CAPM calculator

How do you calculate the cost of equity with CAPM?

The capital asset pricing model (CAPM) prices a share by the one kind of risk that holding many shares cannot remove. Its formula is ke = Rf + beta x (Rm - Rf): the risk-free rate, plus the share's beta times the market premium. Rf is the return on short-term government debt, Rm is the average return on the stock market as a whole, and the difference between them is called the equity risk premium. Beta scales that premium up or down for one particular share.

The arithmetic is three moves: find the premium, multiply it by beta, then add the risk-free rate back. A beta of exactly 1 returns the market return itself. A beta of 0.5 earns half the premium on top of Rf, and a beta of 2 earns twice it. The answer is the return shareholders require for carrying that risk, which makes it the company's cost of equity and the discount rate for equity cash flows of the same risk.

Worked example: CAPM set out the way an exam answer reads

The calculator opens on a risk-free rate of 4%, a market premium of 6% and an equity beta of 1.25:

1. Market premium: given as 6%. When a question gives the market return instead, subtract: 10% - 4% = 6%.
2. Risk premium for this share: 1.25 x 6% = 7.5%.
3. Cost of equity: 4% + 7.5% = 11.5%.

On these defaults the two ways of entering the market figure agree, because a 10% market return with a 4% risk-free rate is the same 6% premium. They split apart once Rf moves. Raise Rf to 5% with the premium held at 6% and the cost of equity becomes 5% + 1.25 x 6% = 12.5%. Raise it to 5% with the market return held at 10% and the premium shrinks to 5%, so the answer is 5% + 1.25 x 5% = 11.25%. Read the question for which figure it holds fixed.

A second example, for a euro-area share with a beta of 0.9: government bills yield 2.5% and the market return is put at 8%, a premium of 5.5%. The cost of equity is 2.5% + 0.9 x 5.5% = 2.5% + 4.95% = 7.45%, below the 8% market return because the share is less exposed to market swings than the market itself.

What are asset beta and equity beta, and how do you ungear a beta?

An equity beta measures the market risk a shareholder carries, and it has two layers. Business risk comes from what the company does: its industry, its cost structure, its customers. Financial risk comes from how it is financed: interest is paid before shareholders receive anything, so more debt makes the returns to equity swing harder. An asset beta, also called an ungeared beta, keeps the business risk and takes out the financial risk.

To ungear: asset beta = equity beta x E / (E + D(1 - t)), where E and D are the market values of equity and debt and t is the corporate tax rate. That version assumes the debt has a beta of zero. An ACCA technical article on CAPM calls this the usual simplifying assumption, because a debt beta is normally very small next to an equity beta. If a question gives a debt beta, add a second term: debt beta x D(1 - t) / (E + D(1 - t)). The (1 - t) appears because tax relief on interest reduces the weight debt puts on shareholders.

How do you regear a beta for a project or an unlisted company?

Regearing runs the same relationship in reverse: equity beta = asset beta x (E + D(1 - t)) / E, which with a zero debt beta is the same as asset beta + asset beta x D(1 - t) / E. It is needed whenever the business you are pricing has no share price of its own, such as an unlisted company, or a project in a different line of business. Find a listed company in that business, take its equity beta, ungear it at the proxy's gearing, then regear it at yours. The default inputs on the second tab work through one case:

The asset beta also gives the cost of equity the company would have with no debt at all: 4% + 0.9333 x 6% = 9.60%. The gap of 1.40 percentage points is what shareholders charge for the financial risk of 25:75 gearing.

A worked example in pounds. A UK group is pricing an unlisted subsidiary. The nearest listed company has an equity beta of 1.2, with equity worth £70 million and debt worth £30 million. The subsidiary will be financed with £10 million of equity and £10 million of debt, tax is 25%, the risk-free rate is 4.5% and the premium 5.5%. Asset beta = 1.2 x 70 / (70 + 30 x 0.75) = 1.2 x 70 / 92.5 = 0.908. Regeared beta = 0.908 x (10 + 10 x 0.75) / 10 = 0.908 x 1.75 = 1.589. Cost of equity = 4.5% + 1.589 x 5.5% = 4.5% + 8.74% = 13.24%. The market values go in as a ratio, so 30 and 70 work exactly as £30 million and £70 million do.

How does each input move the cost of equity?

Beta. Each 0.1 of beta adds one tenth of the premium. On the defaults a beta of 0.8 gives 8.80% and a beta of 1.6 gives 13.60%. The risk-free rate. With the premium held, a higher Rf lifts every cost of equity by the same amount. With the market return held, it works through beta: for a beta above 1 the cost of equity falls, from 11.5% to 11.25% when Rf goes from 4% to 5% at a beta of 1.25, while at a beta of 0.8 it rises from 8.80% to 9.00%.

