ACCA paper f9 financial management study materials F9FM session12 d08

SESSION 12 – CAPITAL ASSET PRICING MODEL OVERVIEW Objective To understand the Capital Asset Pricing Model and its uses in financial management SYSTEMATIC AND UNSYSTEMATIC RISK BETA FACTORS CAPITAL ASSET PRICING MODEL USES OF THE CAPM Well-diversified investor Companies Asset betas Equity betas Use of the equity beta Definitions Measurement of systematic risk Measurement Calculation Interpretation Formula Security Market Line DEGEARING AND REGEARING BETA Project appraisal in a new industry MM and betas ASSUMPTIONS AND LIMITATIONS Assumptions Limitations 1201 SESSION 12 – CAPITAL ASSET PRICING MODEL SYSTEMATIC AND UNSYSTEMATIC RISK 1.1 Definitions Risk, the variability of returns, can be split into two elements: unsystematic risk − systematic risk 1.2 These are the risks that are unique to each company’s shares; − It is the element of risk that can be potentially eliminated by shareholders building a diversified portfolio − It is also known as unique or industry-specific risk − These are the risks that affect the market as a whole rather than specific company shares; − This cannot be diversified away; − Therefore systematic risk still remains even in a well-diversified portfolio; − This is also known as market risk Measurement of systematic risk A well-diversified portfolio of shares still has some degree of risk or variability This is due to the fact that all shares are affected by systematic risk i.e to macro-economic changes Systematic risk will affect the shares of all companies although some will be affected to a greater or lesser degree than others This sensitivity to systematic risk is measured by a beta factor BETA FACTORS 2.1 Measurement Beta factors for quoted shares are measured using historic data and published in”beta books” They are determined by comparing changes in a share’s returns to changes in the stock market returns over a period of many years (5 years data should be used at least) This can be illustrated by the Security Characteristic Line which gives an indication of the share’s sensitivity to market changes The beta factor is estimated from these observations by determining the gradient or slope of the “line of best fit” through the observed points The steeper the slope the more volatile the share and the higher the beta factor 1202 SESSION 12 – CAPITAL ASSET PRICING MODEL Security characteristic line (Ri - Rf) Slope = β Intercept = α (Rm - Rf) Where (Ri − Rf) = the excess return of the share over the risk free return (Rm − Rf) = the excess return of the stock market over the risk free return Rf = the return on a risk-free investment The Security Characteristic Line should in the long run pass through the point where the two axes meet However in the short run this may not always be the case and any short term difference, or abnormal return, is known as the alpha factor 2.2 Calculation A beta factor for a share “i” can also be calculated using linear regression: Bi = Covariance of i with the market Variance of the market' s returns Or Correlation of the share with the market × standard deviation of the share‘s returns Standard deviation of the market’s returns Example A share has a standard deviation of 15% and a correlation coefficient with the market returns of 0.72 The standard deviation of the market is 21% What is the share’s beta factor? Solution 1203 SESSION 12 – CAPITAL ASSET PRICING MODEL 2.3 Interpretation A beta factor therefore simply describes a share’s degree of sensitivity to changes in the market’s returns, caused by systematic risk Beta factor of − this indicates that the share is as sensitive as the market to systematic risk Beta factor > − this means that the share is more sensitive than the market Therefore if the market in general rises by 10% then the returns from this share are likely to be more than 10% Beta factor < − the share is less sensitive than the market and is likely to rise and fall in value less than the market in general CAPITAL ASSET PRICING MODEL 3.1 Formula If the shareholders of a company hold well-diversified portfolios then they are concerned only with systematic risk The return these shareholders require therefore is only a return to cover the systematic risk of an investment Systematic risk is measured by a beta factor - therefore the required return from an investment must be related to the beta factor of that investment This is brought together in the Capital Asset Pricing Model which is a formula that relates required returns to beta factors as measures of systematic risk The CAPM formula is : E(ri) = Rf + i(E(rm)–Rf) E(ri) Rf E(rm) βι = = = = expected/required return from an investment risk free return expected return from the “market portfolio” beta of the investment The Market Portfolio is a portfolio