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Say Company A purchased 100% of Company B, and in 2012 Company turned over a net income of $X

Were Company B to be its own owner, the $X would go in their "pockets", their bank account.

But seeing as B is owned by A, does the latter have full ownership of the $X? Can they claim the whole sum of that income, and if so, what profit does B have left to invest in new ventures?

In realistic terms, BRK purchases 100% of GEICO. In 2014, GEICO – hypothetically speaking – turns over $4 billion in profits

Can BRK then collect that $4 billion, and if so what benefit is that to GEICO; for all their profits to be handed over to BRK; what can they (GEICO) then do for investing since their profits have been handed over, how do they grow? Would BRK offer them an 'allowance'?

What if they owned 10%, a minority holding? Would BRK still be entitled to collect 10% of annual net income?

NB: this is purely based on the subsidiary being a Private company, not going into the question of shares, dividends etc..

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Yes, the owner could claim all the profit. Or they could reinvest all the profit back into the subsidiary. Or they could invest more into the subsidiary. Or some intermediate point along that spectrum.

There's no magic here. It's not very different from the wholly-owned subsidiary just being a division of the owning company. Management makes a decision about where and how much to invest, and that's what happens.

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