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12-5 Valuing an American Option J\&B Drilling Company has recently acquired a lease to drill for natural gas in a remote region of southwest Louisiana and southeast Texas. The area has long been known for oil and gas production, and the company is optimistic about the prospects of the lease. The lease contract has a three-year life and allows J\&B to begin exploration at any time up until the end of the three-year term. J\&B's engineers have estimated the volume of natural gas they hope to extract from the leasehold and have placed a value of $25 million on it, on the condition that explorations begin immediately. The cost of developing the property is estimated to be $23 million (regardless of when the property is developed over the next three years). Based on historical volatilities in the returns of similar investments and other relevant information, J\&B's analysts have estimated that the value of the investment opportunity will evolve over the next three years, as shown in the figure on page 485. The risk-free rate of interest is currently 5%, and the risk-neutral probability of an uptick in the value of the investment is estimated to be 46.26%. a. Evaluate the value of the leasehold as an American call option. What is the lease worth today? b. As one of J\&B's analysts, what is your recommendation about when the company should begin drilling