Cost of equity and the CAPM
The cost of equity is the return shareholders demand to invest in a company's stock. It is not observable directly (unlike the cost of debt, which you can see in bond yields). You must estimate it using a model. The Capital Asset Pricing Model (CAPM) is the most widely used framework, though not the only one.
CAPM says that the cost of equity depends on three things: the risk-free rate, the market risk premium, and the company's beta (a measure of how risky the company is relative to the overall market). The formula is clean, but the inputs require judgment and estimation.
Quick definition
The Capital Asset Pricing Model (CAPM) estimates the cost of equity as:
Re = Rf + β × (Rm - Rf)
Where:
Rf = Risk-free rate (10-year Treasury yield)
β = Beta (systematic risk relative to the market)
Rm - Rf = Market risk premium (historical average excess return of stocks over bonds)
Key takeaways
- CAPM says that only systematic risk (market-wide risk) is compensated. Unsystematic risk (company-specific risk) is diversified away.
- Beta measures systematic risk: a beta of 1.0 means the company moves with the market. A beta of 2.0 means it is twice as volatile as the market.
- The market risk premium is the average excess return of the stock market above the risk-free rate, historically around 5–6% in the US.
- Small changes in estimated beta can shift the cost of equity significantly. A beta of 1.0 gives 4% + 5.5% = 9.5%. A beta of 1.3 gives 4% + 7.15% = 11.15%.
- CAPM is elegant but imperfect. It assumes rational investors, no taxes, and low transaction costs—assumptions the real world violates. Despite its flaws, it remains the standard.
- For a stable, diversified company, CAPM estimates can be reliable. For startups, cyclicals, or companies with changing risk profiles, CAPM estimates are very rough.
- The cost of equity is a key input in WACC (the discount rate for DCF). Getting it wrong cascades into valuation errors.
The three inputs: Rf, β, and (Rm - Rf)
1. Risk-free rate (Rf)
The risk-free rate is the return on a zero-default-risk investment, typically a US government bond.
Which maturity? Use the 10-year Treasury yield for most companies, since DCF cash flows are spread over 10+ years. For very short-term projects, use the 2-year or 5-year Treasury. For perpetual-growth companies (utilities, real estate investment trusts), some analysts use the 20-year or 30-year Treasury.
Current rates (2026): The 10-year Treasury yield is roughly 3.5–4.5%, depending on the time of year and market conditions.
Do not use the current risk-free rate if you are valuing a company in a historical scenario (e.g., valuing Amazon in 2010 for a case study). Use the risk-free rate as of 2010.
2. Beta (β)
Beta measures how much a company's stock moves relative to the overall market. It is calculated as:
β = Covariance(Stock Return, Market Return) / Variance(Market Return)
In plain English: if the market goes up 10%, does the stock go up 10% (β=1), or 15% (β=1.5), or 7% (β=0.7)?
Interpreting beta:
- β = 1.0 → The stock moves with the market. Zero excess volatility.
- β < 1.0 → The stock is less volatile than the market (defensive). Utilities, consumer staples, healthcare often have β < 1.
- β > 1.0 → The stock is more volatile than the market (aggressive). Small-cap stocks, growth stocks, biotech often have β > 1.5.
- β = 0 → The stock does not move with the market (rare; would be perfectly uncorrelated).
- β < 0 → The stock moves opposite the market (extremely rare; would be a perfect hedge).
Where to find beta:
- Financial websites (Yahoo Finance, Bloomberg, SEC Edgar)
- Regression analysis (regress the stock's returns against the market's returns over 3–5 years)
- Industry averages (if the company's own beta is not available, use the median beta of peer companies)
Example betas (approximate, as of 2026):
- Apple: 1.2 (slightly more volatile than market)
- Microsoft: 0.95 (slightly less volatile)
- Tesla: 1.8 (much more volatile)
- Duke Energy: 0.6 (much less volatile, defensive utility)
- A biotech startup: 2.0–3.0 (very volatile, unproven business model)
3. Market risk premium (Rm - Rf)
The market risk premium is the average excess return of the stock market above the risk-free rate. Historically, this has been about 5–6% in the US, though estimates vary depending on the time period and methodology.
The market risk premium is not the expected return of the stock market. The expected return is Rf + Market risk premium. If the risk-free rate is 4% and the market risk premium is 5.5%, then the expected return of the stock market is 4% + 5.5% = 9.5%.
Why is there a market risk premium? Because stocks are riskier than bonds. The stock market is volatile; bond prices are more stable. Investors demand additional compensation (higher expected return) for taking on that volatility.
