9
THE COST OF CAPITAL
AND CAPITAL STRUCTURE
Learning objectives
After studying this chapter, you should have achieved the following learning objectives:
■
a firm understanding of how to calculate a company’s cost of capital and how to
apply it appropriately in the investment appraisal process;
■
the ability to calculate the costs of different sources of finance used by a company
and to calculate the weighted average cost of capital of a company;
■
an appreciation of why, when calculating the weighted average cost of capital, it is
better to use market values than book values;
■
an understanding of how the capital asset pricing model can be used to calculate
risk-adjusted discount rates for use in investment appraisal;
■
the ability to discuss critically whether or not a company can, by adopting a
particular capital structure, influence its cost of capital.
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9.1 CALCULATING THE COST OF INDIVIDUAL SOURCES OF FINANCE
■ ■ ■ INTRODUCTION
The concept of the cost of capital, which is the rate of return required on invested
funds, plays an important role in corporate finance theory and practice. A company’s
cost of capital is (or could be) used as the discount rate in the investment appraisal
process when using techniques such as net present value and internal rate of return. If
we assume that a company is rational, it will want to raise capital by the cheapest and
most efficient methods, thereby minimising its average cost of capital. This will have
the effect of increasing the net present value of the company’s projects and hence its
market value. For a company to try to minimise its average cost of capital, it first
requires information on the costs associated with the different sources of finance available to it. Second, it needs to know how to combine these different sources of finance
in order to reach its optimal capital structure.
The importance of a company’s capital structure, like the importance of dividend
policy, has been the subject of intense academic debate. As with dividends, Miller and
Modigliani argued, somewhat against the grain of academic thought at the time, that a
company’s capital structure was irrelevant in determining its average cost of capital.
They later revised their views to take account of the tax implications of debt finance. If
market imperfections are also considered, it can be argued that capital structure does
have relevance to the average cost of capital. In practice, calculating a company’s cost
of capital can be extremely difficult and time-consuming; it is also difficult to identify
or prove that a given company has an optimal financing mix.
9.1 CALCULATING THE COST OF INDIVIDUAL SOURCES OF FINANCE
A company’s overall or weighted average cost of capital can be used as a discount rate in
investment appraisal and as a benchmark for company performance, so being able to
calculate it is a key skill in corporate finance. The first step in calculating the weighted
average cost of capital (WACC) is to find the cost of capital of each source of long-term
finance used by a company. That is the purpose of this section.
9.1.1 Ordinary shares
Equity finance can be raised either by issuing new ordinary shares or by using retained
earnings. We can find the cost of equity (Ke) by rearranging the dividend growth model
which is considered later in the book in Section 10.4.3:
Ke =
where: Ke
D0
g
P0
=
=
=
=
D0 11 + g2
P0
+ g
cost of equity
current dividend or dividend to be paid shortly
expected annual growth rate in dividends
ex dividend share price
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CHAPTER 9 THE COST OF CAPITAL AND CAPITAL STRUCTURE
Retained earnings have a cost of capital equal to the cost of equity. A common misconception is to see retained earnings as a source of finance with no cost. It is true that
retained earnings do not have servicing costs, but they do have an opportunity cost equal
to the cost of equity, since if these funds were returned to shareholders they could have
achieved a return equivalent to the cost of equity through personal reinvestment.
An alternative and arguably more reliable method of calculating the cost of equity is to
use the capital asset pricing model (CAPM), considered earlier in Chapter 8. The CAPM allows
shareholders to determine their required rate of return, based on the risk-free rate of return
plus an equity risk premium. The equity risk premium reflects both the systematic risk of the
company and the excess return generated by the market relative to risk-free investments.
Using the CAPM, the cost of equity finance is given by the following linear relationship:
where: Rj
Rf
bj
Rm
=
=
=
=
Rj = Rf + [(bj * 1Rm - Rf 2 2]
the rate of return of share j predicted by the model
the risk@free rate of return
the beta coefficient of share j
the return of the market
9.1.2 Preference shares
Calculating the cost of preference shares is usually easier than calculating the cost of ordinary
shares. This is because the dividends paid on preference shares are usually constant. Preference
shares tend to be irredeemable and preference dividends are not tax deductible since they are
a distribution of after-tax profits. The cost of irredeemable preference shares (Kps) can be calculated by dividing the dividend payable by the ex dividend market price as follows:
Kps =
Dividend payable
Market price (ex dividend)
When calculating the cost of raising new preference shares, the above expression can
be modified, as can the dividend growth model, to take issue costs into account.
