Goodwill Formula: Company purchase price - fair market value (shares outstanding * current stock price) or Company purchase price - book value of equity?
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When a company is acquired, the purchase price paid for the business is spread across all of the acquired assets and liabilities (i.e. the target's balance sheet is reset to fair market values for each balance sheet line item on the new parent's consolidated balance sheet). If after going through that exercise, there is still un-allocated purchase price, then that amount is classified as goodwill. It is GAAP's way of recording that "X Factor" of a business that made it enticing to the acquirer to pay more than the fair market value of a target's identifiable net assets when buying the business.
In short, goodwill represents the excess of the purchase price over the fair market value of an acquired company's indentifiable net assets.
To put it more in your original post's terms: Purchase Price Paid - FMV of identifiable net assets = Goodwill recorded.