ACCA P4 Advanced Financial Management - 2010 - Study text - Emile Woolf Publishing
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Chapter 6: Cost of capital
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Answer
Using the asset beta formula and assuming a risk-free cost of debt.
(meaning that
β
D
= 0):
()
0.301 80160
160
05.1
A
−+
×=
β
β
A
= 1.05 × 0.74074 = 0.778
7.4 Using the asset beta formula
The asset beta formula might be used in the following circumstances:
when a company uses the CAPM to estimate a cost of equity and WACC, in a
situation where a capital expenditure project will change the gearing of the
company
to estimate the beta factor for a capital investment project (a project beta), where
the gearing will be different from the company’s current capital structure
in order to estimate a cost of equity in a private company by comparing it with a
similar public company.
7.5 The asset beta formula: changing from one level of gearing to another
A company might be planning a capital investment that will alter its level of
gearing. In these cases, to work out the equity beta factor and cost of equity at the
new level of gearing, it is necessary to calculate the asset beta first (the beta for a
similar ungeared company).
To calculate a cost of equity using the CAPM, where the level of gearing changes,
we can calculate the asset beta and then convert this asset beta to an equity beta on
the basis of the new expected level of gearing.
The approach should be as follows:
Start with the company at its original level of gearing. You should be given the
value of the company (the value of its equity and the value of its debt capital)
and the cost of its equity and debt capital, and the equity beta factor.
You may assume, unless instructed otherwise, that the debt capital in the
company is risk-free, and the simplified version of the asset beta formula can be
used.
Having calculated the asset beta, you can calculate a new equity beta for the
company at its new level of gearing, using the same formula.
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Example
A company has a total current value of $80 million, consisting of $60 million equity
and $20 million of debt capital. The cost of equity is 12% and the pre-tax cost of the
debt capital is 7%. The rate of tax on company profits is 30%. The equity beta factor
is 0.925. The debt capital is risk-free. The return on the market portfolio is 13.67%.
Required
What will be the equity beta factor and the cost of equity in the company, if the
company issues new equity to raise $10 million and uses this money to repay $10
million of debt?
Answer
The equity beta of the company at its current level of gearing is 0.925.
The asset beta of the company (the equity beta of a similar ungeared company) will
be:
()
t1DE
E
EGA
−+
×=
ββ
β
A
= 0.925 × 60/[60 + 20 (1 – 0.30)]
β
A
= 0.925 × 60/74
β
A
= 0.75
We can calculate the total value of the company if it is ungeared, using the data for
the company at its current gearing level.
Total value of an all-equity company:
V
G
= V
U
+ Dt
$80 million = V
U
+ ($20 million × 0.30)
V
U
= $74 million.
At the new level of gearing, the market value of the debt capital will be $10 million
($20 million minus $10 million redeemed). We can calculate the total value of the
company at the new gearing level, using the value of the company if it is ungeared.
V
G
= V
U
+ Dt
V
G
= $74 million + ($10 million × 0.30)
V
G
= $77 million.
Of this total value, $10 million is debt capital; therefore the value of the equity is $67
million.
We now have the information to calculate a beta factor for the equity at the new
level of gearing. The asset beta was calculated earlier, and is 0.75.
Chapter 6: Cost of capital
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()
t1DE
E
EGA
−+
×=
ββ
0.30)-(1 10+67
67
=0.75
EG
×β
0.9054
β
EG
= 0.75
β
EU
= 0.828, say 0.83.
Using the CAPM, we can calculate the cost of equity at the new gearing level as:
7% + 0.83 (13.67 – 7.0)
= 12.5361, say 12.5%.
7.6 Calculating a project beta factor
The CAPM can be applied to capital expenditure appraisal. The cost of capital for a
project can be determined according to the risk of the project. If the beta factor for a
project can be determined, the CAPM can then be used to decide what the cost of
capital for the project should be, allowing for its beta and systematic risk.
In addition, adjustments can be made for differences in gearing.
Example
An all-equity company operates in an industry where its beta factor is 0.90. It is
considering whether to invest in a completely different industry. In this other
industry, the average debt/equity ratio is 40% and the average beta factor is 1.25.
The risk-free rate of return is 4% and the average market return is 7%. If the
company does invest in this other industry, it will remain all-equity financed. The
rate of taxation is 30%. Assume that debt is risk-free.
Required
What cost of capital should be used to evaluate the proposed investment?
