Low budget does not have to mean bad. Just in the way that high budget does not necessarily mean good.
Everything is based on an idea, an emotion, and finally, a superb screenplay. If you don’t have a killer script, you have nothing. Beginning filmmakers get a draft done and think they are finished. Or ten drafts. You are never finished until you reach the day when you have to give the script to the actors to memorize. That’s when you’re done.
When you’re working on a low budget script, you have all the time in the world and your time is free. You can use that time to improve the script. Once you give the script to someone and it gets covered, especially in Hollywood, you can’t change it and you can’t improve it and you can’t fix its reputation.
To specifically answer your question, yes you can make money with a low budget movie but you have to have a good script and then you have to be careful with everything. You also have to have a sales plan built in from the get-go. A lot of beginning filmmakers finish their movie, have a DVD, and then say, “Gosharootie, how do I sell this thing?” If you don’t think about it long, long, long before the end of the production process, you are lost.
The more you learn about the market. The more you learn about finance. The more you will understand about how to get a movie made.
If you don’t make money, you don’t stay in business.
Even with no money, if you’re fun and professional, you can get a good crew. You can get a good script. It does not take an enormous amount of money to rent gear. Someone may own the gear. You can pare down expenses to basically these two: sound and food. On a low budget movie, you still have to pay the location sound recordist and the caterer. The caterer is for your crew to be happy. The sound is so you won’t have crappy sound and have to spend a fortune in post fixing the mess you made. I tell this to students and they don’t listen.
Sound is the most difficult aspect of the low-budget film. Perhaps because it is invisible. I don’t know.
As Kelley Baker says, you need three things to make a good low-budget film. Good script. Good sound. Good actors. If you don’t have all three of those, there is no point in proceeding with the production.
If you do, you have a shot at making money.