Cost of equity, and CAPM in practice

Debt has a contractual rate. Equity does not. Nobody owes shareholders a return, so the cost of equity is not a price anyone quotes — it is the return shareholders require, inferred.

That makes it the softest number in a DCF and the one that moves the answer most.

CAPM

$k_e = r_f + \beta \times (\text{ERP})$

The required return is the risk-free rate plus a reward for bearing market risk, scaled by how much of that risk this company carries.

The logic behind it is chapter 5 of the Quantitative methods subject: diversifiable risk can be removed for free, so nobody is paid for bearing it. Only non-diversifiable risk earns a premium, and beta measures exposure to it.

The three inputs, in India

The risk-free rate. The yield on a government security of matching tenor — in practice the 10-year, because most valuations are long-horizon. It is observable, which makes it the only input of the three that is not an argument. Use the current yield, not a historical average: it is the return actually available today.

Beta. The slope from regressing the stock's returns on an index's, which is chapter 11 of the Quantitative methods subject. Three practical cautions, all from there:

• It is an estimate with a standard error, and a beta printed to two decimals rarely differs significantly from 1
• It depends on the window and frequency chosen — two years of weekly data and five years of monthly give different answers for the same stock
• It depends on the index. A beta against the Nifty 50 is a beta against fifty large companies, not against the Indian economy

For an unlisted company or a new division, the usual method is to take betas of listed comparables, un-lever them to remove their capital structures, average, and re-lever at the target's own.

The equity risk premium. The extra return equities must offer over the risk-free rate. This is the genuinely contested input. It can be estimated from long-run historical excess returns, from a forward-looking implied calculation, or from survey evidence, and the three methods disagree. Reasonable estimates for India span several percentage points.

Working the problem

$k_e = 7\% + 1.2 \times 6\% = 14.2\%$

$k_e = 7\% + 1.0 \times 8\% = 15.0\%$

Two defensible sets of assumptions, 0.8 percentage points apart — and that is a narrow illustration. Widen the premium to 5–9% and beta to 0.9–1.4 and the range runs from roughly 11.5% to 19.6%.

What that implies about a DCF is the point of the exercise. A terminal value computed as $\frac{C}{r-g}$ is acutely sensitive to $r$: at $g = 5\%$, moving $r$ from 12% to 14% cuts the terminal value by more than a fifth. A DCF presented to the rupee has a precision its inputs cannot support, which is why chapter 20 of the Company analysis subject recommends reverse DCF — solving for the growth the price implies — over forecasting a value.

Where CAPM is weakest

Stated plainly, because the model is used far beyond where it is well supported:

Beta is backward-looking. It measures the past relationship of a company that may have changed.

One factor is not enough. The empirical literature has long found returns related to size, value and other characteristics that beta does not capture — which is chapter 10 of the Portfolio theory subject.

It assumes a diversified investor. A promoter with their wealth in one company faces risk CAPM says they should not be paid for. That is not a flaw in the maths; it is a mismatch between the model's investor and many real ones.

It is a model of expected returns, and expectations are not outcomes. SEBI's measurement of individual derivatives traders is a reminder of how far realised results can sit from any expected-return model.

What to do about all this

Three habits make the number usable:

Compute a range, not a figure. Low, central and high, from defensible input ranges.

Sanity-check it. A cost of equity below the cost of debt is wrong — equity is junior and must cost more. One far above what equity investors in that sector appear to accept deserves a second look.

Report the sensitivity, not just the answer. The decision-relevant question is usually whether the project clears the bar across the whole range, not what the point estimate is.

The point

The cost of equity is a required return that nobody contractually owes, so it must be inferred. CAPM builds it as the risk-free rate plus beta times the equity risk premium, of which only the first is observable: beta is an estimate that depends on window, frequency and index, and the equity risk premium is genuinely contested across several percentage points. Produce a range, check it against the cost of debt, and present the sensitivity rather than a point.