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Relationship between NPV and IRR

I am looking for some more detailed information with regard to the relationship between net present value (NPV) and internal rate of return (IRR) (Note: the key factor here is the discount rate used). Furthermore, I was hoping someone might be able to explain how they might analyze projects differently if they had unequal projected years (ie Corporation A had a 5-year projection and corporation B had a 7-year projection).

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Relationship between NPV and IRR

NPV is obtained by discounting all the cash flows by the required rate of return.
It is calculated by summing the present value of the net benefits for each year over a specified period of time, then subtracting the initial costs of the project. A positive NPV means that the project generates a profit, while a negative NPV means that the project generates a loss.

IRR equals the percentage rate by which the net benefits have to be discounted until the point that they equal the initial costs. IRR is closely related to net present value. The rate of return calculated by IRR is the discount rate one would need to apply to the benefits of the project to obtain a net present value of zero.

If we discount all the cash flows at the IRR rate we get an NPV of zero. Or equivalently, the IRR is a discount ...

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Solution discusses relationship between net present value and internal rate of return.

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