Capital Structure and Taxes
1.
One of first and most fundamental theories of modern
finance was developed by Modigliani and Miller [1958]
(hereafter MM). We will focus on the meat of the theory
and its implications.
2.
Although the theory still provides the underpinnings for
basic capital structure theory in finance, many important
issues of capital structure are still largely unresolved.
3.
An important contribution of their work is their method of
analysis. They were one of the first to prove their results
based upon no arbitrage conditions.
4.
The no arbitrage condition allowed many preference-free
theories to be developed, such as the options pricing
theory. Arbitrage-based theories are very general without
having to specify full general equilibrium results that were
common in economics previously.
5.
Finance can be crudely separated into Investments and
Corporate Finance. Many of the topics we have covered
up to this point are associated with Investments and
more specific to asset pricing.
6.
Professor Hegde will be covering mostly Corporate
Finance issues in the next class. Although many of the
topics he will cover relate to the issues we covered, he
will focus more on their implications for finance practices
within a corporation.
7.
I will be presenting one of the basic theories of Corporate
Finance to start you thinking. He will show you how
relaxing many of the assumptions of MM leads to the
new theories of Corporate Finance.
Simple Illustration of MM
Theory
1.
Before we look at the theory in mathematical form, the
basis of the theory can be illustrated simply with the
figure below.
2. REMEMBER: The value of the firm is the discounted
present value of it’s after-tax cash flows going to
bondholders and stockholders.
3. Two basic cases.
A. Without Income Taxes - income goes to
1. stockholders
2. bondholders
B. With Income Taxes - income goes to
1. stockholders
2. bondholders
3. government.
In the second case, because interest paid on debt is tax
deductible we can reduce the amount going to the
government (and increase the amount going to bondholders
and stockholders) by increasing the amount of debt in the
capital structure. This should increase the value of the
bondholders and stockholders claims.
Initial Capital
Structure
Increase Debt
Financing
S
S
B
G
B
G
S is the portion of EBIT paid to Stockholders
B is the portion of EBIT paid to Bondholders
G is the portion of EBIT paid to Government
4. The initial paper by MM simply showed that the total value
of the firm is the size of the pie. Changing the capital structure
may change the size of the slice that goes to any group of
claimants to the pie, but the size of the pie remains fixed given
some simplifying assumptions.
When there are no taxes and transactions costs, there is no
way for a company to increase the value of a share or a bond
by changing the capital structure. If there were, then an
arbitrage would be possible.
5. MM won a Nobel prize for this work. One can argue that
Coase (1960) won a Nobel prize for the same idea, but from
a different perspective. He showed that in the absence of
contracting costs and wealth effects, the assignment of
property rights leaves the use of real resources unaffected.
In other words, under the usual simplifying assumptions,
assets will be allocated to their profit-maximizing use no
matter who owns them.
This shows how a clear understanding of the relatively few
principals of economics (finance) can help you to understand
many economic or financial problems.
Modigliani and Miller’s Initial
Assumptions
1.
Capital markets are frictionless – no transactions costs.
2.
Everyone can borrow and lend at the riskless rate.
3.
No bankruptcy costs.
4.
Firms issue only riskless debt or risky equity.
5.
All firms have the same risk.
6.
Only corporate taxes may exist.
7.
All cash flows are perpetuities.
8.
Corporate insiders and outsiders have the same
information.
9.
Managers maximize shareholder wealth.
1. With all cash flows perpetuities, the all-equity firm’s value is
Vu = E(FCF)/
Where Vu = present value of the unlevered firm
E(FCF) = expected value of the firm’s free cash flow in
each period forever into the future.
 = required return for an all equity firm given its risk.
2. The definition of FCF
FCF = (REV – VC – FCC – dep)(1 – tc) + dep – I
Where REV = revenue, VC = variable costs, FCC = fixed cash
costs such as administration costs, dep = depreciation and I =
investment.
Since we assume no growth, then dep = I so
FCF = (REV – VC – FCC – dep)(1 – tc) = (NOI )(1 – tc)
Under these assumptions, FCF ends up to be the same as net
operating income after tax, which is also the cash flow the firm
would have available if it had no debt. Therefore, firm value is
Vu = E(NOI)(1 – tc)/
3. Maintain the same assumptions but assume that the firm
has debt = D on which it pays interest of kdD (kd is the coupon
rate and D is the face value). The FCF is now split between
interest payments to bondholders and net income (NI) to the
equityholders. The only change to FCF is that interest
payments provide a tax shield so that the total FCF increases
by kdDtc,which is the reduction in taxes paid to the
government simply because we have added bondholders.
FCF = (NOI )(1 – tc) + kdDtc
4. Assuming that the tax shield is a risk free cash flow, we can
discount the tax shield using the before-tax risk free rate of kb,
so that the value of the levered firm VL is,
VL = E(NOI)(1 – tc)/ + kdDtc/kb
Since the debt is a perpetual bond, its market value is
B = kdD/kb so that
VL = E(NOI)(1 – tc)/ + Btc
It is clear that if there is no corporate tax (tc = 0), then the
value of the firm will be unaffected by changes in the capital
structure. This can be seen easily in,
VL = Vu + Btc
Furthermore, to maximize the levered firm value, the firm
should increase the amount of debt as much as possible.
Btc is the present value of the tax shield, sometimes called the
“gain from leverage”.
MM’s Original Arbitrage
Argument
1.
Assume there are no taxes, then MM proved that there is
no optimal capital structure. That is, firm value and equity
value are unaffected by leverage.
2.
To see this, assume that a levered firm and an unlevered
firm are identical (same NOI) except that the levered firm
has debt. Consider three portfolios.
A.
Buy the fraction  of the equity Eu of the unlevered firm.
B.
Buy the fraction  of the equity EL of the levered firm.
Buy the fraction  of the debt D of the levered firm.
C.
Buy the fraction  of the equity Eu of the unlevered firm.
Borrow the amount D at the risk-free rate.
Portfolio Action
Investment
__
Payoff
________________
A
Buy Unlevered Equity
Eu
NOI
B
Buy Levered Equity
Buy Debt
EL
D
(NOI – kdD)
(kdD)
Totals
C
Buy Unlevered Equity
Borrow at risk free rate
Totals
EL + D
NOI
Eu
-D
NOI
-(kdD)
Eu - D
NOI -(kdD)
3. Compare portfolios A and B. Since Vu = Eu and VL = EL + D
we see that each portfolio claims the fraction  in their
respective firms. They receive the same payoff, NOI.
By arbitrage, if the payoffs of the two portfolios is the same
then the investment should also be the same, therefore,
Vu = Eu = VL = EL + D
4. A second way to prove this is with portfolio C. This is called
“homemade leverage” where the investor can produce his
own leverage. This means that if anyone can do it, it can’t
produce much value. Compare C’s total payoff to that of the
levered equity in portfolio B. They are the same payoffs so the
investments must be the same. If investment in portfolio C
was less than the cost of the levered equity, investors would
buy the unlevered equity and borrow until it forced the stock
price up and the two investments were equal. Therefore, we
must have
EL = Eu - D
So rearranging equating to firm values gives
EL + D = VL = Eu = Vu
Weighted Cost of Capital
1.
To get the cost of capital for a levered firms, we can
consider the change in company value due to the
change in investment as follows:
VL = E(NOI) (1 – tc) + B tc = 1
I
I

