I had to replace some cloth diapers recently, which gave me the chance to get a cost estimate.
I use a large flat 4-layer from www.adultclothdiaper.com. Unit cost is $20 plus shipping. I got about 180 nights out of it before it started losing absorbancy and I had to add some extra padding to it. After about 130 nights, it was getting thread bare. I ordered some new ones and did a weight comparison. The new diaper is 18 ounces and the old one is 12. So it had lost a third of its fabric over that time. The cost and duration shows around $0.20 per night, give or take.
I use a plastic pant, and the cost varies a lot there. There are two basic thicknesses: 4 mil and 7 mil. The cost is about $15 either way for a basic pant. The 4 mil went about 45 nights before it started to break up, for a cost of about $0.30 per night. I picked up a 7 mil and used it for about 150 nights without breaking up. It was starting to become noisier and stiffer, but is still useable. My wife decided I needed more to put into rotation to keep the odor down, so I don't know how long it would have gone. But if we take the 150 nights, it becomes $0.10 per night, a third of the cost of the 4-mil.
Together that makes $0.40 for the thin plastic, and $0.20 for the thick. If you are using something durable, like PUL, the price drops again.
For laundry, I rinse it in the shower and drop it in with the bath towels and other whites. Since we use our bath towels once only, we run about 5 loads a week anyway, so it makes little difference. For those using a public laundry, the cost probably doubles.