The coexistence of competitive species with a shared predator is well established. The effect of 'food-value' on predator-prey dynamics has also received much attention. However, the study of a nutrient bound of prey, specifically on predator-mediated competitive-coexistence has not received much attention. Here we study the effects of the caloric content or a nutrient bound of prey on the dynamics of competitive-coexistence with the shared predator in a specific model. We propose and analyze a mathematical model for exploitative competition of two prey species with a shared predator. The change of dynamic stability due to the variation of a nutrient bound of each prey on predator-mediated dynamics is studied through extensive numerical experiments. Our analytical and numerical results demonstrate that variation in a nutrient bound promotes the switching of dynamics and may be treated as a driving force for the dynamics of competitive-coexistence with the shared predator.