I'm a professional software developer working for a company that primarily does contract work. (Note, I don't do much with the sales side, so take most of this with a fair-sized grain of salt.)
IIRC, our overhead rate is around 100% and is considered extremely low for the industry. I'm not going to give my hourly rate, but at a guess, if you're talking US in a region that isn't overly expensive, you're looking at around $70 - $120 per hour at the experience level you mentioned. (Increase this if you're talking to a company that operates out of somewhere expensive, e.g. California.) I'd probably figure on a more conservative overhead rate, so I'd guess customer cost is maybe $200 - $400 per developer-hour.
Now, that said, you obviously didn't give a lot of project details, but "at least 1 year (possibly more)" sounds excessive unless we're talking an awful lot of functions. That said, the only real way to answer this sort of question is to actually solicit bids. Given that you're asking this question, I'm guessing you don't have a lot of software experience yourself. That being the case, the people that do this for a living are probably going to be able to give you a much better time estimate. (Of course, they'll need a lot more details than you've given here to do so.)
Something else I'd point out, however... why do you think you need 15+ years experience? Nothing you listed strikes me as something that needs depth of experience. What you need is breadth of experience. Sure, a pair of senior developers can probably bring that, but it might be more cost-effective to find the right mix of several (4+) junior developers. That would also give some chance of the project getting done faster (in calendar time).