ACCA F9 Financial Management - 2010 - Study text - Emile Woolf Publishing
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Paper F9
Financial management
CHAPTER
16
Cost of capital
Contents
1 Relativecostsofequityanddebt
2 Costofequity
3 Costofdebtcapital
4 Calculatingtheweightedaveragecostofcapital
(WACC)
5 Costofcapitalandgearing
6 Peckingordertheory
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Relative costs of equity and debt
Cost of equity, cost of debt and the weighted average cost of capital (WACC)
Average and marginal cost of capital
Comparing the cost of equity and the cost of debt
The creditor hierarchy
1 Relative costs of equity and debt
1.1 Cost of equity, cost of debt and the weighted average cost of capital
(WACC)
The cost of capital for investors is the return that investors require from their
investment. Companies must be able to make a sufficient return from their own
capital investments to pay the returns required by their shareholders and holders of
debt capital. The cost of capital for investors therefore establishes a cost of capital for
companies.
For each company there is a cost of equity. This is the return required by its
shareholders, in the form of dividends or share price growth
There is a cost for each item of debt finance. This is the yield required by the
lender or bond investor
When there are preference shares, there is also a cost of preference share capital.
The cost of capital for a company is the return that it must make on its investments
so that it can afford to pay its investors the returns that they require.
The cost of capital for investors and the cost of capital for companies should
theoretically be the same. However, they are different because of the differing tax
positions of investors and companies.
The cost of capital for investors is measured as a pre-tax cost of capital
The cost of capital for companies recognises that interest costs are an allowable
expense for tax purposes, and the cost of debt capital to a company should allow
for the tax relief that companies receive on interest payments, reducing their tax
payments. The cost of debt capital for companies is measured as an after-tax
cost.
The weighted average cost of capital (WACC) is the average cost of all the sources
of capital that a company uses. This average is weighted, to allow for the relative
proportions of the different types of capital in the company’s capital structure.
1.2 Average and marginal cost of capital
One approach to the evaluation of capital investments by companies is that all of their
investment projects should be expected to provide a return equal to or in excess of the
Chapter 16: Cost of capital
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WACC. If all their investment projects earn a return in excess of the WACC, the
company will earn sufficient returns overall to meet the cost of its capital and provide
its investors with the returns they require. An alternative is to use the marginal cost of
capital when evaluating investment projects.
The marginal cost of capital is the cost of the next increment of capital raised by the
company.
1.3 Comparing the cost of equity and the cost of debt
The cost of equity is always higher than the cost of debt capital. This is because
equity investment in a company is always more risky than investment in the debt
capital of the same company.
Interest on debt capital is often fixed: bondholders for example receive a fixed
amount of annual interest on their bonds. In contrast, earnings per share are
volatile and can go up or down depending on changes in the company’s
profitability.
Providers of debt capital have a contractual right to receive interest and the
repayment of the debt principal on schedule. If the company fails to make
payments on schedule, the debt capital providers can take legal action to protect
their legal or contractual rights. Shareholders do not have any rights to dividend
payments.
Providers of secured debt are able to enforce their security if the company
defaults on its interest payments or capital repayments.
In the event of insolvency of the company and liquidation of its assets, providers
of debt capital are entitled to payment of what they are owed by the company
before the shareholders can receive any payment themselves out of the
liquidated assets.
Since equity has a higher investment risk for investors, the expected returns on
equity are higher than the expected returns on debt capital.
In addition, from a company’s perspective, the cost of debt is also reduced by the tax
relief on interest payments. This makes debt finance even lower than the cost of equity.
The effect of more debt capital, and higher financial gearing, on the WACC is
considered in more detail later.
1.4 The creditor hierarchy
The creditor hierarchy refers to the order in which proceeds are distributed in the
event of a company insolvency and winding up (liquidation of its assets).
At the top of the hierarchy are secured creditors such as debenture holders and
banks who are entitled to unpaid interest and the principal outstanding on any
loan.
The next are unsecured creditors, such as providers of unsecured debt capital
and trade payables.
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Next are preference shareholders, if the company has any preference shares in
issue. If there are several different classes of preference shares, their priority
ranking for payment depends on their relative class rights.
Ordinary shareholders are at the bottom of the hierarchy and are only entitled to
repayment of capital once all debt holders and preference shareholders have
been paid in full.
The further down the hierarchy a finance provider the greater the risk of loss of
capital. The return required in compensation therefore increases and the cost of
equity will always exceed the cost of debt and preference shares.
There is also a priority ranking for annual income.
Providers of debt capital receive payment of interest out of the company’s
profits before interest and tax
Preference shareholders are paid dividends out of after-tax profits. If the
company is unable to pay preference dividends in any year, the unpaid dividend
accumulates in he case of cumulative preference shares, and the arrears o f
unpaid dividends must be paid in full before dividend payments to ordinary
shareholders can be resumed.
Ordinary shareholders (equity shareholders) are paid dividends out of
distributable profits at the discretion of the company’s directors. For ordinary
shareholders there is a risk that the dividends and share price will be adversely
affected by volatile earnings, and lower-than-expected annual profits.
