Apply the NPV and then the IRR methods to mutually exclusive investments

Mutually exclusive projects:

If the NPV of one project is greater than the NPV of the other project, accept the project with the higher NPV. If both projects have a negative NPV, reject both projects. Accept the project with heigher NPV.If cash flow is different in size then IRR is better.

Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. By contrast, the internal rate of return (IRR) is a calculation used to estimate the profitability of potential investments.
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.
Determining NPV
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.1 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 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 percent 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 NPV of $3.5 million represents the instinct value that will be added to JKL Media if it undertakes this acquisition.
Determining IRR
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 dicount 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 higher-yielding project instead.
Thus, you can see that the usefulness of the IRR measurement lies in its ability to represent any investment opportunity's possible return and compare it with other alternative investments.