Answer
The appropriate discount rate should be one that applies to the industry in which
the investment will be made. We know that the geared beta in this industry is 1.25,
with a debt: equity ratio of 0.40. We can calculate the asset beta (ungeared equity
beta) for the industry as:
()
[]
0.85
88
60
1.25
0.3014060
60
1.25=
A
=×=
−+
×
β
Since the company will be all-equity financed, the cost of equity to apply to the
project is therefore:
4% + 0.85 (7 – 4)% = 6.55%.
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Note: If the company has proposed to finance the project with some debt, the asset
beta could be used to calculate a new geared beta for the appropriate level of
gearing, and a new cost of equity and new WACC could be calculated.
7.7 Estimating an equity beta factor for a private company
The asset beta formula can also be used to estimate the equity beta for a private
company (and its cost of equity) where the private company is comparable in size,
business mix and business risk to a public company whose shares are traded on a
stock market.
Data for the public company can be used to estimate an asset beta, and the asset beta
can then be applied to the private company to obtain an equity beta for the private
company.
Since there is no market data for the private company, an assumption has to be
made that accounting book b=values in the balance sheet are a reasonable
approximation to market values, and the calculations use book values for equity
and debt rather than market values.
Example
An investor is interested in acquiring Greenco, which is a private company with net
assets of $240 million and debt capital of $160 million in its balance sheet.
Greenco can be compared to a public company Redco, which operates in the same
industry and has a similar business mix and business risk. The following
information is available about Redco:
Market value of equity $450 million
Equity beta 1.60
Debt capital Risk-free (debt capital beta = 0)
Price to book value of equity 1.50 times
Gearing (total debt to equity value) 1.25
The rate of tax on profits is 30%. The risk-free rate of interest is 5% and the equity
risk premium is 3%.
Required
Use this information to estimate a cost of equity in Greenco.
Answer
Greenco is a private company and estimating a cost of equity has to be based on a
comparison with the similar public company, Redco.
The asset beta formula uses market values for debt and equity. Although we have
these market values for Redco, we do not have them for Greenco. An assumption
Chapter 6: Cost of capital
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should therefore be that book values are a reasonable approximation for market
values, and book values will be used in the calculations.
It is also assumed that debt in Greenco is risk-free.
Taking data about Redco and book values rather than market values, we can
estimate an asset beta for Redco and then assume that the same asset beta applies to
Greenco.
Market value of Redco equity = $450 million
Price to book value of equity = 1.5
Book value of equity = $450 million/1.5 = $300 million
Debt: equity ratio = 1.25 times
Book value of debt = $300 million × 1.25 = $450 million
()
0.301 450300
300
60.1
A
−+
×=
β
β
A
= 1.60 × 0.4878 = 0.78
This asset beta can be used to estimate an equity beta for Greenco:
0.30)-(1 160+240
240
=0.78
EG
×β
0.6818
β
EG
= 0.78
β
EG
= 1.14
The CAPM can now be used to estimate a cost of equity in Greenco:
K
E
= 5% + 1.14 (3%)
K
E
= 8.42%
Weaknesses with this method
Using the asset beta formula to estimate a cost of equity in a private company, using
data from a comparable public company, has some weaknesses and limitations.
It is assumed that book values are a reasonable approximation for market
values, but this assumption is questionable.
It is assumed that the business risk faced by both companies is the same, which
might not be true.
It is assumed that the cost of debt and equity in the private company is not
affected by factors such as greater default risk, its private company status, and
its smaller size. This assumption is also questionable.
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Paper P4
Advanced Financial Management
CHAPTER
7
Other aspects of capital
investment appraisal
Contents
1 Choosing the method of financing an investment
2 Adjusted present value method (APV method) of
project appraisal
3 Capital rationing
4 Real options
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Choosing the method of financing an investment
Theories about selecting the financing method for an investment
Static trade-off theory
Pecking order theory
Market timing theory
Agency effects on capital structure
1 Choosing the method of financing an investment
1.1 Theories about selecting the financing method for an investment
Capital investments have to be financed, and management must choose which
method of financing they will use. There are different theories about how the
method of financing is decided. These include:
static trade-off theory
pecking order theory
market timing theory.
There is also a view that the choice of financing method is affected by agency costs.
These differing theories are considered in this section.
1.2 Static trade-off theory
Static trade-off theory argues that for each company there is an optimal capital
structure, with an optimal level of gearing.
There is a trade-off between the benefits of taking on more debt and the costs of
higher indebtedness.
The benefits of taking on debt (rather than equity) are mainly in the tax relief
that is obtained on debt interest. Modigliani and Miller have argued that
although the cost of equity rises as gearing increases, the tax relief on debt
means that the company’s weighted average cost of capital falls as gearing rises.
