ACCA P4 Advanced Financial Management - 2010 - Study text

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Chapter 5: Investing: portfolio theory and the CAPM

Example

The following information is available:

Risk-free rate of return

4.0%

Expected market return 7.5%

Standard deviation of market return 1.4%

Standard deviation of return from shares in company ABC 2.5%

Correlation coefficient for returns from shares in Company ABC

and returns from the market as a whole

0.90

Required

(a) Calculate the beta factor for Company ABC shares.

(b) Estimate the returns currently expected from Company ABC shares.

Answer

(a)

1.607=

1.4

2.50.90

ABC

(b) Expected return, shares in Company ABC = 4% + 1.607(7.5 – 4)% = 9.6245%.

4.4 The beta factor of a small portfolio

A portfolio of investments containing just a few securities will not be fully

representative of the market portfolio. Its systematic risk will therefore be different

from the systematic risk for the market as a whole.

The relationship between the systematic risk of a small portfolio and the systematic

risk of the market as a whole can be measured as a beta factor for the portfolio.

A beta factor for a portfolio is the weighted average value of the beta factors of all

the individual securities in the portfolio. The weighting allows for the relative

proportions of each security in the portfolio.

Example

A portfolio contains five securities. The proportions of each security in the portfolio

and the beta factor of each security are as follows:

Security

Proportion of the

portfolio

Beta factor of

the security

1 10% 1.20

2 25%

0.90

3 15%

0.96

4 30%

1.15

5 20%

1.06

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The beta factor for the portfolio is calculated as follows:

Security

Proportion

of the portfolio

Beta factor

of the security

β pβ

1 10%

1.20

0.120

2 25%

0.90

0.225

3 15%

0.96

0.144

4 30%

1.15

0.345

5 20%

1.06

0.212

Beta factor for the portfolio 1.046

4.5 Alpha factor

When shares yield more or less than their expected return (based on the CAPM), the

difference is an abnormal return. This abnormal return might be referred to as the

alpha factor. The alpha factor for a security is simply the balancing figure in the

following formula:

= R

+ β

– R

) + α

Example

The return on shares of company A is 11%, but its normal beta factor is 1.10. The

risk-free rate of return is 5% and the market rate of return is 8%.

There is an abnormal return on the shares:

11% = 5% + 1.10 (8 – 5)% +

α = 2.7%.

Example

An investor tries to buy shares or bonds for his portfolio that provide a positive

abnormal return. He is considering two shares and two bonds for adding to his

portfolio.

The required return on shares is measured by the Capital Asset Pricing Model

(CAPM). The required return for bonds is measured using a model similar to the

CAPM, except that the ‘beta’ for a bond is measured as the ratio of the duration of

the bond in years to the duration of the bond market as a whole.

Chapter 5: Investing: portfolio theory and the CAPM

The following information is available:

Expected actual

return (%)

Standard

deviation of

returns

Correlation

coefficient of returns

with the market

Equity market 11.0 12 1.00

Company X 9.5

0.92

Company Y 12.0

0.83

Bonds Duration (years) Coupon (%) Redemption yield (%)

Bond market 6.0

6.2

Bond P 5.0

6.4

Bond Q 8.5

6.5

The risk-free rate of return is 5%.

Required

Identify which of these investments currently offers a positive abnormal return.

Answer

The first step is to calculate beta factors for the shares and the similar factors for the

bonds.

For shares, the beta factor is calculated as the correlation coefficient multiplied by

the standard deviation of returns for the share, divided by the standard deviation of

market returns.

Security Beta factor

Share X (0.92 × 14)/12 1.073

Share Y (0.83 × 17)/12 1.176

Bond P (5.0/6.0) 0.833

Bond Q (8.5/6.0) 1.417

We can now calculate the required return for each security (using the CAPM) and

compare it with the expected actual returns. The difference is the abnormal return.

For bonds, the redemption yield should be used as the measure of return.

Security

Required

return

Actual expected

return

Abnormal

return

% % %

Share X 5% + 1.073(11

–

5)%

11.44

9.50

–

1.94

Share Y 5% + 1.176(11

–

5)%

12.06

12.00

–

0.06

Bond P 5% + 0.833(6.2

–

5)%

6.00

6.40 + 0.40

Bond Q 5% + 1.417(6.2

–

5)%

6.70

6.50

–

0.20

Only bond P offers a positive abnormal return. If the investor makes investment

decisions on the basis of abnormal returns, he will invest in this bond and add it to

his portfolio. (However, the abnormal return could be eliminated by a rise in the

price of the bond.)

