not used by a project are known, not assumed. Selections must fit into a budget, and this can result in choosing a project not identified as the best in its mutually exclusive set. For example, there might be enough good projects overall so that there is only enough money left to fund the second best project from a particular mutually exclusive set. Further treatment of capital budgeting must wait until the following chapters explain more about how to compute the economic criteria. Until then, it is understood that tentative selections made from single sets of mutually exclusive projects might be adjusted during capital budgeting. However, examining single sets of mutually exclusive projects is not done just for teaching purposes. Such analyses are necessary in practice because they identify the projects that warrant additional design and the resulting improvements in cash flow estimates prior to developing the final capital budget. The actual capital budgeting process considers the same economic measures used for single sets, but it uses them in a slightly different manner, so no calculations are wasted. Any treatment of economic criteria would be incomplete without noting the minimum attractive rate of return (MARR). The MARR is defined as the IRR beneath which a company will not accept a project. If the AMRR characterizes a range of marginal projects, then the MARR would be at the very bottom of this range. For example, if changes in the availability of capital generally cause inclusions or exclusions of projects having IRRs between 7 and 9%, then the AMRR and MARR would be 8% and 7%, respectively. In fact, if management should be willing to accept a project with a lower IRR than 7%, then the MARR could be less than 7%. Nonetheless, the difference in these values is frequently small, so it usually has little effect on which projects are selected and the FTW. Many texts use the term MARR in place of the term AMRR, but the technically correct term is used in this text.

11 8: Economic Criteria Questions Summary This chapter assumes that an organization s investment objective is to select projects in a way that maximizes its wealth at the end of the planning horizon. The transition to the industrial environment begins with a discussion of the capital budgeting problem where available funds permit only a limited number of independent projects to be selected. It can be very difficult to select a subset of projects that exactly maximizes a company s FTW, but ranking projects on their IRRs or B/C ratios provides good and sometimes optimal solutions. These measures are correlated so marginal projects have IRRs clustered about the AMRR regardless of which measure is used. Examining a set of mutually exclusive projects entails assuming that the common amount left available for investment elsewhere is used for better projects that return the AHRR. Differences in funds beyond the common amount are used for marginal projects that return the AMRR. This leads to the FTW equation, and then to the surrogate measures of FW, PW, and EAW. All of these methods define equivalent projects that produce the same FTW as the original project. Thus choosing the best project simply becomes a matter of choosing the largest equivalent. The AMRR is used to compute the measures because it is the growth rate of the marginal projects affected by the acceptance or rejection of an alternative. All of the surrogate criteria measure projects performances relative to the same benchmark of the null alternative of rejecting all alternatives under consideration and accepting a marginal project instead. The FW of an alternative equals the additional funds that a company will have at the end of the planning horizon if the alternative is selected instead of a marginal alternative. Accepting a project with present worth PW has the same effect on FTW as having PW more or less dollars available today for investment in marginal projects instead of the original project. Similarly, accepting a project with equivalent annual worth EAW has the same effect on FTW as having EAW more or less dollars available at times 1, 2,, n to invest in marginal alternatives. Each of these criteria is covered in more detail in the following chapters. Questions Section 1: Capital Budgeting 1.1 An investment costs $5,000 today and returns $3,000 at the end of year 2 and also at the end of year 5. What is the rate of return on this investment? (5.442%) 1.2 What is meant by independent projects as opposed to mutually exclusive projects? 1.3 What is meant by a marginal project? 1.4 If capital budgeting is performed using the B/C heuristic, then explain why marginal projects tend to have IRRs in the vicinity of the AMRR instead of being widely scattered with very high and low values. Section 2: Future Total Worth Model 2.1 Explain the FTW model s assumptions on: a) reinvestment, b) project size, and

12 8: Economic Criteria Questions 12 c) single year projects. 2.2 What is the null alternative when considering industrial projects? 2.3 Suppose that a company has $100,000 of investment capital at time 0, and the IRRs of its average and marginal investments are 15% and 10%, respectively. One of two investments can be chosen, in addition to the null alternative. Investment A requires an initial outlay of $3,000 and then returns $1,800 at the end of year 3 and $2,800 at the end of year 5. Investment B has an initial cost of $4,000 and returns $5,000 after 2 years. a) What is the null alternative in this instance? Is it a feasible alternative? b) Draw the cash flow diagrams for each alternative. c) What is the investment objective? d) What are the year-by-year amounts of investment capital corresponding to each alternative? (At time 5: A = 200,111.05, B = 200,177.54, Null = 199,964.58) e) Which alternative should be chosen? (B) Section 3: Industrial Criteria 3.1 Does accepting the null alternative imply that a marginal project will be accepted in place of a project currently under consideration? Explain. 3.2 Why are FW, PW, and EAW referred to as surrogate criteria? 3.3 What is the definition of an equivalent in an industrial context? 3.4 Use the definition of PW to derive (8-19). 3.5 Continue with problem 2.3 above. a) Use equation (8-10) to verify the correctness of each FTW. b) What are the future worths of each alternative? Compute them using the future worth formula and as the difference in FTWs. How can the FWs be interpreted? (FW A = , FW B = , FW O = 0) c) What are the present worths of each alternative? Use the FTW equation to verify that these amounts will produce the same FTW as the original alternatives. How can the PWs be interpreted? (PW A = 90.95, PW B = , PW O = 0) d) What are the equivalent annual worths of each alternative? Use the FTW equation to verify that these amounts will produce the same FTW as the original alternatives. How can the EAWs be interpreted? (EAW A = 23.99, EAW B = 34.88, EAW O = 0) e) Which alternative should be chosen based only on economic considerations? (B) Section 4: Practical Considerations 4.1 Why are individual sets of mutually exclusive projects examined prior to capital budgeting if it is possible for a preliminary selection not to be a final selection? 4.2 What is the difference between the AMRR and the MARR? Give an example. Bibliography 1. Thuesen, Gerald J., "Decision Techniques for Capital Budgeting Problems," Ph.D. Dissertation, Stanford University, University Microfilms, Ristroph, John H., Economic Criteria, Proceedings of the American Society for Engineering Education 1999 National Conference, June, 1999, Charlotte, NC.