In my understanding, the usage of Future Simple Tense and Future Perfect Tense are almost the same. However, if you would like to convey a special meaning about the precedence of one action against the other you can differentiate it with the use of Future Perfect Tense:
S.1. When my mother comes back home from her office, I will have left for the cinema. This sentence implies that when my mother comes back home, I will not be there at home. It is looking into the past from a point of time in the future and saying what that time would be like (the house without me).
S.2. When my mother comes back home from her office, I will leave for the cinema. This sentence indicates that when my mother comes back home, I will be at home. I will leave after my mother comes back or as soon as my mother comes back home. It is looking into the future conveying that I will be able to see my mother at least for a fraction of a moment before I leave for the cinema.
S.3. I will have done my homework before school.
S.4. I will have done my homework after school.
Here S.4. cannot be accepted as correct English. It will be more meaningful to say "I will do my homework after school. It is because the perfect tense needs an endpoint of time to show the completion of the action like the adverb of time 'before' in S.3. Whereas, in S.4. the adverb of time is 'after' which implies a starting point of a time with no clue to endpoint.
Compare the following two sentences:
S.5. When he reached the cinema, the show had started.
S.6. When he reached the cinema, the show started.
Here in S.6. the show started after/as soon as he reached the cinema. Whereas, in S.5. the show started before he reached the cinema.
Now you can understand that if you want to specifically state the precedence or the completion of the action before a point of time of an action you can use the Perfect Tense; if not, use the Simple Tense. We can also note that in S.5. the show had run at least for a fraction of a second before you reached; and S.6. implies that there is a wait time of at least a fraction of a second for the show to begin.
S.3. I will have done my homework before school.
S.7. I will do my homework before school.
I do not see much difference in the meaning of S.3. and S.7. Both the sentences mean that the homework will be done before school. This is the general sense people make when they use either sentence. Probably, this is why the Simple Future is more commonly used in place of Future Perfect even by the native speakers.
S.8. If you drive at this speed, the show will have started by the time you reach the theatre.
S.9. If you drive at this speed, the show will start by the time you reach the theatre.
Here we can see clearly that S. 8. can be written as S.9. and 9 as 8 without any change in the meaning.
Although we feel the necessity of differentiating Future Perfect from Future Simple in S.1. and S.2., the meaning can be clearly expressed with Future Simple Tense. S.1. When my mother comes back home from her office, I will have left for the cinema. This can be written as "Before my mother comes back home from her office, I will leave for the cinema". S.2. When my mother comes back home from her office, I will leave for the cinema. This can be written as "After/As soon as my mother comes back home from her office, I will leave for the cinema".
