Nobody to my knowledge has every measures the costs of cash, it is just something they accept. With credit cards it is easy to measure because you get a number, but with cash it is not, you have to calculate too many different parameters and figure out what applies where.
I'm pretty sure every single German supermarket chain measures that, it's just a requirement to operate at those margins. The Edeka cooperative published in 2012 that their all-in cash handling cost is 0.14%. The 2013 Steinbeis Cost of Cash study[0] estimated a much higher number of 2.7% for merchants. The truth is probably somewhere in between.
Such studies have also been used to arrive at the EU interchange cap.
