Table A1 Parameters for cost and revenue...

Table A1

Parameters for cost and revenue calculations per equations in the text

Variable name	Description
For Equation 1: Net present value (NPV) as a function of system size and grantsmanship
IO_i	Initial outlay in the year of installation is dependent upon system size. The ith producer’s past 12-months’ electricity use determines annual kWh which is subsequently divided by the solar electricity production potential per kW_DC where the latter is a measure of system size in a physical sense. For installations less the 200 kW_DC in size the cost is $1,700/kW_DC, for installations between 200 and 499 kW_DC ($1,610/kW_DC), 500–999 kW_DC ($1,510/kW_DC), 1–1.999 MW_DC ($1,350/kW_DC), 2–4.999 MW_DC ($1,290/kW_DC), 5–9.999 MW_DC ($1,280/kW_DC), 10–19.999 MW_DC ($1,260/kW_DC) and 20+ MW_DC ($1,250/kW_DC). These costs reflect estimates provided in 2022 by Delta Solar, an Arkansas based solar installer, for fixed panels. The cost estimates are similar to those available at the National Renewable Energy Lab (NREL). For installations greater than 500 kW_DC, tracking technology can be used at an upcharge of 10% with an average productivity increase of 18%. Tracking technology is not evaluated in this analysis. Solar electricity production potential per kW_DC were obtained using the PVWatts tool available at NREL.
GA_i	The Rural Energy for America Program (REAP) offers producers grants of 15–50% of eligible project costs (IO_i) with a maximum of $500,000 per operation. Funding for these grant applications varies. We use 25% in this analysis.
For Equation 2: Annual income tax credit (ITC_n,ik) as a function of income tax credit rate and years to realize the credit
R_ITC	The income tax credit rate is set to 30% per recent legislation for installations between 2023 and 2033. Low-income county, native reservation and/or U.S. manufacture of panels offers higher rates. More details are available at https://www.energy.gov/eere/solar/federal-solar-tax-credits-businesses
Y_ITC,k	Number of years to realize income tax credit is set to either 1 or 5 years in this analysis.
For Equation 3: Cash flows after-tax with a solar system (CFAT_n,S+,ijk) are a function of solar electricity generation, ITC, depreciation, maintenance and insurance, property taxes, remaining electric bill, inverter replacement and repayment of loan(s)
SP_n,i	Pre-tax solar value in year n = K_n,i * ER_n,i where K_n,i is the amount of kWh produced by the system which depends on system size for the ith producer in kW_DC and the ZIP code-dependent amount of kWh produced per kW_DC; and ER_n,i is the ith producer’s variable electricity rate obtained from regressing their monthly electricity charges against their kWh use. The y-intercept of said regression serves as the estimate of monthly fixed access and demand charges (REB_i) whereas the slope estimate is the variable electricity rate. We set the electricity inflation rate at 2% per year. Solar electricity generation (K) degrades at 0.5% per year
ITC_n,ik	see explanation for Eq. 2
For Equation 3 (cont’d)
DEP_ik	Solar panel depreciation for tax purposes in year n (n = 1,2,3,4,5,6) derived using 5-yr Modified Accelerated Capital Recovery System (MACRS) rates (Yr 1 = 20%, Yr 2 = 32%, Yr 3 = 19.2%, Yr 4 = 11.52%, Yr 5 = 20% and Yr 6 = 5.6%). Although the income tax credit essentially lowers the purchase price of the system, the depreciable amount of the system allows for depreciation of half the income tax credit. With a 30% income tax credit, 85% of the purchase cost is eligible for depreciation. Further, pending year of installation, 80% of depreciation can be tax deductible in Yr 1 if installed in 2023, 60% with installation in 2024, 40% in 