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Solar Payback worksheet

Grades 11–12 · CCSS HSF.LE.A.1.c, HSA.SSE.B.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

  1. Problem 1.
    • Electricity use per month: 800 kWh
    • Share of use to cover with solar: 110%
    • Peak sun hours per day: 5 h/day
    • System efficiency (derate): 62%
    • Installed cost: $2 per watt
    • Rebates and incentives: $0
    • Electricity price: $0.11 per kWh
    • Value of each solar kWh: 90% of electricity price
    • Electricity price increase: 2% per year
    • Panel output decline: 0.4% per year
    • Yearly maintenance: $0 per year
    • Years to look ahead: 28 years

    Find: Payback period

  2. Problem 2.
    • Electricity use per month: 900 kWh
    • Share of use to cover with solar: 140%
    • Peak sun hours per day: 5.2 h/day
    • System efficiency (derate): 100%
    • Installed cost: $3 per watt
    • Rebates and incentives: $0
    • Electricity price: $0.20 per kWh
    • Value of each solar kWh: 80% of electricity price
    • Electricity price increase: 2.7% per year
    • Panel output decline: 0.6% per year
    • Yearly maintenance: $0 per year
    • Years to look ahead: 25 years

    Find: Payback period

  3. Problem 3.
    • Electricity use per month: 900 kWh
    • Share of use to cover with solar: 65%
    • Peak sun hours per day: 4 h/day
    • System efficiency (derate): 75%
    • Installed cost: $3 per watt
    • Rebates and incentives: $0
    • Electricity price: $0.15 per kWh
    • Value of each solar kWh: 90% of electricity price
    • Electricity price increase: 2.8% per year
    • Panel output decline: 0.4% per year
    • Yearly maintenance: $0 per year
    • Years to look ahead: 32 years

    Find: Payback period

  4. Problem 4.
    • Electricity use per month: 900 kWh
    • Share of use to cover with solar: 75%
    • Peak sun hours per day: 4.4 h/day
    • System efficiency (derate): 72%
    • Installed cost: $3 per watt
    • Rebates and incentives: $0
    • Electricity price: $0.16 per kWh
    • Value of each solar kWh: 100% of electricity price
    • Electricity price increase: 2% per year
    • Panel output decline: 0.4% per year
    • Yearly maintenance: $0 per year
    • Years to look ahead: 24 years

    Find: Payback period

  5. Problem 5.
    • Electricity use per month: 900 kWh
    • Share of use to cover with solar: 80%
    • Peak sun hours per day: 4 h/day
    • System efficiency (derate): 88%
    • Installed cost: $2 per watt
    • Rebates and incentives: $0
    • Electricity price: $0.18 per kWh
    • Value of each solar kWh: 100% of electricity price
    • Electricity price increase: 2.6% per year
    • Panel output decline: 0.6% per year
    • Yearly maintenance: $0 per year
    • Years to look ahead: 19 years

    Find: Payback period

  6. Problem 6.
    • Electricity use per month: 880 kWh
    • Share of use to cover with solar: 65%
    • Peak sun hours per day: 5.5 h/day
    • System efficiency (derate): 90%
    • Installed cost: $3 per watt
    • Rebates and incentives: $0
    • Electricity price: $0.11 per kWh
    • Value of each solar kWh: 80% of electricity price
    • Electricity price increase: 3% per year
    • Panel output decline: 0.4% per year
    • Yearly maintenance: $0 per year
    • Years to look ahead: 28 years

    Find: Payback period

  7. Problem 7.
    • Electricity use per month: 900 kWh
    • Share of use to cover with solar: 120%
    • Peak sun hours per day: 4.6 h/day
    • System efficiency (derate): 88%
    • Installed cost: $3 per watt
    • Rebates and incentives: $0
    • Electricity price: $0.15 per kWh
    • Value of each solar kWh: 70% of electricity price
    • Electricity price increase: 2.8% per year
    • Panel output decline: 0.5% per year
    • Yearly maintenance: $0 per year
    • Years to look ahead: 32 years

