The CPP-effect makes reference to the process by which the membrane translocation rate of a cargo is enhanced by chemical functionalization with cell-penetrating peptides (CPPs). In this work we combine a simple kinetic model with free-energy calculations to explore the energetic basis of the CPP-effect. Two polyglicines are selected as model hydrophilic cargoes, and nonaarginine as a prototypical CPP. We assess the cargo carrying efficiency of nona-arginine by comparing the adsorption and insertion energies of the cargoes, the cargo-free CPPs, and the CPPcargo complexes, into lipid membranes of varying composition. We also analyze the effect of modifying the type and concentration of anionic lipids, and the implication of these factors on the translocation rate of the CPP-cargo complex. Of particular interest is the evaluation of the catalytic role of palmitic acid (palmitate) as a promoter of the CPP-effect. We also analyse the influence of the size of the cargo on the membrane adsorption and insertion energies. Our results show that the efficiency of nona-arginine as a transmembrane carrier of simple hydrophilic molecules is modulated by the size of the cargo, and is strongly enhanced by increasing the concentration of anionic lipids and of ionized fatty acids in the membrane.