Pike Robert, Neal Bill. Corporate finance and investment: decisions and strategy
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Chapter 19 Does capital structure really matter? 525
There is a useful expression available to show how the various Betas are linked together.
It is important to recall the MM message that underlying business or activity risk is unaf-
fected by the method of financing. If a firm chooses to borrow, thus introducing financial
risk, the shareholders will respond by looking for a higher return as they perceive greater
financial risk affecting their future income, but the risk attaching to the firm’s actual oper-
ating activities is untouched – it is the same firm operating in the same business environ-
ment and operated by the same managers. All that has happened is a repackaging of the
firm’s flow of operating income resulting in lenders now having a prior claim. The size
of the operating income itself is unaffected, only its distribution changes.
Given that the activity risk is unaffected by gearing, we can use the accounting equa-
tion to show the linkages. The accounting equation tells us that the assets are equal to the
methods of financing. Translating this into CAPM terms, the asset Beta (i.e. the activity
Beta) equals the Beta of the methods of finance used to acquire those assets. In other
words, the asset Beta equates to a weighted average of the Betas of the various methods
of financing, according to the importance of each source of finance in the capital structure.
Algebraically, this is given by:
Notice that the tax shield is reflected in applying the term to the debt compo-
nent. Notice also that, as the debt proportion increases, the equity Beta must increase to
preserve the constant asset Beta. It is usual to assume that the debt Beta is zero, although
there is some evidence that corporate debt has a very low Beta, around 0.1 to 0.2.
However, if we do assume a debt Beta of zero, this becomes a very versatile expres-
sion, e.g. when moving into a new activity we can take a firm’s equity Beta and ungear
it to reveal the underlying activity Beta. This is particularly useful when diversifying
into a new activity – we might borrow a Beta from another firm, whose gearing may
differ from our own. In this case, we might ungear the borrowed Beta to strip out that
firm’s financial risk, and then re-gear to incorporate our own firm’s gearing ratio.
To illustrate this, assume we have the following data:
Ungearing the other firm’s equity Beta, assuming the debt Beta is zero, we have:
1.35 60>88 0.92
Beta
A
Beta
E
a
V
S
V
S
V
B
11 T2
b 1.35 a
60
60 4011 T2
b
Own gearing ratio 10% 1debt>equity2
Tax rate
30%
1i.e. debt proportion 40 : 1002
Gearing ratio 1debt>equity2 of this firm 40%
Equity Beta of firm operating in new activity 1.35
11 T2
Beta
A
aBeta
E
V
S
V
S
V
B
11 T2
b aBeta
D
V
B
11 T2
V
S
V
B
11 T2
b
1Equity Beta proportion of equity2 1Debt Beta proportion of debt2
Beta of assets
19.7 LINKING THE BETAS
This corresponds to the result obtained more directly with the CAPM formula. The
two separate components of the geared Beta are shown in Figure 19.3. The increase in
the geared Beta as the debt/equity ratio increases drives up the additional required
premium pro rata.
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526 Part V Strategic financial decisions
Re-gearing to incorporate our own gearing, the equity Beta is given by:
Whence, equity Beta 0.92 107>100 0.98
0.92 Beta
E
100
100 1011 T2
Beta
E
100>107
19.8 MM WITH FINANCIAL DISTRESS
In Section 19.5, we saw how including corporate taxation in the MM model implied
that companies should rely on debt for nearly 100 per cent of their financing. This
implication is clearly at odds with observed practice – few companies gear up to
extreme levels, through fear of insolvency and its associated costs. MM’s omission of
liquidation costs from their analysis was a logical consequence of their perfect capital
market assumptions. In such a market, where investors are numerous and rational, and
have homogeneous expectations and plentiful access to information, the resale value of
assets, even those being sold in a liquidation, will reflect their true economic values.
Investors will recognise the worth of such assets as measured by the present values of
their future income flows, and be prepared to bid up to this value, so that the price
realised by a liquidator should not involve any discount.
In effect, liquidation costs and the other costs of financial distress introduce a new
imperfection into the analysis of capital structure decisions: namely the actual or
expected inability to realise ‘full value’ for assets in a distress sale and the costs of
actions taken to forestall this contingency.
