Professor Kose John
March 2003
NOTES ON CAPITAL STRUCTURE
These notes are meant to supplement Chapters 17 and 18 and part of Chapter 19
of our text book, Brealey and Myers, Seventh Edition. All references are to pages in our
textbook.
In the areas of financing decisions for a corporation there are many unresolved
issues and active debates in the field. Even in a basic course it is hard to avoid them. So
it is very important to examine the area in a systematic order of difficulty.
I.
I.
Perfect Capital Markets - No Taxes
II.
Introduce Corporate Taxes
III.
Frictional Costs of Bankruptcy
IV.
Capital Structure with Corporate Taxes
Perfect Capital Markets/No Taxes:
The main results in this section are the famous MM theorems derived under
assumptions of perfect capital markets and a tax-free economy (see section 17-1). Their
Proposition I states that a firm cannot change the total value of its securities just by
splitting its cash flows into different streams: the firm's value is determined by its real
assets not by the securities it issues. Thus capital structure is irrelevant as long as the
firm's investment decisions are taken as given. A simple proof is given on pgs. 467-468.
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Some key points to note: given an asset or a set of assets, which constitute the
firm, the required rate of return rA from the asset is not affected by borrowing decisions
of the firm. Its expected return (= required return) is determined by A the beta of the
assets via the security market line.
The required return on equity can be determined from the following equations
 D 
 E 
(1) rA  
rD  
rE
DE
DE
(2) rE  rA 
D
rA  rD 
E
The above equation summarizes Proposition II of MM (see pg. 473 of BM).
Again given the asset of the firm A the beta of the assets is not affected by the
borrowing decisions but E the beta of equity will be, according to:
 D 


D E
(3)
A =
(4)
E =  A +
D
 E 
 

D E
D
  
E
A
D
E

This clarifies why the investors require higher returns on levered equity.
It is important to note that rA is the required rate of return on the assets - the cost
of capital of the firm, and it is determined by A , the beta of the assets. These
considerations would apply to any new project (asset) being considered by the firm.
Example 1
The total market value of the common stock of the MM Glass Co. is $60 million,
and the total value of its debt is $40million. The treasurer estimates that the beta of the
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stock is currently 1.5. Also given RF = 0.08 and rM = 0.18. Assume (1) no taxes, (2) D
= 0.
(a) What is the beta of the company's existing portfolio of assets? What is the required
rate of return on the common stock of MM?
A =
60
40
60
1.5  0.9
 E   D  
100
60
100
rE = 0.08 + 1.5(0.18 - 0.08) = 0.23
(b) The company is considering a project which is just an expansion of the company's
present business. What discount rate should they use for computing the NPV of the
project?
rA = 0.08 + 0.9(0.10)
= 0.17
(c) Suppose the company repays 20 million of debt and replaces it with equity. What
would be the beta of its common stock? What would be the beta of its assets? What
would be the new market value of the firm?.
A stay at 0.9
0.9 =
20
0  80  E 
100
100
E 
90
 1.125
80
V = 100 million, same as before
II.
Introduce Corporate Taxes
When we introduce corporate taxes into the scenario the MM position changes:
the interest that the company pays is a tax-deductible expense. The tax-corrected version
of MM's proposition I has that:
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Value of firm = Value if all equity financed + PV tax shield
(5)
VL = VU + tD
as shown in section 18-1, pg. 489. As an implication, if an asset (or a combination of
assets) supports a certain fraction of its value, say
D
, of debt capacity then the total
V
returns from those assets do not have to be rA (as in equation (1)), it can be something
less than rA. The MM formula for the required rate of return on the asset (under some
restrictive assumptions) is
(6)
D

