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6 Example: Marginal cost of capital

6 Example: Marginal cost of capital

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and new shares) will rise from 12% to 14%. The cost of preference shares and the cost of existing bonds
will remain the same, while the after-tax cost of the new bonds will be 9%.
Required

Calculate the company's new weighted average cost of capital, and its marginal cost of capital.

Solution
New weighted average cost of capital
After-tax cost
%
14
10
7.5
9

Source
Equity
Preference
Existing bonds
New bonds

WACC =

2.52  100%
23

= 11.0%
Marginal cost of capital =

(2.52  2.0)  100%
23  20

= 17.3%

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15: The cost of capital  Part E Business finance

Market value
$m
11
2
8
2
23

After-tax cost  Market value

1.54
0.20
0.60
0.18
2.52

Chapter Roundup


The cost of capital is the rate of return that the enterprise must pay to satisfy the providers of funds, and
it reflects the riskiness of providing funds.



The dividend growth model can be used to estimate a cost of equity, on the assumption that the market
value of share is directly related to the expected future dividends from the shares.



The capital asset pricing model can be used to calculate a cost of equity and incorporates risk.
The CAPM is based on a comparison of the systematic risk of individual investments with the risks of all
shares in the market.



The total risk involved in holding securities (shares) divides into risk specific to the company
(unsystematic) and risk due to variations in market activity (systematic).
Unsystematic risk can be diversified away, while systematic or market risk cannot. Investors may mix a
diversified market portfolio with risk-free assets to achieve a preferred mix of risk and return.



The systematic risk in individual company shares can be measured statistically, by analysing historical
returns.
The CAPM model uses a beta factor to measure a share's volatility in terms of systematic risk.
In accordance with portfolio theory, unsystematic risk is ignored in the CAPM, as it is assumed that
unsystematic risk can be diversified away.



Problems of CAPM include unrealistic assumptions and the required estimates being difficult to make.



The cost of debt is the return an enterprise must pay to its lenders.


For irredeemable debt, this is the (post-tax) interest as a percentage of the ex interest market
value of the bonds (or preferred shares).



For redeemable debt, the cost is given by the internal rate of return of the cash flows involved
(interest and capital gain or loss at redemption).

Interest is tax deductible and this is taken into account in the calculations.


The weighted average cost of capital (WACC) is the average cost of capital for all the company's longterm sources of finance, weighted to allow for the relative proportions of each type of capital in the overall
capital structure.
The WACC is calculated by weighting the costs of the individual sources of finance according to their
relative importance as sources of finance.
The WACC represents the return that the company should make on its investments to be able to provide
the returns required by its finance providers.

Part E Business finance  15: The cost of capital

313

Quick Quiz
1

Fill in the blanks.
Cost of capital = (1) ........................................ + (2) premium for ........................................ risk +
(3) premium for ........................................ risk.

2

A share has a current market value of 120c and the last dividend was 10c. If the expected annual growth
rate of dividends is 5%, calculate the cost of equity capital.

3

What type of risk arises from the existing operations of a business and cannot be diversified away?

4

Which of the following risks can be eliminated by diversification?
A
B
C
D

5

Inherent risk
Systematic risk
Market risk
Unsystematic risk

Unsystematic risk is measured by beta factors.
True
False

6

A portfolio consisting entirely of risk-free securities will have a beta factor of (tick one box):
–1
0
1

7

The risk-free rate of return is 8%. Average market return is 14%. A share's beta factor is 0.5. What will its
expected return be?

8

Identify the variables ke, kd, Ve and Vd in the following weighted average cost of capital formula.
 V 
WACC =  e  ke +
 Ve  Vd 

9

When calculating the weighted average cost of capital, which of the following is the preferred method of
weighting?
A
B
C
D

10

314

 Vd 

 kd (1 – T)
 Ve  Vd 

Book values of debt and equity
Average levels of the market values of debt and equity (ignoring reserves) over five years
Current market values of debt and equity (ignoring reserves)
Current market values of debt and equity (plus reserves)

What is the cost of $1 irredeemable debt capital paying an annual rate of interest of 7%, and having a
current market price of $1.50?

15: The cost of capital  Part E Business finance

Answers to Quick Quiz
1

(1)
(2)
(3)

Risk-free rate of return
Business
Financial

2

10(1 0.05)
+ 0.05 = 13.75%
120

3

Systematic or market risk

4

D

5

False. Beta factors measure systematic risk.

6

Zero

7

Expected return = 8 + 0.5 (14 – 8) = 11%

8

ke is the cost of equity
kd is the cost of debt
Ve is the market value of equity in the firm
Vd is the market value of debt in the firm

9

C

10

Cost of debt =

Unsystematic risk is risk that is specific to sectors, companies or projects. Systematic risk (also
known as inherent risk or market risk) affects the whole market and therefore cannot be reduced by
diversification.

