Questions (100 points) Copper plays an important role in assets that generate, transmit, and store electricity, in particular renewable energy infrastructure. Copper mines are thus relevant assets for the energy industry. Moreover, copper mine and oil and gas investments, as well as "gold" or "white" hydrogen ones, share critical similarities. The management team of a mining company is currently evaluating a project that entails the development of a copper mine. The company has three years to decide whether to pursue or forfeit this project. That is, the opportunity to develop the mine is foregone if three years have passed since the current time and the development decision has not yet been taken. Developing the mine entails incurring a capital expenditure and takes one year to complete. Once the mine has been developed, its reserves are 60MMlb. The company can either keep the developed mine inactive by paying a maintenance cost or extract 20MMlb of copper per year, pay a corresponding operating cost, and sell the extracted copper on the wholesale market. Initially the development, maintenance, and extraction costs are $50MM, $1MM per year, and $55MM per year, respectively (the extraction cost corresponds to extracting 20MMlb per year). The current annual risk free interest rate is 4%. The development, maintenance, and extraction costs, as well as the risk free interest rate are projected to increase by 2% per year. Currently the copper forward curve for yearly maturities, that is, the spot price for the current year and the prices for the futures with maturities in the next eight years, is $3.883/lb, $3.926/lb, $3.930/lb, $3.9331b, $3.936/lb, $3.939/lb, $3.942/lb, $3.945/lb, 1 and $3.948/lb. The management team believes that the spot price of copper can only be positive and evolves as a random walk with volatility equal to 0.22. 1. (75 points) Suppose that the developed mine must be abandoned by paying a cost either in the year subsequent to when the decision to extract the last 20MMlb of copper is made or nine years have passed since the current date irrespective of the residual reserves. Currently the abandonment cost is $5MM and it is projected to increase every year by the same percentage factor stated earlier. (a) Determine the optimal value of the development project for (i) the planned approach and (ii) the contingent approach using yearly time increments. (b) Describe the optimal development decision rules in plain language for (i) the planned approach and (ii) the contingent approach. (c) Explain the rationale for these decision rules. 2. (25 points) Suppose that the developed mine can be abandoned in any year by paying the corresponding cost irrespective of the reserves available at the time of abandonment. (a) How does the optimal value of the development project change when it is managed using the planned approach? Explain the reason for this change or absence thereof. (b) Same question for the contingent approach.