Proof 3:

If we assume that individuals have equal access to capital markets then we can prove M&M's irrelevance proposition using an arbitrage argument.

Suppose:

• There is an optimal capital structure that maximizes firm value,
• but the firm does not choose this capital structure.

Then:

• Any investor could provide the optimal capital structure to the capital markets by first buying proportional amounts of the firm's securities and then issuing the optimal proportions on personal account.
• If the market value of the firm is less than that implied by the optimal capital structure, then investors can make riskless (i.e., arbitrage) profits from doing this.
• Every investor would seek to exploit such an opportunity. Not consistent with a market equilibrium.
• In equilibrium, the market value of the firm (even though it has a sub-optimal capital structure) must equal the value implied by the optimal capital structure.
• Thus, it doesn't matter what capital structure a firm chooses because the choice does not affect firm value.