Chapter 16: Cost of capital
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Cost of equity
Methods of calculating the cost of equity
The dividend valuation model method of estimating the cost of equity
The dividend growth model method of estimating the cost of equity
The CAPM method of estimating the cost of equity
2 Cost of equity
2.1 Methods of calculating the cost of equity
The cost of equity is the annual return expected by ordinary shareholders, in the
form of dividends and share price growth. However, share price growth is assumed
to occur when shareholder expectations are raised about future dividends. If future
dividends are expected to increase, the share price will also increase over time. At
any time, the share price can be explained as a present value of all future dividend
expectations.
Using this assumption we can therefore say that the current value of a share is the
present value of future dividends in perpetuity, discounted at the cost of equity (i.e.
the return required by the providers of equity capital).
There are two methods that you need to know for estimating what the share price in
a company ought to be:
the dividend valuation model
the dividend growth model, sometimes called the Gordon growth model.
Each of these methods for obtaining a share price valuation uses a formula that
includes the cost of equity capital. The same models can therefore be used to
estimate a cost of equity if the share price is known. In other words, the dividend
valuation model and dividend growth model can be used either:
to calculate an expected share price when the cost of equity is known, or
to calculate the cost of equity when the share price is known.
Another method of estimating the cost of capital is the capital asset pricing model
or CAPM. This is an alternative to using a dividend valuation model method, and it
produces a different estimate of the cost of equity.
2.2 The dividend valuation model method of estimating the cost of equity
If it is assumed that future annual dividends are expected to remain constant into
the foreseeable future, the cost of equity can be calculated by re-arranging the
dividend valuation model as follows.
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MV
d
r
E
=
where:
r
E
is the cost of equity
d = the expected future annual dividend.
MV is the share price ex dividend.
The formula assumes that dividends are paid annually.
‘Ex dividend’ means that if the company will pay a dividend in the near future, the
share price must be a price that excludes this dividend. For example a company
might declare on 1 March that it will pay a dividend of $0.60 per share to all holders
of equity shares on 30 April, and the dividend will be paid on 31 May. Until 30 April
the share price allows for the fact that a dividend of $0.60 will be paid in the near
future and the shares are said to be traded ‘cum dividend’ or ‘with dividend’. After
30 April, if shares are sold they are traded without the entitlement to dividend, or
‘ex dividend’. This is the share price to use in the cost of equity formula whenever a
dividend is payable in the near future and shares are being traded cum dividend.
Example
A company’s shares are currently valued at $8.20 and the company is expected to
pay an annual dividend of $0.70 per share for the foreseeable future. The cost of
equity in the company can therefore be estimated as:
(0.70/8.20) = 0.085 or 8.5%.
Example
A company’s shares are currently valued at $8.20 and the company is expected to
pay an annual dividend of $0.70 per share for the foreseeable future. The next
annual dividend is payable in the near future and the share price of $8.20 is a cum
dividend price. The cost of equity in the company can therefore be estimated as:
0.70/(8.20 – 0.70) = 0.70/7.50 = 0.093 or 9.3%.
2.3 The dividend growth model method of estimating the cost of equity
If it is assumed that the annual dividend will grow at a constant percentage rate into
the foreseeable future, the cost of equity can be calculated by re-arranging the
dividend growth model.
()
g
MV
g1d
r
E
+
+
=
where:
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r
E
is the cost of equity
d = the annual dividend for the year that has just ended
g is the annual growth rate in dividends, expressed as a proportion (4% = 0.04, 2.5%
= 0.025 etc.)
d (1 + g) is therefore the expected annual dividend next year
MV is the share price ex dividend.
(Note: The formula sheet in your examination uses the expression ‘P
0
’ for the
current market price ex dividend. ‘MV’ is used here because it is probably easier to
recognise and understand.)
The formula assumes that dividends are paid annually.
Example
A company’s share price is $8.20. The company has just paid an annual dividend of
$0.70 per share, and the dividend is expected to grow by 3.5% into the foreseeable
future. The next annual dividend will be paid in one year’s time.
The cost of equity in the company can be estimated as follows:
0.035+
8.20
(1.035) 0.70
=r
E
= 0.123 or 12.3%.
Example
A company’s share price is $5.00. The next annual dividend will be paid in one
year’s time and dividends are expected to grow by 4% per year into the foreseeable
future. The next annual dividend is expected to be $0.45 per share.
The next annual dividend = d (1 + g). The cost of equity in the company can be
estimated as follows:
0.04+
5.00
0.45
=r
E
= 0.13 or 13%.
2.4 The CAPM method of estimating the cost of equity
Another approach to calculating the cost of equity in a company is to use the capital
asset pricing model (CAPM). The CAPM is considered in more detail in the next
chapter. The formula for the model:
R
E
= R
RF
+ β (R
M
– R
RF
)
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Where
R
E
= the cost of equity for a company’s shares
R
RF
= the risk-free rate of return: this is the return that investors receive on risk-free
investments such as government bonds
R
M
= the average return on market investments as a whole, excluding risk-free
investments
β = the beta factor for the company’s equity shares. The nature of the beta factor is
explained in the next chapter.
