Helllo,
I have the must finish by date on the project set to Oct 12 2015. But why would the late finish date be earlier than the ealry finish date? I understand the negative float is due to the project being behind. See snapshot below. 
Why Must Finish By Constraint causes Late Finish to complete earlier than Early Finish?
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Victor
Welcome to PP.
From your screenshot I assume that you use P6. Check the time for your "Must Finish By" - User Preferences --> show time.
It seems that it is earlier than the working time set by your standard calendar. So the assumed final activity is set to Oct 9, the Friday before. In my opinion it is easier to have a milestone "Contractual Finish" with a mandatory constrint, which is more visible than the Must Finish By.
Good luck!
Dieter
Hi Victor,
The arithmetic involved in CPM calculations is not difficult but does need understanding – to see what your software id doing download this paper: http://www.mosaicprojects.com.au/PDF/Schedule_Calculations.pdf
Becuase that's how they work.
Must finish by date on the project means the backward pass calc starts from the must finish by constraint date instead of the project early finish date, as normal.
You wouldn't get negative float if the late date wasn't earlier than the early date -that's what negative float means.