CAPM and the cost of equity

The cost of equity answers one question: what return do shareholders demand for putting their money in this stock instead of something safer? It's a required return, not a promise. And you need it because it's the single biggest input into WACC, which is the discount rate in your DCF. Get the cost of equity wrong and the whole valuation moves.

The market's standard tool for estimating it is the Capital Asset Pricing Model, or CAPM. It's not perfect. Academics have poked holes in it for decades. But it's what banks use, so it's what you need to know cold.

The formula

$r_e = r_f + \beta \times (r_m - r_f)$

Three inputs, that's the whole thing. Read it left to right and it tells a story: start with what you'd earn risk-free, then add extra return for taking on risk, scaled to how risky this particular stock is.

| Input | What it is | Rough range | |---|---|---| | $r_f$ (risk-free rate) | Yield on a long-dated government bond, usually the 10-year Treasury | 3% to 5% | | $\beta$ (beta) | How much the stock moves relative to the market | 0.5 to 2.0 | | $r_m - r_f$ (equity risk premium) | Extra return investors demand for holding stocks over bonds | 5% to 7% |

The term $(r_m - r_f)$ is the equity risk premium, the reward for holding the whole stock market instead of a safe bond. Beta then dials that premium up or down for the specific company.

What beta actually measures

Beta is market sensitivity. It's not "how risky the company feels," it's how the stock moves when the broad market moves.

• $\beta = 1.0$: the stock moves in line with the market. Market up 10%, stock up 10%.
• $\beta = 1.5$: the stock is more volatile. Market up 10%, stock up roughly 15%. Think a cyclical name, luxury goods, high-growth tech.
• $\beta = 0.6$: the stock is defensive. It moves less than the market. Think a regulated utility or a consumer-staples business people buy in any economy.

The intuition: a company whose fortunes swing hard with the economy is riskier to a diversified investor, so that investor demands a higher return. Higher beta, higher cost of equity. Notice CAPM only rewards market risk, the risk you can't diversify away. Company-specific risk (a factory fire, a bad CEO) is assumed to wash out in a diversified portfolio, so you don't get paid for it.

A worked example

Clean numbers, the kind you'd run in an interview without a calculator. Take a risk-free rate of 3%, a beta of 1.2, and an equity risk premium of 6%:

$r_e = 3\% + 1.2 \times 6\% = 3\% + 7.2\% = 10.2\%$

So shareholders demand about a 10.2% return. That number becomes the $r_e$ you plug into WACC. If this same company were financed partly with debt, you'd blend that 10.2% cost of equity with an after-tax cost of debt to get the full discount rate. The cost of equity is an input to WACC, not WACC itself. Hold that thought, because it's the classic trip-up.

Levering and unlevering beta

Here's the piece most beginners skip. You don't usually pull one company's beta and use it raw. Instead you take betas from a set of comparable companies, strip out the effect of each one's debt, average them, then re-apply your company's debt level.

Why? Because debt makes equity riskier. A company with more leverage has more fixed interest payments ahead of shareholders, so its stock swings harder, so its observed (levered) beta is higher. Two identical businesses with different debt loads will show different betas purely because of financing. That has nothing to do with the underlying business risk you're trying to isolate.

The fix is a two-step scrub:

1. Unlever each comparable's beta to strip out its capital structure. This gives you the "asset beta," the risk of the business alone.

$\beta_{unlevered} = \frac{\beta_{levered}}{1 + (1 - t)\,\frac{D}{E}}$

2. Relever the average asset beta at your target company's own debt-to-equity ratio.

$\beta_{relevered} = \beta_{unlevered} \times \left[\,1 + (1 - t)\,\tfrac{D}{E}\,\right]$

The relevered beta is what goes into CAPM. If you skip this and use a comp's raw beta, you're importing that comp's balance sheet into your valuation, which is exactly the noise you wanted to remove.

Where the inputs come from

• Risk-free rate: the current yield on a long-dated government bond, matched to your cash-flow horizon. In the US, that's the 10-year Treasury.
• Equity risk premium: either a long-run historical average of stock returns over bonds, or a forward-looking estimate. Most desks have a house number. Don't invent your own.
• Beta: raw betas are published (Bloomberg, Barra), but for a private company or a clean read on business risk you unlever comps and relever, as above.

How it fits the bigger picture

CAPM feeds cost of equity into WACC. WACC discounts unlevered free cash flow in the DCF to produce enterprise value, which you then bridge to equity value. It's one link in a chain, and it's the link most candidates can recite the formula for but can't reason through.