    Find: Payback period

  8. Problem 8.
    • Electricity use per month: 975 kWh
    • Share of use to cover with solar: 130%
    • Peak sun hours per day: 4 h/day
    • System efficiency (derate): 80%
    • Installed cost: $3 per watt
    • Rebates and incentives: $0
    • Electricity price: $0.13 per kWh
    • Value of each solar kWh: 100% of electricity price
    • Electricity price increase: 2.4% per year
    • Panel output decline: 0.5% per year
    • Yearly maintenance: $0 per year
    • Years to look ahead: 32 years

    Find: Payback period

  9. Problem 9.
    • Electricity use per month: 900 kWh
    • Share of use to cover with solar: 110%
    • Peak sun hours per day: 3.4 h/day
    • System efficiency (derate): 90%
    • Installed cost: $4 per watt
    • Rebates and incentives: $0
    • Electricity price: $0.16 per kWh
    • Value of each solar kWh: 88% of electricity price
    • Electricity price increase: 2.5% per year
    • Panel output decline: 0.4% per year
    • Yearly maintenance: $0 per year
    • Years to look ahead: 24 years

    Find: Payback period

  10. Problem 10.
    • Electricity use per month: 900 kWh
    • Share of use to cover with solar: 72%
    • Peak sun hours per day: 5.5 h/day
    • System efficiency (derate): 75%
    • Installed cost: $3 per watt
    • Rebates and incentives: $0
    • Electricity price: $0.13 per kWh
    • Value of each solar kWh: 90% of electricity price
    • Electricity price increase: 3% per year
    • Panel output decline: 0.6% per year
    • Yearly maintenance: $0 per year
    • Years to look ahead: 20 years

    Find: Payback period

Answer key: Solar Payback worksheet

  1. 1. Payback period: 15.8 years

    1. Work out the energy to make each year: your monthly use × 12 months × the share you want solar to cover

      800 kWh×12×110%=10,560 kWh
    2. Size the system: divide that by what 1 kW of panels makes in a year (365 days × sun hours × efficiency)

      10,560 kWh365×5 h×0.62=9.3327 kW
    3. Price it: size in watts × the installed cost per watt

      9,332.74 W×$2.00=$18,665.49
    4. Take off rebates and incentives to get what you really pay

      $18,665.49−$0.00=$18,665.49
    5. First-year savings: the power you make × its price × how much of that your utility credits, minus upkeep

      10,560 kWh×$0.11×90%−$0.00=$1,045.44
    6. Payback: savings pass the net cost during year 16. By the start of that year you've saved $17,555.68, and the rest takes part of the year

      15+$18,665.49−$17,555.68$1,324.93=15.8376 years
    7. Net gain over 28 years: total savings minus net cost

      $36,524.94−$18,665.49=$17,859.45
  2. 2. Payback period: 9.1 years

    1. Work out the energy to make each year: your monthly use × 12 months × the share you want solar to cover

      900 kWh×12×140%=15,120 kWh
    2. Size the system: divide that by what 1 kW of panels makes in a year (365 days × sun hours × efficiency)

      15,120 kWh365×5.2 h×1=7.9663 kW
    3. Price it: size in watts × the installed cost per watt

      7,966.28 W×$3.00=$23,898.84
    4. Take off rebates and incentives to get what you really pay

      $23,898.84−$0.00=$23,898.84
    5. First-year savings: the power you make × its price × how much of that your utility credits, minus upkeep

      15,120 kWh×$0.20×80%−$0.00=$2,419.20
    6. Payback: savings pass the net cost during year 10. By the start of that year you've saved $23,678.66, and the rest takes part of the year

      9+$23,898.84−$23,678.66$2,912.62=9.0756 years
    7. Net gain over 25 years: total savings minus net cost

      $78,322.39−$23,898.84=$54,423.55
  3. 3. Payback period: 16.7 years

    1. Work out the energy to make each year: your monthly use × 12 months × the share you want solar to cover

      900 kWh×12×65%=7,020 kWh
    2. Size the system: divide that by what 1 kW of panels makes in a year (365 days × sun hours × efficiency)

