Manganese ions in a mixed-valent state of two magnetic configurations, ${\mathrm{Mn}}^{4+}$ and ${\mathrm{Mn}}^{3+},$ play an important role in the magnetoresistance of ${\mathrm{LaMnO}}_{3}$-based systems. We describe each Mn ion with the ${\mathrm{Mn}}^{4+}$ represented by a spin $S=3/2$ (three localized d electrons in the ${t}_{2g}$ orbitals with their spins ferromagnetically coupled) and the ${\mathrm{Mn}}^{3+}$ configuration having an additional localized ${3d\ensuremath{-}e}_{g}$ electron to form a total spin $(S+1/2).$ The ${e}_{g}$ electron hybridizes with conduction electrons (representing the crystal) and the multiple occupancy of the ${e}_{g}$ level is excluded at each site by a large Coulomb energy. We consider a cubic cluster of eight such manganese ions and allow a directed hopping of the ${e}_{g}$ electrons between the Mn sites. Hence, bonding and antibonding levels are formed giving rise to the ferromagnetic double-exchange mechanism, which competes with the antiferromagnetic superexchange between the ${t}_{2g}$ spins of the ions. The spins S are oriented in the magnetic configurations of the A, C, and G phases. In the intermediate valent regime we calculate the ground-state energy, the valence, the population of the various bonding and antibonding resonant levels, the charge susceptibility, the quadrupolar susceptibility, and the response to a charge imbalance between the sites of two ``sublattices'' as a function of the energy of the ${e}_{g}$ level using a mean-field slave-boson formulation. The susceptibilities are a measure for the coupling to phonons, i.e., the formation of small polarons, Jahn-Teller distortions, and charge order, respectively. A crossover between groundstates with different spin configurations is found as a function of the ${e}_{g}$ level energy for reasonable model parameters.