It has recently been noted that FAST (Fast Auroral SnapshoT) mission data of auroral current systems associated with Alfv¿n waves has an electron kinetic energy flux density that is similar to the Poynting vector <Chaston et al., 2002>. In Ultra-Low-Frequency (ULF) wave theory, which considers global wave modes of the magnetosphere (with frequency 1--5 mHz), the traditional dissipation mechanism is taken to be Joule heating associated with ionospheric currents that are fed by the Poynting vector. Hence FAST observations indicate that electron acceleration can supply an additional sink of energy that is of similar magnitude to the traditional one. In this letter we use typical Pc5 parameters to estimate the importance of electron acceleration as a sink of Alfv¿n wave energy for these global waves. We find that the electron dynamics must be treated nonlinearly, and that electron acceleration drains a similar amount of energy from the Alfv¿n wave fields as ionospheric dissipation, and for some events may actually exceed the latter.