Risk and Uncertainty

Breakeven analysis (14 questions)

A mining company is considering whether to invest in a newly discovered mine. The mine is expected to yield 100 kg of gold annually over the next five years. It costs $17 million to purchase the mine. Furthermore, the operating cost in the first year is $1 million and is estimated to increase 10% each year. The price of the newly extracted gold is currently $50,000 per kg and is estimated to increase 5% annually (i.e., the price of the newly extracted gold in the first year of operations is estimated to be $52,500 per kg). Assume that the company uses an annual interest of 7% in their decision making.

Sensitivity analysis (17 questions)

A mining company is considering whether to invest in a newly discovered mine. The mine is expected to yield 100 kg of gold annually over the next five years. It costs $17 million to purchase the mine. Furthermore, the operating cost in the first year is $1 million and is estimated to increase 10% each year. The price of the newly extracted gold is currently $50,000 per kg and is estimated to increase 5% annually (i.e., the price of the newly extracted gold in the first year of operations is estimated to be $52,500 per kg). Assume that the company uses an annual interest of 7% in their decision making.

Risk analysis (5 questions)

A mining company is considering whether to invest in a newly discovered mine. The mine is expected to yield 100 kg of gold annually. There is a 0.25 probability the mine contains 300 kg of gold (i.e., last three years), 0.5 probability it contains 500 kg of gold (i.e., last five years) and 0.25 probability it contains 600 kg of gold (i.e., last six years). It costs $17 million to purchase the mine. Furthermore, the operating cost in the first year is $1 million and is estimated to increase 10% each year. The price of the newly extracted gold is currently $50,000 per kg and is estimated to increase 5% annually (i.e., the price of the newly extracted gold in the first year of operations is estimated to be $52,500 per kg). Assume that the company uses an annual interest of 7% in their decision making.

Option valuation (7 questions)

A mining company is considering whether to invest in a newly discovered mine. The mine is expected to yield 100 kg of gold annually. There is a 0.25 probability the mine contains 300 kg of gold (i.e., last three years), 0.5 probability it contains 500 kg of gold (i.e., last five years) and 0.25 probability it contains 600 kg of gold (i.e., last six years). It costs $17 million to purchase the mine. Furthermore, the operating cost in the first year is $1 million and is estimated to increase 10% each year. The price of the newly extracted gold is currently $50,000 per kg and is estimated to increase 5% annually (i.e., the price of the newly extracted gold in the first year of operations is estimated to be $52,500 per kg). Assume that the company uses an annual interest of 7% in their decision making.

Suppose the mining company can perform a comprehensive analysis to determine the amount of gold the mine contains. The analysis costs $200,000. For simplicity, we assume that the results are available immediately. However, it is highly likely that the mine will no longer be available for purchase if the results are positive. Hence, the gold mine company will want to purchase an option to retain the right to purchase the gold mine for $17 million after the analysis is completed.