Cost of Equity and CAPM
The cost of equity is the return that equity investors require to compensate them for the risk of owning a stock. Unlike debt—which has a stated interest rate and legal claims—equity returns are uncertain and depend on the company's actual performance. The Capital Asset Pricing Model (CAPM) is the standard framework for estimating cost of equity, linking it to three observable or estimable inputs: the risk-free rate, the market risk premium, and the company's beta. Despite CAPM's simplicity and wide acceptance, its inputs require careful thought, and small errors cascade into material valuation errors. Understanding CAPM's strengths, limitations, and how to defend your assumptions is essential for credible DCF analysis.
Quick definition
The Capital Asset Pricing Model (CAPM) calculates the required return on equity as:
Cost of Equity (Re) = Risk-Free Rate + Beta × (Market Risk Premium)
Re = Rf + β × (Rm - Rf)
Where:
- Rf = Risk-free rate (typically 10-year government bond yield)
- β (beta) = Stock's sensitivity to market movements (volatility relative to the market)
- (Rm - Rf) = Market risk premium (historical average market return minus risk-free rate)
Key takeaways
- CAPM estimates cost of equity by adding a risk premium to the risk-free rate, scaled by the company's beta
- Beta measures systematic risk (market-related volatility); companies with high beta are riskier and require higher returns
- The market risk premium is typically 4–6% in historical data but estimates vary widely and are hotly debated
- Cost of equity is the numerator of DCF valuation; errors here propagate through WACC and terminal value
- For private companies, use comparable public company betas, then adjust upward 1–3% for illiquidity risk
- Sensitivity analysis on cost of equity is mandatory; a 1% change creates 10–20% valuation swings
The CAPM formula broken down
The risk-free rate (Rf)
The risk-free rate represents the return available on a zero-risk investment, typically the yield on a government bond. In the U.S., this is commonly the 10-year Treasury yield because it matches a long-term investment horizon.
Why 10-year Treasury?
- A DCF analysis often projects 5–10+ years; a 10-year Treasury maturity aligns with that horizon
- The 10-year rate is sufficiently liquid and observable to avoid ambiguity
- Shorter-duration rates (2-year Treasury) are too influenced by near-term monetary policy
- Longer-duration rates (30-year Treasury) are less liquid and more volatile
Current state (May 2026): Assume a 10-year Treasury yield of approximately 4.0–4.5%. This varies with interest rate expectations and is the starting point for any CAPM calculation.
Risk-free rate for different economies:
- U.S.: 10-year Treasury yield
- Eurozone: German Bund yield (Bundesanleihe)
- UK: 10-year Gilt yield
- Emerging markets: Local government bond yield + country risk premium
Beta (β): Systematic risk
Beta measures how a stock's returns move relative to the overall market. It quantifies systematic risk—the risk that cannot be diversified away.
Beta interpretation:
β = 1.0: Stock moves in line with market (if market is up 10%, stock up 10%)
β > 1.0: Stock is more volatile than market (amplifies market movements)
β < 1.0: Stock is less volatile than market (dampens market movements)
β = 0.5: Stock is half as volatile as market
β = 2.0: Stock is twice as volatile as market
Examples by industry:
- Utilities: β ≈ 0.6–0.8 (stable, low-volatility businesses)
- Consumer staples: β ≈ 0.7–0.9 (defensive, counter-cyclical)
- Financials: β ≈ 1.0–1.3 (tied to economic cycles)
- Technology/Growth: β ≈ 1.3–1.8 (volatile, high-growth)
- Biotech: β ≈ 1.5–2.0+ (high clinical and regulatory risk)
Calculating beta from historical data:
Beta is typically estimated by running a regression of the stock's returns against market returns over 3–5 years:
β = Covariance(Stock Returns, Market Returns) / Variance(Market Returns)
Most analysts use Bloomberg, FactSet, or similar services to access pre-calculated betas rather than computing from scratch.
Levered vs. unlevered beta:
When calculating WACC, you'll encounter two versions:
- Levered beta: Reflects the company's actual leverage and equity risk
- Unlevered (asset) beta: Removes the effect of financial leverage, representing business risk only
For a company with debt, levered beta > unlevered beta because equity investors bear more risk.
To unlever beta:
Unlevered β = Levered β / [1 + (1 - Tax Rate) × (Debt / Equity)]
To relever beta (adjusting for a different capital structure):
Relevered β = Unlevered β × [1 + (1 - Tax Rate) × (Debt / Equity)]
Example:
A company has levered beta of 1.2, debt of $500M, equity of $2,000M, and a 21% tax rate.
Unlevered β = 1.2 / [1 + (0.79 × $500M / $2,000M)]
Unlevered β = 1.2 / [1 + 0.1975]
Unlevered β = 1.2 / 1.1975
Unlevered β = 1.002 ≈ 1.0
The business itself (unlevered) has roughly market-average risk; the debt amplifies equity volatility.
