The Capital Asset Pricing Model (CAPM) is one method of determining a
cost of equity based on the risks faced by shareholders. As such it can be viewed as part of a wider discussion looking at cost of capital. The risk attached to equity Introduction - risk and return Equity shareholders are paid only after all other commitments have been met. They are the last investors to be paid out of company profits.
The same pattern of payment also occurs on the winding up of a company. The order of priority is:
secured lenders legally-protected creditors such as tax authorities unsecured creditors preference shareholders ordinary shareholders.
As their earnings also fluctuate, equity shareholders therefore face the greatest risk of all investors. Since ordinary shares are the most risky investments the company offer, they are also the most expensive form of finance for the company.
The level of risk faced by the equity investor depends on:
volatility of company earnings extent of other binding financial commitments.
Given the link to the volatility of company earnings, it is these investors that will face more risk if the company was to embark on riskier projects.
If we want to assess the impact of any potential increase (or decrease) in risk on our estimate of the cost of finance, we must focus on the impact on the cost of equity.
The return required by equity investors can be shown as
Reducing risk by combining investments
An investor, knowing that a particular investment was risky, could decide to reduce the overall risk faced, by acquiring a second share with a different risk profile and so obtain a smoother average return.
Reducing the risk in this way is known as
In the diagram above, the investor has combined investment A (for example shares in a company making sunglasses) with investment B,(perhaps shares in a company making raincoats). The fortunes of both firms are affected by the weather, but whilst A benefits from the sunshine, B loses out and vice versa for the rain. Our investor has therefore smoother overall returns - i.e. faces less overall volatility / risk and will need a lower overall return.
The returns from the investments shown are negatively correlated - that is they move in opposite directions. In fact they appear to have close to perfect negative correlation - any increase in one is almost exactly matched by a decrease the other.
The diagram above is an exaggeration, as it is unlikely that the returns of any two businesses would move in such opposing directions,but the principle of an investor diversifying a portfolio of holdings to reduce the risk faced is a good one.
However an investor can reduce risk by diversifying to hold a portfolio of shareholdings, since shares in different industries will at least to some degree offer differing returns profiles over time.
Provided the returns on the shares are not perfectly positively correlated (that is they do not move in exactly the same way) then any additional investment brought into a portfolio (subject to a maximum point - see below) will reduce the overall risk faced.
Initial diversification will bring about substantial risk reduction as additional investments are added to the portfolio.
Systematic and non-systematic risk
However risk reduction slows and eventually stops altogether once 15-20 carefully selected investments have been combined.
This is because the total risk faced is not all of the same type.
The risk a shareholder faces is in large part due to the volatility ofthe company's earnings. This volatility can occur because of:
systematic risk - market wide factors such as the state of the economy non-systematic risk - company/industry specific factors.
Systematic risk will affect all companies in the same way (although to varying degrees). Non-systematic risk factors will impact each firm differently, depending on their circumstances.
Diversification can almost eliminate unsystematic risk, but since all investments are affected by macro-economic i.e.systematic factors, the systematic risk of the portfolio remains.
Investors and systematic risk
Rational risk-averse investors would wish to reduce the risk they faced to a minimum and would therefore:
arrange their portfolios to maximise risk reduction by holding at least 15-20 different investments effectively eliminate any unsystematic risk only need to be compensated for the remaining systematic risk they faced.
Determining betas in practice
The returns on the shares of quoted companies can be compared to returns on the whole stock market (e.g. by looking at an index such as the FTSE All shares index). Beta is found as the gradient of the regression line that results.
Betas for projects are found by taking the beta of a quoted company in the same business sector as the project.
Note the quoted beta derived is an equity beta so may need adjusting before use.(see below).
The Capital Asset Pricing Model (CAPM) The formula
The CAPM shows how the minimum required return on a quoted security depends on its risk.
The required return of a rational risk-averse well-diversified investor can be found by returning to our original argument:
This can be further expanded as:
So the formula becomes:
Required return = R
f + β × (R m - R f)
f = risk-free rate
m = average return on the market
m - R f) = equity risk premium (sometimes referred to as average market risk premium)
β = systematic risk of the investment compared to market and therefore amount of the premium needed.
Note: The use of CAPM in Accountancy exams Different accountancy bodies use slightly different versions of the above equation. In particular the LHS is shown as follows: ACCA: "Required return" is given as E(r i) CIMA: "Required return" is given as K e (the cost of equity) ICAEW: "Required return" is given as r j The Security Market Line
The formula is that of a straight line, y = a + bx, with β as the independent variable, R
f as the intercept with the y-axis, (R m - R f) as the slop of the line, and the required return as the dependent variable.
The line itself is called the security market line (SML) and can be drawn as:
If an investment is riskier than average (i.e. the returns more volatile than the average market returns) then β > 1.
If an investment is less risky than average (i.e. the returns less volatile than the average market returns) then β < 1.
If an investment is risk free then β = 0.
CAPM and gearing risk
To calculate a risk adjusted
discount rate for a project a company will need to find a suitable beta factor for the new investment and that these are best estimated with reference to existing companies operating in the same business areas as the project.
The reason this approach works is:
those companies paying above average returns are assumed to have a correspondingly higher than average systematic risk and their beta (the measure of the company's systematic risk compared to the market) is extrapolated accordingly the extrapolated beta is then considered a measure of the risk of that business area.
However, the above only considers the business risk. When using betas in project appraisal, the impact of
financial gearing (hereafter referred to as "gearing") must also be borne in mind. Geared and ungeared betas
Firms must provide a return to compensate for the risk faced by investors, and even for a well-diversified investor, this systematic risk will have two causes:
the risk resulting from its business activities the finance risk caused by its level of gearing.
Consider therefore two firms A and B:
both are identical in all respects including their business operations but A has higher gearing than B: A would need to pay out higher returns any beta extrapolated from A's returns will reflect the systematic risk of both its business and its financial position and would therefore be higher than B's.
Therefore there are two types of beta:
Asset reflects purely the systematic risk of the business area.
Equity reflects the systematic risk of the business area and the company-specific financial structure. Using betas in project appraisal
It is critical in examination questions to identify which type of beta you have been given and what risk it reflects. The steps to calculating the right beta and how to use it in project appraisal are:
(1) Find an appropriate asset beta. This may be given to you in the question. If not, you will need to calculate it by de-gearing a given equity beta. You can do this using the asset beta formula given to you in the exam
However, in many exams, ß
d will be assumed to be zero. This means that the asset beta formula can be simplified to:
e = market value of equity
d = market value of debt
T = corporation tax rate.
When using this formula to de-gear a given equity beta, V
e and V d should relate to the company or industry from which the equity beta has been taken.
If using the
adjusted present value (APV) approach, then this asset beta can be used to calculate a Ke to determine the base case NPV.
If needing a
risk adjusted WACC, then the following steps need to be followed as well.
Note: for a discussion of which approach to use when, please click
here. (2) Adjust the asset beta to reflect the gearing levels of the company making the investment Re-gear the asset beta to convert it to an equity beta based on the gearing levels of the company undertaking the project. The same asset beta formula as given above can be used, except this time V e and V d will relate to the company making the investment. (3) Use the re-geared beta to find K e. This is done using the standard CAPM formula.
Remember that CAPM just gives you a risk-adjusted K e, so once a company has found the relevant shareholders' required return for the project it could combine it with the cost of debt to calculate a risk adjusted weighted average cost of capital. This is discussed in further detail here
Created at 7/13/2012 4:40 PM by System Account
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Last modified at 11/13/2012 11:35 AM by System Account
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