# 1.30 The NPV vs. the IRR: Differences in Methodologies (Summary and Review)

NPV:

• Use of the firm’s “cost of capital” as the discount rate.
• We may think of the cost of capital as an external rate, i.e., external to the formula.
• For now, the cost of capital has been “given.”
• Accept only those projects whose NPV > \$0; reject all others.
• If given two or more competing, or “mutually exclusive,” projects, choose that project, which provides the highest NPV (assuming its NPV > \$0).

IRR:

• Calculate the IRR through an “iterative,” Trial and Error process.
• If the initial NPV > 0, you must raise the discount rate.
• The discount rate, where NPV = 0, is the IRR
• Choose only those independent projects whose IRR exceeds the stated cost of capital;
• This also means that NPV > 0
• If given mutually exclusive projects, choose that project which has the highest IRR (provided the IRR exceeds the firm’s cost of capital)

Note:

Let’s say that at a 10% cost of capital / discount rate, a project’s NPV is \$1,000. In order to get the NPV “down” to zero, the rate must be raised. Thus, if a project’s IRR exceeds the firm’s cost of capital, the project’s NPV, using the cost of capital as the discount rate – mathematically – must be positive.