6.5 Cost of capital: CAPM, India's equity risk premium, WACC

Motivation

The discount rate is the single most sensitive input in 6.3. You need a defensible number, and you need to know how weak its foundations are.

6.5.1The CAPM and its limits#

Setup

Assets $i = 1..n$ with expected returns $\mu$ , covariance $\Sigma$ (positive definite), a risk-free asset at $r_f$ . Investors choose portfolios by mean and variance over one period, share the same beliefs, and can borrow and lend at $r_f$ without limit. Markets are frictionless.

Proposition 6.8CAPM; Sharpe 1964, Lintner 1965

Under these assumptions, in equilibrium every asset satisfies

\mu_i - r_f = \beta_i(\mu_M - r_f), \qquad \beta_i = \frac{\operatorname{Cov}(R_i, R_M)}{\sigma_M^2}, \tag{6.14}

where $M$ is the value-weighted market portfolio.

Derivation sketch

(Full Lagrangian derivations of the tangency portfolio and two-fund separation are in M14 · 14.1, Propositions 14.3 and 14.5.)

Each investor's optimal risky portfolio maximises the Sharpe ratio. Its weights satisfy the first-order condition $\Sigma w_T = \kappa(\mu - r_f\mathbf{1})$ for a scalar $\kappa > 0$ . With common beliefs every investor holds the same $w_T$ , scaled by risk tolerance (two-fund separation).
Market clearing: the aggregate demand for risky assets must equal their supply, so $w_T = w_M$ .
Row $i$ of $\Sigma w_M$ is $\operatorname{Cov}(R_i, R_M)$ . So $\operatorname{Cov}(R_i, R_M) = \kappa(\mu_i - r_f)$ for every $i$ .
Multiply by $w_{M,i}$ and sum: $\sigma_M^2 = \kappa(\mu_M - r_f)$ . Divide step 3 by this to get (6.14).∎

Where it breaks Every assumption is false: no common beliefs, borrowing costs above lending rates, taxes, the market portfolio is unobservable (Roll's critique), and returns are not normal (M02). Empirically the security market line is too flat: low-beta stocks earn more than the CAPM predicts and high-beta stocks less (Fama & French, "The Capital Asset Pricing Model: Theory and Evidence", JEP 18(3), 2004). Practitioners still use CAPM for the cost of equity because the alternatives (multi-factor models) are no more stable out of sample and need more estimated inputs. Treat the output as a number with an error bar of at least ±1.5 pp, and carry that error into 6.7.

6.5.2Estimating beta#

Beta in practice Regress the stock's excess returns on the Nifty 50 or Nifty 500 total-return index's excess returns, using two to five years of weekly or monthly data. The standard error of a single-stock beta is commonly 0.1–0.3. Damodaran prefers bottom-up betas: average the unlevered betas of comparable firms, then relever to the firm's target debt-to-equity $D/E$ :

\beta_L = \beta_U\left[1 + (1-\tau)\frac{D}{E}\right]. \tag{6.15}

Averaging across many firms shrinks the estimation error roughly by $1/\sqrt{k}$ .

6.5.3Country risk and INR cost of equity#

India's equity risk premium (Damodaran, dated) Damodaran's country-risk method: country risk premium (CRP) = sovereign default spread × (σ of equity / σ of sovereign bonds). From his July 2026 update (ctrypremJuly26.xlsx, update dated 1 Jul 2026, spreads corrected 9 Jul 2026):

Item	Value
India Moody's rating	Baa3
Default spread (rating-based)	1.75%
Equity/bond volatility multiplier	1.554
CRP	2.72%
Mature-market ERP	4.20%
Total ERP for India	6.92%
CDS-based alternative: CRP / total ERP	1.12% / 5.32%

The January 2026 update had CRP 2.85% and total ERP 7.08% on a mature ERP of 4.23%. These numbers change every January and July.

INR cost of equity recipe

INR risk-free rate $r_f^{INR}$ = 10-year Government of India bond (G-sec) yield minus India's default spread. The G-sec yield contains a default premium; strip it so that $r_f$ is genuinely riskless. Read the current yield from RBI or CCIL; this module does not quote one.
$k_e = r_f^{INR} + \beta(\text{ERP}_{mature} + \text{CRP})$ , or, if the company's exposure to Indian country risk differs from its market beta (an exporter with USD revenue), $k_e = r_f^{INR} + \beta\,\text{ERP}_{mature} + \lambda\,\text{CRP}$ with $\lambda$ the company's relative exposure.

Worked example

With an illustrative INR risk-free rate of 6.5% (a placeholder, not a quoted yield), $\beta = 1.0$ , mature ERP 4.20% and CRP 2.72%: $k_e = 6.5\% + 6.92\% = 13.42\%$ . With $\beta = 0.8$ : $k_e = 12.04\%$ . (The lab test cost_of_equity(0.065, 1.0, 0.042, 0.0272) returns 0.1342.)

6.5.4Weighted average cost of capital#

WACC

W = \frac{E}{D+E}k_e + \frac{D}{D+E}k_d(1-\tau), \tag{6.16}

with market-value (not book) weights at the target capital structure. Continuing the example: equity ₹800 cr, debt ₹200 cr, pre-tax cost of debt 9%, tax 25.17% gives $W = 0.8(13.42\%) + 0.2(9\%)(0.7483) = 12.08\%$ .

Practitioner notes

The cost of debt is the marginal pre-tax borrowing rate (from the company's rating and current spreads), not interest expense divided by book debt.
Many Indian sell-side reports use $k_e$ of 11–13% without derivation. Ask which $r_f$ , which ERP, and whether the CRP was added twice (once in the G-sec yield, once in the ERP).
For a valuation in USD of an Indian company, use a USD risk-free rate and the same ERP, and convert cash flows at expected forward rates, not the spot rate (M11 covers interest-rate parity).