In this article, Snehasish CHINARA (ESSEC Business School, Grande Ecole Program – Master in Management, 2022-2025) explores the optimal capital structure for firms, which refers to the balance between debt and equity financing. This post dives into the article written by Modigliani and Miller (1958) which explores the case of no corporate tax and a frictionless market (no bankruptcy costs).
Introduction to Capital Structure
Capital structure refers to the mix of debt and equity financing that a company uses to fund its operations and growth. It is a critical component of corporate finance, as it directly impacts a firm’s cost of capital, financial risk, and overall valuation. The choice of capital structure affects a company’s ability to raise funds, weather economic downturns, and pursue strategic investments.
Capital structure is reflected in a company’s balance sheet, which provides a snapshot of its financial position at a given point in time. Specifically, it is composed of two primary financing sources:
- Debt (Liabilities) – Found under the Liabilities section, debt includes short-term borrowings, long-term loans, bonds payable, and lease obligations. Debt financing requires periodic interest payments and repayment of principal, increasing financial obligations but also benefiting from potential tax shields.
- Equity (Shareholders’ Equity) – Located under the Shareholders’ Equity section, equity includes common stock, preferred stock, retained earnings, and additional paid-in capital. Equity financing does not require fixed interest payments but dilutes ownership among shareholders.
Table 1 below gives a simplified version of a balance sheet.
Table 1 – Simplified Balance Sheet Example
Table 1 shows that the firm finances its $350M in assets with $140M in debt (40%) and $210M in equity (60%), demonstrating a debt-to-equity ratio of 0.67 (=140/210). Additionally, the debt ratio, D/(D+E), measures the proportion of total financing that comes from debt 40% (=140/(140+210)). This indicates that a significant portion of capital is funded through borrowed money, allowing the company to take advantage of the use of debt, but also exposing it to higher financial risk if it faces difficulties in meeting debt obligations. These ratios are a few key indicators used to assess a company’s financial leverage and risk exposure.
A higher reliance on debt can lead to increased financial risk due to interest obligations, while too much equity financing may dilute shareholder returns. Therefore, finding an optimal capital structure is crucial for maintaining a healthy balance between risk, return, and financial stability.
Capital structure is one of the most fundamental decisions in corporate finance, influencing a firm’s financial stability, cost of capital, and overall value. At the heart of this discussion lies the Modigliani-Miller (M&M) theorems (M&M 1958 and M&M 1963), which provides the foundational framework for understanding how a company’s choice between debt and equity affects its valuation. However, while MM’s initial work (1958) proposed that capital structure is irrelevant in a frictionless market, real-world complexities such as taxation, bankruptcy costs, and financial distress challenge this assumption, leading to more nuanced theories.
The Modigliani-Miller 1958 Theorem (M&M 1958)
The Modigliani-Miller theorem (M&M 1958), introduced in 1958 by Franco Modigliani and Merton Miller, is a cornerstone of modern corporate finance. It provides a theoretical framework for understanding the role of capital structure in determining a firm’s value. M&M 1958’s core argument is that in a perfect market, a firm’s value is independent of its capital structure, meaning that the choice between debt and equity financing has no impact on firm valuation.
M&M 1958 Proposition I: Capital Structure Irrelevance
For the problem of the determination of the optimal capital structure of the firm, we assume that the firm (and its managers) seek to maximize the financial or economic value of the shareholders’ equity.
M&M’s first proposition states that, in a world with no taxes, no transaction costs, and perfect information, the total value of a firm (V) is unaffected by its financing decisions. Whether a company is financed with 100% equity, 100% debt (almost), or any combination of both, its market value remains the same because investors can create their own leverage through homemade financing.
M&M’s first proposition says that a company’s value is determined by its business operations (profits, assets, and growth potential), not by how it finances those operations. Since in a perfect world, investors can create leverage on their own. If a company doesn’t use debt, an investor can borrow money separately to create the same effect. This means that whether the company uses debt or not, its overall value remains the same.
