Chapter 14
Capital
Structure in a
Perfect Market
Chapter Outline
14.1 Equity Versus Debt Financing
14.2 Modigliani-Miller I: Leverage, Arbitrage, and
Firm Value
14.3 Modigliani-Miller II: Leverage, Risk, and the
Cost of Capital
14.4 Capital Structure Fallacies
14.5 MM: Beyond the Propositions
Learning Objectives
1. Define the types of securities usually used by
firms to raise capital; define leverage.
2. Describe the capital structure that the firm
should choose.
3. List the three conditions that make capital
markets perfect.
Learning Objectives (cont'd)
4. Discuss the implications of MM Proposition I,
and the roles of homemade leverage and the
Law of One Price in the development of the
proposition.
5. Calculate the cost of capital for levered equity
according to MM Proposition II.
6. Illustrate the effect of a change in debt on
weighted average cost of capital in perfect
capital markets.
Learning Objectives (cont'd)
7. Calculate the market risk of a firm’s assets
using its unlevered beta.
8. Illustrate the effect of increased leverage on
the beta of a firm’s equity.
9. Compute a firm’s net debt.
10. Discuss the effect of leverage on a firm’s
expected earnings per share.
Learning Objectives (cont'd)
11. Show the effect of dilution on equity value.
12. Explain why perfect capital markets neither
create nor destroy value.
14.1 Equity Versus Debt Financing
• Capital Structure
– The relative proportions of debt, equity, and other
securities that a firm has outstanding
Financing a Firm with Equity
• You are considering an investment opportunity.
– For an initial investment of $800 this year, the
project will generate cash flows of either $1400 or
$900 next year, depending on whether the
economy is strong or weak, respectively. Both
scenarios are equally likely.
Table 14.1 The Project Cash Flows
Financing a Firm with Equity
(cont'd)
• The project cash flows depend on the overall
economy and thus contain market risk. As a
result, you demand a 10% risk premium over
the current risk-free interest rate of 5% to
invest in this project.
• What is the NPV of this investment
opportunity?
Financing a Firm with Equity
(cont'd)
• The cost of capital for this project is 15%. The
expected cash flow in one year is
– ½($1400) + ½($900) = $1150.
• The NPV of the project is
$1150
NPV  $800 
 $800  $1000  $200.
1.15
Financing a Firm with Equity
(cont'd)
• If you finance this project using only equity, how
much would you be willing to pay for the project?
$1150
PV (equity cash flows) 
 $1000
1.15
– If you can raise $1000 by selling equity in the firm, after
paying the investment cost of $800, you can keep the
remaining $200, the NPV of the project NPV, as a profit.
Financing a Firm with Equity
(cont'd)
• Unlevered Equity
– Equity in a firm with no debt
• Because there is no debt, the cash flows of the
unlevered equity are equal to those of the
project.
Table 14.2 Cash Flows and Returns
for Unlevered Equity
Financing a Firm with Equity
(cont'd)
• Shareholder’s returns are either 40% or
–10%.
– The expected return on the unlevered equity is
• ½ (40%) + ½(–10%) = 15%.
• Because the cost of capital of the project is 15%,
shareholders are earning an appropriate return for the
risk they are taking.
Financing a Firm with Debt and
Equity
• Suppose you decide to borrow $500 initially, in
addition to selling equity.
– Because the project’s cash flow will always be
enough to repay the debt, the debt is risk free, and
you can borrow at the risk-free interest rate of 5%.
You will owe the debt holders
• $500 × 1.05 = $525 in one year.
• Levered Equity
– Equity in a firm that also has debt outstanding
Financing a Firm
with Debt and Equity (cont'd)
• Given the firm’s $525 debt obligation, your
shareholders will receive only $875 ($1400 –
$525 = $875) if the economy is strong and $375
($900 – $525 = $375) if the economy is weak.
Table 14.3 Values and Cash Flows for Debt and
Equity of the Levered Firm
Financing a Firm
with Debt and Equity (cont'd)
• What price E should the levered equity sell for?
• Which is the best capital structure choice for
the entrepreneur?
Financing a Firm
with Debt and Equity (cont'd)
• Modigliani and Miller argued that with perfect
capital markets, the total value of a firm should
not depend on its capital structure.
– They reasoned that the firm’s total cash flows still
equal the cash flows of the project and, therefore,
have the same present value.
Financing a Firm
with Debt and Equity (cont'd)
• Because the cash flows of the debt and equity
sum to the cash flows of the project, by the
Law of One Price the combined values of debt
and equity must be $1000.
– Therefore, if the value of the debt is $500, the
value of the levered equity must be $500.
• E = $1000 – $500 = $500.
Financing a Firm
with Debt and Equity (cont'd)
• Because the cash flows of levered equity
are smaller than those of unlevered equity,
levered equity will sell for a lower price ($500
versus $1000).
– However, you are not worse off. You will still raise a
total of $1000 by issuing both debt and levered
equity. Consequently, you would be indifferent
between these two choices for the firm’s capital
structure.
The Effect of Leverage on Risk and
Return
• Leverage increases the risk of the equity of a
firm.
– Therefore, it is inappropriate to discount the cash
flows of levered equity at the same discount rate of
15% that you used for unlevered equity. Investors
in levered equity will require a higher expected
return to compensate for the increased risk.
Table 14.4 Returns to Equity with
and without Leverage
The Effect of Leverage
on Risk and Return (cont'd)
• The returns to equity holders are very different
with and without leverage.
– Unlevered equity has a return of either 40% or
–10%, for an expected return of 15%.
– Levered equity has higher risk, with a return of
either 75% or –25%.
• To compensate for this risk, levered equity holders
receive a higher expected return of 25%.
The Effect of Leverage
on Risk and Return (cont'd)
• The relationship between risk and return can
be evaluated more formally by computing the
sensitivity of each security’s return to the
systematic risk of the economy.
Table 14.5 Systematic Risk and Risk Premiums for
Debt, Unlevered Equity, and Levered Equity
The Effect of Leverage
on Risk and Return (cont'd)
• Because the debt’s return bears no systematic
risk, its risk premium is zero.
• In this particular case, the levered equity has
twice the systematic risk of the unlevered
equity and, as a result, has twice the risk
premium.
The Effect of Leverage
on Risk and Return (cont'd)
• In summary,
– In the case of perfect capital markets, if the firm is
100% equity financed, the equity holders will
require a 15% expected return.
– If the firm is financed 50% with debt and 50% with
equity, the debt holders will receive a return of 5%,
while the levered equity holders will require an
expected return of 25% (because of their increased
risk).
The Effect of Leverage
on Risk and Return (cont'd)
• In summary,
– Leverage increases the risk of equity even when
there is no risk that the firm will default.
• Thus, while debt may be cheaper, its use raises the cost
of capital for equity. Considering both sources of capital
together, the firm’s average cost of capital with leverage
is the same as for the unlevered firm.
Textbook Example 14.1
Textbook Example 14.1 (cont'd)
Alternative Example 14.1
• Problem
– Suppose the entrepreneur borrows $700 when
financing the project. According to Modigliani and
Miller, what should the value of the equity be?
What is the expected return?
Alternative Example 14.1 (cont'd)
• Solution
– Because the value of the firm’s total cash flows is still
$1000, if the firm borrows $700, its equity will be
worth $300. The firm will owe $700 × 1.05 = $735 in
one year. Thus, if the economy is strong, equity
holders will receive $1400 − 735 = $665, for a return
of $665/$300 − 1 = 121.67%. If the economy is weak,
equity holders will receive $900 − $735 = $, for a
return of $165/$300 − 1 = −45.0%. The equity has an
expected
1 return of 1
(121.67%)  (45.0%)  38.33%
2
2
Alternative Example 14.1 (cont'd)
• Solution
– Note that the equity has a return sensitivity of
121.67% − (−45.0%) = 166.67%, which is
166.67%/50% = 333.34% of the sensitivity of
unlevered equity. Its risk premium is 38.33% − 5%=
33.33%, which is approximately 333.34% of the risk
premium of the unlevered equity, so it is
appropriate compensation for the risk.
