Updated for the 2026-2027 CFA® Level I curriculum.
The Modigliani-Miller (MM) propositions describe how a firm's mix of debt and equity affects its value and its cost of capital. Franco Modigliani and Merton Miller built their theory on a set of simplifying assumptions, then showed what happens to firm value and cost of equity once those assumptions hold or get relaxed.
For CFA Level I, you need to state the assumptions, explain what each proposition concludes, and recognize how adding corporate taxes changes the result. This note covers that ground directly, without drifting into WACC calculations or optimal capital structure decisions, which have their own study notes.
Quick Answer
The MM theory of capital structure says that under strict assumptions (no taxes, no bankruptcy costs, perfect information), a firm's value is independent of its financing mix. This is MM Proposition I.
Proposition II states that cost of equity rises with leverage because equity holders bear more financial risk. When corporate taxes are added, debt creates a tax shield, so firm value increases with leverage instead of staying constant.
Key Takeaways
MM Proposition I (no taxes) states that capital structure does not affect firm value: value of the levered firm equals value of the unlevered firm.
MM Proposition II (no taxes) states that cost of equity increases linearly with the debt-to-equity ratio, because higher leverage means higher financial risk for shareholders.
Every MM conclusion depends on strict assumptions: no taxes, no bankruptcy costs, no transaction costs, and symmetric information.
With corporate taxes added, MM Proposition I changes: firm value increases with leverage because interest payments are tax deductible.
The tax shield value equals the tax rate multiplied by the amount of debt.
MM theory is a benchmark for reasoning, not a description of real capital markets. Real firms face costs the model ignores.
A common trap is applying the no-tax formula to a tax-case question, or the reverse.
What You Need to Know for CFA Level I
Be able to state the MM assumptions before applying either proposition.
Know the conclusion of MM Proposition I under no taxes: capital structure is irrelevant to firm value.
Know the conclusion of MM Proposition II under no taxes: cost of equity rises with leverage.
Be able to apply the MM Proposition II formula to calculate cost of equity at a given debt-to-equity ratio.
Understand how adding corporate taxes changes both propositions, including the interest tax shield.
Recognize that MM propositions serve as a theoretical starting point for later capital structure topics, not a final real-world answer.
What Is the Modigliani-Miller Theory of Capital Structure?
Before MM, many analysts believed a firm could freely raise its value by adjusting the debt-to-equity mix. Modigliani and Miller challenged that view in 1958. They asked what would happen to firm value if markets worked perfectly, with no taxes, no bankruptcy costs, no transaction costs, and equal access to information for all investors.
The assumptions matter because they define the boundary of the conclusion. Under those exact conditions, MM proved that financing decisions do not create or destroy value. Value comes only from the firm's assets and operations, not from how those assets are financed. This is the foundation case, often called the MM theory of capital structure without taxes.
The CFA Level I curriculum asks you to work through this baseline case first, then see how relaxing the no-tax assumption changes the outcome.
Modigliani-Miller Proposition I
MM Proposition I, under the no-tax assumption, states that the value of a levered firm equals the value of an identical unlevered firm.
Where:
= value of the levered firm
= value of the unlevered firm
The logic rests on arbitrage. If a levered firm traded at a higher value than an identical unlevered firm, investors could borrow on their own account, buy shares in the unlevered firm, and replicate the levered firm's payoff at a lower cost. This buying and selling would push prices back until both firms had equal value. In a frictionless market, financing choices cannot create value that does not already exist in the firm's operations.
This is the core of the modigliani and miller proposition 1 result: capital structure is a slicing of the same pie, not a way to make the pie bigger.
Modigliani-Miller Proposition II
MM Proposition II explains what happens to the cost of equity as a firm adds debt, still under the no-tax assumption. As leverage rises, equity holders take on more financial risk, since debt holders get paid first. Shareholders demand a higher return to compensate for that risk.
Where:
= required return on equity
= cost of capital for an all-equity firm
= cost of debt
= debt-to-equity ratio
The relationship is linear. As the debt-to-equity ratio increases, the required return on equity increases proportionally. This is why MM Proposition I still holds even though the cost of equity is rising: the increase in cost of equity offsets the effect of adding cheaper debt, so the firm's overall weighted average cost of capital and total value stay unchanged.
How Taxes Change the Modigliani-Miller Result
The no-tax case is a clean starting point, but real firms pay corporate taxes, and interest expense is tax deductible. MM's later work incorporated this.
