  Income tax systems with pass-through entities transfer a firm's incomes to
the shareholders, which are taxed individually. In 2014, a Chilean tax reform
introduced this type of entity and changed to an accrual basis that distributes
incomes (but not losses) to shareholders. A crucial step for the Chilean
taxation authority is to compute the final income of each individual, given the
complex network of corporations and companies, usually including cycles between
them. In this paper, we show the mathematical conceptualization and the
solution to the problem, proving that there is only one way to distribute
incomes to taxpayers. Using the theory of absorbing Markov chains, we define a
mathematical model for computing the taxable incomes of each taxpayer, and we
propose a decomposition algorithm for this problem. This allows us to compute
the solution accurately and with the efficient use of computational resources.
Finally, we present some characteristics of the Chilean taxpayers' network and
computational results of the algorithm using this network.
