# CHOOSING AMONG ALTERNATIVE PROJECTS - Managerial Economics

The preceding section shows how application of the net present-value method in the capital budgeting process permits a rank ordering of investment projects from most attractive to least attractive. An investment project is attractive and should be pursued as long as the discounted net present value of cash inflows is greater than the discounted net present value of the investment requirement, or net cash outlay.

Decision Rule Conflict Problem

The attractiveness of investment projects increases with the size of NPV. High NPV projects are inherently more appealing and are preferred to low NPV projects. Any investment project that is incapable of generating sufficient cash inflows to cover necessary cash outlays, when both are expressed on a present-value basis, should not be undertaken. In the case of a project with NPV = 0, project acceptance would neither increase nor decrease the value of the firm. Management would be indifferent to pursuing such a project. NPV analysis represents a practical application of the marginal concept, in which the marginal revenues and marginal costs of investment projects are considered on a present-value basis. Use of the NPV technique in the evaluation of alternative investment projects allows managers to apply the principles of marginal analysis in a simple and clear manner. The widespread practical use of the NPV technique lends support to the view that value maximization is the prime objective pursued by managers in the capital budgeting process.

Just as acceptance of NPV > 0 projects will enhance the value of the firm, so too will acceptanceof projects for which the PI > 1 and the IRR > k. Acceptance of projects for which NPV < 0, PI < 1, or IRR < k would be unwise and would reduce the value of the firm. Because each of these project evaluation techniques shares a common focus on the present value of net cash inflows and outflows, these techniques display a high degree of consistency in terms of the project accept/reject decision. This high degree of consistency might even lead one to question the usefulness of having these alternative ways of project evaluation when only one, the NPV method, seems sufficient for decision-making purposes.

However, even though alternative capital budgeting decision rules consistently lead to the same project accept/reject decision, they involve important differences in terms of project ranking. Projects ranked most favorably using the NPV method may appear less so when analyzed using the PI or IRR methods. Projects ranked most favorably using the PI or IRR methods may appear less so when analyzed using the NPV technique.

If the application of any capital budgeting decision rule is to consistently lead to correct investment decisions, it must consider the time value of money in the evaluation of all cash flows and must rank projects according to their ultimate impact on the value of the firm. NPV, PI, and IRR methods satisfy both criteria, and each can be used to value and rank capital budgeting projects. The payback method does not meet both of the preceding criteria and should be used only as a complement to the other techniques. However, each of the NPV, PI, and IRR methods incorporates certain assumptions that can and do affect project rankings. Understanding the sources of these differences and learning how to deal with them is an important part of knowing how to correctly evaluate alternative investment projects.

Reasons for Decision Rule Conflict

As discussed earlier, NPV is the difference between the marginal revenues and marginal costs of an individual investment project, when both revenues and costs are expressed in present value terms. NPV measures the relative attractiveness of alternative investment projects by the discounted dollar difference between revenues and costs. NPV is an absolute measure of the attractiveness of a given investment project. Conversely, the PI reflects the difference between the marginal revenues and marginal costs of an individual project in ratio form. The PI is the ratio of the discounted present value of cash inflows divided by the discounted present value of cash outflows. PI is a relative measure of project attractiveness. It follows that application of the NPV method leads to the highest ranking for large profitable projects. Use of the PI method leads to the highest ranking for projects that return the greatest amount of cash inflow per dollar of outflow, regardless of project size. At times, application of the NPV method can create a bias for larger as opposed to smaller projects—a problem when all favorable NPV > 0 projects cannot be pursued. When capital is scarce, application of the PI method has the potential to create a better project mix for the firm’s overall investment portfolio.

Both NPV and PI methods differ from the IRR technique in terms of their underlying assumptions regarding the reinvestment of cash flows during the life of the project. In the NPV and PI methods, excess cash flows generated over the life of the project are “reinvested” at the firm’s cost of capital. In the IRR method, excess cash flows are reinvested at the IRR. For especially attractive investment projects that generate an exceptionally high rate of return, the IRR can actually overstate project attractiveness because reinvestment of excess cash flows at a similarly high IRR is not possible. When reinvestment at the project-specific IRR is not possible, the IRR method must be adapted to take into account the lower rate of return that can actually be earned on excess cash flows generated over the life of individual projects. Otherwise, use of the NPV or PI methods is preferable.

Ranking Reversal Problem

A further and more serious conflict can arise between NPV and IRR methods when projects differ significantly in terms of the magnitude and timing of cash flows. When the size or pattern of alternative project cash flows differ greatly, each project’s NPV can react quite differently to changes in the discount rate. As a result, changes in the appropriate discount rate can sometimes lead to reversals in project rankings.

