NPV rule and IRR rule

CFA level I / Quantitative Methods: Basic Concepts / Discounted Cash Flow Applications / NPV rule and IRR rule

We have already discussed the NPV rule and the IRR rule. The NPV rule is - select the projects having positive NPV and reject the projects having negative NPV. The IRR rule is - select the projects having IRR greater than their cost of capital and reject the projects having IRR greater than their cost of capital.

Both projects should provide the same answer when it is done for independent projects. However, for mutually exclusive projects, the NPV rule is preferred over the IRR rule as the ranking of the mutually exclusive projects could be different using NPV rule and IRR rule. The ranking can be different because of the following reasons:

• the timing of the cash flows can differ for different project greatly impacting the IRR
• the size/scale of the projects can differ

If the cash inflows occur earlier in the life of the project, then the IRR can become very high. But the NPV of that project could be much lower than the other similar project with lower IRR. It can be seen from the table given below:

	Project A	Project B
Intial outlay	50,000	-50,000
Cash flow for year 1	60,000	20,000
Cash flow for year 2	10,000	30,000
Cash flow for year 3	1,000	50,000
Cash flow for year 4	1,000	70,000
IRR (in percent)	36.51	30.36
NPV (at 8 percent)	14,497.97	23,522.17

We can see from the above table that the IRR of the Project A is higher than Project B but the NPV of Project A is much smaller than that of Project B. Project B will add more wealth for the shareholders and should be selected over Project A.

Other problems with IRR is that some projects have multiple IRR (if the sign of cash flows changes more than once) or no IRR at all.

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