The excitation of Gamow-Teller (GT) and isovector spin monopole (IVSM) J^π=1⁺ modes in ¹¹⁶In by (p,n) and (n,p) charge-exchange reactions on ¹¹⁶Cd and on ¹¹⁶Sn, respectively, is studied within the framework of the quasiparticle random-phase approximation. The calculations have been performed both for schematic and realistic model situations. It appears that the calculated admixture of the IVSM and Gamow-Teller (GT) J^π=1⁺ excitations is negligible and that the contribution to the strength above 20 MeV of excitation energy, in ¹¹⁶In, is due to the IVSM (σr²t^±) mode. This result is compared with the recent experimental work that reported a large amount of both (p,n) and (n,p) strength beyond 10 MeV of excitation energy in ¹¹⁶In. This measured excess strength has led to speculations about its importance for the double beta decay rate of ¹¹⁶Cd.