Your gearing. On the regearing defaults, moving your own finance from 25:75 to 50:50 lifts the equity beta from 1.1667 to 1.6333 and the cost of equity from 11.00% to 13.80%. The tax rate. Its direction depends on which company is more highly geared. With your 25:75 below the proxy's 40:60, tax rates of 0%, 25% and 50% give equity betas of 1.1200, 1.1667 and 1.2250, so more tax means a higher beta. Set your gearing to 60:40, above the proxy's, and the order flips: 2.1000, 1.9833 and 1.8375. Debt beta. A debt beta of 0.1 moves the default asset beta from 0.933 to 0.967, the regeared beta from 1.167 to 1.183 and the cost of equity from 11.00% to 11.10%.

Which risk-free rate, market premium and tax rate go in?

Risk-free rate. No asset is truly free of risk, so a proxy is used. An ACCA technical article notes that for UK shares the yield on UK treasury bills stands in for the risk-free rate. The same idea carries to other markets: use short-term government debt in the currency of the cash flows you are discounting. This page holds no live data, so type in the yield you are working with.

Market premium. This is an estimate, built from long-run history or forward-looking studies, and estimates differ. A question will give it, either directly or as a market return; in practice it is a judgment you should state. Tax rate. Use the rate at which the company gets relief on its interest. For UK companies, the GOV.UK rates table updated on 1 April 2026 gives a main rate of 25% on profits above £250,000 and a small profits rate of 19% on profits under £50,000, with marginal relief between £50,000 and £250,000, for the financial year starting 1 April 2026. Here is the default regearing at each rate:

A company with tax losses gets no immediate relief, which is the 0% row. Where the proxy pays tax at a different rate from your company, ungear at the proxy's rate and regear at yours; this calculator applies one rate to both, so work the two steps separately in that case.

How do you calculate CAPM and beta in Excel or Google Sheets?

With the risk-free rate in B1, the market return in B2 and beta in B3, the cost of equity is =B1+B3*(B2-B1). Entered as 4%, 10% and 1.25 it returns 11.5%. For the gearing steps, put the proxy's equity beta in B4, its equity and debt in B5 and B6 and the tax rate in B7:

• Ungear: =B4*B5/(B5+B6*(1-B7)), which returns 0.9333 for 1.4, 60, 40 and 25%.
• Regear, with the asset beta in B8 and your equity and debt in B9 and B10: =B8*(B9+B10*(1-B7))/B9, which returns 1.1667 for 75 and 25.

Google Sheets takes the same formulas. To estimate a beta from price history in Excel, put the share's periodic returns in one column and the market index's returns for the same periods in the next, then use =SLOPE(share returns, market returns). Microsoft's help page describes SLOPE(known_y's, known_x's) as the slope of the linear regression line through the points, and it returns #N/A when the ranges are empty or hold different numbers of points. The share goes in as known_y's.

Common CAPM and beta mistakes

• Multiplying beta by the market return instead of the premium. 4% + 1.25 x 10% = 16.5%, against the correct 11.5%.
• Using a proxy's equity beta as it stands. It carries the proxy's gearing; ungear it before it means anything for your company.
• Reading a gearing percentage as a ratio. Debt at 40% of total finance is 40:60 debt to equity, so E is 60, not 100.
• Leaving out (1 - t), or using it when ungearing but not when regearing.
• Rounding the asset beta too early. Regearing 0.93 instead of 0.9333 gives 1.1625 and a cost of equity of 10.975% rather than 11.00%.
• Weighting with book values. The gearing in both formulas is at market values wherever prices exist.
• Treating a debt beta as a cost of debt. It is a measure of risk, not a rate, and it is usually zero in a written answer.

What the CAPM calculator leaves out, and a glossary

It applies the model to the figures you type. It does not estimate a beta, choose a premium or look up a yield, and it treats beta as stable over the period you are discounting. CAPM is a single-period model that prices only market risk, so a share's own company-specific risk earns nothing in it. To average several proxies, ungear each one, average the asset betas, then regear once. The cost of equity found here is one input to the WACC calculator, and the bond yield calculator works out the cost of debt that sits beside it.

Systematic risk: risk that diversification cannot remove, the only kind CAPM rewards. Unsystematic risk: risk specific to one company, which a spread of holdings removes. Equity risk premium: Rm - Rf. Equity beta: a share's systematic risk including its financial risk. Asset beta: the same risk with gearing taken out. Proxy company: a listed business in the same line whose beta stands in for one you cannot observe. Security market line: the straight line CAPM draws between the cost of equity and beta.

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