Download Lecture Note One

Lecture Note 1
Valuation under MM
Corporate Finance Lecture Note 1
1
What is in This Note?
• Overview of Modigliani-Miller Proposition I
and II (No Tax)
• Overview of Modigliani-Miller Proposition I
and II (with Corporate Tax)
• Overview of Modigliani-Miller Proposition I
and II (with Corporate and Personal Tax)
• Overview of Modigliani-Miller Proposition I
and II (with Asymmetric Information)
Reference: Chapters 14, 15, and 16 of
Corporate
Finance
Lecture
Noteof
1
RWJJ, Chapters
17,
and
18
BMA
2
Roadmap
 Overview of Modigliani-Miller Propositions I and II
(No Taxes)
 Overview of Modigliani-Miller Propositions I and II
(with corporate Taxes)
 Overview of Modigliani-Miller Propositions I and II
(with both corporate and personal Taxes)
 Overview of Modigliani-Miller Propositions I and II
(with asymmetric information)
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MM Proposition I (No Taxes)
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Roadmap
 Overview of Modigliani-Miller Propositions I

Homemade Leverage and Leveraged Equity
 Assumption of Modigliani-Miller Propositions I
 Modigliani-Miller Propositions I
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Capital Structure and the Pie
• 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=D+E
• If the goal of the firm’s
management is to make the
firm as valuable as possible,
then could the firm pick the
debt-equity ratio that makes
the pie as big as possible?
Corporate Finance Lecture Note 1
S D
E
Value of the Firm
6
MM Proposition I (No Taxes)
Debt Policy is Irrelevant
• MM Proposition I (No Taxes)
– Assumption
– Intuition
– capital structure is irrelevant
E
S D
=
BB
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E
S
D
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Modigliani-Miller Proposition I (No
Taxes)
• The total value of the securities issued by
a firm is independent of the firm’s choice
of capital structure.
• The firm’s value is determined by its real
assets and growth opportunities, not by
the types of securities it issues.
*This is the very step Modigliani-Miller
results, and it holds in an idealized world.
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Assumptions under ModiglianiMiller Proposition I
• 1. Capital structure does not affect investment
policy
• 2. No taxes (corporate taxes, personal taxes, etc)
• 3 Bankruptcy is costless
• 4. Managers maximized shareholders’ (E) value,
not total firm value (the Pie, E+D).
• 5. Perfect and complete capital markets
• 6. Symmetric information (No black box)
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Intuition
• We can create a levered or
(un)levered position by adjusting
the trading in our own account.
• This homemade leverage
suggests that capital structure is
irrelevant in determining the value
of the firm:VL = VU
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Homemade Leverage: An Example
RecessionExpected 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) 3.0% 11.3% 19.7%
We are buying 40 shares of a $50 stock, using $800 in
margin. We get the same ROE as if we bought into a
levered firm.
D $800 2


Our personal debt-equity ratio is:
3
E $1,200
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• 公司的資產負債表/損益
表,
• 股東的資產負債表/損益
表
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Homemade (Un)Leverage: An
Example
RecessionExpected 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 otherwise identical levered firm
along with some of the firm’s debt gets us to the ROE of the
unlevered firm.
This is the fundamental insight of M&M
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• 公司的資產負債表/損益
表,
• 股東的資產負債表/損益
表
Corporate Finance Lecture Note 1
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In-Class Exercise
• Ross, Westerfield, and Jaffe Question 1 (pp. 449)
• Firm has a total market value of $150,000 under
no debt. EBIT (Earnings before interest and
taxes) is $14,000 under normal case and is 40%
higher if in expansion and is 70% lower when it
is recession. There are currently 2,500 shares
outstanding.
• 1. Calculate EPS (Earnings per share)
• 2.Repeat 1 when the firms issues $60,000 to
buyback the shares in the open market.
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In-Class Exercise
Shares repurchased = 1,000 shares ?
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Summary: MM Proposition I (No
Taxes)
 We can create a levered or unlevered
position by adjusting the trading in our own
account.
 This homemade leverage suggests that
capital structure is irrelevant in determining
the value of the firm:
VL = VU
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MM Proposition II (No Taxes)
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Roadmap
 MM Proposition I (No Taxes)



