Auniversity spent $1.8 million to install solar panels atop a parking garage. these panels will have a capacity of 500 kw, have a life expectancy of 20 years and suppose the discount rate is 10%. if electricity can be purchased for costs of $0.10 per kwh, how many hours per year will the solar panels have to operate to make this project break even? (hint: we need that the present value (pv) of the electricity generated by the solar panels be equal to the cost.)

Present value refers to the current value of future sum of money given in a specified rate of return. It’s also the concept that states that the worth of amount today is more than the same amount in future.

This implies that the worth of money received in the future is not up to the worth of money received today.  In this question, we are going to use present value to evaluate the project cost over a certain period of time.

Let y represent the number of hours per year that the solar panel operates:

And the energy produced yearly is 500*y which equals 500y

The revenue saved per year is 500kwh*0.10/kwh which equals 50y, so the revenue saved is $50

The discount rate is 10% and the number of period of years is 20years, therefore  

PV factor of annuity of $1=1/r*(1-1/(1+r)^n)=1/10%*(1-1/(1+10%)^20)= 8.5136

the PV value of revenue saved will be $50y*8.5136(PV factor of annuity of $1) which equals 425.68y and since the cost of solar panel is $1,800,000, then the cost of solar panel will be equals to the PV of the revenue saved. i.e. 1800000=425.68y, which can be solved by y=1800000/425.68 which is 4228.55. so to break even, the solar power must operate at 4228.55 hours

answer(b); ; ; the quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable;