Tool Kit for Capital Structure Decisions:
Modigliani and Miller without Taxes
The weighted average cost of capital is independent of the firm's capital structure.
The WACC of a firm with debt is equal to the unlevered cost of equity.
Example of an arbitrage opportunity in zero-growth firms:
Value of Firm
Value of Firm = Value of Stock + Value of Debt
Portfolio of U,
equal to 10%
in risk free
Debt, and risk
10% of U
of L's Debt
10% of L
CAPITAL STRUCTURE THEORY: ARBITRAGE PROOFS OF THE MODIGLIANI-MILLER MODELS
Franco Modigliani and Merton Miller developed a model to examine the impact of debt on firm value.
first version it is assumed that taxes are zero.
The cost of equity, r
+ Risk premium = r
Suppose that r
We will show that this leads to an arbitrage opportunity.
Value of Stock = (EBIT - r
Compare an investment in L with a "synthetic" investment that duplicates L's leverage using an investment in
U and borrowing on the investor's own account.
Notice that for the same $600,000 investment, you can get $7,500
more in annual income by forming your own portfolio of U and
"home made debt" than you get from an investment in L.
argue that this won't persist--that investors would buy U and
purchase the portfolio, driving up the price of U.
At the same time,
they would sell their shares of L, driving down its price.