  Let $G$ be a graph of order $n$ and size $m$, and let $\mathrm{mc}_{k}\left(
G\right) $ be the maximum size of a $k$-cut of $G.$ It is shown that \[
\mathrm{mc}_{k}\left( G\right) \leq\frac{k-1}{k}\left( m-\frac{\mu_{\min
}\left( G\right) n}{2}\right) , \] where $\mu_{\min}\left( G\right) $ is the
smallest eigenvalue of the adjacency matrix of $G.$
  An infinite class of graphs forcing equality in this bound is constructed.
