The film industry is a prime example of how one can screw themselves. No movie in history every showed a profit; making percentage of profits a null figure.
If you're going to base your bonus on total income it should be based on the gross. X% of total revenue. In effect, this gives you an equity position in the business, and, should the owner ask why that route makes sense, promotes you working harder because the better job you do, the more everybody makes. In the written agreement, be sure and specify the frequency the bonus is paid. Personally, I'd shoot for quarterly payments rather than annual.
That's one approach.
Another, as others have suggested, is a percentage of targeted goals. Defining those goals and targets can often be a chore, however, especially in a start-up situation. For instance, I know of places which pay the chef a bonus based on increased sales. Obviously, that won't work for you.
However, I have a deeper concern. Why did the head chef suddenly depart? We're it me, I'd track him down, buy him a drink, and get the straight skinny. There may be a valid reason. Or it may be that he distrusts the owner, for one reason or another. Maybe it was a question of money (and, if possible, I'd find out what his salary was). Whatever he says, work it into your equation. Maybe I'm just cynical, but it wouldn't surprise me to learn that the chef was promised the moon plus two dollars, and none of it came to pass. That's a very common scenerio with start ups.
My feeling is that the owner is taking advantage of you. What he's doing, I suspect, is having you do all the start-up work at very little cost (the fact is, many fast-food joints pay that much and more). Then, once everything is in-place, there will suddenly be a new head chef running the kitchen, and you'll be left sucking hind teat.
Come what may, as others have suggested, get everything in writing!!!