Equity risk increases wit the level of debt
Proof
Economic Intuition
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Modigliani-Miller Proposition II (No
Taxes)
• We denote the expected returns on assets, debt
and equity by RA, RD , and RE , respectively. Then
D
RE = RA +
(R A  R D )
E
Where D and E are the market values of debt and
equity and
EBIT
EBIT
RA =

Market value of total assets Market value of debt+equity
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Modigliani-Miller Proposition II (No
Taxes)
• Proof:
• Let total market value of the assets, debt, and
equity as A, D, and E, respectively
CFA
CFD  CFE
EBIT


A
A
A
by MMI, A=D+E, so
CFA
CFD  CFE
CFD
CFE
D
E


(
)
(
),
A
D+E
D
D+E
E
D+E
D
E
Thus, R A = R D (
)+R E (
)
D+E
D+E
Algebraic rearrangement gives the result
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Cost of capital: R (%)
MM Proposition II (No Taxes)
RE  RA 
D
 ( RA  RD )
E
RA
RA
RD
RD
Debt-to-equity Ratio D
E
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MM Proposition II (No Taxes)
• 1. Increasing the debt level does not affect
the riskiness of the assets, but it does
increase the riskiness of the equity
• In the same firm, RD is always less than RE,
This is because the debt has a higher
priority and this is less risky. But the
weighted sum of the returns of debt and
equity is always a constant, and is equal to
the return on assets, RA
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In-Class Exercise
• Please evaluate the following argument:
“ Equity is cheap because the firm does not
have to pay investors any dividends if it
does not want to.”
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In-Class Exercise: P/E ratio
• Firm X has expected revenues (or EBIT)
of $5 million per year. It has a capital
structure with $10 million in risk-free debt
paying 4% and 4 million shares which sell
at $10/share. This implies that firm value is
$50 million.
• 1. What are the RA, RD , and RE, and EPS
• 2. What is the P/E ratio?
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In-Class Exercise: P/E ratio
• RA= $5 /(40+10)=10%
D
R E = R A + (R A  R D )  10%  10 / 40*(10%  4%)  11.5%
E
EPS=(5-10*0.04)/4=$1.15/share
P/E=10/1.15=8.7
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Continued
• The CEO decides to boost the P/E ratio in
order to “increase shareholder value”. The
firm issues 1 million new shares at
$10/share and uses the proceeds to buy
back all its debt.
• What are the EPS and P/E ratio?
• Can you evaluate the firms based on the
P/E ratio and EPS?
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In-Class Exercise: P/E ratio
• EPS=(5-)/5=$1/share
P/E=10/1=10
• In evaluating firms, we must focus on
expected cash flows and risk, not P-E
ratios and earnings per share
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In-Class Exercise: Share repurchase
Profit Shares EPS
P/E ratio Share price (per
share)
500
8
100
5
40
• The firm now repurchases 20 shares.
Profit Shares EPS
500
80
6.25
P/E ratio Share price (per
share)
6.4
40
•Can you evaluate the firms based on the P/E ratio and EPS?
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Corporate Taxes and Firm
Value
MM Propositions I and II (with
Corporate Taxes)
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Roadmap
 Corporate Tax Shield
 MM Propositions I and II (with Taxes)
 The implication of optimal debt level under
MM Propositions I and II (with Taxes)
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Capital Structure & Corporate
Taxes
The tax deductibility of interest increases the total distributed
income to both bondholders and shareholders.
Income
Statement of
Firm U
Earnings before interest and taxes
Interest paid to bondholders
Pretax income
Tax at 35%
Net income to stockholders
Total income to both bondholders and
stockholders
$1,000
1,000
350
650
$0+650=$650
Interest tax shield (.35 x interest)
Corporate Finance Lecture Note 1
$0
Income
Statement of
Firm L
$1,000
80
920
322
598
$80+598=$678
$28
32
Corporate Taxes and Value
Interest Tax Shield
• Corporate Taxes Shied: Tax savings
resulting from deductibility of interest
payments.
• More interest payments, more tax savings.
What is the optimal level of debt?
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MM Proposition I (With Taxes)
The total cash flow to debt holders, and equity holders
( EBIT  RD D )  (1  TC )  RD D
The present value of this stream of cash flows is VL
Clearly ( EBIT  RD D)  (1  TC )  RD D 
 EBIT  (1  TC )  RD D  (1  TC )  RD D
 EBIT  (1  TC )  RD D  RD DTC  RD D
The present value of the first term is VU
The present value of the second term is TCD
 VL  VU  TC D
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MM Proposition I (With Taxes)
The present value of this stream of cash flows RD DTc is DTc
Assuming that: (1) the the positive tax bracket is perpetual and
(2) assume that the it has the same risk as the interest on the debt
RD DTc
 DTc
RD
The present value of this stream of cash flows EBIT  (1  TC ) is VU
Assuming that: (1) the the EBIT is perpetual and
(2) RA : The cost of capital to an all-equity firm.
EBIT  (1  TC )
 VU
RA
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All equity-firm and levered firm
Taxes
Equity
TAXES
Equity
Corporate Finance Lecture Note 1
Debt
36
MM Proposition II (With Taxes)
• We denote the expected returns on assets, debt
and equity by RA, RD , and RE, respectively. Then
D
R E = R A + (1  TC )(R A  R D )
E
Where D and E are the market values of debt and
equity and
EBIT
EBIT
RA =

