Can someone explain the Modigliani-Miller propositions on capital structure?

The Modigliani-Miller (M&M) propositions are the starting point for understanding how a firm's choice between debt and equity financing affects its value. Let me build up from the simplest case.

M&M Proposition I — Firm Value:

Without taxes (perfect markets):

The total value of a firm is unaffected by its capital structure. Whether Northwind Corp finances with 100% equity or 50/50 debt-equity, the firm is worth the same. The logic: investors can create any leverage on their own ("homemade leverage"), so they won't pay extra for a firm to do it.

With taxes:

Debt creates a tax shield (interest is tax-deductible), so the levered firm is worth more:

V_Levered = V_Unlevered + (T × D)

If Northwind is worth $100M unlevered, has a 30% tax rate, and takes on $40M of debt:

V_Levered = $100M + (0.30 × $40M) = $112M

M&M Proposition II — Cost of Equity:

Without taxes:

As a firm adds debt, the cost of equity increases linearly. Equity holders demand higher returns because leverage makes their cash flows riskier. But WACC stays constant — the cheaper debt is exactly offset by more expensive equity.

With taxes:

Cost of equity still rises with leverage, but WACC decreases because the tax shield makes debt even cheaper. This implies 100% debt is optimal — which seems absurd.

The trade-off theory resolves this:

In reality, beyond some point:

• Financial distress costs increase (lawyers, lost customers, bankruptcy)
• Agency costs of debt increase (restrictive covenants, asset substitution)

The optimal capital structure balances the tax benefits of debt against distress/agency costs.

Exam tip: Know the assumptions underlying each proposition — perfect markets, no taxes, no distress costs. The exam often asks you to identify which assumption, if relaxed, leads to a different conclusion.

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