Brealey, Myers. Principles of Corporate Finance. 7th edition
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Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
17. Does Debt policy
Matter?
© The McGraw−Hill
Companies, 2003
Therefore, a share in the levered company must also sell for $10. If Macbeth goes
ahead and borrows, it will not allow investors to do anything that they could not
do already, and so it will not increase value.”
The argument that you are using is exactly the same as the one MM used to
prove proposition I.
CHAPTER 17
Does Debt Policy Matter? 471
3.00
2.50
2.00
1.50
1.00
0.50
0.00
500
1000 1500 2000
Earnings per share
(EPS), dollars
Equal proportions
debt and equity
Expected EPS with
debt and equity
Expected
operating
income
Operating
income, dollars
Expected EPS
with all equity
All equity
FIGURE 17.1
Borrowing increases Macbeth’s
EPS (earnings per share) when
operating income is greater than
$1,000 and reduces EPS when
operating income is less than
$1,000. Expected EPS rises from
$1.50 to $2.
Operating Income ($)
500 1,000 1,500 2,000
Earnings on two shares ($) 1 2 3 4
Less interest at 10% ($) 1 1 1 1
Net earnings on investment ($) 0 1 2 3
Return on $10 investment (%) 0 10 20 30
Expected
outcome
TABLE 17.3
Individual investors can
replicate Macbeth’s leverage.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
17. Does Debt policy
Matter?
© The McGraw−Hill
Companies, 2003
Implications of Proposition I
Consider now the implications of proposition I for the expected returns on Mac-
beth stock:
472 PART V
Dividend Policy and Capital Structure
17.2 HOW LEVERAGE AFFECTS RETURNS
Current Structure: Proposed Structure:
All Equity Equal Debt and Equity
Expected earnings per share ($) 1.50 2.00
Price per share ($) 10 10
Expected return on share (%) 15 20
Leverage increases the expected stream of earnings per share but not the share
price. The reason is that the change in the expected earnings stream is exactly off-
set by a change in the rate at which the earnings are capitalized. The expected re-
turn on the share (which for a perpetuity is equal to the earnings–price ratio) in-
creases from 15 to 20 percent. We now show how this comes about.
The expected return on Macbeth’s assets is equal to the expected operating in-
come divided by the total market value of the firm’s securities:
We have seen that in perfect capital markets the company’s borrowing decision
does not affect either the firm’s operating income or the total market value of its se-
curities. Therefore the borrowing decision also does not affect the expected return
on the firm’s assets .
Suppose that an investor holds all of a company’s debt and all of its equity. This
investor would be entitled to all the firm’s operating income; therefore, the ex-
pected return on the portfolio would be equal to .
The expected return on a portfolio is equal to a weighted average of the expected
returns on the individual holdings. Therefore the expected return on a portfolio
consisting of all the firm’s securities is
6
We can rearrange this equation to obtain an expression for , the expected return
on the equity of a levered firm:
r
E
r
A
a
D
D E
r
D
b a
E
D E
r
E
b
a
proportion
in equity
expected return
on equity
b
Expected return
on assets
a
proportion
in debt
expected return
on debt
b
r
A
r
A
Expected return on assets r
A
expected operating income
market value of all securities
r
A
6
This equation should look familiar. We introduced it in Chapter 9 when we showed that the company
cost of capital is a weighted average of the expected returns on the debt and equity. (Company cost of cap-
ital is simply another term for the expected return on assets, .) We also stated in Chapter 9 that chang-
ing the capital structure does not change the company cost of capital. In other words, we implicitly as-
sumed MM’s proposition I.
r
A
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
17. Does Debt policy
Matter?
© The McGraw−Hill
Companies, 2003
r
E
r
A
D
E
1r
A
r
D
2
a
expected return
on assets
expected return
on debt
b
Expected return
on equity
expected return
on assets
debt–equity
ratio
CHAPTER 17 Does Debt Policy Matter? 473
Proposition II
This is MM’s proposition II: The expected rate of return on the common stock of a
levered firm increases in proportion to the debt–equity ratio (D/E), expressed in
market values; the rate of increase depends on the spread between , the expected
rate of return on a portfolio of all the firm’s securities, and , the expected return
on the debt. Note that if the firm has no debt.