Example
The rate of return available for investors on government bonds is 4%. The average
return on market investments is 7%. The company’s equity beta is 0.92.
Using the CAPM, the company’s cost of equity is therefore:
4% + 0.92 (7 – 4)% = 6.76%.
Example
A company’s shares have a current market value of $13.00. The most recent annual
dividend has just been paid. This was $1.50 per share.
Required
Estimate the cost of equity in this company in each of the following circumstances:
(a) The annual dividend is expected to remain $1.50 into the foreseeable future.
(b) The annual dividend is expected to grow by 4% each year into the foreseeable
future
(c) The CAPM is used, the equity beta is 1.20, the risk-free cost of capital is 5%
and the expected market return is 14%.
Answer
(a) Cost of equity =
1.50
13.00
= 0.115 or 11.5% .
(b)
Cost of equity =
1.50 1.04
(
)
13.00
+0.04 = 0.16 or 16%
.
(c)
Cost of equity = 5% + 1.20 (14 – 5)% = 15.8%.
Chapter 16: Cost of capital
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Cost of debt capital
Cost of variable rate debt (floating rate debt)
Cost of irredeemable fixed rate debt (perpetual bonds)
Cost of redeemable fixed rate debt (redeemable fixed rate bonds)
Cost of convertible debt
Cost of preference shares
3 Cost of debt capital
Each item of debt finance for a company has a different cost. This is because
different types of debt capital have differing risk, according to whether the debt is
secured, whether it is senior or subordinated debt, and the amount of time
remaining to maturity. (Note: Longer-dated debt normally has a higher cost than
shorter-dated debt).
3.1 Cost of variable rate debt (floating rate debt)
The cost of debt can be calculated as either a pre-tax cost or an after-tax cost.
Investors are interested in the pre-tax cost. Companies that borrow are interested in
the after-tax cot of debt, for the purpose of calculating their cost of capital.
The pre-tax cost of variable rate debt (also called floating rate debt), such as the
cost of a bank loan, is the current interest rate payable on the debt.
The after-tax cost of variable rate debt is the pre-tax cost multiplied by a factor (1 –
t), where t is the rate of tax on company profits.
For example, suppose that a company is currently paying interest at 6% on its bank
loan of $10 million, and the rate of tax on company profits is 25%. The pre-tax cost
of the debt is 6% and the after-tax cost is 6 (1 – 0.25) = 4.5%.
For the purpose of calculating a weighted average cost of capital (WACC, explained
later), the cost of the debt would be its after-tax cost of 4.5% and its market value
(for the purpose of weighting the cost of capital) would be $10 million, which is the
amount of the loan.
3.2 Cost of irredeemable fixed rate debt (perpetual bonds)
The cost of irredeemable fixed rate bonds, which might be described as perpetual
bonds, is calculated as follows:
Pre-tax cost Post-tax cost
MV
i
r
D
=
()
MV
t1i
r
D
−
=
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where:
r
D
is the cost of the debt capital
i is the annual interest payable on each $100 (nominal value) of the bonds.
t is the rate of tax on company profits.
MV is the market value of $100 nominal value of bonds, excluding any interest
currently payable.
Example
The coupon rate of interest on a company’s irredeemable bonds (‘perpetual bonds’)
is 6% and the market value of the bonds is 103.60. The tax rate is 25%.
(a) The pre-tax cost of the debt is 6/103.60 = 0.058 or 5.8%.
(b) The after-tax cost of the bonds is 6 (1 – 0.25)/103.60 = 0.043 or 4.3%.
3.3 Cost of redeemable fixed rate debt (redeemable fixed rate bonds)
The cost of redeemable bonds is their redemption yield. This is the return, expressed
as an average annual interest rate or yield, that investors in the bonds will receive
between ’now’ and the maturity and redemption of the bond, taking the current
market value of the bonds as the investment. It is the investment yield at which the
bonds are currently trading in the bond market.
This is calculated as the rate of return that equates the present value of the future
cash flows payable on the bond (to maturity) with the current market value of the
bond. In other words, it is the IRR of the cash flows on the bond to maturity,
assuming that the current market price is a cash outflow.
A problem arises with calculating the pre-tax and the after-tax cost of redeemable
bonds, because the redemption of the principal at maturity is not an allowable
expense for tax purposes. The post-tax cost of redeemable debt could therefore be
calculated in either of two ways. Each gives a different cost of capital:
Method 1. Calculate the pre-tax cost of debt (the IRR of the cash flows ignoring
debt) and then apply the factor (1 – t) to reach the post-tax cost of debt
Method 2. Calculate the post-tax cost of debt as the IRR of the future cash flows,
allowing for tax relief on the interest payments and the absence of tax relief on
the principal repayment.
If in doubt, use Method 2. However, Method 1 might be more appropriate if it is
assumed that the company will replace the redeemable debt at maturity with a new
issue of similar debt capital. So either Method 1 or Method 2 might be valid. Read
the requirements of the question carefully, to see whether you are given any
instructions about which method to use.