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4.6 Advantages and disadvantages of the CAPM

The CAPM is based on some simplifying assumptions. For example, the CAPM

assumes:

 A perfect capital market

 Uniformity of investor expectations

 All forecasts (expectations) are made in the context of just one time period.

In spite of these simplifying assumptions, the CAPM appears to be reliable in

practice.

Advantages of CAPM Weaknesses of CAPM

It provides a measurable relationship between

risk and return.

It can be difficult to estimate values for the risk-

free rate and market rate of return, and the beta

factor for a security.

It can be used to estimate the cost of capital for

securities, notably equity shares.

It focuses on systematic risk only and ignores

unsystematic risk. Unsystematic risk is

significant for an investor who does not have a

well-diversified portfolio.

It can be adapted to establishing a required (risk-

adjusted) DCF return on capital investments by a

company.

It makes no distinction between the ways in

which a security provides its return (for example

dividends or share price increase).

4.7 Using the CAPM for capital investment appraisal

The CAPM can be used by companies for capital investment appraisal. Some types

of capital investment projects are more risky than others. For example, the

systematic risk of investing in the manufacture of cars may be higher than the

systematic risk of investing in a retailing business. Similarly, the risk of investing in

one country may be higher than the risk of investing in another country, due to

differences in the business environment or economic conditions.

This suggests that the expected returns from particular investments should be

adjusted to allow for differences in systematic risk.

If a beta factor for a particular project can be established, a risk-adjusted cost of

capital can be applied to the project. This risk-adjusted cost of capital should then be

used to calculate the project NPV.

For example, if a project’s beta factor is 1.30, the risk-free rate of return is 4.5% and

the market rate of return is 7%, the discount rate used to calculate the project NPV

would be:

4.5% + 1.30 (7 – 4.50)%

= 7.75%, say 8%.

Chapter 5: Investing: portfolio theory and the CAPM

4.8 International CAPM

The capital asset pricing model is usually applied to a single stock market, and the

market portfolio represents all the securities that are traded on that market.

However, the same general principles of the CAPM can be applied to international

investment.

International investors build a portfolio of investments that enables them to invest

world-wide. The ‘world market’ consists of all the main securities, such as company

shares, traded in different stock markets throughout the world.

International investors may wish to monitor returns from the ‘world market’, and

may wish to assess returns from individual securities by comparing their return

with the expected return from the world market as a whole.

An international capital asset pricing model for individual securities would be:

= R

+ β

– R

)

where R

is the average return from the world market as a whole.

Problems with the international CAPM

There are several problems with using an international CAPM.

 A risk-free rate of return has to be selected, but which securities are risk-free?

Returns on government securities vary between different countries. A risk-free

security for an international CAPM might be the returns on government

securities in a stable currency.

 The world market portfolio has to be identified. The world market may be based

on an international (world market) stock index, but there may be different views

about what should be in the portfolio.

 In practice, it is difficult for many investors to acquire a portfolio of investments

that represents the world market. However, many institutional investors do

attempt to do this, by:

− investing directly in stock markets around the world

− investing in international (global) companies, and

− possibly also investing in collective investments, such as mutual funds and

open-ended investment companies (Oeics).

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Paper P4

Advanced Financial Management

CHAPTER

Cost of capital

Contents

1 Weighted average cost of capital (WACC)

2 Cost of equity

3 Cost of debt capital

4 Calculating the WACC

5 Cost of capital and gearing

6 Change in gearing, the WACC and capital

investment appraisal

7 Asset beta

Paper P4: Advanced financial management

Weighted average cost of capital (WACC)

 Cost of equity, cost of debt and the weighted average cost of capital (WACC)

 WACC and capital investment appraisal

 Comparing the cost of equity and the cost of debt

1 Weighted average cost of capital (WACC)

1.1 Cost of equity, cost of debt and the weighted average cost of capital

(WACC)

The cost of capital for investors is the return that investors require from their

investment. Companies must be able to make a sufficient return from their own

capital investments to pay the returns required by their shareholders and holders of

debt capital. The cost of capital for investors therefore establishes a cost of capital for

companies.

 For each company there is a cost of equity. This is the return required by its

shareholders, in the form of dividends or share price growth

 There is a cost for each item of debt finance. This is the yield required by the

lender or bond investor

 When there are preference shares, there is also a cost of preference share capital,

which is the dividend yield required by the shareholders.

