Our assumptions are as follows. Rob is interested in purchasing a permission to extract gold for the next 3 years. He analysed the project and came up with the following information:

He has an initial investment of $40000 to start the gold extraction;

he would be able to extract 2kg of gold every three months for the first 1.5 years and 3kg every three months for the remaining time, but he needs 3 months to start extracting;

He will have to afford extraction costs of $18,000 every 3 months to run the mine for the first 1.5 years. Accordingly, as the extraction increases, extraction cost for the remaining time increases to $27,000.

He can abandon the mine at any time at a cost of $10000, if he does not abandon the mine he would have to pay this cost at the end of the permission.

The current market value of gold is $23,000 per kilogram and from the historical data the log relative change in the market price of gold over a year is distributed as

ln ( +1 / ) ~(, 2 )

Where =8% and =25%. The risk-free rate is 4%.

1. Construct a binomial lattice for gold prices and mine profits on the quarter basis. Explain your logic.

2. If the permission costs $350000, would he purchase it? Fully justify your response noting the following: you need to treat the gold mining as an option and get its price and compare its price with the permission cost to see whether he would like to take it or not.

3. Suppose that he 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? (Hint: 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 he would like to pay for the insurance.) Clearly identify any assumptions that you have had to make