Unlevered cost of equity

What Is Unlevered Cost of Equity?

The unlevered cost of equity, also known as the asset cost of capital, represents the theoretical rate of return required by investors in a company that has no debt in its capital structure. This fundamental concept in corporate finance quantifies the inherent business risk of a firm's assets, independent of any financial risk introduced by debt financing. It essentially answers: What would equity investors demand if the company were financed solely by equity, without the complicating effects of financial leverage and its associated tax benefits?

History and Origin

The concept underlying the unlevered cost of equity is deeply rooted in the Modigliani-Miller (M&M) theorem, a cornerstone of modern financial theory developed by economists Franco Modigliani and Merton Miller in the late 1950s. Their seminal work, particularly the first proposition, asserted that in a world without taxes, bankruptcy costs, or agency costs, a firm's value is independent of its capital structure. This "irrelevance proposition" implies that how a company chooses to finance its operations (through debt or equity) does not affect its total value.⁵

While the original M&M theorem simplified the world significantly, it provided a powerful analytical framework. It allowed finance professionals to separate a company's operating risk from its financial risk. The unlevered cost of equity thus emerged as the theoretical cost of capital for an all-equity firm, capturing only the business risk inherent in its operations. Subsequent adaptations of the M&M theorem accounted for factors like corporate taxes, introducing the concept of a tax shield that makes debt financing advantageous and leads to differences between unlevered and levered cost of equity.

Key Takeaways

• The unlevered cost of equity reflects the return required by investors for a company with no debt, isolating business risk.
• It is a crucial input in valuation models, especially when assessing companies with varying debt levels.
• Calculating the unlevered cost of equity often involves adjusting a company's beta for its capital structure.
• It serves as the appropriate discount rate for the unlevered free cash flows to the firm.
• The concept is fundamental in understanding the impact of capital structure decisions on a firm's value.

Formula and Calculation

The unlevered cost of equity is typically derived from the levered cost of equity, often using a variant of the Hamada formula or by unlevering the equity beta. The most common approach involves unlevering the equity beta and then using the Capital Asset Pricing Model (CAPM).

First, calculate the unlevered beta ((\beta_U)) from the levered beta ((\beta_L)):

Where:

• (\beta_U) = Unlevered Beta (Asset Beta)
• (\beta_L) = Levered Beta (Equity Beta)
• (T) = Corporate Tax Rate
• (D) = Market Value of Debt
• (E) = Market Value of Equity

Once the unlevered beta is determined, the unlevered cost of equity ((r_U)) can be calculated using the Capital Asset Pricing Model (CAPM):

Where:

• (r_U) = Unlevered Cost of Equity
• (R_f) = Risk-Free Rate (e.g., yield on long-term government bonds)
• (R_m) = Expected Market Return
• ((R_m - R_f)) = Market Risk Premium

Interpreting the Unlevered Cost of Equity

The unlevered cost of equity represents the expected rate of return on an all-equity financed company, reflecting only its operational business risks. A higher unlevered cost of equity indicates a greater inherent business risk within the company's core operations, irrespective of how those operations are financed. This measure is crucial for comparing companies across different industries or with diverse capitalization structures because it removes the distortion caused by varying levels of debt.

For instance, two companies in the same industry might have very different levered costs of equity due to their debt levels. By unlevering their respective costs of equity, an analyst can gain a clearer understanding of which company's underlying business is riskier, providing a more "apples-to-apples" comparison of their operational exposures. This allows for a focus on the core profitability and risk profile of the business itself.

Hypothetical Example

Consider a hypothetical technology startup, "InnovateTech," that currently operates with no debt. Its equity beta is observed to be 1.2, reflecting its sensitivity to market movements. The current risk-free rate is 3%, and the market risk premium is 6%.

Using the CAPM, InnovateTech's unlevered cost of equity would be calculated as:

(r_U = 3% + 1.2 \times 6% = 3% + 7.2% = 10.2%)

Now, imagine InnovateTech decides to take on significant debt to fund an expansion. Its equity beta would increase due to the added financial risk. If its corporate tax rate is 25%, its market value of debt (D) is $50 million, and its market value of equity (E) is $100 million, then its debt-to-equity ratio (D/E) is 0.5.

Suppose after taking on debt, its new levered beta is 1.6. We can check the unlevered beta:

(\beta_U = \frac{1.6}{1 + (1 - 0.25) \times 0.5} = \frac{1.6}{1 + 0.75 \times 0.5} = \frac{1.6}{1 + 0.375} = \frac{1.6}{1.375} \approx 1.16)

Slightly different from the initial 1.2, which could be due to rounding or inherent model limitations. However, the key takeaway is that the unlevered cost of equity, even with new financing, seeks to represent the business's inherent risk, not the risk amplified by borrowing.

Practical Applications

The unlevered cost of equity is a vital metric in various financial analyses and decision-making processes, particularly within the realm of corporate valuation and capital budgeting.

