The Solar Panel Payback Claim
A household is quoted $6,400 for a 5 kW solar system. The salesperson claims it will 'pay for itself in four years'. The household's electricity bill is $2,100 per year. The quote estimates the system will generate 6,500 kWh per year, and that 60% of that will be used in the home while 40% is exported to the grid. The household pays 28 cents per kWh for electricity bought from the grid, and receives 8 cents per kWh for electricity exported. Assume the household's usage pattern means every self-consumed kWh displaces a grid kWh.
1. Calculate the annual saving and the actual payback period, and compare it with the salesperson's claim.
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Self-consumed energy: 60% × 6,500 = 3,900 kWh. Each displaces a 28c purchase, saving 3,900 × $0.28 = $1,092. Exported energy: 40% × 6,500 = 2,600 kWh. Earns 2,600 × $0.08 = $208. Total annual benefit = $1,092 + $208 = $1,300.
Payback = $6,400 ÷ $1,300 ≈ 4.9 years.
The salesperson's 'four years' claim is optimistic. Four years would require $1,600 per year, which is $300 more than the calculation supports. The claim may assume a higher self-consumption rate or ignore the low export tariff. The realistic payback is closer to five years, before any panel degradation or maintenance.
2. Identify one assumption that, if wrong, would most change the conclusion.
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The most sensitive assumption is the 60% self-consumption rate. Export earns only 8c versus 28c displaced - a 20c difference per kWh. If the household is out during the day and self-consumes only 35%:
- Self-consumed: 0.35 × 6,500 = 2,275 kWh × $0.28 = $637
- Exported: 0.65 × 6,500 = 4,225 kWh × $0.08 = $338
- Total = $975; payback = 6,400 ÷ 975 ≈ 6.6 years.
So a 25-point drop in self-consumption pushes payback from ~4.9 to ~6.6 years. The conclusion (whether the system pays back quickly) hinges heavily on when the household uses power, not just how much the panels generate. A good answer names this and shows the arithmetic.