In the context of the table you provided, the initial value refers to the fine owed when no days are overdue, or when it is overdue for 0 days. Since the fine only starts at 30 cents for 2 days overdue, it can be inferred that the fine is 0 cents for 0 days overdue.
So, the initial value (fine for 0 days overdue) would be 0 cents.