Hendrickson, C., McNeil, S. “Project Selection from Alternatives”
The Engineering Handbook.
Ed. Richard C. Dorf
Boca Raton: CRC Press LLC, 2000
© 1998 by CRC PRESS LLC
183
Project Selection from Alternatives
183.1 Problem Statement for Project Selection
183.2 Steps in Carrying Out Project Selection
183.3 Selection Criteria
Net Present Value • Other Methods
183.4 Applications
183.5 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.
183.1 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
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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.
183.2 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
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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.
183.3 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
© 1998 by CRC PRESS LLC
values of A(t; x):
NPV(x) =
n
X
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)
NPV(x)(1 + MARR)n
[(1 + MARR)n ¡ 1]
(183:6)
EUAV(x) =
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.
183.4 Applications
To illustrate the application of these techniques and the calculations involved, two examples are
presented.
Example 183.1 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.
Initial cost
Annual maintenance and operating costs
Annual benefits
Annual benefits less costs
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Alternative 1
$15 000 000
$15 000
$1 200 000
$1 185 000
Alternative 2
$25 000 000
$10 000
$1 900 000
$1 890 000
Solution. The net present values for a MARR of 5% are given as follows:
NPV(1) = (¡15 000 000) + (1 185 000)=(1 + 0:05) + (1 185 000)=(1 + 0:05)2
+ (1 185 000)=(1 + 0:05)3 + ¢ ¢ ¢ + (1 185 000)=(1 + 0:05)30
= $3 216 354
NPV(2) = (¡15 000 000) + (1 890 000)=(1 + 0:05) + (1 890 000)=(1 + 0:05)2
+ (1 890 000)=(1 + 0:05)3 + ¢ ¢ ¢ + (1 890 000)=(1 + 0:05)30
= $4 053 932
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 183.2 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
$100 000
$10 000
$36 000
$26 000
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:
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NPV(2) ¡ 100 000 + (26 000)=(1 + 0:05)
+ (26 000)=(1 + 0:05)2 + ¢ ¢ ¢ + (26 000)=(1 + 0:05)5
(183:7)
= $12 566
5. Using the criterion NPV(2) > 0 , alternative 2 is selected.
6. To determine the sensitivity of the result to some of the assumptions, consider Table 183.1.
The table indicates that additional investment in the automated method is justifiable at the
MARR of 5% if the acquisition costs decrease or the labor savings increase. However, if the
MARR increases to 10% or the acquisition costs increase, then the investment becomes
uneconomical.
Table 183.1 Energy Price Escalation Rates
Acquisition Cost
($)
50 000
100 000
150 000
50 000
100 000
150 000
Labor Saving
($)
36 000
36 000
36 000
45 000
45 000
45 000
Maintenance and
Operation ($)
10 000
10 000
10 000
10 000
10 000
10 000
0.05
MARR
0.01
0.15
$62 566
$12 566
($37 434)
$101 532
$51 532
$1 532
$48 560
($1 440)
($51 440)
$82 678
$32 678
($17 322)
$37 156
($12 844)
($62 844)
$67 325
$17 325
($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.
183.5 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.
© 1998 by CRC PRESS LLC
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. 1992. Engineering Economics for Capital Investment Analysis, 2nd ed.
Prentice Hall, Englewood Cliffs, NJ.
Hendrickson, C. and Au, T. 1989. Project Management for Construction. Prentice Hall,
Englewood Cliffs, NJ.
McNeil, S. 1992. 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. 1993. 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.
© 1998 by CRC PRESS LLC