ABC Ltd$.$ has been generating substantial cash flow from its operations. The company's stock has been trading at a price below its intrinsic value, and its management believes that repurchasing shares will benefit the company and its shareholders. The firm has announced a share buyback plan to purchase up to $10\%$ of its outstanding shares over the next year.

After the buyback, how will the earnings per share $($EPS$)$ likely be affected if the company's overall earnings remain constant?

EPS will remain unchanged, as the number of shares has not changed.

EPS will increase, as fewer shares are outstanding.

EPS will increase, but only if the stock price rises.

EPS will decrease, as fewer shares are outstanding.