The cost of capital CAPM

WHAT IS THE COST OF CAPITAL

The expected return on a portfolio composed by all the company’s equity and debt is called the company cost of capital. It can be also interpreted as the opportunity cost of capital, when deciding to invest in the company’s assets, and also the discount rate that the firm has to use when considering investments in average-risk projects. If a firm has no debt, then the cost of capital the firm faces is only the expected return on the firm’s stock. The cost of capital is computed as follows:

Where rf is the safe rate at which the company issues debt, β is the beta of the company (we talked about firms’ betas in our previous lecture). Be careful: the company’s cost of capital is not the right discount rate that the firm has to use when considering projects that are more (or less) risky than the normal activities of the firm. You can use the same discount rate only for projects that have the same level of risk. If this is not the case, when calculating value of a firm you, should calculate and discount separately each project according to their level of riskiness. The opportunity cost therefore must not be considered as standard for each project because it depends on what you want to use it for. Calculating the cost of capital is still worth it because many of the projects a firm will be able to complete bear the same level of risk. Furthermore, it is easier to value the risk of other projects by using as a starting point the average risk instead of estimating that same risk starting from 0.

THE FIRM’S VALUE

The sum of the debt and equity of a firm constitute the company’s value (D+E=V). A firm value equals the firm’s asset value. The debt ratio is the proportion of the value of the firm made up of debt (D/V) while the value made up of the firm’s equity is the equity ratio (E/V). Remember that we are considering market values and not book values (the ones you will find the company’s balance sheet). This distinction is important because the equity market value is generally higher than their book value so, the D/V ratio is much higher in the accounting records and the E/V ratio is much lower. The returns the company has to promise when using debt is lower than the ones it has to promise to stockholders because stocks bear a higher level of risk. The company’s cost of capital is calculated as the weighted average of the returns it promises to debt holders and stock holders. The cost of capital computed in this way is called the weighted average cost of capital (WACC).

WHAT IF YOU HAVE TAXES

If a company needs to pay taxes, you have to take those into consideration when computing the WACC. The after tax WACC is modified in:

In the formula Tc is the corporate tax rate. Notice that only the part of the WACC related to debt is affected by the taxes. Be careful when interpreting this formula: the cost of debt is always less than the one of capital. You could wrongly think of reducing the WACC by employing more debt and less equity. This is not a good strategy, because the more the company is in debt the riskier it will be for investors to invest in it and therefore the higher return they will demand.

HOW TO ESTIMATE BETA

When you consider the risk of a stock, only a small part of it is due to the movements of the market. This kind of risk is denoted by R-squared (R^2). The most important factors influencing the risk of a stock is the firm specific risk which is diversifiable. The beta of a stock can be estimated by looking at how much that stock responded to market movements in the past. This measure obviously is not 100% precise because movements is the past suffer from some “noise”: other factors that could have affected the stock returns. This is because generally when estimating the beta it is often used also a confidence interval.

ASSET BETA

We can calculate the risk of a project with the asset beta βa. We can simply calculate it by using the riskiness (betas) of both debt and capital:

A LITTLE MORE ABOUT THE CAPM

It is important to remember that the CAPM can try to predict costs of capital for short periods of time and not for the long term. You can try to use the CAPM by using long term interests instead of short term ones but this would not result in an accurate estimate. A more precise way of computing the CAPM in the long run is to use the risk premium computed using the market return and the short term treasury bills rate. If you choose to do so you have to estimate the return you expect from holding those treasury bills for the desired period of time. You can do so by subtracting from the long run yield on bonds the risk premium from holding those bonds instead of treasury bills (which is on average 1.5%).