Welcome to Cost of Capital: Advanced Topics!

Hello there! If you’ve made it to Level II, you already know the basics of the Weighted Average Cost of Capital (WACC) from Level I. But in the real world (and on the Level II exam), the numbers aren't always handed to you on a silver platter. This chapter is all about the detective work required to estimate these costs accurately. We’ll look at how to handle divisions and projects with distinct risk profiles, how to adjust for international risks and currencies, and how to treat taxes and flotation costs properly.

Don't worry if some of these formulas look intimidating at first. We’ll break them down piece by piece. Think of the Cost of Capital as the hurdle rate—the minimum expected return an investment must earn to satisfy its capital providers. If we get this number wrong, our whole capital budgeting and valuation process is distorted. Let's dive in!

1. Estimating the Cost of Equity: Beyond the Basics

In Level I, we mostly relied on the standard Capital Asset Pricing Model (CAPM). In Level II, we acknowledge that different settings require tailored models. We have three main frameworks to estimate the Cost of Equity (\(r_e\)):

A. The CAPM and Equity Risk Premium (ERP) Estimation

The standard CAPM formulation is: \(r_e = R_f + \beta [E(R_m) - R_f]\)

The core challenge is estimating the Equity Risk Premium (ERP), \([E(R_m) - R_f]\):

  • Historical Trend Approach: Computes the historical mean difference between equity market returns and government bond yields over a long horizon. (Limitation: Historical returns are sensitive to survivorship bias and may not reflect forward-looking expectations.)
  • Forward-Looking (Gordon Growth Model) Approach: Backs out the implied expected return from current market pricing and dividend forecasts:
    \(ERP = (\text{Dividend Yield}) + (\text{Expected Long-Term Growth Rate}) - (\text{Current Risk-Free Rate})\)

B. Multi-Factor Models

When market risk alone is insufficient to explain return variations, we can employ multi-factor models such as the Fama-French Three-Factor Model:

\(r_e = R_f + \beta_{\text{mkt}} \times ERP + \beta_{\text{SMB}} \times \text{SMB} + \beta_{\text{HML}} \times \text{HML}\)

  1. Market Risk: Traditional market sensitivity beta.
  2. Size Risk (SMB - Small Minus Big): Accounts for the empirical return premium demanded by smaller market capitalization firms.
  3. Value Risk (HML - High Minus Low): Accounts for the value premium associated with high book-to-market equities versus growth equities.

C. The Build-Up Method for Private Companies

For privately held entities lacking observable market prices or beta estimates, analysts use the Build-Up Method. Starting from a liquid benchmark risk-free rate, risk premiums are sequentially added:

\(r_e = R_f + \text{Equity Risk Premium} + \text{Size Premium} + \text{Specific Company/Industry Risk Premium}\)

2. Pure-Play Method and Estimating Beta

When valuing a private company, or an individual corporate division with a risk profile that differs from the parent company, we use the pure-play method by identifying publicly traded comparable peers in the same line of business.

Unlevering and Relevering Beta

Because peer companies have different financial leverage, we must strip out debt risk to isolate asset (operating) risk, then relever for the target entity's capital structure:

  1. Unlever the comparable firm's beta:
    \(\beta_{\text{Asset}} = \frac{\beta_{\text{Equity}}}{1 + ((1 - t_{\text{peer}}) \times \frac{D_{\text{peer}}}{E_{\text{peer}}})}\)
  2. Relever using the target entity's capital structure and tax rate:
    \(\beta_{\text{Target}} = \beta_{\text{Asset}} \times \left[1 + \left((1 - t_{\text{target}}) \times \frac{D_{\text{target}}}{E_{\text{target}}}\right)\right]\)

Adjusted Beta (Mean Reversion)

Historical regression betas often exhibit mean reversion toward 1.0 over time. Blume's adjustment applies a standard weighting:

\(\text{Adjusted Beta} = \left(\frac{2}{3} \times \text{Raw Beta}\right) + \left(\frac{1}{3} \times 1.0\right)\)

3. Divisional and Project Cost of Capital

A frequent error in corporate finance is evaluating every project or division using the overall company WACC. The corporate WACC reflects the average risk of the firm's existing aggregate operations. If applied indiscriminately:

  • High-Risk Projects: Using the firm WACC understates the required hurdle rate, causing the firm to incorrectly accept value-destroying, overly risky projects.
  • Low-Risk Projects: Using the firm WACC overstates the hurdle rate, causing the firm to reject profitable, safe investments.