Market value of total assets Market value of debt+equity
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MM Proposition II (With Taxes)
• Proof:
• Let total market value of the assets, debt, and equity as A, D, and
E, respectively
by MMI with taxes, VL =D+E=VU +TC D, soVU  E +(1-TC )D
EBIT(1  TC )
D+E CFD  (EBIT-CFD )(1  TC )
D+E CFDTC

(
)
(
)
VU
VU
D+E
VU
D+E
D+E CFD (1  TC )
D
D+E CFE
E
(
)
(
),
VU
D
D+E
VU
E
D+E
Thus, R A =
D
E
(1  TC )R D +R E (
)
VU
VU
Algebraic rearrangement gives the result
RE (
V
E
D
D
)  RA 
(1  TC )R D , R E  R A U 
(1  TC )R D
VU
VU
E
E
Plug in VU  E +(1-TC )D, R E  R A 
D
(1  TC )(R A -R D )
E
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MM Proposition II (with Taxes)
• 1. Increasing the debt level does not affect
the riskiness of the assets, but it does
increase the riskiness of the equity
• In the same firm, RD is always less than RE,
This is because the debt has a higher
priority and this is less risky. But the
weighted sum of the returns of debt and
equity is always a constant, and is equal to
the return on assets, RA
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MM Proposition I and II (With Taxes)
Firm Value =
Value of All Equity Firm + PV Tax Shield
Cost of equity capital
D
R E = R A + (1  TC )(R A  R D )
E
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Tax Shield Effect
Value of firm under
MM with corporate
taxes and debt
Value of firm (V)
Present value of tax
shield on debt
VL = VU + TCD
Maximum
firm value
VU = Value of firm with no debt
0
Debt (D)
D*
Optimal amount of debt
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In-Class Exercise
• Ross, Westerfield, and Jaffe Question 2 (pp. 449)
• Firm has a total market value of $150,000 under
no debt. EBIT (Earnings before interest and
taxes) is $14,000 under normal case and is 40%
higher if in expansion and is 70% lower when it
is recession. The corporate tax rate is 40%.
There are currently 2,500 shares outstanding.
• 1. Calculate EPS (Earnings per share)
• 2.Repeat 1 when the firms issues $60,000 to
buyback the shares in the open market. Debt
pays 5% interest.
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EBIT
Interest
Taxes
NI
EPS
%EPS
Recession
Normal
Expansion
$4,200
$14,000
$19,600
0
0
0
1,680
5,600
7,840
$2,520
$8,400
$11,760
$1.01
$3.36
$4.70
–70
–––
+40
Recession
Normal
Expansion
$4,200
$14,000
$19,600
3,000
3,000
3,000
480
4,400
6,640
NI
$720
$6,600
$9,960
EPS
$.48
$4.40
$6.64
–89.09
–––
+50.91
EBIT
Interest
Taxes
%EPS
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Corporate Taxes and Firm
Value under the Presence of
Financial Distress Costs
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Roadmap
 What are the costs of financial distress?
 What are the direct and indirect costs of
financial distress
 The implication of optimal debt level under
MM Propositions I and II with significant costs
of financial distress
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Corporate Taxes and Firm Value
Interest Tax Shield
Financial Distress Ccosts
Costs of Financial Distress - Costs arising from
bankruptcy or distorted business decisions before
bankruptcy.
•Direct Costs: Legal and administrative costs
•Indirect Costs: Impaired ability to conduct
business (e.g., lost sales)
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Financial Distress
Costs of Financial Distress - Costs arising from
bankruptcy or distorted business decisions
before bankruptcy.
Market Value = Value if all Equity Financed
+ PV Tax Shield
- PV Costs of Financial
Distress
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Tax Savings 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 + TCD
Maximum
firm value
Present value of
financial distress costs
V = Actual value of firm
VU = Value of firm with no debt
0
Debt (D)
D*
Optimal amount of debt
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Capital Structure and the Pie
Model Revisited
• Taxes and bankruptcy costs can be viewed as just