Current market values of debt and equity (ignoring reserves)
0.07
= 4.67%
1.50

Now try the questions below from the Practice Question Bank

Number

Level

Marks

Approximate time

Section A Q27

Examination

2

4 mins

Section B Q6 – Q10

Examination

10

20 mins

Section C Q18

Introductory

N/A

39 mins

Part E Business finance  15: The cost of capital

315

316

15: The cost of capital  Part E Business finance

Capital structure

Topic list

Syllabus reference

1 Capital structure theories

E4 (a), (b), (c), (d)

2 Impact of cost of capital on investments

E3 (e)(i)(ii)(iii)(iv)

Introduction
This chapter considers the impact of capital structure on the cost of capital.
The practical application of this comes in Section 2 where we consider various
ways of incorporating the effects of changing capital structure into cost of
capital and net present value calculations.

317

Study guide
Intellectual level
E3

Sources of finance and their relative costs

(e)

Impact of cost of capital on investments including:

(i)

The relationship between company value and cost of capital

(ii)

The circumstances under which WACC can be used in investment appraisal

(iii)

The advantages of the CAPM over WACC in determining a project-specific
cost of capital

(iv)

Application of CAPM in calculating a project-specific discount rate

E4

Capital structure theories and practical considerations

(a)

Describe the traditional view of capital structure and its assumptions.

2

(b)

Describe the views of Miller and Modigliani on capital structure, both
without and with corporate taxation, and their assumptions.

2

(c)

Identify a range of capital market imperfections and describe their impact on
the views of Miller and Modigliani on capital structure.

2

(d)

Explain the relevance of pecking order theory to the selection of sources of
finance.

1

2

Exam guide
The theories covered in this chapter could be needed in a discussion part of a question. Gearing and
ungearing a beta is an essential technique to master using the formula which will be given to you in the exam.

1 Capital structure theories
FAST FORWARD

6/09, 6/11, 12/13

Some commentators believe that an optimal mix of finance exists at which the company's cost of capital
will be minimised.
A company should seek to minimise its weighted average cost of capital. By doing so, it minimises its cost
of funds. The weighted average cost of capital is an average cost of all the different sources of finance that
a company uses. By changing the proportions of each type of finance, it will alter its WACC.
So how can a company adjust its financing structure in such a way that its WACC is minimised?
There are different views on the answer to this question. One is the so-called 'traditional' view. Another is
a view proposed by Modigliani and Miller.
The traditional view concludes that there is an optimal capital mix of equity and debt at which the
weighted average cost of capital is minimised.
However, the alternative view of Modigliani and Miller (assuming no tax) is that the firm's overall
weighted average cost of capital is not influenced by changes in its capital structure.
Both views agree that:

318



The cost of equity is higher than the cost of debt.



As the level of gearing increases, the larger proportion of debt in the capital structure means that
there is a larger proportion of lower-cost finance.



However, as the level of gearing rises, the cost of equity also rises to compensate shareholders for
the higher risk.



As gearing increases, the higher proportion of low-cost debt but the rising cost of equity pull the
WACC in opposite directions.

16: Capital structure  Part E Business finance

1.1 The traditional view
FAST FORWARD

Under the traditional theory of cost of capital, the weighted average cost of capital declines initially as
gearing increases, but then rises as gearing increases further. The optimal capital structure is at the
gearing level where WACC is lowest.
The traditional view is as follows.
(a)

As the level of gearing increases, the cost of debt remains unchanged up to a certain level of
gearing. Beyond this level, the cost of debt will increase.

(b)

The cost of equity rises as the level of gearing increases and financial risk increases. There is a
non-linear relationship between the cost of equity and gearing.

(c)

The weighted average cost of capital does not remain constant, but rather falls initially as the
proportion of debt capital increases, and then begins to increase as the rising cost of equity (and
possibly of debt) becomes more significant.

(d)

The optimum level of gearing is where the company's weighted average cost of capital is
minimised.

The traditional view about the cost of capital is illustrated in the following figure.

WACC
Cost of
capital

1

2

P

Gearing increasing

At point 1, the cost of capital falls as the level of debt finance increases. This is because debt is cheaper
than equity.
Point P shows the optimum level of debt: cheap debt finance minimises the cost of capital.
At point 2, the cost of capital increases as the level of debt finance continues to increase. This is because
above the optimum level of debt finance, the company is perceived to be high risk by shareholders and
lenders, who start to demand a higher level of return.
The figure below shows the same cycle, illustrating the changes in cost of capital, cost of debt and cost of
equity.

Part E Business finance  16: Capital structure

319

Cost of
capital

ke
k0

kd

0

P

Level of gearing

Where ke is the cost of equity in the geared company
kd is the cost of debt
k0 is the weighted average cost of capital

1.2 Net operating income view of WACC: Modigliani-Miller (MM)
FAST FORWARD

Modigliani and Miller stated that, in the absence of tax relief on debt interest, a company's capital
structure would have no impact on its WACC. WACC would be the same regardless of the company's
capital structure.
The net operating income approach takes a different view of the effect of gearing on WACC. In their 1958
theory, Modigliani and Miller (MM) proposed that the total market value of a company, in the absence of
tax relief on debt interest, will be determined only by two factors.




