  We present a preliminary lattice determination of the masses and decay
constants of the pseudoscalar and vector mesons $B_c$ and $B_c^*$. Our analysis
is based on the gauge configurations produced by the European Twisted Mass
Collaboration with $N_f = 2 + 1 + 1$ flavors of dynamical quarks. We simulated
at three different values of the lattice spacing and with pion masses as small
as 210 MeV. Heavy-quark masses are simulated directly on the lattice up to
$\sim 3$ times the physical charm mass. The physical b-quark mass is reached
using the ETMC ratio method. Our preliminary results are: $M_{B_c} =
6341\,(60)$ MeV, $f_{B_c} = 396\,(12)$ MeV, $M_{B_c^*} / M_{B_c} =
1.0037\,(39)$ and $f_{B_c^*} / f_{B_c} = 0.987\,(7)$.
