The authors apply the coherent potential approximation to the problem of metal-insulator transitions in the model of Falicov and Kimball (1969). It is shown that, even after taking into account the changes in the conduction band density of states due to the random distribution of scattering centres as electrons are promoted from localized to itinerant states, depending on the values of the parameters of the model, the following possibilities appear: (a) insulating phase at all temperatures, (b) metallic phase at all temperatures, (c) smooth or (d) first order transitions between these two phases as the temperature increases. The 'excitonic phases' of Ramirez et al (1970) are shown to correspond to the split band regime of the coherent potential approximation.