In addition to all rights and powers granted to a private act hospital authority under title 7, chapter 57, part 6, such a private act hospital authority shall be exempt from the payment of any taxes or fees to the state or any subdivisions thereof, or to any officer or employee of the state or any subdivision thereof, except as hereinafter provided. This exemption does not include fees paid by private act hospital authorities as required by §68-11-216. All property of an authority residing within the boundaries of its creating or participating governing authorities or entities shall be exempt from all county and municipal taxes; provided, that the authority shall pay all county and municipal fees. An authority may agree to the payment of tax equivalents to the creating or participating governing authority or entity. Authorities shall be required to apply to the state board of equalization for claims for exemption of property residing outside the boundaries of their creating or participating governing authorities or entities. The claims for exemption shall be determined by the state board of equalization, following application in the manner required by §67-5-212, and exemptions shall be: