The low-temperature macroscopic phase separation in La$_{0.5}$Ba$_{0.5}$CoO$_{3-\delta}$ cobaltite

La$_{0.5}$Ba$_{0.5}$CoO$_{2.87}$ has been characterized with neutron and synchrotron powder diffraction and magnetization measurements. This compound was shown to have a cubic crystal structure at temperatures above 200 K whereas slightly above the Curie point $T_c\sim170$ K the structural separation into two different pseudocubic phases gradually develops upon cooling. The structural transformation is reversible. At 2 K the sample consists of G-type antiferromagnetic oxygen-poor and ferromagnetic oxygen-rich phases (approximately 33% and 66% respectively).