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 messy data, different models for equity, and how to avoid common pitfalls that can ruin a valuation.
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 return a company must earn to satisfy its investors. If we get this number wrong, our whole valuation is wrong. Let's dive in!
1. Estimating the Cost of Equity: Beyond the Basics
In Level I, we mostly used the Capital Asset Pricing Model (CAPM). In Level II, we acknowledge that the market is more complex. We have three main ways to estimate the Cost of Equity (\(r_e\)):
A. The CAPM Refresher
The formula remains: \(r_e = R_f + \beta [E(R_m) - R_f]\)
The challenge here is the Equity Risk Premium (ERP), which is the \([E(R_m) - R_f]\) part. There are two ways to estimate it:
- Historical Trend: Looking at the past. (Problem: The past doesn't always predict the future!)
- Forward-looking (Gordon Growth Model): We estimate the ERP based on current dividends and expected growth.
Formula: \(ERP = (\text{Dividend Yield}) + (\text{Expected Growth Rate}) - (\text{Current Long-term Government Bond Yield})\)
B. Multi-Factor Models
Sometimes, one factor (the market) isn't enough to explain returns. We might use the Fama-French Three-Factor Model. It looks at:
- Market Risk: The standard CAPM beta.
- Size Risk (SMB - Small Minus Big): Small companies are riskier and usually demand higher returns.
- Value Risk (HML - High Minus Low): "Value" stocks (high book-to-market) often outperform "growth" stocks.
Quick Tip: If a question gives you multiple "betas" and "premiums," you are likely looking at a multi-factor model. Just multiply each beta by its specific premium and add them to the risk-free rate!
C. The Build-Up Method
This is often used for private companies where we don't have a "beta." We start with the Risk-Free Rate and keep adding "building blocks" of risk:
\(r_e = R_f + \text{Equity Risk Premium} + \text{Size Premium} + \text{Specific Risk Premium}\)
Key Takeaway: Choosing the right model depends on the data available. If you have a public company with plenty of data, CAPM or Multi-factor is great. If it's a small private firm, use the Build-Up method.
2. The Art of Estimating Beta
Beta measures how much a stock moves relative to the market. But historical beta can be "noisy."
Adjusted Beta (Blume’s Method)
Studies show that over time, a company’s beta tends to move toward the market average of 1.0. If a company has a super-high beta today, it will likely be lower in five years. If it's super-low, it will likely rise.
The Formula: \( \text{Adjusted Beta} = (\frac{2}{3} \times \text{Unadjusted Beta}) + (\frac{1}{3} \times 1.0) \)
Memory Aid: Think of Beta as a rubber band. You can stretch it far away from 1.0, but it always wants to snap back toward the middle.
Beta for Non-Public Companies (Pure-Play Method)
What if the company isn't traded? We find a "Comparable" public company and "borrow" their beta. But wait! Debt affects beta. More debt means more risk (and a higher beta). We must unlever the peer's beta and then relever it for our company.
Step-by-Step:
- Find a comparable public company.
- Unlever their beta to find the "Asset Beta" (risk without debt):
\( \beta_{Asset} = \frac{\beta_{Equity}}{1 + ((1 - t) \times \frac{D}{E})} \) - Relever it using your company's debt-to-equity ratio:
\( \beta_{Target} = \beta_{Asset} \times [1 + ((1 - t) \times \frac{D}{E})] \)
Common Mistake: Forgetting to use the comparable's D/E ratio when unlevering and the target's D/E ratio when relevering. Don't mix them up!
Key Takeaway: Beta needs to be adjusted for both time (moving toward 1.0) and leverage (removing and adding the effects of debt).
3. Estimating the Cost of Debt
The Cost of Debt (\(r_d\)) is the rate a company would pay if it issued debt today. Do not use the "coupon rate" from bonds issued five years ago!
The Two Main Methods:
- Yield-to-Maturity (YTM) Approach: If the company has liquid bonds trading, the YTM on those bonds is the best estimate of the current market cost of debt.
- Debt Rating Approach: If there's no liquid bond price, look at the company's credit rating (e.g., AA or Baa). Find the yield on other bonds with that same rating and similar maturity. This is your "pre-tax" cost of debt.
The Tax Shield Reminder: Because interest is tax-deductible, the "real" cost to the company is lower.
Formula: \( \text{After-tax cost of debt} = r_d \times (1 - \text{Tax Rate}) \)
Key Takeaway: Always use the current market rate and always remember to multiply by (1 - t). Equity does NOT get this tax break!
4. Flotation Costs: The Right Way vs. The Wrong Way
When a company issues new stocks or bonds, they have to pay investment bankers. These are called Flotation Costs.
The Wrong Way: Some people increase the Cost of Equity percentage (e.g., saying the cost is 12% instead of 10% to cover the fees). The CFA curriculum says DON'T do this! It distorts the cost of capital forever.
The Right Way: Treat flotation costs as a cash outflow at Time 0 in your NPV calculation. It’s a one-time "start-up" expense.
Analogy: Imagine buying a house. The real estate agent's commission is like a flotation cost. You don't say your mortgage interest rate is higher; you just acknowledge that you had to pay a big chunk of cash on the day you bought the house.
Key Takeaway: Flotation costs are a dollar amount deducted from the initial cash flow (NPV), not an increase in the WACC percentage.
5. Final "Checklist" for Your Exam
Don't worry if this seems like a lot of moving parts. On exam day, just ask yourself these questions:
- Is it a private company? Look for the Build-up method or Pure-play beta.
- Did they give me a tax rate? Use it for debt, but never for equity.
- Are there flotation costs? Subtract them from the initial investment (\(CF_0\)).
- Is the Beta historical? Check if you need to use Blume's adjustment to move it toward 1.0.
Quick Review Box:
1. WACC = \( (w_e \times r_e) + (w_d \times r_d \times (1-t)) + (w_p \times r_p) \)
2. Unlevered Beta = Beta with 0 debt.
3. ERP = Market return minus Risk-free rate.
4. Flotation Costs = Initial cost, not a % adjustment to WACC.
You've got this! Corporate Issuers is often one of the more intuitive sections once you master these specific adjustments. Keep practicing those "unlevering/relevering" calculations!