Question

Discuss Modigliani and Miller's Propositions I and II in a perfect world without taxes nor distress costs. List the basic assumptions, results, and intuition of the model. Based on this model, if the original unlevered firm value is $100 million and the CFO is planning to carry out a leveraged recapitalization to a debt equity ratio of 1:1. What’s the levered firm value? If the unlevered equity requires 10% annual return and the debt requires a 6% of annual return, what’s the required return for the levered equity?

Answer 1

Corporate Finance, Sections 001 and 002

The Modigliani and Miller propositions say the following: Suppose that there are no

taxes or costs of financial distress. Then

I The value of the firm is independent of the percentage of debt or equity in its capital structure.

II The cost of equity capital is increasing in the percentage of debt in the capital structure. In fact,

RE = Ro + D/E(Ro – RD)

where r0 is the cost of capital if the firm were financed entirely with equity.

The first statement says that the choice of capital structure is irrelevant for maximizing the value of the firm. The value of the firm is determined by the left hand side of the balance sheet (the assets) rather than the right hand side (the capital structure). The second statement says that the greater the percentage of debt in the capital structure, the greater the rate of return required by equity holders. Both of these statements will need to be modified when we introduce taxes and bankruptcy costs (costs of financial distress).

In other words it can be simplified as follows

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):

VL = VU

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 (M&M I):

RE = Ro + D/E(Ro – RD)

where r0 is the cost of capital if the firm were financed entirely with equity

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.

Vlevered = Vunlevered + Tax * Debt

		$ mil
Value of Unlevered firm =	100
New D/E ratio = 1:1
VL = VU
Hence New value = 100 $ mil
RE = Ro + D/E(Ro – RD)
Ro =	10%
D/E = 1:1
RD	6%
RE = Ro + D/E(Ro – RD)
RE =	14%