GAAP utilises full good will and under IFRS a choice can be made between either full good will or partial.
Full Good Will: Excess of fair value of company over fair value of net asset. Company A purchase 75% of Company B for $450m where its fair net asset value is $ 560 m. Fair value is thus 450/0.75 = $600m. Good will be $40 m (600 - 560) under both equity and acquisition. Take note that good will is already accounted for within the investment account under equity method (ie good will is not a separate asset in addition of investment account). For acquisition method, all target company B asset and liability will be included in company A balance sheet together with an additional good will item of $40m. Thus the increase in $40m good will in asset will see a similar $40m increase in the minority interest. Minority interest without goodwill originally (excess purchase price) is $110m (560-450). Thus after including good will of $40m the minority interest is $150m. This can also be calculated as minority interest * fair value of company ([1-0.75]*600)
Partial Good Will Example: Excess of purchase price over proportional fair value of net asset. Company A purchase 75% of Company B for $450m where its fair net asset value is $ 560 m. Good will be $30 m (450 - 560*0.75) under both equity and acquisition. Similarly good will is already accounted in the investment account for equity method. Noticed the lesser value in good will. For acquisition method, all target company B asset and liability will be included in company A balance sheet together with an additional good will item of $30m. Thus the increase in $30m good will in asset will see a similar $30m increase in the minority interest. Minority interest without goodwill originally (excess purchase price) is $110m (560-450). Thus after including good will of $30m the minority interest is $140m. This can also be calculated as minority interest * fair value net asset ([1-0.75]*560)
In general, the addition of Good will for acquisition method implies a similar addition in the minority interest. For equity, you just need to take note of that good will is always included within investment account.
[made some corrections to my calculations above]