We can check out this formula for Macbeth Spot Removers. Before the decision
to borrow
If the firm goes ahead with its plan to borrow, the expected return on assets is
still 15 percent. The expected return on equity is
The general implications of MM’s proposition II are shown in Figure 17.2. The
figure assumes that the firm’s bonds are essentially risk-free at low debt levels.
Thus is independent of D/E, and increases linearly as D/E increases. As the
firm borrows more, the risk of default increases and the firm is required to pay
higher rates of interest. Proposition II predicts that when this occurs the rate of in-
crease in slows down. This is also shown in Figure 17.2. The more debt the firm
has, the less sensitive is to further borrowing.
Why does the slope of the line in Figure 17.2 taper off as D/E increases? Es-
sentially because holders of risky debt bear some of the firm’s business risk. As the
firm borrows more, more of that risk is transferred from stockholders to bond-
holders.
The Risk–Return Trade-off
Proposition I says that financial leverage has no effect on shareholders’ wealth.
Proposition II says that the rate of return they can expect to receive on their shares
increases as the firm’s debt–equity ratio increases. How can shareholders be indif-
ferent to increased leverage when it increases expected return? The answer is that
any increase in expected return is exactly offset by an increase in risk and therefore
in shareholders’ required rate of return.
r
E
r
E
r
E
r
E
r
D
.20, or 20%
.15
5,000
5,000
1.15 .102
r
E
r
A
D
E
1r
A
r
D
2
r
A
1,500
10,000
.15, or 15%
r
E
r
A
expected operating income
market value of all securities
r
E
r
A
r
D
r
A
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
17. Does Debt policy
Matter?
© The McGraw−Hill
Companies, 2003
Look at what happens to the risk of Macbeth shares if it moves to equal debt–
equity proportions. Table 17.4 shows how a shortfall in operating income affects
the payoff to the shareholders.
The debt–equity proportion does not affect the dollar risk borne by equity-
holders. Suppose operating income drops from $1,500 to $500. Under all-equity
financing, equity earnings drop by $1 per share. There are 1,000 outstanding
shares, and so total equity earnings fall by . With 50 percent
debt, the same drop in operating income reduces earnings per share by $2. But
there are only 500 shares outstanding, and so total equity income drops by
, just as in the all-equity case.
However, the debt–equity choice does amplify the spread of percentage re-
turns. If the firm is all-equity-financed, a decline of $1,000 in the operating in-
come reduces the return on the shares by 10 percent. If the firm issues risk-free
debt with a fixed interest payment of $500 a year, then a decline of $1,000 in the
operating income reduces the return on the shares by 20 percent. In other words,
$2 500 $1,000
$1 1,000 $1,000
474 PART V
Dividend Policy and Capital Structure
Risk-free debt Risky debt
debt
equity
D
E
Rates of return
r
E
= Expected return on equity
r
A
= Expected return on assets
r
D
= Expected return on debt
=
FIGURE 17.2
MM’s proposition II. The expected return on
equity increases linearly with the debt–equity
ratio so long as debt is risk-free. But if leverage
increases the risk of the debt, debtholders
demand a higher return on the debt. This causes
the rate of increase in to slow down.r
E
r
E
Operating Income
$500 $1,500
All equity: Earnings per share ($) .50 1.50
Return on shares (%) 5 15
50 percent debt: Earnings per share ($) 0 2
Return on shares (%) 0 20
TABLE 17.4
Leverage increases the risk of
Macbeth shares.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
17. Does Debt policy
Matter?
© The McGraw−Hill
Companies, 2003
the effect of leverage is to double the amplitude of the swings in Macbeth’s
shares. Whatever the beta of the firm’s shares before the refinancing, it would be
twice as high afterward.
Just as the expected return on the firm’s assets is a weighted average of the ex-
pected return on the individual securities, so likewise is the beta of the firm’s as-
sets a weighted average of the betas of the individual securities:
7
We can rearrange this equation also to give an expression for , the beta of the eq-
uity of a levered firm:
Now you can see why investors require higher returns on levered equity. The re-
quired return simply rises to match the increased risk.
In Figure 17.3, we have plotted the expected returns and the risk of Macbeth’s
securities, assuming that the interest on the debt is risk-free.
8

