Cutting precise, large diameter holes with a power drill or cordless drill can be challenging. One can use a hole saw, paddle (or spade) bit or a forstner bit of the proper diameter. While each one has it's advantages, the forstner typically drills the cleanest large-diameter holes. Forstner bits can also be tricky to use in a hand-operated drill, as they're better suited for use in a drill press. The problem with using forstner bits in a hand-operated drill is that the bits have a tendency to "walk" a bit away from the center, particularly if the tip of the bit is somewhat worn down.
There is a simple way to combat this problem. Drill a hole through a piece of scrap stock with the forstner bit you need for your project piece. It really won't matter if the forstner bit walks at the beginning of the drilling of this piece of scrap, because once the main cutters of the forstner bit engages the stock, it really cannot walk any farther.
You can then center the scrap piece of stock over the workpiece where you need your hole and clamp it in place. Then, use this scrap piece as a guide for your forstner bit to drill through the workpiece. The scrap will hold the bit in place and prevent it from walking across the workpiece.