Hendrickson, C., McNeil, S. Project Selection from Alternatives The Engineering Handbook. Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000

Transcription

1 Hendrickson, C., McNeil, S. Project Selection from Alternatives The Engineering Handbook. Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000

2 183 Project Selection from Alternatives Problem Statement for Project Selection Steps in Carrying Out Project Selection Selection Criteria Net Present Value Other Methods Applications Conclusion Chris Hendrickson Carnegie Mellon University Sue McNeil Carnegie Mellon University Practical engineering and management requires choices among competing alternatives. Which boiler should be used in a plant? Which computer should be purchased for a design office? Which financing scheme would be most desirable for a new facility? These are practical questions that arise in the ordinary course of engineering design, organizational management, and even personal finances. This chapter is intended to present methods for choosing the best among distinct alternatives Problem Statement for Project Selection The economic project selection problem is to identify the best from a set of possible alternatives. Selection is made on the basis of a systematic analysis of expected revenues and costs over time for each project alternative. Project selection falls into three general classes of problems. Accept-reject problems (also known as a determination of feasibility) require an assessment of whether or not an investment is worthwhile. For example, the hiring of an additional engineer in a design office is an accept-reject decision. Selection of the best project from a set of mutually exclusive projects is required when there are several competing projects or options and only one project can be built or purchased. For example, a town building a new sewage treatment plant may consider three different configurations, but only one configuration will be built. Finally, capital budgeting problems are concerned with the selection of a set of projects when there is a budget constraint and many, not necessarily competing, options. For example, a state highway agency will consider many different

3 highway rehabilitation projects for a particular year, but generally the budget is insufficient to allow all to be undertaken, although they may all be feasible Steps in Carrying Out Project Selection A systematic approach for economic evaluation of projects includes the following major steps [Hendrickson, 1989]: 1. Generate a set of project or purchase alternatives for consideration. Each alternative represents a distinct component or combination of components constituting a purchase or project decision. We shall denote project alternatives by the subscript x, where x = 1;2;::: refers to projects 1, 2, and so on. 2. Establish a planning horizon for economic analysis. The planning horizon is the set of future periods used in the economic analysis. It could be very short or long. The planning horizon may be set by organizational policy (e.g., 5 years for new computers or 50 years for new buildings), by the expected economic life of the alternatives, or by the period over which reasonable forecasts of operating conditions may be made. The planning horizon is divided into discrete periods usually years, but sometimes shorter units. We shall denote the planning horizon as a set of t = 0;1;2;3;:::;n, where t indicates different periods, with t = 0 being the present, t = 1 the first period, and t = n representing the end of the planning horizon. 3. Estimate the cash flow profile for each alternative. The cash flow profile should include the revenues and costs for the alternative being considered during each period in the planning horizon. For public projects, revenues may be replaced by estimates of benefits for the public as a whole. In some cases revenues may be assumed to be constant for all alternatives, so only costs in each period are estimated. Cash flow profiles should be specific to each alternative, so the costs avoided by not selecting one alternative (say, x = 5) are not included in the cash flow profile of the alternatives (x = 1, 2, and so on). Revenues for an alternative x in period t are denoted B(t;x), and costs are denoted C(t;x). Revenues and costs should initially be in base-year or constant dollars. Base-year dollars do not change with inflation or deflation. For tax-exempt organizations and government agencies, there is no need to speculate on inflation if the cash flows are expressed in terms of base-year dollars and a MARR without an inflation component is used in computing the net present value. For private corporations that pay taxes on the basis of then-current dollars, some modification should be made to reflect the projected inflation rates when considering depreciation and corporate taxes. 4. Specify the minimum attractive rate of return (MARR) for discounting. Revenues and costs incurred at various times in the future are generally not valued equally to revenues and costs occurring in the present. After all, money received in the present can be invested to obtain interest income over time. The MARR represents the trade-off between monetary amounts in different periods and does not include inflation. The MARR is usually expressed as a percentage change per year, so that the MARR for many public projects may be stated as