Market risk premium (Rm - Rf)
The market risk premium is the additional return investors demand for holding risky stocks versus risk-free bonds. Theoretically, it's the expected return on the market minus the risk-free rate going forward. In practice, analysts use historical averages.
Historical data:
U.S. equity market returns have averaged approximately 10% nominally over the past 100 years, and real returns (inflation-adjusted) about 7%. With a risk-free rate of 4%, this implies a 6% market risk premium.
However, estimates vary widely:
- Damodaran (NYU): 5.5–6.5% (uses long-term historical data)
- Ibbotson (academic consensus): 5.0–6.0% (updated annually)
- Dimson et al. (Triumph of the Optimists): 3.5–4.5% for developed markets (uses global data)
- Forward-looking surveys: 4.0–5.5% (analyst expectations, not historical)
Why estimates diverge:
- Historical periods vary (past 20 years vs. past 100 years produce different averages)
- Different starting assumptions (real vs. nominal returns; with vs. without dividends)
- Structural changes in the economy and market (is historical equity risk premium still valid?)
- Forward-looking vs. historical (what will markets return going forward, not what they returned?)
Best practice:
Use a 5–6% market risk premium for most U.S. companies, unless you have strong conviction that forward-looking risk premiums have shifted. For sensitivity, run scenarios with 4.5% and 6.5% premiums to see the range.
Calculating cost of equity: worked examples
Example 1: Mature industrial company
Inputs:
- Risk-free rate: 4.0%
- Beta: 1.1 (slightly riskier than market)
- Market risk premium: 5.5%
Cost of Equity = 4.0% + 1.1 × 5.5%
Cost of Equity = 4.0% + 6.05%
Cost of Equity = 10.05% ≈ 10%
Example 2: Defensive utility company
Inputs:
- Risk-free rate: 4.0%
- Beta: 0.7 (less risky than market)
- Market risk premium: 5.5%
Cost of Equity = 4.0% + 0.7 × 5.5%
Cost of Equity = 4.0% + 3.85%
Cost of Equity = 7.85% ≈ 7.9%
Example 3: High-growth technology company
Inputs:
- Risk-free rate: 4.0%
- Beta: 1.5 (more volatile than market)
- Market risk premium: 5.5%
Cost of Equity = 4.0% + 1.5 × 5.5%
Cost of Equity = 4.0% + 8.25%
Cost of Equity = 12.25% ≈ 12.3%
Estimating beta for private companies
Private companies have no stock price, so beta must be estimated. The standard approach is to use comparable public company betas, then adjust for size and illiquidity.
Step 1: Identify comparable public companies
Find 3–5 public companies in the same industry with similar business models and scale.
Step 2: Collect levered betas
Pull levered betas for each comparable from a database (Bloomberg, Yahoo Finance, company investor relations materials).
Step 3: Unlever and relever
Unlever the comparables' betas (remove their specific leverage), then relever using the private company's target capital structure.
Step 4: Adjust for size and illiquidity
Private companies typically face higher risk due to:
- Size risk: Smaller companies are riskier (1–2% premium)
- Illiquidity risk: Cannot easily sell shares (1–3% premium)
Add 1–3% to the cost of equity calculation to reflect these risks.
Example:
Three comparable public software companies have levered betas of 1.4, 1.5, and 1.3 (average 1.4). Their average D/E ratio is 0.1 (minimal debt). Unlever this beta:
Unlevered β = 1.4 / [1 + (0.79 × 0.1)] = 1.4 / 1.079 = 1.30
For the private company with target D/E of 0.2:
Relevered β = 1.30 × [1 + (0.79 × 0.2)] = 1.30 × 1.158 = 1.51
Base cost of equity (4% RF + 1.51 × 5.5% MRP) = 12.3%. Add 2% illiquidity premium = 14.3% cost of equity.
Sensitivity analysis on cost of equity
Cost of equity directly impacts WACC and enterprise value. A 1% swing in cost of equity creates 10–20% valuation swings.
Sensitivity table: Impact on enterprise value
Assume a company with 80% equity, 20% debt, 21% tax rate, 4% cost of debt, 4% risk-free rate, 5.5% market risk premium:
Beta | Cost of Equity | WACC | Enterprise Value (assuming stable cash flows)
0.8 | 8.4% | 6.95% | Base × 1.20
1.0 | 9.5% | 7.85% | Base × 1.08
1.2 | 10.6% | 8.74% | Base × 0.98
1.4 | 11.7% | 9.63% | Base × 0.90
A 0.4-point beta swing (from 1.0 to 1.4) reduces enterprise value by approximately 8–10%.
Common CAPM mistakes
Using current market risk premiums instead of long-term historical averages. In bull markets, investors are complacent and the implied equity risk premium drops (market expects only 3–4% excess returns). In bear markets, risk premiums spike to 8–10%. Use long-term averages (5–6%) unless you have explicit forward-looking conviction.
