  We present the results of paramagnetic LDA band structure calculations: band
dispersions, densities of states and Fermi surfaces, for the new iron based
high-temperature superconductor LiOHFeSe. Main structural motif providing bands
in the vicinity of the Fermi level is FeSe layer which is isostructural to the
bulk FeSe prototype superconductor. The bands crossing the Fermi level and
Fermi surfaces of the new compound are typical for other iron based
superconductors. Experimentally it was shown that introduction of Fe ions into
LiOH layer gives rise to ferromagnetic ordering of the Fe ions at T$_C$=10K. To
study magnetic properties of [Li$_{0.8}$Fe$_{0.2}$OH]FeSe system we have
performed LSDA calculations for $\sqrt 5 \times \sqrt 5$ superlattice and found
ferromagnetism within the Li$_4$Fe(OH) layer. To estimate the Curie temperature
we obtained Fe-Fe exchange interaction parameters for Heisenberg model from our
LSDA calculations, leading to theoretical value of Curie temperature 10.4K in
close agreement with experiment.