To illustrate the potential for conflict between NPV and IRR rankings and the possibility of ranking reversals, Table 15.5 shows a further development of the SVCC plant investment project example. Assume that the company is considering the original new plant investment project in light of an alternative proposal to buy and remodel an existing plant. Old plant and equipment can be purchased for an initial cash outlay of $11.5 million and can be remodeled at a cost of$2 million per year over the next 2 years. As before, a net working capital investment of $6.6 million will be required just prior to opening the remodeled production facility. For simplicity, assume that after year 2, all cash inflows and outflows are the same for the remodeled and new plant facilities. Note that the new plant proposal involves an initial nominal cash outlay of$25.8 million, whereas the remodeled plant alternative involves a nominal cash outlay of $22.1 million. In addition to this difference in project size, the two investment alternatives differ in terms of the timing of cash flows. The new plant alternative involves a larger but later commitment of funds. To see the implications of these differences, notice how the “remodel old plant” alternative is preferred at and below the firm’s 15 percent cost of capital using NPV and PI methods, even though the IRR of 25.06 percent for the new plant project exceeds the IRR of 23.57 percent for the “remodel old plant” alternative. Also troubling is the fact that the relative ranking of these projects according to NPV and PI methods is reversed at higher discount rates. Notice how the “build new plant” alternative is preferred using NPV and PI techniques when a 25 percent discount rate is employed. Comparison-of-the-“Build-New-Plant”-Versus-“Remodel-Old-Plant”-Investment-Project-Example-Using Figure displays the potential conflict between NPV, PI, and IRR project rankings at various interest rates by showing the effect of discount rate changes on the NPV of each alternative investment project. This net present-value profile relates the NPV for each project to the discount rate used in the NPV calculation. Using a k = 0 percent discount rate, the NPV for the “build new plant” investment project is$38.4 million, and it is $42.1 million for the “remodel old plant” alternative. These NPV values correspond to the difference between nominal dollar cash inflows and outflows for each project and also coincide with NPV line Y-axis intercepts of$38.4 million for the “build new plant” project and $42.1 million for the “remodel old plant” alternative. The X-axis intercept for each curve occurs at the discount rate where NPV = 0 for each project. Becaise NPV = 0 when the discount rate is set equal to the IRR, or when IRR = k, the X-axis intercept for the “build new plant” alternative is at the IRR = 25.06 percent level, and it is at the IRR = 23.57 percent level for the “remodel old plant” alternative. Figure illustrates how ranking reversals can occur at various NPV discount rates. Given higher nominal dollar returns and, therefore, a higher Y-axis intercept, the “remodel old plant” alternative is preferred when very low discount rates are used in the NPV calculation. Given a higher IRR and, therefore, a higher X-axis intercept, the “build new plant” alternative is preferred when very high discount rates are used in the calculation of NPV. Between very high and low discount rates is an interest rate where NPV is the same for both projects. A reversal of project rankings occurs at the crossover discount rate, where NPV is equal for two or more investment alternatives. In this example, the “remodel old plant” alternative is preferred when using the NPV criterion and a discount rate k that is less than the crossover discount rate. The “build new plant” alternative is preferred when using the NPV criterion and a discount rate k that is greater than the crossover discount rate. This ranking reversal problem is typical of situations in which investment projects differ greatly in terms of their underlying NPV profiles. Hence, a potentially troubling conflict exists between NPV, PI, and IRR methods. Making the Correct Investment Decision The ranking reversal problem and suggested conflict between NPV, PI, and IRR methods is actually much less serious than one might imagine. Many comparisons between alternative investment projects involve neither crossing NPV profiles nor crossover discount rates as shown in Figure. Some other project comparisons involve crossover discount rates that are either too low or too high to affect project rankings at the current cost of capital. As a result, there is often no meaningful conflict between NPV and IRR project rankings. When crossover discount rates are relevant, they can be easily calculated as the IRR of the cash flow difference between two investment alternatives. To see that this is indeed the case, consider how cash flows differ between each of the two plant investment alternatives considered previously. The “build new plant” alternative involves a smaller initial cash outflow of$1.2 million versus $11.5 million, a$10.3 million saving, but it requires additional outlays of $2 million at the end of year 1 plus an additional$12 million at the end of year 2. Except for these differences, the timing and magnitude of cash inflows and outflows from the two projects are identical. The IRR for the cash flow difference between two investment alternatives exactly balances the present-value cost of higher cash outflows with the present-value benefit of higher cash inflows. At this IRR, the cash flow difference between the two investment alternatives has an NPV equal to zero. When k is less than this crossover IRR, the investment project with the greater nominal dollar return will have a larger NPV and will tend to be favored. In the current example, this is the “remodel old plant” alternative. When k is greater than the crossover IRR, the project with an earlier cash flow pattern will have the larger NPV and be favored. In the current example, this is the “build new plant” alternative.

When k equals the crossover IRR, the cash flow difference between projects has an NPV = 0, and each project has exactly the same NPV.

Once an economically relevant crossover discount rate has been determined, management must decide whether to rely on NPV or IRR decision rules in the resolution of the ranking reversal problem. Logic suggests that the NPV ranking should dominate because that method will result in a value-maximizing selection of projects. In most situations, it is also more realistic to assume reinvestment of excess cash flows during the life of a project at the current cost of capital k. This again favors NPV over IRR rankings. As a result, conflicts between NPV and IRR project rankings are usually resolved in favor of the NPV rank order. Given the size-based conflict between the NPV and PI methods, which one should be relied on in the ranking of potential investment projects? The answer depends upon the amount of available resources. For a firm with substantial investment resources and a goal of maximizing shareholder wealth, the NPV method is better. For a firm with limited resources, the PI approach allocates scarce resources to the projects with the greatest relative effect on value. Using the PI method, projects are evaluated on the basis of their NPV per dollar of investment, avoiding a possible bias toward larger projects. In some cases, this leads to a better combination of investment projects and higher firm value. The PI, or benefit/cost ratio, approach has also proved to be a useful tool in public-sector decision making, where allocating scarce public resources among competing projects is a typical problem.

As seen in the evaluation of alternative capital budgeting decision rules, the attractiveness of investment projects varies significantly depending on the interest rate used to discount future cash flows. Determination of the correct discount rate is a vitally important aspect of the capital budgeting process. This important issue is the subject of the next section.

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