The total earnings of the company
The level of operating (business) risk attached to those earnings

The total market value would be computed by discounting the total earnings at a rate that is appropriate to
the level of operating risk. This rate would represent the WACC of the company.
Thus Modigliani and Miller concluded that the capital structure of a company would have no effect on its
overall value or WACC.

1.2.1 Assumptions of net operating income approach
Modigliani and Miller made various assumptions in arriving at this conclusion, including:
(a)

A perfect capital market exists, in which investors have the same information, on which they act
rationally, to arrive at the same expectations about future earnings and risks.

(b)

There are no tax or transaction costs.

(c)

Debt is risk free and freely available at the same cost to investors and companies alike.

Modigliani and Miller justified their approach by the use of arbitrage.

Key term

Arbitrage is when a purchase and sale of a security takes place simultaneously in different markets, with
the aim of making a risk-free profit through the exploitation of any price difference between the markets.
Arbitrage can be used to show that once all opportunities for profit have been exploited, the market values of
two companies with the same earnings in equivalent business risk classes will have moved to an equal value.

Exam focus
point

320

The proof of Modigliani and Miller's theory by arbitrage is not examinable.

16: Capital structure  Part E Business finance

If Modigliani and Miller's theory holds, it implies:
(a)
(b)

The cost of debt remains unchanged as the level of gearing increases.
The cost of equity rises in such a way as to keep the weighted average cost of capital constant.

This would be represented on a graph as shown below.
Cost of
capital

ke

ko

kd

0

Level of gearing

1.3 Example: Net operating income approach
A company has $5,000 of debt at 10% interest, and earns $5,000 a year before interest is paid. There are
2,250 issued shares, and the weighted average cost of capital of the company is 20%.
The market value of the company should be as follows.
Earnings
Weighted average cost of capital

$5,000
0.2

Market value of the company ($5,000  0.2)
Less market value of debt
Market value of equity

$
25,000
5,000
20,000

The cost of equity is therefore

5,000  500 4,500
=
= 22.5%
20,000
20,000

and the market value per share is

1
4,500

= $8.89
2,250
0.225

Suppose that the level of gearing is increased by issuing $5,000 more of debt at 10% interest to
repurchase 562 shares (at a market value of $8.89 per share) leaving 1,688 shares in issue.
The weighted average cost of capital will, according to the net operating income approach, remain
unchanged at 20%. The market value of the company should still therefore be $25,000.
Earnings
Weighted average cost of capital

$5,000
0.2

Market value of the company
Less market value of debt
Market value of equity

$
25,000
10,000
15,000

Annual dividends will now be $5,000 – $1,000 interest = $4,000.

Part E Business finance  16: Capital structure

321

The cost of equity has risen to

4,000
= 26.667% and the market value per share is still:
15,000

4,000
1

= $8.89
1,688
0.2667
The conclusion of the net operating income approach is that the level of gearing is a matter of indifference
to an investor, because it does not affect the market value of the company, nor of an individual share. This
is because as the level of gearing rises, so does the cost of equity in such a way as to keep both the
weighted average cost of capital and the market value of the shares constant. Although, in our example,
the dividend per share rises from $2 to $2.37, the increase in the cost of equity is such that the market
value per share remains at $8.89.

1.4 Market imperfections
In 1963 Modigliani and Miller modified their theory to admit that tax relief on interest payments does
lower the weighted average cost of capital. The savings arising from tax relief on debt interest are the tax
shield.
However, whereas the traditional approach to gearing and WACC is that there is an optimal level of gearing
where WACC is minimised, MM took a different view. They argued that the weighted average cost of
capital continues to fall, up to gearing of 100%.
Cost of
capital

ke

ko
kd after tax

0

Gearing up to 100%

This suggests that companies should have a capital structure made up entirely of debt. This does not
happen in practice due to the existence of other market imperfections which undermine the tax
advantages of debt finance.

1.4.1 Bankruptcy costs
MM's theory assumes perfect capital markets so a company would always be able to raise finance and
avoid bankruptcy. In reality, however, at higher levels of gearing there is an increasing risk of the company
being unable to meet its interest payments and being declared bankrupt. At these higher levels of gearing,
the bankruptcy risk means that shareholders will require a higher rate of return as compensation.

1.4.2 Agency costs
At higher levels of gearing there are also agency costs as a result of action taken by concerned debt
holders. Providers of debt finance are likely to impose restrictive covenants, such as restriction of future
dividends or the imposition of minimum levels of liquidity in order to protect their investment. They may
also increase their level of monitoring and require more financial information.

322

16: Capital structure  Part E Business finance