A lot! I have a 40x50 barn which is insured for $80,000. Your barn will be 30% larger than that.
My barn is post and beam, built in the 1800's, so replacing it with a new post and beam barn would cost $80K or more. I chose $80K for the insurance as I would build a smaller barn if this one burned down. I don't need that much space. If you went with metal, it would be less. I've heard a radio ad for $30K for a 5000 sq ft metal building. You don't say where you live, but that can impact costs by 20-30% as well. Are you doing the work yourself, or hiring a contractor?
Are you sure you want drywall in a barn? Normally interior walls are plywood or board. Drywall is not normally used unless you plan to heat and air condition it. Moisture can be a problem with drywall.
Also check your taxes on a barn that size. Depending where you live, it could be $0 to several thousand dollars a year. That makes a smaller barn a consideration as well since its not just construction cost.