In this paper, novel perovskite compounds XMgO$_3$ (X = Na, K and Rb) have been investigated intensively in the framework of density functional theory. The results of the magnetic and electronic properties of the perovskite reveal that the three perovskites are ferromagnets and are half-metals which make them idealfor spintronic devices. The magnetic moment of each perovskite is 3 μB. The compounds are also found to be mechanically and thermodynamically stable. From their B/G ratios, it is found that they are ductile and have highspecific heat capacities. When subjected to strains below their equilibrium lattice constants, the three compounds lose their magnetic moment.