CAPM and WACC Explained

The cost of capital is a cornerstone of corporate finance, representing the minimum return a company must earn on its investments to satisfy its investors and maintain its value.

Whether evaluating a new project, valuing a business, or optimizing capital structure, an accurate cost of capital is critical.

What is the Cost of Capital (WACC)?

The cost of capital is the weighted average of a company’s cost of debt and equity, reflecting the return required by investors to compensate for risk.

It serves as the hurdle rate for investments: projects must yield returns above this rate to create value.

The Capital Asset Pricing Model (CAPM): Cost of Equity

CAPM is the most widely used method to calculate the cost of equity. It quantifies the return investors demand based on the risk-free rate, market risk, and a company’s specific risk profile.

CAPM calculates the cost (expected return) of equity capital based on expected stock market performance / risks and the company's share price sensitivity to movements in the overall market (beta).

Formula:

Cost of Equity (Re)= Rf + β × (Rm−Rf)

Where:

• Rf​ = Risk-Free Rate
• β = Unlevered Beta (Systematic Risk)
• Rm = Expected return of the asset
• Rm−Rf​ = Market Risk Premium (MRP)

1. Risk-Free Rate (Rf)

• Definition: The return on a risk-free investment (e.g., government bonds).
• Best Practice: Use a bond maturity matching the investment horizon (e.g., 10-year Treasury yield for long-term projects).

2. Beta (βe) - Levered Beta

• Definition: Measures a stock’s volatility relative to the market.
  • β = 1: Moves with the market.
  • β > 1: More volatile than the market.
  • β < 1: Less volatile than the market.
• Calculation: Derived from historical stock returns regressed against market returns.

3. Market Risk Premium (Rm−Rf)

• Definition: The excess return investors expect for bearing market risk.
• Estimation: Use historical averages (e.g., 5-6% for the S&P 500) or forward-looking surveys.

Example:
If Rf = 2%, β = 1.2, and Rm−Rf = 5%:

Re = 2% + 1.2 × 5% = 8%

Calculating Unlevered Beta: For Private Companies or New Projects

This process involves unlevering a levered beta of a similar public company then using the calculated unlevered beta to calculate the levered beta for the private company or new project with its own specific capital structure.

What is Unlevered Beta?

A company's total risk is influenced by two main factors:

1. Business Risk (or Operational Risk): This is the inherent risk of a company's operations, how sensitive its revenues and costs are to economic cycles, industry trends, and competitive forces. It's the risk directly tied to what the company does.
2. Financial Risk: This risk arises from a company's use of debt financing (leverage). The more debt a company takes on, the higher its financial obligations (interest payments, principal repayments), which increases the risk of financial distress or even bankruptcy.

Levered beta (equity beta) captures both business risk and financial risk. It tells you how volatile a company's stock is relative to the market, taking into account its existing debt.

Unlevered beta (asset beta) isolates the business risk by removing the impact of financial leverage. It essentially tells you what a company's beta would be if it were entirely equity-financed, with no debt.

Why is Unlevered Beta Important?

Unlevered beta is incredibly useful for several reasons:

• Comparing Companies with Different Capital Structures: By unlevering their betas, you can strip away the financial risk and compare their underlying business risk, providing a much clearer picture of their operational volatility. This is crucial for making informed investment decisions.
• Valuation of Private Companies or New Projects: When valuing a private company or a new project that doesn't have its own publicly traded stock, analysts often use the unlevered beta of comparable publicly traded companies. This unlevered beta can then be re-levered using the target company's or project's specific capital structure to estimate its appropriate cost of equity.

How to Calculate Unlevered Beta

The formula for unlevering beta involves adjusting the levered beta for the company's debt-to-equity ratio and its tax rate.

βU​ = βL ​/ [1 + ((1−T) ∗ (D/E))]

Where:

• βU​ = Unlevered Beta
• βL​ = Levered Beta (the beta you typically find online)
• T = Corporate Tax Rate
• D/E = Debt-to-Equity Ratio (Market Value of Debt / Market Value of Equity)

Let's break down the components:

• Levered Beta (βL​): This is your starting point. You can usually find this on financial data providers like Bloomberg, Yahoo Finance, or Google Finance.
• Corporate Tax Rate (T): This is the company's effective corporate tax rate.
• Debt-to-Equity Ratio (D/E): This ratio reflects the company's financial leverage.

