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How I understand this:
you combine assets and liabilities at fair value plus any goodwill (in CFAI example full goodwill I think) and to have A=L+E you need to have minority int also booked with same principles, in this case because they bought 50pct it is the same amount they paid.
Say you (X) pay cash 100 for 50pct of a company (Y) and it is equal to fair values of assets and liabilities (so zero goodwill):
you combine in books of X 100 % of assets and liabilities of Y at fair values (say 300 assets and 100 liabilities)
assets are minus 100 cash plus 300 assets = + 200
liabilities are plus 100
to have A=L+E you need to add 100 to minority interest
when the goodwill is not zero, then there is the full or partial goodwill issue

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