# What is the cost of equity?

Two weeks ago, we learned about a company’s beta.  Last week, we used the company’s beta when we learned about the capital asset pricing model.  This week, we are going to take things a little further.  In today’s post, we are going to be talking about the cost of equity.

Investopedia states that “a firm’s cost of equity represents the compensation that the market demands in exchange for owning the asset and bearing the risk of ownership.”  Traditionally, you would calculate the cost of equity using the dividend capitalization model but what if the firm you are studying does not pay dividends?  We can still use our capital asset pricing model to get the cost of capital.

If the firm that you are studying doesn’t offer a dividend, what else will it do with the money?  It will invest it in a project and use the profits for future dividends or future investment in other projects.  If you put yourself in the shoes of the investor, they could invest in something that pays an immediate dividend and reinvest the dividend in something else.  Alternatively, they could invest in something that doesn’t pay an immediate dividend but pays one down the road.  They are going to want to invest in the option that pays the most, though.  This means that the investor will be happy if the new project pays more than a security of comparable risk would pay.

According to the third edition of Corporate Finance: Core Principles & Applications, “the discount rate of a project should be the expected return on a financial asset of comparable risk.”

The Cost of Equity can be estimated as [pmath size=10]R_s = R_f + beta*(R_m – R_f)[/pmath]

Where [pmath size=10]R_f[/pmath] is the risk-free rate, [pmath size=10]R_m – R_f[/pmath] is the market risk premium, and [pmath size=10]beta[/pmath] is the stock beta.

This assumes that the stock’s beta is the same as the project’s beta and the firm has no debt.  If the assumptions are not true, the above equation would need to be adjusted.

Let’s look at a quick example.  The risk-free rate of return is typically equal to the United States three-month Treasury bill rate.  As of writing this, it is 0%.  Lets say that the firm has a beta of 1.2 and that the new project has the same risk as the rest of the firm.  Lets also say that the market risk premium equals 7%.

The cost of equity would be:  [pmath size=10]R_s = 0% + (1.2*7%) = 8.4%[/pmath]

According to the third edition of Corporate Finance: Core Principles & Applications, almost three-fourths of U.S. companies use the CAPM in capital budgeting.