If that is indeed the cost you are paying, then the local Pepsi bottler is giving your organization a very special deal (which makes perfect sense, since it's a non-profit and they're trying to engender brand loyalty).
My wife and I own several restaurants, both franchise and independent, and the actual cost generally ranges from $0.012 per ounce to $0.008 per ounce, and the cups are definitely not free (and generally run between $0.04 and $0.12 each, plus lids at $0.02-$0.04 each and straws, which cost about $0.015 each), plus the CO2, which is difficult to price per ounce but has a cost. So while soda does indeed have a significant markup, it's not "free" by any stretch. For example, a large soda at McDonald's (which I assume is 32 ounces) probably costs the franchisee about $0.25-$0.35, plus the royalties they pay to corporate, which I think are around 5-7% (we don't own a McDonald's, but we do own a few of a large franchise brand so I'm basing my speculation off the deals that are in place with those brands and their soda vendors of choice).
The dollar menu is a means of drawing guests in and trying to upsell them, as well as an example of a high volume, low margin sales strategy that is definitely working for them!