M&M propositions in perfect versus real markets
| M&M Proposition | Perfect World | Real World |
|---|---|---|
| I: Value | Unaffected by capital structure | Debt creates a tax shield that increases value |
| II: Cost of equity | Rises linearly with leverage | Rises with leverage but tax shield partially offsets |
| Optimal structure | Doesn’t exist (irrelevance) | Exists where tax benefit = marginal distress cost |
The levered-firm value equation
Value of Levered Firm = Value Unlevered + PV(Tax Shield) − PV(Distress Costs)
Why the tax shield lowers WACC to a point
The tax shield is the reason debt lowers WACC up to a point. Beyond that point, rising distress costs and higher cost of equity from increased risk offset the tax benefit.
Test M&M Proposition II across two peers
Does capital structure matter under Proposition I
Capital structure as a tradeoff, not a free lunch
Firm value under leverage with no taxes
Three frictions that break Modigliani-Miller
Going deeper (optional). Up next: the three frictions that break Modigliani-Miller in practice — an advanced aside you can skip on first pass and come back to anytime. Continue when you're curious.
Going Deeper — the three frictions that break Modigliani-Miller in practice. M&M Proposition I says capital structure is irrelevant in a world with no taxes, no bankruptcy costs, and no agency costs. The real world has all three. (1) Taxes: interest is deductible, creating a tax shield that scales with leverage and pulls the optimal structure toward more debt. (2) Bankruptcy and distress costs: at high leverage, the probability of distress and the deadweight cost of distress (lost customers, lost suppliers, fire-sale asset values) creates an offsetting drag. (3) Agency costs: high leverage can constrain value-destroying empire-building, but can also force underinvestment in maintenance and R&D. The trade-off theory says the optimum is where the marginal tax shield equals the marginal expected distress cost. AI prompt: "For this ticker, estimate the trade-off-theory optimal leverage given its tax rate, asset volatility, and industry distress costs. Compare to current debt-to-equity. Is management under-levered, over-levered, or about right?"
Sit with the ideas.
Company X (all-equity, cost of equity 10%) is considering levering up to 30% debt at a 5% pre-tax cost of debt (tax rate 25%). Assuming the cost of equity rises to 11.5% due to the added financial risk, what happens to WACC?