7. [25 points] The "PowerGen" company is building a 100 Megawatt (1 MW =105 watt) natural gas-fueled electric power plant. PowerGen obtains a loan at 6% interest to finance building the plant over three years. PowerGen spends the following total amounts each year (for equipment, engineering, construction). Year 1: $50 million Year 2: $25 million Year 3: $100 million The plant starts producing electricity in year 4. a) What is the present value (at the time the plant begins operation) of the total capital investment in building the plant, counting interest during construction? The power plant operates at an average annual capacity factor of 80%. b) How many kilowatt hours (kWh) of electricity are produced per year? The energy conversion efficiency of natural gas to electricity in the plant is 40%. (40% of the energy in natural gas is converted to electricity). Natural gas costs $4 per Gigajoule (GJ). (1 GJ = 277.8 k Wh) c) How much natural gas is used per year to produce electricity? d) What is the total cost each year for natural gas for the power plant? The plant operates for 20 years after opening. PowerGen's investors expect a 12% rate of return on their investment.e) What is the capital recovery factor CRF, assuming a plant lifetime of 20 years? Fixed operation and maintenance costs for the plant (labor) are 3% of the total capital investment cost of the plant. Find the present value (at the time the plant begins operation) of: f) the total capital investment in building the plant the natural gas input to the plant h) the fixed operation and maintenance costs 1) Find the lifecycle cost of the plant ($ j) What is the annualized lifecycle cost of the plant ($/yr)? k) Estimate the levelized cost of electric power from this plant ($/kWh).a) Loan at Year 1: = 50 million for 3 years @6%= 50 * (1+6/100)^3 = 59.55 million Year 2: = 25 million for 2 years = 25 *(1+6/100)^2 = 28.09 Million Year 3: =100 Million for 1 year = 100 * (1+6/100) = 106 million. Present Value at beginning of 4th year = 59.55 + 28.09 + 106 million = 193.64 million b) Capacity of the plant = 100MW = 100,000kW Annual Capacity Factor = 80% KWh of energy produced per year = Capacity * Annual Capacity Factor * Number of hours in a year = 100,000 * 80% * 365 * 24 = 700,800,000KWh c) Let the amount of natural Gas used be x GJ. = 277.8 * x KWh So conversion to electricity = 0.4* 277.8 * x Now 0.4* 277.8 * x = 700,800,000 or x = 700,800,000 /(0.4*277.8) GJ or x = 6306.7GJ d) Cost of 1GJ natural Gas = $4 Total cost to run the plant per year = 4 * 6306.7 = $25226.8