Correct Practice: Estimate a division-specific or project-specific cost of capital by finding pure-play peer firms in that specific operating sector, unlevering their betas, and relevering them to match the target division's risk and capital structure.

4. International Cost of Capital: Country and Currency Risk

When capital is invested internationally, particularly in emerging markets, additional risk factors must be accounted for.

A. Country Risk Premium (CRP)

Investing in countries with political, economic, or legal risks requires an added return over the developed-market benchmark. We estimate the Country Risk Premium (CRP) using the sovereign yield spread adjusted for the relative volatility of equity versus sovereign debt:

\(CRP = \text{Sovereign Yield Spread} \times \left( \frac{\sigma_{\text{equity}}}{\sigma_{\text{sovereign bond}}} \right)\)

Where the Sovereign Yield Spread is the difference between the yield of government bonds denominated in a common currency (such as USD-denominated sovereign debt) and US Treasury yields of comparable maturity. The revised cost of equity incorporating country risk is:

\(r_e = R_f + \beta [E(R_m) - R_f] + CRP\)

B. Currency Consistency

A fundamental rule in multinational financial analysis is that cash flows and discount rates must match in terms of currency and inflation expectations:

  • Nominal vs. Real: Discount nominal cash flows with a nominal hurdle rate; discount real cash flows with a real hurdle rate.
  • Currency Matching: Foreign currency cash flows must be discounted using a discount rate established in that same foreign currency. Alternatively, convert future foreign cash flows to domestic currency using forward exchange rates and discount at the domestic required return.

5. Estimating the Cost of Debt

The Cost of Debt (\(r_d\)) represents the current market rate the company would pay to issue new debt today—not the historical coupon rate on existing liabilities.

  1. Yield-to-Maturity (YTM) Approach: If the company has actively traded, liquid bonds, the current market YTM represents the pre-tax cost of debt.
  2. Debt Rating Approach: If the company does not have liquid bonds, assign a synthetic or agency credit rating (e.g., BBB) and identify the market yield on benchmark bonds with equivalent ratings and maturities.

Because interest payments are tax-deductible in most jurisdictions, the after-tax cost of debt is:
\(\text{After-Tax Cost of Debt} = r_d \times (1 - t)\)

6. Treatment of Flotation Costs

Flotation costs are fees paid to investment banks, underwriters, and legal counsel when issuing new securities. There are two competing methods to reflect them, but only one is methodologically sound:

  • The Incorrect Method: Adding flotation costs directly as an ongoing percentage premium to the cost of equity (\(r_e\)) or WACC. This penalizes cash flows into perpetuity for a one-off issuance fee, distorting multi-period project valuations.
  • The Correct Method: Treat flotation costs as an upfront cash outflow at Time 0 within the Net Present Value (NPV) calculation:
    \(NPV = \sum_{t=1}^{n} \frac{CF_t}{(1 + WACC)^t} - (\text{Initial Capital Outlay} + \text{Flotation Costs})\)

7. Exam Summary Checklist

  • Project vs. Company WACC: Match the hurdle rate to the risk of the project, not the average risk of the parent company.
  • Pure-Play Beta: Unlever peer beta using peer D/E and tax rate; relever using target D/E and tax rate.
  • Country Risk: Scale sovereign spread by the equity-to-bond volatility ratio to calculate \(CRP\).
  • Currency Rule: Never mix domestic discount rates with foreign currency cash flows.
  • Flotation Costs: Deduct from initial cash flow at \(t = 0\); do not adjust WACC upward.