In last week’s article I made the on-the-surface ludicrous claim that the value of a solar power system at the end of ten years may be greater than the value of that same system at the date of purchase and installation, even when accounting for the loss in energy efficiency of said solar system over 10 years. Today I will explain how I reached that conclusion.
Use Household Power Consumption Data
While I won’t reproduce the data here, our daily power consumption (over summer and winter months) tells me that our motel uses on average 10.19 kWh per day during daylight hours.
Find the Average Daily Output of the System
The average daily output of the solar power system is 5.148 kWh per day. This is based on a 1.5 kWh system on a north facing roof at 30 degrees. I have queried these statistics with the installer and they believe the figure to be realistic and accurate because it is based on the equipment along with current NIWA data for my region.
Apply a Suitable Margin of Safety
Just in case the installer is wrong, I have applied a 25% margin of safety in my calculations. This assumes that on a system that should produce an average of 5.148 kWh per day, only 3.861 kWh will actually be used.
I will use a conservative estimate, because in addition to the possible variation in generation estimate accuracy, there is also the problem that there may be overlap between the system generating power and using power. Just because the system generates 1.3 kWh during a particular hour, does not mean that I will always have a need for that power at that particular time of day. Since it is not being applied directly to my appliances, it would simply be sent to the grid, at a lower rate of return, if indeed any rate of return at all. For this reason, I think it is wise to factor in a 25% margin of safety, to cover the ‘overlap’.
Use This Figure to Calculate Your Daily Savings (ex GST)
My current cost of daytime energy usage is 24.3c per kWh. Multiplying this by the expected average daily energy saving of 3.861 kWh yields just over 93.82c per day, ex GST.
Then Calculate the Annual Savings (ex GST)
Now we can simply multiply the above figure by 365 to get the annual savings (ex GST) that the solar power system can accomplish in the first year – just over $342.45.
Apply the Rate of Energy Price Inflation
Now we get to the good stuff. The average annual increase in retail electricity prices has been 3.2% during the years 2004 to 2013. We therefore apply an inflation rate of 3.2% per year to discover the gradual price increase of the same amount of electricity over the lifespan of the solar panels (25 years). Calculations applying the rate of energy price inflation to the value of the energy consumption reduced can be found here.
Apply Reducing Energy Efficiency Levels
At the same time as prices are going up, however, the energy efficiency of your solar panels is diminishing. Manufacturer guidelines suggest that over the lifespan of the panels, energy efficiency will diminish by 20%. I have assumed based on this, that at the end of 10 years, energy efficiency will have reached midway – ie the panels will be 90% efficient.
Calculations that factor in the drop in energy efficiency over time can be found here. Note that at the end of ten years, based on the calculations above, our solar panels will have saved us around $3773.60 in actual power energy costs.
Apply Risk-Free Discount Rate
The next stage is to use the Risk Free Rate (the rate of the 10 year NZ Government Bond Rate) to calculate the value of each year’s revenue stream adjusted for the opportunity cost of a risk free investment in NZ Government Bonds. This risk free rate compounds each year, so the further into the future the revenue stream gets, the less it is worth in present value dollars.
Calculations on applying the risk free rate can be found here.
Calculating the Net Present Value
Finally, we add together the sum of all discounted future cashflows (from Year 10 onwards) to reach the “Net Present Value” of a solar power system at the end of 10 years. It is noticeable that even after 10 years, the system will have saved us $3773.60 in actual cashflows and will retain its value fairly well – going up from an original purchase and installation price of $5647.83 ex GST to a value at the end of ten years of $5747.13 ex GST – an increase in value of almost $100 even after it has been fully depreciated using the IRD depreciation schedule.
Conclusion
It is interesting that, even using a fairly conservative margin of safety, solar panels can retain their value rather well, provided that the calculations that underpin their implementation are based on realistic actual records of household energy use over time. In essence, small solar systems tied to actual household energy consumption tend to hold their value rather well.
The interesting thing is that this valuation is driven by inflation. Were it not for a (generally) steady upwards march in retail energy prices, the valuation would be nowhere near as positive and the panels would decline in value over time, rather than retain their value at a steady rate.
