Chapter 14
Berk and DeMarzo
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
14.1 Equity Versus Debt
Financing
• The relative proportion of debt and equity
a firm has outstanding is called its capital
structure.
• The most common cases:
– Financing a Firm with Equity
– Financing a Firm with Debt and Equity
14.1 Equity Versus Debt
Financing
• How should we chose between debt and
equity?
• Does capital structure matter?
• Why or why not?
• MM gave us the tools to answer these
questions.
• MM were the first to use the Law of One
Price to prove a theoretical claim.
Table 14.1 The Project Cash Flows
•Since the two states of the economy are equally
likely, the expected cash flow is $1,150.
•If the cost-of-capital is 15%, then the NPV of this
investment is: -$800 + 1150/1.15 = $200
•Since the PV of the investment is $1150/1.15 =
$1000, an entrepreneur can raise $1,000 by selling
equity, keeping $200 for herself.
Table 14.2 Cash Flows and Returns
for Unlevered Equity
Equity in a firm with no debt is called unlevered
equity. Investors are entitled to all cash flows.
Given investors’ initial $1000 investment, the
expected return on the unlevered equity is:
0.5 x 40% + 0.5 x -10% = 15%
Table 14.3 Values and Cash Flows for
Debt and Equity of the Levered Firm
Will adding leverage affect the value of the firm?
Suppose the risk-free rate is 5%.
Notice that the remaining equity is called levered
equity.
Table 14.3 Values and Cash Flows for
Debt and Equity of the Levered Firm
• What price should the remaining equity
sell for?
• Which is the best capital structure choice
for the entrepreneur?
• Can he make more than $200?
• Remember that this is a perfect market.
Table 14.3 Values and Cash Flows for
Debt and Equity of the Levered Firm
• The cash flows of the company will be the same.
• The entrepreneur’s financing choice wont effect
the likelihood of a weak or strong economy, thus
the required return won’t change.
• Thus, the PV will still equal $1000.
• And, by the law of one price, no matter how you
cut it, Debt + Equity will equal $1000.
• Thus, E = $1000 – $500 = $500
Table 14.3 Values and Cash Flows for
Debt and Equity of the Levered Firm
• Before Modigliani and Miller, it was common to
believe that:
0.5$875  0.5$375
E
 $543
1.15
But, this logic overlooks the fact that the
leverage increases the risk of the equity of the
firm. Therefore, a discount rate of 15% is too low.
Table 14.4 Returns to Equity
with and without Leverage
Given an initial investment of $500, equity holders
earn a higher return in good times and a lower one
in bad times.
Table 14.4 Returns to Equity
with and without Leverage
The increased risk is compensated with an
increased expected (or required) return: 25%
rather than 15%.
Table 14.5 Systemic Risk and Risk
Premiums for Debt, Unlevered Equity,
and Levered Equity
Because levered equity has twice the systematic
risk as unlevered equity, the risk premium for
unlevered equity is twice that of levered equity.
Example 14.1 Leverage and
the Equity Cost of Capital
Example 14.1 Leverage and the Equity
Cost of Capital
Date 0
Date 1
Strong
Weak
Firm
1000
1400
900
Debt
200
210
210
Equity
800
1190
690
Strong Return = (1190/800) – 1 = 48.75%
Weak Return = (690/800) – 1 = – 13.75%
Exp. Return = 0.5(48.75%) + 0.5 (13.75%) = 17.5%
Example 14.1 Leverage and the Equity
Cost of Capital
Question 3, P.453
Parameters
r
rf
Unlevered Date 0
Value
Debt
Equity
Levered
Debt
Equity
Firm
10%
5%
Date 1: prob. Value
Date 1: prob. Return
Exp Return
80%
20%
80%
20%
40
50
20
0,25
-0,5
10%
19,05
20,95
40
20
30
50
20
0
20
0,05
0,43
0,05
-1
5%
14,55%
Double-click table to open Excel
14.2 Modigliani-Miller (MM) I:
Leverage, Arbitrage, and Firm Value
•
This section shows how MM relates to the Law
of One Price
• If:
1. Investors and firms can trade the same
securities in a competitive market
2. There are no taxes or transaction costs
3. A firm’s financing decision does not affect the
cash flows from its operations, then:
• MM Proposition 1: 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.
14.2 Modigliani-Miller (MM) I:
Leverage, Arbitrage, and Firm Value
•
•
•
•
MM argument is an application of the law of one
price (LOP).
The total amount of cash paid out to all the firm’s
security holders equals the total cash generate
by the firm’s assets.
By the LOP, the firm’s securities and assets
must have the same value.
As long as the firm’s financing decision does not
affect its cash flows from assets, the decision
can not affect the value of those assets.
Table 14.6 Replicating Levered Equity
Using Homemade Leverage
Suppose an investor wanted to earn a higher
expected return, and thus would prefer more
leverage. In this case, the investor can build that
leverage himself. This is called Homemade
Leverage.
Table 14.7 Replicating Unlevered
Equity by Holding Debt and Equity
Suppose the entrepreneur used debt, but the
equity holder wanted to reduce her risk and
expected return.
She could do this by buying debt from the firm,
recreating an unlevered payoff.
