Introduc corporate finance ch15

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
Debt
Equity
Debt/Equity ratio

$20,000
$0
$20,000
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
Recession

Expected

Expansion

$1,000

$2,000

$3,000

0

0

0

$1,000

$2,000

$3,000

EPS

$2.50

$5.00

$7.50

ROA

5%

10%

15%

ROE

5%

10%

15%

EBIT
Interest
Net income

Current Shares Outstanding = 400 shares


EPS and ROE Under Proposed
Capital Structure
Recession

Expected

Expansion

$1,000

$2,000

$3,000

640

640

640

Net income

$360

$1,360

$2,360

EPS

$1.50

$5.67

$9.83

ROA

5%

10%

15%

ROE

3%

11%

20%

EBIT
Interest

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

Expected

Expansion

$1,000

$2,000

$3,000

640

640

640

Net income

$360

$1,360

$2,360

EPS

$1.50

$5.67

$9.83

ROA

5%

10%

15%

ROE

3%

11%

20%

EBIT
Interest

Proposed Shares Outstanding = 240 shares


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 ModiglianiMiller 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

$1.50

$5.67

$9.83

Earnings for 24 shares

$36

$136

$236

Plus interest on $800 (8%)

$64

$64

$64

$100

$200

$300

5%

10%

15%

EPS of Levered Firm

Net Profits
ROE (Net Profits / $2,000)

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 +

rWACC =

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 = VU



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 = V U + 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

rWACC =

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

Levered
Recession

Expected

Expansion

$1,000

$2,000

$3,000

640

640

640

EBT

$360

$1,360

$2,360

Taxes (Tc = 35%)

$126

$476

$826

$234+640

$468+$640

$1,534+$640

$874

$1,524

$2,174

$650+$242

$1,300+$224

$1,950+$224

$874

$1,524

$2,174

EBIT
Interest ($800 @ 8% )

Total Cash Flow
(to both S/H & B/H):
EBIT(1-Tc)+TCrBB


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
EBIT

Levered
$1,000

$1,000

Interest

-50 (rB*B)

EBT

1,000

950

Tax (0%)
Net Income 1,000
CF(B+S)

$1,000

950
$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
EBIT

Levered

$1,000

$1,000

Interest

-50

EBT
Tax(34%)
Net Income
CF(B+S)

1,000
-340
660
$660

950
-323
627
$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