Who determines company value at IPO?
The Owners based on the advice from Lead Bankers and other Independent auditors who would determine the value of the company at the time of listing. At times instead of determining a fixed price a range is given [lower side and higher side]. The Market participants [FI / Institutional Investor Segments] then decide the price by bidding at an amount.
There are multiple aspects in play that help stabalize the IPO and roles of various parties. A quick read of question with IPO tagIPO tag is recommended
Edits:
Generally at a very broad level, one of the key purpose of the IPO is to either encash Owner equity [Owner wants some profits immediately] or Raise additional Capital. More often it is a mix of both.
If the price is too low, one loose out on getting the true value, this would go to someone else. If the price is too high, then it may not attract enough buyers or even there are buyers, there is substantial -ve sentiment. This is not good for the company. Read the question From Facebook's perspective, was the fall in price after IPO actually an indication that it went well?From Facebook's perspective, was the fall in price after IPO actually an indication that it went well?
This puts determining the price of IPO more in the realm of art than science. There are various mechanism [Lead bankers, Institutional Investors, Underwriters] the a company would put in place to ensure the IPO is success and that itself would moderate the price to realistic level. More often the price is kept slightly lower to create a positive buzz about the stock.