The formulas
Ke = Rf + β × (Rm − Rf) + any size or company-specific premium. Regression beta = Cov(Ra, Rm) ÷ Var(Rm). Unlevered beta = βL ÷ (1 + (1 − t) × D ÷ E); relevered beta = βu × (1 + (1 − t) × D ÷ E target). The CAPM goes back to Sharpe (1964) and Lintner (1965); the unlevering form to Hamada (1972).
When to use it
Use it to build or test a cost of equity input: a discount rate in a goodwill impairment or fair value model, a build-up for a private company, or a quick reasonableness check against a rate management used. The WACC calculator takes the result as an input.
Limits
CAPM is a single-factor model and its inputs are estimates. Beta is unstable over short windows, size and company-specific premiums are judgmental, and the Hamada relationship assumes constant debt and a tax shield worth the full tax rate. Use consistent market values for D and E. Illustrative figures only. Check the result against your firm's methodology before relying on it.
Common questions
What is the CAPM formula?
Cost of equity = risk-free rate + beta × equity risk premium. Beta measures how much the stock moves with the market. A beta of 1.2 means the stock has historically moved 1.2% for every 1% move in the market.
What is the equity risk premium?
The return investors expect from the market portfolio over the risk-free rate. It is an estimate, not an observable price, and published estimates differ by source and method. Document which one you use and the date.
How is beta calculated from returns?
Beta is the slope of a regression of the asset’s returns on the market’s returns, equal to their covariance divided by the variance of the market returns. The result depends on the index, the window and the return interval, so state all three.
Why unlever and relever beta?
Observed beta reflects the capital structure of the company or peer it came from. Debt adds financial risk to equity holders. To apply a peer’s beta to a different company, remove the peer’s leverage to get an asset beta, then add back the target’s leverage. This page uses the Hamada form, which treats debt as risk-free for beta purposes and applies the tax shield.
Where does CAPM show up in audit and valuation work?
In the discount rate for goodwill impairment tests under ASC 350, fair value measurements under ASC 820 and acquisition accounting under ASC 805. A discount rate in a management estimate is a typical area where an auditor tests the inputs and the method.
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