Question

I need help to solve it as soon as possible. Thanks

You decide to grab a cold drink outside Sadler. You notice that the Sadler Center courtyard is equipped with an interesting device - an Enerfusion Orion system. The system is a picnic table equipped with solar panels, batteries for storing energy, and charging stations. How cool! You do a bit of research and find out the following: Purchase and installation of the system costs $10.795. The system can generate 200 Watts of power per hour. Energy is priced by the kilowatt-hour (KH), and one KWH typically costs $0.12 in Virginia The picnic table was funded with your student fees (ie, the Green Fee) and you're keen to analyze the financial implications of this purchase. A (2 pts) Assume the system receives an average of 5 hours of useful sun per day to charge the system's batteries, and the system will last for 10 years. For simplicity, assume that energy cost savings are realized and compounded annually. You're not sure about the opportunity cost of W&M's capital, but you heard that the endowment carns an average of 4% per year. Using NPV, determine whether this was a good investment ID 49

Answer 1

Information given in question is

Initial investment = $10,795 (i.e. purchase & installation of system cost)

The system can generate 200 watts of power per hour (i.e. 200/1000 =0.20 KWH)

Cost of 1 KWH of power in virginia = $0.12

Average useful sun per day to charge system = 5 hours

A. Calculation of NPV of the project when discount rate is 4%

NPV = PV of Cash Inflow - PV of cash outflow

NPV = Saving of energy cost per year *PVAF(4%, 10year) - $10,795

NPV = $43.80(note 1)* 8.11 - $10,795

NPV = $355.22 - $10,795

NPV = -$10439.78

Conclusion: As the NPV of the project is negative, hence it is not a good investment.

B. Calculation of payback period:

Payback period = Initial investment/ annual positive cash inflow

Payback period = $10,795/ $43.80(note 1)

Payback period = 246.46 years

The one short coming of payback period is that it does not consider the time value of money.

C.

Information given:

Life of System = 100 years

discount rate = 1%

other informations are same as given above

Calculation of energy KWH rate to make project viable:

Project is viable when NPV is 0

NPV = PV of Cash Inflow - PV of Cash Outflow

0 = Saving of energy cost per year* PVAF(1%, 100 years) -$10,795

0 =(Energy generated per hour * average useful sun hours per day * no. of days in a year * KWH rate)* PVAF(1%, 100 years) -$10,795

$10795 = (.2 KWH* 5hour* 365 days* KWH rate) * 63.03

$10795 = 23005.95 * KWH rate

KWH rate to make project viable = $10795/23005.95

KWH rate to make project viable = $0.47

Comments on likelyhood of the change:

KWH rate required to make project viable is $0.47 while the current rate is $0.12

Required rates are 3.91 times more than the current rates. Thus the possibilities of this rate is very low.

Working Note:

1 Calculation of Cash Inflow per year

Cash inflow per year = Saving of power cost per year

Saving of power cost per year = Energy generated per hour * average useful sun hours per day * no. of days in a year * KWH rate in virginia

= 0.200 kwh * 5 hours * 365 * $0.12

= $43.80