Modigliani and Miller (MM) proved, under a very restrictive set of assumptions, that how a firm finances its operations has no effect on the value of the entire firm.

Assumptions:

• Homogenous expectations: Investors agree on a given investment's expected cash flows.
• Perfect capital markets: There are no brokerage costs, no taxes and no bankruptcy costs;
• Risk-free rate: Investors can borrow and lend at the same rate as corporations;
• No agency costs: Managers always act to maximize shareholder wealth.
• Independent decisions: Financing and investment decisions are independent of each other.

MM Propositions without Taxes

There are two almost equivalent ways of looking at the same problem:

• Is the value of a levered firm (V_L = D + E) different from the value of an unlevered firm (V_U)? (MM1)
• Is the WACC of a levered firm different from the WACC of an unlevered firm? (MM2)

The M&M results are based on absence of arbitrage. Assume there are two firms identical in investments but different capital structure. If they are all equity financed, they should have identical required rate of returns. But, if one firm is levered (V_L) and the other is unlevered (V_U), V_U has to be equal to V_L otherwise an arbitrage profit could be made!

MM Proposition 1: A firm's value is determined by its assets, not its capital structure. This implies that there is no optimal capital structure!

WACC equals the required rate of return of the firm's assets (ROA), which is determined by the firm's investment decisions, not capital structure.

MM Proposition 2: WACC is invariant to capital structure under the previous assumptions.

The cost of equity of a levered firm is equal to the cost of equity of an unlevered firm plus a risk premium which depends on the degree of financial leverage: r_e = r₀ + (r₀ - r_d)(D/E), where r₀ is the cost of all-equity firm.

Reductions in capital costs as a result of using more lower cost debt (r_d) are exactly offset by increases in the cost of levered equity (r_e) due to added financial risk.

The equity's beta, β_e, rises as more debt is used: β_e = β_a + (β_a - β_d)(D/E)

The important thing here is not the formulas presented in the textbook, but the intuition of the model. Capital structure irrelevance theory is all about slicing a pie: the size of the pie represents the value of a firm. It is determined by the size of the pie pan, not how it is sliced. With a given pie pan, the size of the pie will be always the same no matter how you slice it. Similarly, the value of a firm depends on the firm's assets, not its capital structure. With a given asset base, the value of the firm remains the same no matter how the firm finances its investments. Capital structure only affects the distribution of the firm's value among debt holders and equity holders.

MM Propositions with Taxes

The value of a firm is still determined by the firm's assets, which generate cash flows. By levying taxes, the government joins debt-holders and shareholders to share the cash flows (and thus, the value) of the firm.

MM Proposition 1 with Taxes:

• The value of an unlevered firm is equal to EBIT (1-T) capitalized at the cost of equity. V_U = EBIT (1 - T)/r_e.
• The value of a levered firm is equal to the value of an unlevered firm of the same risk class, plus the value of the interest tax savings capitalized at the cost of debt: V_L = V_U + T x D.

The deductibility of interest expense favours the use of debt financing for companies. Since this tax shelter accrues to shareholders, using debt will increase the value of the entire equity. The more the firm borrows, the greater the tax shelter, and thus the higher the share value of the stock. Therefore, if other MM assumptions hold, firms will maximize debt in their capital structures: the optimal capital structure in a tax world will be infinitely close to 100% debt!

MM Proposition 2 with Taxes:

The cost of equity of a levered firm is equal to the cost of equity of an unlevered firm plus a risk premium which depends on both the degree of leverage and the corporate tax rate: r_e = r₀ + (r₀ - r_d) (1-T) (D/E)

As debt-equity ratio (thus the financial risk) rises, so does the cost of equity. However, the weight of equity declines as the firm uses more debt. The reduction in the cost of debt can more than offset the effect of rising cost of equity. Therefore the cost of capital (WACC) declines as the firm uses more debt.

The existence of (higher) personal tax rate on interest income than on dividend income, however, reduces the advantage of debt financing to a company. In the Miller model, debt financing may add or lower value.

Costs of Financial Distress

More leverage can magnify financial losses, which can put a company into financial distress.

• Direct costs are the various costs of filing for bankruptcy, hiring lawyers and accountant, etc.
• Indirect costs include higher borrowing costs (Lenders charge higher interest rates to firms in financial trouble.), a loss of employee morale and productivity, agency costs of debt, etc.

The threat of bankruptcy and the bankruptcy costs discourage firms from pushing their use of debt to excessive levels. Firms whose earnings are more volatile, all else equal, face a greater chance of bankruptcy and should use less debt than more stable firms.