The total cost of a system (brought back to present value: NPV) divided by the total amount of energy it produces is called **Levelized Cost of Electricity** or (**LCOE**). LCOE is measured in units of $/Watt or $/Kilowatt.

LCOE equations can be very complicated. The total value of the system has a lot more than just initial cost and yearly revenues. However, for this section we will keep it simple. We will begin the LCOE analysis by examining the numerator. The total life cycle cost of the system is all of the costs, and benefits now and in the future, all brought back to the present value. It is essentially a complicated NPV formula.

Now, to examine the total lifetime power produced (the denominator of the LCOE equation) we will *also* bring the total **power** back to present value. Let’s begin with the basics. Again – we are looking at the *denominator* of the LCOE equation.

All solar systems degrade over time. This degradation will be denoted as δ, and its power output for year “n” is:

Where Q_{n} is the amount of power produced that year, and Q_{0} is the amount of power produced in the first year. Therefore the total power produced over the system’s lifetime (n years) is:

Even *power* in the future needs to be adjusted back to “present value” (of power). We do this by applying the same Present Worth factor adjustment for dollars. Therefore our LCOE equation becomes:

If we examine the case of our $15,000 system, let’s assume that it produces 5000 kWh / year on the first year, has a δ of 0.05%. Use a discount factor of 2% (instead of the IRR of the system), we see that our NPV becomes:

$13,451. Note that the line that was previously “IRR” has been changed to the discount factor of 2%. This value of $13,451 is our NPV, and our numerator in the LCOE equation. Now we will calculate the denominator of the equation (total lifetime power produced). We can use excel to execute the following equation:

We do this very similarly to how we created the financial spreadsheet, but we also need a degradation factor line.

So we can see the total **present value** of the power produced by the system over its lifetime is 133,697 kWh. We can now complete our LCOE analysis.

LCOE is a very useful figure in comparing two similar technologies. For example, if the system described above could have been installed with a 1-axis tracker, for an additional $10,000, but then also output an additional 2,000 kWh / year (1), we could perform an auxiliary LCOE analysis to compare the two technologies, by modifying both the numerator (cost = cost + $10,000), and the denominator (power produced = power produced + additional power produced), and determine a new LCOE for the alternatively proposed system. Once completed, the LCOE will tell the homeowner which is the better investment. In this case we get:

So the homeowner should *not* go for the 1-axis tracker upgrade based on the LCOE analysis.