An NPV profile is a graph created by plotting NPV on the y-axis and discount rate on the x-axis. NPV profile is convex to the origin.
Comparison of NPV and IRR
For an independent project with a conventional cash flow pattern, NPV and IRR approaches agree on decisions, but in the case of mutually exclusive projects, there might be disagreement. Disagreement arises when project cash flow distribution differs or their scale differs. When that happens, NPV should always be the preferred approach. It is because IRR assumes a higher reinvestment rate, which is unrealistic. Further, since NPV points to a project which maximum dollar value, it should be preferred because it is better to earn a lower return on a large project than a higher return on a small project.
Even though academic literature preaches the use of NPV and IRR, in practice many companies use the payback period. Larger firms tend to prefer NPV and IRR. Private companies prefer the payback period more often. Companies managed by people with finance/business background prefer discounted cash flow techniques.