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bankers set the price. they do valuations(can use comparables) to determine what the company is worth. they price and market the stock.
bankers guage the interest in the stock by doing whats called 'road shows' where they pitch the company to various large investors(institutions like pension funds, mutual funds, etc).
its all based on the demand for the stock and not really on some form of actual valuation, which is why you see more ipo's in bull markets because there's more demand which means a higher price to book value.
if the issuing company wants to set the price higher than what the bank says it should be based on demand, they'll have to sell less shares. there's only so much demand for a stock.
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