Levered cost of equity

What Is Levered Cost of Equity?

Levered cost of equity refers to the rate of return required by equity investors in a company that uses both debt and equity in its capital structure. This concept is fundamental to corporate finance, reflecting the heightened financial risk equity holders bear when a company takes on debt. As a company increases its debt financing, the fixed obligations to creditors make the remaining equity more volatile, thereby demanding a higher expected return from shareholders. This increased expectation is precisely what the levered cost of equity quantifies.

History and Origin

The theoretical underpinnings of the levered cost of equity are deeply rooted in the work of Franco Modigliani and Merton Miller, particularly their 1958 and 1963 propositions on capital structure. Their initial theorem, the Modigliani-Miller theorem without taxes, suggested that a firm's value and its overall cost of capital are independent of its capital structure in perfect markets. However, the subsequent "Modigliani-Miller Theorem with Taxes" recognized the tax deductibility of interest payments, which creates a tax advantage for debt. This led to the insight that while debt can reduce a firm's overall cost of capital by providing a tax shield, it also increases the risk for equity holders, necessitating a higher levered cost of equity. The Federal Reserve Bank of San Francisco has discussed how the Modigliani-Miller propositions provide insights into capital structure and firm value⁵.

Key Takeaways

Levered cost of equity represents the return demanded by equity investors in a company with outstanding debt.
It is higher than the unlevered cost of equity because debt increases the risk borne by shareholders.
The calculation typically involves adjusting the unlevered cost of equity for the effects of financial leverage and corporate taxes.
Understanding the levered cost of equity is crucial for investment valuation and capital budgeting decisions.
It forms a critical component in determining a firm's weighted average cost of capital.

Formula and Calculation

The levered cost of equity ($R_E$) is commonly calculated using the adjusted capital asset pricing model (CAPM) formula or by unlevering and relevering the beta of comparable companies. One common approach derived from the Modigliani-Miller Proposition II with taxes is:

R_E = R_U + (R_U - R_D) \left( \frac{D}{E} \right) (1 - T)

Where:

$R_E$ = Levered cost of equity
$R_U$ = Unlevered cost of equity (the cost of equity if the firm had no debt)
$R_D$ = Cost of debt (the interest rate a company pays on its debt)
$D$ = Market value of the company's debt
$E$ = Market value of the company's equity financing
$T$ = Corporate tax rate

Alternatively, using the levered beta ($\beta_L$):

R_E = R_f + \beta_L (R_M - R_f)

Where:

$R_f$ = Risk-free rate
$\beta_L$ = Levered beta
$(R_M - R_f)$ = Market risk premium

The levered beta can be calculated from the unlevered beta ($\beta_U$) as:

\beta_L = \beta_U \left[ 1 + \left( \frac{D}{E} \right) (1 - T) \right]

Interpreting the Levered Cost of Equity

The levered cost of equity provides insight into how a company's financing choices affect its shareholder's required rate of return. A higher levered cost of equity indicates that shareholders demand greater compensation for the increased financial risk introduced by the company's debt. This value serves as a crucial discount rate for the cash flows attributable to equity holders in valuation models, such as the dividend discount model. Investors and analysts use it to assess the attractiveness of a company's stock relative to its risk profile.

Hypothetical Example

Consider Company ABC, which is evaluating its levered cost of equity.

Unlevered cost of equity ($R_U$) = 10%
Cost of debt ($R_D$) = 5%
Market value of debt ($D$) = $50 million
Market value of equity ($E$) = $100 million
Corporate tax rate ($T$) = 25%

Using the formula:

R_E = R_U + (R_U - R_D) \left( \frac{D}{E} \right) (1 - T)

R_E = 0.10 + (0.10 - 0.05) \left( \frac{\$50 \text{ million}}{\$100 \text{ million}} \right) (1 - 0.25)

R_E = 0.10 + (0.05) (0.50) (0.75)

R_E = 0.10 + (0.05) (0.375)

R_E = 0.10 + 0.01875

R_E = 0.11875 \text{ or } 11.875\%

In this example, Company ABC's levered cost of equity is 11.875%. This is higher than its unlevered cost of equity of 10%, reflecting the additional risk undertaken by equity investors due to the company's leverage.