containing every share on the stock market CAPM is the equation of the Security Market Line 1204 SESSION 12 – CAPITAL ASSET PRICING MODEL 3.2 Security Market Line The Security Market Line is a graph that indicates the required return from any investment given its beta factor Forecast returns from investments can be compared to the figure from the security market line to indicate whether that investment is under or over valued Return Security market line x Rb Rm x Ra Rf Ba Bb Beta Where Ra = the forecast return from investment A The required return of an investment with a beta of zero (risk free) will be the risk free return The required return of an investment with a beta of will be the market return Consider investment A - it is forecast to earn higher returns than the CAPM would predict given its beta It is therefore temporarily under-priced This is referred to as a “positive alpha” investment Consider investment B - it would appear to be temporarily over priced – a “negative alpha” investment In the long run market forces should ensure that all investments give the returns predicted by the Security Market Line 1205 SESSION 12 – CAPITAL ASSET PRICING MODEL USES OF THE CAPM 4.1 Well-diversified investors If an investor already holds a well-diversified portfolio then that investor will be concerned only with systematic risk The CAPM is therefore relevant The investor will be satisfied only if a potential investment gives a high enough return given its sensitivity to market risk as measured by its beta factor Example An investment has an forecast return over the next year of 12% The beta of the investment is estimated at 0.9 The risk free rate is 5% and the market return is 15% Should a well-diversified investor buy this investment? Solution 4.2 Companies Companies should not diversify their activities simply to reduce the risk of their shareholders Shareholders can diversify their shareholdings much more easily than a company can diversify its activities If shareholders are already well-diversified then the company should concern itself, on behalf of the shareholders, simply with the systematic risk of potential projects Therefore the aim of a company, with well-diversified shareholders, should be to determine the required return from its investment projects and then compare this to the forecast return If the project is the same risk as that of the existing activities of the company then the existing WACC can be used However if the project is of a different risk type to the existing activities then the existing WACC will not be appropriate In these instances a tailor-made discount rate for that type of project must be determined using the CAPM 1206 SESSION 12 – CAPITAL ASSET PRICING MODEL 4.3 Asset betas Any company is made up of its assets or activities These assets will have a certain amount of risk depending upon their nature These assets will have a beta factor that recognises the sensitivity of such assets to systematic risk This beta factor is the asset beta and measures the systematic business risk of the company It can also be referred to as an ungeared beta factor 4.4 Equity betas The equity beta measures the sensitivity to systematic risk of the returns to the equity shareholders in a company In an all-equity financed company, or ungeared company, the only risk that is incurred is business risk Therefore in an ungeared company the asset beta and the equity beta are the same However in a geared company the equity shareholders face not only business risk, measured by the asset beta, but also a degree of financial risk Therefore in a geared company the equity beta > the asset beta Equity betas can also be called geared betas 4.5 Use of the equity beta The equity beta measures the sensitivity to market risks of the equity shareholders’ returns If the equity beta is used in the CAPM this gives the required return for the equity shareholders The required return of shareholders = the cost of equity geared (Keg) The CAPM can therefore be used as an alternative to the Dividend Valuation Model for estimating the cost of equity of a company Example The equity beta of a company is estimated to be 1.2 The risk free return is 7% and the return from the market is 15% Estimate the cost of equity of the company? Solution 1207 SESSION 12 – CAPITAL ASSET PRICING MODEL DEGEARING AND REGEARING BETA 5.1 Project appraisal in a new industry It has already been noted that a company’s existing WACC is only a relevant discount rate for a project with the same level of business risk as existing activities If the project is in a different industry (or country) then a discount rate to reflect the business risk of that industry is required A company in a similar industry can be found and its beta discovered If that company is geared then its equity beta will contain