Incorporating financial distress
Denoting the ‘costs of financial distress’ by FD, the value of a geared company becomes:
From this, we may conclude that the financial manager should attempt to maximise the
gap between tax benefits and financial distress costs, i.e. and that there exists an
optimal capital structure where company value is maximised. This occurs where the mar-
ginal benefit of further tax savings equals the marginal cost of anticipated financial
distress. This occurs with debt of in Figure 19.4.
The costs of financial distress rise with gearing once the market starts to perceive a
substantially increased risk of financial failure. The likelihood of FD being non-zero
depends on the probability distribution of the firm’s earnings profile. For example, in
the Lindley example in Chapter 18, for gearing ratios up to 50 per cent the probability
of inability to meet interest payments is zero, but it would be 0.25 for any higher gear-
ing ratio. For most companies, the probability, p, of financial distress will increase with
the book values of debt, B, so that the FD function increases with gearing. If d denotes
the expected percentage discount on the pre-liquidation value in the event of a forced
sale, the expected costs of financial distress are:
FD 1p d V
g
2
X
*
1TB FD2,
V
g
V
u
3TB FD4
costs of financial distress
The costs incurred as a firm
approaches, and ultimately
reaches, the point of insolvency
Self-assessment Activity 19.5
Ungear a Beta of 1.45 if:
■ Tax
rate 30%
■ The debt–equity ratio
1:2
(Answer in Appendix A at the back of the book)
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Chapter 19 Does capital structure really matter? 527
and the value of the geared firm is:
This suggests that market imperfections can be exploited to raise company value so
long as TB exceeds Notice that the inverted ‘U’-shaped value profile
now appears remarkably similar to the traditional version and, of course, is associated
with a mirror-image WACC schedule.
You may recall our earlier comment that, after introducing market imperfections such
as tax, the MM model begins to look more like the traditional version. With the inclusion
of financial distress costs, this resemblance is closer still. However, the discussion of the
impact of personal taxation in Appendix III shows that the debate is not yet dead.
1p d V
g
2.
V
g
V
u
1TB p d V
g
2
19.9 CALCULATING THE WACC
Before progressing, you may find it useful to reread Chapter 11, where we discussed the
hierarchy of discount rates and required rates of return, but deferred consideration of the
problems posed by mixed capital structures until Chapter 18.
The WACC is the overall required return needed to satisfy all stakeholders. It is also
the required return on the assumption that new projects are financed in exactly the
same way as existing ones. If the company is all-equity financed, then the WACC is
simply the return required by shareholders.
Gearing does not affect the underlying risk of the company’s business activities. If
a company uses debt capital, it is merely repackaging its operating income into differ-
ent proportions of debt interest and equity income, but not influencing the size or the
riskiness of this income before appropriation. What does change is the riskiness of the
stream of residual equity income, which is why the equity Beta rises, pulling up with
it the return required by shareholders.
We can explore this preposition with the case of Higear. The relevant figures for
Higear were:
Value of debt V
B
£1 m
Value of equity V
S
£2.80 m
Shareholders’ required return k
eg
22.5%
Interest cost of debt i 10%
Rate of corporate tax T 30%
FD
TB
X
*
0
V
u
Company value
V
g
=
V
u
+
[
TB
–
FD
]
V
g
=
V
u
+
TB
Book value of debt
Figure 19.4
Optimal gearing with
liquidation costs
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528 Part V Strategic financial decisions
The expression for the WACC in the MM case with corporate tax is:
Using the data for Higear, this expression yields:
Alternatively, we can obtain the same result by using the expression:
■ Relaxing critical assumptions
Two important questions now arise. First, what happens to the discount rate if a com-
pany diversifies into an activity with a risk profile different from existing operations?
Second, what happens if the gearing ratio is altered? The first issue is easier to handle.
Allowing for different risks
Imagine Higear proposes to diversify into a higher risk business. Because the discount
rate applicable to evaluating this project should reflect the systematic risk involved, the
required return previously calculated is no longer appropriate. To cope with this prob-
lem, the following procedure is suggested:
1 Select a company already operating in the target activity, ideally, one with operat-
ing characteristics very similar to those exhibited by the project, and identify its
Beta coefficient, e.g by using the RMS.
