What Is the Cost of Equity? Formula and Examples

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The cost of equity is the rate of return shareholders require for owning a company’s stock, given the risk they take. From the company’s side, it is the return its equity-funded investments must earn to justify using shareholders’ capital. It is usually written as ke (or Re) in corporate finance. It cannot be observed directly, so it is estimated with a model, most often the capital asset pricing model (CAPM) or the dividend growth model.

What the Cost of Equity Means

• For an investor, the cost of equity is the minimum return that makes a stock worth holding instead of a lower-risk alternative. If the expected return on a share falls short of it, the investor is not being paid enough for the risk.
• For a company, it is the hurdle rate that projects financed with equity must clear. A project expected to return 7% does not add value if shareholders require 10%.

A company can raise money by borrowing or by selling ownership. Debt must be repaid on a schedule, but lenders have a prior claim on cash flows and assets, and interest payments reduce taxable income in jurisdictions such as the U.S. Equity never has to be repaid, yet shareholders are residual claimants: they are paid only after lenders, with no guaranteed dividends or share price. That extra risk is why equity is normally the more expensive source of capital.

Cost of Equity Formulas

Dividend Growth Model

The dividend growth model (also called the dividend capitalization model, or the Gordon growth model) treats a share’s value as the present value of dividends that grow at a constant rate forever. Rearranging that valuation for the discount rate gives the cost of equity:

Cost of equity = D1 ÷ P0 + g

where:

• D1 = expected dividend per share for next year
• P0 = current market price per share
• g = expected constant growth rate of dividends

The first term is the forward dividend yield; the second is the growth shareholders expect on top of it. The model only applies to companies that pay dividends, and it assumes growth is stable and lower than the cost of equity itself. It suits mature dividend payers such as utilities better than fast-growing firms that reinvest all their earnings.

CAPM Formula for Cost of Equity

The capital asset pricing model links required return to market risk:

Cost of equity = Rf + β × (Rm − Rf)

where:

• Rf = risk-free rate of return
• β = the stock’s beta
• Rm = expected market return
• (Rm − Rf) = the equity risk premium

CAPM does not need dividends, so it can be applied to any stock with a usable beta. Its logic is that investors can diversify away company-specific risk, so they are only compensated for exposure to the overall market.

The Three Inputs

• Risk-free rate. Analysts typically use a government bond yield, often the 10-year U.S. Treasury rather than a T-bill, because equity is a long-lived claim and a long-maturity rate better matches the investment horizon.
• Beta. Beta measures how much a stock’s returns move relative to the market, usually estimated by regressing the stock’s returns against an index such as the S&P 500. A beta of 1.0 moves with the market; above 1.0 means larger swings; below 1.0 means smaller ones. A higher beta raises the cost of equity.
• Equity risk premium. This is the extra return investors expect from stocks over the risk-free rate. It can be estimated from historical averages or from forward-looking models, and the choice of method is one of the largest sources of disagreement between analysts.

Worked Examples

All figures below are hypothetical and chosen to show the mechanics.

CAPM example. Assume a risk-free rate of 4%, an expected market return of 9% and a beta of 1.2.

Cost of equity = 4% + 1.2 × (9% − 4%) = 4% + 6% = 10%

If beta were 0.8 with everything else unchanged, the result would be 4% + 0.8 × 5% = 8%. The less volatile stock carries a lower required return.

Dividend growth example. Assume a share trades at $50, next year’s dividend is expected to be $2.00, and dividends are expected to grow 4% a year.

Cost of equity = $2.00 ÷ $50 + 4% = 4% + 4% = 8%

Note that D1 is the next dividend. If you only have the dividend just paid (D0), multiply it by (1 + g) first. Using D0 directly understates the result.

Implied dividend example. Solving the same equation for the dividend gives D1 = P0 × (ke − g). With a price of $40, a cost of equity of 9% and growth of 3%, the implied next-year dividend is $40 × (9% − 3%) = $2.40.

