Automatic dishwashers are really cheap per hour saved. The actual costs will vary widely (esp. in the US, where the cost of electricity is much lower than where I live), but our best estimate at the time of buying was $2/hour saved (based on halving the 30 minutes we need to do the dishes, and assuming it breaks the moment it's out of warranty - not entirely unreasonable, since we pretty much bought the cheapest option.) Locally, about half is depreciation of the dishwasher and half is electricity/washing powder/water (negligible).

(I've brought this up before: http://lesswrong.com/lw/9pk/rationality_quotes_february_2012/5tsb.)