Failing to adjust beta for leverage changes. If a company was acquired with significant debt, its levered beta might spike from 1.0 to 1.8. Unlevering and relevering ensures you're using a beta appropriate to the company's target capital structure, not a temporary distortion.
Using 1-year beta instead of 3–5 year beta. One year of returns is too noisy. A single bad quarter might spike beta artificially. Use 3–5 year estimates to smooth volatility.
Neglecting industry-specific betas for conglomerates. A company with both low-beta utilities and high-beta venture capital should use weighted-average betas by segment, not a blended corporate beta.
Applying the same market risk premium to all companies and regions. Different markets have different risk profiles. Emerging market equity risk premiums might be 8–10%, while developed markets are 5–6%. Adjust MRP by geography and company risk profile.
Building CAPM into WACC
Once cost of equity is calculated via CAPM, it plugs directly into WACC:
WACC = (E/V × Re) + (D/V × Rd × (1 - Tc))
Where Re is the CAPM-derived cost of equity.
Full example:
- Market cap: $2,000M (E)
- Debt: $500M (D)
- Total capital: $2,500M (V)
- Levered beta: 1.2
- Risk-free rate: 4.0%
- Market risk premium: 5.5%
- Cost of debt: 4.5%
- Tax rate: 21%
Step 1: Cost of equity via CAPM
Re = 4.0% + 1.2 × 5.5% = 4.0% + 6.6% = 10.6%
Step 2: After-tax cost of debt
Rd(1 - Tc) = 4.5% × (1 - 0.21) = 3.555%
Step 3: WACC
WACC = (2000/2500 × 10.6%) + (500/2500 × 3.555%)
WACC = (0.80 × 10.6%) + (0.20 × 3.555%)
WACC = 8.48% + 0.711%
WACC = 9.19%
This 9.2% WACC then serves as the discount rate for all DCF cash flows.
Real-world examples
Pharmaceutical company: Rf 4%, β 1.0, MRP 5.5% → Re = 9.5%. Moderate risk (stable cash flows, regulatory risk).
Biotech startup: Rf 4%, β 1.8, MRP 5.5% → Re = 13.9%. High risk (clinical trials, binary outcomes, no approved products).
Regulated utility: Rf 4%, β 0.6, MRP 5.5% → Re = 7.3%. Low risk (predictable cash flows, regulatory stability).
Emerging market retailer: Rf 4%, β 1.3 (local), MRP 7.0% (country premium) → Re = 4% + 1.3 × 7% = 13.1%. Higher risk due to country and currency risk.
FAQ
Q: Why is the risk-free rate the 10-year Treasury and not shorter or longer?
A: The 10-year Treasury matches the typical DCF horizon and is a good proxy for the long-term cost of capital. Shorter rates (2-year) are too influenced by near-term Fed policy. Longer rates (30-year) are less liquid and more volatile.
Q: Can beta be negative?
A: Theoretically yes, if a stock moves opposite the market (counter-cyclical). In practice, negative betas are extremely rare and signal either a data error or a structural hedge (like an inverse ETF).
Q: How do I know if my beta estimate is reasonable?
A: Compare to peer companies in the same industry. If your company's beta is 2.0 and competitors are all 1.0–1.2, investigate why (higher leverage? more volatile business model?). Outlier betas require explanation.
Q: Should I adjust CAPM for company-specific risk?
A: No. CAPM captures only systematic (market) risk via beta. Unsystematic (company-specific) risk is diversifiable and should not affect required return. However, for private companies, you add an illiquidity premium outside CAPM.
Q: What if I don't believe the current market risk premium?
A: Use sensitivity analysis. Run scenarios with 4.5%, 5.5%, and 6.5% MRP, and show how valuation changes. This transparency is better than imposing a non-consensus assumption without acknowledgment.
Related concepts
- Beta and systematic risk: How market risk is measured and scaled
- Market risk premium and historical returns: Long-term equity returns relative to bonds
- Risk-free rate and Treasury yields: Anchor for cost of equity
- WACC and discount rates: CAPM output feeds directly into WACC
- Private company valuation adjustments: Illiquidity and size premiums for non-public firms
Summary
The Capital Asset Pricing Model is the standard framework for estimating cost of equity, linking it to the risk-free rate, beta (systematic risk), and the market risk premium. Cost of equity represents the return equity investors require, given business and financial risk. Beta is the critical input—it measures sensitivity to market movements and varies by industry (utilities near 0.6–0.8, growth tech near 1.3–1.8). The market risk premium is typically 5–6% based on long-term historical data but is widely debated; use sensitivity analysis to test your assumption. For private companies, use comparable public company betas, unlever them, relever using target capital structure, and add 1–3% for illiquidity risk. Cost of equity feeds directly into WACC, the discount rate for all DCF calculations. Small errors in cost of equity (0.5–1%) propagate into 10–20% valuation errors, making CAPM precision essential. Defend your beta, risk-free rate, and market risk premium with data and logic; do not default to round numbers or industry folklore.