(a) The property of a housing authority used exclusively for public purposes and not for profit is declared to be public property, and this property and the authority shall be exempt from all taxes and special assessments from the state or any state public body.
(b) Any property of an authority used for commercial, business, or industrial purposes shall be assessed and ad valorem taxes paid on it in the manner provided by law for the assessment and payment of taxes on other property, and the authority shall furnish the assessor with a certified statement, in writing, of the value at which the property was originally acquired to assist the assessor in arriving at the assessable value of it as provided by law.
(c) An authority may agree to make payments in lieu of taxes to a state public body for the benefit of a public housing project. However, in no event shall such payments exceed the estimated cost to the state public body of the improvements, services, or facilities to be so furnished.