14.2 Modigliani-Miller I: Leverage, Arbitrage, and
Firm Value
• The Law of One Price implies that leverage will
not affect the total value of the firm.
– Instead, it merely changes the allocation of cash
flows between debt and equity, without altering
the total cash flows of the firm.
14.2 Modigliani-Miller I: Leverage, Arbitrage, and
Firm Value (cont'd)
• Modigliani and Miller (MM) showed that this result holds more
generally under a set of conditions referred to as perfect capital
markets:
– Investors and firms can trade the same set of securities at competitive
market prices equal to the present value of their future cash flows.
– There are no taxes, transaction costs, or issuance costs associated with
security trading.
– A firm’s financing decisions do not change the cash flows generated by
its investments, nor do they reveal new information about them.
14.2 Modigliani-Miller I: Leverage, Arbitrage, and
Firm Value (cont'd)
• MM Proposition I
– In a perfect capital market, the total value of a firm
is equal to the market value of the total cash flows
generated by its assets and is not affected by its
choice of capital structure.
MM and the Law of One Price
• MM established their result with the
following argument:
– In the absence of taxes or other transaction costs,
the total cash flow paid out to all of a firm’s
security holders is equal to the total cash flow
generated by the firm’s assets.
• Therefore, by the Law of One Price, the firm’s securities
and its assets must have the same total market value.
Homemade Leverage
• Homemade Leverage
– When investors use leverage in their own portfolios
to adjust the leverage choice made by the firm.
• MM demonstrated that if investors would
prefer an alternative capital structure to the
one the firm has chosen, investors can borrow
or lend on their own and achieve the same
result.
Homemade Leverage (cont'd)
• Assume you use no leverage and create an allequity firm.
– An investor who would prefer to hold levered
equity can do so by using leverage in his own
portfolio.
Table 14.6 Replicating Levered
Equity Using Homemade Leverage
Homemade Leverage (cont'd)
• If the cash flows of the unlevered equity serve
as collateral for the margin loan (at the riskfree rate of 5%), then by using homemade
leverage, the investor has replicated the
payoffs to the levered equity, as illustrated in
the previous slide, for a cost of $500.
– By the Law of One Price, the value of levered equity
must also be $500.
Homemade Leverage (cont'd)
• Now assume you use debt, but the investor
would prefer to hold unlevered equity. The
investor can re-create the payoffs of unlevered
equity by buying both the debt and the equity
of the firm. Combining the cash flows of the
two securities produces cash flows identical to
unlevered equity, for a total cost of $1000.
Table 14.7 Replicating Unlevered
Equity by Holding Debt and Equity
Homemade Leverage (cont'd)
• In each case, your choice of capital structure
does not affect the opportunities available to
investors.
– Investors can alter the leverage choice of the firm
to suit their personal tastes either by adding more
leverage or by reducing leverage.
– With perfect capital markets, different choices of
capital structure offer no benefit to investors and
does not affect the value of the firm.
Textbook Example 14.2
Textbook Example 14.2 (cont'd)
Alternative Example 14.2
• Problem
– Suppose there are two firms, each with date 1 cash
flows of $1400 or $900 (as shown in Table 14.1).
The firms are identical except for their capital
structure. One firm is unlevered, and its equity has
a market value of $1010. The other firm has
borrowed $500, and its equity has a market value
of $500. Does MM Proposition I hold? What
arbitrage opportunity is available using homemade
leverage?
Alternative Example 14.2 (cont'd)
• Solution
– MM Proposition I states that the total value of each
firm should equal the value of its assets. Because
these firms hold identical assets, their total values
should be the same. However, the problem
assumes the unlevered firm has a total market
value of $1010, whereas the levered firm has a
total market value of $500 (equity) + $500 (debt) =
$1000. Therefore, these prices violate MM
Proposition I.
Alternative Example 14.2 (cont'd)
• Solution
– Because these two identical firms are trading for
different total prices, the Law of One Price is
violated and an arbitrage opportunity exists. To
exploit it, we can buy the equity of the levered firm
for $500, and the debt of the levered firm for $500,
re-creating the equity of the unlevered firm by
using homemade leverage for a cost of only $500 +
$500 = $1000. We can then sell the equity of the
unlevered firm for $1010 and enjoy an arbitrage
profit of $10.
