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ME 353
Case #4
ME 353
Case 4: Solar II
06 April 2023
Lokprabhat Katasani, Cade Wetherill
NOTE:
In the original “HO15 Case4.pdf” file, the P90 Solar Flux listed was 281 W/m^2 and the PV
Degradation values were listed as being 0.5%, 1.0%, and 1.5% per year. However, in the “Solar Case
Template v5.1 w Ranges” spreadsheet, these values were listed as being 218 W/m^2 and 0.25%, 0.5%,
and 0.75%. For this case, the values of 218 W/m^2 and 0.5%, 1.0%, and 1.5% per year were used
respectively. The values used were meant to be representative of the original “HO15 Case4.pdf” file with
the exception of the 281 W/m^2 value, which is assumed to be a typo due to the wording implying low
uncertainty between the solar flux values (“Eric thinks there is some uncertainty regarding these numbers,
but not a lot.”).
Social Value (i.e., the true value of the system without tax breaks)
Using a tornado diagram, identify the biggest drivers of uncertainty?
Figure 1
: Tornado Diagram Showing the Differences Between Low/High Society NPV and Mean Society
NPV for System A
When looking at the tornado diagram seen in Figure 1 above, the most significant drivers of uncertainty
are the “Increase in Usage due to Solar”, “Collector Efficiency”, and the “Social Cost of Carbon”.
“Increase in Usage due to Solar” is the largest driver of uncertainty by a significant margin, which is
understandable due to society caring much more with the environmental output of Eric’s home instead of
how long Eric actually spends living in his home.
What are the important breakeven values for different input parameters?
After isolating every single different input parameter that affected the NPV of the system for society, no
1
ME 353
Case #4
single input parameter caused the NPV to be positive (breakeven). However, the biggest difference
caused by the input was from “Increase in Usage due to Solar”, for system A and B. This uncertainty
caused the NPV to get extremely close to 0, as when the electricity usage decreased by 2%, the
resulting graph displayed a range of around -8,000 to -1000 dollars for system A and around -7,500 to
-500 dollars for system B.
Create a cumulative distribution for the present value of the system to society. What is the
probability that the system will have a negative present value?
Figure 2
: Risk Cumulative Distribution for NPV of System A (Left) and System B (Right) to Society
In terms of value to society, System A will have a negative net present value 92.7% of the time, while
System B will have a negative net present value 93.2% of the time.
Are Eric’s solar panels a good investment from society’s perspective?
While Eric’s solar panels are a good investment from a purely environmental perspective, for the solar
panels will be less damaging to the environment than electricity on its own as seen in Case #3, they’re a
terrible investment from a financial perspective. With only a 7.3% chance for System A to have a positive
present value over standard electricity and a 6.8% chance for System B to have a positive present value
over standard electricity, it’s quite the gamble financially, with a significant chance of financial failure.
Society would be much more well off spending the money elsewhere.
Eric’s Value
Using a tornado diagram, identify the biggest drivers of uncertainty.
2
ME 353
Case #4
Figure 3
: Tornado Diagram Showing the Differences Between Low/High Society NPV and Mean Society
NPV for System A
For Eric, his home parameters are by far the most significant drivers of uncertainty when it comes to the
possible ranges between the P10 and P90 values. Staying in his home for 15 years and selling his home to
someone willing to pay an extra $5000 for his solar panels alone add a total of $12,653 to his net profit
value. The “Increase in Usage due to Solar” once again serves as a large driver of uncertainty, though not
as large as Eric’s home parameters are.
What are the important breakeven values for different input parameters?
When testing how each individual input parameter affected the NPV for the homeowner, the “Impact on
Home Value” caused the biggest difference in the NPV. If the system A increases the value of the house
by $3,460, the NPV of the system becomes zero (breakeven). However, even on the upper bound of
$5,000 for system B, the NPV becomes very close to breakeven at -$870.
Along with the “impact on home value” the “increase in consumption due to solar” also has a massive
impact on the NPV of the system for the homeowner, however, this factor alone does not cause a
breakeven. For system A, it causes a range of around -8,000 to -1,000 dollars. For system B, it causes a
range of around -8,200 to -2,000.
Create a cumulative distribution for the present value of the system to Eric. What is the
probability that the system will have a negative present value?
3
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ME 353
Case #4
Figure 4
: Risk Cumulative Distribution for NPV of System A (Left) and System B (Right) to Homeowner
In terms of value to Eric, System A will have a negative net present value 77.2% of the time, while
System B will have a negative net present value 86.4% of the time.
Is this a good investment from Eric’s perspective? Which system is best and why?
Once again, the added uncertainties make the investment seem very poor. While not as terrible as
the investments are for society, System A only having a 22.8% chance and System B only having
a 13.6% chance to turn a positive present value make both systems very hard to recommend.
System A is slightly better due to having an extra 9.2% chance to turn positive over System B, the
chance of the net present value is simply way too large to be considered a worthwhile financial
investment. While it may be better environmentally, the solar panels seem to be a very poor
financial investment for Eric give his uncertainty estimates.
4
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