International Review of Business, Trade, and Economics
Closed-Loop Valuation Theory: Structural Admissibility, Claimant Boundaries, and Computational Proof through Model C
Abstract
Hany Hassanien Badr
This paper advances closed-loop valuation from a general structural-convergence framework into a theory of structural admissibility and then subjects that theory to a computational proof through Model C, an author-controlled 28-worksheet system. Part I formalizes a claimant-boundary principle: numerical equality is required only when two routes value the same economic claim at the same date under aligned capital, cash-flow, discount-rate, and terminal assumptions; when boundaries differ, non-equality is admissible only if the difference is explicitly bridged and economically explained. The theory further distinguishes local closure from global closure, requires capital continuity, claimant conservation, return- income-cash-flow transformability, discount-rate congruence, temporal discipline, terminal-state legitimacy, reversibility, and visible failure, and treats structural refusal as a valid outcome when these conditions are not jointly satisfied. Part II applies these propositions to Model C for 2005-2009 and the continuing state. The workbook reproduces FCFE through three substantive derivations and a fourth dependent audit representation, reconstructs FCFF from FCFE by restoring debt movement and workbook-reported after-tax interest, and keeps fixed WACC, standalone required return on equity, realized ROE, and the author-defined WACE mapping analytically distinct. DCF and EVA converge on operating value of 74,268.4586 and, after the model’s opening claim bridge, common-equity value of 73,718.4586. The standalone FCFE route produces a different per-share value because its displayed claimant boundary is not identical; the difference is reported rather than suppressed, illustrating the boundary principle. At the continuing-value boundary, FCFE continuing value of 108,791.1362 plus debt movement of 2,121.0000 and a 9,377.9090 financing residual reconcile exactly to FCFF continuing value of 120,290.0452. Because that residual is formulaically derived as a difference, the paper preserves the workbook’s tax-shield label but does not treat it as an independently derived tax-shield valuation. The combined contribution is a falsifiable valuation-control architecture in which the existence of a number is insufficient: value becomes admissible only after the path to value closes at every relevant boundary.