There is no rule in English that you can apply mechanically to determine which of several competing noun phrases is the antecedent of a pronoun. A bald assertion that "it correctly refers to xxx" is probably wrong.
However, there may be a pragmatic reason to identify one or other possible antecedent. Your use of the possessive "predecessor's" matches "project's", and suggests that the predecessor is the same kind of thing as the project, and therefore that "its" refers to the project; but this conclusion is pragmatic not formal, and probably also depends on the particular words (eg knowing that the predecessor of something is likely to be the same kind of entity as the something).
Having said which, I concur with cornbread ninja that there are clearer ways of wording it.