ACCA paper f9 financial management study materials F9FM session11 d08

WEIGHTED AVERAGE COST OF CAPITAL WEIGHTED AVERAGE COST OF CAPITAL AND GEARING GEARING Ü Calculation of WACC Ü Limitations of WACC Ü Ü The effects of gearing Traditional view of capita

OVERVIEW

Objective

Ü To understand the weighted average cost of capital (WACC) of a company and how it is estimated

Ü To understand the effect of gearing on the WACC of a company

Ü To discuss the theories of Modigliani and Miller

WEIGHTED

AVERAGE COST

OF CAPITAL

WEIGHTED AVERAGE COST OF CAPITAL AND GEARING

GEARING

Ü Calculation of WACC

Ü Limitations of WACC Ü Ü The effects of gearing Traditional view of capital structure

Ü Modigliani and Miller’s theories

1 WEIGHTED AVERAGE COST OF CAPITAL

1.1 Calculation of WACC

Ü Companies are usually financed by both debt and equity, i.e they use some degree of financial/capital gearing We must therefore calculate a weighted average cost of capital (WACC) which represents a company’s average cost of long-term finance This

will give us a potential discount rate for project appraisal using NPV

Ü In the previous session we saw how to estimate the cost of equity and the cost of

various types of debt

Ü We weight the various costs of debt and equity using their respective market values

WACC =

+ + + +

+ + +

+

D D E

D K D K E K

2 1

2 d2 1 d1 eg

Written as

WACC =

D E

D K E

Keg d +

+

OR WACC = Keg

D E

E + + Kd

D E

D + Where:

E = Total market value of equity

D = Total market value of debt

Keg= Cost of equity of a geared company

Kd = Cost of debt to the company (i.e the post tax cost of debt)

In the exam the formula is given as follows:

Vd Ve

Ve









Vd Ve







 + Where:

Ve = Total market value of equity Vd = Total market value of debt

Ke = Cost of equity geared

Kd = Pre-tax cost of debt T = corporation tax rate

Note that the post tax cost of debt = Kd (1 – T) for irredeemable debentures or bank loans

If you are given a redeemable bond then you should calculate the IRR of its post-tax cash

flows which directly gives you the post-tax cost of debt

Project has same business risk as existing operations

Project is financed

by existing pool of funds

Proportion of debt to equity does not change

A company’s current WACC is used as the discount rate only if

i.e a company’s existing WACC can only be used as the discount rate for a potential project

if that project does not change the company’s:

Ü Gearing level i.e Financial Risk

Ü Business Risk

Ü More detail on the important concepts of Financial Risk and Business Risk is found in the next section

Example 1

A company has in issue:

45 million $1 ordinary shares

10% irredeemable loan stock with a book value of $55million

The loan stock is trading at par

Estimate the WACC

Solution

1.2 Limitations of WACC

LIMITATIONS

CALCULATION

OF Ke

− market value of shares

= present value of dividend stream

− market value of debt

= present value of interest/principal

assess projects

which

− have similar operating risk to

that of the company

− are financed by the company’s pool

of funds, ie have same financial risk

− historical data used to estimate future growth rates

− Gordon’s model assumes all growth is financed by retained earnings

equilibrium

taxation

CALCULATION OF Kd

̈ Difficulty in incorporating all forms of long term finance, eg

̈ Current liability but often

has permanent core

variable element

(i) taking the redemption value, or

(ii) converting into shares

unless data is available to suggest conversion

affect the value of the loans to be included and interest payments

Ü These problems are particularly difficult for unquoted companies which have no share

price available and possibly irregular dividend payments

Ü In this case it may be advisable to estimate the WACC of a quoted company in the same industry and with similar gearing and then add a (subjective) premium to reflect the (perceived) higher risk and lower marketability of unquoted shares

Ü The current WACC reflects the current risk profile of the company: both

Business risk – The variability in the operating earnings of the company i.e the

volatility of EBIT due to the nature of the industry

and

Financial risk – The additional variability in the return to equity as a result of

introducing debt i.e using financial gearing Interest on debt is a committed fixed cost

which creates more volatile bottom line profits for shareholders

Ü As a company gears up two things happen

WACC = Ke E + Kd D

E + D

̈ Ke increases due to

the increased financial

risk

̈ All else equal, this

pushes up the value

of WACC

̈ The proportion of debt relative to equity

in the capital structure increases

̈ Since Kd < Ke this pushes the value of WACC down, all else equal

Ü The effect of increased gearing on the WACC depends on the relative sizes of these two opposing effects