4 10%. The value of MARR is usually set for an entire organization based upon the opportunity cost of investing funds internally rather than externally in the financial markets. For public projects the value of MARR is a political decision, so MARR is often called the social rate of discount in such cases. The equivalent value of a dollar in a following period is calculated as (1 + MARR), and the equivalent value two periods in the future is (1 + MARR) (1 + MARR) = (1 + MARR) 2. In general, if you have Y dollars in the present [denoted Y(0)], then the future value in time t [denoted Y(t)] is Y(t) = Y(0)(1+MARR) t (183:1) or the present value, Y(0), of a future dollar amount Y(t) is Y(0) = Y(t)=(1+MARR) t (183:2) 5. Establish the criterion for accepting or rejecting an alternative and for selecting the best among a group of mutually exclusive alternatives. The most widely used and simplest criterion is the net present value criterion. Projects with a positive net present value are acceptable. Only one from a group of mutually exclusive alternatives can be chosen. For example, the alternatives might be alternative boilers for a building or alternative airport configurations. From a set of mutually exclusive alternatives, the alternative with the highest net present value is best. The next section details the calculation steps for the net present value and also some other criterion for selection. 6. Perform sensitivity and uncertainty analysis. Calculation of net present values assumes that cash flow profiles and the value of MARR are reasonably accurate. In many cases assumptions are made in developing cash flow profile forecasts. Sensitivity analysis can be performed by testing a variety of such assumptions, such as different values of MARR, to see how alternative selection might change. Formally treating cash flow profiles and MARR values as stochastic variables can be done with probabilistic and statistical methods Selection Criteria Net Present Value Calculation of net present values to select projects is commonly performed on electronic calculators, on commercial spreadsheet software, or by hand. The easiest calculation approach is to compute the net revenue in each period for each alternative, denoted A(t;x): A(t;x) = B(t;x) C(t;x) (183:3) where A(t;x) may be positive or negative in any period. Then, the net present value of the alternative, NPV(x), is calculated as the sum over the entire planning horizon of the discounted

5 values of A(t;x): NPV(x) = nx A(t;x)=(1+MARR) t (183:4) t=0 Other Methods Several other criteria may be used to select projects. Other discounted flow methods include net future value [denoted NFV(x)] and equivalent uniform annual value [denoted EUAV(x)]. It can be shown [Au, 1992] that these criteria are equivalent where NFV(x) = NPV(x)(1+MARR) n (183:5) EUAV(x) = NPV(x)(1+MARR)n [(1+MARR) n 1] (183:6) The net future value is the equivalent value of the project at the end of the planning horizon. The equivalent uniform annual value is the equivalent series in each year of the planning horizon. Alternatively, benefit-to-cost ratio (the ratio of the discounted benefits to discounted costs) and the internal rate of return [the equivalent MARR at which NPV(x) = 0] are merit measures, each of which may be used to formulate a decision. For accept-reject decisions, the benefit-to-cost ratio must be greater than one and the internal rate of return greater than the MARR. However, these measures must be used in connection with incremental analyses of alternatives to provide consistent results for selecting among mutually exclusive alternatives [see, for instance, Au (1992)]. Similarly, the payback period provides an indication of the time it takes to recoup an investment but does not indicate the best project in terms of expected net revenues Applications To illustrate the application of these techniques and the calculations involved, two examples are presented. Example Alternative Bridge Designs. A state highway agency is planning to build a new bridge and is considering two distinct configurations. The initial costs and annual costs and benefits for each bridge are shown in the following table. The bridges are each expected to last 30 years. Alternative 1 Alternative 2 Initial cost $ $ Annual maintenance and operating costs $ $ Annual benefits $ $ Annual benefits less costs $ $