For a firm with market value V, total assets A, and financed by debt D and equity E:
According to M&M Proposition I, in a frictionless world:
where:
- VL is the value of a levered firm using debt.
- VU is the value of a unlevered firm not using debt but only equity
- No taxes (in reality, firms pay corporate taxes).
- No bankruptcy costs (in reality, firms pay costs if they go bankrupt).
- No financial distress (in reality, too much debt can make investors nervous).
Figure 1. Firm Value vs Debt Ratio according to M&M 1958: Proposition I
In Figure 1, according to M&M 1958 Proposition I, the firm value remains constant regardless of the debt ratio. The flat blue line represents the idea that whether a firm is 100% equity-financed or takes on debt, its total value does not change in a perfect world with no taxes, no bankruptcy costs, and no market imperfections.
M&M 1958 Proposition II: Cost of Equity and Leverage Relation
While M&M Proposition I states that firm value is independent of capital structure, Proposition II explains how leverage affects the cost of equity (and then then total cost of financing measured by the weighted average cost of capital or WACC). It shows that as a firm increases its debt, equity becomes riskier, leading to an increase in the cost of equity (rE) to compensate for higher financial risk.
When a firm increases its leverage, its cost of debt (rD) is typically lower than its cost of equity (rE) due to the priority of debt holders in the capital structure and the fixed nature of interest payments. However, as leverage rises, the firm’s equity becomes riskier because debt obligations take precedence, amplifying the volatility of residual earnings available to shareholders. According to Modigliani-Miller Proposition II, this higher financial risk leads to an increase in the required return on equity (rE), as shareholders demand greater compensation for bearing the amplified risk exposure.
where:
- rE = cost of equity for a levered firm
- rU = cost of equity for an unlevered firm
- rD = cost of debt
- D/E = debt to equity ratio measuring leverage
This formula highlights that with higher leverage, the cost of equity increases, offsetting any benefit from the lower cost of debt. Thus, while leverage amplifies returns, it also raises financial risk, maintaining the firm’s overall cost of capital.
Shareholders bear more risk as leverage increases due to the following reasons –
- Residual Claimants: Shareholders are last in line for cash flows, meaning higher debt increases fixed interest obligations, reducing the certainty of equity returns.
- Earnings Volatility: With more debt, small fluctuations in operating profits cause larger swings in equity returns, making equity riskier.
- Default & Financial Distress Risk: If debt levels rise too much, the firm faces a higher probability of default or financial distress, further increasing required equity returns.
The Weighted Average Cost of Capital (WACC) is a key financial metric that represents a firm’s overall cost of financing by combining the costs of equity and debt. Under Modigliani-Miller Proposition II (1958), the WACC is given by the formula:
Where:
- WACC = Weighted Average Cost of Capital
- E = Value of equity
- D = Value of debt
- rE = Cost of equity (which increases with leverage)
- rD = Cost of debt (fixed by assumption)
M&M 1958 Proposition II states that as a firm increases its debt financing, its cost of equity rE rises to compensate for the additional financial risk. However, because debt is cheaper than equity, the lower cost of debt rD balances out the increase in rE, keeping WACC constant.
Figure 2. Modigliani-Miller View Of Gearing And WACC: No Taxation (MM 1958 Proposition II)
Based on Figure 2, implication for firms are as follows:
- In a world with no taxes and bankruptcy costs, leverage does not create or destroy firm value.
- Higher leverage increases equity risk, leading to higher required returns for shareholders.
- The Weighted Average Cost of Capital (WACC) remains constant regardless of debt-equity mix.
If a company borrows money (takes on debt), it must pay interest no matter how well the business performs. If profits drop, shareholders get whatever is left after paying the debt, which makes equity riskier. Because of this extra risk, shareholders demand a higher return, which increases the cost of equity.
Case Study: Implications of M&M 1958 (Optimal Capital Structure with no taxes)
Alpha Corp operates in a perfect capital market (no taxes, no bankruptcy costs, and no market imperfections). It has two financing options:
- Option 1: Fully equity-financed (No debt)
- Option 2: 40% Debt, 60% Equity
Each option funds a $100 million investment that generates an annual operating income of $10 million. The risk-free interest rate is 5%, and the required return on equity is 10%.
Figure 3. Simplified Balance Sheet of Alpha Corp
Table 2. M&M 1958: an Example
Based on Table 2, the key takeaways are as follows:
1. Firm Value Remains Constant
- In both financing scenarios (100% Equity vs. 40% Debt, 60% Equity), the total value of the firm remains $100M.
- This aligns with Modigliani-Miller Proposition I (1958), which states that in a perfect capital market, capital structure does not impact firm value.
2. Cost of Equity Increases with Leverage
- In the 100% equity scenario, the required return on equity (rE) is 10%.
- When the firm takes on 40% debt, the cost of equity (rE) increases to 13%, reflecting the additional financial risk borne by equity holders.
- This aligns with Modigliani-Miller Proposition II (1958), which states that as leverage increases, equity holders require a higher return due to increased financial risk.
3. WACC Remains Constant
- Despite the change in capital structure, the Weighted Average Cost of Capital (WACC) remains at 10%.
- This reinforces M&M Proposition II, which states that in a perfect market, using debt does not lower the firm’s overall cost of capital.
4. Impact on Cash Flows & Present Values
- Equity holders receive lower cash flows ($8M) under 40% debt financing due to interest payments ($2M) to debt holders.
- However, the present value of debt ($40M) + present value of equity ($60M) = $100M, meaning that the firm’s total value remains unchanged regardless of financing choices.
Table 3. Cash Flow for shareholders using cost of equity
Table 4. Cash Flow for debt holders using cost of debt
The Discounted Cash Flow (DCF) approach is used to determine the value of equity (E) and debt (D) by discounting their respective cash flows.
1. Cash Flows to Shareholders (Equity Holders)
- Formula: CF to Equity= Operating Income −Interest Payments
- Computation:
- 100% Equity Case:10M−0=10M
- 40% Debt, 60% Equity Case:10M−2M=8M
2. Cash Flows to Debt Holders
- Formula: CF to Debt= Interest Payment = Debt × rD
- Computation: 40% Debt, 60% Equity Case: 40M×5%=2M
3. Present Value (PV) of Equity and Debt Using DCF
- DCF Formula for constant perpetual cash flows:
- For Equity Holders:
- 100% Equity Case: PVE = 10M/10% = 100M
- 40% Debt, 60% Equity Case: PVE = 8M/13% = 60M
- For Debt Holders (PV of Debt):
- 40% Debt, 60% Equity Case: PVD= 2M/5% = 40M
The firm’s total value is always equal to the sum of the present values of equity and debt. This confirms the Modigliani-Miller capital structure irrelevance theorem, which states that in a perfect market, the financing mix does not change the total value of the firm.
Takeaways on Optimal Debt Structure and Bankruptcy Costs from M&M 1958 Propositions
The Modigliani-Miller Theorem provides a foundational understanding of how capital structure affects firm value. Proposition I tells us that in a perfect market with no corporate tax, the choice between debt and equity does not impact a company’s total value. However, Proposition II highlights that increasing debt makes equity riskier, which raises the cost of equity and offsets the benefits of cheaper debt.
Why Should I Be Interested in This Post?
The Modigliani-Miller (MM) 1958 theorem revolutionized corporate finance by demonstrating that, in a perfect market without corporate taxes, a firm’s capital structure (debt vs. equity) does not affect its overall value. This insight laid the foundation for modern finance theory, influencing corporate decisions on capital budgeting, M&A, and risk management. While real-world factors like taxes and bankruptcy costs modify MM’s conclusions, its core principles remain central to understanding cost of capital, leverage effects, and financial strategy. MM 1958 theory provides a theoretical framework that underpins advanced topics in corporate valuation, investment strategy, and capital markets.
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