Company with help of lead managers (merchant bankers or syndicate members) decides the price or price band of an IPO.
SEBI, the regulatory authority in India or Stock Exchanges do not play any role in fixing the price of a public issue. SEBI just validate the content of the IPO prospectus.
Companies and lead managers do lots of market research and road shows before they decide the appropriate price for the IPO. Companies carry a high risk of IPO failure if they ask for a higher premium. Many a time investors do not like the company or the issue price and don’t apply for it, resulting unsubscribe or undersubscribed issue. In this case companies’ either revise the issue price or suspends the IPO.