What it means
Investors demand a higher return for taking more risk, but not all risk is equal. The risk that a particular company loses a contract, suffers a fire or launches a failed product can be reduced almost to nothing by holding many companies: the failures of some are offset by the successes of others.
What cannot be diversified away is the risk that the whole market falls, taking every company with it. CAPM's central claim is that the market pays a premium only for the second kind of risk, and that an asset's exposure to it is captured in a single number, beta.
The formula has three inputs. The risk-free rate is the return on an investment with no default risk, in practice the yield on a government bond of a maturity matching the investment horizon.
The market risk premium is the extra return investors expect from the whole equity market over the risk-free rate, estimated from long-run history (typically 4% to 7%) or from current market prices. Beta is estimated by regressing the asset's historical returns against the market's, or, for an unlisted company or a project, by taking the betas of comparable listed companies, removing the effect of their borrowing (unlevering) and adding back the effect of the subject's own borrowing (relevering).
The output is the cost of equity: the return that shareholders require for the risk they bear. Combined with the after-tax cost of debt in proportion to the company's capital structure, it gives the weighted average cost of capital, the discount rate for the company's cash flows.
A company whose projects return more than this rate creates value; one whose projects return less destroys it, however profitable they look in accounting terms. The model has well-known limitations.
Its assumptions (investors hold diversified portfolios, can borrow and lend at the risk-free rate, share the same expectations) are simplifications. Beta estimates vary with the period and index used and are unstable over time.
Empirical tests find that the relationship between beta and return is weaker than the model predicts, and that other factors such as company size and value characteristics explain returns that CAPM does not. Extensions (multi-factor models, size and country premiums) address some of this at the cost of complexity.
Despite the criticism, CAPM remains the standard because it is simple, transparent, and produces a defensible number that everyone in a negotiation can check. Practical use requires judgement about each input, and the honest approach is to show a range.
A cost of equity of 9% to 11% is more useful than a false precision of 9.73%, and the valuation should be tested across the range.
In practice
Real-world examples.
Example
A regulator sets the allowed return for a water company using CAPM with a beta of 0.7, producing a cost of equity of 7.8%.
Example
An investment bank values a takeover target at a WACC of 9% derived from CAPM and the target's capital structure.
Example
A pension fund evaluates its equity manager against a CAPM-based benchmark and finds the manager's excess return is explained by a higher beta rather than skill.
Think of it
“CAPM is like a sliding scale that says riskier rides should be more thrilling. More risk must mean more reward.
Formula
Calculation
Expected Return = Risk-free rate + Beta x (Expected market return minus Risk-free rate)
Cost of Equity = Rf + Beta x Market risk premium
Relevered Beta = Unlevered beta x [1 + (1 minus Tax rate) x Debt / Equity]
Worked example. A private logistics company wants to value a proposed expansion. Inputs:
- Risk-free rate: 10-year government bond yield, 4.0%
- Market risk premium: 5.5%
- Comparable listed logistics companies have an average equity beta of 1.15 at an average debt-to-equity ratio of 0.5, with a tax rate of 25%
- The company's own debt-to-equity ratio is 0.8
Unlever the comparables' beta: 1.15 / [1 + 0.75 x 0.5] = 1.15 / 1.375 = 0.84
Relever for the company: 0.84 x [1 + 0.75 x 0.8] = 0.84 x 1.6 = 1.34
Cost of equity = 4.0% + 1.34 x 5.5% = 4.0% + 7.36% = 11.4%
Weighted average cost of capital: debt is 0.8 / 1.8 = 44% of capital and equity 56%; the company borrows at 6.5%, after tax 4.9%.
WACC = 0.56 x 11.4% + 0.44 x 4.9% = 6.4% + 2.2% = 8.5%
The expansion is expected to return 10% on the capital invested. At an 8.5% cost of capital it creates value. Sensitivity: with a market risk premium of 6.5% the cost of equity is 12.7% and WACC 9.3%; the project still clears the hurdle but with less margin. With a beta of 1.5 (a more cyclical comparable set), cost of equity is 12.25% and WACC 9.0%. The finance team presents a WACC range of 8.5% to 9.5% and recommends the project on the basis that it clears the top of the range.
Second example, a share. An investor is considering a utility with a beta of 0.6 and a technology company with a beta of 1.5, with the same risk-free rate and premium. Required returns: utility 4.0% + 0.6 x 5.5% = 7.3%; technology 4.0% + 1.5 x 5.5% = 12.25%. If the investor's analysis suggests the technology company will return 11%, it is not adequately compensating for its risk, even though 11% exceeds the utility's 7.3%.Case study
Seen in the real world.
A manufacturing group had used a discount rate of 12% for all projects for as long as anyone could remember. A new finance director rebuilt it from CAPM: risk-free rate 3.5%, market risk premium 5.5%, a relevered beta of 1.1 from comparables, giving a cost of equity of 9.55%; with 35% debt at an after-tax cost of 3.9%, the WACC was 7.6%. The difference was large enough to change decisions.
A plant modernisation rejected the previous year at 12% had a return of 10.5% and was revived; it went on to deliver. But the finance director also introduced a differentiated rate for the group's two divisions: the industrial division, with cyclical customers, had comparables with betas around 1.3 and a divisional WACC of 8.4%, while the consumer division's comparables had betas around 0.8 and a WACC of 6.7%.
The consumer division, which had been starved of investment under the single 12% rate because its steady projects rarely cleared it, now received capital for projects returning 8% to 9% that created value at its true cost of capital, and the industrial division's marginal projects faced a properly higher bar. Over three years the group's return on invested capital rose from 9% to 12%, and the finance director's board paper credited most of the improvement to replacing a rate that nobody could justify with one that everyone could check.
Watch out
Common mistakes.
- Using a single company-wide discount rate for projects and divisions with different risk, which starves safe projects and over-funds risky ones.
- Using a comparable company's equity beta without adjusting for differences in borrowing.
- Presenting the CAPM output as a precise figure. The inputs are estimates; show a range and test the decision across it.
Questions
People also ask.
What beta should a project use?
The beta of the business the project is in, not the beta of the company doing it, if the two differ.
Does CAPM work for private companies?
Yes, using betas from comparable listed companies, unlevered and relevered. Some practitioners add a premium for size or illiquidity, which the model itself does not include.
Why is beta more important than total volatility?
Because diversified investors bear only the market-related part of an asset's risk. A volatile stock with low correlation to the market adds little risk to a diversified portfolio.
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