Different sources use different estimates:
- Historical average (since 1926): ~5–6%
- Forward-looking (based on dividend yields and growth expectations): ~4.5–5.5%
- Damodaran's estimate (updated frequently): varies, but typically 5–6%
For a beginner, using 5–5.5% is standard.
Putting it together: a full CAPM calculation
Example 1: Microsoft
Assumptions:
- Risk-free rate (Rf): 4.0%
- Beta (β): 0.95
- Market risk premium (Rm - Rf): 5.5%
Calculation:
Re = 4.0% + 0.95 × 5.5% = 4.0% + 5.225% = 9.225%
Microsoft shareholders demand a 9.225% return (according to CAPM).
Example 2: Duke Energy (utility)
Assumptions:
- Risk-free rate (Rf): 4.0%
- Beta (β): 0.65
- Market risk premium (Rm - Rf): 5.5%
Calculation:
Re = 4.0% + 0.65 × 5.5% = 4.0% + 3.575% = 7.575%
Duke Energy shareholders demand a 7.575% return. Lower than Microsoft, because Duke is less volatile (lower beta).
Example 3: A biotech startup
Assumptions:
- Risk-free rate (Rf): 4.0%
- Beta (β): 2.2
- Market risk premium (Rm - Rf): 5.5%
Calculation:
Re = 4.0% + 2.2 × 5.5% = 4.0% + 12.1% = 16.1%
The biotech startup shareholders demand a 16.1% return. Much higher, reflecting the high risk and volatility.
Beta: deep dive
Beta is the most slippery input in CAPM. It is empirical (you calculate it from historical data), but the historical period matters. A 2-year regression versus a 5-year regression gives different betas. And historical beta does not guarantee future beta.
How to estimate beta
Method 1: Use published beta (from Yahoo Finance, Bloomberg, etc.)
This is fastest. Most financial websites publish a company's beta, usually calculated from 1–3 years of daily or weekly returns versus the S&P 500.
Caveat: Published betas differ across sources because of different regression periods and methodologies.
Method 2: Calculate beta yourself
Regress the stock's historical returns (Y-axis) against the market's historical returns (X-axis):
Stock Return = α + β × Market Return + ε
The slope (β) is your estimate. Use 2–5 years of data. Daily or weekly returns reduce noise from short-term volatility.
Example: If you regress Tesla's returns against S&P 500 returns from 2021–2026, you might get β = 1.8. This means Tesla historically moved 1.8× as much as the market.
Method 3: Use industry average beta
If the company is too small to have reliable published beta, use the median or average beta of comparable companies in the same industry.
Example: If a small robotics company has no published beta, look at Boston Dynamics, Tesla, and other robotics firms. Use their average beta (adjusted for leverage differences, if significant).
Beta adjustments
Published betas and calculated betas are levered betas—they reflect the company's current capital structure (debt and equity mix).
If you want to estimate beta for a company with a different capital structure (e.g., you are projecting what beta would be if it took on more debt), you can:
-
Unlever the beta (remove the effect of debt):
βu = βL / [1 + (1 - T) × (D/E)] -
Relever the beta (apply new debt):
βL = βu × [1 + (1 - T) × (D/E)]
For example, if a company's levered beta is 1.2, debt-to-equity is 0.5, and tax rate is 21%:
βu = 1.2 / [1 + (1 - 0.21) × 0.5] = 1.2 / 1.395 = 0.86
If the company then takes on more debt and raises debt-to-equity to 1.0:
βL = 0.86 × [1 + (1 - 0.21) × 1.0] = 0.86 × 1.79 = 1.54
Higher leverage increases beta, increasing the cost of equity.
Beta limitations
Beta is imperfect for several reasons:
-
It measures only systematic risk — CAPM assumes unsystematic risk (company-specific) is diversified away. But many stock investors are not fully diversified. A single-stock investor cares about total volatility, not just beta.
-
History is not predictive — A company's past beta does not guarantee its future beta. A company that went through a business transformation may have different risk going forward.
-
Beta changes with leverage — As a company's debt changes, its beta changes. This is often not reflected in historical beta.
-
Beta assumes linear relationship — The market may go up 10% in a year, and a stock might go up 15% (β=1.5). But what if the market crashes 20%? The stock might crash 35% or 25%, depending on non-linearities. Beta assumes the relationship is constant.
-
Small-cap and illiquid stocks have estimation error — The smaller the company, the more noise in the regression, and the less reliable the beta estimate.