E

A
D
E
1
A

D
2
Beta of equity
beta of
assets
debt–equity
ratio
a
beta of
assets
beta of
debt
b

E

A
a
D
D E

D
b a
E
D E

E
b
Beta of
assets
a
proportion
of debt
beta of
debt
b a
proportion
of equity
beta of
equity
b
CHAPTER 17
Does Debt Policy Matter? 475
7
This equation should also look old-hat. We used it in Section 9.3 when we stated that changes in the
capital structure change the beta of stock but not the asset beta.
8
In this case and .
E

A
1D/E2
A

D
0
Risk
Debt
Equity
All firm's assets
Expected rates
of return
β
E
β
A
β
D
r
A
=
.15
r
E
=
.20
r
D
=
.10
FIGURE 17.3
If Macbeth is unlevered, the
expected return on its equity
equals the expected return on its
assets. Leverage increases both
the expected return on equity ( )
and the risk of equity ( ).
E
r
E
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
17. Does Debt policy
Matter?
© The McGraw−Hill
Companies, 2003
What did financial experts think about debt policy before MM? It is not easy to say
because with hindsight we see that they did not think too clearly.
9
However, a “tra-
ditional” position has emerged in response to MM. In order to understand it, we
have to discuss the weighted-average cost of capital.
The expected return on a portfolio of all the company’s securities is often re-
ferred to as the weighted-average cost of capital:
10
The weighted-average cost of capital is used in capital budgeting decisions to
find the net present value of projects that would not change the business risk of
the firm.
For example, suppose that a firm has $2 million of outstanding debt and 100,000
shares selling at $30 per share. Its current borrowing rate is 8 percent, and the fi-
nancial manager thinks that the stock is priced to offer a 15 percent return. There-
fore and . (The hard part is estimating
,
of course.) This is all we
need to calculate the weighted-average cost of capital:
Note that we are still assuming that proposition I holds. If it doesn’t, we can’t use
this simple weighted average as the discount rate even for projects that do not
change the firm’s business “risk class.” As we will see in Chapter 19, the weighted-
average cost of capital is only a starting point for setting discount rates.
Two Warnings
Sometimes the objective in financing decisions is stated not as “maximize overall
market value” but as “minimize the weighted-average cost of capital.” If MM’s
proposition I holds, then these are equivalent objectives. If MM’s proposition I
does not hold, then the capital structure that maximizes the value of the firm also
minimizes the weighted-average cost of capital, provided that operating income is
independent of capital structure. Remember that the weighted-average cost of cap-
ital is the expected rate of return on the market value of all of the firm’s securities.
.122,
or 12.2%
a
2
5
.08 b a
3
5
.15 b
Weighted-average cost of capital a
D
V
r
D
b a
E
V
r
E
b
V D E 2 3 $5 million
E 100,000 shares $30 per share $3 million
D $2 million
r
E
r
E
.15r
D
.08
Weighted-average cost of capital r
A
a
D
V
r
D
b a
E
V
r
E
b
476 PART V Dividend Policy and Capital Structure
17.3 THE TRADITIONAL POSITION
9
Financial economists in 20 years may remark on Brealey and Myers’s blind spots and clumsy reason-
ing. On the other hand, they may not remember us at all.
10
Remember that in this chapter we ignore taxes. In Chapter 19, we shall see that the weighted-average
cost of capital formula needs to be amended when debt interest can be deducted from taxable profits.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
17. Does Debt policy
Matter?
© The McGraw−Hill
Companies, 2003
Anything that increases the value of the firm reduces the weighted-average cost of
capital if operating income is constant. But if operating income is varying too, all
bets are off.
In Chapter 18 we will show that financial leverage can affect operating income
in several ways. Therefore maximizing the value of the firm is not always equiva-
lent to minimizing the weighted-average cost of capital.
Warning 1 Shareholders want management to increase the firm’s value. They are
more interested in being rich than in owning a firm with a low weighted-average
cost of capital.
Warning 2 Trying to minimize the weighted-average cost of capital seems to en-
courage logical short circuits like the following. Suppose that someone says,
“Shareholders demand—and deserve—higher expected rates of return than bond-
holders do. Therefore debt is the cheaper capital source. We can reduce the
weighted-average cost of capital by borrowing more.” But this doesn’t follow if the
extra borrowing leads stockholders to demand a still higher expected rate of re-
turn. According to MM’s proposition II the cost of equity capital increases by just
enough to keep the weighted-average cost of capital constant.
This is not the only logical short circuit you are likely to encounter. We have
cited two more in practice question 5 at the end of this chapter.
Rates of Return on Levered Equity—The Traditional Position
You may ask why we have even mentioned the aim of minimizing the weighted-
average cost of capital if it is often wrong or confusing. We had to because the tra-
ditionalists accept this objective and argue their case in terms of it.
The logical short circuit we just described rested on the assumption that , the
expected rate of return demanded by stockholders, does not rise as the firm bor-
