The payback period is the time it takes for a project's cash inflows to repay its initial cash outflows. It is calculated by dividing the initial investment by the annual cash inflow. The document provides an example of calculating the 2.5 year payback period of Machine X, which costs $25,000 with annual cash inflows of $10,000. Since Machine X's payback period is less than the company's maximum of 3 years, it would be purchased.