I've read pricing on EV lithium ion battery packs is at around $450/kWh... that'd put it between $18,000 and $38,250 depending on which model you buy. It's definitely the largest cost component of the car.
Yes, the batteries are very expensive. Doubling the battery capacity adds $20,000 to the cost of the car. Most likely the batteries will have a 5 year lifespan, so the amortized operating costs of the batteries may be around $20,000/5 = $4,000 per year. There's also the issue of the environmental costs of the manufacture and of the disposal. These factors are seldom mentioned or discussion tolerated these days, buried under talk of going green and the low cost of the electricity to recharge.
The battery pack and associated circuitry is a array of solid state components.
An internal combustion engine has thousands of different parts - many of them moving, unmonitored and uncontrolled.
The EV is much simpler to manufacture and maintain. The GM EV1 was famously robust and low maintenance.
Personally i believe this is one of the reasons the previous generation of EV's were canceled - it radically changes the profit spread on a vehicle. The old school manufacturers make a lot af profit on vehicle maintenance and parts - this is about to change.
The part count on a typical automobile is 30000 according to toyota - I would love to know what the Model S count is - even with the 6000 battery cells.
Often these problems are solved through complexity. ICEs have very limited ranges of torque efficiency, so we work around them using a complex transmission. Other complexity eliminated by an electric vehicle: induction & emissions systems, environmental controls, ECU/fuel control & associated sensor networks, NVH suppression, fuel storage & delivery, belt-driven accessories (inverter, A/C, power steering).
Granted an electric motor is simpler and more durable than an internal combustion engine. The rest of the car, though, is still a car. It has a transmission, suspension, brakes, etc. all of which will need maintenance and repair like an ordinary car. And it remains to be seen how the battery packs will hold up over time, warranty notwithstanding.
Transmission? There is no transmission -- electric motors have flat torque curves, so there's no need. It has a "gearbox," but it's basically just a differential. The transmission is one of the most expensive and arguably the most complex parts of an automobile powered by an internal combustion engine. Ever priced one of these? It's around $4,000-$10,000 for a replacement -- manual or automatic.