Ah, so, my units don’t match yours because my gas company bills in “therms” – which are a unit of energy, not of volume (they apply a conversion factor when they calculate the bill.) A therm is 100,000 BTU, or enough energy to heat 100,000 lbs of water by 1 degree Fahrenheit (see, these are all very silly US units…) I decided to stick with therms through the calculations, because it comes up with some nice reasonable dollar figures in the end, rather than having to deal with fractions of cents. A MCF of gas is about 10.37 therms of heat energy, so your gas rate in my units would be about $0.96/therm. Electricity is also billed in units of energy, and one therm is 29.3 kWh. (So, an electric space heater would consume 29.3 kWh to put out one therm of heat.)
Going through my silly calculations, then (ignore the weird formatting, the forum software thinks this is code so it’s highlighting certain keywords):
For the furnace:
$0.96/therm (gas rate)
---------------------- = $1.03/therm (gas bill per unit heat)
0.93 (efficiency)
$0.085/kWh (electric rate) * 0.5 kW (furnace fan, 500W)
------------------------------------------------------------------ =
75,000 BTU/h (furnace input) * 0.93 / 100,000 BTU/thm (conversion)
$0.0425/hr (cost to run furnace fan)
----------------------------------- = $0.061/therm (elec. bill per unit heat)
0.698 thm/hr (furnace heat output)
Total for furnace: $1.09/therm
For the heat pump
To match $1.09/therm with your heat pump, here’s the calculation:
$0.085/kWh * 29.3 kWh/therm (unit conversion)
--------------------------------------------- = $1.09/therm (to match furnace)
COP
Rearranging it, we get:
COP =
$.085/kWh (elec. rate) * 29.3 kWh/therm (conversion)
---------------------------------------------------- = 2.28
$1.09/therm (furnace cost per unit heat)
End result
So, looking at the data sheet, you could set your switchover point as low as 5-10 degrees! Whether the unit can actually provide enough heat for your home at that temperature is another question, but your thermostat should handle that for you. Given you have a 75,000 BTU/hr furnace, unless the furnace is drastically oversized, I suspect the heat pump wouldn’t be sufficient, producing only around 18,000 BTU/hr at those temps.
One thing you should make sure of is that the electric rate you quoted was inclusive of both generation and delivery charges – for whatever reason, at least in my state, the utility puts these two prices on very different parts of the website.