The item they're selling for $13 could be a low/zero margin product usually used to bait further purchases or tips. Another issue they noted was people not tipping as if they had paid $13, but tipping as if they had paid $3.
That would explain it - however, what items fit that profile in a coffee shop? Certainly I can't think of anything from my local.
The tipping is a legitimate issue, however, I bet there are people that spent less than the full value of the coupon, tipping the scales back in the other direction, so I believe my back of the napkin analysis stands.
Coffee shops are interesting because the food / pastries are low-margin while the coffee is high-margin. And people are much more likely to just buy coffee than to just buy a pastry. So as your average check increases, your margins go down.
The tipping is a legitimate issue, however, I bet there are people that spent less than the full value of the coupon, tipping the scales back in the other direction, so I believe my back of the napkin analysis stands.