OVERVIEW
Objective
¾
To understand the weighted average cost of capital (WACC) of a company and how it is estimated.¾
To understand the effect of gearing on the WACC of a company.¾
To discuss the theories of Modigliani and Miller.WEIGHTED AVERAGE COST
OF CAPITAL
WEIGHTED AVERAGE COST OF CAPITAL
AND GEARING
GEARING
¾ Calculation of WACC ¾ Limitations of WACC
¾ The effects of gearing
1
WEIGHTED AVERAGE COST OF CAPITAL
1.1
Calculation of WACC
¾
Companies are usually financed by both debt and equity, i.e. they use some degree of financial/capital gearing. We must therefore calculate a weighted average cost of capital (WACC) which represents a company’s average cost of long-term finance. This will give us a potential discount rate for project appraisal using NPV.¾
In the previous session we saw how to estimate the cost of equity and the cost of various types of debt.¾
We weight the various costs of debt and equity using their respective market values.WACC =
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:
WACC = ke
Ve = Total market value of equity Vd = Total market value of debt Ke = Cost of equity geared
Kd = Pre-tax cost of debt T = corporation tax rate
Project has same business risk as existing operations Project is financed
by existing pool of funds
Proportion of debt to equity does not change
A company’s current WACC is used as the discount rate only 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:
¾
Gearing level i.e. Financial Risk¾
Business Risk¾
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 The loan stock is trading at par.
Share price $1.50
Dividend 15c (just paid)
Dividend growth 5% pa
Corporation tax 33%
Estimate the WACC.
1.2
Limitations of WACC
LIMITATIONS
THEORETICAL PRACTICAL
CALCULATION OF Ke
Assumes perfect capital market
Assumes
− market value of shares
= present value of dividend stream − market value of debt
= present value of interest/principal
Current WACC can only be used to
assess projects which
− have similar operating risk to that of the company
− are financed by the company’s pool of funds, ie have same financial risk
Estimation of “g”
− historical data used to estimate future growth rates − Gordon’s model assumes all growth is financed by retained earnings
CALCULATION OF Kd
Assumes constant tax rates
Bond price may not be in equilibrium
Difficulty in incorporating all
forms of long term finance, eg
BANK OVERDRAFT CONVERTIBLE
LOAN STOCK FOREIGN LOANS
Current liability but often
has permanent core
Must be aplit between fixed and
variable element
Put fixed element in calculation
Final cash flow is uncertain
Investor has option of
(i) taking the redemption value, or
(ii) converting into shares
Assume it will be redeemed
unless data is available to suggest conversion
Exchange rates will
¾
These problems are particularly difficult for unquoted companies which have no share price available and possibly irregular dividend payments.¾
In this case it may be advisable to estimate the WACC of a quoted company in the same industry and with similar gearing and then add a (subjective) premium to reflect the (perceived) higher risk and lower marketability of unquoted shares.2
THE EFFECTS OF GEARING
¾
The current WACC reflects the current risk profile of the company: bothBusiness risk – The variability in the operating earnings of the company i.e. the volatility of EBIT due to the nature of the industry
and
Financial risk – The additional variability in the return to equity as a result of
introducing debt i.e. using financial gearing. Interest on debt is a committed fixed cost which creates more volatile bottom line profits for shareholders.
¾
As a company gears up two things happen. WACC = Ke E + Kd DE + D
Ke increases due to
the increased financial risk.
All else equal, this
pushes up the value of WACC
The proportion of
debt relative to equity in the capital
structure increases.
Since Kd < Ke this
pushes the value of WACC down, all else equal
¾
The effect of increased gearing on the WACC depends on the relative sizes of these two opposing effects.¾
There are two main schools of thought Traditional view
3
TRADITIONAL VIEW OF CAPITAL STRUCTURE
3.1
Reasoning
¾
The traditional view has no theoretical foundation – often described as the “intuitive approach”. It is based upon the trade-off caused by gearing i.e. using more (relatively cheap) debt results in a rising cost of equity. The model can also be referred to as the “static trade-off model”.¾
It 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.¾
At higher levels of gearing the increased financial risk outweighs this benefit and WACC rises.Cost of
capital Ke
WACC
Kd
D/E Optimal
gearing
¾
Note 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.¾
This is referred to as financial distress risk – not to be confused with financial risk which occurs even at relatively safe levels of debt.3.2
Conclusions
¾
There is an optimal gearing level (minimum WACC).3.3
Project finance — implications
¾
If the company is optimally geared Raise finance so as to maintain the existing gearing ratio
¾
If the company is sub-optimally geared Raise debt finance so as to increase the gearing ratio towards the optimal
¾
If the company is supra-optimally geared Raise equity finance so as to reduce the gearing ratio back to the optimal
3.4
Approach
¾
Appraise the project at the existing WACC If the NPV of the project is positive the project is worthwhile
¾
Appraise the finance If marginal cost of the finance > WACC the finance is not appropriate and should
be rejected.
If this was the case the company could raise finance in the existing gearing ratio
4
MODIGLIANI AND MILLER’S THEORIES
4.1
Introduction
¾
Modigliani and Miller (MM) constructed a mathematical model to provide a basis for company managers to make financing decisions.¾
Mathematical models predict outcomes that would occur based on simplifying assumptions.¾
Comparison of the model’s conclusions to real world observations then allowsresearchers to understand the impact of the simplifying assumptions. By relaxing these assumptions the model can be moved towards real life.
¾
MM’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 riski.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.
