This question is about NPV and real options.

(a) [9 marks] Consider a mine producing 10,000 pounds of copper one year from now. The current forecast is that copper price next period will be either $0.6 per pound if demand is low or $1.1 per pound if demand is high. The extraction cost is $0.8 per pound. $1 invested in the market portfolio today will be worth either $1.3 in the good state of economy or $0.8 in the bad state. The states of the economy are perfectly correlated with the demand for copper. The risk- free rate is 5%. The company has an abandonment option after observing prices, i.e., it can stop producing when prices are low. Calculate the risk-neutral probabilities and the value of the mine.

(b) [8 marks] Find the value of the company in part (a) when it does not have an abandonment option and has to continue extraction irrespective of whether the prices are high or low. How much would this company be willing to pay to have an abandonment option?

(c) [8 marks] Consider a mine producing 5,000 ounces of gold in years 1 and 2 from now. The cost of extraction and refinement is $1700 per ounce. The 1-year forward price of gold is $1600 and the 2-year forward price is $1900. The company does not have an abandonment option. The riskless spot rates for lending and borrowing for 1 and 2 years are r1=5% and r2=7%, respectively. What is the present value of the mine’s cash flows?