How can I cut a near perfect circle out of a plastic bottle? I am hoping to make a simple spinner treat dispenser for my Australian shepard. Basically it is plastic container with a rod/dowel suspending them in the air. Treats or food are put inside and the weight holds the bottle down. If the dog uses sufficient force the bottle will spin around and some treats will fall out. There are many different overall designs but it basically looks like this:



Image from goodshomedesign.com

I am likely overthinking this but would like to know either way. I need to cut out circles from these bottles. Cutting the circles with something like a box cutter seems likely but that is hardly a precise tool. Theoretically I will be applying pressure to force the blade where I need to cut. If the plastic gives I will be putting in hard edges instead of cutting curves. This bothers me since hard edges might prevent the bottle from resting properly in the device, spinning around or could cause it to start prematurely tear the plastic.

I realize it is just plastic bottles and they can be replaced but I think this is something still worth knowing. I suppose I could melt a perfect circle into the bottle but I am not so sure about that. I could score a circle into the bottle first but I still think that might be difficult with a 2L bottle. 

How can I cut a relatively perfect circle out of a plastic bottle like a 2L pop bottle?
Kind of off the wall, but here goes:

Fill the bottle with water and put it in the freezer until the water becomes solid ice. (best not put the cap on in order to allow for expansion of ice.

Using your drill press or hand held drill make your hole.