Cost of Capitalintermediate

Cost of Equity and the CAPM

The cost of common equity $k_e$ is the return shareholders demand, and it is the hardest WACC input to pin down because equity holders are residual claimants with no promised payment. The standard estimate is the capital asset pricing model (CAPM), which prices only systematic risk. A stock’s required return equals the risk-free rate $k_{rf}$ plus its beta times the equity risk premium $(k_m - k_{rf})$ . Beta measures sensitivity to the market, so high-beta stocks demand a larger premium. The same equation traces the security market line.

Try it yourself

CAPM & the Security Market Line

The CAPM prices an asset by its systematic risk β: E(R_i) = R_f + β_i·(E(R_m) − R_f). Plotted against β this is the Security Market Line, from R_f at β = 0 through the market at β = 1. An asset above the line is under-valued and one below it is over-valued. The gap is its alpha.

CAPM required return at β = 1.109.6%

Market risk premium E(R_m) − R_f 6.0%

Risk-free rate R_f3.0%

Market return E(R_m)9.0%

Asset beta β1.10

Show actual expected return (reveals alpha)

Try this

At β = 1.10 the CAPM requires 9.6%: the risk-free 3.0% plus β times the 6.0% market risk premium. Tick the box above to compare an actual return and read off alpha.

SML vs CML. This is the SML: it uses β and prices every asset, fairly priced or not. The CML uses total risk σ and applies only to efficient portfolios. Same market point, different risk axis.

Discuss: if a stock plots above the SML, what should buying pressure do to its price, and where does the point move as it re-prices?

Why it matters

Investors hold diversified portfolios, so firm-specific shocks wash out and only market-wide risk is left to be rewarded. Beta captures exactly that exposure. A beta of one means the stock moves with the market, a beta above one means it amplifies market swings and so deserves a higher return. In the idealised CAPM world alpha is zero, so the cost of equity rests entirely on the risk-free rate, beta and the market premium. In practice many analysts blend CAPM with a Fama-French or dividend-growth estimate, as the Champion Energy example illustrates.

Formulas

CAPM cost of equity

k_e = k_{rf} + \beta_e\,(k_m - k_{rf})

Here

k_{rf}

is the risk-free rate,

\beta_e

the equity (levered) beta and

(k_m - k_{rf})

the equity risk premium. In the idealised model alpha is zero, so systematic risk alone drives the required return.

Beta from regression

\beta_e = \dfrac{\mathrm{Cov}(R_i,\,R_m)}{\mathrm{Var}(R_m)}

Estimated by regressing the firm’s excess returns on the market’s excess returns, typically using several years of weekly or monthly data to smooth out short-run noise.

Worked examples

Scenario

A large-cap stock has a beta of 1.10. The risk-free rate is 2.5 percent and the equity risk premium is 5.5 percent. Estimate the cost of equity using the CAPM.

Solution

Substitute into the CAPM. $k_e = 2.5\% + 1.10 \times 5.5\% = 2.5\% + 6.05\% = 8.55\%$ . The 6.05 percent above the risk-free rate is the reward for the stock’s systematic risk. A purely firm-specific risk, such as a single lawsuit, would not raise this number, because a diversified investor can offset it.

Common mistakes

✗CAPM rewards total risk. It prices only systematic, non-diversifiable risk through beta. Firm-specific risk earns no premium because diversification removes it.
✗Beta is a fixed property of a stock. It is an estimate from past returns, sensitive to the return frequency and the look-back window, and the past is an imperfect guide to the future.
✗The risk-free rate and the equity risk premium are the same thing. The risk-free rate is the base return on a safe asset. The equity risk premium is the extra return the whole market demands above it.
✗CAPM is the final word on the cost of equity. Empirical studies find beta explains future returns weakly, which is why analysts add a size premium or use Fama-French and DCF estimates alongside it.

Revision bullets

•Cost of equity is the hardest WACC input, since equity holders are residual claimants
•CAPM: $k_e$ equals risk-free rate plus beta times the equity risk premium
•Only systematic risk is priced, beta measures it, alpha is zero in the ideal model
•Beta comes from regressing excess stock returns on excess market returns
•Beta is unstable, so use a multi-year window and read it with caution
•In practice blend CAPM with Fama-French and dividend-growth estimates

Quick check

According to the CAPM, the cost of equity for a stock with a beta of 0.8, a risk-free rate of 3 percent and an equity risk premium of 6 percent is

In the CAPM, firm-specific (nonsystematic) risk earns no risk premium because

Connected topics

WACC Cost of Debt Levered Beta Risk Premiums Pure-Play Method

Sources

Titman & Martin
Titman, S. & Martin, J. D. Valuation: The Art and Science of Corporate Investment Decisions. Pearson.
Chapter on the cost of common equity. The CAPM, the systematic versus nonsystematic split and the Apple worked example follow this text.
Sharpe (1964); Lintner (1965)
Sharpe, W. F. "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk." Journal of Finance, 19(3), 1964, pp. 425-442; Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. Review of Economics and Statistics, 47(1), 13-37.
Original derivation of the capital asset pricing model and the security market line.
Banz (1981)
Banz, R. W. "The Relationship Between Return and Market Value of Common Stocks." Journal of Financial Economics, 9(1), 1981, pp. 3-18.
Documents the size premium that motivates adding a small-firm adjustment to a CAPM cost of equity.

How to cite this page

Dr. Phil's Quant Lab. (2026). Cost of Equity and the CAPM. Derivatives Atlas. https://phucnguyenvan.com/concept/sabv-cost-of-equity-capm

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