Interview Questions229

    CAPM and the Cost of Equity

    How the Capital Asset Pricing Model derives the cost of equity from the risk-free rate, beta, and the equity risk premium.

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    8 min read
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    3 interview questions
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    Introduction

    The cost of equity is the return that equity investors require to compensate them for the risk of owning the company's stock. It is the most important component of WACC for most companies (since equity typically represents a larger portion of the capital structure than debt) and directly determines the discount rate in the DCF model.

    The Capital Asset Pricing Model (CAPM) is the standard framework for estimating the cost of equity in investment banking. While CAPM has well-known theoretical limitations, it remains the dominant model because it is intuitive, transparent, and produces inputs that can be sourced from observable market data.

    The CAPM Formula

    Cost of Equity=Rf+β×ERPCost\ of\ Equity = R_f + \beta \times ERP

    Where:

    • R_f = Risk-free rate
    • \beta = Beta (the stock's sensitivity to market movements)
    • ERP = Equity risk premium (the excess return investors require for holding equities over risk-free assets)

    Each component requires a specific input, and the choices the analyst makes for each one affect the final cost of equity and, through WACC, the entire DCF output.

    Component 1: The Risk-Free Rate

    The risk-free rate represents the return on a theoretically riskless investment. In practice, the yield on a 10-year US Treasury bond is the standard proxy for US dollar-denominated valuations. The 10-year maturity is used because it approximates the duration of the cash flows in a typical DCF (5-10 year projection period plus terminal value).

    As of early 2026, the 10-year Treasury yield is approximately 4.2-4.5%, significantly higher than the 1.5-2.0% range that prevailed in 2020-2021. This increase has a direct impact on valuations: a higher risk-free rate increases the cost of equity, increases WACC, and reduces the present value of future cash flows in every DCF model.

    Component 2: Beta

    Beta measures the systematic risk of the stock: how much the stock's returns move relative to the broader market. A beta of 1.0 means the stock moves in line with the market. A beta above 1.0 means it is more volatile (and riskier) than the market. A beta below 1.0 means it is less volatile.

    In the CAPM formula, beta scales the equity risk premium to reflect the specific company's risk. A high-beta company (beta of 1.5, typical of a cyclical industrial or a high-growth technology company) has a higher cost of equity than a low-beta company (beta of 0.6, typical of a utility or consumer staple), reflecting the higher risk that equity investors bear.

    Where to Source Beta

    • Raw (observed) beta: Calculated by regressing the stock's historical returns against a market index (typically the S&P 500) over a 2-5 year period. Available from Bloomberg, FactSet, and other data providers.
    • Adjusted beta: Bloomberg's adjusted beta applies a formula that blends the raw beta toward 1.0 (on the theory that all betas tend toward the market average over time). Adjusted beta is the most commonly used in investment banking.
    • Unlevered beta: Strips out the effect of the company's capital structure, allowing comparison across companies with different leverage. Used when constructing a beta from a peer group. Detailed in the beta article.
    Beta (CAPM)

    A measure of a stock's sensitivity to systematic (market-wide) risk. A beta of 1.0 indicates that the stock moves in line with the market. A beta of 1.3 means the stock is 30% more volatile than the market on average, while a beta of 0.7 means it is 30% less volatile. In the CAPM, beta scales the equity risk premium to reflect the specific company's risk level. Beta captures only systematic risk (risk that cannot be diversified away), not company-specific risk, which CAPM assumes investors have eliminated through portfolio diversification.

    Component 3: The Equity Risk Premium (ERP)

    The equity risk premium is the incremental return that investors demand for holding the market portfolio of equities over the risk-free rate. It represents the compensation for bearing the systematic risk of the equity market as a whole.

    Equity Risk Premium (ERP)

    The additional return that investors demand for holding equities (risky assets) over risk-free government bonds. The ERP is the most debated input in the CAPM because it is not directly observable and different estimation methods produce materially different values. Historical approaches (measuring past equity returns above Treasury returns) yield 5-7%. Forward-looking (implied) approaches, which back out the premium from current stock prices and expected growth, typically yield 4-6%. The choice of ERP has a significant impact on every DCF: for a company with a beta of 1.2, a 1% change in ERP shifts the cost of equity by 1.2 percentage points, which can move the implied enterprise value by 10% or more.

