Hickock Mining is evaluating when to open a gold mine. The mine has $48,000$ ounces of gold left that can be mined, and

mining operations will produce $6,000$ ounces per year. The required return on the gold mine is $12$ percent, and it will cost $$34$

million to open the mine. When the mine is opened, the company will sign a contract that will guarantee the price of gold for

the remaining life of the mine. If the mine is opened today, each ounce of gold will generate an after$-$tax cash flow of $$1,400$

per ounce. If the company waits one year, there is a $60$ percent probability that the contract price will generate an after$-$tax

cash flow of $$1,600$ per ounce and a $40$ percent probability that the after$-$tax cash flow will be $$1,300$ per ounce. What is the

value of the option to wait?