Question

Explain, in your own words, how MM uses the arbitrage process to prove the validity of Proposition I. Also, list the major MM assumptions and explain why each of these assumptions is necessary in the arbitrage proof.

 

Answer 1

Modigliani and Miller show that the value of a leveraged firm must be equal to the value of an unleveraged firm. If this is not the case, investors in the leveraged firm will sell their shares (assume they owned 10%). They will then borrow an amount equal to 10% of the debt of the leveraged firm. Using these proceeds, they will purchase 10% of the stock of the unlevered firm (which provides the same return as the leveraged firm) with a surplus left to be invested elsewhere. This arbitrage process will drive the price of the stock of the leveraged firm down and drive up the price of the stock of the unlevered firm. This will continue until the value of both stocks are equal.

 

The assumptions of the MM model are:

·   Firms must be in a homogeneous business risk class. If the firms have varying degrees of risk, the market will value the firms at different rates. The earnings of the firms will be capitalized at different costs of capital.

·   Investors have homogeneous expectations about expected future EBIT. If investors have different expectations about future EBIT then individual investors will assign different values to the firms. Therefore, the arbitrage process will not be effective.

·   Stocks and bonds are traded in perfect capital markets. Therefore, (a) there are no brokerage costs and (b) individuals can borrow at the same rate as corporations. Brokerage fees and varying interest rates will, in effect, lower the surplus available for alternative investment.

·   Investors are rational. If by chance, investors were irrational, then they would not go through the entire arbitrage process in order to achieve a higher return. They would be satisfied with the return provided by the leveraged firm.

 

·   There are no corporate taxes. With the existence of corporate taxes the value of the leveraged firm (VL) must be equal to the value of the unlevered firm (VU) plus the tax shield provided by debt (TD).