How to Calculate Levered Beta from Unlevered Beta

You take the calculated industry average unlevered beta and re-lever it using the target company's (or project's) specific debt-to-equity ratio and tax rate. This step introduces the target's unique financial risk back into the beta.

βL ​= βU ​∗ [1 + (1−T) ∗ (D/E)]

Beyond CAPM: Adjusting for Real-World Complexities

While CAPM provides a foundation, real-world applications often require adjustments:

1. Country Risk Premium

• Use Case: For companies in emerging markets, add CRP to account for political/economic instability.

2. Size Premium

• Use Case: Smaller firms face higher risks. Add 2-4% based on historical size premiums.

3. Company-Specific Risk Premium

• Use Case: Private companies or unique risks (e.g., litigation, regulatory changes).

Why is CAPM important?

• Cost of Equity Calculation: CAPM is the most widely used method to estimate the cost of equity, a crucial component of WACC.
• Investment Appraisal: It helps investors determine if an asset offers a sufficient expected return to justify its risk. If the expected return calculated by CAPM is less than the investor's required return, they might reconsider the investment.
• Portfolio Management: It assists in constructing diversified portfolios by understanding the risk contribution of individual assets.

Limitations of CAPM

• Assumptions: It relies on several simplifying assumptions, such as rational investors, perfect markets, and access to all information, which may not hold true in the real world.
• Estimation Challenges: Estimating future market returns and accurate betas can be challenging and prone to error.
• Single-Factor Model: It only considers systematic risk, ignoring other factors that might influence returns.

Weighted Average Cost of Capital (WACC)

WACC represents the average rate of return a company expects to pay to all its capital providers – both debt and equity holders. It's a critical discount rate used in discounted cash flow (DCF) valuation models to determine the present value of a company's future cash flows. Essentially, WACC is the minimum return a company must earn on its existing asset base to satisfy its creditors and shareholders.

WACC combines the cost of equity and debt, weighted by their proportions in the capital structure:

Formula:

WACC = (E/V × Re) + (D/V × Rd × (1−T))

Where:

• E = Market value of equity
• D = Market value of debt
• V = MV of Equity + MV of Debt
• Re = Cost of Equity (CAPM)
• Rd = Cost of Debt (pre-tax / effective interest rate)
• T = Tax rate
  • The cost of debt is tax-deductible, hence the (1−T​) adjustment, which accounts for the tax shield.

Example:

• Re = 8%, Rd = 4%, T = 25%, E/V = 60%, D/V = 40%

WACC = (60% × 8%) + (40% × 4% × 75%) = 6%

Why is WACC important?

• Valuation: WACC is the discount rate used to present value a company's free cash flows to the firm (FCFF - unlevered) in a DCF model. A lower WACC generally leads to a higher valuation.
• Investment Decisions: Companies use WACC as a hurdle rate for evaluating new projects. If a project's expected return is less than the WACC, it might not be undertaken, as it won't generate sufficient returns to cover the cost of financing.
• Capital Structure Decisions: Understanding WACC helps companies optimize their mix of debt and equity to minimize their overall cost of capital.

Key considerations for WACC:

• Market Values: Always use market values for equity and debt, not book values, as market values reflect current investor expectations.
• Cost of Equity: CAPM is the dominant method for estimating Re​.
• Cost of Debt: This can be derived from the company's existing debt interest rates or by looking at the yield on comparable corporate bonds.
• Tax Shield: The tax deductibility of interest payments significantly reduces the effective cost of debt.

Practical Application: Evaluating a Project

Suppose a project requires a $1M investment and promises $120k annual cash flow.

• WACC = 6% → NPV = $120k / 0.06 −$1M = $1M (Profitable)
• WACC = 12% → NPV = $120k / 0.12−$1M = $0 (Breakeven)

Conclusion: The project is viable only if WACC ≤ 12%.

Conclusion

CAPM provides the crucial input for the cost of equity within the WACC calculation. A robust financial model will leverage both concepts to arrive at sound valuations and strategic recommendations.

By mastering CAPM, adjusting for real-world risks, and understanding WACC, businesses and investors can make informed decisions that align with their risk tolerance and strategic goals.

Understanding these fundamental concepts is essential for anyone involved in financial analysis, corporate finance, or investment management.