I
We set this equal to one because at the margin, an additional
$1 in investment increases the company’s value by $1
since for the marginal investment NPV = 0. That is,
VL = I . From this we get
(1 – tc)E(NOI) = ( 1 - tc[B/I]) = ( 1 - tc[B/VL])
I
The first term is the after-tax change in net operating cash
flows due to the investment – the after-tax return on the
project. The next two terms are the opportunity cost of
capital for the project. Therefore, the weighted average
cost of capital (WACC) is
WACC = ( 1 – tc[B/VL])
We can see that if there is no tax, then the cost of capital is
fixed no matter what the capital structure. If there is tax,
then the cost of capital decreases as we add more debt
to the capital structure.
This equation defines the cost of capital relative to the allequity cost of . With taxes, the debt tax shield reduces
the average cost, and a higher tax rate means a lower
capital cost, as the government subsidizes investment.
The Traditional Definition of
WACC
1.
To get the traditional WACC from the definition above,
we assume, like MM, that [B/I] = [B/VL] = [B/ VL].
This just means that the marginal use of debt to finance
new investments equals the average use of debt in the
capital structure.
We have already assumed that debt pays the risk-free
return and since VL = EL + B, then
cost of debt = (1 – tc)kb[B/(EL + B)]
with
WACC = ( 1 – tc[B/VL]) =  -  tc[B/(EL + B)]
Add and subtract the cost of debt from RHS to get
WACC = (1 – tc)kb[B/(EL + B)] +  -  tc[B/(EL + B)]
- (1 – tc)kb[B/(EL + B)]
Now combine the last 3 terms and note that [B/(EL + B)] =
[B/EL] [EL/(EL + B)]
 EL
 B EL 
 B EL 
B
B EL 
WACC  (1  tc )kb L
 
