A copper mine has 10 pounds of reserves that we can extract at no cost a year from now. The mine also has additional reserves of 5 pounds that can also be extracted a year from now but at a cost of $8 per pound. One-year forward price of copper is $9 per pound. An analyst estimate the copper price next year is either $13 in a good economy or $7 in a bad economy. The risk free rate is 5% per annum.

If you can decide whether to extract the additional reserve after observing the market price of copper next year, what is the value of mine?