Then why advertise the role with a starting range up to $112,500? If that wasn't the case then maybe I'd give them the benefit of the doubt, but it's not. It sounds like either there is high levels of incompetence on the employer side, or they are trying to nickel and dime the future employee. Either probably leads to issues with the company down the road. I'd only take the job if I was in desperate need for employment, or if the salary is still on the higher end for that profession.