 L
 tc  L
 (1  tc )kb  L
L
L
L
E B
E B  E L 
B  E
E B  E 
E B  E 
WACC  (1  tc )kb
B
B 
B
B  E L 
 


1



t

(
1

t
)
k


c
c
b
E L  B   E L 
EL
E L   B  E L 
B
B  E L 

WACC  (1  tc )kb L
    (1  tc )(   kb ) L  
E B 
E   B  E L 
Now we have the WACC in the traditional form where the
weights are the proportions of debt and equity in the capital
structure. This means that the required rate of return for equity
for a leveraged firm is
KE =  + (1 – tc)( - kb)[B/EL]
Here we see that the required return decreases with an
increase in the tax rate and increases with an increase in debt
relative to equity.
Now we can combine the cost of debt and equity to get:
 EL 
B
WACC  (1  tc )kb L
 kE 
L
E B
B

E


1.
The graphs above illustrate how the cost of equity and the
WACC changes with leverage.
2.
Graph (a) shows that with no taxes the WACC stays
constant because the cost of equity rises to exactly offset
the lower cost of debt as more debt is added to the capital
structure.
3.
Graph (b) shows that with taxes, the cost of equity rises but
not as steeply as when there are no taxes. Therefore, as
cheap debt is added to the capital structure, the WACC falls.
Traditional Theory of Cost of
Capital
Ke
Cost of
Capital
Kavg
minimum
Kd
optimal
Debt to Equity Ratio
1.
The traditional theory of WACC had little rigorous theory to
support it. It was assumed that as one added cheap debt to the
capital structure, WACC would fall.
2.
But at some point, it was assumed that the probability of
bankruptcy would rise so high that the WACC would increase as
lenders and stockholders required higher returns.
Two Capital Structure Theories of Leverage
a. Traditional - Share Price will Increase with
Leverage up to a Point (Too Much Risk)
b. Net Operating Income Theory (MM) - Any
Increase in Leverage and EPS will be Offset by
Increased Risk (Assuming No Taxes)
Leaving the Share Price Unchanged.
Illustration using the constant growth model.
P = D1/ (kE - g)
Increasing leverage may increase D1 and g but
will increase beta (risk) so that kE will increase.
Theoretically, P stays the same because the
positive effect of the increase in D1 and g is just
offset by the negative effect of the kE increase.
MM With Personal Taxes as
Well as Corporate Taxes
1.
Miller (1977) shows how personal taxes on stock income
of ts and on bond income tb can change the effects of
leverage on the WACC. The value of the unlevered firm
will be
Vu = E(NOI)(1 – tc)(1 – ts)/
Here, the numerator is now the shareholder income after
corporate and personal income taxes. For the levered
firm we have
VL = E(NOI)(1 – tc)(1 – ts)/ + kdD[(1 – tb) - (1 – tc)(1 – ts)]/kb
Since B = kdD(1 – tb)/kb then
VL = Vu + [1 - (1 – tc)(1 – ts)/(1 – tb)]B
Now the gain from leverage is likely to be smaller because we
typically have a smaller tax rate on stock income than
bond income, i.e., ts < tb. If ts = tb then we have the same
formula as without personal taxes.
If (1 – tc)(1 – ts) = (1 – tb), then there is no gain from debt, the
positive effect of corporate tax deductibility is offset by
the large personal tax on bond income.
When this occurs, the tax rate on bonds is so large relative to
stocks that bondholders demand a very large before-tax
rate of return. This forces interest payments up enough
so that even after corporations deduct the interest, it is
cheaper to use equity than debt.
Example: SI Inc. is an all-equity firm that generates EBIT of
$3 million per year. Its cost of equity capital is 16
percent, its marginal corporate tax rate is 35
percent, and it has 1 million shares outstanding.
a What is SI’s market value?
b. If SI issues $4 million of debt and uses it to buy
back some shares, what will be its new market
value and new equity value?
c. Show that the change in per-share value goes
up even though total equity decreases.
a. Vu = $3,000,000(1 - .35) / .16 = $12,187,500
b. VL = $12,187,500 + (.35)($4,000,000)=$13,587,500
equity = $13,587,500 - $4,000,000 = $9,587,500
c. Before buyback, share price= $12,187,500/1,000,000
= 12.187
After buyback of $4,000,000/12.187 = 328,218 shares
we get a new price of
P =$9,587,500/(1,000,000 - 328,218) = 14.27
Synthesis of MM and CAPM
1.
MM assumed that all firms had the same risk. One way
to relax this assumption is to combine MM and the