Ü There are two main schools of thought

̌ Traditional view

̌ Modigliani and Miller’s theories

3 TRADITIONAL VIEW OF CAPITAL STRUCTURE

3.1 Reasoning

Ü The traditional view has no theoretical foundation – often described as the “intuitive approach” It is based upon the trade-off caused by gearing i.e using more (relatively cheap) debt results in a rising cost of equity The model can also be referred to as the

“static trade-off model”

Ü It is believed that Ke rises only slowly at low levels of gearing and therefore the benefit

of using lower cost debt finance outweighs the rising Ke

Ü At higher levels of gearing the increased financial risk outweighs this benefit and WACC rises

Cost of

WACC

Kd

D/E Optimal

gearing

Ü Note that at very high levels of gearing the cost of debt rises This is due to the risk of default on debt payments i.e credit risk

Ü This is referred to as financial distress risk – not to be confused with financial risk which

occurs even at relatively safe levels of debt

3.2 Conclusions

Ü There is an optimal gearing level (minimum WACC)

Ü However there is no straightforward method of calculating Ke or WACC or indeed the optimal capital structure The latter can only be found by trial and error

3.3 Project finance — implications

Ü If the company is optimally geared

̌ Raise finance so as to maintain the existing gearing ratio

Ü If the company is sub-optimally geared

̌ Raise debt finance so as to increase the gearing ratio towards the optimal

Ü If the company is supra-optimally geared

̌ Raise equity finance so as to reduce the gearing ratio back to the optimal

Ü Appraise the project at the existing WACC

̌ If the NPV of the project is positive the project is worthwhile

Ü Appraise the finance

̌ If marginal cost of the finance > WACC the finance is not appropriate and should

be rejected

̌ If this was the case the company could raise finance in the existing gearing ratio and the WACC would not rise

4 MODIGLIANI AND MILLER’S THEORIES

4.1 Introduction

Ü Modigliani and Miller (MM) constructed a mathematical model to provide a basis for company managers to make financing decisions

Ü Mathematical models predict outcomes that would occur based on simplifying

assumptions

Ü Comparison of the model’s conclusions to real world observations then allows

researchers to understand the impact of the simplifying assumptions By relaxing these assumptions the model can be moved towards real life

Ü MM’s assumptions include:

̌ Rational investors

̌ Perfect capital market

̌ No tax (either corporate or personal) – although they later relaxed the assumption

of no corporate tax

̌ Investors are indifferent between personal and corporate borrowing

̌ No financial distress risk i.e no risk of default even at very high levels of debt

̌ There is a single risk-free rate of borrowing

̌ Corporate debt is irredeemable

4.2 Theory without tax

Ü MM expressed their theory as two propositions

Ü MM considered two companies - both with the same size and with the same level of business risk

̌ One company was ungeared − Co U

̌ One company was geared − Co G

Ü MM’s basic theory was that in the absence of corporation tax the market values (V) and

WACC’s of these two companies would be the same (proposition 1)

WACCg = WACCu

Ü MM argued that the costs of capital would change as gearing changed in the following manner:

̌ kd would remain constant whatever the level of gearing

̌ ke would increase at a constant rate as gearing increased due to the perceived

increased financial risk (proposition 2)

̌ the rising ke would exactly offset the benefit of the additional cheaper debt in order for the WACC to remain constant

This can be shown as a graph:

Cost of

capital

WACC

D/E

Ke

Kd

Ü Conclusion

̌ There is no optimal gearing level;

̌ The value of the company is independent of the financing decision

̌ Only investment decisions affect the value of the company

Ü This is not true in practice because the assumptions are too simplistic There are

differences between the real world and the model

Ü Note that MM never claimed that gearing does not matter in the real world They said that it would not matter in a world where their assumptions hold They were then in a position to relax the assumptions to see how the model’s predictions would change

Ü The first assumption they relaxed was the no corporate tax assumption

4.3 Theory with tax

Ü When MM considered corporation tax then their conclusions regarding capital structure were altered This is due to the tax relief available on debt interest – the “tax shield”

Illustration 1

Consider two companies, one ungeared, Co U, and one geared, Co G, both of

the same size and level of business risk

Co U Co G

Returns to the investors:

The investors in G receive in total each year $7m more than the investors in U

This is due to the tax relief on debt interest and is known as the tax shield

Tax shield = kd × D × t

where kd = pre-tax cost of debt

D = current market value of the debt

MM assume that the tax shield will be in place each year to perpetuity and

therefore has a present value, which can be found by discounting at the rate

applicable to the debt, kd

PV of tax shield =

kd

t D

Kd× ×

The difference in market value between G and U should therefore be that G

has a higher market value due to the tax shield and this extra value is made up

of the present value of the tax shield

MM expressed this as:

