You should first and foremost consult a lawyer specializing in labor law in your jurisdiction, firing people depending on your location can be easy or nigh-on impossible.

That said, I'd be very straight with this person, explain that you no longer wish to continue with them. If their contract will lapse within the next 6 months or so I wouldn't do anything other than maybe just buying out their contract for a lump sum. Otherwise just wait it out and hire your new guy/gal when you can afford it.

I'm not sure I like the 'we could pay a lot less' bit since that seems to indicate your motive is more economical than tied to this persons performance.