Corporate Finance
Lecture 8
Announcements

2nd quiz
– Opens at midnight tonight
– Valid for 48 hours
– Closes at midnight of Thursday

2nd case : Boeing 7E7
– Questions will be posted on May 8
– Delivery deadline: May 13
– Discussion: May 15
Topics covered



MM proposition without tax
MM proposition with tax
Cost of financial distress
– Direct cost
– Indirect cost


Reducing cost of debt
Integration of tax benefit and financial
distress cost of debt
Modigliani and Miller (MM)
Proposition (no taxes)

Proposition I
– Firm value is not affected by leverage
VL = VU

Capital structure does not change firm
value
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
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
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
0
$2,000
$5.00
10%
10%
Expansion
$3,000
0
$3,000
$7.50
15%
15%
Expected
$2,000
640
$1,360
$5.67
10%
11%
Expansion
$3,000
640
$2,360
$9.83
15%
20%
Homemade Leverage:
An Example
EPS of Levered Firm
Earnings for 24 shares
Recession
Expected
Expansion
$1.50
$5.67
$9.83
$36
$136
$236
Homemade Leverage:
An Example
Recession Expected
Expansion
EPS of Unlevered Firm
$2.50
$5.00
$7.50
Earnings for 40 shares
Less interest on $800 (8%)
Net Profits
ROE (Net Profits / $1,200)
$100
$64
$36
3%
$200
$64
$136
11%
$300
$64
$236
20%
Buying 40 shares of a $50 stock, 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
The MM Propositions II (No Taxes)

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
The MM Proposition II (No Taxes)
The derivation is straightforward:
rWACC =
B
S
´ rB +
´ rS
B +S
B +S
B
S
´ rB +
´ rS = r0
B +S
B +S
Then set rWACC = r0
B +S
multiply both sides by
S
B +S
B
B +S
S
B +S
´
´ rB +
´
´ rS =
r0
S
B +S
S
B +S
S
B
B +S
´ rB + rS =
r0
S
S
B
B
´ rB + rS = r0 + r0
S
S
rS = r0 +
B
(r0 - rB )
S
Cost of capital: r (%)
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
B
Debt-to-equity Ratio S
The MM Proposition I (Corp. Taxes)
Shareholde rs in a levered firm receive
Bondholders receive
( EBIT - rB B ) ´ (1 - TC )
rB B
Thus, the total cash flow to all stakeholde rs is
( EBIT - rB B ) ´ (1 - TC ) + rB B
The present value of this stream of cash flows is VL
( EBIT - rB B ) ´ (1 -TC ) + rB B =
= EBIT ´ (1 -TC ) - rB B ´ (1 -TC ) + rB B
= EBIT ´ (1 -TC )
The present value of the first term is VU
The present value of the second term is TCB
+ rB BTC
\VL = VU +TC B
The MM Proposition II (Corp. Taxes)
Start with M&M Proposition I with taxes:
Since
VL = S + B
VL =VU +TC B
 S + B = VU +TC B
VU = S + B(1 -TC )
The balance sheet of a levered firm can be written as
Vu=Value of
unlevered firm
B=Debt
TcB=Tax shield
S=Equity
The MM Proposition II (Corp. Taxes)
The cash flows from each side of the balance sheet must equal:
SrS + BrB =VU r0 +TC BrB
SrS + BrB = [S + B(1 -TC )]r0 +TC rB B
Divide both sides by S
rS +
B
B
B
=
+
+
rB [1
(1 TC )]r0
TC rB
S
S
S
Which reduces to
rS = r0 +
B
´ (1 -TC ) ´ (r0 - rB )
S
The Effect of Financial Leverage on the Cost of
Debt and Equity Capital with Corporate Taxes
Cost of capital: r
(%)
rS = r0 +
rS = r0 +
B
 (r0 - rB )
SL
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
Expected
$2,000
0
$2,000
$700
Expansion
$3,000
0
$3,000
$1,050
$650
$1,300
$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+$224
$874
Tax effect of debt



