When comparing two projects, the use of the NPV and the IRR methods may give different results. A project selected according to the NPV may be rejected if the IRR method is used.

Suppose there are two alternative projects, X and Y. The initial investment in each project is $2,500. Project X will provide annual cash flows of $500 for the next 10 years. Project Y has annual cash flows of $100, $200, $300, $400, $500, $600, $700, $800, $900, and $1,000 in the same period. Using the trial and error method explained before, you find that the IRR of Project X is 17% and the IRR of Project Y is around 13%. If you use the IRR, Project X should be preferred because its IRR is 4% more than the IRR of Project Y. But what happens to your decision if the NPV method is used? The answer is that the decision will change depending on the discount rate you use. For instance, at a 5% discount rate, Project Y has a higher NPV than X does. But at a discount rate of 8%, Project X is preferred because of a higher NPV.

The purpose of this numerical example is to illustrate an important distinction: The use of the IRR always leads to the selection of the same project, whereas project selection using the NPV method depends on the discount rate chosen.

**PROJECT SIZE AND LIFE**

There are reasons why the NPV and the IRR are sometimes in conflict: the size and life of the project being studied are the most common ones. A 10-year project with an initial investment of $100,000 can hardly be compared with a small 3-year project costing $10,000. Actually, the large project could be thought of as ten small projects. So if you insist on using the IRR and the NPV methods to compare a big, long-term project with a small, short-term project, don’t be surprised if you get different selection results. (See the equivalent annual annuity discussed later for a good way to compare projects with unequal lives.)

**DIFFERENT CASH FLOWS**

Furthermore, even two projects of the same length may have different patterns of cash flow. The cash flow of one project may continuously increase over time, while the cash flows of the other project may increase, decrease, stop, or become negative. These two projects have completely different forms of cash flow, and if the discount rate is changed when using the NPV approach, the result will probably be different orders of ranking. For example, at 10% the NPV of Project A may be higher than that of Project B. As soon as you change the discount rate to 15%, Project B may be more attractive.

**WHEN ARE THE NPV AND IRR RELIABLE?**

Generally speaking, you can use and rely on both the NPV and the IRR if two conditions are met. First, if projects are compared using the NPV, a discount rate that fairly reflects the risk of each project should be chosen. There is no problem if two projects are discounted at two different rates because one project is riskier than the other. Remember that the result of the NPV is as reliable as the discount rate that is chosen. If the discount rate is unrealistic, the decision to accept or reject the project is baseless and unreliable. Second, if the IRR method is used, the project must not be accepted only because its IRR is very high. Management must ask whether such an impressive IRR is possible to maintain. In other words, management should look into past records, and existing and future business, to see whether an opportunity to reinvest cash flows at such a high IRR really exists. If the firm is convinced that such an IRR is realistic, the project is acceptable. Otherwise, the project must be reevaluated by the NPV method, using a more realistic discount rate.