      7,020 kWh365×4 h×0.75=6.411 kW
    3. Price it: size in watts × the installed cost per watt

      6,410.96 W×$3.00=$19,232.88
    4. Take off rebates and incentives to get what you really pay

      $19,232.88−$0.00=$19,232.88
    5. First-year savings: the power you make × its price × how much of that your utility credits, minus upkeep

      7,020 kWh×$0.15×90%−$0.00=$947.70
    6. Payback: savings pass the net cost during year 17. By the start of that year you've saved $18,207.60, and the rest takes part of the year

      16+$19,232.88−$18,207.60$1,382.64=16.7415 years
    7. Net gain over 32 years: total savings minus net cost

      $44,771.51−$19,232.88=$25,538.64
  4. 4. Payback period: 14.5 years

    1. Work out the energy to make each year: your monthly use × 12 months × the share you want solar to cover

      900 kWh×12×75%=8,100 kWh
    2. Size the system: divide that by what 1 kW of panels makes in a year (365 days × sun hours × efficiency)

      8,100 kWh365×4.4 h×0.72=7.005 kW
    3. Price it: size in watts × the installed cost per watt

      7,004.98 W×$3.00=$21,014.94
    4. Take off rebates and incentives to get what you really pay

      $21,014.94−$0.00=$21,014.94
    5. First-year savings: the power you make × its price × how much of that your utility credits, minus upkeep

      8,100 kWh×$0.16×100%−$0.00=$1,296.00
    6. Payback: savings pass the net cost during year 15. By the start of that year you've saved $20,146.51, and the rest takes part of the year

      14+$21,014.94−$20,146.51$1,616.73=14.5372 years
    7. Net gain over 24 years: total savings minus net cost

      $37,522.63−$21,014.94=$16,507.68
  5. 5. Payback period: 8.1 years

    1. Work out the energy to make each year: your monthly use × 12 months × the share you want solar to cover

      900 kWh×12×80%=8,640 kWh
    2. Size the system: divide that by what 1 kW of panels makes in a year (365 days × sun hours × efficiency)

      8,640 kWh365×4 h×0.88=6.7248 kW
    3. Price it: size in watts × the installed cost per watt

      6,724.78 W×$2.00=$13,449.56
    4. Take off rebates and incentives to get what you really pay

      $13,449.56−$0.00=$13,449.56
    5. First-year savings: the power you make × its price × how much of that your utility credits, minus upkeep

      8,640 kWh×$0.18×100%−$0.00=$1,555.20
    6. Payback: savings pass the net cost during year 9. By the start of that year you've saved $13,340.88, and the rest takes part of the year

      8+$13,449.56−$13,340.88$1,819.94=8.0597 years
    7. Net gain over 19 years: total savings minus net cost

      $35,469.57−$13,449.56=$22,020.00
  6. 6. Payback period: 15.6 years

    1. Work out the energy to make each year: your monthly use × 12 months × the share you want solar to cover

      880 kWh×12×65%=6,864 kWh
    2. Size the system: divide that by what 1 kW of panels makes in a year (365 days × sun hours × efficiency)

      6,864 kWh365×5.5 h×0.9=3.7991 kW
    3. Price it: size in watts × the installed cost per watt

      3,799.09 W×$3.00=$11,397.26
    4. Take off rebates and incentives to get what you really pay

      $11,397.26−$0.00=$11,397.26
    5. First-year savings: the power you make × its price × how much of that your utility credits, minus upkeep

      6,864 kWh×$0.11×80%−$0.00=$604.03
    6. Payback: savings pass the net cost during year 16. By the start of that year you've saved $10,901.10, and the rest takes part of the year

      15+$11,397.26−$10,901.10$886.15=15.5599 years
    7. Net gain over 28 years: total savings minus net cost

