I think that the new company_____ very well

a_ does

b) will do

Each answer seems reasonable to me. If we choose a, we mean that the new company has just opened they does very well. If we choose the others, we mean that we reckon the new company which never opened before can do very well in future, don't we?

So how about this sentence:

Alan has been invited to work for a new company to produce for business. Everyone thinks that it ____ very well.

a) does

b) will do

I don't know what it here refers to, so I'm lost and confused whether to make the perfect choice.
1-- Does does not work there. Present simple is for timeless habit, but this is a new company. We could say that IBM does very well.

2-- 'Produce for business'
is not native English, so I wonder if there are other problems in your example. 'It', I suppose, refers to the new company, so I choose 'will do' again.
Sorry, it must be" produce software"