3.15.3. Mutually exclusive projects

The IRR rule may give the wrong ranking of mutually exclusive projects that differ in economic life or scale of required investment. If we use The IRR to rank mutually exclusive projects, we must examine the IRR on each incremental investment. Consider project A and B:

	Cash Flows ($)
Project	C0	C1	IRR (%)	NPV at 10%
A	-10.000	+20.000	100	+8.18
B	-20.000	+35.000	75	+11.818

Table 3.8

Projects A and В both are good investments, but В has the higher NPV and is, therefore, better. If manager follow the IRR rule, manager has satisfaction of earning a 100 percent rate of return; if manager follow the NPV rule, manager is $11.818 richer. It is possible to salvage the IRR rule in this case by looking at the internal rate of return on the incremental flows. And manager asks themselves whether it is worth making the additional investment in В. The incremental flows from undertaking В rather than an are as follows:

	Cash Flows ($)
Project	C0	C1	IRR (%)	NPV at 10%
B-A	-10.000	+13.000	50	+3.636

Table 3.9

The IRR on the incremental investment is 50 percent, which is also well in excess of the 10 percent opportunity cost of capital. So we should prefer project В to project A. Sometimes manager may have problems when series of incremental cash flows may involve several changes in sign. In this case there are likely to be multiple IRRs and we will be forced to use the NPV rule after all.

3.16. The cost of capital for near-term and distant cash flows

The cost of capital for near-term cash flows may be different from the cost for distant cash flows. The IRR rule requires us to compare the project’s IRR with the opportunity cost of capital. But sometimes there is an opportunity cost of capital for one year cash flows, a different cost of capital for two-year cash flows, and so on. In these cases there is no simple yardstick for evaluating the IRR of project. It is possible to assume that the opportunity cost of capital is the same for all the cash flows, C1, C2, C3, etc.

NPV = (3.7)

The IRR rules tell us to accept a project if the IRR is greater than the opportunity cost of capital. But what do we do when we have several opportunity cost of capital? Managers may have trouble for the IRR whenever the term structure of interest rates becomes important. Many firms use the IRR, thereby implicitly assuming that there is no difference between short-term and long-term rate of interest. They do this for simplicity. Four examples manager had given of things that can go wrong with IRR. This does not mean that IRR is worse the other measures. The IRR rule is less easy to use than NPV, but, used properly it gives the same result.

	Cash Flows ($)
Project	C0	C1	C2	C3	IRR (%)	NPV at 8%
A	-9.0	2.9	4.0	5.3	15.58	1.4
B	-9,000	2,560	3,540	4,530	8.01	1.4

Table 3.10