  The electronic structure and magnetic properties of a newly predicted stable
ternary compound La$_{18}$Co$_{28}$Pb$_{3}$ are studied using electronic
structure analysis. The ground state of this compound is ferromagnetic, with
three positions of nonequivalent magnetic Co atoms. A strong dependence of
magnetic properties on volume shows that this system is situated near the point
of magnetic instability. A coexistence of high- and low-spin ferromagnetic
states as a function of volume near equilibrium was discovered. A corresponding
spin tunneling splitting was estimated. The stability of the theoretically
predicted magnetic ground state was tested by varying the Hubbard parameter.
The thermal spin fluctuations were added to estimate the paramagnetic moment
and a Curie temperature. The necessity of experimental verification of the
obtained results is emphasized.