Alternative Example 14.2 (cont'd)
Date 0
Date 1: Cash Flows
Cash Flow
Strong
Economy
Weak
Economy
Buy levered
equity
-$500
$875
$375
Buy levered
debt
-$500
$525
$525
Sell unlevered
equity
$1,010
$1,400
-$900
Total cash flow
$10
$0
$0
Note that the actions of arbitrageurs buying the levered firm’s equity
and debt and selling the unlevered firm’s equity will cause the price of
the levered firm’s equity to rise and the price of the unlevered firm’s
equity to fall until the firms’ values are equal.
The Market Value Balance Sheet
• Market Value Balance Sheet
– A balance sheet where:
• All assets and liabilities of the firm are included (even
intangible assets such as reputation, brand name, or
human capital that are missing from a standard
accounting balance sheet).
• All values are current market values rather than
historical costs.
– The total value of all securities issued by the firm
must equal the total value of the firm’s assets.
Table 14.8 The Market Value
Balance Sheet of the Firm
The Market Value Balance Sheet
(cont'd)
• Using the market value balance sheet, the
value of equity is computed as follows:
Market Value of Equity 
Market Value of Assets  Market Value of Debt and Other Liabilities
Textbook Example 14.3
Textbook Example 14.3 (cont'd)
Alternative Example 14.3
• Problem
– Assume that the social media app you developed
has gone viral and you decided to sell the company,
which has $60 million in assets.
– You plan on splitting the firm into equity, debt, and
warrants, and you expect to sell $10 million in debt
and $15 million in warrants.
– What will the value of the equity be in a perfect
capital market?
Alternative Example 14.3 (cont'd)
• Solution
– According to MM Proposition I, the total value of
all securities issued should equal the value of the
assets, or $60 million.
– Given that the debt is worth $10 million and the
warrants are worth $15 million, the value of the
equity must be $35 million.
Application: A Leveraged
Recapitalization
• Leveraged Recapitalization
– When a firm uses borrowed funds to pay a large
special dividend or repurchase a significant amount
of outstanding shares
Application: A Leveraged
Recapitalization (cont'd)
• Example:
– Harrison Industries is currently an all-equity firm
operating in a perfect capital market, with 50
million shares outstanding that are trading for $4
per share.
– Harrison plans to increase its leverage by
borrowing $80 million and using the funds to
repurchase 20 million of its outstanding shares.
Application: A Leveraged
Recapitalization (cont'd)
• Example
– This transaction can be viewed in two stages.
• First, Harrison sells debt to raise $80 million in cash.
• Second, Harrison uses the cash to repurchase shares.
Table 14.9 Market Value Balance Sheet after Each Stage of
Harrison’s Leveraged Recapitalization ($ millions)
Application: A Leveraged
Recapitalization (cont'd)
• Example
– Initially, Harrison is an all-equity firm and the
market value of Harrison’s equity is $200 million
(50 million shares × $4 per share = $200 million)
and equals the market value of its existing assets.
Application: A Leveraged
Recapitalization (cont'd)
• Example
– After borrowing, Harrison’s liabilities grow by $80
million, which is also equal to the amount of cash
the firm has raised. Because both assets and
liabilities increase by the same amount, the market
value of the equity remains unchanged.
Application: A Leveraged
Recapitalization (cont'd)
• Example
– To conduct the share repurchase, Harrison spends
the $80 million in borrowed cash to repurchase 20
million shares ($80 million ÷ $4 per share = 20
million shares).
– Because the firm’s assets decrease by $80 million
and its debt remains unchanged, the market value
of the equity must also fall by $80 million, from
$200 million to $120 million, for assets and
liabilities to remain balanced.
Application: A Leveraged
Recapitalization (cont'd)
• Example
– The share price is unchanged.
• With 30 million shares remaining, the shares are worth
$4 per share, just as before ($120 million ÷ 30 million
shares = $4 per share).
14.3 Modigliani-Miller II: Leverage, Risk, and the
Cost of Capital
• Leverage and the Equity Cost of Capital
– MM’s first proposition can be used to derive an
explicit relationship between leverage and the
equity cost of capital.
