Contraction Mapping Principle

Let M be a compact metric space. Let $\displaystyle \Phi : M \rightarrow M$ be such that $\displaystyle d(\Phi (x), \Phi (y)) < d(x, y), \forall x, y \in M, x \neq y$. Show that $\displaystyle \Phi$ has a unique fixed point.

I'd like to use the Contraction Mapping Principle. I can see that M is complete (as it is a compact metric space), but am not sure where to find a constant $\displaystyle c \in [0,1) $ such that $\displaystyle d(\Phi (x), \Phi (y)) \leq c \cdot d(x, y)$. Any advice?