QUESTION FOUR The CFO of Octavia Ltd, a mining company, has long wanted to enter the market for rhodium, a scarce precious metal. It has the option of starting mining in one of the locations where it owns mining rights, but the CFO is worried that the current price does not justify starting mining immediately. The CFO wants a report on the profitability of the mining rights to the CEO and the board. The report should address the current value of the mining rights and the optimal plan for investment over the next couple of years. The following table sets out the current value of rhodium and the likely annual price changes: Value Likelihood Current price US$350,000 per kilogram Annual appreciation 40% increase Likelihood 50% Annual depreciation 20% reduction Likelihood 50% You also have the following information about the market conditions: The risk-free rate of return 3% The average return on the market index 7% The mining project, once started, is likely to run for ten years. You expect the site to produce an annual quantity of rhodium of 100kg. The investment cost is US$400m. Your report should address the following points: a) Is the CFO correct that the investment in mining rights is currently unprofitable? (5 marks) b) What is the implied beta-risk of the investment in rhodium? (5 marks) C) A mining right is an option the owner can exercise at future dates. Explain why a discounted cash flow approach to the valuation is inappropriate and that instead, we use a valuation method based on risk-neutral probabilities. (10 marks) d) What are the risk-neutral probabilities in this case? (10 marks) c) Work out the value of the mining rights and the optimal exercise of the mining rights over the next two years. (20 marks) [TOTAL: 50 MARKS] QUESTION FOUR The CFO of Octavia Ltd, a mining company, has long wanted to enter the market for rhodium, a scarce precious metal. It has the option of starting mining in one of the locations where it owns mining rights, but the CFO is worried that the current price does not justify starting mining immediately. The CFO wants a report on the profitability of the mining rights to the CEO and the board. The report should address the current value of the mining rights and the optimal plan for investment over the next couple of years. The following table sets out the current value of rhodium and the likely annual price changes: Value Likelihood Current price US$350,000 per kilogram Annual appreciation 40% increase Likelihood 50% Annual depreciation 20% reduction Likelihood 50% You also have the following information about the market conditions: The risk-free rate of return 3% The average return on the market index 7% The mining project, once started, is likely to run for ten years. You expect the site to produce an annual quantity of rhodium of 100kg. The investment cost is US$400m. Your report should address the following points: a) Is the CFO correct that the investment in mining rights is currently unprofitable? (5 marks) b) What is the implied beta-risk of the investment in rhodium? (5 marks) C) A mining right is an option the owner can exercise at future dates. Explain why a discounted cash flow approach to the valuation is inappropriate and that instead, we use a valuation method based on risk-neutral probabilities. (10 marks) d) What are the risk-neutral probabilities in this case? (10 marks) c) Work out the value of the mining rights and the optimal exercise of the mining rights over the next two years. (20 marks) [TOTAL: 50 MARKS]
