Economic Analysis - Evaluating Alternatives

A common problem addressed in investment analysis is to select the best of a collection of mutually exclusive alternatives. We illustrate on this page the comparison of two alternatives with different lives. The Economics add-in provides the tools for the analysis.

The Problem

 A plant manager is deciding between two machines. Machine A has an initial cost of \$9,000. It has no salvage value at the end of its six-year useful life. The annual operating cost of machine A is \$5,000. Machine B costs \$16,000 new and has a resale value of \$4,000 at the end of its nine-year economic life. Its operating costs are \$4,000 per year. Do an analysis to determine which machine should be purchased. Assume that operating costs are paid at the end of each year and that the minimum acceptable rate of return is 10%.

The first step in the analysis is to create two projects to represent the two alternatives. Note that the alternatives involve no revenue. For comparison problems it is often the case that the alternatives are revenue neutral, so revenue is simply left out of the analysis. The alternatives have lives of 6 years and 9 years respectively. We use the least common multiple of the lives, 18 years, for the study period. The study period is computed automatically with the comparison step described below.

The solution is already apparant from the computations performed on the form. For A, the NPW over the study period is -\$57955, and for B the NPW over the study period is -\$53175. Project B with the greatest NPW should be selected.

The result is also indicated by the cells labeled Uniform(Life). These hold the NAW of the projects. Again we see that project B has the greatest NAW.

Compare Projects

The Compare Projects command from the Economics menu provides for the comparison of two projects previously defined. The command presents the dialog below. We identify the defender of the comparison to be the alternative with the smallest initial investment, project A with an investment of \$9000. The challenger is the alternative with the greatest investment, project B with an investment of \$16000. The comparison is to determine if the extra investment of B over A is justified for a 10% MARR.

In this sense we evaluating a single alterantive, the incremental investment of B over A. We represent the increment as project B - A. The investment in B - A is \$7000. The returns for B - A are the differences in the annual return for B over A.

The add-in creates a comparison form as shown below. The form is dynamic because cells in the project definition regarding the study period and MARR are linked by equations to this form. Changing the MARR on the form will change the computed NPW and NAW.

The results in the comparison are shown on the form. Machine B is the optimum selection. The NPW and NAW is presented in the middle rows of the form. The cells at the bottom of the form describe the results for the incremental investment of B over A. The NPW of the increment is positive indicating that the incremental investment ( \$7000) has a return greater than the MARR. The Internal Rate of Return of the incremental investment is almost 19%,

The Cash Flows for the Increment

The cash flow display shows the difference between the cash flows for the challenger and the cash flows for the defender (B - A). This is a mixed investment in that the cumulative cash flow changes sign three times. This is often the case with alternatives with different lives. The IRR of the increment is almost 19% as observed earlier. There may be multiple solutions for the IRR for mixed cash flows.

The cash flow for the incremental investment is graphed below. Although the two projects have very simple cash flows, the incremental cash flows are quite complex because of the necessity of using a study period different than the lives.

We have illustrated the evaluation of a single project when inflation and taxes are neglected. The form holding the project data may be much more complex than the simple example presented here. A project may have several investments occurring at different times and many annual receipts and disbursements. There is no limit to the complexity the add-in can handle except the size of the worksheet and the limitations of the user's computer.

The evaluation of projects with taxes and inflation is more complex requiring additional data and more difficult computations. The add-in handles these variations with no added difficulty for the user beyond providing data for the additional features.

Comparing more than Two Projects

More than two projects can also be compared by first defining the projects and then choosing Compare Multiple from the Economics menu. The figure below shows the form for the comparison of three mutually exclusive alternatives. The details of the example are provided in the Computations section.

The add-in automatically determines the study period as the least common multiple of the lives of the alternatives. The NPW and NAW measures are displayed on the form and the best alternative is selected. Incremental analysis can be performed for more than two projects by ranking the alternatives in order of initial investment. The alternatives are considered in a pairwise fashion until the best is determined. The add-in does not perform this analysis automatically, but the user can do the appropriate steps by a formulating a series of pairwise comparisons.

Operations Management / Industrial Engineering
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by Paul A. Jensen