the capital asset pricing model
relevant to ACCA Qualification Paper F9
the cost of equity
Section F of the Study Guide for Paper F9 contains several references to the Capital Asset Pricing Model (CAPM). This article introduces the CAPM and its components, shows how it can be used to estimate the cost of equity, and introduces the asset beta formula. Two further articles will look at applying the CAPM in calculating a project-specific discount rate, and will review the theory, and the advantages and disadvantages of the CAPM. Whenever an investment is made, for example in the shares of a company listed on a stock market, there is a risk that the actual return on the ...view middle of the document...
The sum of systematic risk and unsystematic risk is called total risk1. THE CAPITAL ASSET PRICING MODEL The CAPM assumes that investors hold fully diversified portfolios. This means that investors are assumed by the CAPM to want a return on an investment based on its systematic risk alone, rather than on its total risk. The measure of risk used in the CAPM, which is called ‘beta’, is therefore a measure of systematic risk. The minimum level of return required by investors occurs when the actual return is the same as the expected return, so that there is no risk at all of the return on the investment being different from the expected return. This minimum level of return is called the ‘risk-free rate of return’. The formula for the CAPM, which is included in the Paper F9 formulae sheet, is as follows: E(ri) = Rf + βi(E(rm) - Rf) E(ri) = return required on financial asset i Rf = risk-free rate of return βi = beta value for financial asset i E(rm) = average return on the capital market This formula expresses the required return on a financial asset as the sum of the risk-free rate of return and a risk premium – βi(E(rm) Rf) – which compensates the investor for the systematic risk of the financial asset. If shares are being considered, E(rm) is the required return of equity investors, usually referred to as the ‘cost of equity’. The formula is that of a straight line, y = a + bx, with βi as the independent variable, Rf as the intercept with the y axis, (E(rm) - Rf) as the slope of the line, and E(ri) as the values being plotted on the straight line. The line itself is called the security market line (SML), as shown in Figure 1. FIGURE 1: THE SECURITY MARKET LINE Return E(ri) Rm Rf SML
In order to use the CAPM, investors need to have values for the variables contained in the model. THE RISK-FREE RATE OF RETURN In the real world, there is no such thing as a risk-free asset. Short-term government debt is a relatively safe investment, however, and in practice, it can be used as an acceptable substitute for the risk-free asset. In order to have consistency of data, the yield on UK treasury bills is used as a substitute for the risk-free rate of return when applying the CAPM to shares that are traded on the UK capital market. Note that it is the yield on treasury bills which is used here, rather than the interest rate. The yield on treasury bills (sometimes called the yield to maturity) is the cost of debt of the treasury bills. January 2008 student accountant 69
Because the CAPM is applied within a given financial system, the risk-free rate of return (the yield on short-term government debt) will change depending on which country’s capital market is being considered. The risk-free rate of return is also not fixed, but will change with changing economic circumstances. THE EQUITY RISK PREMIUM Rather than finding the average return on the capital market, E(rm), research has concentrated on finding an appropriate value for (E(rm) - Rf), which...