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please answer part A-D and provide a step by step solution

problem asks you to calculate the NPV (net present value) of a PV installation as a function of the simple payback time T and of the system lifetime t. Note that T and NPV depend on the solar energy, and on the cost of grid power, in a given location. For simplicity we will assume that - The role of inflation has been factored out, so that the annual income is constant. - We pay back the capital cost without using a loan. (You could include a loan in the calculation, but then the result would depend on the assumed loan rate and period.) - The income from the system is simply (the energy generated) x (the cost of grid power). (In a full calculation, we would need to subtract out fixed costs, maintenance costs, taxes.) For a fixed annual income A [$/yr) and a given discount rater (fraction/yr), the NPV of the PV system is NPV = CCT Ae-rt at D However, we need to pay back the capital cost C [$] which is incurred at t = 0, and therefore is not discounted. Assume that during the first Tyears of operation, where T is the simple payback time, T=CIA, all profits are used internally to repay C. (As a sikeplification we are not discounting the internal payback.) Then NPV = - + Set tar Ae - dc a. Carry out the integral and show the formula. b. Assume T = 5 years, = 25 years, and r = 0.06 / yr. What is the NPV as a fraction of C? c. The plot from the McKinsey Quarterly is copied below. We will only make use of the solar energy yield (X-axis, annual kWh/ kW peak) and the average cost of grid electricity (Y-axis, cents per kWh). Assume that we install a system rated at 10 kW peak and that the cost of installed PV (at the residential scale) is $2.00 /W. Calculate the annual income A for the United Kingdom, Brazil and India. d. Note that the United Kingdom and Brazil have a similar cost of electricity but a big difference in solar energy, and that Brazil and India have similar solar energy but a big difference in the cost of electricity. For each location, calculate the NPV as a fraction of C. Use r= 0.06 / yr. (These numbers show why solar works better economically in the UK than in India. But that is (These numbers show why solar works better economically in the UK than in India. But that is not the whole story: if grid power is subsidized in India, then the real cost of power is higher.) 1 400 Denmark 350 Germany California (Tier 4) Italy 300 Spair Japan 256 United Kingdom $ 20c France New York New Jersey 150 Pennsylvania Ohio Australia Brazil India (peak rate) Georgia California (base) Florida USA Texas China South Africa Canada India (base) 106 DO 50 South Korea 0 700 1.900 800 900 1,000 1.100 1.200 1.300 1,400 1.500 1,500 TTOO 800 Solar-energy yield, specific annual yield in kilowatt hour/kilowatt peak (KWIKWP) problem asks you to calculate the NPV (net present value) of a PV installation as a function of the simple payback time T and of the system lifetime t. Note that T and NPV depend on the solar energy, and on the cost of grid power, in a given location. For simplicity we will assume that - The role of inflation has been factored out, so that the annual income is constant. - We pay back the capital cost without using a loan. (You could include a loan in the calculation, but then the result would depend on the assumed loan rate and period.) - The income from the system is simply (the energy generated) x (the cost of grid power). (In a full calculation, we would need to subtract out fixed costs, maintenance costs, taxes.) For a fixed annual income A [$/yr) and a given discount rater (fraction/yr), the NPV of the PV system is NPV = CCT Ae-rt at D However, we need to pay back the capital cost C [$] which is incurred at t = 0, and therefore is not discounted. Assume that during the first Tyears of operation, where T is the simple payback time, T=CIA, all profits are used internally to repay C. (As a sikeplification we are not discounting the internal payback.) Then NPV = - + Set tar Ae - dc a. Carry out the integral and show the formula. b. Assume T = 5 years, = 25 years, and r = 0.06 / yr. What is the NPV as a fraction of C? c. The plot from the McKinsey Quarterly is copied below. We will only make use of the solar energy yield (X-axis, annual kWh/ kW peak) and the average cost of grid electricity (Y-axis, cents per kWh). Assume that we install a system rated at 10 kW peak and that the cost of installed PV (at the residential scale) is $2.00 /W. Calculate the annual income A for the United Kingdom, Brazil and India. d. Note that the United Kingdom and Brazil have a similar cost of electricity but a big difference in solar energy, and that Brazil and India have similar solar energy but a big difference in the cost of electricity. For each location, calculate the NPV as a fraction of C. Use r= 0.06 / yr. (These numbers show why solar works better economically in the UK than in India. But that is (These numbers show why solar works better economically in the UK than in India. But that is not the whole story: if grid power is subsidized in India, then the real cost of power is higher.) 1 400 Denmark 350 Germany California (Tier 4) Italy 300 Spair Japan 256 United Kingdom $ 20c France New York New Jersey 150 Pennsylvania Ohio Australia Brazil India (peak rate) Georgia California (base) Florida USA Texas China South Africa Canada India (base) 106 DO 50 South Korea 0 700 1.900 800 900 1,000 1.100 1.200 1.300 1,400 1.500 1,500 TTOO 800 Solar-energy yield, specific annual yield in kilowatt hour/kilowatt peak (KWIKWP)

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