Practical Applications

The levered cost of equity is a vital input in numerous financial analyses. It is a key component in calculating the weighted average cost of capital (WACC), which is used extensively in capital budgeting to evaluate potential projects and in corporate valuation for mergers and acquisitions. Financial analysts rely on it to determine the fair value of a company's stock and to make investment recommendations. It also plays a role in assessing the optimal capital structure for a firm, helping management balance the benefits of debt financing with the increased risk to equity holders. The CFA Institute highlights the importance of understanding the various methods and assumptions involved in estimating the cost of capital for analysts and investors⁴. The decision to use financial leverage can significantly impact a firm's value and the returns expected by investors, as discussed by the CFA Institute³.

Limitations and Criticisms

While the concept of levered cost of equity is fundamental, its practical application faces several challenges and criticisms. Estimating the accurate inputs, particularly the unlevered beta and the future debt-to-equity ratio, can be difficult. The assumptions of stable capital structures and constant tax rates may not hold true in dynamic market conditions. Furthermore, the reliance on historical data for beta calculations might not accurately reflect future financial risk exposures. Critics also point out that the models, including the CAPM, are based on simplifying assumptions about market efficiency and investor rationality that may not fully capture real-world complexities. Estimating the cost of capital, including the levered cost of equity, involves numerous and often complex assumptions². The Harvard Law School Forum on Corporate Governance has addressed the challenges and complexities inherent in estimating the cost of capital. Additionally, while leverage can amplify returns, it also increases the risk of financial distress, a factor that shareholders will demand compensation for, and excessive reliance on debt can lead to significant downsides¹.

Levered Cost of Equity vs. Unlevered Cost of Equity

The distinction between levered and Unlevered cost of equity is crucial in corporate finance.

Feature	Levered Cost of Equity	Unlevered Cost of Equity
Definition	The return required by equity holders in a company with existing debt.	The return required by equity holders if the company had no debt (all-equity financed).
Risk Reflection	Reflects both business risk and financial risk (due to debt).	Reflects only the company's business risk, independent of its capital structure.
Usage	Used for valuing the equity portion of a leveraged firm and calculating WACC.	Used to determine the cost of equity for a project or firm, irrespective of financing.
Relationship to Debt	Increases with higher levels of debt financing.	Unaffected by the level of debt.

The primary point of confusion often arises because the unlevered cost of equity represents the inherent business risk of a company's assets, independent of how those assets are financed. In contrast, the levered cost of equity specifically accounts for the added risk that debt imposes on shareholders.

FAQs

What is the primary factor that causes the levered cost of equity to be higher than the unlevered cost of equity?

The primary factor is financial risk, which increases for equity holders as a company takes on more debt. When a company has fixed obligations to creditors, a larger portion of its operating income must go towards debt service, making the residual earnings available to shareholders more volatile and, therefore, riskier.

How does the corporate tax rate impact the levered cost of equity calculation?

The corporate tax rate reduces the effective cost of debt because interest payments are often tax-deductible. This tax shield makes debt financing cheaper than it otherwise would be. In the formula for levered cost of equity, the $(1-T)$ factor applied to the debt-to-equity ratio reduces the impact of leverage on the cost of equity, effectively reflecting the tax benefits of debt.

Is the levered cost of equity used in the Weighted Average Cost of Capital (WACC)?

Yes, the levered cost of equity is a crucial component in calculating the weighted average cost of capital (WACC). WACC is the average rate of return a company expects to pay to all its security holders (both debt and equity financing) to finance its assets. The levered cost of equity represents the cost of the equity portion in this weighted average.

Can a company reduce its levered cost of equity by taking on more debt?

Not necessarily. While debt can offer a tax advantage, taking on excessive debt increases financial risk. Beyond a certain point, the increased risk to equity holders will cause the levered cost of equity to rise sharply, potentially offsetting any tax benefits and increasing the overall cost of capital. Financial models strive to find an optimal capital structure that balances these factors.