# How to calculate cost of equity capital in CAPM?

|The **Capital Asset Pricing Model** is a technique for calculating the cost of equity capital which involves current risk-free rate, beta and market risk premium for common stocks.

The formula to calculate Cost of equity is:

**Cost of equity = Current risk-free rate + (beta x market risk premium for common stocks)**

**What is Risk-Free rate?**

The risk-free rate, as its name implies, is the return available from an investment that carries no risk. In practice, U.S. Treasury bill rates often are used as a proxy for the risk-free rate. Some companies, however, consider a longer-term Treasury bond rate to be a more appropriate risk-free rate to use in developing the cost of equity.

**What is a Beta?**

**Beta** is a measure of the risk of a particular stock compared to the entire stock market. It is the covariance of the stock with the market. It is derived by running a regression analysis between the returns on a specific stock and those of a broad index of stocks such as the SAP 500. A stock with a beta of more than one has greater volatility than the under-lying market, and vice versa. The Capital asset pricing model (**CAPM**) states the expected risk premium for a given stock is proportional to its beta. Although the Capital asset pricing model is widely used, the accuracy of betas for particular company stocks has been questioned in recent years.

WATCH THIS:A more difficult problem for you and other owners of private companies is that a beta for such companies cannot be calculated. There is no way to compare the performance of your company’s value to the stock market as a whole. One approach to estimating a beta in this situation is simply to make a managerial judgment about how well the company’s performance tracks the overall market. Another way to estimate a beta is to look for the betas of comparable companies that are traded. Calculations of betas are available from several sources, such as Value Line.

**What is a Market-risk Premium?**

The **market-risk premium** is the incremental rate of return required by investors to hold a well-diversified portfolio of stocks rather than risk-free securities. The historical difference between the stock-market return and the risk-free rate, used in the formula above, is available in the frequently used yearbook, Stocks, Bonds, Bills and Inflation, published by Ibbotson Associates of Chicago. According to the 2002 Yearbook, the compound annual return for United States Treasury Bills between the end of 1925 and the end of 1998 was 3.8 percent. Over the same period, the compound annual return for large company stocks was 10.2 percent and for small company stocks 12.1 percent. Therefore, the market risk premium for large company stocks was 6.4 percent (10.2 minus 3.8 percent) and for small companies 8.3 percent (12.1 minus 3.8 percent).

The Capital asset pricing model cost-of-equity calculation for a small company with a beta of 1.2 is calculated as: 3.8% + (1.2 x 8.3%) = 13.96%.