One way to look at solar payback time time is to note that an installed system will cost something like \(\$ 3,000\) for each \(\mathrm{kW}_{\mathrm{p}}\) (peak capacity), and that you'll produce \(x \mathrm{kWh}\) from that \(1 \mathrm{~kW}_{\mathrm{p}}\) array if your region gets \(x\) hours of full-sun- equivalent on average. Since each kWh of electricity costs something like \(\$ 0.15\), it becomes straightforward to compute the value per day as \(\$ 0.15 x\), and determine how long to match the \$3k investment. The result is independent of the actual array size, depending only on the cost per \(W_{p}\), the solar yield at your location, and the cost of electricity. What would the payback time be, in years, if the cost is \(\$ 3 / W_{p}, 17\) the yield is 6 hours per day of full-sun-equivalent, and electricity in your region costs \(\$ 0.15 / \mathrm{kWh}\) ?

Step by step solution

01

Calculate the daily value of the solar energy produced

The daily value of the solar energy produced can be calculated as the product of the average number of full-sun-equivalent hours per day (x) and the cost of electricity per kWh. Daily value produced = \(x \cdot \$ 0.15\) Substituting the given values, Daily value produced = \(6 \cdot \$ 0.15 = \$ 0.90\)

02

Calculate the payback time in days

To find the payback time, we need to divide the installation cost by the daily value of the solar energy produced. Payback time (days) = \(\dfrac{\text{Installation Cost}}{\text{Daily Value Produced}}\) Payback time (days) = \(\dfrac{\$ 3,000}{\$ 0.90}\) Payback time (days) = \(3,333.33\) days

03

Convert the payback time to years

We can convert the payback time from days to years by dividing the payback time in days by the number of days in a year (assuming 365 days). Payback time (years) = \(\dfrac{\text{Payback Time in Days}}{365}\) Payback time (years) = \(\dfrac{3,333.33}{365}\) Payback time (years) ≈ \(9.13\) years The payback time for the solar panel investment, given the mentioned conditions, would be approximately 9.13 years.

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