SISL > 2012 Sustainability in Math Workshop > Activities > Economics of installing Solar PV panels: is it worth it to the individual?

Economics of installing Solar PV panels: is it worth it to the individual?

Martin Walter, University of Colorado, Boulder
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We go through the financial calculations involved in an actual solar photovoltaic system installed (near) Denver, Colorado, in 2013.

Learning Goals

Make the transition to renewable energy and:

Prepares students to build effective coalitions
Engages students in civil discourse/ communications that lead to more effective decisions
Catalyzes collective actions
Advances students' literacy around sustainability issues
Encourages self-reflection and personal development of their "voice" for solving societal challenges
Promotes creative visioning around sustainable futures

Context for Use

This activity is available to just about any level of student from elementary school to college, i.e., almost ``K through grey.''

Description and Teaching Materials

This is a summary of the calculation. This is a real life example.

I just bought a 6kW solar PV system for $35,000 which is supposed to last for 20
to 25 years. Is it worth it? (I might add that $10,000 of this is to build a structure, since no roof space is available,
to place the collectors on--so we are heavily weighting the calculations against solar to begin with.)

Fact one: 10kW (pv system) = 14,586 kWh/year (according to the utility company in Denver, Colorado).

Thus a 6kW system = 8751.6kWh/yr.

I use about 4000kWh/yr for my house and 4000kWh/yr for a Nissan Leaf 100% electric car.

Thus my system generates 751.6 excess kWh/yr above my basic needs.

Now for costs.
If we pay 10 cents per kWh for coal generated electricity, my yearly costs would be
8000*.1 or 800 dollars. This is $16,000 to $20,000, assuming no costs increase
for coal electricity over the 20 to 25 years. (Actually coals costs increase several percent
per year.)

(Note that in 2013 there is a 30% tax credit, so the cost to me of the $35,000 system is
$24,500. So the system, in reality, looks like it pays for itself if one
takes into account coal-cost increases.)

However, there is more.

4000kWh/year represents 12,000 miles of travel/year for the Leaf, all electric car.

So recall that the coal-cost of 4000kWh/yr for the house for 20 to 25 years gives us
$400*20=8000 to 400*25=10,000 dollars for the house.
Next, if a car gets 50 miles per gallon, at $4/gallon gas, then
12,000 miles cost 12000/50*4=960 dollars a year.
This is 19200 dollars for 20 years.
Now the solar electric really pays for itself.

So the economics works out for the individual.
It really works for society (are you listening Congress), for if
we don't make the transition from fossil fuels to renewable energy soon,
climate change will make the planet uninhabitable for humans.

Also the costs of building the panels versus building the power plant
are, we assume, built into the costs to the consumer.
The total costs to the environment are not.

Teaching Notes and Tips

This activity can be completed in about 20 minutes of class time. Note that there currently is a 30% tax credit, so the cost to the individual of the system under consideration (in dollars) is .7*35000=24500.

References and Resources

See the book ``Mathematics for the Environment,'' by Martin Walter, CRC Press/Taylor&Francis

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