Well, I personally don't like to heat with wood anymore but this is how I calculated things. Are you sure you only pay $0.13/kWh? I pay $0.13/kWh with $0.19/kWh in delivery fees. In summer if I take my electric bill/kWh I pay $0.29/kWh and $0.34/kWh in winter as winter is more expensive. Also, I'm not sure if air heat exchangers are like geothermal, where heating is not as efficient as cooling. That's to say, a 300% efficient geothermal typically means it's 200%-250% efficient at heating and 350-400% at cooling, making it a better investment if electricity is cheap and used mostly for cooling (aka not New England), and when cooling you can put the heat into your water tank.
I bought a house back in 2004, was going through oil like water (about $3,000/year back in 2004). I bought a wood insert and had it installed and 6 cords of wood for $4,700 investment and saved $2,300 the first year (-$2400)
2nd year 2 cords of wood burned (I fixed a major heat loss and was getting better with insert) with $1300 saved = $-1100
3rd year I insulated attic with 24" insulation and replaced windows dropping wood to 1.5 cords and saved $1100 = $0 (broke even)
<from this point wood was just given to me from neighbors, work, etc. I've not bought wood since>
4th year bought solar hot water system for $3,500 and saved $1700 in oil from hot water & wood = -$1800
5th year insulated basement after seeing how cold exposed cement gets lowering wood use to 1 cord = $0 (broke even)
6th year didn't do much but saved $1800 in oil = +$1800
7th ditto but oil got more expensive = +3700
8th ditto but oil got more expensive = +$5700
9th ditto = +$7700
10th = Since I wasn't using oil boiler, and gaskets needed to be hot to seal properly it had been dripping slowly over the years and rotted to the point it couldn't be repaired so I needed new boiler. $7850 for new boiler that was stainless, and cold start (meaning it's designed to not deteriorate/leak when not in use for months) = -$150
11th = 1 cord used for heating ($0 given to me), 4 gallons/oil used for year ($10) + ($48 in electricity to run solar pumps/yr) = $58/yr for all my heating & hot water needs. -$2000
12th year = Added a couple solar panels for supplemental heating (just 2) so they don't do much but I don't need to light a fire as much. Down to 0.6 - 0.75 cords/wood and 4 gallons/year oil + ($48/year to run solar pump) solar for hot water
All said and done, I personally find wood to be a lot of work, I trek in a lot of dirt, my walls and house get dirty from burning wood, I have to deal with ash, and cleaning the chimney, when I light a fire it's about 40 minutes/day I feel wasted. With all the $ spent, could I go back, I wish I'd just done a good solar heating system, put some PV panels to boot for electricity, and replaced the boiler. Probably be at the same cost as I am now, without the hassle and dirtiness of wood.