another claim on the cash flows of the firm.
• Let G and L stand for payments to the government
and bankruptcy lawyers, respectively.
• VT = E + D + G + L
E
D
L
G
• The essence of the M&M intuition is that VT depends on the
cash flow of the firm; capital structure just slices the pie.
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Taxes and Firm Value
MM Proposition I (with
Corporate Taxes and Personal
Taxes)
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Personal Taxes and Firm Value
• Interest payments are only taxed at the
individual level since they are tax
deductible by the corporation, so the
bondholder receives: (1-TB)
• Dividends face double taxation (firm and
shareholder), which suggests a
stockholder receives the net amount: (1-TC)
x (1-TS)
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Personal Taxes
• If TS= TB then the firm should be financed
primarily by debt (avoiding double tax).
• The firm is indifferent between debt and
equity when:
(1-TC) x (1-TS) = (1-TB)
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Asymmetric Information and Firm
Value
Stock-for-debt
exchange offers
Stock price falls
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New Equity Issues
• Background information:
1. There are two equally probable states of
nature. The true state is revealed to
management at t=0 and to investors at t=1.
2. The firm has no cash and the firms want to
issue stock to raise $100.
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New Equity Issues
Good
Bad
No New Equity
$250
$130
Corporate Finance Lecture Note 1
Issue New Equity
$350
$230
58
New Equity Issues
Questions:
 What is the firm’s expected value, with or without
new equity issue?
 With new equity issue, what is the firm’s expected
value that the old shareholders get, if the state is
Good and if the state is Bad?
 If the managers have superior information about
the firm’s prospect, should they issue new equity
when the state is Good?
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New Equity Issues
Firm Value (Issue no new equity) =
(0.5)(250 + 130) = $190
Firm Value (New equity) =
(0.5)(350 + 230) = $290
Note that old shareholders have a claim to the
portion (190/290), or 65.5% of the value of the
firm if it issues new equity.
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New Equity Issues
Thus, if the firm issues equity and the
state is good, old shareholders are worth:
(190/290)(350) = $229.31
And, if the firm issues equity and the
state is bad, old shareholders are worth:
(190/290)(230) = $150.69
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New Equity Issues
Let’s pull these numbers together, and see what
happens if the management knows that the
state is likely to be good or bad, and they are
acting on behalf of the old shareholders:
Old shareholder payoffs:
Good news
Bad news
Do Nothing
$250.00
$130.00
Corporate Finance Lecture Note 1
Issue Equity
$229.31
$150.69
62
New Equity Issues
• The equilibrium payoffs:
Do Nothing
Equity
• Good news
• Bad news
Issue
$250.00
$230
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New Equity Issues
The optimal strategy for old equity is to not
issue equity if they know state will be good,
and issue equity if the state will be bad!
But, markets can figure this out too: As a
result, they will knock down the value of the
firm when a new equity is announced!
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Conclusion
• What are the Modigliani-Miller Propositions I and
II under perfect world?
• What are the implications of optimal debt level
under Modigliani-Miller Propositions I and II?
• What are the Modigliani-Miller Propositions I and
II with corporate taxes?
• What are the implications of optimal debt level
under Modigliani-Miller Propositions I and II with
corporate taxes?
• Why the stock price drops when there is an
Stock-for-debt exchange offer?
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