Question

1. Modigliani and Miller (MM) have two propositions that they present under three different sets of assumptions, or cases. The first proposition discusses firm value, and the second proposition estimates the WACC.

a) In case 1, MM conclude that how you finance a firm “just doesn’t matter”. What are the key assumptions in this model and how does each influence MMs conclusion? Draw and label a graph and explain what happens to the cost of debt, the cost of equity, and the WACC in case 1. (i.e., in addition to drawing the graph, you must also explain why lines are increasing/decreasing/flat and so on.)

b) In case 2, MM conclude you should finance the firm 100% with debt. What is the key assumption change that they make? Repeat the graph from part a) with your new depictions and explanations of the cost of debt, the cost of equity, and the WACC.

Answer 1

The Modigliani-Miller theorem states that a company's capital structure is not a factor in its value. Market value is determined by the present value of future earnings, the theorem states.

ASSUMPTIONS OF MODIGLIANI AND MILLER APPROACH

• There are no taxes.
• Transaction cost for buying and selling securities, as well as the bankruptcy cost, is nil.
• There is a symmetry of information. This means that an investor will have access to the same information that a corporation would and investors will thus behave rationally.
• The cost of borrowing is the same for investors and companies.
• There is no floatation cost, such as an underwriting commission, payment to merchant bankers, advertisement expenses, etc.
• There is no corporate dividend tax.

Proposition 1:

Where:

• VU = Value of the unlevered firm (financing only through equity)
• VL = 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:

Where:

• rE = Cost of levered equity
• ra = Cost of unlevered equity
• rD = 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.