Consider a mine that contains $75$ million lbs$.$ of copper. Extraction costs are $$0\mathrm{.}80$ per lb$.$

Copper price next year is projected to be $$1\mathrm{.}00$ per lb$.$ if demand high and $$0\mathrm{.}40$ if demand low.

Year $1$ forward price of copper is $$0\mathrm{.}60$

Risk$-$free rate is $5\%.$

No extraction may take place after next year due to new environmental regulations.

A$.$ Draw the binomial tree as we did in class and show the expected cash flows from operating the mine

B$.$ What is the implied probability of the demand for copper to be high next year?

C$.$ What is the present value of the mine if it produces copper unconditionally $($whether the demand is high or low$)$

D$.$ What is the optimal strategy for operating the mine, will it include shutting down in some cases? What is the value of the mine under this strategy?