When you aren't sure how to value the assets and business of a company, optics unavoidably make a difference in the way you trade the company's stock. Look at all these software and tech services companies that are priced off of wonky numbers like EV/sales multiples if you don't believe me.
If people see a strong bid, they may be more likely to perceive it as bullishness, which influences their own trading decisions. As a result, the company may actually end up with a higher eventual valuation once the IPO dust has settled and the price has found an equilibrium.
Not to mention that the offered stake isn't the whole company.
its in the company's interest to have IPO investors (their first public mkt investors) rewarded, as it keeps them from selling too much, and it attracts other investors to the stock. dropbox is still unprofitable, so it will probably need to raise more equity in the future, and it helps to reward your early investors
it also makes the investment banks happy -- their clients made money on the deal. if dropbox's banks are happy, that helps dropbox, bc as mentioned above, it will need their services again
the happier public market investors are, the higher the stock price will go. most employees cant sell stock for at least a few months, and if outside public investors are happy, then by the time employees can sell, the stock will be worth much more
if you price too high and all the proceeds accrue to the company rather than investors, you get a debacle like facebooks IPO, where the stocked dropped and didnt recover for over a year
What is the volume trading at 44% above the opening price?
When you put $700mm of securities on the market you need to price them low enough so that investors hold.