14.3 Modigliani-Miller II: Leverage, Risk, and the
Cost of Capital (cont'd)
• Leverage and the Equity Cost of Capital
–E
• Market value of equity in a levered firm
–D
• Market value of debt in a levered firm
–U
• Market value of equity in an unlevered firm
–A
• Market value of the firm’s assets
14.3 Modigliani-Miller II: Leverage, Risk, and the
Cost of Capital (cont'd)
• Leverage and the Equity Cost of Capital
– MM Proposition I states that
E  D  U  A.
– The total market value of the firm’s securities is
equal to the market value of its assets, whether the
firm is unlevered or levered.
14.3 Modigliani-Miller II: Leverage, Risk, and the
Cost of Capital (cont'd)
• Leverage and the Equity Cost of Capital
– The cash flows from holding unlevered equity can
be replicated using homemade leverage by holding
a portfolio of the firm’s equity and debt.
14.3 Modigliani-Miller II: Leverage, Risk, and the
Cost of Capital (cont'd)
• Leverage and the Equity Cost of Capital
– The return on unlevered equity (RU) is related to
the returns of levered equity (RE) and debt (RD):
E
D
RE 
RD  RU
E  D
E  D
14.3 Modigliani-Miller II: Leverage, Risk, and the
Cost of Capital (cont'd)
• Leverage and the Equity Cost of Capital
– Solving for RE:
RE
D

RU 
( RU  RD )
E
Risk without
leverage
Additional risk
due to leverage
• The levered equity return equals the unlevered return, plus a
premium due to leverage.
– The amount of the premium depends on the amount of leverage,
measured by the firm’s market value debt-equity ratio, D/E.
14.3 Modigliani-Miller II: Leverage, Risk, and the
Cost of Capital (cont'd)
• Leverage and the Equity Cost of Capital
– MM Proposition II:
• The cost of capital of levered equity is equal to the cost
of capital of unlevered equity plus a premium that is
proportional to the market value debt-equity ratio.
• Cost of Capital of Levered Equity
rE
D
 rU 
(rU  rD )
E
14.3 Modigliani-Miller II: Leverage, Risk, and the
Cost of Capital (cont'd)
• Leverage and the Equity Cost of Capital
– Recall from above:
• If the firm is all-equity financed, the expected return on
unlevered equity is 15%.
• If the firm is financed with $500 of debt, the expected
return of the debt is 5%.
14.3 Modigliani-Miller II: Leverage, Risk, and the
Cost of Capital (cont'd)
• Leverage and the Equity Cost of Capital
– Therefore, according to MM Proposition II, the
expected return on equity for the levered firm is
rE
500
 15% 
(15%  5%)  25%
500
Textbook Example 14.4
Textbook Example 14.4 (cont'd)
Alternative Example 14.4
• Problem
– Suppose the entrepreneur in Alternative Example
14.1 borrows only $700 when financing the project.
• Recall that the expected return on unlevered equity is
15% and the risk-free rate is 5%.
– According to MM Proposition II, what will be the
firm’s equity cost of capital?
Alternative Example 14.4 (cont’d)
• Solution
– Because the firm’s assets have a market value
of $1000, by MM Proposition I the equity will
have a market value of $300. Then, using Eq.
14.5,
$700
rE  15% 
15%  5%  38.33%
$300
– This result matches the expected return
calculated in Example 14.1.
Capital Budgeting and the
Weighted Average Cost of Capital
• If a firm is unlevered, all of the free cash
flows generated by its assets are paid out to its
equity holders.
– The market value, risk, and cost of capital for the
firm’s assets and its equity coincide and therefore
rU  rA
Capital Budgeting and the Weighted Average Cost
of Capital (cont'd)
• If a firm is levered, project rA is equal to the
firm’s weighted average cost of capital.
