  Using density functional theory calculations, the ground state structure of
BaFeO$_3$ (BFO) is investigated with local spin density approximation (LSDA).
Cubic, tetragonal, orthorhombic, and rhombohedral types BFO are considered to
calculate the formation enthalpy. The formation enthalpies reveal that cubic is
the most stable structure of BFO. Small energy difference between the cubic and
tetragonal suggests a possible tetragonal BFO. Ferromagnetic(FM) and
anitiferromagnetic (AFM) coupling between the Fe atoms show that all the
striochmetric BFO are FM. The energy difference between FM and AFM shows room
temperature ferromagnetism in cubic BFO in agreement with the experimental
work. The LSDA calculated electronic structures are metallic in all studied
crystallographic phases of BFO. Calculations including the Hubbard potential
$U,i.e.$ LSDA+$U$, show that all phases of BFO are half-metallic consistent
with the integer magnetic moments. The presence of half-metallicity is
discussed in terms of electronic band structures of BFO.
