How to shoot studio white back drop to a darker grey?

I have a white back drop for a model shoot, however the backdrop comes out too white, ideally I want it a grey tone, like 40 - 50% of black. All photos will be converted to black and white usuages.

I'm using Nikon D90, 60mm Macro lens, SB800 speed light and a reflector.

Your professional advice is greatly appreciated!

Under expose the backdrop.

Here is an example done in studio. That backdrop is a pure white seamless paper backdrop.

In this shot, it's a plain beige wall.

You just need your backdrop under exposed by around one stop while properly exposing your subject.

Position your model several meters in front of the backdrop, and do not have any lights pointing towards it.

This is the best tutorial I have seen for how to use a white background and turn it into any color background you want. Make sure you read part II as well:

https://zackarias.com/for-photographers/photo-resources/white-seamless-tutorial-part-1-gear-space/