Example 2 Chapter 9 OT Notes – Discounted Cash Flow – Machine Replacement Period

Hi, I have a question regarding Example 2 in Chapter 9 of Open Tuition notes.

It regards the problem how often machine should be replaced.
I understand the technique but I don’t understand why, at the end, we don’t divide just by the number of years? Why are we dividing by numbers from Annuity Table?

Your help will be much appreciated.