Cost of equity in detail — CAPM and beyond

Cost of equity is the annual percentage return shareholders demand to bear the risk of holding a company's stock instead of something safer. Unlike the cost of debt — where a public bond's yield to maturity gives you a market-observable number — there is no quoted price for cost of equity. It must be estimated, and the standard tool is the Capital Asset Pricing Model. CAPM is forty years old, has known weaknesses, and remains the dominant working framework because every other proposed model is even more sensitive to inputs or even harder to estimate consistently.

The CAPM formula

  Ke   =   Rf   +   β   ×   ERP

Variable glossary — every input explained

• Ke — the cost of equity, the annual percentage return equity investors require, expressed as a decimal. The output you plug into WACC. For a Kenyan listed bank Ke typically falls 17-22%; for a US large-cap consumer-staples name 8-10%.
• Rf — the risk-free rate, the yield on a long-dated government bond in the same currency as the cash flows being discounted. For US-dollar cash flows: the 10-year US Treasury yield, currently around 4.0-4.5%. For Kenyan-shilling cash flows: the 10-year Kenyan government T-bond yield, currently around 14-15%. Currency mismatch between Rf and cash flows is the single largest source of error in emerging-market DCFs.
• β — beta, the sensitivity of the company's equity returns to the market's returns. Dimensionless. A beta of 1.0 means the stock moves in line with the market; 1.5 means it amplifies market moves by 50%; 0.6 means it dampens them. Sourced either from a regression of historical stock returns on market returns or — better for emerging-market thinly-traded names — from comparable-company unlevered betas re-levered at the target's capital structure.
• ERP — the equity risk premium, the expected excess return of equities over the risk-free rate, expressed as a decimal. Captures the additional return required for bearing equity risk vs holding the risk-free bond. Estimates: 5-7% for the US, 9-13% for Kenya (US ERP plus a country-risk premium of 4-6%).
• β × ERP — the company's risk premium, the additional return required above the risk-free rate for bearing this particular company's equity risk. A high-beta company in a high-ERP country (a Kenyan bank with β=1.2 and ERP=12%) carries a 14.4% risk premium above the risk-free rate.

The risk-free rate — match the currency

In US-dollar valuations, use the 10-year US Treasury yield. In KES valuations, use the 10-year Kenyan government bond yield. Match the currency of your cash flows to the currency of your risk-free rate — never use a US Rf to discount KES cash flows. The mismatch is the single largest source of error in emerging-market DCFs because it pretends a USD-equivalent valuation is a KES valuation, but the underlying inflation, growth, and risk premium for KES are fundamentally different. For long-horizon valuations the 10-year tenor is the standard choice; some practitioners use the 20- or 30-year for terminal-value discounting.

Beta — the sensitivity input

Beta measures how much a stock moves relative to the market index. The formal definition is the covariance of stock returns with market returns, divided by the variance of market returns:

                  Cov ( R_stock,  R_market )
  β    =    ─────────────────────────────────
                        Var ( R_market )

where:
  R_stock   =  the periodic (weekly or monthly) return on the stock
  R_market  =  the periodic return on the market index over the same period
  Cov       =  the covariance between the two return series
  Var       =  the variance of the market return series

In practice, beta is most commonly estimated as the slope coefficient
in an OLS regression of R_stock on R_market over 2-5 years of weekly
or monthly observations. Bloomberg's BETA function reports this number
directly; for thinly-traded Kenyan stocks the standard error around
the slope is large enough that the point estimate is unreliable.

A beta of 1.0 means a 1% market move produces a 1% expected stock move.
A beta of 1.5 means a 1% market move produces a 1.5% expected stock move.
Beta is dimensionless.

For thinly-traded Kenyan stocks the regression-beta approach produces unstable estimates because there are few independent return observations and many of them are zero (no trade that day). The senior practitioner's alternative is a 'comparable-company beta': take the average unlevered beta of comparable companies (de-lever each by its own D/E and tax rate via the Hamada equation), then re-lever at the target company's capital structure. This yields a more stable, more defensible number that reflects business risk rather than trading noise.

Hamada equation — relating levered and unlevered beta:

  β_levered  =  β_unlevered  ×  [ 1  +  (1 − t)  ×  ( D / E ) ]

where:
  β_levered    =  the beta you observe in the market, including effect of leverage
  β_unlevered  =  the beta of the underlying business operations, abstracting from leverage
  t            =  marginal corporate tax rate (decimal)
  D / E        =  debt-to-equity ratio at market values

Two-step process for a thinly-traded target:
  1. Take 5-8 comparable companies. For each, observe β_levered, t, D/E.
     Compute β_unlevered for each comp using the formula above.
     Average across comps for a stable business-risk beta.
  2. Re-lever to the target's capital structure:
     β_target  =  β_unlevered_avg  ×  [ 1  +  (1 − t_target) × (D/E)_target ]

Equity risk premium — and the country-risk premium debate

ERP is the expected excess return of equities over the risk-free rate. The standard developed-market estimate is 5-7%, drawn from one of three approaches: historical (long-run realised excess return), implied (back out the ERP that justifies current equity prices), or survey (Pablo Fernandez's annual survey of textbook authors and CFO estimates). Each gives slightly different numbers; reasonable analysts disagree by 1-2 percentage points.

For Kenya and other emerging markets, the additional country-risk premium reflects political, currency, and institutional risks not captured by the developed-market ERP. Damodaran publishes country-risk premiums annually; Kenya's typical CRP is around 4-6% on top of the developed-market ERP, giving a total Kenyan ERP of around 9-13%. Three honest schools of thought on how to handle the country risk: (1) add CRP to ERP — the standard practice; (2) adjust cash flows for country risk and use a developed-market ERP — cleaner conceptually, hard to execute; (3) scale by relative volatility — historical Kenya equity volatility divided by US equity volatility, times the US ERP. Each gives different numbers; document your choice and apply it consistently across the comparable set.

Putting it all together — a worked Kenyan example

Computing cost of equity for a Kenyan listed bank, mid-2025:

  Rf — 10-year Kenyan T-bond yield:                14.0%
  β   — comparable-bank unlevered beta = 0.85
         Tax-adjusted target D/E ≈ 0.20 (banks have leverage but most is non-interest-bearing deposits)
         Re-levered β = 0.85 × [1 + (1 − 0.30) × 0.20] = 0.85 × 1.14 = 0.97
  ERP — developed-market ERP (Damodaran):           5.5%
        Plus Kenya country risk premium (Damodaran): 5.0%
        Total Kenya ERP:                            10.5%

  Ke  =  Rf  +  β  ×  ERP
      =  0.14  +  0.97  ×  0.105
      =  0.14  +  0.102
      =  0.242  =  24.2% nominal KES

Reading: equity investors in this Kenyan bank require approximately
a 24.2% annual return in shilling terms to compensate for the bank's
beta-adjusted exposure to Kenya country risk. This is the Ke that
flows into the WACC computation in the previous module.