In a lot of cases, a buyout like this one is the first step in taking the company public. The company used to be public, but changed to a limited partnership in the 80's after a couple of takeover scares. Wouldn't be surprised to see that happening soon.
So when you sell your business to them, you can generally expect that you will be servicing more debt, not less. Granted, a smart equity firm will leave enough money in to run the business well but this may mean a lower selling price than Cedar Fair would hope for. If the buyer can't draw out as much cash, they won't pay as much.