2 If the surrogate company’s gearing differs from that of Higear, the Beta must be
adjusted by removing the effect of the surrogate’s own gearing, and then super-
imposing Higear’s gearing on the resulting ungeared Beta.
3 Calculate the WACC incorporating the surrogate activity Beta, adjusted for
Higear’s own gearing.
Assume Higear plans to enter an activity already served by Semigear, whose equity
Beta is 1.8, and which has a debt/equity ratio of 1:2. Semigear’s Beta is ungeared as
follows:
The geared Beta applicable to Higear’s capital structure (i.e. million debt and
million equity) is:
1.33
31.254 1.663
1.33 c1
£1 m
£2.80 m
11 30% 2d
b
g
b
u
c1
V
B
V
S
11 T2d
£2.80£1
b
u
b
g
1
V
B
V
S
11 T2
1.8
1
1
2
11 30% 2
1.8
1.35
1.33
18.4%
20% 0.92
20% c1 30%
£1 m
£3.80 m
d
k
o
k
eu
c1 T
V
B
V
S
V
B
d
16.6% 1.8% 18.4%
122.5% 0.742 17% 0.262
k
o
a22.5%
£2.80 m
£2.80 m £1 m
b c10%11 30%2
£1 m
£2.80 m £1 m
d
k
o
ak
eg
V
S
V
S
V
B
b ci11 T2
V
B
V
S
V
B
d
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Chapter 19 Does capital structure really matter? 529
For this risk, and with a 9 per cent market risk premium, Higear’s shareholders require
a return of:
Finally, the WACC applicable to this activity risk and Higear’s own gearing is:
The second issue, the effect of a change in gearing, poses more of a conundrum.
Allowing for a change of gearing
In the Higear example, no change in gearing was envisaged when financing new projects.
However, as we have repeatedly warned, a significant change in gearing affects the
market values of both debt and equity capital: for example, shareholders may respond
adversely to higher gearing and the higher financial risk. Also, the value of debt may
be marked down in the market. To compute the WACC, we would have to assess the
new return required by shareholders, given by:
where
To value the equity, i.e. to derive a measure for we would need to apply the (per-
petuity) expression for valuing a stream of post-tax geared equity income:
We now encounter a circular problem, since the market value depends on and
to find we need to know the market value!
A possible solution is to work in terms of a ‘tailor-made’ WACC based on the pro-
ject’s characteristics (i.e. its systematic risk, allowing for any divergence from existing
operations) and on the project’s own financing. For example, imagine the project in the
previous example were to be financed 20 per cent by debt and 80 per cent by equity.
You should verify that with that shareholders would seek a
return of 24 per cent, and that the WACC is:
As it happens, use of the WACC in this situation may be inappropriate anyway,
since unless the firm is at, and adheres to, the target ratio, the WACC and the marginal
cost of capital (MCC) will diverge. If the firm is below the optimal capital structure,
the MCC is less than WACC, and the MCC exceeds the WACC when it overshoots the
optimal gearing ratio. We found, in Chapter 18, that when the firm departs from the
optimal gearing ratio, the appropriate required return is the MCC:
However, to calculate the MCC we again need to know the market values of both
equity and debt at the higher level of gearing, i.e. we encounter the circular problem
described earlier. It is clear that the WACC is suitable only for small-scale projects that
do not materially disturb the gearing ratio, and that the theoretically more correct
MCC is also problematic.
MCC
Change in total returns required by shareholders and lenders
Amount available to invest
124% 4>52 110% 31 T4 1>52 119.2% 1.4%2 20.6%
b
g
1.56,b
u
1.33,
k
eg
,
k
eg
,
V
S
1E iB211 T2
k
eg
V
S
,
b
u
the ungeared Beta coefficient
k
eu
R
f
b
u
1ER
m
R
f
2
k
eg
k
eu
1k
eu
i211 T2
V
B
V
S
R
f
b
g
1ER
m
R
f
2
k
eg
,
125.0% 0.742 110% 31 30% 4 0.262 18.5% 1.8% 20.3%
ER
j
R
f
b
g
3ER
m
R
f
4 10% 1.66339% 4 25%
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530 Part V Strategic financial decisions
An ‘off-the-cuff’ solution is to work in terms of book values. This pragmatic
approach has the merit of simplicity, as book values do not vary with gearing, and it
might be appropriate for unlisted firms, which by definition have no market values.
