The response from mrerick is a good one; we have debated in my classes whether or not there actually was a will, since there is no proof that the document Antony displays to the plebeians is that which he claims. According to the historian Plutarch, there really was a will, and it contained the bequests described in Shakespeare's play. But probably the most important thing is what Antony's plan to supress it says about his character.

Act 4.1, lines 8-9:
..., and we shall determine
How to cut off some charge in legacies.

Antony is going to manipulate Caesar's will in order to reduce the amount of money given to the common people. It is unclear what Anthony is planning on doing with this money, although we can make an educated guess that he will use it to fund his armies for the upcoming battle. There is some debate as to whether or not the will actually existed - Anthony could have been faking it during Act III, but once he read the terms of the will to the people (fake or not), he needed to reduce that amount for his own purposes.

It's probably also important to note that getting Caesar's will was only a secondary motive for sending Lepidus away. Antony's main concern was discussing Lepidus's worthiness with Octavius.