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Goodwill can have a number of meanings but this brief article contemplates it's meaning as a financial asset.
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Goodwill that appears on a balance sheet is always 'purchased' Goodwill.  That is, it is not generated by some mechanism internal to the company and then created as an asset.
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Goodwill normally arises from the purchase of a business where the price paid exceeds the fair value of the net assets acquired.  Consider the purchase of an extremely profitable business that had a very low asset base.  If the buyer paid, say, $2 million for a company whose net assets where only worth $1.3 million, the $700 thousand difference would be treated as goodwill.
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On a strictly theoretical basis, Goodwill is the present value of the superior earnings stream of a business, capitalized in perpetuity.  Put another way, you would only pay $2 million for a business with assets of $1.3 million if you thought you would make a lot more money than that sort of investment would normally generate.
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Management must review the asset value of Goodwill every year to determine if it is still a legitimate asset.  If it is not, the asset must either be reduced or written off completely.  Reverting to the previous example, suppose the business purchased had a competitor that opened a location just across the street, and that ongoing profits would be reduced.  Management would be required to reduce, if not write off completely, the value of Goodwill.
 
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