18 Consider the problem of Wind Resources (described in the section "The Timing Option" in this chapter). WRI is contemplating develop- ing an attractive wind farm site it owns in southern California. A con- sultant estimates that at the current natural gas price of 6 cents/kWh (cents per kilowatt hour), immediate development will yield a profit of $10 million. However, natural gas prices are quite volatile. Suppose the price in one year will be either 8 cents/kWh or 4 cents/kWh with equal probability. According to the consultant, WRI's profit will jump to $30 million at a price of 8 cents/kWh and fall to a loss of $10 million at 4 cents/kWh. Because the company won't receive these profits for one year, discount them to the present at a high, risk-adjusted rate of 25 percent. WRI is now considering whether to wait to develop the wind farm. a. Draw a decision tree that captures WRI's decision. b. What should WRI do? What is the resulting NPV of this project? c. What is the value of the option to wait? d. Suppose that the change in natural gas prices in one year will be more dra- matic than originally envisioned in the problem. In particular, gas prices will either rise to 12 cents/kWh or fall to 2 cents/kWh with equal prob- ability. According to the consultant, WRI's profit will be $60 million at a price of 12 cents/kWh or fall to a loss of $30 million at 2 cents/kWh. What is the new value of the option to wait? How is the value of the option affected by the wider dispersion of natural gas prices?