What Moves the Cost of Equity

• Interest rates. Under CAPM, a higher risk-free rate raises the cost of equity one for one, all else equal.
• Market risk appetite. When investors demand a larger premium for holding stocks, the equity risk premium rises and so does every company’s cost of equity.
• Business risk. Companies with cyclical revenue, high fixed costs or uncertain cash flows tend to have higher betas.
• Leverage (debt-to-equity). More debt makes the remaining equity riskier, because lenders are paid first and earnings become more volatile after interest. A common way to capture this is the Hamada equation, which adjusts an unlevered (asset) beta for leverage:

Levered β = Unlevered β × [1 + (1 − tax rate) × D/E]

For example, with a hypothetical unlevered beta of 0.9, a 21% tax rate and a D/E ratio of 0.5, levered beta is 0.9 × (1 + 0.79 × 0.5) ≈ 1.26. Raising D/E raises beta and therefore the cost of equity; paying down debt lowers it.

Beta also rises with higher operating leverage or a shift into more cyclical businesses. Because it is estimated from past price data, it changes with the measurement period and the index used.

How the Cost of Equity Is Used

• Valuation. In a discounted cash flow (DCF) model, the cost of equity discounts cash flows to equity holders, or feeds into WACC when discounting cash flows to the whole firm.
• Capital budgeting. Companies compare a project’s expected return, or its internal rate of return, with the hurdle rate. A project with positive net present value at that rate adds value.
• Financing decisions. Comparing the cost of equity with the cost of debt helps management decide whether to issue shares or borrow.

Cost of Equity vs. Related Measures

Cost of Equity vs. Cost of Capital (WACC)

The cost of capital is the blended cost of all funding sources. It is usually measured as the weighted average cost of capital, which weights the cost of equity and the after-tax cost of debt by their share of the capital structure. For instance, with a hypothetical 8% cost of equity, a 4% after-tax cost of debt and a 50/50 mix, WACC is 6%. Shifting toward cheaper debt lowers WACC only up to a point, because the added leverage also raises the cost of equity, as the Hamada equation shows.

Cost of Equity vs. Return on Equity

Return on equity (ROE) is an accounting result: net income divided by shareholders’ equity. The cost of equity is a market-based required return. When ROE consistently exceeds the cost of equity, the company is earning more on shareholders’ capital than they demand; when it falls short, it is not covering that requirement.

Cost of Retained Earnings vs. New Equity

Retained earnings are not free. Shareholders could have received that cash and invested it elsewhere, so the cost of retained earnings is generally treated as equal to the cost of equity. Issuing new shares costs more, because underwriting and other flotation costs reduce the proceeds. In the dividend growth model this is handled as ke = D1 ÷ [P0 × (1 − f)] + g, where f is the flotation cost as a percentage of the price.

Weighted Average Cost of Equity

When a company has more than one class of equity, such as common and preferred stock, the weighted average cost of equity multiplies each class’s cost by its share of total equity value and adds the results. Preferred stock is often costed as its fixed dividend divided by its price.

Limitations

• Both models rely on estimates. Beta, the equity risk premium and dividend growth are forecasts or historical proxies, and small changes move the result. In the CAPM example above, raising the premium from 5% to 6% lifts the cost of equity from 10% to 11.2%.
• CAPM’s assumptions are simplified. It assumes one source of systematic risk and well-diversified investors. Multi-factor models exist because size, value and other factors have been used to explain returns that beta alone does not.
• The dividend model breaks easily. It does not work without dividends, and it gives unreliable results when growth is unstable or close to the cost of equity.
• Private companies lack market data. With no share price or beta, analysts borrow betas from comparable listed companies, unlever and relever them, and often add premiums for size or illiquidity.
• Different methods give different answers. Many analysts calculate several estimates and use a range rather than a single figure.

FAQs

The Bottom Line

The cost of equity matters to investors judging whether a stock pays enough for its risk and to managers setting hurdle rates, valuing cash flows and choosing between issuing shares or borrowing. Because beta, the equity risk premium and dividend growth are all estimates, small changes shift the result. A sensible approach is to calculate several estimates with CAPM and, for dividend payers, the dividend growth model, then work from a range.