Capital Structure
15.1 The Capital-Structure Question and The Pie
Theory
15.2 Maximizing Firm Value versus Maximizing
Stockholder Interests
15.3 Financial Leverage and Firm Value: An Example
15.4 Modigliani and Miller: Proposition II (No Taxes)
15.5 Taxes
15.6 Summary and Conclusions
The Capital-Structure Question and The Pie
Theory


The value of a firm is defined to be the sum
of the value of the firm’s debt and the firm’s
equity.
V=B+S
• If the goal of the management
of the firm is to make the firm as
valuable as possible, the the firm
should pick the debt-equity ratio
that makes the pie as big as
possible.
S
B
Value of the Firm
The Capital-Structure Question
There are really two important questions:
1. Why should the stockholders care about
maximizing firm value? Perhaps they should be
interested in strategies that maximize shareholder
value.
2. What is the ratio of debt-to-equity that maximizes
the shareholder’s value?
As it turns out, changes in capital structure benefit the
stockholders if and only if the value of the firm
increases.
Financial Leverage, EPS, and ROE
Consider an all-equity firm that is considering going into debt.
(Maybe some of the original shareholders want to cash out.)
Current
Assets
$20,000
Debt
$0
Equity
$20,000
Debt/Equity ratio
0.00
Interest rate
n/a
Shares outstanding
400
Share price
$50
Proposed
$20,000
$8,000
$12,000
2/3
8%
240
$50
EPS and ROE Under Current Capital
Structure
EBIT
Interest
Net income
EPS
ROA
ROE
Recession
$1,000
0
$1,000
$2.50
5%
5%
Expected Expansion
$2,000
$3,000
0
0
$2,000
$3,000
$5.00
$7.50
10%
15%
10%
15%
Current Shares Outstanding = 400 shares
EPS and ROE Under Proposed Capital
Structure
EBIT
Interest
Net income
EPS
ROA
ROE
Recession
$1,000
640
$360
$1.50
5%
3%
Expected Expansion
$2,000
$3,000
640
640
$1,360
$2,360
$5.67
$9.83
10%
15%
11%
20%
Proposed Shares Outstanding = 240 shares
EPS and ROE Under Both Capital Structures
All-Equity
Recession
EBIT
$1,000
Interest
0
Net income
$1,000
EPS
$2.50
ROA
5%
ROE
5%
Current Shares Outstanding = 400 shares
Expected
$2,000
0
$2,000
$5.00
10%
10%
Expansion
$3,000
0
$3,000
$7.50
15%
15%
Levered
Recession
EBIT
$1,000
Interest
640
Net income
$360
EPS
$1.50
ROA
5%
ROE
3%
Proposed Shares Outstanding = 240 shares
Expected
$2,000
640
$1,360
$5.67
10%
11%
Expansion
$3,000
640
$2,360
$9.83
15%
20%
Financial Leverage and EPS
12.00
Debt
10.00
EPS
8.00
6.00
4.00
No Debt
Advantage
to debt
Break-even
point
2.00
0.00
1,000
(2.00)
Disadvantage
to debt
2,000
3,000
EBIT
EBI in dollars, no taxes
Assumptions of the Modigliani-Miller
Model




Homogeneous Expectations
Homogeneous Business Risk Classes
Perpetual Cash Flows
Perfect Capital Markets:





Perfect competition
Firms and investors can borrow/lend at the same rate
Equal access to all relevant information
No transaction costs
No taxes
Homemade Leverage: An Example
Recession Expected Expansion
EPS of Unlevered Firm
$2.50
$5.00
$7.50
Earnings for 40 shares
$100
$200
$300
Less interest on $800 (8%)
$64
$64
$64
Net Profits
$36
$136
$236
ROE (Net Profits / $1,200)
3%
11%
20%
We are buying 40 shares of a $50 stock on margin. We get the
same ROE as if we bought into a levered firm.
Our personal debt equity ratio is:
B $800 2


3
S $1,200
Homemade (Un)Leverage: An Example
Recession Expected Expansion
EPS of Levered Firm
$1.50
$5.67
$9.83
Earnings for 24 shares
$36
$136
$236
Plus interest on $800 (8%)
$64
$64
$64
Net Profits
$100
$200
$300
ROE (Net Profits / $2,000)
5%
10%
15%
Buying 24 shares of an other-wise identical levered firm along with
the some of the firm’s debt gets us to the ROE of the unlevered firm.
This is the fundamental insight of M&M
The MM Propositions I & II (No Taxes)

Proposition I


Firm value is not affected by leverage
VL = VU
Proposition II

Leverage increases the risk and return to stockholders
rs = r0 + (B / SL) (r0 - rB)
rB is the interest rate (cost of debt)
rs is the return on (levered) equity (cost of equity)
r0 is the return on unlevered equity (cost of capital)
B is the value of debt
SL is the value of levered equity
Cost of capital: r (%)
The Cost of Equity, the Cost of Debt, and the Weighted Average
Cost of Capital: MM Proposition II with No Corporate Taxes
r0
rS  r0 
rW ACC 
B
 (r0  rB )
SL
B
S
 rB 
 rS
BS
BS
rB
rB
Debt-to-equity Ratio B
S
Implications of the MM No-Tax
Propositions




Capital structure is irrelevant in an MM world
without corporate taxes.
VL = V U
The value of the firm (“size of the pie”) is
determined by the firm’s capital budgeting
decisions. Capital structure determines only
how the pie is sliced.
Increasing the extent to which a firm relies on
debt increases both the risk and the expected
return to equity – but not the price per share.
The MM Propositions I & II (with Corporate Taxes)