6 Solution. The net present values for a MARR of 5% are given as follows: NPV(1) = ( )+( )=(1+0:05)+( )=(1+0:05) 2 +( )=(1+0:05) 3 + +( )=(1+0:05) 30 = $ NPV(2) = ( )+( )=(1+0:05)+( )=(1+0:05) 2 +( )=(1+0:05) 3 + +( )=(1+0:05) 30 = $ Therefore, the department of transportation should select the second alternative, which has the largest net present value. Both alternatives are acceptable since their net present values are positive, but the second alternative has a higher net benefit. Example Equipment Purchase. Consider two alternative methods for sealing pavement cracks [McNeil, 1992]. The first method is a manual method; the second is an automated method using a specialized equipment system. Which method should be used? We shall solve this problem by analyzing whether the new automated method has revenues and benefits in excess of the existing manual method. Solution. Following the steps outlined earlier, the problem is solved as follows: 1. The alternatives for consideration are (1) the existing manual method, and (2) the automated method. The alternatives are mutually exclusive because cracks can only be sealed using either the existing method or the new method. 2. The planning horizon is assumed to be 6 years to coincide with the expected life of the automated equipment. 3. The cash flow profile for alternative 2 is given in the following table: System acquisition costs $ Annual maintenance and operating costs $ Annual labor savings $ Annual savings over costs $ The values are estimated using engineering judgment and historical cost experience. We assume that the productivity and revenues for both alternatives are the same and treat labor savings as additional benefits for alternative 2. Therefore, only the net present value for alternative 2, which represents the result of introducing the automated method, need be computed. 4. The MARR is assumed to be 5%. The net present value is computed as follows:

7 NPV(2) (26000)=(1+0:05) +(26000)=(1+0:05) 2 + +(26000)=(1+0:05) 5 (183:7) = $ Using the criterion NPV(2) > 0, alternative 2 is selected. 6. To determine the sensitivity of the result to some of the assumptions, consider Table The table indicates that additional investment in the automated method is justifiable at the MARR of 5% if the acquisition costs decrease or the labor savings increase. However, if the MARR increases to 10% or the acquisition costs increase, then the investment becomes uneconomical. Table Energy Price Escalation Rates Acquisition Cost ($) MARR Labor Saving ($) Maintenance and Operation ($) $ $ $ $ ($1 440) ($12 844) ($37 434) ($51 440) ($62 844) $ $ $ $ $ $ $1 532 ($17 322) ($32 675) This example illustrates the use of the net present value criteria for an incremental analysis, which assumes that the benefits are constant for both alternatives and examines incremental costs for one project over another Conclusion This chapter has presented the basic steps for assessing economic feasibility and selecting the best project from a set of mutually exclusive projects, with net present value as a criterion for making the selection. Defining Terms Alternatives: A distinct option for a purchase or project decision. Base year: The year used as the baseline of price measurement of an investment project. Cash flow profile: Revenues and costs for each period in the planning horizon. Equivalent uniform annual value: Series of cash flows with a discounted value equivalent to the net present value. Minimum attractive rate of return (MARR): Percentage change representing the time value of money.

8 Net future value: Algebraic sum of the computed cash flows at the end of the planning horizon. Net present value: Algebraic sum of the discounted cash flows over the life of an investment project to the present. Planning horizon: Set of time periods from the beginning to the end of the project; used for economic analysis. References Au, T. and Au, T. P Engineering Economics for Capital Investment Analysis, 2nd ed. Prentice Hall, Englewood Cliffs, NJ. Hendrickson, C. and Au, T Project Management for Construction. Prentice Hall, Englewood Cliffs, NJ. McNeil, S An analysis of the costs and impacts of the automation of pavement crack sealing. Proc. World Conf. on Transp. Res. Lyon, France, July. Park, C. S Contemporary Engineering Economics. Addison Wesley, Reading, MA. Further Information A thorough treatment of project selection is found in Engineering Economics for Capital Investment Analysis. Many examples are presented in Contemporary Engineering Economics.