– Unlevered Cost of Capital (pretax WACC)
Equity
Debt
 Fraction of Firm Value  

 Fraction of Firm Value  

rwacc  

 


 

 Financed by Equity   Cost of Capital 
 Financed by Debt   Cost of Capital 
E
D

rE 
rD
E  D
E  D
rwacc  rU  rA
Capital Budgeting and the Weighted Average Cost
of Capital (cont'd)
• With perfect capital markets, a firm’s WACC is
independent of its capital structure and is
equal to its equity cost of capital if it is
unlevered, which matches the cost of capital of
its assets.
• Debt-to-Value Ratio
– The fraction of a firm’s enterprise value that
corresponds to debt
Figure 14.1
WACC and
Leverage
with Perfect
Capital Markets
(a) Equity, debt, and weighted
average costs of capital for
different amounts of leverage.
The rate of increase of rD and
rE, and thus the shape of the
curves, depends on the
characteristics of the firm’s
cash flows.
(b) Calculating the WACC for
alternative capital structures.
Data in this table correspond
to the example in Section
14.1.
Capital Budgeting and the Weighted Average Cost
of Capital (cont'd)
• With no debt, the WACC is equal to the
unlevered equity cost of capital.
• As the firm borrows at the low cost of capital
for debt, its equity cost of capital rises. The net
effect is that the firm’s WACC is unchanged.
Textbook Example 14.5
Textbook Example 14.5 (cont'd)
Alternative Example 14.5
• Problem
– Honeywell International Inc. (HON) has a
market debt-equity ratio of 0.5.
– Assume its current debt cost of capital is 6.5%,
and its equity cost of capital is 14%.
– If HON issues equity and uses the proceeds to
repay its debt and reduce its debt-equity ratio
to 0.4, it will lower its debt cost of capital to
5.75%.
Alternative Example 14.5 (cont’d)
• Problem
– With perfect capital markets, what effect will
this transaction have on HON’s equity cost of
capital and WACC?
Alternative Example 14.5 (cont’d)
• Solution
– Current WACC
rwacc 
E
D
2
1
rE 
rD 
14% 
6.5%  11.5%
ED
ED
2 1
2 1
– New Cost of Equity
D
rE  rU  (rU  rD )  11.5%  0.4(11.5%  5.75%)  13.8%
E
Alternative Example 14.5 (cont’d)
• Solution
– New WACC
rNEWwacc
1
0.4

13.8% 
5.75%  11.5%
1  0.4
1  0.4
– The cost of equity capital falls from 14% to 13.8%,
while the WACC is unchanged.
Computing the WACC
with Multiple Securities
• If the firm’s capital structure is made up of
multiple securities, then the WACC is
calculated by computing the weighted average
cost of capital of all of the firm’s securities.
Textbook Example 14.6
Textbook Example 14.6 (cont'd)
Levered and Unlevered Betas
• The effect of leverage on the risk of a firm’s
securities can also be expressed in terms of
beta:
U
E
D

E 
D
E  D
E  D
Levered and Unlevered Betas
(cont'd)
• Unlevered Beta
– A measure of the risk of a firm as if it did not
have leverage, which is equivalent to the beta of
the firm’s assets.
• If you are trying to estimate the unlevered beta
for an investment project, you should base
your estimate on the unlevered betas of firms
with comparable investments.
Levered and Unlevered Betas
(cont'd)
 E  U
D

( U   D )
E
• Leverage amplifies the market risk of a firm’s
assets, βU, raising the market risk of its equity.
Textbook Example 14.7
Textbook Example 14.7 (cont’d)
Textbook Example 14.8
Textbook Example 14.8 (cont’d)
14.4 Capital Structure Fallacies
• Leverage and Earnings per Share
– Example
• LVI is currently an all-equity firm. It expects to generate
earnings before interest and taxes (EBIT) of $10 million
over the next year. Currently, LVI has 10 million shares
outstanding, and its stock is trading for a price of $7.50
per share. LVI is considering changing its capital structure
by borrowing $15 million at an interest rate of 8% and
using the proceeds to repurchase 2 million shares at
$7.50 per share.