In a world without taxes, debt does not affect firm
value.
When there are corporate taxes, the firm value is
positively related to its debt --Debt reduces the
firm’s tax liability
With taxes, the sum of the debt plus the equity of
the levered firm is greater than the equity of the
unlevered firm.
Total Cash Flow to Investors
All-equity firm
S
G
Levered firm
S
G
B
This is how cutting the pie differently can
make the pie larger: the government takes a
smaller slice of the pie!
Costs of financial distress


Direct costs: Legal and administrative
costs
Indirect costs:
– Impaired ability to conduct business
– Agency costs: conflicts between the
shareholders and the debtholders
Incentive to take large risks
 Incentive toward underinvestment
 Milking the property

Balance Sheet for a Company in Distress
Assets
BV MV
Cash
$200 $200
Fixed Asset$400 $0
Total
$600 $200
Liabilities BV MV
LT bonds $300 $200
Equity
$300 $0
Total
$600 $200
What happens if the firm is liquidated today?
The bondholders get $200; the shareholders get nothing.
Selfish Strategy 1: Take Large Risks
The Gamble
Win Big
Lose Big
Probability
10%
90%
Payoff
$1,000
$0
Cost of investment is $200 (all the firm’s cash)
Required return is 50%
Expected CF from the Gamble = $1000 × 0.10 + $0 =
$100
$100
NPV = –$200 +
(1.50)
NPV = –$133
Selfish Stockholders Accept Negative
NPV Project with Large Risks

Expected CF from the Gamble
– To Bondholders = $300 × 0.10 + $0 = $30
– To Stockholders = ($1000 – $300) × 0.10 + $0 = $70
PV of Bonds Without the Gamble = $200
PV of Stocks Without the Gamble = $0

PV of Bonds With the Gamble:

PV of Stocks With the Gamble:

Debtholder expropriation by shareholders


$30
$20 =
(1.50)
$70
$47 =
(1.50)
Selfish Strategy 2: Underinvestment





Consider a government-sponsored project that
guarantees $350 in one period
Cost of investment is $300
the firm only has $200 now
the stockholders will have to supply an additional
$100 to finance the project
$350
Required return is 10% NPV = –$300 + (1.10)
NPV = $18.18
Should we accept or reject?
Selfish Strategy 2: underinvestment
Firm
Without PV
project
With
project
CF at
t=1
PV
Debt
Equity
Selfish Strategy 2: Underinvestment
Firm
Debt
Equity
Without PV
project
200
200
0
With
project
CF at
t=1
350
300
50
PV
-100
-300
-200
+350/1.1 +300/1.1 +50/1.1
=18.18
=72.73 =-54.55
Selfish Strategy 3: Milking the Property


Liquidating dividends
Increase perquisites to shareholders
and/or management
Protective Covenants



Agreements to protect bondholders
Negative covenant:
– Pay dividends beyond specified amount.
– Sell more senior debt & amount of new debt is
limited.
Positive covenant:
– Maintain good condition of assets.
– Provide audited financial information.
– Working capital requirement.
Integration of Tax Effects
and Financial Distress Costs
Value of firm under
MM with corporate
taxes and debt
Value of firm (V)
Present value of tax
shield on debt
VL = VU + TCB
Present value of
financial distress costs
Maximum
firm value
V = Actual value of firm
VU = Value of firm with no debt
0
Debt (B)
B*
Optimal amount of debt
The Pie Model

VT = S + B + G + L
S
B
L


Marketed claims: VM = S + B
Nonmarketed claims: VN = G + L
G
Signaling



The firm’s capital structure is
optimized where the marginal subsidy
to debt equals the marginal cost.
Investors view debt as a signal of firm
value.
A manager that takes on more debt
than is optimal in order to fool
investors will pay the cost in the long
run.