To add to @keshlam's answer slightly a stock's price is made up of several components:
- total assets - total liabilities (the book value)
- the net present value (NPV) of all future cashflows (adjusted by risk)
- a risk premium
the only one of these that is known even remotely accurately at any time is the book value on the day that the accounts are prepared. Even completed cashflows after the books have been prepared contain some slight unknowns as they may be reversed if stock is returned, for example, or reduced by unforeseen costs.
Future cashflows are based on (amongst other things) how many sales you expect to make in the future for all time. Exercise for the reader: how many iPhone 22s will apple sell in 2029? Even known future cashflows have some risk attached to them; customers may not pay for goods, a supplier may go into liquidation and so need to change its invoicing strategy etc.. Estimating the risk on future cashflows is highly subjective and depends greatly on what the analyst expects the exact economic state of the world will be in the future.
Investors have the choice of investing in a risk free instrument (this is usually taken as being modelled by the 10 year US treasury bond) that is guaranteed to give them a return. To invest in anything riskier than the risk free instrument they must be paid a premium over the risk free return that they would get from that. The risk premium is related to how likely they think it is that they will not receive a return higher than that rate. Calculation of that premium is highly subjective; if I know the management of the company well I will be inclined to think that the investment is far less risky (or perhaps riskier...) than someone who does not, for example.
Since none of the factors that go into a share price are accurately measurable and many are subjective there is no "right" share price at any time, let alone at time of IPO. Each investor will estimate these values differently and so value the shares differently and their trading, based on their ever changing estimates, will move the share price to an indeterminable level.
In comments to @keshlam's answer you ask if there is enough information to work out the share price if a company buys out the company before IPO. Dividing the price that this other company paid by the relative ownership structure of the firm would give you an idea of what that company thought that the company was worth at that moment in time and can be used as a surrogate for market price but it will not and cannot accurately represent the market price as other investors will value the firm differently by estimating the criteria above differently and so will move the share price based on their valuation.