Hybrid-exchange density functional theory calculations are carried out to determine the effects of A-site doping on the electronic and magnetic properties of the manganite series La1-xCaxMnO3. This study focuses on the ground state of an ordered Ca occupancy in a periodic structure. It is shown that the hybrid-exchange functional, Becke three-parameter Lee-Yang-Parr (B3LYP), provides an accurate and consistent description of the electronic structure for LaMnO3, CaMnO3, and La0.75Ca0.25MnO3. We have quantified the relevant structural, magnetic, and electronic energy contributions to the stability of the doped compound. An insight into the exchange coupling mechanism for the low hole density region of the phase diagram, where a polaron (anti-Jahn-Teller) forms, is also provided. This study completes a microscopic description of the lightly doped insulator with an antiferromagnetic-to-ferromagnetic and metal-to-insulator transition.