It is therefore beneficial to take in more debt and increase gearing up to the point
where the marginal costs of extra debt start to exceed the marginal benefits of
extra debt.
The marginal costs of extra debt are related to the greater risks from ‘financial
distress.’ If lenders perceive that a company with high levels of debt could be in
financial distress (and in danger of failing to make payments of interest and
repayments of loan capital on schedule), it becomes much more difficult to raise
extra debt finance. The cost of debt might therefore increase substantially to
compensate a lender for the high credit risk.
The optimal gearing level for a company is reached at a point where:
the marginal benefits of taking on additional debt capital
equals the marginal costs of taking on the extra debt.
Chapter 7: Other aspects of capital investment appraisal
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The optimal gearing level varies between companies, depending on their
profitability. A very profitable company can take on higher gearing because the
marginal costs of financial distress will not become significant until the gearing level
is very high.
For a company with low profitability, the situation is different. These companies
provide low returns to their shareholders, and increasing the gearing level by
borrowing more would increase the risks of bankruptcy and the cost of borrowing.
Companies with low profits will therefore try to avoid additional borrowing, and
they will also be reluctant to incur the costs of making new equity issues. To finance
an investment, they will therefore rely on retained profits. They might even decide
against investing in a capital project with a positive NPV unless they can finance it
with funds from retained profits.
Static trade-off theory summarised
Static trade-off theory therefore states that:
Companies have an optimal level of gearing.
In choosing the method of financing for a new investment, they will try to
maintain or achieve the optimal gearing level.
The optimal gearing level is higher for companies with high profits than
companies with low profits.
This means that there is a positive correlation between profitability and gearing
level.
1.3 Pecking order theory
Pecking order theory takes a different view of gearing and methods of financing
new investments. It was put forward by Myers in 1984 as a challenge to static trade-
off theory.
This theory states that companies show preferences for the source of finance that
they use. There is an order of preference or ‘pecking order’.
1st. The source of finance that is preferred most is retained earnings.
2nd. Debt capital is the source of finance second in the order of preference.
3rd. New equity capital (an issue of new shares) is the least preferred source of
finance for investment.
This means that if a company has an opportunity to invest in a capital project with a
positive NPV, it will prefer to fund the project from retained profits. If it is unable to
do this, it will look for debt capital to finance the investment. Only if retained profits
and debt capital are unavailable (because cash flows are weak and profitability is
low) will the company consider a new issue of shares.
Companies are likely to choose a long-term dividend policy that will allow them to
finance future investments largely through retained earnings.
The reasons for the pecking order of preferences for sources of finance can be
explained by practical considerations.
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Using retained earnings is convenient. If a company wants to finance a new
investment with equity, it is much simpler and cheaper to use retained earnings
than to arrange a new share issue. Retained earnings are also much more
convenient than new borrowing.
If a company cannot finance an investment with retained earnings, it will prefer
new borrowing to a new issue of shares because borrowing is cheaper. It is
cheaper to arrange a loan than to issue new shares. The cost of debt is also less
because of the tax relief on interest payments.
Pecking order theory states that the gearing of a company is the result of a series of
financing decisions based on these preferences for sources of finance. An optimal
level of gearing does not exist, and companies do not try to achieve an optimal
gearing level.
Pecking order theory summarised
Pecking order theory therefore states that:
Companies do not have an optimal level of gearing.
In choosing the method of financing for a new investment, they have an order of
preference: retained earnings followed by new debt capital followed by an issue
of new shares.
Companies with high profits can rely on retained profits as a source of finance
more than companies with low profits.
This means that there is a negative correlation between profitability and gearing
level.
1.4 Market timing theory
Market timing theory states that the choice of financing method for companies can
be driven by opportunities in the capital markets. These opportunities occur because
of ‘asymmetries of information’. These occur when the managers of a company have
more information and better information about the company than shareholders and
other investors.
Management should know when the future prospects for the company are better
than investors are expecting, and when the prospects for the future are worse than
investors are expecting. Company management might therefore recognise occasions
when the company’s shares are currently under-valued or over-valued.
Companies will therefore wish to make a new issue of shares when they
consider the share price to be over-valued.
They will consider share repurchases when they consider the share price to be
under-valued.
Taking advantage of opportunities in the market to issue new shares or buy back
existing shares affects the gearing level. A company therefore does not have a target
optimal gearing level. Its financing decisions are determined more by market
opportunity and market timing.