## Lesson 9

Economics

Both solar electric and solar water-heating systems provide useful forms of energy for consumption in the home, but at a different cost. This lesson provides simple economic comparison between the systems — the amount of time required to payback the cost of the system and its installation.

### Solar Domestic Water-Heating Systems

To make economic calculations, we’ll use the same example we used in Lesson 3: a family of four consuming 80 gallons of hot water a day. The hot water temperature is set at 120 degrees F, the cold water inlet temperature is 55 degrees F, and the hot water tank has a heat loss of 2,147 Btus a day. The total daily heat energy demand was calculated in Lesson 3 to be 45,081 Btus.

Given that the energy in 3,413 Btus of heat is equal to the energy in 1 kWh of electricity, we can compare the cost of using fuel oil, natural gas, or electricity as the energy source to heat the daily hot water demand in this example. Fuel oil is sold by the gallon and on average contains 139,000 Btus per gallon. Natural gas is sold sometimes by the MCF (thousand cubic feet) and sometimes by DekaTherm (DKT). For the purposes of this example, both are 1,000,000 Btus.

Keep in mind that the efficiency of converting from one source of energy to another is not usually 100%. For this example, the use of electricity to heat water can be considered to be 100% efficient because all of the energy from electric resistance heating goes into heating the water, so there are no losses. Fuel-burning appliances must be vented, and some of the energy from burning the fuel carries the products of combustion out of the house. About 70% of the energy content of both natural gas and fuel oil is used to heat the water in the water tank, and the remaining 30% escapes up the flue. Because some energy is lost up the flue, more Btus of gas or oil must be purchased than Btus of electricity.

The following table shows the annual cost of providing the example hot water demand for various fuel prices. The annual Btu demand for heating the hot water in the example is 16,454,565 Btus.

16,454,565 Btu / 3413 Btu per KWh = 4,821 KWh 16,454,565 Btu/70% Efficiency = 23,506,521 Btu input of natural gas, propane, or fuel oil.

Electricity (4,821 kWh needed) |
Cost |
Natural Gas (16.5 Mcf needed) |
Cost |
Fuel Oil (118 gallons needed) |
Cost |

Purchased at $0.10/kWh | $482 | 23.5 purchased at $10/Mcf | $235 | 169 purchased at $2.50/gal. | $423 |

Purchased at $0.15/kWh | $723 | 23.5 purchased at $13/Mcf | $306 | 169 purchased at $2.75/gal. | $465 |

Purchased at $0.20/kWh | $964 | 23.5 purchased at $16/Mcf | $376 | 169 purchased at $3.00/gal. | $507 |

In Lesson 3’s example, the solar energy system provides 3.54 MWh per year to the hot water. 3.54 MWh*3413000 Btu per MWh is 12.08 million Btu per year, which provides 12.08/16.5 or 73 percent of the heating fuel on an annual basis. The following table provides the savings for each fuel and the calculated simple payback for a solar water-heating system that costs $5,200 to install. The simple payback is calculated as the cost of the solar system divided by the cost savings per year.

Electric example: Annual Savings = 12,080,000 Btu/3413 Btu per KWh*$0.10 per KWh = $353.94 savings per year. $5200.00 installed cost /$353.94 annual savings = 14.7 years simple payback |

Natural gas example: Annual Savings = 12,080,000 Btu * $10.00 per DKT/1,000,000 Btu per DKT * .70 Efficiency = $172.57 savings per year. $5200.00 installed cost /$172.57 annual savings = 30.1 years simple payback. |

Fuel oil example: Annual Savings = 12,080,000 Btu * $2.50 per gallon of fuel oil/130,000 Btu per gallon of fuel oil * .70 Efficiency = $331.86 savings per year. $5200.00 installed cost /$331.87 annual savings = 15.7 years simple payback |

Electricity |
Savings |
Payback |
Natural Gas |
Savings |
Payback |
Fuel Oil |
Savings |
Payback |

$0.10/kWh | $354 | 14.7 yr | $10/Mcf | $173 | 30.0 yr | $2.50/gal | $331 | 15.7 yr |

$0.15/kWh | $531 | 9.8 yr | $13/Mcf | $224 | 23.2 yr | $2.75/gal | $365 | 14.2 yr |

$0.20/kWh | $708 | 7.34 yr | $16/Mcf | $276 | 18.8 yr | $3.00/gal | $398 | 13.1 yr |

A federal tax credit of 30% of the system cost (up to a limit of $2,000) is available to homeowners or businesses installing a solar water-heating system. For this example, the federal tax credit reduces the cost of the system by $1,560. The table below reflects the after-tax paybacks using the cost for the solar water-heating system as $3,640.

Electricity |
Savings |
Payback |
Natural Gas |
Savings |
Payback |
Fuel Oil |
Savings |
Payback |

$0.10/kWh | $354 | 10.3 yr | $10/Mcf | $173 | 21.0 yr | $2.50/gal | $331 | 10.9 yr |

$0.15/kWh | $531 | 6.9yr | $13/Mcf | $224 | 16.3 yr | $2.75/gal | $365 | 9.97 yr |

$0.20/kWh | $708 | 5.1 yr | $16/Mcf | $276 | 13.2 yr | $3.00/gal | $398 | 9.1 yr |

### Photovoltaic Systems

Calculating the simple payback for a solar electric system is less complicated than running the numbers for a solar water-heating system. If a 2-kilowatt (peak) DC system is installed and it produces 2,300 kWh a year for consumption in the building, the simple payback is calculated as follows:

Simple Payback = (Cost of the PV system installation) divided by (the cost of electricity times the number of kWh produced by the system)

The installed cost of a PV system ranges from $8 to $10 per DC watt of capacity. For a 2-kilowatt system, the cost ranges from $16,000 to $20,000. Using electricity costs of $0.10, $0.15, and $0.20 per kilowatt-hour, the annual savings from producing 2,300 kWh is $230, $345, and $460 respectively.

$16,000.00 system cost/ 2300KWh per year*$0.10 per KWh = 69.6 years simple payback

With the federal tax credit:

$14,000.00 system cost/2300KWh per year*$0.10 per KWh = 60.9 years simple payback

There are other reasons that people install solar energy systems, such as reducing greenhouse gases, reducing the need for more power plants, reducing consumption fossil fuels, and reducing environmental destruction.

There are other economic analysis methods that can tell you more about the value of installing a solar energy system, but the final analyses are only as good as the input data. For example, it is difficult, if not impossible, to estimate what the future cost for fuels and interest rates will be. In the long run, the simple payback comparison is a quick, easy way to compare between systems using present day costs for fuel and equipment.

### Questions

- Would a solar water-heating system be more cost-effective for a homeowner with electric resistance heat, or a homeowner with natural gas heat?
- What is the payback period range for the 2 kW PV system example (given above) that is connected to a utility that charges $0.08 per kWh? For $0.25/kWh?
- What are the payback period changes for the conditions given in question 2 when the federal tax credits are factored into the calculations?
- How does switching from electricity to natural gas or fuel oil change the simple payback for a solar water-heating system?