Proposition I (with Corporate Taxes)

Firm value increases with leverage
VL = VU + T C B

Proposition II (with Corporate Taxes)

Some of the increase in equity risk and return is offset by
interest tax shield
rS = r0 + (B/S)×(1-TC)×(r0 - rB)
rB is the interest rate (cost of debt)
rS is the return on equity (cost of equity)
r0 is the return on unlevered equity (cost of capital)
B is the value of debt
S is the value of levered equity
The Effect of Financial Leverage on the Cost
of Debt and Equity Capital
Cost of capital: r
(%)
rS  r0 
B
 (1  TC )  (r0  rB )
SL
r0
rW ACC 
B
SL
 rB  (1  TC ) 
 rS
BSL
B  SL
rB
Debt-to-equity
ratio (B/S)
Total Cash Flow to Investors Under
Each Capital Structure with Corp. Taxes
All-Equity
EBIT
Interest
EBT
Taxes (Tc = 35%
Total Cash Flow to S/H
Recession
$1,000
0
$1,000
$350
$650
Expected
$2,000
0
$2,000
$700
$1,300
Expansion
$3,000
0
$3,000
$1,050
$1,950
Expected
$2,000
640
$1,360
$476
$468+$640
$1,524
$1,300+$224
$1,524
Expansion
$3,000
640
$2,360
$826
$1,534+$640
$2,174
$1,950+$224
$2,174
Levered
EBIT
Interest ($800 @ 8% )
EBT
Taxes (Tc = 35%)
Total Cash Flow
(to both S/H & B/H):
EBIT(1-Tc)+TCrBB
Recession
$1,000
640
$360
$126
$234+640
$874
$650+$242
$874
Total Cash Flow to Investors Under
Each Capital Structure with Corp. Taxes
All-equity firm
S
G
Levered firm
S
G
B
The levered firm pays less in taxes than does the allequity firm.
Thus, the sum of the debt plus the equity of the levered
firm is greater than the equity of the unlevered firm.
An Example (no taxes):

Imagine you have discovered an investment
alternative which produces expected EBIT of $1,000
forever. Similar (unlevered) projects in the market
have a required return r0 of 10%. You must put up
$5,000 of your own money to invest in this project.

You have two financing alternatives:


Unlevered: you issue yourself $5,000 in equity, SU
Levered: you sell yourself $1,000 debt, B, and $4,000
equity S. The debt pays the market rate rB of 5%.
Example, continued

Annual cash flows, depending on your choice
of financing, are:
Unlevered
Levered
EBIT
$1,000
$1,000
Interest
-50 (rB*B)
EBT
1,000
950
Tax (0%)
Net Income 1,000
950
CF(B+S) $1,000
$1,000
Example continued,
Proposition I:
VU=SU=EBIT/r0 = $1,000/.1=$10,000
VL= B + S = $10,000
S = $10,000 - $1,000 = $9,000

Example, continued





Proposition II:
rS = r0 + (B/S)(r0 - rB )
r0 = .10 + ($0/$10,000)(.10-.05) = 10%
rS = .10 +($1,000/$9,000)(.10-.05)=10.56%
WACC = (1,000/10,000)(5%) +
(9,000/10,000)(10.56%) = 10% = r0
An Example of MM Propositions I & II
with Corporate Taxes

Consider the same investment and financing
alternatives as for the no tax example, but now TC =
34%,
Unlevered
Levered
EBIT
$1,000
$1,000
Interest
-50
EBT
1,000
950
Tax(34%)
-340
-323
Net Income
660
627
CF(B+S)
$660
$677
A Debt versus Equity Problem

The market value of a firm that has $500,000
in debt is $1,700,000. The expected value of
EBIT is a perpetuity. The interest rate on
debt (pretax) is 10%. The company is
subject to a 34% tax rate. If the company
were 100% equity financed, the equity
holders would have a 20% required return.
What is the net income of the firm? What
would be the market value of the firm if it
were 100% equity financed?
Example Continued






VL=VU + TCB
$1,700 = VU + (.34)*($500)
=> VU =$1,530
VU = EBIT (1- TC )/r0
$1,530 = EBIT *(1-.34)/.2
=> EBIT = $463, 636
Summary: No Taxes


In a world of no taxes, the value of the firm is
unaffected by capital structure.
This is M&M Proposition I:
VL = VU

Prop I holds because shareholders can achieve any
pattern of payouts they desire with homemade
leverage.

In a world of no taxes, M&M Proposition II states that
leverage increases the risk and return to stockholders
B
rS  r0   (r0  rB )
SL
Summary: Taxes




In a world of taxes, but no bankruptcy costs, the value of the firm
increases with leverage.
This is M&M Proposition I:
VL = VU + TC B
Prop I holds because shareholders can achieve any pattern of
payouts they desire with homemade leverage.
In a world of taxes, M&M Proposition II states that leverage
increases the risk and return to stockholders.
B
rS  r0   (1  TC )  (r0  rB )
SL
Bankruptcy Costs




So far, we have seen M&M suggest that financial
leverage does not matter, or imply that taxes cause
the optimal financial structure to be 100% debt.
In the real world, most executives do not like a
capital structure of 100% debt because that is a
state known as “bankruptcy”.
In the next chapter we will introduce the notion of a
limit on the use of debt: financial distress.
The important use of this chapter is to get
comfortable with “M&M algebra”.