The firm energy rights of a hydro plant is a parameter used in some electricity markets to define the maximum amount of energy that a power plant can trade through contracts. In a centralized dispatch scheme, the coordinated operation of the hydro plants generates a synergetic gain in the system firm energy, in this setting, a question that often arises is how to fairly allocate this energy among each hydro plant. This work proposes a formulation to compute the firm energy rights of hydro plants using cooperative game theory and the last addition allocation method. The main goal is to integrate the interests of hydro agents with the needs of the regulatory agencies, searching in the core of the game for solutions that give the right incentives to the optimal system development. In order to make simulations of real instances possible, it is proposed a reformulation of the traditional mixed integer linear programming model that computes the core constraints, which induces a significant speed-up of the algorithm solution time. It is shown an application of the proposed methodology to a real instance representing the Brazilian electric power system.