Let $\gamma(G)$ and $\iota(G)$ be the domination and independent domination numbers of a graph $G$, respectively. In this paper, we define the Price of Independence of a graph $G$ as the ratio $\frac{\iota(G)}{\gamma(G)}$. Firstly, we bound the Price of Independence by values depending on the number of vertices. Secondly, we consider the question of computing the Price of Independence of a given graph. Unfortunately, the decision version of this question is $\Theta_2^p$-complete. The class $\Theta_2^p$ is the class of decision problems solvable in polynomial time, for which we can make $O(\log(n))$ queries to an NP-oracle. Finally, we restore the true characterization of domination perfect gaphs, i.e. graphs whose the Price of Independence is always $1$ for all induced subgraphs, and we propose a conjecture on futher problems.