Question

A university spent $1.6 million to install solar panels atop a parking garage. These panels will have a capacity of 800 kilowatts (kW) and have a life expectancy of 20 years. Suppose that the discount rate is 30%, 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?

A.1,206.35

B.2,010.58

C.3,015.87

D.2,211.64

If the solar panels can operate only for 1,810 hours a year at maximum, the project break would or would not even. Continue to assume that the solar panels can operate only for 1,810 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

$175,582.11

$79,810.05

$159,620.10

$207,506.13

Answer 1

Initial Expenditure is $1.6 million

Revenue is 0.3 per kwh and capacity is 800 Kwh hence revenue per hour is 0.3*800 = $240

Annual Revenue assuming plant operates for x hours will be 240 * x = $240x

$240x will be annual revenue for 20 years

Present Value of $240x over 20 years will be given by P*(1-(1+r)^-n)/r where P=240x, n=20, r= 30%

Hence Present Value = 240x * (1-(1+30%)^-20)/30%

= 240x * (1- 1.3^-20)/0.3

= 240x * (1-0.00526)/0.3

= 800x * 0.99474

= 795.792x

The present value should be equal to initial investment to breakeven

Hence 795.792x = 1600000

or, x = 1600000/795.792

= 2010.58

Hence Plant must at least operate for 2010.58 hours to break even i.e option B

If Solar Plant will operate for 1810 hours plant will not break even as it is less than 2010.58 hrs

By operating for 1810 hours plant will generate a Revenue with Present Value = 795.792x = 795.792 * 1810 = 1440383.52

Hence to break even the university will need a grant of balance amount i.e 1600000 - 1440383.52 = $159616.48

Hence Option C is the correct answer.