A university spent $1.6 million to install solar panels atop a parking garage. T

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 20%, that electricity can be purchased at $0.20 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?

3,285.71

2,053.57

2,258.93

1,026.79

If the solar panels can operate only for 1,848 hours a year at maximum, the project (would/would not) break even.

Continue to assume that the solar panels can operate only for 1,848 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 __________________.

Explanation / Answer

Solution:

The Correct Answer (B)

Working note:

Initial investment = $1.6 million or $1600000

Time n = 20 years

R = 20%

Let, uninform annual cost = P

Then,

1600000 = P*(1-1/1.2^20)/.20

P = 1600000/4.8695

P = $328596.07

Let, number of hours per year required to achieve the breakeven = N

Then,

N = 328596.07/(.2*800)

N = 2053.7 hours

Correct Answer:

Project will not achieve break even.

Grant of $21187.2

Working note:

The gap between the 2053.7 hours and 1848 hours, will be fulfilled by the grant.

So,

Size of the grant = 0.2*800*(2053.7 - 1849)

Size of the grant = $293786.3

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