How do NPV and IRR differ?

I read other similar questions, but am still not getting it. I know that NPV analyzes profitability of an investment. NPV compares the value of a dollar today and in the future. When the NPV of an investment is positive it should be accepted and when it鈥檚 negative it should be rejected because cash flows might also be negative. I know that IRR is the discount rate that makes the NPV of cash flow from an investment equal to zero. So I was thinking, one obvious difference would be that one analyzes profit and the other is a discount rate. I'm not sure how to further contrast the two.

To find NPV, you discount the cash flows of a project back to the present at a reate that reflects the risk of the project. This number could be positive, negative or zero. If it is positive -- then it is a project that you should consider taking on

WIth the IRR method, you find the rate that sets the project value to zero. You then compare that the IRR to a hurdle rate. The hurdle rate is the rate that reflects the risk of the project (the same one you use in the NPV method). If the IRR is higher than the hurdle rate -- then it is a project you should consider taking on.

Under most conditions all positive NPV projects should also have an IRR greater than the hurdle rate -- so they will both tell you which projects are good. The difference is that the NPV method also tells you how much the project is worth, while the IRR method only tells you that it is good.

Let's look at an example.

Suppose that the risk free rate is 5% per year. Suppose you have two possible projects. In project one, you lend me a nickle now and I pay you back a dime in one year. In project two you lend me a million dollars and I agree to pay you back $1.1 MM in a year. Suppose that I can assure you that both of these projects are risk free.

Both projects have an IRR that exceeds the hurdle rate. Both projects have a positive NPV. The first project has a much better IRR -- and the second project has a much higher NPV.