A regional electric utility that currently relies on natural gas for power generation is studying options for supplying power to its customers. It has all of the following options: Coal: A 50 megawatt (Mw) coal plant with a capital cost of $50 million and operating costs of $5 million per year plus the cost of coal. The coal plant would operate at 33 percent efficiency for converting heat for burning coal into electricity, and can expect a 50 percent load factor (capacity factor) and will last for 30 years. Under these assumptions, there are enough local resources (the cheapest source) to supply the power plant with coal for 30 years at a cost of $2.00 per million Btu (MMBtu). Wind: The region has two potential sites for commercial-scale wind farms. One could support 10 Mw of capacity with a 30 percent load factor. The other could support 20 Mw of capacity, but can only expect a 25 percent load factor. Both wind farms have a capital cost of $1,000 per kilowatt (kw) of installed capacity, and an annual operating and maintenance cost of $50 per year for each kw of installed capacity. The wind mills are expected to last for 20 years before needing to be replaced. Natural gas: The utility already has 200 Mw of natural gas capacity that is running on an average of 30 percent efficiency. It could build a new 50 Mw plant for additional capacity using modern combined cycle technology that would yield 50 percent efficiency. The capital cost of the new plant would be $10 million, and the operating and maintenance costs of both new and old gas plants is $50 per kw per year, exclusive of the cost of natural gas. Both new and existing gas plants have an expected life of 30 years. The expected load factor for the natural gas plants is 30 percent. The utility has an existing contract for 30 years to purchase up to 6 trillion Btu of natural gas per year at a price of $5.00 per MMbtu. If it wants to use more the 6 trillion Btu in a year, it can purchase as much additional gas as it needs, but has to pay $9.00 per MMbtu.

When the utility burns fossil fuels to generate electricity, it generates air pollution, but neither the utility nor its customers pay for any of the damages that the pollution causes. Now suppose that the utility has to pay a tax on emissions of one pollutant, carbon dioxide (CO₂), the major component of greenhouse gas pollution. Assume that the utility's coal contains 95.2 kg per million Btu (natural gas has less, 53 kg per million Btu. Wind power produces no direct CO₂emissions. If the tax rate is $50 per metric ton of CO₂, calculate the levelized cost of power for each source, including the tax.

Please show detailed calculations so that I can follow and learn--thank you!