If a company does not have a permanent establishment in Japan, then it is not subject to Japanese tax on its Japanese business activities. Category 1 applies. If it does have a permanent establishment in Japan, them the company is subject to Japanese tax on so much of its profits as are attributable to its branch in Japan. Category 3 applies. Transfer pricing works as follows.
Some countries impose no income-tax or impose negligible income tax.
Examples of such countries are Cook Islands, Vanuatu, Hong Kong, Cayman Islands, Liechtenstein, Channel Islands. A person could set up a company in one of these tax havens and arrange for all of his profits to be derived by this company. Consequently, he would have no tax to pay on his world-wide operations. Suppose instead a company is incorporated in the Cook Islands. All the profit is now being made by the Cook Islands company.