Nevertheless, it is desirable to work, whenever possible, in terms of market values,
given that most investors are more concerned with the current values of their invest-
ments, and the returns thereon, than with historic Balance Sheet values.
Fortunately, as we shall see in the next section, help is at hand.
19.10 THE ADJUSTED PRESENT VALUE METHOD (APV)
The adjusted present value (APV) of a project is simply the ‘essential’ worth of the proj-
ect, adjusted for any financing benefits (or costs) attributable to the particular method
of financing it. The rationale for the APV method was provided by Myers (1974), using
MM’s gearing model with corporate tax, but is valid only so long as the WACC profile
is declining due to the value of the tax shield. In Section 19.5, we saw that the value of
a geared firm, is the value of an equivalent all-equity-financed company, plus a
tax shield, TB, which is the discounted tax savings resulting from the tax-deductibility
of debt interest:
This can be translated from the value of a firm to the value of an individual project.
However, different projects can probably support different levels of debt. For example,
they may involve different inputs of easily resaleable fixed assets and may also have
different levels of operational gearing. As a result, it may be more appropriate to eval-
uate the effects of the financing of each project separately.
The APV is calculated in three steps:
Step 1 Evaluate the ‘base case’ NPV, discounting at the rate of return that sharehold-
ers would require if the project were financed wholly by equity. This rate is
derived by ungearing the company’s equity Beta.
Step 2 Evaluate separately the cash flows attributable to the financing decision,
discounting at the appropriate risk-adjusted rate.
Step 3 Add the present values derived from the two previous stages to obtain the
APV. The project is acceptable if the APV is greater than zero.
A simple example will illustrate the use of the APV.
■ Using the APV: Rigton plc
Rigton plc has a gearing ratio, measured by debt/equity at market values, of 20 per
cent. The equity Beta is 1.30. The risk-free rate is 10 per cent and a return of 16 per
cent is expected from the market portfolio. The rate of corporate tax is 30 per cent.
Rigton proposes to undertake a project requiring an outlay of million, financed
partly by equity and partly by debt. The project, a perpetuity, is thought to be able to
support borrowings of million at an interest rate of 12 per cent, thus imposing
interest charges of £0.36 million. It is expected to generate pre-tax cash flows of £2.3
million p.a.
Using the formula developed earlier for the ungeared Beta:
b
u
b
g
c1
V
B
V
S
11 T2d
1.30
1 0.2011 0.302
1.30
1.14
1.14
£3
£10
V
g
V
u
TB
V
g
,V
g
,
adjusted present value
The inherent value of a project
adjusted for any financial ben-
efits and costs stemming from
the particular method(s) of
financing
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Chapter 19 Does capital structure really matter? 531
This yields a required return on ungeared equity of:
The base case NPV is:
The present value of the tax savings, i.e. the tax shield, TB, is given by:
The adjusted present value is thus:
and the project appears worthwhile. The significance of this result is that, although the
base case NPV is negative, the project is rescued by the tax shield of million. An
essentially unattractive project is rendered worthwhile by the taxation system.
In the Rigton example, the project creates wealth only for Rigton’s shareholders.
From the perspective of the overall economy, it is wealth-reducing and, unless there
are compelling ‘social’ reasons to justify it, should not be undertaken. This sort of rea-
soning led the UK government in 1984 to reduce the rate of Corporation Tax in order
to lower the tax advantage of debt financing, and hence reduce the extent to which
investment decisions were likely to be distorted by the system of tax breaks.
£0.90
APV £0.42 m £0.90 m £0.48 m
TiB
i
10.30210.1221£3 m2
0.12
10.3021£0.36 m2
0.12
£0.108 m
0.12
£0.9 m
£0.42 m
£10 m £9.58 m
NPV £10 m
£2.3 m11 0.302
0.168
£10 m
£1.61 m
0.168
0.168,
i.e. 16.8%
ER
j
R
f
b
u
1ER
m
R
f
2 0.10 1.14 10.16 0.102 10.10 0.0682
Self-assessment activity 19.6
What is the APV and how is it calculated?
