MGF of the Sample Mean of Exponentials

Let $X_1,\dots,X_n$ be i.i.d. $\mathrm{Exponential}(\beta)$ with rate $\beta$, and let \[ \bar X_n=\frac{1}{n}\sum_{i=1}^n X_i. \] Find the MGF of $\bar X_n$, and recover $E[\bar X_n]$ and $\mathrm{Var}(\bar X_n)$ from it.