Determining value of a deer mount?

Two good answers here already.

Mounting a deer head these days costs about $500, and the hunter has to provide the head with antlers. As another has commented, most folks simply don't want to have someone else's deer mount in their homes. The idea is to show a trophy animal that they themselves have shot - so there is usually a story to be told when discussing the mount.

One more thing to take into consideration is that taxidermy is an art that has evolved over the many decades that it has been practiced. Back in the 1950s and earlier, most deer head mounts were "looking straight". From at leat the 1970s onward, most mounts are "shoulder mounts" that have more of the front of the beast showing, and usually have the animal looking to one side. (It's a more natural pose.)

We really need a photograph to discuss value.

Maybe post a picture of it?

"Points" are the individual 'spikes' of the antler. There can be the same amount on both sides, or there can be an uneven number. The more there are, the more it might be worth.

Is the mount just the antlers? The head? Shoulders forward? The entire deer? That will probably affect the value.

I hate to break it to you, but there aren't a lot of people willing to pay for a deer mount that they didn't shoot. If a business near you hangs goofy stuff on the walls from the local area, you might try offering/selling it to them. Since it was given to you, anything you make off it is pure profit. Unless it's really something special, you should probably try to get it off your hands for whatever someone offers.

There is really not too much demand for someone else's deer mount.

Places like Bass Pro Shop, Cabelas, and some restaurants may buy one for a decoration. $50 may be good.