A copper mine has 100 pounds of raw material that we can extract one year from now. The extraction costs are $0.30 per pound which we would incur one year from now. The one-year forward price of copper is $0.35 per pound. Our analysts estimate that one year from now, the copper price will be either $0.60/pound in a good economy or $0.20/pound in a bad economy. The risk-free rate is 4%. If we don't extract the copper one year from today, Christian Slater will set off a nuclear bomb in the mine shaft and we will lose access to the mine forever.
a. Suppose we must decide today if we will extract the copper in one year’s time. Find the value of the mine.
b. Suppose we can wait until we know if the economy is good or bad (and thus, we will know the price of copper) before deciding whether or not to extract the copper. Find the value of the mine.