How do net operating loss carryforwards (NOLs) enter a valuation, and why don't you just deduct them like net debt?

NOLs are a tax asset: they shelter future taxable income, so their value is the present value of the cash taxes they save, not their face amount. Two approaches: model the tax savings explicitly inside the FCF (lower cash taxes in the years the NOLs are used, given expected profitability and any annual usage limitation), or value them separately and add the PV as a non-operating asset to operating EV. You can't just subtract the face value like debt because the benefit depends on generating enough taxable profit to use them, the timing of usage, expiry, and ownership-change limitations. For a loss-making target the NOLs may be worth little; for a profitable acquirer, meaningfully more.