Sensitivity of cost of equity to beta
Because cost of equity is a key input in WACC, small errors in beta can swing your valuation:
Example: A company with assumptions:
- Rf = 4%
- Market risk premium = 5.5%
If β = 1.0: Re = 4% + 5.5% = 9.5%
If β = 1.2: Re = 4% + 6.6% = 10.6%
If β = 0.8: Re = 4% + 4.4% = 8.4%
A 0.2 difference in beta (1.0 vs 1.2) changes the cost of equity by 1.1 percentage points, which cascades into WACC and then into DCF value. For a perpetuity (terminal value), a 1% change in discount rate swings the value by 20–30%.
This is why sensitivity analysis is critical: always show how valuation changes across a range of betas.
Alternatives to CAPM
CAPM is standard, but other models exist:
-
Three-factor model (Fama-French) — Adds factors for size (small-cap premium) and value (value-stock premium) beyond just beta. More complex but sometimes more accurate.
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Multi-factor model — Adds additional factors like momentum, quality, or dividend yield. Used by sophisticated institutions.
-
Build-up method — For private companies or startups, add risk premiums to the risk-free rate for specific risks (business risk, leverage risk, size risk, illiquidity risk).
For beginners and most professionals, CAPM is sufficient. If you are valuing a small, illiquid, or unproven company, a build-up method (adding 3–5% premiums) might be more intuitive than trying to estimate a reliable beta.
FAQ
Q: What if I think the company's beta will change in the future?
A: You can use a time-varying WACC. For example, if a startup becomes stable and profitable (lowering risk), you might use a higher beta (higher cost of equity) in years 1–5 and a lower beta in year 10. However, for simplicity, most models use constant WACC throughout.
Q: Should I use the beta from the company's website, or calculate my own?
A: Use a reliable published source (Yahoo Finance, Bloomberg, FactSet, your brokerage). If you want to verify, calculate it yourself. But published beta from major sources is usually sufficient.
Q: What if the market risk premium is different from 5.5%?
A: Sensitivity-test it. Show valuation at market risk premiums of 4.5%, 5.0%, 5.5%, 6.0%, and 6.5%. This will expose how much your answer depends on the market risk premium assumption.
Q: Is CAPM used in practice by real investors?
A: Yes, widely. Buy-side analysts, sell-side equity research, and corporate finance teams all use CAPM to estimate cost of equity. It is not perfect, but it is standard.
Q: What is alpha in CAPM?
A: In the regression Stock Return = α + β × Market Return + ε, alpha is the intercept—the stock's excess return not explained by market movements. For a stock that keeps up with the market, α ≈ 0. For a star manager's portfolio, α > 0 (outperformance). CAPM assumes α = 0 for all stocks on average. Alpha is important in portfolio management but not directly used in DCF valuation.
Q: Why doesn't CAPM account for the risk that the company goes bankrupt?
A: It does, indirectly. A company with high bankruptcy risk has high beta (volatile stock price) and high cost of debt. Both raise WACC. CAPM is a simplified model; it does not explicitly model default probability. For companies with material default risk, some analysts add a default premium on top of CAPM.
Related concepts
- Systematic risk — Market-wide risk (economic growth, interest rates, inflation). Reflected in beta.
- Unsystematic risk — Company-specific risk (management, product, competition). Assumed diversified away in CAPM.
- Cost of equity — The return shareholders demand; estimated via CAPM.
- WACC — Blended cost of equity and debt; used as the discount rate in DCF.
- Leverage — High debt increases beta (financial risk), increasing the cost of equity.
Summary
CAPM is the standard model for estimating cost of equity: Re = Rf + β × (Rm - Rf). It is clean, mathematically elegant, and widely used. The three inputs (risk-free rate, beta, market risk premium) are all estimable from market data, though with varying degrees of precision.
The biggest risks are overconfidence in beta (especially for small or volatile companies) and anchoring to a "standard" market risk premium without updating it. Always sensitivity-test both beta and market risk premium to see how much your DCF value depends on these assumptions.
Cost of equity is the foundation for WACC, which is the discount rate for DCF. Get it roughly right, and your valuation will be reasonable. Get it badly wrong (e.g., using 5% WACC for a startup or 15% WACC for a utility), and your valuation will be nonsense.
In the next chapter (after we complete the DCF foundation articles), we will move on to cost of debt and the after-tax adjustment—how to estimate the cost of debt from bond yields and credit ratings, and why the tax deduction on interest matters.
Next
Cost of debt and the after-tax adjustment
Authority: CFA Institute (CAPM and cost of capital), Eugene Fama and Kenneth French (factor models), Aswath Damodaran (valuation methodologies and beta estimation).