## Cost of Equity Formula

The cost of equity is the return a company requires to decide if an investment meets capital return requirements. It is used in business valuation to see whether a business is a good investment risk. Companies often use the Capital Asset Pricing Model (CAPM) to calculate it.

Here is the formula according to the CAPM:

Cost of Equity = Risk-Free Rate + Beta * (Market Return – Risk-Free Rate)

Where:

- Risk-Free Rate is the return on a risk-free investment, such as a U.S. Treasury Bond.
- Beta represents the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. Beta is used in the CAPM, which calculates the expected return of an asset based on its beta and expected market returns.
- Market Return is the total return on the market as a whole.

For example, if the risk-free rate is 2%, the beta of the stock is 1.5, and the market return is 8%, then the cost of equity would be:

Cost of Equity = 2% + 1.5 * (8% – 2%) = 11%

This means that the company’s cost of equity, or the return required by a shareholder for investing in that company, is 11%.

Please note, this calculation assumes that the market risk premium is the same for all securities, which might not always be the case. Also, it assumes that the only risk is systematic risk (measured by beta), ignoring unsystematic risk.

## Example of the Cost of Equity Formula

Let’s provide an example using the CAPM formula for the cost of equity:

Cost of Equity = Risk-Free Rate + Beta * (Market Return – Risk-Free Rate)

Suppose we have the following data for a hypothetical company:

- Risk-Free Rate: 2%
- Beta: 1.2
- Market Return: 10%

We can substitute these values into the formula:

Cost of Equity = 2% + 1.2 * (10% – 2%)

Solving this equation gives:

Cost of Equity = 2% + 1.2 * 8%

Cost of Equity = 2% + 9.6% = 11.6%

So, in this example, the cost of equity or the return required by an investor for investing in this company is 11.6%. This means that in order to attract investors, the company needs to offer a return on equity of at least 11.6%.