      $24,391.16−$11,397.26=$12,993.90
  7. 7. Payback period: 16.2 years

    1. Work out the energy to make each year: your monthly use × 12 months × the share you want solar to cover

      900 kWh×12×120%=12,960 kWh
    2. Size the system: divide that by what 1 kW of panels makes in a year (365 days × sun hours × efficiency)

      12,960 kWh365×4.6 h×0.88=8.7715 kW
    3. Price it: size in watts × the installed cost per watt

      8,771.45 W×$3.00=$26,314.36
    4. Take off rebates and incentives to get what you really pay

      $26,314.36−$0.00=$26,314.36
    5. First-year savings: the power you make × its price × how much of that your utility credits, minus upkeep

      12,960 kWh×$0.15×70%−$0.00=$1,360.80
    6. Payback: savings pass the net cost during year 17. By the start of that year you've saved $25,935.26, and the rest takes part of the year

      16+$26,314.36−$25,935.26$1,953.68=16.194 years
    7. Net gain over 32 years: total savings minus net cost

      $63,170.11−$26,314.36=$36,855.75
  8. 8. Payback period: 16.9 years

    1. Work out the energy to make each year: your monthly use × 12 months × the share you want solar to cover

      975 kWh×12×130%=15,210 kWh
    2. Size the system: divide that by what 1 kW of panels makes in a year (365 days × sun hours × efficiency)

      15,210 kWh365×4 h×0.8=13.0223 kW
    3. Price it: size in watts × the installed cost per watt

      13,022.26 W×$3.00=$39,066.78
    4. Take off rebates and incentives to get what you really pay

      $39,066.78−$0.00=$39,066.78
    5. First-year savings: the power you make × its price × how much of that your utility credits, minus upkeep

      15,210 kWh×$0.13×100%−$0.00=$1,977.30
    6. Payback: savings pass the net cost during year 17. By the start of that year you've saved $36,536.62, and the rest takes part of the year

      16+$39,066.78−$36,536.62$2,667.11=16.9487 years
    7. Net gain over 32 years: total savings minus net cost

      $85,819.61−$39,066.78=$46,752.83
  9. 9. Payback period: 20.6 years

    1. Work out the energy to make each year: your monthly use × 12 months × the share you want solar to cover

      900 kWh×12×110%=11,880 kWh
    2. Size the system: divide that by what 1 kW of panels makes in a year (365 days × sun hours × efficiency)

      11,880 kWh365×3.4 h×0.9=10.6366 kW
    3. Price it: size in watts × the installed cost per watt

      10,636.58 W×$4.00=$42,546.33
    4. Take off rebates and incentives to get what you really pay

      $42,546.33−$0.00=$42,546.33
    5. First-year savings: the power you make × its price × how much of that your utility credits, minus upkeep

      11,880 kWh×$0.16×88%−$0.00=$1,672.70
    6. Payback: savings pass the net cost during year 21. By the start of that year you've saved $41,008.54, and the rest takes part of the year

      20+$42,546.33−$41,008.54$2,529.78=20.6079 years
    7. Net gain over 24 years: total savings minus net cost

      $51,449.34−$42,546.33=$8,903.01
  10. 10. Payback period: 14.5 years

    1. Work out the energy to make each year: your monthly use × 12 months × the share you want solar to cover

      900 kWh×12×72%=7,776 kWh
    2. Size the system: divide that by what 1 kW of panels makes in a year (365 days × sun hours × efficiency)

      7,776 kWh365×5.5 h×0.75=5.1646 kW
    3. Price it: size in watts × the installed cost per watt

      5,164.63 W×$3.00=$15,493.90
    4. Take off rebates and incentives to get what you really pay

      $15,493.90−$0.00=$15,493.90
    5. First-year savings: the power you make × its price × how much of that your utility credits, minus upkeep

      7,776 kWh×$0.13×90%−$0.00=$909.79
    6. Payback: savings pass the net cost during year 15. By the start of that year you've saved $14,909.99, and the rest takes part of the year

      14+$15,493.90−$14,909.99$1,264.95=14.4616 years
    7. Net gain over 20 years: total savings minus net cost

      $22,966.25−$15,493.90=$7,472.36