The reactivity of phenol, lithium phenoxide (LiOPh), and sodium phenoxide (NaOPh) with the cyclic tetramer of bisphenol A polycarbonate (BPA-PC) has been investigated using density functional calculations. The potential energy of the system is computed using a suitable reaction coordinate and relaxing all other degrees of freedom by Car-Parrinello molecular dynamics. Both LiOPh and NaOPh catalyze ring opening with small energy barriers (Delta E 4.0, 2.5 kcal/mol, respectively) to a chain with a phenyl carbonate at one end and a phenoxide at the other, a "living polymer". The barrier is large for phenol (Delta E > 40 kcal/mol), but the total energy differences between the reactants and the chain are very small in all three molecules. We discuss the balance between changes in entropy and energy, and we compute the vibrational properties of metastable intermediate species.