4.2
Theory without tax
¾
MM expressed their theory as two propositions.¾
MM considered two companies - both with the same size and with the same level of business risk. One company was ungeared − Co U One company was geared − Co G
¾
MM’s basic theory was that in the absence of corporation tax the market values (V) and WACC’s of these two companies would be the same. (proposition 1)Vg = Vu
¾
MM argued that the 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 perceived
increased financial risk (proposition 2)
the rising ke would exactly offset the benefit of the additional cheaper debt in order
for the WACC to remain constant. This can be shown as a graph:
Cost of capital
WACC
D/E
Ke
Kd
¾
Conclusion There is no optimal gearing level;
The value of the company is independent of the financing decision Only investment decisions affect the value of the company.
¾
This is not true in practice because the assumptions are too simplistic. There are differences between the real world and the model¾
Note 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 hold. They were then in a position to relax the assumptions to see how the model’s predictions would change.¾
The first assumption they relaxed was the no corporate tax assumption.4.3
Theory 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.
Co U Co G
$m $m
EBIT 100 100
Interest − 20
____ ____
PBT 100 80
Tax @ 35% 35 28
____ ____
Dividends 65 52
____ ____ Returns to the investors:
Equity 65 52
Debt − 20
____ ____
65 72
____ ____ The investors in G receive in total each year $7m more than the investors in U. This is due to the tax relief on debt interest and is known as the tax shield. Tax shield = kd × D × t
where kd = pre-tax cost of debt
D = current market value of the debt
t = tax rate
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.
PV of tax shield =
kd t D Kd× ×
= D × t
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:
¾
When corporation tax is introduced MM argue that the costs of capital will 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 perceived financial risk WACC falls as gearing increases due to the additional tax relief on the debt interest.
Cost of capital
WACC
D/E
Ke
Kd
¾
The relationship between the WACC of a geared company, according to MM, and the WACC (Ke) of an ungeared company is:WACCg = Keu
+ −
D E
Dt
1
where Keu = cost of equity in an ungeared company D = market value of debt in the geared company E = market value of equity in the geared company t = corporate tax rate
¾
The formula for the cost of equity is:Illustration 1 — continued
Returning to the previous illustration these MM formulae can now be illustrated.
Suppose that the business risk of the two companies requires a return of 10% and the return required by the debt holders in Co G is 5%.
Co U
Market value of Co U will be the market value of the equity. This will be the dividend capitalised at the equity holders’ required rate of return
MVu =
1 .
065 = $650m
Keu = 10% i.e. required rate of return for business risk (U has no financial risk)
Co G
Market value of the equity of Co G is determined by the equity shareholders’ analysis of their net operating income into its constituent parts and the capitalisation of those elements at appropriate rates:
MVe =
Market value of debt is determined by the debt holders capitalising their interest at their required rate of return:
MVd =
05 .
020 = $400m
∴ Total market value of Co G = MVg = $390m + $400m = $790m
The MM formula that describes the relationship between the market values of equivalent companies at various gearing levels can be illustrated here:
MVg = MVu + Dt
MM’s WACC relationship can also be illustrated
Firstly, WACC by the usual approach:
Keg =
value
MarketDividend = 39052 = 13.33%
(assumes no growth in dividends)
Kd = 5% × (1 − 35%) = 3.25%
WACC = 13.33% × 790
390 + 3.25% × 790
400 = 8.23%
Then by using MM/s formula: WACC = Keu (1− D E
Dt
+ )
Keu = 10%
= 10% (1−
400 390
% 35 400
+
× )
= 8.23%
MM’s equation for the cost of equity can also be checked
Keg = Keu + (1 – T) (Keu – kd) E D
= 10 + (1-0.35)(10-5) 390 400
¾
Conclusion The logical conclusions to be drawn from MM’s theory with tax is that there is an
optimal gearing level and that this is at 99.9% debt in the capital structure.
This implies that the financing decision for a company is vital to its overall market
value and that companies should gear up as far as possible.
¾
This is not true in practice; companies do not gear up to 99.9%. Why not? In practice there are obviously many other factors that will limit this conclusion
¾
These factors include the risk of financial distress;
the existence of not only corporate tax but also personal taxes;
¾
Thus in practice there are a series of factors that a company will need to consider in deciding how to raise finance.4.4
Practical considerations in choosing a gearing level
¾
These will include: business risk of the project; existing level of financial gearing:
level of operational gearing – the proportion of fixed to variable operating costs. If
this is high then the company may not wish to use debt as this increases the level of fixed costs even further;
type and quality of the assets; expected growth;
personal tax position of the shareholders and debt holders. internal and external limits to debt availability;
tax exhaustion (not enough profit to fully utilise the tax shield)
agency costs (increasingly restrictive debt covenants e.g. restricting dividends) issue costs
asymmetry of information – potential providers of finance may over-estimate the
risk of the company and refuse to provide capital at reasonable cost. Therefore the managers may have a preference for using internal finance i.e. retained earnings, limiting the level of gearing;
Key points
³
WACC estimates the company’s average cost of long-term finance.³
It is therefore a potential discount rate to use for the calculation of theNPV of possible projects. However the existing WACC should only be used if the project would not change the company’s business risk or level of gearing i.e. financial risk.
³
There are various, and conflicting, models of how financial gearing affects the WACC – traditional trade-off theory, Modigliani and Miller without tax and MM with corporate tax. Each model has useful elements even if the conclusions of such models lack practical relevance.FOCUS
You should now be able to:
