ACCA F9 Financial Management - 2010 - Study text

Подождите немного. Документ загружается.

Chapter 17: Capital asset pricing model (CAPM)

Answer

(a)

()

(

)

()

0.301200600

0.301200

05.0

0.301200600

600

25.1

−+

−

×+

−+

×=

= (1.25

× 600/740) + 0.05 × 140/740)

= 1.0135 + 0.0095 = 1.023

(b) If the debt capital is risk-free, the asset beta is 1.0135 (see workings above).

It is often assumed that debt capital is risk-free because the estimate of the asset beta

is not affected significantly by this simplifying assumption.

Relevance of asset beta

The asset beta is a beta factor that reflects the business risk of a particular business

operation. It can be used to estimate a cost of equity capital for a specific capital

investment project and so a project specific discount rate for use with DCF analysis.

This is explained in a later section.

2.7 Advantages and disadvantages of the CAPM

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

assumes:

 A perfect capital market, in which all investors have access to all available

information about the financial markets

 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. The advantages and disadvantages of the CAPM are summarised in the

following table.

Advantages of CAPM Weaknesses of CAPM

It provides a measurable relationship

between risk and return.

It can be difficult to estimate

statistically reliable 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).

Paper F9: Financial management

316 Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides © EWP

The cost of capital for capital investment appraisal

 CAPM and the WACC

 The beta factor of a security

 Formula for the CAPM

 The beta factor of a small portfolio

 Alpha factor

 Advantages and disadvantages of the CAPM

3 The cost of capital for capital investment appraisal

3.1 CAPM and the WACC

The capital asset pricing model can be used to calculate a cost of equity for any

company. It can also be used to calculate a cost of capital for corporate debt, but this

is less likely to feature in your examination. The cost of equity calculated using the

CAPM can then be used in the calculation of the company’s weighted average cost

of capital.

The CAPM probably provides a more reliable estimate of the cost of equity than the

dividend valuation model or the dividend growth model, because:

 The CAPM ignores volatility in returns caused by unsystematic risk factors,

which should not affect the cost of equity for well-diversified investors

 the beta factor for each company is measured statistically from historical stock

market data.

In your examination you might be required to calculate a cost of equity using the

CAPM and then use your cost of equity to calculate a WACC.

3.2 Company value and cost of capital

The previous chapter explained how the cost of capital can be calculated from

expected returns (dividends or interest) and the market value of securities. It is also

possible, using the same mathematical method, to calculate what the market value

of shares or bonds ought to be, given expectations of future returns (dividends and

interest) and the cost of capital. One basic rule is that for a given size of expected

future returns, the total value of a company is higher when the cost of capital is

lower.

By making simplifying assumptions of constant annual operating profits, and

paying out all earnings as dividends each year, we can state a formula linking the

total value of a company to its WACC:

Total market value (debt + equity) =

Annual profits before interest

WACC

Chapter 17: Capital asset pricing model (CAPM)

There is a direct relationship between expected future returns for investors, the cost

of capital and the total market value of a company.

A similar concept is applied in investment appraisal and DCF analysis of capital

projects. There is a relationship between:

(a) the future cash flows that a capital investment project will be expected to

provide

(b) the cost of capital, and

With investment appraisal using DCF analysis, the expected future cash flows (cash

profits) from a capital investment project are discounted at a cost of capital. The

total value of the company should increase if the project has a positive NPV when

the cash flows are discounted at the appropriate cost of capital. The expected

increase in the value of the company should be the amount of the NPV.

The appropriate cost of capital for calculating the NPV should be a cost of capital

that represents the investment risk of the project and the returns that the project

must earn to meet the requirements of the providers of the capital.

3.3 Average and marginal cost of capital

The marginal cost of capital of a capital investment project is the additional

minimum return that the project must provide to meet the requirements of the

providers of the capital. The cost of the additional capital required for a new capital

investment project can be defined as the

marginal cost of capital. There will be an

increase in the total value of the company from investing in a project only if its NPV

is positive when its cash flows are discounted at the marginal cost of the capital.

The

average cost of capital is the cost of capital of all existing capital, debt and

equity. This is represented by the WACC.

Capital investments should be discounted at their marginal cost of capital, but are

usually discounted at the company’s WACC.

This is because it is generally assumed that the effect of an individual project on the

company’s marginal cost of capital is not significant; therefore all investment

projects can be evaluated using DCF analysis and the WACC, on the assumption

that the WACC will be unchanged by investing in the new project.

In some cases, however, this assumption is not valid. The marginal cost of capital is

not the WACC in cases where:

 The capital structure will change because the project is a large project that will be

financed mainly by either debt or equity capital, and the change in capital

structure will alter the WACC. If the WACC changes, the marginal cost of capital

and the WACC will not be the same.

