How do you determine a companys intrinsic value per share?

The intrinsic value of shares is determined by the market. You can determine the book value by looking at the balance sheet information. You can do all kinds of ysis to determine a fair value of the shares, but in the final ysis, the intrinsic value is determined by market participants doing such yses and acting on their conclusions. Given that the market has all available information, the best estimate of a stock value is the current price.