Question

Be sure to write clear steps for your derivations

Explain MM Proposition I and II for capital structure. Provide some examples of the costs and benefits associated with debt and equity under market imperfections, and explain the concept of optimal capital structure.

Answer 1

The main idea of the M&M theory is that the capital structure of a company does not affect its overall value.

The first version of the M&M theory was full of limitations as it was developed under the assumption of perfectly efficient markets, in which the companies do not pay taxes, while there are no bankruptcy costs or asymmetric information.

The M&M Theorem in Perfectly Efficient Markets

This is the first version of the M&M Theorem with the assumption of perfectly efficient markets. The assumption implies that companies operating in the world of perfectly efficient markets do not pay any taxes, the trading of securities is executed without any transaction costs, bankruptcy is possible but there are no bankruptcy costs, and information is perfectly symmetrical.

Proposition 1 (M&M I):

Where:

• V_U = Value of the unlevered firm (financing only through equity)
• V_L = Value of the levered firm (financing through a mix of debt and equity)

The first proposition essentially claims that the company’s capital structure does not impact its value. Since the value of a company is calculated as the present value of future cash flows, the capital structure cannot affect it. Also, in perfectly efficient markets, companies do not pay any taxes. Therefore, the company with a 100% leveraged capital structure does not obtain any benefits from tax-deductible interest payments.

Proposition 2 (M&M I):

Where:

• r_E = Cost of levered equity
• r_a = Cost of unlevered equity
• r_D = Cost of debt
• D/E = Debt-to-equity ratio

The second proposition of the M&M Theorem states that the company’s cost of equity is directly proportional to the company’s leverage level. An increase in leverage level induces higher default probability to a company. Therefore, investors tend to demand a higher cost of equity (return) to be compensated for the additional risk.

DURING MARKET IMPERFECTION THE VALUE of the firm is highest when it uses 100% debt t, the differential tax treatment encourages firms to use debt financing because debt provides a tax shield that add to the value of the company

Where:

• t_c  = Tax rate
• D = Debt

The optimal caital structure maximizes firms value and minimises the weighted average cost of capital