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 15.1. 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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