Question

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 \(\$ 0.15 / \mathrm{kWh}\) ?

Short answer

Answer: The payback time for the solar panel investment is approximately 9.13 years.

Step-by-step solution

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 = \(6 \cdot \$ 0.15 = \$ 0.90\)

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

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.

Key concepts

Solar Energy Calculation

To calculate the value derived from solar energy, we need to consider both the capacity of the solar array and the average sunlight it receives. Imagine a scenario: you have invested in a solar panel system with a peak capacity of 1 kW, costing you approximately \(3,000. This system will generate energy based on the number of full-sun equivalent hours available in your location. If your region enjoys about 6 hours of full-sun equivalent daily, this means your solar array will produce 6 kWh of electricity each day. Considering that electricity costs approximately \)0.15 per kWh, you can calculate the daily financial benefit of this energy production by multiplying these values together: \[ \text{Daily Value Produced} = 6 \, \text{kWh} \times \\(0.15/\text{kWh} = \\)0.90 \]Hence, each day, your system saves you $0.90 on electricity, providing an essential foundation for understanding the payback timeline of your investment.

Investment Payback Period

The payback period is a crucial concept that describes how long it will take for an investment to break even. For solar panels, this period is determined by comparing the initial cost of the system with the savings from electricity production. Calculating the payback period involves dividing the installation cost by the daily savings. In this case, the installation costs \(3,000, and you're saving \)0.90 per day from it. Hence: \[ \text{Payback Time (days)} = \frac{\\(3,000}{\\)0.90} = 3,333.33 \, \text{days} \]To make it more accessible, we convert this figure into years, which helps in grasping long-term impacts and making informed decisions. The conversion uses a simple division by 365 days (assuming no leap years), giving us:\[ \text{Payback Time (years)} = \frac{3,333.33}{365} \approx 9.13 \, \text{years} \]Therefore, it would take just over 9 years for the solar panel system to pay for itself through savings, highlighting the importance of future cost and energy considerations in your investment.

Solar Panel Economics

Understanding the economics behind solar panels can help in assessing its viability as a cost-saving tool. Solar panel economics involves not just the initial investment but also factors like location, typical energy consumption, and energy prices. Key points to consider are:

• Initial Cost: This is the upfront cost of setting up a solar power system, typically around $3 per watt for the system in our exercise.
• Energy Cost Savings: The amount saved depends greatly on the local electricity price, which we've used as $0.15 per kWh.
• Government Incentives: Many regions offer rebates or tax credits for solar installations, which can lower the effective payback time.
• Energy Production: The efficiency of a solar panel system is dictated by the amount of sunlight received—which varies by geographical location—and the quality of the panels used.

Evaluating these factors together can help determine whether solar panels are a sound financial decision in your specific context. They offer not just economic benefits but also environmental advantages, contributing to cleaner and more sustainable energy consumption.