2025 and 20% in 2026 and is commonly referred to as bonus depreciation. The remainder of depreciation after bonus depreciation is spread over the six-year schedule if the producer is assumed to be able to realize income tax credits in the first year. With delayed income tax credit realization we depreciate using 5-yr MACRS adding half the income tax credit across the six-year schedule. The user has the option to modify 5-yr MACRS to straight line depreciation with zero salvage over a user-specified useful life. This latter option was not used in this analysis
M&I_n,i	Maintenance charges are set to $5.00 per kW_DC with an additional $5.50 per kW_DC for insurance based on personal communication with Dr. Brothers (2022). Both inflate at an estimated 1% per year using similar assumptions as those provided in the System Advisor Model (SAM) of NREL. Maintenance costs increase by 10% with tracking technology which was not modeled in this analysis
PT_n,i	Property tax expenses in year n were based on a property tax rate of 0.75% of book value using straight line depreciation and a 20 yr useful life with zero salvage value and IO_i as the initial cost of the Solar System
REB_n,i	The y-intercept of the regression of monthly utility charges against kWh use serves as the estimate of monthly fixed access and demand charges that are multiplied by 12 months to calculate annual charges. If estimated REB_i are negative, a $5/month charge was assumed with the variable electricity rate (ER_i) modified to fit the linear regression through the modified y-intercept and average monthly charges and use. These charges inflate at 2% per year
IV_n,i	Inverters are needed to convert direct current from solar panels to alternating current before grid connection. Inverter replacement occurs in years 12 and 24 over the life of the system. Inverter replacement costs $70 per kW_DC in year 12 and $60 per kW_DC in year 24 (Source: Personal communication with Dr. Brothers, Delta Solar and SAM tool provided by the National Renewable Energy Lab)
For Equation 3 (cont’d)
ITS_n,ijk	Depreciation, maintenance and insurance, property taxes, remaining utility charges, inverter replacement and interest charges on financing are all tax deductible. State income tax savings were calculated using a 5% state income tax rate. Federal income tax savings were calculated using a 20% federal income tax on the same cost items net of state income taxes. The PSA tool user can modify tax rates. Interest expenses vary for the ith producer based on number of loans, loan length and time to realize income tax credit
AF_ijk	Fraction of financing needs (IO_i – GA_i) secured by solar panels, solar generation and income tax credits is set to 1 or 100% if using one loan to repay over either 10 or 20 yrs. A second loan option is available to finance income tax credit realization over 1 or 5 yrs separate from the first loan now secured by solar panels and solar generation only. Financing options and realization of income tax credits and hence impacts timing of principal payments and interest cost
P&I_1,n,ijk	Principal and interest on the first (equipment) loan
P&I_2,n,ijk	Principal and interest on the second (ITC) loan
For Equation 4: Cash flows after-tax without a solar system (CFAT_n,S-,ijk) is a function of electricity use, electricity inflation and state and federal income tax rates
EB_n,i	Annual electrical bills as provided by producer i inflate at 2% per year. Since utility charges are income tax deductible, we calculate after-tax electricity charges as shown in the text. Note that electricity use is not modeled to change over the 30 yr useful life of the system which is appropriate as long as electricity use does not decline over time