(Answer in Appendix A at the back of the book)
■ Further aspects
Before leaving the APV, several related issues are worth examining.
1 The APV in practice is affected by the terms and conditions of a pre-arranged sched-
ule for debt interest and capital repayment. Sometimes, the calculations can be
exceptionally tedious. Rather than using the convenient assumption of perpetual
debt financing, let us assume that the debt plus interest must be repaid over
two years, with interest and two equal capital payments occurring at end-year.
Table 19.2 shows the repayment schedule and the resulting tax savings.
With no tax delay assumed, the present value of the tax savings is:
£0.108 m
11.122
£0.054 m
11.122
2
1£0.096 m £0.043 m2 £0.139 m
Table 19.2
The tax shield with
finite-life debt
Balance of Balance of
loan at start Interest loan at end
of year at 12% Tax saving 30%) Repayment of year
0
£1.5 m
130% £0.18 m2 £0.054 m
£0.18 m£1.5 m
£1.5 m£1.5 m
130% £0.36 m2 £0.108 m
£0.36 m£3.0 m
1T
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532 Part V Strategic financial decisions
Obviously, the value of the tax shield is much lower with the shorter payment profile.
2 Although our example focused on the side-effects of debt financing, the APV rou-
tine can be easily applied to any other financing costs and benefits, many of which
are awkward to handle with the simple WACC. For example, if equity capital is
externally raised, normally there are various issuing and underwriting costs to bear.
Including these would alter the APV formula as follows:
A similar treatment would be applied to subsidised borrowing costs, investment
grants and tax savings from exploiting investment allowances.
3 Tax savings are not certain because they depend on the inherent profitability of the
company. As this is a random variable, the company’s ability to set off interest pay-
ments (and other tax reliefs) against income is also random. Our examples assume
continuous profitability, but if there are periods during which the company is
expected to be tax-exhausted, this should be allowed for in the computation of the
APV. If the future pattern of liability to tax is uncertain, then it is not appropriate to
use a risk-free rate to discount the tax savings.
4 Finally, we have glossed over the issues that impact on the debt-supporting capac-
ity of particular projects. In principle, the debt capacity of a project is given by the
present value of future expected earnings from the firm as a whole, taking into
account any existing borrowings. It might seem obvious that more profitable com-
panies are able to borrow relatively more than unprofitable companies. However,
this assumes that there are no costs of financial distress. Enhanced borrowing abil-
ity for more profitable companies is not universal, since a would-be lender would
still look at the break-up value of the enterprise. In the final analysis, the crucial fac-
tor which governs debt capacity is how much can be raised by a distress sale of
assets.
APV Base case NPV Tax shield PV of issue costs
Self-assessment activity 19.7
How would you identify the point beyond which a firm would be unable to borrow?
(Answer in Appendix A at the back of the book)
19.11 WHICH DISCOUNT RATE SHOULD WE USE?
Specifying the correct discount rate to use when a new project involves financing and
other differences from parent company activities is something of a puzzle. Now that we
have examined the main variations on the discount rate theme, this check-list should help.
If the new project has a:
Case 1 Similar business risk and capital structure as the parent company.
Use the parent’s WACC.
Case 2 Higher/lower business risk than the parent but similar financing mix.
Adjust the Beta, using a surrogate firm’s Beta as a basis but adjust for relative
gearing, i.e. ungear the surrogate Beta and gear up the residual equity Beta.
Then use the parent’s capital structure weights to calculate the WACC.
Case 3 Similar business risk, but capital structure different from that of the parent.
Use the parent’s equity Beta, gear it for the project financing mix and then
use the project’s financing mix to find the project WACC.
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Chapter 19 Does capital structure really matter? 533
SUMMARY
Chapters 18 and 19 have covered extensive ground, attempting to isolate the critical
variables relating company value to capital structure. In this process, we have moved
from the somewhat crude ‘traditional’ version to the pure and less pure MM analyses,
before arriving at the model displayed in Figure 19.4. This closely resembles the tradi-
tional theory itself, with its U-shaped cost of capital schedule and optimal capital
structure. We have established that the benefits of debt stem mainly from market imperfec-
tions, especially the tax relief on debt interest, but that a different type of imperfection, distress
costs, can offset these tax breaks at higher levels of gearing. In addition, even the tax bene-
fits of gearing may be overstated as they depend on the particular mix of personal and
corporate tax rates faced by the company and its stakeholders (see Appendix III).