r* = rA 1  t 
V

where rA is the required rate of return (determined based on A of the project) as if it was
all equity financed,
D
is the contribution of the project to the debt capacity (of the firm)
V
as a proportion of the project's present value. If the new projects are financed with the
same leverage as the firm as a whole the firm's leverage ratio might be used for
D
.
V
r* can be called the adjusted cost of capital.
Example 2
Consider the following project:
t =0
- 1 million
t=1
90,000
t=2
t=3. . .
90,000
90,000
The expected inflows are after-tax. The borrowing rate is 7% and the marginal
tax rate is 46%, the project is financed by 40% debt and it expands the firm's borrowing
power by 40% of the project's book value, i.e., by 400,000. If the project were all-equity-
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financed its required rate of return would have been 0.10. Should the project be
accepted?
r* = 0.1 [(1 - 0.46 (0.40) ] = 0.0816
rA = 0.10
t = 0.46
D/V  0.40
NPV  - lm 
90,000
 102,941  0
.0816
The decision should be to accept the project. It is easy to see that such a project would
not have been acceptable without considering the contribution it makes to the debt
capacity of the levered firm. In other words the value of the tax shields influences
decision about the project.
The other popular formula for calculating the adjusted cost of capital r* is called
the weighted average cost of capital (it is also used heavily in basic text books).
(7 )
r *  rD 1 - t 
D
E
 rE
V
V
Thus, if the appropriate required rates of return on debt and equity are known equation
(7) might yield the adjusted cost of capital. Practitioners often use a similar method. It is
called the (after-tax) weighted average cost of capital.(WACC). See section 19.1 and 19.2
of the textbook, pg.524-532.
Discounting the base case cash flows with the WACC directly gives the Adjusted Present
Value (APV): see section 19.4 of the textbook.
III.
Frictional Costs of Bankruptcy
Now we add into our scenario some possible imperfections such as costs
associated with bankruptcy and financial distress. These costs are assumed to play a
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significant role when the leverage ratio is very high. An analysis of the possible effect of
such frictional costs is given in Section 18-3, pgs. 497-510. The basic conclusion is that
the monotonic increase of firm value with leverage might not hold and interior "optimal"
capital structures might exist, where the marginal value of tax shields is off-set by the
marginal increase in bankruptcy costs. This is called the trade-off theory of capital
structure.
IV.
Capital Structure with Corporate and Personal Taxes
These notes supplement Chapter 18 of the textbook, especially sections 18-1 and
18-2.
The central idea in section 18-1 is that corporate tax deductibility of debt is a
source of value and the levered firm value is higher due to the present value of tax shield
from debt, pg 490-493. In section 18-2, the consequences of personal taxes are also
brought in. The point here is that the market value of corporate claims (i.e., the value of
the firm) is determined by the cash flows from the firm which end up in the market net of
all taxes, corporate and personal. In other words, the preferential treatment of payments
to debt holders by the taxing authority at corporate level may be partially (or completely)
offset by the adverse treatment of bond income for personal taxation. This trade-off is
illustrated in Figure 18-1, pg. 495. .
Now it is clear that the net advantage to corporate borrowing will depend on the
structure of taxation (in terms of its treatment of debt and equity at corporate and
personal levels) and the market equilibrium for corporate securities.
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1.With corporate taxation:
If debt and equity income are taxed at the same personal rate, then the corporatelevel advantage to debt persists and the value of the levered firm exceeds that of the
unlevered firm by TCD, the present value of tax shields. (see section 18.1 of text). This
corresponds with our conclusion when we ignored personal taxation.
2. Effect of personal taxes:
As presented in section 18.2 of text, Miller focuses on the case where all equity
income comes as unrealized capital gains. Thus there is no personal tax on equity
income, but bond income is taxed at a rate depending on the investor's tax
bracket. Miller shows that, in equilibrium, tax deductibility at corporate level is
exactly offset by the personal taxation at the investor level. There is no advantage
to corporate borrowing from the point of view of its shareholders.
3. A Compromise Theory:
Tax Shields other than those from debt are considered along with uncertain
income in a compromise theory by DeAngelo and Masulis (Journal of Financial
Economics, March 1980). Here the expected corporate tax shield may be decreasing with
incremental amounts of debt borrowed. The resulting equilibrium is such that there is
some tax advantage to borrowing. Its value to the firm, say T*D, is lower than that in the
MM (Tax-Corrected) regime; i.e., 0 < T* < TC.
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