Don't overload the onchange event by auto-submitting, it's counterintuitive to what people expect of a select control.
I think you should A/B test this and by that I mean create a version of the button that mentions the one month free and one that presents the facts in a different way. Try to think like a salesperson. Would a salesperson come up to you and say, "You know, you can sign up for this for $10/month or you can pay me $110 and I'll give you a free month!"? Maybe. But maybe he'd say "Check out this incredible deal - just $110 for 12 months service! That's only $9.17 compared to $10/month for the regular price! You're saving $10! This deal ends soon so I don't know if I'll be able to hook you up if you don't decide quickly!"
My point is that you should consider how to write your copy in a way that sells the user on this annual deal. Obviously the reason the package deal exists is because you want them to sign up for it, so consider the right copy to balance between getting your deal sold with communicating the right information.
37signals have near-standardised the pricing page with their approach for Basecamp and other products. They promote the Premium plan, which isn't the cheapest, but they balance that by claiming it's the "best value" and "the sweet spot" and "only $99/month". Subtle copy here is salesmanship - Jason Fried would have been a great car salesman :-)