Michael owns a gold mine. There are 7kg of gold remaining in the mine.

Michael extracts the gold at a constant rate of 1kg per month. The cost

of mining the gold and delivering it to the market is $35,000 per kg. As-

sume that the log relative change in the market price of gold over a year is

distributed as

ln(P(t+1)/Pt) ~N(5.5%,30%)

The risk-free rate is 4% pa. The mine can be abandoned at time 1 at the net

cost of $10000: the net cost abandonment increases every month by 1%. If

the mine is not abandoned before it is exhausted the owner of the mine will

still have to pay the cost of abandonment (in 7 months). Assume that the

cost of storing gold is small comparing to the market price of gold and other

costs. The current price of gold is $46,000 per kg.

1. Construct a binomial lattice for gold prices and mine profits assuming

one month time period between subsequent nodes.

2. Michael is approached by Pete the Prospector with an offer to sell the

mine for $70,000. Should Michael accept the offer? (Hint: You should

calculate the NPV of the gold mining by regarding it as an American

option, as you need to decide whether you abandon this mining or keep

it going at each time step.)

3. Explain why you do not need to know the cost of capital to answer Part 2 (Hint: You should think this question based on state price used in option pricing issues).