A silver mine has reserves of 25,000 troy ounces of silver. For simplicity, assume the following schedule for extraction, ore purification, and sale of the silver ore:
|
Extraction and Sale Date
|
Troy Ounces
|
|
Today
|
10,000
|
|
One Year from now
|
10,000
|
|
Two year from now
|
5,000
|
Also assume the following:
• The mine, which will exhaust its supply of silver ore in two years, is assumed to have no salvage value.
• There is no option to shut down the mine prematurely.
• The current price of silver is $4 per troy ounce.
• Today's forward price for silver settled one year from now is $4.20 per troy ounce.
• Today's forward price for silver settled two years from now is $4.50 per troy ounce.
• The cost of extraction, ore purification, and selling is $2 per troy ounce now and at any point over the next two years.
• The risk-free return is 5 percent per year.
What is the value of the silver mine?