Private equity firms invest money on behalf of their clients and return to them the lion's share of the profits. Elevation Partners will also keep a percentage of profits - this is typically around 20% but can vary from firm to firm. In addition, firms typically charge an annual fee based on the size of the fund. Some firms also charge a fee to investors for buying a company.
Elevation Partners' share of its profit made Friday is probably in the area of $30.8 million. Bono's take depends on the particulars of Elevation Partners and how it divvies up its profits. The company website lists six other managing directors excluding Bono, a senior advisor, two associates and seven-person administrative team. Bono's share could be as low as $4.4 million, or one-seventh of the profit (there are seven managing partners). Facebook latest S-1 filing mentions only four of the seven managing directors: Fred Anderson, Paul Hewson (Bono's given name), Roger McNamee, and Bret Pearlman.
Elevation Partners and Bono don't own 100% of the remaining 40.1 million shares, either. The company can lay claim to less than 20% of their current $1.46 billion value (as of 2pm ET Friday) because it will return 80% of the profit - or $1.17 billion at current valuation - to its investors (it will be less than 20% of their current value because Elevation Partners' cost basis for the shares need to be taken into account). Bono will be left with an unknown fraction of that 20%.