Question

A university spent $1.4 million to install solar panels atop a parking garage These panels will have a capacity of 400 kilowatts (kW) and have a life expectancy of 20 years. Suppose that the discount rate is 10%, that electricity can be purchased at $0.30 per kilowatt-hour (kWh), and that the marginal cost of electricity production using the solar panels is zero. Hint: It may be easier to think of the present value of operating the solar panels for 1 hour per year first. Approximately how many hours per year will the solar panels need to operate to enable this project to break even? 685.18 1,370.36 2,055.54 If the solar panels can operate only for 1,233 hours a year at maximum, the project break even. Continue to assume that the solar panels can operate only for 1,233 hours a year at maximum. In order for the project to be worthwhile (i.e., at least break even), the university would need a grant of at least

Answer 1

Initial Cost = $1.4 million

Let the no of hours be x, then total electricity production is 400*x = 400x units

Hence Annual Savings = 400x * 0.3 = $120x

PV of Annual Savings over 20 yer life = A*(1-(1+r)^-n)/r

=120x*(1-(1+10%)^-20)/10%

=120x*(1-1.1^-20)/0.1

=120x*(1-0.1486)/0.1

=120x*0.8514/0.1

=$1021.63x

To break even, Initial cost = PV of Annual Saving

or, 1400000 = 1021.63x

or, x = 1400000/1021.63

or, x = 1370.36

Hence the No of hours = 1370.36 Hours

If the Solar Panels operate for 1233 hours, it is less than the hours required to break even hence the project will not break even

PV of Annual Saving at 1233 hours = 1021.63*1233 = 1259669.79

Hence Grant Required = 1400000-1259669.79 = $140330.21