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Why does the internal rate of return equate to a net present value of zero?

Internal rate of return and net present value are discounted cash flow techniques. To discount means to remove the interest contained within the future cash amounts.

If the net present value of an investment or project is more than $0, the project is earning more than the interest rate used to discount the future cash amounts. If the net present value of a project is less than $0, the project is earning less than the interest rate used to discount the future cash amounts.

If the present value of a project is exactly $0, the project is earning exactly the interest rate used to discount the future cash amounts. In other words, if a project has an internal rate of return of 15%, and you discount the project's future cash amounts by 15%, the project's net present value will be exactly $0.