EFN507 Chap.7 Estimating the Cost of Equity with the CAPM
Estimating the Cost of Equity with the CAPM
From beta to a required return
Week 5 prices risk with the CAPM: a required return equals the risk-free rate plus beta times the market risk premium, for the firm, its debt and its equity alike.
Because betas are value weighted, the beta of a firm's assets is a blend of its debt and equity betas, which is why equity beta rises with leverage.
Estimating it in practice
The Week 5 tutorial builds a full estimate for a listed company: choose comparable firms, compute returns from prices, dividends and share splits, estimate beta, choose a long-horizon risk-free rate and a premium, and judge whether the resulting WACC is believable.
The formula sheet supplies the levering and unlevering formulas with a debt beta and tax, and the Scholes and Williams adjustment for thinly traded shares. Textbook problems add standard errors, confidence intervals and the case for using an industry beta.
What this chapter covers
- 01
The CAPM for debt, equity and the whole firm
- 02
Asset beta as a value-weighted blend
- 03
Unlevering a comparable firm and relevering for the project
- 04
Choosing the risk-free rate and the market risk premium
- 05
Standard errors, industry betas and thin trading
- 06
Survey evidence on how Australian firms apply the CAPM
Worked example · free
Relevering a comparable firm's beta
- +1Unlever: (1.30 + 0.10 × 0.7 × 0.5) ÷ (1 + 0.7 × 0.5) = 0.989.
- +1Relever: 0.989 × (1 + 0.7 × 0.25) − 0.10 × 0.7 × 0.25 = 1.144.
- +1Cost of equity: 4% + 1.144 × 6% = 10.87%.
- +1WACC: 0.20 × 5.5% × 0.7 + 0.80 × 10.87% = 9.46%.
Key terms
- Capital asset pricing model
- The model in which a required return equals the risk-free rate plus beta times the market risk premium.
- Market risk premium
- The expected return on the market portfolio in excess of the risk-free rate.
- Equity beta
- The sensitivity of a share's return to the market return, which includes the effect of the firm's borrowing.
- Scholes and Williams beta
- A beta adjusted for infrequent trading by combining lagged, same-period and leading estimates.
Estimating the Cost of Equity with the CAPM FAQ
Why not use a comparable firm's equity beta directly?
Its equity beta reflects its own borrowing as well as its business risk. Unlevering removes the comparable's financing, and relevering at your project's ratio adds back the right amount; skipping both steps misprices your project whenever the debt ratios differ.
Which risk-free rate should a long-lived project use?
A long-horizon government bond yield that matches the timing of the project's cash flows. A short-term bill rate describes a one-period investment. Measure the market risk premium against the same kind of security for consistency.
How large is the market risk premium?
There is no single agreed figure; the tutorial answers call the value open to debate. Survey evidence reviewed in the unit shows Australian firms most often use a premium of around 6%, so any other choice should be explained.
What should I do if a firm's own beta has a large standard error?
Treat the estimate with caution. A 95% confidence interval spans about two standard errors either side, often wide enough to include the industry average, and an industry beta averaged over many firms is usually the more reliable input.
Why adjust beta for thin trading?
Shares that trade infrequently respond to market news late, so a same-period regression understates their beta. The Scholes and Williams adjustment adds betas estimated on the previous and next period's market returns and scales for market autocorrelation.
Does the debt beta really matter?
It matters when leverage is high. Assuming zero is a common simplification, but a positive debt beta lowers the asset beta you infer from a levered equity beta. The tutorial answers report results both ways, so state your assumption.
Exam move
Unlever and relever three comparables, average their asset betas, and build a WACC with a stated risk-free rate and premium. Check every relevering by reversing it to recover the original beta.
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