  Boron carbide (B$_4$C) has been well studied both theoretically and
experimentally in its bulk form due to its exceptional hardness and use as a
high temperature thermoelectric. However, the properties of its two-dimensional
nanosheets are not well established. In this paper, using van der Waals
corrected density-functional theory (DFT) simulations, we show that the bulk
B$_4$C can be cleaved along different directions to form B$_4$C nanosheets with
low formation energies. We find that there is minimal dependence of the
formation energies on the cleavage planes and surface terminations. Whilst the
density of states of the bulk B$_4$C indicate that it is a semiconductor, the
B$_4$C nanosheets are found to be predominantly metallic. We attribute this
metallic behaviour to a redistribution of charges on the surface B-C bonds of
the films. The Seebeck coefficients of the the B$_4$C films remain comparable
to those of the bulk, and are nearly constant as a function of temperature. Our
results provide guidance for experimental synthesis efforts and future
application of B$_4$C nanosheets in nanoelectronic and thermoelectric
applications.
