Joining the China-led Asian Infrastructure Investment Bank will cost Japan about ¥360 billion and give it a stake about half that of Beijing, according to government estimates in a document obtained by Bloomberg.

Japan's initial contribution would be ¥180 billion, before doubling when the AIIB raises capital levels, according to the estimate from Tokyo, which is calculated on the size of each member's gross domestic product. It would be the second-largest stakeholder with 14.7 percent, behind China at 28.5 percent, the document shows.

Japan and the U.S. have so far declined China's invitation to become part of the AIIB, even though allies such as the U.K., Australia, South Korea, Germany and France have embraced it. The U.S. shaped institutions like the World Bank and International Monetary Fund, and along with Japan dominates the Asian Development Bank (ADB).