If I’m working with a public company in a DCF, how do I calculate its per-share value?

Once you get to Enterprise Value, ADD cash and then subtract debt, preferred stock, and noncontrolling interest (and any other debt-like items) to get to Equity Value.

Then, you need to use a circular calculation that takes into account the basic shares outstanding, options, warrants, convertibles, and other dilutive securities. It’s circular because the dilution from these depends on the per-share price – but the per-share price depends on number of shares outstanding, which depends on the per-share price. 

To resolve this, you need to enable iterative calculations in Excel so that it can cycle through to find an approximate per-share price.