Hello TechExams

I'm curious about the way STP costs work. I'm reading the book again (prior to posting here), but I just want to make sure of something. In the topology below, S1 is the root bridge. I thought it sends its cost as 0 by default to all connected switches.
That being said, according to the text, S2 changed its cost on the FA0/1 port to 1. So when it forwards its Hello BPDU to S3, shouldn't the cost be 1 + 19 = 20 (which is default cost for 100 Mbps connected between S3 and S2), or do I have this wrong?