Market. Underwriters(banks) work with management to determine a fair spo price when management desires fresh capital. The value of the offered shares at the spo is based upon the current market price and the price the underwriters are willing to pay and management is willing to sell.
Those shares are then offered to the public at a higher price than the discount negotiated between the aforementioned entities. The public then buys and sells those offered shares driving the market in the direction of the majority(buyers/sellers).