Example 14.2 Homemade
Leverage and Arbitrage
Example 14.2 Homemade
Leverage and Arbitrage
Question 4, p. 453
Suppose there are no taxes. Firm ABC has no debt, and firm XYZ has debt of $5000 on which it pays interest of 10% each
year. Both companies have identical. Fill in the table below showing the payments debt and equity holders of each firm will
receive given each of the two possible levels of free cash flows.
e cash flows could be replicated by
ng
ebt cash flows would be
quity cash flows would be
otal cash flows of
10,00% of the debt and
50,00
per year
30,00
or
80,00
or
10,00
50,00
50,00
100,00
ose you hold 10% of the equity of XYZ. If you can borrow at 10%, what is an alternative
equity in XYZ would
10,00% provide cash flows of
e cash flows could be replicated by
wing
would receive dividends of
ay interest of Double-click table
total cash flow of
30,00
to
or
500,00
and buying
80,00
or
open
(50,00 )Excel
per year
30,00
or
50,00
10,00
100,00
(50,00
50,00
Table 14.8 The Market Value
Balance Sheet of the Firm
Equation 14.1
Example 14.3 Valuing Equity
When There Are Multiple
Securities
Example 14.3 Valuing Equity
When There Are Multiple
Securities
Table 14.9 Market Value Balance Sheet
After Each Stage of Harrison’s Leveraged
Recapitalization ($ million)
Question: What happened to the risk and
required return for equity?
14.3 Modifliani-Miller II: Leverage, Risk, and
the Cost of Capital
• Why can’t we lower the overall cost-ofcapital by choosing a particular capital
structure?
• Next, we show that 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.
Equation 14.2
MM proposition 1 states that:
•E is the value of levered equity
•D is the value of debt,
•U is the value of unlevered equity
•A is the value of the firm’s assets
In words, we can use homemade leverage to
replicate any financing mix.
Equation 14.3
Thus, the realized return to unlevered
equity is:
•RE is the realized return to levered equity
•RD is the realized return to debt
•RU is the realized return to unlevered equity.
Equation 14.4
Rearranging Equation 14.3 gives us the
return to levered equity.
We see that by increasing leverage (D), we
magnify the RE relative to the unlevered
case, thus increasing risk. The increase is
proportional to the D-E ratio.
Equation 14.5 Cost of Capital of
Levered Equity
We can write this relationship in terms of
expected returns as well.
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 of the debt-toequity ratio.
Example 14.4 Computing the
Equity Cost of Capital
Example 14.4 Computing the
Equity Cost of Capital
Capital Budgeting and the WACC
• Suppose you are the CFO of Yahoo. You
want to calculate the value of a new
project – A social networking website for
coal miners.
• You estimate the expected cash flows, but
what is the appropriate cost-of-capital?
• One option, find a comparison business
whose assets have the same risk.
Equation 14.6
If the comparison business is unlevered
then,
You can use the unlevered equity cost of
capital to value your project.
But, what if the comparison firm is
levered?
Equation 14.7 Weighted Average Cost
of Capital (No Taxes)
From the homemade leverage argument, we know
that the return on the firm’s assets is not changed
by its capital structure (again assuming we are in a
no-market-imperfections world).
Thus, the cost-of-capital is the weighted average of
the firm’s equity and debt cost-of-capital – WACC.
Equation 14.8
•In a perfect market, a firm’s WACC is
independent of capital structure.
•It’s equal to the cost-of-capital of unlevered
equity, which equals the expected return on the
firm’s assets.
Example: two capital structures
Date 0
E
Date 1
Strong
Weak Strong Weak Ex. R
200
280
180
0.4
-0.1
0.15
Date 0
Date 1
Strong
Firm
Date 1 return
Date 1 return
Weak
Strong
Weak
Ex. R
200
280
180
0.40
-0.10
0.150
D
80
84
84
0.05
0.05
0.050
E
120
196
96
0.63
-0.20
0.216
What is the WACC of the restructured firm?
Figure 14.1 WACC and Leverage with
Perfect Capital Markets
As the fraction of the
firm financed with
debt increases, both
the equity and the
debt become riskier
and their cost of
capital rises. Yet,
because more
weight is put on the
lower-cost debt, the
weighted average
cost of capital
remains constant.
Example 14.5 Reducing Leverage and
the Cost of Capital
Example 14.5 Reducing Leverage and
the Cost of Capital
Example 14.6 WACC with Multiple Securities
Firm
Debt
Equity
Warrant
Today
1000
500
440
60
Strong
1400
525
665
210
Weak
900
525
375
0
Example 14.6 WACC with Multiple
Securities
Equation 14.9
Equation 14.10
Levered beta reflects increased risk
introduced by leverage.
Equation 14.11
If the firm’s debt is risk free, then we
can write:
We can see explicitly how leverage
amplifies the market risk of firm’s
equity.
This is one explanation why firms in
same industry have different BE.
Example 14.7 Airline Betas
Example 14.7 Airline Betas
Equation 14.12
Example 14.8 Cash and Beta
Example 14.8 Cash and Beta
14.4 Capital Structure Fallacies
• Leverage and Earnings per Share
• Equity, Issuances, and Dilution
Figure 14.2 LVI Earnings per Share with
and without Leverage
The sensitivity of EPS
to EBIT is higher for a
levered firm than for an
unlevered firm. Thus,
given assets with the
same risk, the EPS of a
levered firm is more
volatile.
Example 14.9 The MM Propositions and
Earnings per Share
Example 14.9 The MM Propositions and
Earnings per Share
14.5 MM: Beyond the
Propositions
• Nobel Prize: Franco Modigliani and Merton
Miller