Ü When corporation tax is introduced MM argue that the costs of capital will change as follows:

̌ Kd (the required return of the debt holders) remains constant at all levels of gearing

̌ Ke increases as gearing levels increase to reflect additional perceived financial risk

̌ WACC falls as gearing increases due to the additional tax relief on the debt interest

Cost of

capital

WACC

D/E

Ke

Kd

Ü The relationship between the WACC of a geared company, according to MM, and the WACC (Ke) of an ungeared company is:









 +

− D E

Dt

where Keu = cost of equity in an ungeared company

D = market value of debt in the geared company

E = market value of equity in the geared company

t = corporate tax rate

Ü The formula for the cost of equity is:

Keg = Keu + (1 – T) (Keu – kd)

E D

Illustration 1 — continued

Returning to the previous illustration these MM formulae can now be

illustrated

Suppose that the business risk of the two companies requires a return of 10%

and the return required by the debt holders in Co G is 5%

Co U

Market value of Co U will be the market value of the equity This will be the

dividend capitalised at the equity holders’ required rate of return

MVu =

1

065 = $650m Keu = 10% i.e required rate of return for business risk (U has no financial

risk)

Co G

Market value of the equity of Co G is determined by the equity shareholders’

analysis of their net operating income into its constituent parts and the

capitalisation of those elements at appropriate rates:

MVe =

0.1

EBIT −

0.1

35%

@



 0.05



 0.05

35%

@ relief tax

=

1 0

35 1 0





−







05 0

7 05 0 20

= 1,000 − 350 − (400 - 140) = $390m

Market value of debt is determined by the debt holders capitalising their

interest at their required rate of return:

MVd =

05

020 = $400m

∴ Total market value of Co G = MVg = $390m + $400m = $790m

The MM formula that describes the relationship between the market values

of equivalent companies at various gearing levels can be illustrated here:

$790m = $650m + ($400m×35%)

MM’s WACC relationship can also be illustrated

Firstly, WACC by the usual approach:

Keg =

value MarketDividend =

39052 = 13.33%

(assumes no growth in dividends)

WACC = 13.33% ×

790

390 + 3.25% ×

790

400 = 8.23%

Then by using MM/s formula: WACC = Keu (1−

D E

Dt + )

400 390

% 35 400 +

= 8.23%

MM’s equation for the cost of equity can also be checked

Keg = Keu + (1 – T) (Keu – kd)

E D

= 10 + (1-0.35)(10-5)

390

400

= 13.33%, (as per the dividend valuation model above)

Ü Conclusion

̌ The logical conclusions to be drawn from MM’s theory with tax is that there is an

optimal gearing level and that this is at 99.9% debt in the capital structure

̌ This implies that the financing decision for a company is vital to its overall market value and that companies should gear up as far as possible

Ü This is not true in practice; companies do not gear up to 99.9% Why not?

̌ In practice there are obviously many other factors that will limit this conclusion

Ü These factors include

̌ the risk of financial distress;

̌ the existence of not only corporate tax but also personal taxes;

Ü Thus in practice there are a series of factors that a company will need to consider in deciding how to raise finance

4.4 Practical considerations in choosing a gearing level

Ü These will include:

̌ business risk of the project;

̌ existing level of financial gearing:

̌ level of operational gearing – the proportion of fixed to variable operating costs If

this is high then the company may not wish to use debt as this increases the level

of fixed costs even further;

̌ type and quality of the assets;

̌ expected growth;

̌ personal tax position of the shareholders and debt holders

̌ internal and external limits to debt availability;

̌ tax exhaustion (not enough profit to fully utilise the tax shield)

̌ agency costs (increasingly restrictive debt covenants e.g restricting dividends)

̌ issue costs

̌ asymmetry of information – potential providers of finance may over-estimate the risk of the company and refuse to provide capital at reasonable cost Therefore the

managers may have a preference for using internal finance i.e retained earnings,

limiting the level of gearing;

̌ market sentiment

Key points

ÐWACC estimates the company’s average cost of long-term finance

ÐIt is therefore a potential discount rate to use for the calculation of the

NPV of possible projects However the existing WACC should only be

used if the project would not change the company’s business risk or level

of gearing i.e financial risk

ÐThere are various, and conflicting, models of how financial gearing affects

the WACC – traditional trade-off theory, Modigliani and Miller without

tax and MM with corporate tax Each model has useful elements even if

the conclusions of such models lack practical relevance

FOCUS

You should now be able to:

Ü understand the weighted average cost of capital, how it is estimated and

when it should be used;

Ü discuss the theories of Modigliani and Miller, their assumptions, implications and limitations;

Ü evaluate the impact of varying capital structures on the cost of capital