Both of these measurements are primarily used in capital budgeting, the process by which companies determine whether a new investment or expansion opportunity is worthwhile. Given an investment opportunity, a firm needs to decide whether undertaking the investment will generate net economic profits or losses for the company.
To do this, the firm estimates the future cash flows of the project and discounts them into present value amounts using a discount rate that represents the project's cost of capital and its risk. Next, all of the investment's future positive cash flows are reduced into one present value number. Subtracting this number from the initial cash outlay required for the investment provides the net present value (NPV) of the investment.
Let's illustrate with an example: suppose JKL Media Company wants to buy a small publishing company. JKL determines that the future cash flows generated by the publisher, when discounted at a 12% annual rate, yields a present value of $23.5 million. If the publishing company's owner is willing to sell for $20 million, then the NPV of the project would be $3.5 million ($23.5  $20 = $3.5). The $3.5 million dollar NPV represents the intrinsic value that will be added to JKL Media if it undertakes this acquisition.
So, JKL Media's project has a positive NPV, but from a business perspective, the firm should also know what rate of return will be generated by this investment. To do this, the firm would simply recalculate the NPV equation, this time setting the NPV factor to zero, and solve for the now unknown discount rate. The rate that is produced by the solution is the project's internal rate of return (IRR).
For this example, the project's IRR could, depending on the timing and proportions of cash flow distributions, be equal to 17.15%. Thus, JKL Media, given its projected cash flows, has a project with a 17.15% return. If there were a project that JKL could undertake with a higher IRR, it would probably pursue the higheryielding project instead. Thus, you can see that the usefulness of the IRR measurement lies in its ability to represent any investment opportunity's return and to compare it with other possible investments.
To learn more, read Taking Stock Of Discounted Cash Flow, Anything But Ordinary: Calculating The Present And Future Value Of Annuities and Investors Need A Good WACC.

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Net Present Value  NPV
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Net Present Value Rule
A rule stating that an investment should be accepted if its net ... 
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Pooled Internal Rate Of Return  PIRR
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