Question

You are investigating the feasibility of installing a solar system at your house. You are thinking of installing 20 panels. Each panel has a capacity of 248.1 W. The current average cost for panels, including installation, is around $4.50/W. The solar cells are expected to operate at around 13% capacity. You will get a federal tax rebate worth 30% of the installation cost. You will also get a rebate from the state of New Jersey. Obviously, installing the system would save you every year what you would spend on energy.

Assuming an energy cost of $0.17 per kWh and that the cells operate for 25 years at 13% capacity continuously (this means that they operate 8760 hours per year) and that you consume everything that your system generates :

1. Determine the NPV for discount rates between 1% to 5% with an increment of 1% (this is the opportunity cost of your money—say what you would get in a money market account)

2. In deciding whether or not to do this project the state rebate is important. How much should be the state rebate to make the project appealing to you in each of the cases considered.

NOTE: The relationship between W and kWh is the relationship between power (kW) and energy (kWh). Thus energy=power multiplied by time.   Also, 1000W=1kW.

3. Because the price of energy is volatile you are not happy with your previous computations and you would like to wait one year to see where prices go. If you assume that the PV of the savings have a volatility (standard deviation) of 30% and that the one year T bill is 3% what would be the state rebate for each case computed that would convince you not to wait one year and invest right away.

4. Compare the results at point 2 and point 3.

Answer 1

1
Capacity of 20 panels (20*248.1)	4962	W	Initial Cost	$(15,630.30)
Total Cost (4962*4.5)	$ 22,329.00		PV	NPV
Federal tax Rebate @ 30%	$    6,698.70		1%	$5,525.66
Annual Energy Cost (y1 - y25)	$        960.62		2%	$3,124.39
((4962*13%)/1000*8760)*0.17			3%	$1,097.18
			4%	($623.37)
			5%	($2,091.33)
2
Total Cost (4962*4.5)	$ 22,329.00		Initial Cost	$(13,538.07)
Federal tax Rebate @ 30%	$    6,698.70		PV	NPV
State tax Rebate @9.37%	$    2,092.23		1%	$7,617.88
Annual Energy Cost (y1 - y25)	$        960.62		2%	$5,216.62
			3%	$3,189.40
			4%	$1,468.86
			5%	$0.90