Waring Solar Systems provides solar panels and other energy-efficient technologi

Question

Waring Solar Systems provides solar panels and other energy-efficient technologies for buildings. In response to a customer inquiry, the company is conducting a feasibility study to determine if so- lar panels will provide enough energy to pay for themselves within the payback period. Capacity is measured in MWh/year (1000 kWh). This figure is determined by the number of panels installed and the amount of sunlight the panels receive each year. Ca- pacity can vary greatly due to weather conditions, es- pecially clouds and snow. Engineers have determined that this client should use an 80MWh/year system. The cost of the system and installation is $80,000. The amount of power the system will produce is normally distributed with a standard deviation of 10 MWh/year. The solar panels become less efficient over time mostly due to clouding of their protective cases. The annual loss in efficiency is normally dis- tributed with a mean of 1% and a standard deviation of 0.2% and will apply after the first year. The cli- ent currently obtains electricity from its provider at a rate of $0.109/kWh. Based on analysis of previous years’ electric bills, the annual cost of electricity is expected to increase following a triangular distribu- tion with most likely value of 3%, min of 2.5%, and max of 4%, beginning with the first year. The cost of capital is estimated to be 5%. Develop a simulation model to find the net present value of the technol- ogy over a 10-year period, including the system and installation cost. What is the probability that the sys- tem will be economical?

Explanation / Answer

YEAR CASH FLOW P/F TO 5% ACTUAL VALUE (P/F)^2 VAR (P/F)^2*VAR 0 80000 1 80000 1 0.0972 0.0972 1 800 0.95 761.90 0.91 4.9028 4.4470 2 800 0.91 725.62 0.82 4.9028 4.0335 3 800 0.86 691.07 0.75 4.9028 3.6585 4 800 0.82 658.16 0.68 4.9028 3.3184 5 800 0.78 626.82 0.61 4.9028 3.0099 6 800 0.75 596.97 0.56 4.9028 2.7301 7 800 0.71 568.55 0.51 4.9028 2.4762 8 800 0.68 541.47 0.46 4.9028 2.2460 9 800 0.64 515.69 0.42 4.9028 2.0372 10 800 0.61 491.13 0.38 4.9028 1.8478 VAN 8.72 VAR 29.9019 STRD DESV 5.4683 P(Exp VAN < 5%)= 1-P(Z=(Exp VAN - VAN)/Strd desv P(Exp VAN < 5%)= 1-P(Z=(5-8.72)/5.42) The probability of the system will be economical is 24.83% P(Exp VAN < 5%)= 1-P(-.68) P(Exp VAN < 5%)= 1 - .7517 = .2483 *P is present value rate and F is future value rate For the triangular distribution E(X) = (a+b+c)/3 (3+2.5+4)/3 3.1667 VAR(X)= (a^2+b^2+c^2)-(a*b+a*c+b*c)/18 (31.25-29.5)/18 0.0972

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