question archive Lithium Mining Ltd plans to buy the rights of opening a small lithium mining in Bolivia
Lithium Mining Ltd plans to buy the rights of opening a small lithium mining in Bolivia
Subject:FinancePrice:2.86 Bought8
Lithium Mining Ltd plans to buy the rights of opening a small lithium mining in Bolivia. The price of lithium is $12000 per ton. Next year it is expected to be either 10% higher or 10% lower. The Total Average Cost (TAC) of lithium production is $12700 (per ton). Ignore all other investment costs, depreciation and taxes. It is expected that the mining can produce 100 000 tons. If the company decides to buy the mining but does not operate it within 1 year, it must pay $ 5 million in order to clean up the area around the mining and loses its contract (option expires). The appropriate interest rate for such risk sectors is 5%. Assume that you evaluate the lithium mining as a real option. What is the value of that lithium mining today? Explain clearly and show your calculations.
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Current stock price, S0 = 12,000
Quantum of lithium, Q = 100,000
Up state:
Up factor, u = 10% higher = 1 + 10% = 1.10
Su = stock price in up state = u x S0 = 1.10 x 12,000 = 13,200
Cash flow from operating the mine, Cu = (Su - TAC) x Q = (13,200 - 12,700) x 100,000 = 50,000,000
Down State:
Down factor, d = 10% lower = 1 - 10% = 0.90
Sd = stock price in up state = d x S0 = 0.90 x 12,000 = 10,800
Since Sd < TAC, it doesn't make sense to produce lithium.
Cash flow from not operating the mine, Cd = - 5,000,000
Probability of an up state = p = (1 + r - d) / (u - d) = (1 + 5% - 0.9) / (1.1 - 0.9) = 0.75
Hence, the value of that lithium mining today = Value of the option = [p x Cu + (1 - p) x Cd] / (1 + r) = [0.75 x 50,000,000 + (1 - 0.75) x (-5,000,000)] / (1 + 5%) = 34,523,810