• Valuation of Leveraged Firms: When valuing a company with debt using a discounted cash flow (DCF) model, particularly the Adjusted Present Value (APV) method, the unlevered cost of equity serves as the discount rate for the unlevered free cash flows. This separates the value of the operating assets from the value added by debt financing (e.g., tax shields).
• Mergers and Acquisitions (M&A): In M&A, buyers often need to assess the target company's core business value independent of its existing capital structure, as the buyer may impose a new financing structure. The unlevered cost of equity provides a clean measure of the target's business risk.
• Benchmarking and Comparability: It allows for a standardized comparison of the business risk across companies in the same industry, regardless of their individual financial leverage. This is particularly useful when performing comparable company analysis, enabling analysts to identify truly similar businesses.
• Capital Budgeting: While the Weighted Average Cost of Capital (WACC) is often used for capital budgeting, the unlevered cost of equity can be employed to evaluate specific projects or divisions within a diversified company, especially if those projects have different business risks than the company's overall average. For financial institutions, the calculation of the cost of capital is particularly complex given their unique balance sheet structures.⁴
• Private Company Valuation: For private companies that lack readily observable market data, analysts often look to publicly traded comparable companies. The unlevered beta of these public companies can be calculated, averaged, and then re-levered to reflect the private company's specific target capital structure. Aswath Damodaran provides insights into estimating the cost of equity for privately owned businesses, highlighting why it might be higher than an otherwise equivalent public company due to diversification differences.³

Limitations and Criticisms

While the unlevered cost of equity offers a valuable perspective by isolating business risk, it is not without limitations and criticisms.

• Assumption of Perfect Capital Markets: The foundational Modigliani-Miller theorem, from which the concept largely stems, relies on strong assumptions of perfect capital markets (no taxes, no transaction costs, no bankruptcy costs, symmetric information). While later versions incorporated taxes, real-world markets are imperfect, introducing frictions that the unlevering process may not fully capture.
• Beta Estimation Challenges: Accurate estimation of beta is critical for calculating the unlevered cost of equity. Beta is backward-looking and can be unstable, particularly for companies undergoing significant operational or structural changes. Financial service companies, in particular, pose challenges for unlevering and relevering betas.²
• Circular Logic: In practice, valuing private companies or projects often involves a circularity: the capital structure impacts the cost of equity, but the value of equity (a component of capital structure) depends on the cost of equity itself. This requires iterative calculations or assumptions about target capital structures.
• Relevance of Tax Shield: The unlevering formula typically accounts for the corporate tax shield on debt. However, the actual benefit of this tax shield can vary depending on a company's profitability and tax jurisdiction, potentially leading to inaccuracies if a simplified tax rate is used.
• Risk-Free Rate and Market Risk Premium: The accuracy of the unlevered cost of equity also depends on the selection of the appropriate risk-free rate and market risk premium, both of which can be subject to debate and can fluctuate.¹

Despite these limitations, the unlevered cost of equity remains an indispensable tool for analysts seeking to understand a company's fundamental business risk, separate from its financing decisions.

Unlevered Cost of Equity vs. Levered Cost of Equity

The distinction between unlevered cost of equity and levered cost of equity is fundamental to understanding how capital structure influences investor returns and company valuation.

The unlevered cost of equity offers a pure measure of a company's operational risk, useful for comparing businesses regardless of their financing decisions. In contrast, the levered cost of equity represents the actual return required by equity investors given the company's specific mix of debt and equity. It accounts for the amplified risk equity holders bear due to the presence of fixed debt obligations. Analysts often use both, depending on the specific valuation approach or analysis being performed.

FAQs

Why is the unlevered cost of equity important?

The unlevered cost of equity is important because it isolates a company's inherent business risk from its financial risk. This allows for a clearer comparison of different companies or projects, independent of their debt levels. It is also crucial for certain valuation methodologies, like the Adjusted Present Value (APV) approach.

Can a company have a negative unlevered cost of equity?

Theoretically, no. The unlevered cost of equity, calculated using models like CAPM, requires a positive risk-free rate and a positive market risk premium, combined with a positive beta for most operating companies. A negative unlevered cost of equity would imply that investors expect to lose money on a risk-free investment, or that the company's assets provide a hedging benefit, which is highly unusual and generally not realistic for a standalone business.

How does the unlevered cost of equity relate to Weighted Average Cost of Capital (WACC)?

The unlevered cost of equity is a component and a foundational concept for understanding WACC. While WACC incorporates both the cost of equity and the after-tax cost of debt, weighted by their proportions in the capital structure, the unlevered cost of equity essentially represents the WACC if the company had no debt. The WACC captures the overall cost of capital for a firm with a mix of debt and equity, whereas the unlevered cost of equity focuses solely on the equity return without the impact of leverage.

Is the unlevered cost of equity the same as the cost of equity for a private company?

Not necessarily. While a private company might not have publicly traded debt or equity, the unlevered cost of equity is a theoretical construct for an all-equity firm, regardless of its public or private status. For a private company, estimating its cost of equity often involves looking at comparable public companies, unlevering their betas, and then potentially re-levering or adjusting for liquidity and specific private company risks. The concept of diversification and its impact on required return is particularly relevant here.

Does the unlevered cost of equity change with a company's debt levels?

No, the unlevered cost of equity theoretically does not change with a company's debt levels. Its purpose is to represent the cost of equity for the underlying business assets as if there were no debt. As a company takes on more debt, its levered cost of equity increases (due to higher financial risk for equity holders), but the unlevered cost of equity, reflecting only business risk, should remain constant assuming the core operations and industry risk don't change.