14.4 Capital Structure Fallacies
(cont'd)
• Leverage and Earnings per Share
– Example
• Suppose LVI has no debt. Because there is no interest
and no taxes, LVI’s earnings would equal its EBIT and
LVI’s earnings per share without leverage would be
Earnings
$10 million
EPS 

 $1
Number of Shares
10 million
14.4 Capital Structure Fallacies
(cont'd)
• Leverage and Earnings per Share
– Example
• If LVI recapitalizes, the new debt will obligate LVI to make
interest payments each year of $1.2 million/year.
– $15 million × 8% = $1.2 million
• As a result, LVI will have expected earnings after interest
of $8.8 million.
– Earnings = EBIT – Interest
– Earnings = $10 million – $1.2 million = $8.8 million
14.4 Capital Structure Fallacies
(cont'd)
• Leverage and Earnings per Share
– Example
• Earnings per share rises to $1.10
– $8.8 million ÷ $8 million shares = $1.10
• LVI’s expected earnings per share increases with
leverage.
14.4 Capital Structure Fallacies
(cont'd)
• Leverage and Earnings per Share
– Example
• Are shareholders better off?
– NO! Although LVI’s expected EPS rises with leverage, the risk of
its EPS also increases. While EPS increases on average, this
increase is necessary to compensate shareholders for the
additional risk they are taking, so LVI’s share price does not
increase as a result of the transaction.
Figure 14.2 LVI Earnings per Share
with and without Leverage
Textbook Example 14.9
Textbook Example 14.9 (cont'd)
Equity Issuances and Dilution
• Dilution
– An increase in the total of shares that will divide a
fixed amount of earnings
• It is sometimes (incorrectly) argued that issuing
equity will dilute existing shareholders’
ownership, so debt financing should be used
instead.
Equity Issuances and Dilution
(cont'd)
• Suppose Jet Sky Airlines (JSA) currently has no
debt and 500 million shares of stock
outstanding, which is currently trading at a
price of $16.
• Last month the firm announced that it would
expand and the expansion will require the
purchase of $1 billion of new planes, which will
be financed by issuing new equity.
Equity Issuances and Dilution
(cont'd)
• The current (prior to the issue) value of the the
equity and the assets of the firm is $8 billion.
– 500 million shares × $16 per share = $8 billion
• Suppose JSA sells 62.5 million new shares
at the current price of $16 per share to raise
the additional $1 billion needed to purchase
the planes.
Equity Issuances and Dilution
(cont'd)
Equity Issuances and Dilution
(cont'd)
• Results
– The market value of JSA’s assets grows because of
the additional $1 billion in cash the firm has raised.
– The number of shares increases.
• Although the number of shares has grown to 562.5
million, the value per share is unchanged at $16 per
share.
Equity Issuances and Dilution
(cont'd)
• As long as the firm sells the new shares of
equity at a fair price, there will be no gain or
loss to shareholders associated with the equity
issue itself.
• Any gain or loss associated with the transaction
will result from the NPV of the investments the
firm makes with the funds raised.
14.5 MM: Beyond the
Propositions
• Conservation of Value Principle for
Financial Markets
– With perfect capital markets, financial transactions
neither add nor destroy value, but instead
represent a repackaging of risk (and therefore
return).
• This implies that any financial transaction that appears
to be a good deal may be exploiting some type of market
imperfection.
Discussion of Data Case Key
Topic
How much does Apple Inc. (ticker symbol
AAPL) owe in public (corporate bond) debt? If
the company is considering adding debt to its
capital structure, what would Modigliani and
Miller say about the change?
Source: FINRA
Chapter Quiz
1. How does the risk and cost of capital of
levered equity compare to that of unlevered
equity? Which is the superior capital structure
choice in a perfect capital market?
2. What is a market value balance sheet?
3. In a perfect capital market, how will a firm’s
market capitalization change if it borrows in
order to repurchase shares? How will its share
price change?
Chapter Quiz
4. With perfect capital markets, as a firm increases its leverage,
how does its debt cost of capital change? Its equity cost of
capital? Its weighted average cost of capital?
5. If a change in leverage raises a firm’s earnings per share,
should this cause its share price to rise in a perfect market?
6. Consider the questions facing Dan Harris, CFO of EBS, at the
beginning of this chapter. What answers would you give based
on the Modigliani-Miller Propositions? On what
considerations should the capital structure decision be
based?