Complete Question:
A university spent $1.6 million to install solar panels atop a parking garage. These panels will have a capacity of 900 kilowatts (kw) and have a life expectancy of 20 years, suppose that the discount rate is 10%, that electricity can be purchased at S0.20 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. 1,670
B. 1,044.09
C. 1,148.50
D. 730.86
Answer:
Option B. 1,044.09
Step-by-step explanation:
To calculate the breakeven point, simply calculate the future value of investment that equals the present value (Investment of $1.6 million).
Mathematically,
Present Value = Future value * Annuity at 10% rate for 20 years
Here
Present Value of investment is $1.6 million
Annuity Factor at 10% for 20 years = [1 - 1/(1 + 10%)^20 years] / 10%
= 8.5136
Future value for 20 years = Hourly rate of electricity consumption * Maximum capacity * Number of electricity units in annual consumption
Hourly rate is $0.2 per KWH
Maximum capacity is 900 KWH
and
Number of electricity units is "X"
By putting values, we have:
$1.6 million = ($0.2 per KWH * 900 KWH * X) * 8.5136
$1,600,000 = X * 180 x 8.5136
$1,600,000 = X * 1,532.45
X = $1,600,000 / 1,532.45 = 1044.09 KWH