ABV ABV Discount Rates & Capital Structure 2 — Questions and Answers
Question 1: What is the Capital Asset Pricing Model (CAPM) formula for the cost of equity?
- Ke = Rf + Beta × (Rm – Rf) (Correct answer)
- Ke = Rf – Beta × ERP
- Ke = Beta × Rm + Risk-Free Rate
- Ke = ERP + Size Premium / Beta
Correct answer: Ke = Rf + Beta × (Rm – Rf)
CAPM states that cost of equity equals the risk-free rate plus beta multiplied by the equity risk premium (market return minus risk-free rate).
Question 2: In CAPM, what does beta measure?
- A company's total risk including unsystematic risk
- A company's systematic (market) risk relative to the overall market (Correct answer)
- The correlation between a company's revenue and GDP
- The volatility of a company's debt relative to its equity
Correct answer: A company's systematic (market) risk relative to the overall market
Beta measures how much a stock's returns move relative to the broader market; a beta of 1.2 means 20% more volatility than the market.
Question 3: What is the 'build-up method' for estimating the cost of equity in a private company valuation?
- A method that calculates cost of equity from WACC by subtracting after-tax cost of debt
- An additive model that sums the risk-free rate, equity risk premium, size premium, industry risk premium, and company-specific risk premium (Correct answer)
- A technique that builds up the cost of equity from observable bond yields only
- A bottom-up approach that aggregates divisional betas to form a company-wide cost of equity
Correct answer: An additive model that sums the risk-free rate, equity risk premium, size premium, industry risk premium, and company-specific risk premium
The build-up method is preferred for private companies where no observable beta exists, stacking individual risk components to arrive at a total required return.
Question 4: Which published source is most commonly cited for the historical equity risk premium and size premium used in U.S. business valuations?
- Federal Reserve Beige Book
- Duff & Phelps (now Kroll) Cost of Capital Navigator / SBBI Yearbook (Correct answer)
- IRS Revenue Ruling 59-60
- AICPA Statement on Standards for Valuation Services No. 1
Correct answer: Duff & Phelps (now Kroll) Cost of Capital Navigator / SBBI Yearbook
The Kroll/Duff & Phelps Cost of Capital Navigator and the historical SBBI data are the standard U.S. sources for ERP and size premium estimates.
Question 5: What is the 'company-specific risk premium' (CSRP) in the build-up method?
- A required premium for owning shares in a publicly traded small-cap company
- An adjustment for idiosyncratic risks unique to the subject company not captured by other premium components (Correct answer)
- The difference between the subject company's beta and the industry average beta
- The premium added for lack of marketability in private company equity
Correct answer: An adjustment for idiosyncratic risks unique to the subject company not captured by other premium components
The CSRP captures risks such as key-person dependency, customer concentration, or weak management that are not reflected in systematic risk measures.
Question 6: How does an increase in the risk-free rate affect the cost of equity under both CAPM and the build-up method?
- It decreases cost of equity because bond prices rise
- It increases cost of equity because the risk-free rate is an additive component in both models (Correct answer)
- It has no effect because the equity risk premium adjusts to offset changes in the risk-free rate
- It only affects WACC, not the cost of equity
Correct answer: It increases cost of equity because the risk-free rate is an additive component in both models
Both CAPM and the build-up model begin with the risk-free rate as a base; a higher risk-free rate directly increases the required return on equity.
ABV ABV Discount Rates & Capital Structure 2
What is the Capital Asset Pricing Model (CAPM) formula for the cost of equity?