9.1.3 Bonds and convertibles
There are three major types of bonds or loan notes: irredeemable bonds, redeemable
bonds and convertible bonds. The cost of irredeemable bonds is calculated in a similar way
to that of irredeemable preference shares. In both cases, the model being used is one that
values a perpetual stream of cash flows (a perpetuity). Since the interest payments made
on an irredeemable bond are tax deductible, it will have both a before- and an after-tax
cost of debt. The before-tax cost of irredeemable bonds (Kib) can be calculated as follows:
Kib =
Interest rate payable
Market price of bond
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9.1 CALCULATING THE COST OF INDIVIDUAL SOURCES OF FINANCE
The after-tax cost of debt is then easily obtained if the corporate taxation rate (CT) is
assumed to be constant:
Kib 1after tax2 = Kib(1 - CT)
To find the cost of redeemable bonds we need to find the overall return required by
providers of debt finance, which combines both revenue (interest) and capital (principal)
returns. This is equivalent to the internal rate of return (Kd) of the following valuation model:
P0 =
where: P0
I
CT
RV
Kd
n
=
=
=
=
=
=
I11 - CT 2
11 + Kd 2
+
I11 - CT 2
11 + Kd 2
2
+
I11 - CT 2
11 + Kd 2
3
+
###
+
I11 - CT 2 + RV
current ex interest market price of bond
annual interest payment
corporate taxation rate
redemption value
cost of debt after tax
number of years to redemption
11 + Kd 2 n
Note that this equation will give us the after-tax cost of debt. If the before-tax cost is
required, I and not I(1 – CT) should be used. Linear interpolation can be used to estimate
Kd (see ‘The internal rate of return method’, Section 6.4).
Alternatively, instead of using linear interpolation, the before-tax cost of debt can be
estimated using the bond yield approximation model developed by Hawawini and Vora
(1982):
P - NPD
d
n
Kd =
P + 0.61NPD - P2
I + c
where:
I
P
NPD
n
=
=
=
=
annual interest payment
par value or face value
net proceeds from disposal (market price of bond)
number of years to redemption
The after-tax cost of debt can be found using the company taxation rate (CT):
Kd 1after tax2 = Kd(1 - CT)
The cost of capital of convertible debt is more difficult to calculate. To find its cost we
must first determine whether conversion is likely to occur (see ‘The valuation of convertible bonds’, Section 5.7). If conversion is not expected, we ignore the conversion value
and treat the bond as redeemable debt, finding its cost of capital using the linear interpolation or bond approximation methods described above.
If conversion is expected, we find the cost of capital of convertible debt using linear
interpolation and a modified version of the redeemable bond valuation model given earlier. We modify the valuation model by replacing the number of years to redemption (n)
with the number of years to conversion, and replacing the redemption value (RV) with
the expected future conversion value (CV) (see ‘Market value’, Section 5.7.2).
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CHAPTER 9 THE COST OF CAPITAL AND CAPITAL STRUCTURE
It must be noted that an after-tax cost of debt is appropriate only if the company is in
a profitable position, i.e. it has taxable profits against which to set its interest payments.
9.1.4 Bank borrowings
The sources of finance considered so far have all been tradeable securities and have a
market price to which interest or dividend payments can be related in order to calculate
their cost. This is not the case with bank borrowings, which are not in tradeable security
form and which do not have a market value. To approximate the cost of bank borrowings,
therefore, the average interest rate paid on the loan should be taken, making an appropriate adjustment to allow for the tax deductibility of interest payments. The average interest
rate can be found by dividing the interest paid on bank borrowings by the average
amount of bank borrowings for the year. Alternatively, the cost of debt of any bonds or
traded debt issued by a company can be used as an approximate value for the cost of debt
of its bank borrowings.
9.1.5 The relationship between the costs of different sources of finance
When calculating the costs of the different sources of finance used by a company, a logical
relationship should emerge between the cost of each source of finance on the one hand
and the risk faced by each supplier of finance on the other. Equity finance represents the
highest level of risk faced by investors. This is due both to the uncertainty surrounding
dividend payments and capital gains, and to the ranking of ordinary shares at the bottom
of the creditor hierarchy (see Figure 9.1) should a company go into liquidation. New equity
issues therefore represent the most expensive source of finance, with retained earnings
working out slightly cheaper owing to the savings on issue costs over a new equity issue.