CAPM. The CAPM defines required returns for assets
with different risks. Both MM and the CAPM give us a
definition for the cost of equity capital. We can merge
these definitions and gain some insights.
For a leveraged firm we have
KE =  + (1 – tc)( - kb)[B/EL] = Rf + [E(Rm) – Rf]L
Now substitute for kb = Rf and  = Rf + [E(Rm) – Rf]u and
rearrange to get
L = [1 + (1 – tc)(B/EL)] u
The value of this expression is that if we know the levered
beta we can get the unlevered beta or vise versa. We
can also see that the levered beta decreases with the tax
rate and increases with the debt level.
NOTE: It is usually assumed that there is an optimal capital
structure so that (B/EL) is the same for all projects. Then,
the decision to invest in a project is only dependent on its
risk and potential cash flows. But if a project is special
because it can be financed with greater debt capacity
than alternative projects, then the investment decision
will affect the capital structure, which in turn, affects the
risk of the project and its required return.
1.
MM and the follow-on papers show that many financial
practices, and capital structure manipulation in particular,
are unlikely to increase firm value.
2.
In order to show that a practice has value, one must
show either that it increases net cash flows to
shareholders or decreases firm risk or both and that
investors cannot perform the manipulation on their own.
3.
In the 1960’s, many conglomerate mergers were
conducted because it was believed that the net risk of
the combined firms would fall. By the 1980’s, many
mergers proved to be bad for shareholders. First,
investors could always combine firm shares on their own
to achieve diversification. Second, the combined firms
often were inefficient because management could not
run two business well at the same time. Recently,
researchers are reconsidering when mergers are
valuable and when they are not.
4.
The use of derivatives to manage a firm’s risk is another
case in point. Should corporate managers be using
futures, options and swaps to hedge risk or add risk?
The argument against says that corporate managers
should concentrate on running their businesses – they
will reduce value by trying to use derivatives they are not
expert in. The argument in favor says that corporate
managers should know which risks they are expert in
and which risks it is best to let others bear. The firm
should only keep risks for which it thinks it can earn an
acceptable return.
Possible Reasons for
Different Capital Structures
1.
Bankruptcy costs may be substantial, including legal
costs, lost real options, lost customer relations, and
bondholder-stockholder conflict costs.
2.
Transactions costs may be substantial, including large
homemade leverage costs for shareholders, margin
expenses and shortsale restrictions.
3.
Investors may face a different tax rate than corporations
and different levels of progression.
4.
Imperfect information may make it difficult for
shareholders to undo company leverage or properly
monitor firm managers. Capital structure may be used as
an incentive tool for managers to work hard – more debt
– more pressure on management to produce good
returns or else face bankruptcy and being fired.
Implies – add a slice to the earlier pie chart where
the slice goes to management or covers management
inefficiencies – then argue that more debt reduces this
slice, giving more to bondholders and stockholder.
But it seems that this could be handled with
incentive compensation and monitoring instead of taking
on more debt and, therefore, bankruptcy risk.
Steven Ross, The Determinants
of Financial Structure: The
Incentive Signal Approach, (Bell
Journal of Economics, 1977)
Separating Equilibrium: A signaling mechanism arises
naturally in the market to signal information to market
participants which allows them to “separate” or determine
which firms have good future prospects and which don’t.
Ross suggests that MM’s assumption that all market
participants know what future firm cash flows will be is wrong.
Asymmetric information - managers know more than
investors.
Assume managers can’t trade their own stock.
Managers can use the firm’s capital structure to signal.
Manager compensation (M) is,
V1