 A new capital project might have completely different business risk

characteristics from the normal business operations of the company. If the

business risk for a project is completely different, the required return from the

Paper F9: Financial management

318 Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides © EWP

project will also be different. In such cases, the CAPM might be used to establish

a suitable marginal cost of capital for capital investment appraisal of the specific

project.

3.4 Using the CAPM for capital investment appraisal

Some types of capital investment projects are more risky than others because the

business risk is greater. 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. Investing in the construction of residential houses might be less

risky than investing in the construction of office blocks. 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.

Since different types of business operation have different business risk, the asset

betas of each type of business operation are also different.

When there are significant differences in business risk between different capital

investment projects, if follows that the required return 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.

The calculation of a project-specific discount rate is explained in the next section.

Chapter 17: Capital asset pricing model (CAPM)

Project-specific discount rates

 The need for project-specific discount rates

 Proxy companies and proxy betas

 Using proxy betas to estimate an asset beta

 Using an asset beta to calculate an equity beta: re-gearing the asset beta

 Summary of the steps for calculating a project-specific discount rate

4 Project-specific discount rates

4.1 The need for project-specific discount rates

A specific discount rate should be used for DCF appraisal of capital projects where

either:

 the business risk of the new project is different from the business risk of the

company’s other business operations, or

 the financial risk will be different because financing the project will involve a

major change in the company’s capital structure.

For examination purposes, the syllabus focuses on obtaining a cost of capital for

specific projects where the business risk will be significantly different.

4.2 Proxy companies and proxy betas

To calculate a suitable cost of capital to use in DCF analysis for a specific project

where business risk is different from the company’s normal business operations, the

first step is to estimate the business risk.

The business risk of a business operation or capital investment project can be

measured by the asset beta for that type of business.

An estimate of the asset beta can be obtained from the beta factors of quoted

companies that operate in the same industry and markets. For example if a house-

building company is considering a project to construct a new road bridge, for which

the business risk will be very different, it can estimate an asset beta for a bridge-

building project by obtaining the beta factors of quoted companies in the bridge-

building industry.

These companies that operate in the relevant industry and markets are called ‘proxy

companies’ and the beta factors of their shares are called ‘proxy equity betas’.

It is assumed that the business risk within the proxy equity betas of these proxy

companies is similar to the business risk in the new capital investment project that

the company is considering.

Paper F9: Financial management

320 Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides © EWP

4.3 Using proxy betas to estimate an asset beta

For each of the proxy companies selected, an asset beta can be calculated using the

asset beta formula. In your examination you might be told to assume that debt

capital in the proxy companies is risk-free; therefore the asset beta for each company

can be calculated using the formula:

()

t1DE

EGA

−+

×=

ββ

The asset betas for the proxy companies will not be exactly the same, but they

should be similar.

An asset beta for the capital investment project might therefore be estimated as the

average of the asset betas of the proxy companies. For example if three proxy

companies have been selected and their asset betas are 1.14, 1.20 and 1.22, an

estimate of a suitable asset beta would be (1.14 + 1.20 + 1.23)/3 = 1.19.

4.4 Using an asset beta to calculate an equity beta: re-gearing the asset

beta

An asset beta measures business risk but not financial risk. If a company is geared,

or intends to finance a project with a mixture of equity and debt capital, the equity

beta for the project will be higher than the asset beta.

The asset beta should therefore be re-geared, and converted into an equity beta,

using the asset beta formula and data about the capital structure of the company.

For examination purposes it will normally be assumed that the company’s debt

capital is risk-free, therefore the equity beta is calculated as:

AEG

= ÷

()

t1DE

−+

Having calculated an equity beta, the CAPM can be used to calculate a cost of equity

for the project.

 This cost of equity can then be used to calculate a weighted average cost of

capital for the project, allowing for the capital structure of the company.

 Alternatively, an examination question might instruct you to assume that the

project-specific cost of equity you calculate should be used as the discount rate

(cost of capital) for capital investment appraisal of the project.

4.5 Summary of the steps for calculating a project-specific discount rate

The steps for calculating a project-specific discount rate for a project with different

business risk can be summarised as follows.

Identify some proxy companies.

For each of these proxy companies, obtain the available market data about

their capital structure and beta factors.

Chapter 17: Capital asset pricing model (CAPM)

3 For each proxy company, convert the available data in to an asset beta, using

the asset beta formula.

Calculate an average asset beta from the asset betas of the proxy companies.

Convert this asset beta into a ‘geared equity’ beta for the company, using

available data about its capital structure. You will normally be told to assume

that the debt capital of the company is risk-free.

This geared equity beta should be used to calculate a cost of equity for the

project, using the CAPM.

Either this cost of equity can then be used in the calculation of a weighted

average cost of capital for the project, or you will be instructed to use the cost

of equity as the cost of capital for DCF analysis of the capital investment

project.

