According to the theorem of parallel axes, the moment of inertia $I$ of a body about any axis is given by $I = I_{cm} + md^2$, where $I_{cm}$ is the moment of inertia about a parallel axis passing through the center of mass, $m$ is the mass of the body, and $d$ is the perpendicular distance between the two axes.

Here, the moment of inertia about the center of mass (mid-point) is $I_{cm} = I_0$. The perpendicular distance from the center of mass to one of the ends is $d = \frac{L}{2}$. Therefore, the moment of inertia about the end is: $I = I_0 + M\left(\frac{L}{2}\right)^2 = I_0 + \frac{ML^2}{4}$