  Motivated by the physics of Pr-based cobaltites, we study the effect of the
external magnetic field in the hole-doped two-band Hubbard model close to
instabilities toward the excitonic condensation and ferromagnetic ordering.
Using the dynamical mean-field theory we observe a field-driven suppression of
the excitonic condensate. The onset of a magnetically ordered phase at the
fixed chemical potential is accompanied by a sizable change of the electron
density. This leads us to predict that Pr$^{3+}$ abundance increases on the
high-field side of the transition.
