  We present a numerical study based on Monte Carlo algorithm of the magnetic
properties of a mixed Ising ferrimagnetic model on a cubic lattice where spins
$\sigma =\pm 1/2$ and spins $S=0,\pm 1$ are in alternating sites on the
lattice. We carried out exact ground state calculations and employ a Monte
Carlo simulation to obtain the finite-temperature phase diagram of the model. A
compensation point appears when the next-nearest-neighbor interaction between
the spins $\sigma =\pm 1/2$ exceeds a minimum value. We found a strong
dependence of the compensation temperature with the interactions in the
Hamiltonian, particulary the crystal field and the external field. An applied
field can change the range of values of the compensation temperature from zero
up to a maximum value that depends on the field.
