A gold mine will produce 2000 pounds of gold next year and 1500 pounds in two years

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A gold mine will produce 2000 pounds of gold next year and 1500 pounds in two years. After that the mine will be close forever. Suppose for simplicity that there are no operating expenses. The forward price of gold delivered one year from now is $10,000/pound, and no forward market is available for delivery in two years. The risk free rate is 5% and the cost of capital for gold mines is 10%. Suppose that, in the second year, the gold price fluctuates so it can be $12,000/pound or $9,000/pound with equal probabilities.

a. Find the value of the gold mine. (Hint: if you are really clueless, you can do part b first and then go back to part a.)

b. Suppose now that the mine can be operated for one year only (i.e., ignore any information for year two). Form the tracking portfolio for the gold mine and value the mine in this case.