Some mathematical magic

The magician will perform some mathematical magic.
He asks his guest to secretly pick any two digit number and then perform a number of operations on it.

1. If the number is even, divide by 2, if it is odd subtract 3 and then divide by 2.
2. Multiply by 3.
3. Add 5.
4. If the number has 3 digits, subtract 102.
5. Multiply by 6.
6. Subtract 21.
7. Compute the sum of the digits and continue with this sum. For example if you have 41, continue computing with 5=4+1. *
8. If the number has only a single digit, multiply by 2.
9. Subtract 5.

At this point, the magician reveals the number the guest arrived at after step 9.

How does this trick work?

Edit: * As noted in the comments, it can happen that you have a negative number at this point. In this case just ignore the minus sign in front. So for example the sum of digits of -16 would be 7.