The structural and magnetic properties of spinel compounds CoB2O4 (B = Cr, Mn and Fe) are studied using the DFT+U method and generalized gradient approximation. We concentrate on understanding the trends in the properties of these materials as the B cation changes, in terms of relative strengths of crystal fields and exchange fields through an analysis of their electronic densities of states. We find that the electron-electron correlation plays a significant role in obtaining the correct structural and electronic ground states. Significant structural distortion in CoMn2O4 and 'inverted' sublattice occupancy in CoFe2O4 affects the magnetic exchange interactions substantially. The trends in the magnetic exchange interactions are analysed in terms of the structural parameters and the features in their electronic structures. We find that the Fe states in CoFe2O4 are extremely localised, irrespective of the symmetry of the site, which makes it very different from the features of the states of the B cations in two other compounds. These results provide useful insights into the trends in the properties of CoB2O4 compounds with variation of B cation, which would help in understanding the results of recent experiments on doping of Mn and Fe in multiferroic CoCr2O4.