  We model the quantities appearing in Internal Revenue Service (IRS) tax
guidance for calculating the health insurance premium tax credit created by the
Patient Protection and Affordable Care Act, also called Obamacare. We ask the
question of whether there is a procedure, computable by hand, which can
calculate the appropriate premium tax credit for any household with
self-employment income. We motivate current IRS tax guidance, which has had
self-employed taxpayers use a fixed point iteration to calculate their premium
tax credits since 2014. Then, we give an example showing that the IRS iteration
can lead to a divergent sequence of iterates. As a consequence, IRS guidance
does not calculate appropriate premium tax credits for tax returns in certain
income intervals, adversely affecting eligible beneficiaries. A bisection
procedure for calculating premium tax credits is proposed. We prove that this
procedure calculates appropriate premium tax credits for a model of simple tax
returns. This is generalized to the case where premium tax credits are received
in advance, which is the most common one in applications. We outline the
problem of calculating appropriate premium tax credits for models of general
tax returns. While the bisection procedure will work with the tax code in its
current configuration, it could fail, eg, in states which have not expanded
Medicaid, if a new deduction with certain properties were to arise.