Example

An all-equity company operates in an industry where its beta factor is 0.90. It is

considering whether to invest in a completely different industry. In this other

industry, the average debt/equity ratio is 40% and the average beta factor is 1.25.

The risk-free rate of return is 4% and the average market return is 7%. If the

company does invest in this other industry, it will remain all-equity financed. The

rate of taxation is 30%. Assume that debt is risk-free.

Required

What cost of capital should be used to evaluate the proposed investment?

Answer

The appropriate discount rate should be one that applies to the industry in which

the investment will be made. We know that the ‘geared beta’ in this industry is 1.25,

with a debt: equity ratio of 0.40. We can calculate the asset beta for the industry as:

()

[]

0.85

1.25

0.3014060

1.25=

=×=

−+

Since the company will be all-equity financed, the cost of equity to apply to the

project is therefore:

4% + 0.85 (7 – 4)% = 6.55%.

Example

A company is planning to invest in a project in a new industry where it has not

invested before. The asset beta for the project has been estimated as 1.35. The project

will be financed two-thirds by equity capital and one-third by debt capital. The rate

of taxation on company profits is 30%.

Assume that the debt capital is risk-free.

Paper F9: Financial management

The risk-free rate of return is 3% and the market return is 8%.

What cost of equity should be used to calculate the marginal cost of capital for this

project?

Answer

The asset beta of 1.35 allows for business risk only and assumes that the project will

be all-equity financed. The asset beta can be converted into a ‘geared beta’ for the

equity capital as follows:

0.30)-(1 1+2

=1.35

= (1.35 × 2.70)/2 = 1.8225.

The beta factor for the equity finance can be used to obtain a cost of capital for the

equity, using the CAPM.

r = 3% + 1.8225 (8 – 3)% = 12.1125%, say 12%.

Since the debt capital is risk-free, its pre-tax cost is 3%. The cost of capital for the

project, financed two-thirds by equity and one-third by debt, is:

[2/3

× 12%] + [1/3 × 3% × (1 – 0.30)] = 8.7%.

Example

A company is considering whether to invest in a new capital project where the

business risk will be significantly different from its normal business operations. The

company is financed 80% by equity capital and 20% by debt capital.

It has identified three companies in the same industry as the proposed capital

investment and has obtained the following information about them:

(1) Company 1 has an equity beta of 1.05 and is financed 30% by debt capital and

70% by equity.

(2) Company 2 has an equity beta of 1.24 and is financed 50% by debt capital and

50% by equity.

(3) Company 3 has an equity beta of 1.15 and is financed 40% by debt capital and

60% by equity.

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

company profits is at the rate of 30%. Assume that the debt capital in each company

is risk-free.

Chapter 17: Capital asset pricing model (CAPM)

Required:

Calculate a project-specific discount rate for the project, assuming that this is:

(a) the project-specific cost of equity for the project, or

(b) the weighted average of the project-specific equity cost and the company’s

cost of debt capital.

Answer

Asset betas can be calculated for each proxy company as follows:

Company 1

()

[]

0.81

1.05

0.3013070

1.05=

=×=

−+

Company 2

()

[]

0.73

1.24

0.3015050

1.24=

=×=

−+

Company 3

()

[]

0.78

1.15

0.3014060

1.15=

=×=

−+

The average of these asset betas is (0.81 + 0.73 + 0.78)/3 = 0.77.

The asset beta for the capital project is 0.77. This should now be re-geared to obtain

an equity beta for the project.

()

[]

0.3012080

=77.0

−+

= 0.77 [80 + 20(1 – 0.30)]/80

= 0.77 × 94/80 = 0.90.

The project-specific cost of equity is now calculated using the CAPM:

= 5% + 0.90 (8 – 5)% = 7.7%

(a) If the

project-specific discount rate is taken to be the project-specific cost of

equity, the discount rate for the project should be 7.7%.

(b) If the

project-specific discount rate is taken to be a weighted average cost of

capital, this is calculated as follows:

Sourceoffinance Marketvalue After‐taxcost

 r MV×r

Equity 80% 0.077 0.0616

Debtcapital:cost=(5%

×(1–0.30) 20% 0.035 0.0070

0.0686

The project-specific cost of capital would now be 6.86%, say 6.9%.

Paper F9: Financial management

Summary: using the CAPM to obtain a project-specific discount rate

The WACC is often used as the cost of capital in capital expenditure appraisal

because it is assumed that individual projects will not significantly affect the

WACC. The WACC is therefore an acceptable measure of the marginal cost of

capital.

A different situation arises when a new project will significantly affect the capital

gearing or have significantly different business risk. In these cases, an appropriate

cost of equity capital can be estimated using the asset beta formula, and assuming a

risk-free cost of debt capital. The CAPM can therefore be used to obtain a project-

specific discount rate.

ACCA F9 Financial Management - 2010 - Study text - Emile Woolf Publishing

Подождите немного. Документ загружается.