rows more. Suppose, just for the sake of argument, that this is true. Then , the
weighted-average cost of capital, must decline as the debt–equity ratio rises.
Take Figure 17.4, for example, which is drawn on the assumption that share-
holders demand 12 percent no matter how much debt the firm has and that bond-
holders always want 8 percent. The weighted-average cost of capital starts at 12
percent and ends up at 8. Suppose that this firm’s operating income is a level, per-
petual stream of $100,000 a year. Then firm value starts at
and ends up at
The gain of $416,667 falls into the stockholders’ pockets.
11
Of course this is absurd: A firm that reaches 100 percent debt has to be bankrupt.
If there is any chance that the firm could remain solvent, then the equity retains
V
100,000
.08
$1,250,000
V
100,000
.12
$833,333
r
A
r
E
r
E
CHAPTER 17 Does Debt Policy Matter? 477
11
Note that Figure 17.4 relates and to D/V, the ratio of debt to firm value, rather than to the debt–
equity ratio D/E. In this figure we wanted to show what happens when the firm is 100 percent debt-
financed. At that point and D/E is infinite.E 0
r
D
r
E
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
17. Does Debt policy
Matter?
© The McGraw−Hill
Companies, 2003
some value, and the firm cannot be 100 percent debt-financed. (Remember that we
are working with the market values of debt and equity.)
But if the firm is bankrupt and its original shares are worthless pieces of paper,
then its lenders are its new shareholders. The firm is back to all-equity financing! We
assumed that the original stockholders demanded 12 percent—why should the
new ones demand any less? They have to bear all of the firm’s business risk.
12
The situation described in Figure 17.4 is just impossible.
13
However, it is possi-
ble to stake out a position somewhere between Figures 17.3 and 17.4. That is exactly
what the traditionalists have done. Their hypothesis is shown in Figure 17.5. They
hold that a moderate degree of financial leverage may increase the expected equity
return , although not to the degree predicted by MM’s proposition II. But irre-
sponsible firms that borrow excessively find shooting up faster than MM predict.
Consequently, the weighted-average cost of capital declines at first, then rises.
Its minimum point is the point of optimal capital structure. Remember that mini-
mizing is equivalent to maximizing overall firm value if, as the traditionalists as-
sume, operating income is unaffected by borrowing.
Two arguments might be advanced in support of the traditional position. First, it
could be that investors don’t notice or appreciate the financial risk created by “mod-
erate” borrowing, although they wake up when debt is “excessive.” If so, investors in
moderately leveraged firms may accept a lower rate of return than they really should.
r
A
r
A
r
E
r
E
478 PART V Dividend Policy and Capital Structure
Zero debt 100 percent debt
.08
.12
r
E
= Expected return on equity
r
D
= Expected return on debt
r
A
= Weighted-average
cost of capital
debt
Rates of return
firm value
D
V
=
FIGURE 17.4
If the expected rate of return demanded
by stockholders is unaffected by
financial leverage, then the weighted-
average cost of capital declines as the
firm borrows more. At 100 percent debt
equals the borrowing rate . Of
course this is an absurd and totally unre-
alistic case.
r
D
r
A
r
A
r
E
12
We ignore the costs, delays, and other complications of bankruptcy. They are discussed in Chapter 18.
13
This case is often termed the net-income (NI) approach because investors are assumed to capitalize in-
come after interest at the same rate regardless of financial leverage. In contrast, MM’s approach is a net-
operating-income (NOI) approach because the value of the firm is fundamentally determined by oper-
ating income, the total dollar return to both bondholders and stockholders. This distinction was
emphasized by D. Durand in his important, pre-MM paper, “Cost of Debt and Equity Funds for Busi-
ness: Trends and Problems of Measurement,” in Conference on Research in Business Finance, National Bu-
reau of Economic Research, New York, 1952.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
17. Does Debt policy
Matter?
© The McGraw−Hill
Companies, 2003
That seems naive.
14
The second argument is better. It accepts MM’s reasoning as
applied to perfect capital markets but holds that actual markets are imperfect. Im-
perfections may allow firms that borrow to provide a valuable service for in-
vestors. If so, levered shares might trade at premium prices compared to their the-
oretical values in perfect markets.
Suppose that corporations can borrow more cheaply than individuals. Then it
would pay investors who want to borrow to do so indirectly by holding the stock
of levered firms. They would be willing to live with expected rates of return that
do not fully compensate them for the business and financial risk they bear.
Is corporate borrowing really cheaper? It’s hard to say. Interest rates on home
mortgages are not too different from rates on high-grade corporate bonds.
15
Rates on
margin debt (borrowing from a stockbroker with the investor’s shares tendered as
security) are not too different from the rates firms pay banks for short-term loans.
There are some individuals who face relatively high interest rates, largely because
