Optical properties of the CdTe single quantum wells with barriers made either of ternary MnMgTe or quaternary CdMnMgTe compounds were investigated by use of photoluminescence and reflectivity spectroscopy as a function of magnetic field. The samples were grown by molecular beam epitaxy. Optical spectra are characterized by small linewidths and small Stokes shifts pointing at a high quality of the structures. Apart from the features related to confined excitons, also a line, attributed to donor bound excitons, is observed in majority of the spectra. The use of quaternary material to make barriers with a constant value of Mn molar fraction made possible, by varying the ratio of Cd to Mg molar fractions, fabrication of structures with the depth of the confining potential adjustable while remaining magnetically unchanged. On the other hand by varying the ratio of Mn to Mg contents we could affect magnetic properties of these structures without changing the potential depth in the absence of a magnetic field. From the magnetic field dependence of the photoluminescence we found that the free- to bound exciton-related emission intensity ratio strongly depended on the quantum well width as well as on the magnetic ion content in the barriers.