How do net present value (NPV) and internal rate of return (IRR) relate to each

Question

How do net present value (NPV) and internal rate of return (IRR) relate to each other mathematically? How does modified internal rate of return (MIRR) compare to internal rate of return (IRR)? How do net present value (NPV) and internal rate of return (IRR) relate to each other mathematically? How does modified internal rate of return (MIRR) compare to internal rate of return (IRR)? How do net present value (NPV) and internal rate of return (IRR) relate to each other mathematically? How does modified internal rate of return (MIRR) compare to internal rate of return (IRR)?

Explanation / Answer

Internal rate of return (IRR) is a metric used in capital budgeting measuring the profitability of potential investments. Internal rate of return is a discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. IRR calculations rely on the same formula as NPV does.

To calculate IRR using the formula, one would set NPV equal to zero and solve for the discount rate r, which is here the IRR. Because of the nature of the formula, however, IRR cannot be calculated analytically, and must instead be calculated either through trial-and-error or using software programmed to calculate IRR.

Generally speaking, the higher a project's internal rate of return, the more desirable it is to undertake the project. IRR is uniform for investments of varying types and, as such, IRR can be used to rank multiple prospective projects a firm is considering on a relatively even basis. Assuming the costs of investment are equal among the various projects, the project with the highest IRR would probably be considered the best and undertaken first.

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