So, let's see if I understand you right.
You started working in a small/medium sized company last July, and after about six months you developed a (hefty) bonus plan without clearly establishing the value performance basis upon which the bonus was to be awarded. Now you need to be ready with the math to show just how and why you've delivered necessary to collect reward...only thing is, the reward wasn't agreed upon by top management.
Now I don't want to be unkind, but you've dug yourself a hole haven't you?
It's high time to do some serious homework. This will not be quick, and you will need some cost figures from your controller or accountant.
But, it's still possible to show your department's value with a coherent project plan that talks the money with articles and (two) calculators available through this thread:
Now I have a hard question for you. What makes you believe you're the rightful owner of all that bonus money? What have you done to structure your department's bonus plan after your predecessor left? Did you only make your plan, as though your singular efforts yanked this company from peril?
Anyone who's effort joined toward a successful venture in improvement should be recognized. If you take a (hefty) bonus and others receive little or nothing while they run like hamsters in an exersize wheel, soon enough you'll have a larger problem than math.
I'm happy to supply calculators and such for showing the value of our work. However, IMO you have a long ways to go in your journey.