  We consider the static, spherically symmetric and asymptotically flat BPS
extremal black holes in ungauged N = 2 D = 4 supergravity theories, in which
the scalar manifold of the vector multiplets is homogeneous. By a result of
Shmakova on the BPS attractor equations, the entropy of this kind of black
holes can be expressed only in terms of their electric and magnetic charges,
provided that the inverse of a certain quadratic map (uniquely determined by
the prepotential of the theory) is given. This inverse was previously known
just for the cases in which the scalar manifold of the theory is a homogeneous
symmetric space. In this paper we use Vinberg's theory of homogeneous cones to
determine an explicit expression for such an inverse, under the assumption that
the scalar manifold is homogeneous, but not necessarily symmetric. As immediate
consequence, we get a formula for the entropy of BPS black holes that holds in
any model of N = 2 supergravity with homogeneous scalar manifold.
