In this paper the Structural Theory of Thermoeconomics is proposed as a standard and common mathematical formulation for all thermoeconomic methodologies employing thermoeconomic models that can be expressed by linear equations. In previous works it has been demonstrated that the Exergy Cost Theory (ECT), the AVCO approach and the Thermoeconomic Functional Analysis (TFA) can be dealt with the Structural Theory. In this paper, it is demonstrated that the Last-in-First-Out (LIFO) approach, a thermoeconomic cost accounting method, can also be reproduced with the Structural Theory. The LIFO and the Structural Theory are both applied to a combined cycle plant and it is shown that the equation systems obtained from both methods are the same. Moreover, a procedure to develop the productive structure representing the thermoeconomic model of LIFO (i.e. from which the same costing equations are obtained as with the LIFO approach) is explained in detail, which provides the tools to reproduce the costs obtained from LIFO with the Structural Theory for complex energy systems. This paper concludes a series of research works where it has been demonstrated that the most developed thermoeconomic optimization and cost accounting methodologies, as all of them employ thermoeconomic models that can easily be linearized, can be dealt with by the mathematical formalism of the Structural Theory.