Is REx worth it?

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Just one advice: No Rex! Buy a 120 Ah version!
Less weight, more ev mileage.
Less maintenance, so much lower running costs.
Rex owners use the Rex almost never . Results of a bmw survey. That's why they ended selling them in Europe.
You can use the space of the Rex for extra storage (Wokeby trunk extension)
Why pay more for something you'll almost never use and can give you headaches.

Good luck with your next i3!
I have had a REX car for 4 years now. And i have used it on some longer journeys. It has been an absolute blessing having the REX when either a) you don't have time to recharge (or cant be bothered waiting) or b) turn up at a charger and find its broken, wont work because of an account issue, or some one else is using it. I reckon on long journeys turning up at a charger which you cant use is about 1 in 5 so its not that rare an occurance. I do not know what I would have done without the REX. ~I will add however that if I had a longer range battery like Berlindriver suggests this might not have been a problem in the first place. Most of my driving in the i3 is in and out of town or to and from work and i charge at home and the REX is not needed.
I am rather interested in this aspect. Recently (1 month ago ) I purchased a BMW Rex with a 60ah range battery (2015 model) . Thanks to our London Mayor's fanaticism to get more money from people. Anyway. This Rex has a limited (upto 70mile) range. I have a high degree of trepidation regarding longer term reliability re engine. Charging on public networks costs from 50p upwards per kwh. Home charging is roughly 30p+ /kwh (I do understand there may be cheaper ways ). As I understand, petrol has theoretically 9kwh energy in 1 litre. Which on a pure cost works out to 17p/kwh (based on £1.50/ltr) . Appreciate petrol engines are not efficient hence possible loss of 50% in conversion (may be even less) ? which perhaps means it may cost 34p /kwh. Taking in to account grid cost of minimum 50p (as far as I have seen ), burning petrol (E5) to charge appears to me cheaper than charging at any grid stations. This also assumes there are chargers available, free to plug in. Not to mention the charging times which can be upwards of 1 hour to just get some charge in (7kw). Grid electricity is also inefficient. There will be transmission losses there too, not to mention generation losses ? Appreciate, electric is one of the most flexible energy sources to store and acquire. Unsure where BMW got there data from re Rex? As I do find the flexibility of a portable generator in the boot useful. Yes, of course, having a larger battery etc may go a way to alleviate problem I may face and does weigh less but the option to have a generator running and adding to the range is useful in the model I currently have. I would of course, love a 120ah or more battery. I do appreciate the lure of pure electric and the elimination of a petrol engine. Currently the cost of electricity on the charging network is too high ( UK ) Have seen charges of upto a minimum 75p /kwh and further a minimum connection charge at times of 30p just to connect? Yuk.

The figures re costings efficiency I obtained from a quick web scan are really a rough guess from the small research done.
I would love to read a better write up from more knowledgable persons here about costings and efficiencies.
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Making a truly accurate informed cost comparison is difficult for the average person because there are so many unknown variables. I do know impirically that charging at a public station ranges from 35 cents per kw on up to who knows how much at a highway rest stop. Ethanol-free premium gas costs about 3.00/gal in my market, and electricity at my home runs about 15 cents per kw.
The efficiency of my 2017 Rex averages 4.4 mi/kw electric and is supplemented by 36 mi/gal via the range extender.
Given 120 miles @ 27.2 kw = 4.4m/kw and 88 miles @ 2.4 gals = 36 mpg
4.4 miles @ 15 cents = 3.5 cents/mile
4.4 miles @ 35 cents = 8 cents/mile
36 miles @ $3.00 = 8 cents/mile

Clearly charging at home is the cheapest and most convenient method. Using the Rex to get home or to the next public charger is comparable to the cost of public charging but there are trade offs. I can fill my Rex tank in a minute at a self serve gas station, but then it takes a bit of annual maintenance and is another system that might fail and require repair. Purchasing a Rex equipped i3 is also arguably a little more expensive but there is a much broader market range 2014-2021.

I normally can go several days without charging but then maybe once a month or so I need to stretch my charge with the Rex. There is a grocery store on my route to the big city that has several free L2 chargers and I can pick up 20 miles or so while grocery shopping. I could do similar - charge enough to get home at a fast DC charger too kind of like getting $5 worth of gas instead of automatically filling the tank.

So my conclusion is whether you get an i3 with or without a Rex might be a wash depending on your budget, how much you use the car or how far you need to go every day, availability of public chargers in your area, and whether you can charge at home.
This is one of those things where understanding the regional infrastructure and where the car will be driven really is critical to the decision. Again, a 60Ah BEV here (Eugene, OR) imposes impossibilities. A 120Ah imposes fewer of them, but they still exist. REx with the smaller pack overcomes all of them.
Grid electricity is also inefficient. There will be transmission losses there too, not to mention generation losses ?
There will, but why do you need to care about these? There will be numerous energy losses in refining crude oil into petrol and distributing it to your local forecourt, but do you have to account for those when working out if a petrol car makes financial sense? Those losses are already factored in to the price that you pay at the pump, and the same applies to losses in the electricity network.
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You are correct that the cost of road side chargers has increased a lot and financially its not so attractive. The electric charging makes more sense when you charge at home. As i said in my first response to this question the REX makes sense from a practicality point of view, and i have never tried to make cost comparisons, since for me that's not the point.
I'm not the only person with an employer who allows EVs to be plugged in at work. So my charging expenses are largely paid for. I occasionally plug in at home, and even more rarely on the road. If DCFC charging rates were 4x what they are today, I'd still be saving a ton of money vs. buying gas.

I'm mindful of the fact that DC fast charging is a service, not a commodity. I'm paying a premium for a fast charge. The comparison of the DCFC kWh cost vs. what I pay at home is almost irrelevant.