The BAPE kids by A Bathing Ape magazine book (mook) is out now. A bit pricy at 1800 yen, it comes with a square boston bag in a colorful nylon material. Quite a nice large size, with long handles and a zipper on top, I am rather happy with it. If the nylon holds up to regular usage, it's quite a reasonable price, considering that a tshirt from BAPE kids cost 4000+ yen.
The fabric is a bit rough, but seems sturdy. The mook is quite nice; they've packaged it so that the gift bag is separate from the mook (rather a catalog really) so you can keep the mook itself around and throw away the cardboard packaging that protects the gift. I actually plan on giving the mook to some friends as I think they'll be amused by the pictures of the fashionable families pictured. The kids are absolutely adorable too.