Not sure about other types of company formation but I believe a gōdō gaisha (合同会社?) has a capital requirement of 1 Yen.
If you want a visa sponsored by the company you need to capitalize at 5 million yen. This is true with either a KK or GK (yes, 合同会社 is correct), but a KK is more of a pain in the *** paperwork wise so I went with a GK. The cost from my lawyer would have been essentially the same to form either one. The primary difference for my company would have been that most Japanese know what a KK is and trust it, but don't necessarily know what a GK is. I don't care, my only purely Japanese clients are a couple of pro bono cases I took because the kids absolutely needed some help and the families couldn't find what they needed from the local systems. So they pay for an interpreter and I provide services for free.
It's not about creating the business, that's easy and relatively cheap if you have good Japanese skills, it's about whether you want to actually live here after you create it. For those of us who rely on our businesses to sponsor our visas, this becomes an important point. It means we pay people to create the business in a way that ensures that we can then pay them again to use the business to sponsor our visas. Not cheap if you want it done right by people who actually know what they're doing. It cost me somewhere in the neighborhood of 500,000 - 700,000 JPY to create the business and get the visa IIRC.
This ignores all the other money one has to actually spend, which Patrick is 100% right about. My business was showing a profit of about 200,000 JPY (aside from all expenses, including my (minimal) salary) from the day my visa came through but, even now after 5 months of successful business, I'm just getting out of the hole I put myself in monetarily. I'm hoping that by the 1-year mark I've fully paid back my investment and the only reason I consider that possible is that I happen to be in a field which is quite highly valued and underserved for expatriate needs.
Expect to drop about 1.5 Million JPY on expenses, and that's if you're thrifty and have some experience with Japan. Though I'm a bit drunk, so let's assume I could be off by perhaps half a million yen. Really depends on how you plan to live while working through the process. I grew up broke, so I'm actually feeling quite flush living in my low-income UR apartment barely over the border from Chiba, and before I had a visa I spent considerably less during the 6 months of waiting and hoping nothing went horribly wrong.
I'm happy to break it down for anyone really interested, and I bet if I worked with Patrick on it (based on my assumption that he is running a successful business here in Japan) we could pretty well lay out the expected expenses and how to make it possible in the face of some rather insane policies both public and private.
I don't think that would be useful, though, because anyone who can appropriately fund and run a business here doesn't need a tutorial.
