In this study the elastic properties of a fcc Fe0.87Mn0.13 random alloy are studied by ab initio calculations. Ground state lattice parameters and elastic properties are calculated with Density Functional Theory using the Exact Muffin-Tin Orbital method and the Coherent Potential Approximation. Several magnetic models, approximations and distortion techniques are evaluated for optimized results, which are obtained by a Disordered Local Moment model with the Frozen Core and Generalized Gradient approximations using volume-conserving distortions.  Conclusively the longitudinal sound velocities are calculated from second order elastic stiffness constants and visualized by two different codes. The importance of magnetism for elastic properties is confirmed, as is the usefulness of the optimized computational scheme; all quantities obtained via the scheme is in accord with earlier theoretical and experimental results. Volume-conserving distortions are found to be more precise than volume-altering for calculation of elastic constants but also to be highly dependent on the precision of bulk modulus determination. The two sound-velocity codes are in complete agreement.