Problem 3: (20 points) Firm X is considering building a plant that will manufacture heaters powered by natural gas. The plant will cost $1 million to build, which the firm must pay immediately if it builds the plant. If built, the plant will produce 2,000 heaters this year. It will then become completely obsolete (with no salvage value) at year-end due to advancing technology. In addition to the expenditure to build the plant, the cost of manufacturing each heater will be $1,000 for labor and materials, payable at the end of the year. talisered b) (7 points) Suppose now that there is no forward market for heaters. However, there is a spot market for natural gas. In particular, the price of natural gas is currently $2 per mm BTU (thousand British Thermal Units). In a year, the natural gas price will be either $4 per mm BTU or $1 per mm BTU. Suppose that if the price of natural gas rises to $4, demand for natural gas heaters will be very low and the market price of your heaters will be $900. If the price of natural gas falls to S1, demand for the heaters will be very high, and their market price will be $3,000. Assume for simplicity that natural gas incurs no storage costs. The risk-free rate is 4%. Suppose that Firm X learns next year's natural gas prices only after it decides to construct the plant and manufacture the heaters. Find the NPV of building the plant