Cost of equity (E)

What is the CAPM formula?

ANSWER: E(ri) = rf + βL × (E(rM) − rf)
• Required return = risk-free rate + levered beta × market risk premium.
• Only systematic risk is priced.
• Know by heart.

What is the CAPM beta and what does it measure?

ANSWER: β = cov(ri, rM) / var(rM) = slope of regressing excess stock returns on excess market returns
• Measures SYSTEMATIC risk only (vs size premium which proxies idiosyncratic risk).
• Exam Q EXAM1 7a.

What is the Hamada formula?

ANSWER: βE = βA + (βA − βD) × D/E × (1 − T)
• Same shape as the leverage formula (rE → βL, rA → βU, rD → βD). βD = 0 unless the firm is in distress; in distress drop (1 − T).
• Used to unlever peer betas and relever at sector D/E.

What is the asset (unlevered) beta?

ANSWER: Beta of the firm if 100% equity financed; reflects business risk only
• Comparable across firms with different leverage.
• KPMG gives sector asset betas (e.g. industrial manufacturing 0.90).

How do you unlever a beta (βD = 0)?

ANSWER: βA = βL / (1 + (1 − T) × D/E)
• Then relever: βL = βA × (1 + (1 − T) × D/E).
• Remember D/E = (D/V)/(1 − D/V).

What is the debt beta?

ANSWER: βD = (rD − rf) / MRP
• Systematic risk of debt; ≈ 0 for healthy firms, > 0 near distress.
• Using βD > 0 gives lower levered betas.

What is the adjusted (Blume) beta formula?

ANSWER: Adjusted β = 1 + 2/3 × (raw β − 1)
• Pulls raw regression betas towards 1 because betas mean-revert over time.

How do you compute the beta for a private company?

ANSWER: 1) select listed peers 2) regress raw betas, adjust 3) unlever each with Hamada (own D/E) 4) average asset beta 5) relever with sector D/E
• Same procedure is often used for listed firms too (more stable than own beta).

What are the issues in estimating beta?

ANSWER: Very sensitive to outliers; choice of market index (Roll's critique); time interval/horizon; thin trading; low R²; peer choice; gross vs net debt; which Hamada; capital structure choice
• Exam Q EXAM1 6a: name two, about the estimation procedure (not CAPM theory).

Why do practitioners use sector averages in the WACC?

ANSWER: The WACC discounts FCF over 10–20 years and in the long run profitability and capital structure revert to the sector average
• Also company-specific betas are noisy.
• Exam Q EXAM1 6b.

What is the build-up model for the cost of equity?

ANSWER: E(ri) = rf + β × MRP + CRP + SSP
• CAPM plus country risk premium and small size premium.
• Know by heart.

What is the risk-free rate and how do you choose it?

ANSWER: YTM of a 10Y Treasury of a developed country (US or German Bund)
• Match currency of the cash flows and duration of equity cash flows (10–15y).
• Mostly driven by LT inflation expectations (2–3%).
• Compensation for inflation + opportunity cost.

What is the market risk premium (MRP) and its current level?

ANSWER: MRP = E(rM) − rf; today ≈ 6–8%, peak ≈ 6.5% (KPMG survey)
• Expected excess return of the market over the risk-free rate; forward-looking concept but estimated from history/surveys.

What are the issues in estimating the MRP?

ANSWER: Forward-looking but estimated from history; which period; arithmetic vs geometric average (geometric always lower); local vs global investor
• Standard practice: long-term period.

What is the country risk premium (CRP)?

ANSWER: Extra premium for investing in riskier countries: legal, regulatory, currency, sovereign default risk
• Proxied by sovereign CDS spreads.
• Use when risk can't be diversified, investors aren't global, or it's not in the cash flows.

What are the 3 ways to include the CRP?

ANSWER: 1) local 10Y treasury yield (or Bund/UST + country CDS) 2) add CDS to the MRP 3) both
• CRP appears in both cost of equity and cost of debt formulas.

What is the size premium (SSP)?

ANSWER: Extra return small firms earn above CAPM (Ibbotson)
• CAPM can't explain small-cap returns.
• Reflects higher business risk, illiquidity and idiosyncratic risk.

What are typical Ibbotson size premia?

ANSWER: Mid-cap ~1.1%, low-cap ~1.9%, micro-cap ~3.8%, smallest decile ~6%, tiniest (<$96m) ~11.7%
• Largest decile slightly negative (−0.4%).

What is the BDO small firm premium model?

ANSWER: Score-based premium model incl. idiosyncratic factors
• Factors chosen ad hoc ('what works'), but transparent and includes idiosyncratic risk — unlike CAPM beta.

What is the implied cost of equity?

ANSWER: rE ≈ 1/PE (if ROE = rE)
• Large firms PE 10–20 → 5–10%; small firms PE ≈ 5 → ~20%.
• That 20% cannot come from CAPM → argument for size premium.

What are the 4 ways to estimate the cost of equity?

ANSWER: 1) historical average returns 2) CAPM 3) empirical factor models (Fama-French, APT) 4) implied cost of equity (1/PE, dividend yield)
• Exam Q (EXAM4 Q7a).

What are the empirical problems of CAPM?

ANSWER: Market portfolio unobservable (Roll's critique); betas don't explain cross-sectional variation in future returns
• Plus strong assumptions: homogeneous expectations, everyone diversified, no transaction costs, unlimited borrowing.

What range of cost of equity does CAPM typically give?

ANSWER: ≈ 5–15% (rf 3–4%, β 0.5–1.5, MRP 5–6%)
• Too low for micro caps (~20% realized/implied) → size premium needed.

What is the strength/weakness of the Fama-French model?

ANSWER: Explains realized returns well, but hardly predicts future excess returns
• Same problem as CAPM: parameters estimated from 2–5 years of history.

What is the Shiller CAPE?

ANSWER: Price / average inflation-adjusted earnings of the past 10 years
• 1/CAPE tracks the average required return on equity (implied measure).

How is risk included in a DCF (formally vs in practice)?

ANSWER: Formally only via the WACC (systematic risk). In practice also by lowering expected FCF, adding a distress premium, and pricing idiosyncratic risk
• Exam Q EXAM1 7b.