Independent Vector Extraction aims at the joint blind source extraction of $K$ dependent signals of interest (SOI) from $K$ mixtures (one signal from one mixture). Similarly to Independent Component/Vector Analysis (ICA/IVA), the SOIs are assumed to be independent of the other signals in the mixture. Compared to IVA, the (de-)mixing IVE model is reduced in the number of parameters for the extraction problem. The SOIs are assumed to be non-Gaussian or noncircular Gaussian, while the other signals are modeled as circular Gaussian. In this paper, a Cramér-Rao-Induced Bound (CRIB) for the achievable Interference-to-Signal Ratio (ISR) is derived for IVE. The bound is compared with similar bounds for ICA, IVA, and Independent Component Extraction (ICE). Numerical simulations show a good correspondence between the empirical results and the theory.