homework and exercises - Inserting metal into parallel plate capacitor

The plates of an isolated parallel plate capacitor with a capacitance C carry a charge Q. The plate separation is d. Initially, the space between the plates contains only air. Then, an isolated metal sheet of thickness 0.5d is inserted between, but not touching, the plates. How does the potential difference between the plates change as a result of inserting the metal sheet?

The answer is: The potential difference will decrease. How do I get this result, it seems right but how do I reason it out?

$$V = Ed$$

There was mention about "E is the same outside the conductor. But the field inside is 0.". But in the formula, E is the field outside conductor right? If so it remains the same? Then $d = 0.5d$?