M   0V0 (1  r )   1 
V1  C

if
if
V1  D 


V1  D 

Where 0 and 1 are positive constants
r is the one period interest rate
V0=V1/(1+r) and V1 are the current and future firm values
D is the face value of firm debt
C is a penalty paid if bankruptcy occurs (V1 < D)
Assumptions
1. There are two types of firms, a successful type A and an
unsuccessful type B, and the value of type A greater than the
value of type B. Va > Vb
2. D* is the maximum amount of debt that an unsuccessful
firm can carry without going bankrupt.
3. D > (<) D* means management signals it is type A (B).
For a signaling equilibrium, management compensation must
be such that managers of type A firms and type B firms make
more if they truthfully signal their firm’s type.
For type A and then type B, the manager compensation is
 0V1a   1V1a

Ma  
 0V1b   1V1a

 0V1a   1 (V1b  C )

Mb  
 0V1b   1V1b

if
D*  D  V1a
(Tell
if
D  D*
( Lie)
if
if
D*  D  V1a
D  D*
the
truth)




( Lie)
(Tell
the



truth)

Results of model – similar to
many other signaling
results, e.g. dividends etc.
1. Clearly, managers of firms of type A will tell the truth by
choosing D > D* because they earn more compensation if
they do because Vb < Va.
2. Managers of type B firms don’t necessarily have the same
incentives. Compensation must be set such that they earn
more by correctly choosing D < D* to signal that they are type
B. This is true when
 0V1a   1 (V1b  C)   0V1b   1V1b
Or
 0 (V1a  V1b )   1C
This condition says that the management compensation gain
from lying must be less than the management compensation
loss. The LHS is the management share of gain from initially
fooling the market that it is a type A when it is really a type B.
The RHS is the penalty due to bankruptcy.
Unsuccessful firms don’t have enough cash to avoid
bankruptcy if D > D* and lying managers will earn less,
therefore, a signaling equilibrium accurately separates firms
into high-priced (P = Va ) and low-priced (P = Vb) .
Without this signaling, all of the firms will trade at the same
price because investors cannot distinguish one from another.
If half of the firms are type A and half type B, then the market
price for all firms will be
P = .5 Va + .5 Vb.
To get the price of equity, one needs to subtract the value of
the debt in each case.