A tax break for investor-owned hospitals that was tucked into a deal last spring aimed at saving the Illinois Medicaid program from collapse will cost the cash-strapped state at least $10 million a year in lost revenue, according to an analysis by The Associated Press. Hospital industry officials say the tax credit recognizes the free care they provide to the uninsured. But some state officials were puzzled about how for-profit hospitals were able to land a major tax break in the intense closed-door negotiations at a time Springfield was grappling with a dire financial crisis.