In our

**capital asset pricing model**formula, we've got the**risk-free rate**(Rf)**,**that's the rate of return you'd earn on an investment that has zero risk like a 3-month US Treasury bill or something like that. Then you add to that the**beta (βi)**of this stock, that's a measure of the**systemic risk**of that stock. We're gonna multiply it by the**market risk premium,**which is**the expected rate of return**for the market portfolio**(Rm)**minus**the risk-free rate (Rf)**that's our market risk premium. That is going to give us the expected return of that stock which is also the cost of equity. So the expected return and the cost of equity they're actually the same thing.This is the rate of return let's say that it's Walmart, so there's an investor in Walmart and they're expecting to earn a certain return given the

**systematic risk**of the stock of Walmart. So the cost of equity from the perspective of the firm this**Ri**is equity. So this is equity that they have issued these shares and then people bought the shares and so forth, so they've got equity. You could think about it as the cost of equity for this firm. I'm going to show you an example of how they actually calculate this out because that's all pretty abstract.Let's take a fictional company called

**Titania**and we'll estimate the cost of equity capital for titania using the CAPM. So let's say that we've got our**risk-free rate is**2%, the**expected return**for the market portfolio was**10%**and then we've got**the beta**of titania which is the measure of systemic risk of this company of the stock is 1.20. Now we can just plug in our capital asset pricing model (CAPM). What we're trying to solve for the**Ri,**the expected rate of return or the cost of equity. So we don't know that but we know everything on the right-hand side of our formula. We know the risk-free rate and we know the expected return for the market portfolio. If you're actually trying to calculate this for a company and you're thinking what do I use for the market portfolio? You could look at the rate of return for the**S&P 500**something like that, you could use that as a measure for the market portfolio. So we've got our market portfolio the return is**10%**but then we subtract to get the market risk premium. We have to subtract the**risk-free rate**from the**expected rate of return**for the market portfolio. So that gives us the actual market risk premium is 8%. This**8%**is the expected rate of return for a portfolio that would have a beta of**1**.So it's basically the expected, this is the rate of return for barring market risk. Now we multiply that by

**the beta**of titania because titania does not have a beta of**1**it just doesn't move exactly with the market. So it's actually more risk because it has a higher beta than**1**. It's**1.2,**so we multiply the**8%**market premium times the beta of the stock which is**1.2,**and that gives us**9.6%**and then we add to that the**risk-free rate**, so that gives us**11.6%**. That is the expected rate of return for titania if we're looking at titania stock which is the cost of equity capital.It's easier to think intuitively about the cost of debt than anything about the interest rate paid by a company on its debt but the cost of equity is a little less intuitive so we use this capital asset pricing model (CAPM). We said look there's

**11.6%**is the cost of equity for titania. Now notice something if we were to**increase**the beta, if we were to say take it from**1.2**to**1.8**we increase the beta as we increase this, we are going to increase the**cost of equity**. If you increase the beta you increase the cost of equity. What does that mean? The systematic risk, as the risk of titania increases then the people who are investing in titania hold shares of stock, and titania they are going to demand a greater return given that they have a higher risk. More risk means the investors are going to want a greater reward. So as the risk goes up as beta gets higher and higher the cost of equity increases as well.