There is a cost in time and dedication from both the student and the teacher. There is a cost in materials, for either the student, the teacher, or both. As was pointed out earlier, there is a cost in intangibles for both the teacher and the student.Ive taught guitar for years and never charged a cent. Running my business is my day job, away from work if Im passionate about something and good enough to teach it, then Im happy to share the passion and dont expect anything in return.
You may go to your student's home or they may come to you, thus eliminating the cost of renting space, and since you do not depend on your income from guitar instruction for sustenance, you are able to absorb whatever monetary costs are involved.
The fact that you may be the one covering the costs and without passing that onto your students does not make it free; it simply means that someone else (you in this case) is footing the bill.
You are happy to share the passion, and that is your return, your dividend. The best things in life cannot be attained simply by paying for them, so I am sure that you reap many times in that dividend the expense you put forth.