Solution (source code)

= Solution

At the up node, both immediate exercise and continuation are zero. At the down node the exercise value is $864-576=288$, while the discounted continuation value is $R^{-1}(480/3)=120$. Exercise there is optimal. At time zero immediate exercise pays zero, so
$$
\boxed{V_0=R^{-1}\left(\frac13\cdot288\right)=72.}
$$