An automatic litter box is quite the investment as you know. You really need to consider what other expenses you'll have in addition to purchasing the box.
Items such as disposable litter trays, waste receptacles, extra litter and other parts such as batteries are things you will also need to think about replacing (depending on which box you purchase).
Some boxes, such as the Litter Robot are quite simple to maintain. Click on the link to check out some reviews of this box and see how it fares with real testers!
Another point that you need to remember is that just because it is electric, doesn't mean that it is completely hands free.
Some people might think that you just set it and forget it but unfortunately, this is not the case.
You will still need to maintain the box every few days and most certainly on a weekly basis (depending on how many cats you have in your household).
Still, many automatic box owners confess that they cannot imagine their lives without one.
You be the judge on whether these boxes are worth an investment for you. Just try to remember the above facts about maintenance, purchasing batteries, disposable receptacles, etc.
Once you make the purchase, you may always slowly wean your cat to the box and some manufacturers have a money back guarantee if you are not satisfied. Just check the product package.