assess

To determine, estimate or judge the value of; to evaluate; to estimate.

He assessed the situation.

An insurance adjuster will assess the damage.

To impose or charge, especially as punishment for an infraction.

The referee assessed a penalty for delaying the game.

A $10.00 late fee will be assessed on all overdue accounts.

To calculate and demand (the tax money due) from a person or entity.

Once you've submitted a tax return, the Tax Department will assess the amount of tax you still owe.