The cost of capital for a company is the return that it must make on its investments

so that it can afford to pay its investors the returns that they require.

The cost of capital for investors and the cost of capital for companies should

theoretically be the same. However, they are different because of the differing tax

positions of investors and companies.

 The cost of capital for investors is measured as a pre-tax cost of capital. This is a

return ignoring taxation.

 The cost of capital for companies recognises that interest costs are an allowable

expense for tax purposes, and the cost of debt capital to a company should allow

for the tax relief that companies receive on interest payments, reducing their tax

payments. The cost of debt capital for companies is measured as an after-tax

cost.

The weighted average cost of capital is the average cost of all the sources of capital

that a company uses. This average is weighted, to allow for the relative proportions

of the different types of capital in the company’s capital structure.

Chapter 6: Cost of capital

Example: pre-tax and after-tax cost of debt

A company has a bank loan of $100,000 on which it pays interest at 8%. The rate of

tax on company profits is 25%.

Gross interest on the loan each year is $8,000 and the pre-tax cost of the debt is 8%.

This means that the company needs to make a profit of $8,000 each year before tax

and interest in order to cover the interest cost of the debt. Tax relief on the interest is

$2,000, which means that the tax charge for the company is reduced by $2,000 each

year. The company therefore needs to make a profit after tax of $6,000 to cover the

cost of the debt interest, and the after-tax cost of the debt is just 6%. The $6,000 after

tax profit plus the reduction in the tax charge of $2,000 together provide the return

of $8,000 that is needed to cover the cost of the debt interest.

The after tax cost of debt is simply:

 the pre-tax cost of debt

 multiplied by a factor (1 – t) where t is the rate of tax on profits.

1.2 WACC and capital investment appraisal

One approach to the evaluation of capital investments by companies is that all their

investment projects should be expected to provide a return equal to or in excess of the

WACC. If all their investment projects earn a return in excess of the WACC, the

company will earn sufficient returns overall to meet the cost of its capital and provide

its investors with the returns they require.

This principle is often applied in practice. The general rule is that when capital

investment projects are evaluated using the NPV method, the cost of capital to be used

is the WACC. This is on the assumption that the capital project will not alter the risk

profile of the company’s investments and the risk with the new project is similar to the

risks with the rest of the company’s business operations.

The principle is often applied when the financing for a new capital investment changes

the company’s WACC. On the assumption that the capital project will not alter the risk

profile of the company’s investments, the NPV of the new project should be calculated

using the new WACC that will exist after the project has been undertaken and financed.

An alternative approach to the evaluation of capital investment projects, which does not

use these assumptions, is the adjusted present value method or APV method. (This is

explained in another chapter.)

1.3 Comparing the cost of equity and the cost of debt

For investors and for companies, the cost of their equity is always higher than the

cost of their debt capital. This is because equity investment in a company is always

more risky than investment in the debt capital of the same company.

In addition, from a company’s perspective, the cost of debt is also reduced by the tax

relief on interest payments. This makes debt finance even lower than the cost of equity.

The effect of more debt capital, and higher financial gearing, on the WACC is

considered in more detail later.

Paper P4: Advanced financial management

Cost of equity

 Methods of calculating the cost of equity

 Cost of equity: the dividend valuation model method

 Cost of equity: the dividend growth model method

 Gordon’s growth approximation

 Cost of equity: CAPM method

2 Cost of equity

2.1 Methods of calculating the cost of equity

There are several methods for estimating the cost of equity in a company. These are

the dividend valuation model method, the dividend growth model method and the

CAPM method. The three methods are described briefly in this section, though you

might be familiar with them already.

2.2 Cost of equity: the dividend valuation model method

If it is assumed that future annual dividends are expected to remain constant into

the foreseeable future, the cost of equity can be calculated as follows:

where:

is the cost of equity

d = the expected future annual dividend

MV is the share price ex dividend. The ex dividend share price is a price that

excludes any dividend that has been declared and is payable in the near future.

Example

A company’s shares are currently valued at $11.70 and the company is expected to

pay an annual dividend of $1.40 per share for the foreseeable future. The cost of

equity in the company can therefore be estimated as:

(1.40/11.70) = 0.1197 or 11.97%, say 12%.

ACCA P4 Advanced Financial Management - 2010 - Study text - Emile Woolf Publishing

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