Calculating Facebook's cost of equity using CAPM

¶ … equity at Facebook is to use the capital asset pricing model. The formula for CAPM is as follow:

Rj = RF + ?j [RM - RF]

The first step to determining the cost of equity is to gather the different variables go into CAPM. The risk free rate is the first such variable. The risk free rate reflects the rate of return that an investor can earn on an investment that has no risk The only investments that are deemed to have no risk are Treasury securities. This is because the U.S. Treasury prints money, so there is zero risk that these will not be repaid. There is risk that the payment will not have the same real value, but it will have the same nominal value as expected.

According to the U.S. Treasury webpage, a one-year Treasury bond carries with it a rate of 0.13%. This is the risk free rate to be used in the capital asset pricing model calculation.

The next step is to calculate the market risk premium. This is assumed to be 5%. This means that the component of CAPM that is [RM - RF] is 5%. The expression RM must be 6%, given this.

The remaining variable is the beta, which is the expression of the correlation between the performance of the company and performance of the general market. The beta essentially is the firm-specific risk of the company while the other components of CAPM are the risk-free rate and the market risk premium. Facebook began trading in May, 2012. There is a beta listed on Yahoo Finance of 1.77 for Facebook, so this can be used to calculate the cost of equity for the company using CAPM.

Other Models

There are two other models that can be used to price out the cost of equity for these companies. The first is the dividend growth model and the second is the arbitrage pricing model. Using the dividend growth model is challenging because it relies on the company to pay a dividend. Right now, there is no dividend at Facebook. The model, in these situations, relies on the expectation of future dividend for its logic, but at this point there is no expectation of a future dividend so this model is challenged to be useful for a company like Facebook.

The arbitrage pricing model can be used. It has the same underlying logic as the capital asset pricing model. However, instead of using market returns as the critical variable, any number of different variables can be chosen. These variables are usually macroeconomic indicators that are linked to the business, such as GDP, unemployment, trade statistics and interest rates. Often, a basket of these variables is used, with weights assigned to reflect the importance of that variable.

The APT can thus be used for Facebook. This would happen by choosing which variables are important and then assigning weights to them. Then, the figures for those variables would be gathered, and a regression run on them to determine the degree to which they correlate with changes in the firm's stock price. This is the same mechanism used to determine a firm's beta. When plugged into the APT calculation, a weighted average of the different variables is used in order to derive the final number determining the value of the firm based on the current state of those variables.

Sources

Campbell, H. (1995). The CAPM - WWWFinance. Retrieved May 2012 from http://www.duke.edu/~charvey/Classes/ba350/riskman/riskman.htm

Investopedia.com (2012). Financial concepts: capital asset pricing model (CAPM). Retrieved May 2012 from http://www.investopedia.com/university/concepts/concepts8.asp

Yahoo! Finance. Retrieved November 18, 2013 from http://finance.yahoo.com/