The cost of capital of preference shares will be less than the cost of equity for two
reasons. First, preference dividends must be paid before ordinary dividends; hence, there
is less risk of their not being paid. Second, preference shares rank higher in the creditor
hierarchy than ordinary shares and so there is less risk of failing to receive a share of liquidation proceeds.
1 Fixed charge creditors
2 Costs of liquidation
Increasing
priority
3 Preferential creditors (including employees, PAYE and VAT)
4 Floating charge creditors
Decreasing
priority
5 Unsecured creditors
6 Preference shareholders
7 Ordinary shareholders
Figure 9.1 Creditor hierarchy and the order of asset distribution on bankruptcy
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9.2 CALCULATING WEIGHTED AVERAGE COST OF CAPITAL
There is no uncertainty with respect to interest payments on debt, unless a company
is likely to be declared bankrupt. Debt is further up the creditor hierarchy than both preference shares and ordinary shares, implying that debt finance has a lower cost of capital
than both. Whether bank borrowings are cheaper than bonds will depend on the relative
costs of obtaining a bank loan and issuing bonds, on the amount of debt being raised,
and on the extent and quality of security used. Generally speaking, the longer the period
over which debt is raised, the higher will be its cost of capital: this is because lenders
require higher rewards for giving up their purchasing power for longer periods of time.
Additionally, the risk of default also increases with time. The cost of capital convertible
debt depends on when and whether the debt is expected to convert into ordinary shares.
If convertible debt is not expected to convert, its cost of capital will be similar to the cost
of capital of redeemable bonds of a similar maturity. If convertible debt is expected to
convert, its cost of capital will be between those of redeemable bonds and ordinary
shares. The longer the time period before conversion, the closer will be the cost of capital
of convertible debt to that of redeemable bonds and vice versa.
The relationships discussed above are evident in the example of a WACC calculation
given below.
9.2 CALCULATING WEIGHTED AVERAGE COST OF CAPITAL
Once the costs of a company’s individual sources of finance have been found, the overall
WACC can be calculated. In order to calculate the WACC, the costs of the individual
sources of finance are weighted according to their relative importance as sources of
finance. The WACC can be calculated either for the existing capital structure (average
basis) or for additional incremental finance (marginal basis). The problem of average
versus marginal basis WACC is discussed in the next section.
The WACC calculation for a company financed solely by debt and equity finance is
represented by:
WACC =
where: Ke
E
Kd
CT
D
=
=
=
=
=
Kd 11 - CT 2 * D
Ke * E
+
1D + E2
1D + E2
cost of equity
value of equity
before@tax cost of debt
corporate taxation rate
value of debt
This equation will expand in proportion to the number of different sources of finance
used by a company. For instance, for a company using ordinary shares, preference shares
and both redeemable and irredeemable bonds, the equation will become:
WACC =
Kps * P
Kib 11 - CT 2Di
Krb 11 - CT 2Dr
Ke * E
+
+
+
E + P + Di + Dr
E + P + Di + Dr
E + P + Di + Dr
E + P + Di + Dr
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CHAPTER 9 THE COST OF CAPITAL AND CAPITAL STRUCTURE
where P, Di and Dr are the value of preference shares, irredeemable bonds and redeemable bonds, respectively.
9.2.1 Market value weightings or book value weightings?
We now need to determine the weightings to be attached to the costs of the different
sources of finance. The weightings allow the calculated average to reflect the relative
proportions of capital used by a company. We must choose between book values or market values. Book values are easily obtained from a company’s accounts whereas market
values can be obtained from the financial press and from a range of financial databases.
While book values are easy to obtain, using them to calculate the WACC cannot be
recommended. Book values are based on historical costs and rarely reflect the current
required return of providers of finance, whether equity or debt. The nominal value of an
ordinary share, for example, is usually only a fraction of its market value. In the following
example, an ordinary share with a nominal value of £1 has a market value of £4.17. Using
book values will therefore understate the impact of the cost of equity finance on the average cost of capital. As the cost of equity is always greater than the cost of debt, this will
lead to the WACC being underestimated. This can be seen in the following example by
comparing the WACC calculated using market values with the WACC calculated using
book values. If the WACC is underestimated, unprofitable projects will be accepted. As
mentioned earlier, some sources of finance, such as bank loans, do not have market values. There is no reason, theoretically, why book values and market values cannot be used
in conjunction with each other. Hence when making WACC calculations it is recommended to use as many market values as possible.