So in response to the question posed at the start of the chapter, ‘Does capital struc-
ture matter?’ the answer seems to be ‘yes’, but in a number of complex ways. Debt, or
rather, excessive debt, certainly matters to the owners but it may not destroy value.
Distressed, but operationally viable, companies can still survive. For non-distressed
companies, debt can offer significant tax advantages.
Key points
■ MM argue that, as the method of financing a company does not affect its funda-
mental wealth-creating capacity, the use of debt capital, under perfect market con-
ditions, has no effect on company value.
■ Shareholders respond to an increase in the likely variability of earnings, i.e. finan-
cial risk, by seeking higher returns to offset exactly the apparent benefits of ‘cheap’
debt.
■ The appropriate cut-off rate for new investment is the rate of return required by
shareholders in an equivalent ungeared company.
■ When corporate taxation is introduced, the tax deductibility of debt interest creates
value for shareholders via the tax shield, but this is a wealth transfer from
taxpayers.
■ The value of a geared company equals the value of an equivalent ungeared com-
pany plus the tax shield:
■ With corporate taxation, the rate of return required by the geared company’s share-
holders is less than that in the all-equity company, reflecting the tax benefits.
■ A further effect of corporation taxation is to lower the overall cost of capital, which
appears to fall continuously as gearing increases.
■ However, this result relies on the absence of default risk and the consequent costs of
financial distress incurred as a company reaches or approaches the point of insolvency.
■ For geared companies, the required return can be derived by combining with the
after-tax debt cost to obtain the WACC.
Continued
k
e
V
g
V
u
TB
Case 4 Higher/lower business risk, and a different capital structure.
Use the project Beta, and, as in Case 2, gear it for the project financing, and
calculate the WACC using the project financing mix.
Case 5 Complex mixture of risk, financial structure, and side effects. Use the APV method.
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534 Part V Strategic financial decisions
■ However, the WACC is acceptable only under restrictive conditions: in particular,
when project financing replicates existing gearing, and when project risk is identi-
cal to that of existing activities.
■ To resolve the problems of the WACC, the adjusted present value can be used. This
is the ‘basic’ worth of the project, i.e. the NPV assuming all-equity financing,
adjusted for any financing benefits such as tax savings on debt interest, or costs
such as issue expenses.
■ Eventually, the costs of financial distress may begin to outweigh the benefits of the
tax shield. A major cost of financial distress is the inability to achieve ‘full market
value’ in a ‘distress sale’.
■ There is, in theory, an optimal capital structure where the marginal benefit of tax
savings equals the marginal cost of financial distress.
■ In reality, while companies should balance the benefits of the tax shield against the
likelihood of financial stress costs, most finance directors will restrain gearing lev-
els, especially as tax savings are uncertain, depending on fluctuations in corporate
earnings.
Further reading
Look at the original articles by Modigliani and Miller (1958, 1963). Other important articles are
those by Myers (1974, 1984), which analyse the interactions between financing and investment
decisions, and Miller’s attempt to resurrect the capital structure irrelevance thesis (1977) and his
subsequent Nobel lecture (1991). As ever, Copeland and Weston (2004) offer a more rigorous,
mathematical development. A resumé of current thinking on capital structure theory can be
found in Barclay et al. (1995). Luehrman (1997a,b) offers two articles on the present state of val-
uation theory and analysis, with strong emphasis on APV, and also on strategic options.
APPENDIX I
DERIVATION OF MM’S PROPOSITION II
Given that:
and
we may write
Substituting for E,
k
e
k
o
1V
S
V
B
2 iB
V
S
k
o
V
S
k
o
V
B
iB
V
S
k
o
1k
o
i2
V
B
V
S
E k
o
V
o
k
o
1V
S
V
B
2
k
e
1E iB2
V
S
E
V
S
V
B
E
V
o
k
o
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