Is NOI calculated before or after taxes?

It depends on which taxes. Property taxes are an operating expense and come out before NOI. Income taxes do not. NOI is calculated before income tax, before mortgage interest and before depreciation, so it shows what the property earns regardless of who owns it or how they financed it.

On the default property, the $3,600 property tax bill is inside the $10,230 of operating expenses that produce $18,270 of NOI. The owner's federal and state income tax on the rental is calculated later, after interest and depreciation, on the tax return.

Use the property tax you will actually pay after purchase. Many counties reassess on sale, and a seller's bill based on an old assessment can understate yours by 30% or more, which overstates NOI by the same dollars.