Example
Calculating weighted average cost of capital
Strummer plc is calculating its current weighted average cost of capital on both a book
value and a market value basis. You have the following information:
Financial position statement as at 31 December
Non-current assets
Current assets
Current liabilities
5% bonds (redeemable in 6 years)
9% irredeemable bonds
Bank loans
Ordinary shares (50p nominal value)
7% preference shares (£1 nominal value)
Reserves
£000
33,344
15,345
(9,679)
(4,650)
(8,500)
(3,260)
22,600
6,400
9,000
7,200
22,600
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9.2 CALCULATING WEIGHTED AVERAGE COST OF CAPITAL
1 The current dividend, shortly to be paid, is 23p per share. Dividends in the future
are expected to grow at a rate of 5 per cent per year.
2 Corporation tax is currently 30 per cent.
3 The interest rate on bank borrowings is currently 7 per cent.
4 Stock market prices as at 31 December (all ex dividend or ex interest):
Ordinary shares
Preference shares
5% bonds
9% irredeemable bonds
£4.17
89p
£96 per £100 bond
£108 per £100 bond
Step one: Calculating the costs of individual sources of finance
1 Cost of equity: using the dividend growth model:
Ke = [D0(1 + g)>P0] + g
= [23 * (1 + 0.05)/417] + 0.05
= 10 .8 per cent
2 Cost of preference shares:
Kps = 8>89 = 9.0 per cent
3 Cost of redeemable bonds (after tax): using the Hawawini–Vora bond yield
approximation model:
Krb =
5 + 1100 - 962 >6
100 + 0.6196 - 1002
Krb(before tax) = 5 .8%
Krb(after tax) = 5 .8 * (1 - 0 .30) = 4 .1 per cent
4 Cost of bank loans (after tax):
Kbl 1after tax2 = 7 * (1 - 0.30) = 4.9 per cent
5 Cost of irredeemable bonds (after tax):
Kib 1after tax2 = 9 * (1 - 0.30)>108 = 5.8 per cent
Step two: Calculating book and market values of individual sources
of finance
Source of finance
Ordinary shares
Preference shares
Redeemable bonds
Irredeemable bonds
Bank loans
Total
Book value (£000)
6,400 + 7,200 = 13,600
9,000
4,650
8,500
3,260
39,010
Market value (£000)
6,400 * 4.17 * 2 = 53,376
9,000 * 0.89 = 8,010
4,650 * 96/100 = 4,464
8,500 * 108/100 = 9,180
3,260
78,290
➨
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CHAPTER 9 THE COST OF CAPITAL AND CAPITAL STRUCTURE
Step three: Calculating WACC using book values and market values
WACC (book values) = (10 .8% * 13,600/39,010) + (9 .0% * 9,000/39,010)
+ (4 .1% * 4,650/39,010) + (4 .9% * 3,260/39,010)
+ (5 .8% * 8,500/39,010)
= 8 .0 per cent
WACC (market values) = (10 .8% * 53,376/78,290) + (9 .0% * 8,010/78,290)
+ (4 .1% * 4,464/78,290) + (4 .9% * 3,260/78,290)
+ (5 .8% * 9,180/78,290)
= 9 .4 per cent
9.3 AVERAGE AND MARGINAL COST OF CAPITAL
As mentioned earlier, the cost of capital can be calculated in two ways. If it is calculated
on an average basis using balance sheet data and book values or market values as weightings, as in the above example, it represents the average cost of capital currently employed.
This cost of capital represents historical financial decisions. If it is calculated as the cost
of the next increment of capital raised by a company, it represents the marginal cost of
capital. The relationship between average (AC) cost of capital and marginal (MC) cost of
capital is shown in Figure 9.2.
The relationship between the average cost and marginal cost curves can be explained
as follows. When the marginal cost is less than the average cost of capital, the average cost
of capital will fall. Once the marginal cost rises above the average cost of capital, however,
the marginal cost of capital will pull up the average cost of capital, albeit at a slower rate
than that at which the marginal cost is rising.
Should we use the marginal or the average cost of capital when appraising investment
projects? Strictly speaking, the marginal cost of capital raised to finance an investment
project should be used rather than an average cost of capital. One problem with calculating
Cost (%)
AC
MC
0
Gearing (debt/equity)
Figure 9.2 The marginal cost and the average cost of capital
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