; and (2) by adding at the end the following: (d) Royalties (1) Definitions In this subsection: (A) Assessment value (i) In general The term assessment value , with respect to Federal coal, means the gross proceeds accruing to the lessee or the affiliate of the lessee’s first arm’s length contract for the sale of Federal coal. (ii) Exception If the Secretary cannot identify any arm’s length contract for the sale of Federal coal, then the assessment value means a price imputed by the Secretary based on the coal price index. (B) Arm’s length contract The term arm’s length contract means a contract, agreement, or transaction for the sale of Federal coal that is between parties that are independent of each other and that are not affiliates. (C) Affiliate The term affiliate , with respect to a lessee, means a party that controls, is controlled by, or is under common control with the lessee, and includes a parent or subsidiary company. (D) Coal price index The term coal price index means the schedule of average market prices of Federal coal (in United States dollars) at final sale, based on the quality and type of the Federal coal, as determined by the Secretary, in consultation with the Administrator of the Energy Information Administration. (E) Secretary The term Secretary means the Secretary of the Interior. (2) Payment rate (A) In general Except as provided in subparagraph (B), a lease shall require payment of a royalty in such amount as the Secretary shall determine, which shall not be less than 12.5 percent of the assessment value of Federal coal. (B) Exception In the case of Federal coal recovered by an underground mining operation, the Secretary may establish such lower royalty payment rate as the Secretary determines to be appropriate in lieu of the royalty payment rate described in subparagraph (A). (3) Administration (A) Reporting The Secretary shall ensure that any purchaser of Federal coal shall annually submit to the Secretary a report containing such information as the Secretary determines to be