A coal mine has reserves of 50,000 tonnes. For simplicity, assume the following schedule for extraction, coal
Question:
A coal mine has reserves of 50,000 tonnes. For simplicity, assume the following schedule for extraction, coal purification, and sale of the coal:
| Extraction and Sale Time | Tonnes |
| Today | 10,000 |
| One year from now | 15,000 (good state) |
| 10,000 (bad state) | |
| Two years from now | 15,000 |
The coal extraction one year from now depends on the state of the economy. In two years? time the mine is sold, where the residual value of the mine will be equal to the value of the unextracted coal. You also know that there is no option to shut down the mine prematurely.
The current price of coal is ?150 per tonne. Today?s forward price for coal settled one year from now is ?165 per tonne, and today?s forward price for coal settled two years from now is ?175 per tonne. The cost (of coal extraction, purification and selling) is ?50 per tonne now and grows at 25% per year. The risk-free rate of return is 5% per year, and assume that it is appropriate discount rate for the coal mine. You can assume that the price of the coal (whatever it is) will be the same in both states.
Moreover, you are told that ?15 invested in the market portfolio today grows as follows:
- What is the risk-neutral probability of the good state realisation?
- What is the value of the coal mine (to 2 decimal places)?
Expert Answer:
a What is the riskneutral probability of the good state realisation Riskneutral probability of the ... View the full answer
