The design of corporate tax structures

We consider the corporate tax structuring problem (TaxSP), a combinatorial optimization problem faced by firms with multinational operations. The problem objective is nonlinear and involves the minimization of the firm's overall tax payments i.e. the maximization of shareholder returns. We give a dynamic programming (DP) formulation of this problem including all existing schemes of tax-relief and income-pooling. We apply state space relaxation and state space descent to the DP recursions and obtain an upper bound to the value of optimal TaxSP solutions. This bound is imbedded in a B&B tree search to provide another exact solution procedure. Computational results from DP and B&B are given for problems up to 22 subsidiaries. For larger size TaxSPs we develop a heuristic referred to as the Bionomic Algorithm (BA). This heuristic is also used to provide an initial lower bound to the B&B algorithm. We test the performance of BA firstly against the exact solutions of TaxSPs solvable by the B&B algorithm and secondly against results obtained for large-size TaxSPs by Simulated Annealing (SA) and Genetic Algorithms (GA). We report results for problems of up to 150 subsidiaries, including some real-world problems for corporations based in the US and the UK.