Fin management materials / 2P4AFM-Session03_j08

SESSION 03 – WEIGHTED AVERAGE COST OF CAPITAL AND GEARING

OVERVIEW

Objective

¾To estimate the weighted average cost of capital (WACC) of a company.

¾To apply and evaluate the various theories of how capital structure affects the WACC.

¾To discuss practical influences on gearing.

WEIGHTED

AVERAGE COST

OF CAPITAL

THE IMPACT OF

GEARING ON

WACC

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SESSION 03 – WEIGHTED AVERAGE COST OF CAPITAL AND GEARING

1WEIGHTED AVERAGE COST OF CAPITAL

1.1Calculation of WACC

¾A firm’s long-term finance is often a mixture of both equity and debt i.e. using some degree of financial gearing/leverage. The average cost of long-term finance is known as the WACC - the weighted average cost of capital.

¾We have already seen how to calculate the cost of equity and the cost of various types of corporate debt.

¾We now weight the various costs of long-term finance using their respective market values.

WACC = Keg E +ED + Kd E D+ 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:

Note that the post tax cost of debt only = 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.

¾At any moment in time a firm can estimate its existing WACC.

¾The existing WACC may be a suitable discount rate for estimating the NPV of potential projects – but is not automatically the appropriate rate.

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SESSION 03 – WEIGHTED AVERAGE COST OF CAPITAL AND GEARING

A company’s existing WACC should only be used as the discount rate for a potential project 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:

¾Gearing level i.e. Financial Risk

¾Operational risk i.e. Business Risk

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

Solution

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SESSION 03 – WEIGHTED AVERAGE COST OF CAPITAL AND GEARING

3STATIC TRADE-OFF THEORY

3.1Reasoning

¾The traditional view has little theoretical foundation – often described as the “intuitive approach”. It is based upon the trade-off caused by financial gearing i.e. using more (relatively cheap) debt results in a rising cost of equity.

¾It 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.

¾At higher levels of gearing the increased financial risk outweighs this benefit and WACC rises.

WACC

Kd

D/E

Optimal gearing

¾Note 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.

¾This is referred to as financial distress risk – not to be confused with financial risk which occurs even at relatively safe levels of debt.

3.2Conclusions

¾There is an optimal gearing level (minimum WACC).

¾However there is no method of calculating Ke or WACC or indeed the optimal capital structure. The latter needs to be found by trial and error.

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SESSION 03 – WEIGHTED AVERAGE COST OF CAPITAL AND GEARING

4MODIGLIANI AND MILLER’S THEORIES

4.1Introduction

¾Modigliani and Miller (MM) constructed a mathematical model to attempt to provide a basis for financial managers to make finance decisions.

¾Mathematical models predict outcomes that would occur based on simplifying assumptions.

¾Comparison of the model’s conclusions to the real world observations then allows researchers to understand the impact of the simplifying assumptions. By relaxing these assumptions in turn the model can be moved towards real life.

¾MM’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.

4.2Theory without tax

¾MM expressed their theory as two propositions.

¾MM considered two companies - both with the same size and in the same line of business therefore both having the same level of business risk.

One company was ungeared − Co U

One company was geared − Co G

¾MM’s basic theory was that because each firm would have the same operating profit it would have the same total market value (V) and the same WACC (proposition 1)

WACCg = WACCu

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SESSION 03 – WEIGHTED AVERAGE COST OF CAPITAL AND GEARING

¾MM argued that the individual 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 increased financial risk (proposition 2)

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

This can be shown as a graph:

Cost of

capital

Ke

WACC

Kd

D/E

¾Conclusion

There is no optimal gearing level;

The value of the company is independent of the finance decisions

Only investment decisions affect the value of the company.

¾This is not true in practice because the assumptions are too simplistic. There are differences between the real world and the model

¾Note 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 were correct. They were then in a position to relax the assumptions to see how the model predictions would change.

¾The first assumption they relaxed was the no corporate tax assumption.

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SESSION 03 – WEIGHTED AVERAGE COST OF CAPITAL AND GEARING

4.3Theory with tax

Illustration 1

Consider two companies, one ungeared, Co U, and one geared, Co G, both of the same size and level of business risk.

The investors in G receive $7m more than the investors in U. This is due to the tax relief on debt interest and is known as the tax shield.

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.

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:

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SESSION 03 – WEIGHTED AVERAGE COST OF CAPITAL AND GEARING

¾When corporation tax is introduced MM argue that the individual costs of capital 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 financial risk

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

WACC

Kd

D/E

¾The relationship between the WACC of a geared company and the WACC of an ungeared company is:

This formula is not provided in the exam.

¾The formula for the cost of equity is: Keg = Keu + (1 – T) (Keu – kd) DE

¾This is provided on the formulae sheet in the following format:

ke = kei + (1 – T) (kei – kd) Vd Ve

Where kd = pre-tax cost of debt

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