of the costs lenders incur in making and servicing small loans. There are economies
of scale in borrowing. A group of small investors could do better by borrowing via a
corporation, in effect pooling their loans and saving transaction costs.
16
CHAPTER 17 Does Debt Policy Matter? 479
Rates of return
debt
equity
D
E
=
r
E
(MM)
r
E
(traditional)
r
A
(traditional)
r
A
(MM)
r
D
Traditionalists believe there is an optimal
debt–equity ratio that minimizes
r
A
.
FIGURE 17.5
The dashed lines show MM’s view of the
effect of leverage on the expected
return on equity and the weighted-
average cost of capital . (See Figure
17.2.) The solid lines show the traditional
view. Traditionalists say that borrowing
at first increases more slowly than MM
predict but that shoots up with
excessive borrowing. If so, the
weighted-average cost of capital can be
minimized if you use just the right
amount of debt.
r
E
r
E
r
A
r
E
14
This first argument may reflect a confusion between financial risk and the risk of default. Default is
not a serious threat when borrowing is moderate; stockholders worry about it only when the firm goes
“too far.” But stockholders bear financial risk—in the form of increased volatility of rate of return and
higher beta—even when the chance of default is nil. We demonstrated this in Figure 17.3.
15
One of the authors once obtained a home mortgage at a rate
1
⁄2 percentage point less than the contem-
poraneous yield on long-term AAA bonds.
16
Even here there are alternatives to borrowing on personal account. Investors can draw down their sav-
ings accounts or sell a portion of their investment in bonds. The impact of reductions in lending on the
investor’s balance sheet and risk position is exactly the same as increases in borrowing.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
17. Does Debt policy
Matter?
© The McGraw−Hill
Companies, 2003
But suppose that this class of investors is large, both in number and in the aggregate
wealth it brings to capital markets. Shouldn’t the investors’ needs be fully satisfied by
the thousands of levered firms already existing? Is there really an unsatisfied clientele
of small investors standing ready to pay a premium for one more firm that borrows?
Maybe the market for corporate leverage is like the market for automobiles.
Americans need millions of automobiles and are willing to pay thousands of dol-
lars apiece for them. But that doesn’t mean that you could strike it rich by going
into the automobile business. You’re at least 50 years too late.
Where to Look for Violations of MM’s Propositions
MM’s propositions depend on perfect capital markets. We believe capital markets
are generally well-functioning, but they are not 100 percent perfect 100 percent of
the time. Therefore, MM must be wrong some times in some places. The financial
manager’s problem is to figure out when and where.
That is not easy. Just finding market imperfections is insufficient.
Consider the traditionalists’ claim that imperfections make borrowing costly
and inconvenient for many individuals. That creates a clientele for whom corpo-
rate borrowing is better than personal borrowing. That clientele would, in princi-
ple, be willing to pay a premium for the shares of a levered firm.
But maybe it doesn’t have to pay a premium. Perhaps smart financial managers
long ago recognized this clientele and shifted the capital structures of their firms
to meet its needs. The shifts would not have been difficult or costly to make. But if
the clientele is now satisfied, it is no longer willing to pay a premium for levered
shares. Only the financial managers who first recognized the clientele extracted
any advantage from it.
Today’s Unsatisfied Clienteles Are Probably Interested in Exotic Securities
So far we have made little progress in identifying cases where firm value might
plausibly depend on financing. But our examples illustrate what smart financial
managers look for. They look for an unsatisfied clientele, investors who want a par-
ticular kind of financial instrument but because of market imperfections can’t get
it or can’t get it cheaply.
MM’s proposition I is violated when the firm, by imaginative design of its capital
structure, can offer some financial service that meets the needs of such a clientele. Ei-
ther the service must be new and unique or the firm must find a way to provide some
old service more cheaply than other firms or financial intermediaries can.
Now, is there an unsatisfied clientele for garden-variety debt or levered equity?
We doubt it. But perhaps you can invent an exotic security and uncover a latent de-
mand for it.
In the next several chapters we will encounter a number of new securities that
have been invented by companies and advisers. These securities take the com-
pany’s basic cash flows and repackage them in ways that are thought to be more
attractive to investors. However, while inventing these new securities is easy, it is
more difficult to find investors who will rush to buy them.
17
Imperfections and Opportunities
The most serious capital market imperfections are often those created by govern-
ment. An imperfection which supports a violation of MM’s proposition I also cre-
480 PART V
Dividend Policy and Capital Structure
17
We return to the topic of security innovation in Section 25.8.