Implications of Modigliani-Miller Propositions on Capital Structure

In the context of Modigliani-Miller Propositions concerning capital structure, consider the following statements regarding the impact of leverage on a firm's value:

Statement 1: In a world with no taxes, the value of a leveraged firm is equal to the value of an unleveraged firm.

Statement 2: When corporate taxes are considered, leveraging a firm increases its overall value due to the tax shield provided by debt financing.

Statement 3: The presence of bankruptcy costs and agency costs negates the benefits gained from a tax shield in a leveraged firm.

Based on Modigliani-Miller Theorem, which of the following statements is CORRECT?