## Irr2088

The two decision rules yield different results. The net present value rule suggests that project B is the better project, while the internal rate of return rule leans towards project A. This is not surprising, given the differences in scale.

Which rule yields the better decision? The answer depends on the capital rationing constraints faced by the business making the decision. When there are no capital rationing constraints (i.e., the firm has the capacity to raise as much capital as it needs to take prospective projects), the net present value rule provides the right answer - Project B should be picked over Project A. If there are capital rationing constraints, however, then taking Project B may lead to the rejection of good projects later on. In those cases, the internal rate of return rule may

Capital Rationing: This refers to the scenario where the firm does not have sufficient funds - either on hand or in terms of access to markets - to take on all of the good projects it might have.

Profitability Index (PI): The profitability index is the net present value of a project divided by the initial investment in the project - it is a scaled version of NPV.

provide the better solution. The capital rationing question is dealt with in more detail in Chapter 6.

Another approach to scaling NPV: The Profitability Index

Another way of scaling the net present value is to divide it by the initial investment in the project. Doing so provides the profitability index which is another measure of project return.

Net Present Value

Profitability Index =-

Initial Investment

In Illustration 5.17, for instance, the profitability index can be computed as follows for each project:

Profitability Index for Project A = $467,937/$1,000,000 = 46.79%

Profitability Index for Project B = $ 1,358,664/ $10,000,000 = 13.59%

Based on the profitability index, project A is the better project, after scaling for size.

In most cases, the profitability index and the internal rate of return will yield similar results. As we will see in the next section, the differences between these approaches can be traced to differences in reinvestment assumptions.

### Differences in Reinvestment Rate Assumption

While the differences between the NPV rule and the IRR rules due to scale are fairly obvious, there is a subtler, and much more significant difference between the two rules, relating to the reinvestment of intermediate cash flows. As pointed out earlier, the net present value rule assumes that intermediate cash flows are reinvested at the discount rate, whereas the IRR rule assumes that intermediate cash flows are reinvested at the IRR. As a consequence, the two rules can yield different conclusions, even for projects with the same scale, as illustrated in Figure 5.10.

Figure 5.10: NPV and IRR - Reinvestment Assumption

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