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Fuel Cost Comparisons - the "break even" price

What is the break even price for propane vs electricity, or for natural gas vs electricity? In other words, at what price per gallon (or price per mcf) is propane (or natural gas) more economical than electricity for heating or water heating.

To find this magical price, we'll use the following assumptions:

90% efficiency propane (or natural gas) furnace
60% efficiency propane (or natural gas) water heater (standard)
100% efficiency electric resistance heat (baseboard, ceiling cable)
250% efficiency air-source heat pump (standard)
350% efficiency geothermal heat pump (standard)
92% efficiency electric water heater (standard)
100,000 BTU per ccf of natural gas
3,413 BTU per kilowatt hour of electricity
91,500 BTU per gallon of propane
Midwest Electric standard residential rate, $0.10 per kWh
40,032 BTU per day in water heating energy use
80 million BTU annual home heating

Water Heaters

Electric Cost:
(40,032 / 3,413 / .92 efficiency) x $0.10 = $1.28 per day

Propane Equivalent:
(40,032 / 91,500 / .60 efficiency) x Y = 0.73Y
Solve for Y:
$0.73Y = $1.28
Y = $1.75
So, Propane would have to cost less than $1.75 per gallon in order for it to be more economical than electricity for water heating (based on the assumptions).

Natural Gas Equivalent:
(40,032 / 100,000 / .60 efficiency) x Y = 0.67Y
Solve for Y:
$0.67Y = $1.28
Y = $1.91
So, Natural Gas would have to cost less than $1.91 per ccf (or $19.10 per mcf) for it to be more economical than electricity for water heating (based on the Assumptions).

Heating Comparison

Electric Resistance:
(1,000,000 / 3,413 / 1) x $0.10 = $29.30 per million BTU

Propane Equivalent:
(1,000,000 / 91,500 / .9 efficiency) x Y = 12.14Y
Solve for Y:
$12.14Y = $29.30
Y = $2.41.  So, Propane would have to cost less than $2.41 per gallon for it to be more economical than electric resistance heat (ie, baseboard).

Natural Gas Equivalent:
(1,000,000 / 100,000 / .9 efficiency) x Y = 11.11Y
Solve for Y:
$11.11Y = $29.30
Y = $2.64
So, Natural Gas would have to cost less than $2.64 per ccf (or $26.40 per mcf) for it to be more economical than electric resistance heat (ie, baseboard).

Electric Air-Source Heat Pump:

(1,000,000 / 3,413 / 2.5 efficiency) x $.10 = $11.72 per million BTU

Propane Equivalent:
(1,000,000 / 91,500 / .9 efficiency) x Y = 12.14Y
$12.14Y = $11.72
Y = $0.97
So, Propane would have to cost less than 97 cents per gallon for it to be more economical than an air-source heat pump.

Natural Gas Equivalent:
(1,000,000 / 100,000 / .9 efficiency) x Y = 11.11Y
Solve for Y:
$11.11Y = $11.72
Y = $1.05
So, Natural Gas would have to cost less than $1.05 per ccf (or $10.50 per mcf) for it to be more economical than an air-source heat pump.

Electric Geothermal:

(1,000,000 / 3,413 / 3.5 efficiency) x $.10 = $8.37 per million BTU

Propane Equivalent:
(1,000,000 / 91,500 / .9 efficiency) x Y = 12.14Y
$12.14Y = $8.37
Y = $0.69
So, Propane would have to cost less than 69 cents per gallon for it to be more economical than geothermal.

Natural Gas Equivalent:
(1,000,000 / 100,000 / .9 efficiency) x Y = 11.11Y
Solve for Y:
$11.11Y = $8.37
Y = $0.75
So, Natural Gas would have to cost less than $0.75 per ccf (or $7.50 per mcf) for it to be more economical than geothermal.