    The ERP is not directly observable and must be estimated. The two main approaches:

    • Historical ERP: Based on the long-term average excess return of equities over risk-free assets. Over the past century, US equities have returned approximately 5-7% above Treasury bonds, depending on the measurement period. This is the most commonly cited range.
    • Forward-looking (implied) ERP: Derived from current market prices and expected earnings growth, representing the market's current assessment of the premium. Aswath Damodaran of NYU publishes a widely used implied ERP estimate, which as of early 2026 is approximately 4.5-5.5%.

    Most investment banks use an ERP in the 5-7% range, with the specific figure varying by bank and by the valuation context. Some banks have a standardized house view on ERP that is used consistently across all models to ensure comparability across engagements. Others allow deal teams to select an ERP within an approved range based on the specific market environment. The ERP selected has a meaningful impact on the final valuation: a 1% change in ERP (e.g., from 5.5% to 6.5%) shifts the cost of equity by the company's beta (if beta is 1.2, the cost of equity moves by 1.2%), which flows through WACC and affects the entire DCF output.

    For emerging market valuations, the ERP is typically higher to reflect greater political, currency, and liquidity risk. A common approach is to start with the US ERP and add a country risk premium based on sovereign credit default swap spreads or sovereign bond yield spreads.

    CAPM ComponentTypical SourceCurrent Range (2026)
    Risk-free rate10-year US Treasury yield4.2-4.5%
    BetaBloomberg adjusted beta or peer group median0.6-1.8x (varies by sector)
    Equity risk premiumDamodaran implied ERP or historical average4.5-6.5%
    Implied cost of equityCAPM formula output7-15% (varies widely)

    Putting It Together: A Worked Example

    For a mid-cap industrial company with an adjusted beta of 1.1:

    • Risk-free rate: 4.3% (current 10-year Treasury yield)
    • Beta: 1.1x
    • ERP: 5.5%
    Cost of Equity=4.3%+1.1×5.5%=4.3%+6.05%=10.35%Cost\ of\ Equity = 4.3\% + 1.1 \times 5.5\% = 4.3\% + 6.05\% = 10.35\%

    This 10.35% cost of equity becomes the equity component of the WACC calculation.

    Interview Questions

    3
    Interview Question #1Medium

    How do you calculate the cost of equity using CAPM?

    re=rf+β×ERPr_e = r_f + \beta \times ERP

    Where: - rfr_f = risk-free rate (typically the yield on the 10-year or 20-year US Treasury bond) - β\beta = beta, a measure of the stock's systematic risk relative to the market - ERP = equity risk premium (the additional return investors demand for holding equities over risk-free assets, typically 5-7%)

    For example, with a 4.0% risk-free rate, beta of 1.2, and 6.0% ERP: rer_e = 4.0% + 1.2 x 6.0% = 11.2%

    CAPM is the standard approach in investment banking despite its theoretical limitations because it provides a systematic, defensible framework for estimating the cost of equity.

    Interview Question #2Medium

    Cost of equity: risk-free rate is 4.5%, beta is 1.3, equity risk premium is 6%. What is the cost of equity?

    Using CAPM:

    re=4.5%+1.3×6%=4.5%+7.8%=12.3%r_e = 4.5\% + 1.3 \times 6\% = 4.5\% + 7.8\% = 12.3\%

    The cost of equity is 12.3%.

    Interview Question #3Medium

    What happens to a company's cost of equity if its beta increases from 1.0 to 1.5?

    Using CAPM with a risk-free rate of 4% and ERP of 6%:

    Before: rer_e = 4% + 1.0 x 6% = 10%

    After: rer_e = 4% + 1.5 x 6% = 13%

    The cost of equity increases by 300 basis points (from 10% to 13%). This higher cost of equity flows into WACC, increasing the discount rate and decreasing the DCF valuation.

    A higher beta reflects greater systematic risk (more volatile relative to the market). This could result from increased leverage, entering a riskier business line, or the market perceiving the company as more sensitive to economic cycles.

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