It depends the fan....which is what? What is the bottom of coffer to the FLOOR? It was 10" and coffer added? Or it is 120 inches to floor after the coffer: )

And you need to show fan and specs for the desired fan

As Jan said it depends on a number of factors.

I would want the fan 12 inches below the bottom of the coffer.

If the fan is too close to the coffer the air currents will be buffeted around inside the coffer and create soil patterns.