both business risk and financial risk However that company will probably have a different level of gearing compared to our company This requires us to first “degear” the beta to find the asset beta, and then “regear” to reflect our company’s level of financial risk 5.2 MM and betas The following formula (based on Modigliani and Miller’s models) can be used to convert an equity beta to an asset beta (and vice-versa):     Vd(1 − T ) Ve d e +  a=   (Ve + Vd(1 − T ))   (Ve + Vd(1 − T ))  where βa = βe = βd = Ve = Vd= T = asset beta equity beta beta of corporate debt market value of equity market value of debt corporation tax rate If the exam question does not give a beta factor for debt then assume that debt is risk free i.e βd = 1208 SESSION 12 – CAPITAL ASSET PRICING MODEL Example A plc produces electronic components but is considering venturing into the manufacture of computers A plc is ungeared with an equity beta of 0.8 The average equity beta of computer manufacturers is 1.4 and the average gearing ratio is 1:4 The risk free return is 5%, the market return 12% and the rate of Corporation Tax 33% If A plc is to remain an equity financed company what discount rate should it use to appraise a computer manufacture project? Solution Example Suppose that A plc from the previous example has a gearing ratio of 1:2 It still wishes to enter into the same computer manufacturing project What is the discount rate that should be used for A plc for a computer manufacturing project? Solution 1209 SESSION 12 – CAPITAL ASSET PRICING MODEL ASSUMPTIONS AND LIMITATIONS OF THE CAPM 6.1 Assumptions total risk can be split between systematic risk and unsystematic risk; unsystematic risk can be completely diversified away; all of a company’s shareholders hold well-diversified portfolios a risk-free security exists; perfect capital markets 6.2 Limitations it is a single period model; it is a single index model - beta being the only variable to explain different required returns on different investments Lack of data for the model – particularly in developing markets CAPM tends to over-state the required return on very high risk companies and understate the returns on very low risk companies Many of the assumptions not hold in real life Key points CAPM is an alternative to the Dividend Valuation Model (DVM) for estimating a company’s cost of equity Beta factors measure systematic risk and therefore CAPM should only be used if the company’s shareholders have themselves used portfolio theory to diversify way unsystematic risk Despite its assumptions and limitations CAPM is a more flexible model than DVM as it allows the estimation of project-specific discount rates FOCUS You should now be able to: understand the meaning and significance of systematic and unsystematic risk; appreciate the uses of the CAPM for financial management; discuss the assumptions and limitations of CAPM 1210 SESSION 12 – CAPITAL ASSET PRICING MODEL EXAMPLE SOLUTIONS Solution Beta factor = 0.72 × 15 21 = 0.51 Solution Required return = + 0.9 × (15 − 5) = 14% Expected return = 12% Therefore the investor should not invest Solution Ke = + 1.2 × (15 − 7) = 16.6% Solution Using MM formula find the asset beta of the computer industry:     Vd(1 − T ) Ve d e +  a=   (Ve + Vd(1 − T ))   (Ve + Vd(1 − T ))  Ba = 1.4 + (1 × 0.67) Asset beta = 1.2 As A plc is ungeared then this asset beta is the appropriate beta for use in the CAPM in order to determine the discount rate that A plc should use for a computer manufacture project: Required return = = + 1.2(12 − 5) 13.4% 1211 SESSION 12 – CAPITAL ASSET PRICING MODEL Solution Using MM formula find the asset beta of the computer industry:     Vd(1 − T ) Ve d e +  a=   (Ve + Vd(1 − T ))   (Ve + Vd(1 − T ))  Ba = 1.4 + (1 × 0.67) Asset beta = 1.2 In order to find the discount rate for A plc this asset beta must be converted into an equity beta appropriate to A plc: 1.2 = Be + (1 × 0.67) 1.2 = 0.749 × Be Be = 1.6 Ke of A plc if in computer manufacture = + 1.6 (12 – 5) = 16.2% The discount rate that A plc must use is the WACC that it would have if its Ke were 16.2% In the absence of any other information assume Kd is 5% (risk free rate) Discount rate 1212 = 16.2% × = 11.92% + (1 – 0.33) × ... and significance of systematic and unsystematic risk; appreciate the uses of the CAPM for financial management; discuss the assumptions and limitations of CAPM 1210 SESSION 12 – CAPITAL ASSET... beta discovered If that company is geared then its equity beta will contain both business risk and financial risk However that company will probably have a different level of gearing compared to... first “degear” the beta to find the asset beta, and then “regear” to reflect our company’s level of financial risk 5.2 MM and betas The following formula (based on Modigliani and Miller’s models)