Bond premium discount FCFF

When calculating FCFF from NI, why is the premium subtracted and discount added?

I do not understand the logic of the direction of the signs.

What “premium”?

Do you possibly mean the amortization of a discount/premium that appears in interest expense?

If so, it’s a non-cash charge (just as depreciation is), so it needs to be removed.

The amortization of the premium hits the P&L? I thought it was just a reduction in B/P as a contra liab.

Yes.

For a premium, you debit Bonds Payable, and credit Interest Expense.

For a discount, you credit Bonds Payable and debit Interest Expense.