Now assume that Projects S and L are mutually exclusive rather than independent. That is, we can choose either Project S or Project L, or we can reject both, but we cannot accept both projects. Notice in Figure 7-4 that as long as the cost of capital is greater than the crossover rate of 7.2 percent, then (1) NPVS is larger than NPVL and
FIGURE 7-4 Net Present Value Profiles: NPVs of Projects S and L at Different Costs of Capital
See Ch 07 Tool Kit.xls.
Net Present Value ($)
300'
Project L's Net Present Value Profile
-100
FIGURE 7-4 Net Present Value Profiles: NPVs of Projects S and L at Different Costs of Capital
Project L's Net Present Value Profile
300'
-100
Project S's Net Present Value Profile y
Cost of Capital_NPVS_NPVL
Project S's Net Present Value Profile y
Cost of Capital_NPVS_NPVL
5 180.42 206.50
10 78.82 49.18
(2) IRRS exceeds IRRL. Therefore, if r is greater than the crossover rate of 7.2 percent, the two methods both lead to the selection of Project S. However, if the cost of capital is less than the crossover rate, the NPV method ranks Project L higher, but the IRR method indicates that Project S is better. Thus, a conflict exists if the cost of capital is less than the crossover rate.8 NPV says choose mutually exclusive L, while IRR says take S. Which is correct? Logic suggests that the NPV method is better, because it selects the project that adds the most to shareholder wealth. But what causes the conflicting recommendations?
Two basic conditions can cause NPV profiles to cross, and thus conflicts to arise between NPV and IRR: (1) when project size (or scale) differences exist, meaning that the
8The crossover rate is easy to calculate. Simply go back to Figure 7-1, where we set forth the two projects' cash flows, and calculate the difference in those flows in each year. The differences are CFS — CFl = $0, + $400, +$100, —$100, and —$500, respectively. Enter these values in the cash flow register of a financial calculator, press the IRR button, and the crossover rate, 7.17% ^ 7.2%, appears. Be sure to enter CF0 = 0 or else you will not get the correct answer.
cost of one project is larger than that of the other, or (2) when timing differences exist, meaning that the timing of cash flows from the two projects differs such that most of the cash flows from one project come in the early years while most of the cash flows from the other project come in the later years, as occurred with our Projects L and S.
When either size or timing differences occur, the firm will have different amounts of funds to invest in the various years, depending on which of the two mutually exclusive projects it chooses. For example, if one project costs more than the other, then the firm will have more money at t = 0 to invest elsewhere if it selects the smaller project. Similarly, for projects of equal size, the one with the larger early cash inflows—in our example, Project S—provides more funds for reinvestment in the early years. Given this situation, the rate of return at which differential cash flows can be invested is a critical issue.
The key to resolving conflicts between mutually exclusive projects is this: How useful is it to generate cash flows sooner rather than later? The value of early cash flows depends on the return we can earn on those cash flows, that is, the rate at which we can reinvest them. The NPV method implicitly assumes that the rate at which cash flows can be reinvested is the cost of capital, whereas the IRR method assumes that the firm can reinvest at the IRR. These assumptions are inherent in the mathematics of the discounting process. The cash flows may actually be withdrawn as dividends by the stockholders and spent on beer and pizza, but the NPV method still assumes that cash flows can be reinvested at the cost of capital, while the IRR method assumes reinvestment at the project's IRR.
Which is the better assumption—that cash flows can be reinvested at the cost of capital, or that they can be reinvested at the project's IRR? The best assumption is that projects' cash flows can be reinvested at the cost of capital, which means that the NPV method is more reliable.
We should reiterate that, when projects are independent, the NPV and IRR methods both lead to exactly the same accept/reject decision. However, when evaluating mutually exclusive projects, especially those that differ in scale and/or timing, the NPV method should be used.
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What you need to know about… Project Management Made Easy! Project management consists of more than just a large building project and can encompass small projects as well. No matter what the size of your project, you need to have some sort of project management. How you manage your project has everything to do with its outcome.