Starfleet Accounting
According to the script of the Star Trek: Deep Space Nine fifth season episode "For the Uniform", Starfleet Accounting was a subdivision of Starfleet.
According to a scene which did not make it into the broadcast version of the episode, Starfleet Accounting received the bill when Starfleet officers ordered food or drinks at Quark's. In the scene, Miles O'Brien complained to Quark that Starfleet Accounting had been all over him for ordering six cases of Champagne for the night shift, the implication being that Quark was billing O'Brien for stuff he didn't order. (Star Trek: Deep Space Nine Companion - A Series Guide and Script Library)
As the scene never made it into an episode, and thus never into canon, it is unknown how the economies of the Federation and the Ferengi Alliance would work together. In the Cards would refer to this open question thoroughly.