Under the with-tax case, MM Proposition I becomes:
Where:
= corporate tax rate
= amount of debt
The term is the value of the interest tax shield. Because interest payments reduce taxable income, debt financing now creates real value. Firm value increases as leverage increases, up to the assumptions of the model.
MM Proposition II under taxes adjusts to:
The term reduces the rate at which the cost of equity rises because part of the effect of added debt is offset by the corporate tax shield.
Worked Example
A firm is entirely equity financed and worth $50 million, with a cost of capital of 10%. The firm issues $10 million in debt at a cost of 6% and uses the proceeds to repurchase equity. The corporate tax rate is 25%.
Under the with-tax MM Proposition I:
The firm's value rises by $2.5 million, the value of the tax shield, purely from adding debt. This shows why the tax case produces a different conclusion than the no-tax case, where value would have stayed at $50 million.
What the MM Propositions Teach About Real-World Capital Structure
MM theory does not claim that capital structure is irrelevant in practice. It identifies the conditions under which it would be irrelevant, then gives analysts a benchmark for measuring the effect of real-world frictions. Bankruptcy costs, taxes, agency costs, and information asymmetry all exist, and each pulls the real answer away from the clean MM result.
For Level I, treat MM as the reference point. Later material on optimal and target capital structure builds directly on this base by adding the costs MM assumed away. Without the MM benchmark, those later trade-offs are harder to interpret correctly.
Common Exam Traps
Ignoring the stated assumptions. A question may describe a world with bankruptcy costs or taxes, then ask for the MM no-tax conclusion. Read the assumptions in the question stem before choosing a formula.
Confusing firm value with equity value. MM Proposition I addresses total firm value, not the value of equity alone. Adding debt can change the equity value even when total firm value stays constant under the no-tax case.
Assuming leverage never affects required return. Proposition I says firm value is unchanged in the no-tax case, but Proposition II clearly says cost of equity increases with leverage. These are two different conclusions, not a contradiction.
Using the wrong formula for the tax case. Applying instead of when the question specifies corporate taxes is a frequent scoring error. Check whether taxes are mentioned before selecting a formula.
Treating MM as a real-world capital structure rule. MM is a theoretical model built on strict assumptions. Exam questions sometimes test whether you understand that real capital structure decisions involve costs the base model excludes.
Practice Question
A company operates in a market with no corporate taxes, no bankruptcy costs, and no transaction costs. The company is currently unlevered with a value of $80 million and a cost of capital of 12%. Management is considering issuing debt and using the proceeds to repurchase shares.
According to Modigliani-Miller Proposition I, what will happen to the value of the firm after the debt issuance?
Firm value will increase because debt is cheaper than equity.
Firm value will remain at $80 million because capital structure does not affect value under these assumptions.
Firm value will decrease because higher leverage increases financial risk.
Correct Answer: B
Under the no-tax, no-bankruptcy-cost MM assumptions stated in the question, Proposition I holds that . Changing the financing mix does not change firm value, since value comes from the firm's operations, not its capital structure.
Option A. This confuses the cost of individual capital sources with total firm value. Debt may be cheaper than equity, but under MM Proposition I, cost of equity rises to offset that difference, leaving firm value unchanged.
Option C. This applies a real-world concern (financial distress risk) that the question's stated assumptions explicitly rule out. Under the no-tax MM case, added leverage raises cost of equity, not firm value.
Continue Your CFA Level I Prep With KeyPoint
Use structured lessons, practice questions, mock exams, and progress tracking to focus on the time you have left
FAQs About Modigliani-Miller Capital Structure Propositions
What is the main conclusion of the MM theory of capital structure?
Under strict assumptions of no taxes and no bankruptcy costs, firm value does not depend on the mix of debt and equity used to finance it. Value comes from the firm's assets and operations.
What is the difference between MM Proposition I and Proposition II?
Proposition I addresses total firm value and states it stays constant with leverage in the no-tax case. Proposition II addresses cost of equity and states it rises as leverage increases, since equity holders take on more financial risk.
Does the MM theory apply in real markets?
The base MM model assumes away taxes, bankruptcy costs, and transaction costs. Real markets have these frictions, so real capital structure decisions weigh benefits like the tax shield against costs like financial distress. MM provides the theoretical starting point for that analysis.