These prizes really confuse me. Wouldn't it cost more than $20 million just to get something into LEO with existing technology? How can mounting a robotic lunar mission possibly be done for less than that?
The intention of the prize is not to cover the costs but to kickstart an ambitious private space movement. One needs to be very lean, inventive, and somewhat risk-taking under those conditions. It forces one to think of business models that make the whole thing independent from a possible prize money (and government funding, which under GLXP rules is limited to 10%).
Don't underestimate the PR value. Space Ship One cost $25M to win the $10M X-Prize, but having a big prize can capture the imagination of the media and by extension the public.