Variable name	Description
For Equation 1: Net present value (NPV) as a function of system size and grantsmanship
IO_i	Initial outlay in the year of installation is dependent upon system size. The ith producer’s past 12-months’ electricity use determines annual kWh which is subsequently divided by the solar electricity production potential per kW_DC where the latter is a measure of system size in a physical sense. For installations less the 200 kW_DC in size the cost is $1,700/kW_DC, for installations between 200 and 499 kW_DC ($1,610/kW_DC), 500–999 kW_DC ($1,510/kW_DC), 1–1.999 MW_DC ($1,350/kW_DC), 2–4.999 MW_DC ($1,290/kW_DC), 5–9.999 MW_DC ($1,280/kW_DC), 10–19.999 MW_DC ($1,260/kW_DC) and 20+ MW_DC ($1,250/kW_DC). These costs reflect estimates provided in 2022 by Delta Solar, an Arkansas based solar installer, for fixed panels. The cost estimates are similar to those available at the National Renewable Energy Lab (NREL). For installations greater than 500 kW_DC, tracking technology can be used at an upcharge of 10% with an average productivity increase of 18%. Tracking technology is not evaluated in this analysis. Solar electricity production potential per kW_DC were obtained using the PVWatts tool available at NREL.
GA_i	The Rural Energy for America Program (REAP) offers producers grants of 15–50% of eligible project costs (IO_i) with a maximum of $500,000 per operation. Funding for these grant applications varies. We use 25% in this analysis.
For Equation 2: Annual income tax credit (ITC_n,ik) as a function of income tax credit rate and years to realize the credit
R_ITC	The income tax credit rate is set to 30% per recent legislation for installations between 2023 and 2033. Low-income county, native reservation and/or U.S. manufacture of panels offers higher rates. More details are available at https://www.energy.gov/eere/solar/federal-solar-tax-credits-businesses
Y_ITC,k	Number of years to realize income tax credit is set to either 1 or 5 years in this analysis.
For Equation 3: Cash flows after-tax with a solar system (CFAT_n,S+,ijk) are a function of solar electricity generation, ITC, depreciation, maintenance and insurance, property taxes, remaining electric bill, inverter replacement and repayment of loan(s)
SP_n,i	Pre-tax solar value in year n = K_n,i * ER_n,i where K_n,i is the amount of kWh produced by the system which depends on system size for the ith producer in kW_DC and the ZIP code-dependent amount of kWh produced per kW_DC; and ER_n,i is the ith producer’s variable electricity rate obtained from regressing their monthly electricity charges against their kWh use. The y-intercept of said regression serves as the estimate of monthly fixed access and demand charges (REB_i) whereas the slope estimate is the variable electricity rate. We set the electricity inflation rate at 2% per year. Solar electricity generation (K) degrades at 0.5% per year
ITC_n,ik	see explanation for Eq. 2
For Equation 3 (cont’d)
DEP_ik	Solar panel depreciation for tax purposes in year n (n = 1,2,3,4,5,6) derived using 5-yr Modified Accelerated Capital Recovery System (MACRS) rates (Yr 1 = 20%, Yr 2 = 32%, Yr 3 = 19.2%, Yr 4 = 11.52%, Yr 5 = 20% and Yr 6 = 5.6%). Although the income tax credit essentially lowers the purchase price of the system, the depreciable amount of the system allows for depreciation of half the income tax credit. With a 30% income tax credit, 85% of the purchase cost is eligible for depreciation. Further, pending year of installation, 80% of depreciation can be tax deductible in Yr 1 if installed in 2023, 60% with installation in 2024, 40% in 2025 and 20% in 2026 and is commonly referred to as bonus depreciation. The remainder of depreciation after bonus depreciation is spread over the six-year schedule if the producer is assumed to be able to realize income tax credits in the first year. With delayed income tax credit realization we depreciate using 5-yr MACRS adding half the income tax credit across the six-year schedule. The user has the option to modify 5-yr MACRS to straight line depreciation with zero salvage over a user-specified useful life. This latter option was not used in this analysis
M&I_n,i	Maintenance charges are set to $5.00 per kW_DC with an additional $5.50 per kW_DC for insurance based on personal communication with Dr. Brothers (2022). Both inflate at an estimated 1% per year using similar assumptions as those provided in the System Advisor Model (SAM) of NREL. Maintenance costs increase by 10% with tracking technology which was not modeled in this analysis
PT_n,i	Property tax expenses in year n were based on a property tax rate of 0.75% of book value using straight line depreciation and a 20 yr useful life with zero salvage value and IO_i as the initial cost of the Solar System
REB_n,i	The y-intercept of the regression of monthly utility charges against kWh use serves as the estimate of monthly fixed access and demand charges that are multiplied by 12 months to calculate annual charges. If estimated REB_i are negative, a $5/month charge was assumed with the variable electricity rate (ER_i) modified to fit the linear regression through the modified y-intercept and average monthly charges and use. These charges inflate at 2% per year
IV_n,i	Inverters are needed to convert direct current from solar panels to alternating current before grid connection. Inverter replacement occurs in years 12 and 24 over the life of the system. Inverter replacement costs $70 per kW_DC in year 12 and $60 per kW_DC in year 24 (Source: Personal communication with Dr. Brothers, Delta Solar and SAM tool provided by the National Renewable Energy Lab)
For Equation 3 (cont’d)
ITS_n,ijk	Depreciation, maintenance and insurance, property taxes, remaining utility charges, inverter replacement and interest charges on financing are all tax deductible. State income tax savings were calculated using a 5% state income tax rate. Federal income tax savings were calculated using a 20% federal income tax on the same cost items net of state income taxes. The PSA tool user can modify tax rates. Interest expenses vary for the ith producer based on number of loans, loan length and time to realize income tax credit
AF_ijk	Fraction of financing needs (IO_i – GA_i) secured by solar panels, solar generation and income tax credits is set to 1 or 100% if using one loan to repay over either 10 or 20 yrs. A second loan option is available to finance income tax credit realization over 1 or 5 yrs separate from the first loan now secured by solar panels and solar generation only. Financing options and realization of income tax credits and hence impacts timing of principal payments and interest cost
P&I_1,n,ijk	Principal and interest on the first (equipment) loan
P&I_2,n,ijk	Principal and interest on the second (ITC) loan
For Equation 4: Cash flows after-tax without a solar system (CFAT_n,S-,ijk) is a function of electricity use, electricity inflation and state and federal income tax rates
EB_n,i	Annual electrical bills as provided by producer i inflate at 2% per year. Since utility charges are income tax deductible, we calculate after-tax electricity charges as shown in the text. Note that electricity use is not modeled to change over the 30 yr useful life of the system which is appropriate as long as electricity use does not decline over time

Source(s): Table created by authors

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