Question 2 Woody is interested in purchasing a permission to extract gold for the next 5 years. He analysed the project and came up with the following information: 3> He will have to afford fixed costs of $25,000 every 6 months to run the mine (Note: the fixed cost will start from t = 0): 3* He has an initial investment of $30000 to start the gold extraction; 3; He would be able to extract 2kg of gold every six months for the first 2 years and 8kg every six months for the remaining time, but he needs 6 months to start extracting; > He can abandon the mine at any time at a cost of $7000, if he does not abandon the mine he would have to pay this cost at the end of the permission. The current market vaiue of gold is $28000 per kilogram and from the historical data the log relative change in the market price of gold over a year is distributed as Pt+1 ln( Pt ) - Nrp, 02), where p = 8% and 0' = 25%. The risk free rate is 4%. 1. Construct a binomial lattice for gold prices and mine profits assuming six-month time period between subsequent nodes. 2. if the permission costs $350000, would Woody purchase it'? Explain. (Hint: treat the gold mining as an option and get its price, and compare its price with the permission cost to see whether Woody would like to take it or not) 3. Suppose that Woody can buy an insurance which would cover the losses in the case he has to abandon the mine before expiry of the permission. What would be the maximum price he would pay for this insurance? (m: treat the gold mining as an option, and compare its price with and without this insurance. The difference between the two prices will be the maximum price Woody would like to pay for the insurance.)