A comparative analysis of two cylindrical complex-frequency-shifted perfectly matched layers (CFS-PML) absorbing boundary condition (ABC) for bi-dimensional (2-D) finite-volume (FV) simulations in the frequency domain is presented. The impact of CFS-PML parameters on the wave absorption, as well as on the condition number of the associated system matrix is investigated by comparing the performance of two PML loss profiles, viz., polynomial and geometric grading. FV-CFS-PML results are validated against analytical solution. Numerical results show that inclusion of a CFS-PML within the FV computational domain increases the condition number of the system matrix and therefore the use of CFS-PML 3-D FV simulations is limited.