  We describe the value set $\{f(z_0)\,:\, f:\mathbb{D}\to\mathbb{D} \text{
univalent}, f(0)=0, f'(0)= e^{-T} \},$ where $\mathbb{D}$ denotes the unit disc
and $z_0\in\mathbb{D}\setminus\{0\}$, $T>0,$ by applying Pontryagin's maximum
principle to the radial Loewner equation.
