No one does things for free, or out of the goodness of their heart (business folks that sign papers). This new company will make money somehow somewhere, I'd be looking for where. My company was letting pur sales lady go around and sell darn near full maintenance contracts for dirt cheap. The company was loosing money, but she was making big bucks on commission, with an absentee boss. Then she'd turn around and be dishonest and try to charge customers for proposer things that were covered by the contract. We got a new boss that figured her out and she left.
Anyhow what im getting at is old sayings are true. Follow the money. And if it sounds to good to be true, it probably is. Definitely figure out this new company's plan to make money from this.
For example, my companies current business model is lie cheat and steal customers money. Charge them for the maintenance according to the contract and NEVER show up. The only customers that see my face are breakdowns and customers that want a refund for missed maintenance visits. If this new company is truly cheaper, are they going to show up on time and do that quality work they should? What's your recourse if they don't show up? I wouldn't sign anything that allows a number of visits per year. It's gotta be on time. 4 visits in December is not the same as four quarterly maintenance visits.
In case you couldn't tell, I'm a mechanic with a bit of experience in contracts etc, not office staff.