Interest sits between operating-income and pre-tax profit. It is why two identical businesses can report very different net-income: one is financed with equity, the other with debt. Removing this difference is the whole point of ebitda and ev-ebitda.
Interest is normally tax deductible, which is why the cost-of-debt in a wacc calculation is taken after tax. Rising rates hit floating-rate borrowers immediately and fixed-rate borrowers only when they refinance.
Example: Northwind Tools carries $420M of debt at an average 4.3%, giving $18M of interest. If refinancing pushed the average rate to 7%, interest would be $29M and pre-tax profit would fall by $11M on unchanged operations.
Related: operating-income