Стоимость собственного капитала и CAPM

Определение required return on equity Стоимость собственного капитала (Cost of Equity) — доходность, требуемая акционерами за инвестирование в компанию. Это opportunity cost капитала и критический input для WACC и оценки. CAPM — dominant model для оценки cost of equity. Концепция cost of equity Required return: акционеры требуют return, compensating за risk инвестиции. Higher risk — higher required return. Cost of equity — это minimum return, которую компания должна earn чтобы satisfy equity investors. Opportunity cost: investors могут инвестировать elsewhere. Cost of equity отражает return of альтернативных инвестиций comparable risk. Not directly observable: в отличие от cost of debt (coupon rate, yield), cost of equity не наблюдается напрямую. Требуется estimation. CAPM: Capital Asset Pricing Model CAPM formula: Re = Rf + β × (Rm - Rf). Где Re — cost of equity, Rf — risk-free rate, β — beta (systematic risk), (Rm - Rf) — equity risk premium. Intuition: expected return = risk-free return + premium for bearing systematic risk. Premium proportional to amount of systematic risk (beta). Risk-free rate (Rf) Theoretical: return on zero-risk investment. In practice: government bonds of issuer's currency (US Treasuries для USD, Bunds для EUR). Maturity matching: use Rf matching project/valuation horizon. For long-term valuation, 10-year или 20-year government bonds. Current rate vs historical average: use current rate для forward-looking analysis. Historical average may smooth short-term distortions. Beta (β) Systematic risk measure: beta indicates sensitivity of stock returns to market returns. β = Covariance(stock, market) / Variance(market). Interpretation: β = 1: stock moves with market; β > 1: more volatile than market (amplifies movements); β Estimation: regress historical stock returns against market index returns. Slope of regression = beta. Bloomberg, Reuters provide estimated betas. Issues: beta unstable over time, depends on estimation period, frequency, index choice. Adjusted beta: (2/3 × raw beta) + (1/3 × 1) — mean-reversion adjustment. Equity Risk Premium (Rm - Rf) ERP: excess return investors expect from equities over risk-free rate. Compensation for bearing equity market risk. Historical approach: average historical excess return of stocks over bonds. US long-term: ~5-7% (depends on period, methodology). Forward-looking approach: implied ERP from current market prices using DDM. If market P/E high, implied ERP lower. Current practice: practitioners use 4-6% ERP для developed markets. Emerging markets add country risk premium. CAPM example Rf = 3%, β = 1.2, ERP = 5%. Cost of equity = 3% + 1.2 × 5% = 9%. Interpretation: investors require 9% return to invest in this stock. 3% for time value (risk-free), 6% for systematic risk. CAPM limitations Assumptions: investors rational, markets frictionless, single-period horizon, investors hold market portfolio. Reality differs. Single factor: CAPM uses only market risk. Research shows other factors matter (size, value, momentum). Multi-factor models (Fama-French) address this. Beta estimation: historical beta may not predict future. Industry average или comparable company beta often used. Alternative approaches Build-up method: Rf + ERP + Size premium + Company-specific risk. For private companies без tradable beta. Dividend Growth Model (DDM): P = D₁/(Re-g), solve for Re = D₁/P + g. Works если dividends stable, growth predictable. Bond yield plus risk premium: Re = company's bond yield + equity premium (3-5%). Simple approximation. Unlevered и relevered beta Observed beta includes financial leverage effect. To isolate business risk: unlevered beta = β / (1 + (1-T) × D/E). Applying to different capital structure: relever using target D/E. βlevered = βunlevered × (1 + (1-T) × D/E). Industry beta: unlever peer betas, average, relever for target company. Useful для private company или changing capital structure. Practical considerations Sensitivity: small changes in assumptions (Rf, ERP, beta) significantly impact cost of equity и valuation. Cross-check: compare estimated cost of equity to industry norms, company's historical returns, alternative methods. Document assumptions: clearly state Rf, ERP, beta source/methodology. Enables reviewers to assess и challenge.