Since it goes public for the first time, there's no market price available to be considered for offers.
No, the price is set by the company but crucially is agreed with the underwriter, who undertakes to buy any shares that don’t sell in the market. It’s almost always a premium to the company’s asset value, or there would be no point in the IPO. But it’s generally below the anticipated market price, to give a first-day profit to the IPO investors and reduce the risk to the underwriter.
There are two components involved in determining an IPO's price.
First, the investment bank determines the value of the company.
Next, the company does an IPO Roadshow and is often called a Dog & Pony Show. It lasts for a couple of weeks as the company pitches the IPO to institutional investors (hedge funds, analysts, fund managers, banks). The higher the interest in the IPO, the higher its per share price it will be.