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FINM 7402 MM Theory of Capital Structure
创建日期：2024-06-01 15:47:10
所属分类：金融Finance
标签： FINM 7402
MM Theory of Capital Structure

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FINM 7402 Corporate Finance (Advanced)

MM Theory of Capital Structure
Week 2
Reading: Chapter 14
CRICOS code 00025B
• CAPM:
• Regress asset excess return (Ri – Rf) on market excess return (Rm- Rf).
• Estimate a company’s cost of equity using the CAPM equation
• Estimate the cost of debt, given a company’s yield to maturity (y), probability
of default (p), and expected loss rate (L).
rd = (1 - p)y + p(y - L) = y - pL
= Yield to Maturity – Prob(default) * Expected Loss Rate
• Estimate a company’s cost of debt using the CAPM equation
Recall Week1 …
2
ri=rf +βi × (E[RMkt ]-rf )
FINM7402
( ) ( ) i f i i Mkt f iR r R r− = + − +α β ε
CRICOS code 00025B
• Cost of equity capital: , β = + β∗ E −
• Cost of debt capital: , β
= + β∗ E −
• Asset cost of capital: , β
Firm beta as weighted average: the beta of a firm is the weighted average of the betas of its
individual components
β: unlevered beta , asset beta, also commonly denoted as β
β: levered beta, equity beta , also commonly denoted as β
Recall Week1 …
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DEA ED
D
ED
E βββ
+
+
+
=
DEA rED
Dr
ED
Er
+
+
+
=
CRICOS code 00025B
Practice
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CRICOS code 00025B
Solution
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CRICOS code 00025B
• 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
• Based on expected business cash flows, the value of the firm is
= �
=1

(1+)
Capital Structure and the Pie
If the goal of the firm’s management is to
make the firm as valuable as possible,
then the firm should pick the debt-equity
ratio that makes the pie as big as
possible.
Value of the Firm
S DE
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DEA rED
Dr
ED
Er
+
+
+
=
CRICOS code 00025B
• Definition
How a business (firm) finances its overall operations and growth by using
different sources of funds, eg, debt, equity, etc.
• Optimal capital structure [the big question!]
The capital structure which maximizes the value of a company.
• Does the value of the cash flows depend on how it is divided between
payments to lenders and shareholders?
Background on Capital Structure
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CRICOS code 00025B
• a perfect market with no taxes
• a slightly less perfect market with taxes
• a world in which the costs of financial distress matter
• a world with other transactions costs
• a world with conflicts of interest between managers and shareholders, or
debtholders and shareholders
The answer depends on the ‘world’ we are in
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CRICOS code 00025B
A perfect market with no taxes or any of the other imperfections listed in
previous slide.
Assumptions:
• Homogeneous Expectations
• Perpetual Cash Flows
• Perfect Capital Markets:
o Perfect competition
o Firms and investors can borrow/lend at the same rate
o Equal access to all relevant information
o No transaction costs
o No taxes
Modigliani & Miller Analysis (MM)
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CRICOS code 00025B
• The market value of any firm is independent of its capital structure.
If a company has a given set of assets, changing debt to equity will change the way
net operating income is divided between lenders and shareholders but will not
change the value of the company.
VL = VU = E + D
Financial decisions are irrelevant for firm value. In particular, the choice of
capital structure is irrelevant.
Proof:
All purely financial transactions are zero NPV investments, i.e., no arbitrage
opportunity. Thus, they neither increase nor decrease firm value.
MM’s Proposition I
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CRICOS code 00025B
• MM theory is established based on the Law of One Price: in a perfect capital market, the
firm’s choice of capital structure does not change the cash flows generated by its assets,
hence, the capital structure decision will no change the value of the firm.
• Two firms producing the same cash flows must have the same value --- No arbitrage
• If not, it is an “arbitrage opportunity”: possible to generate a riskless profit that requires no
initial investment:
- buy the one with the low price,
- sell the one with the high price,
- keep the difference in prices,
- future cash flows will cancel out
• Competition among investors should drive any arbitrage opportunities out of the market
Proof by Arbitrage
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CRICOS code 00025B
• Two firms, U and L.
• Firm U is unlevered and Firm L is levered.
• Firm L has borrowed $4,000,000 at 7.5%.
• Both firms make a profit of $900,000 --- producing same cash flows.
• Required equity return is 10% [insensitive to risk, violate MM].
Arbitrage Example
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CRICOS code 00025B
Firm U (Unlevered):
• Value of equity =
• Value of firm =
Arbitrage Example
=
$900,000 $9,000,000
0.10
+ = + =$9M 0 $9MD E
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CRICOS code 00025B
Firm L (Leveraged):
value of firm =
Leverage create value ?!
Arbitrage Example
−
=
=
$900,000 $300,000value of equity
0.1
$6,000,000
= ×
=
interest expense 0.075 $4,000,000
$300,000
+ = + =$6M $4M $10MD E
FINM7402 14
CRICOS code 00025B
• Arbitrager: sells 10% of Firm L and buys Firm U with the cash raised
• Firm L: VL = $10M, 60% Equity + 40%Debt
• 10% Firm L = $1M, 60% Equity ($0.6m) + 40%Debt ($0.4M)
In other words, the arbitrager raised $1M cash by selling $0.6M equity of firm L
and borrowing $0.4M of debt (with debt interest 7.5%).
The Arbitrage Process
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CRICOS code 00025B
• Work out the return if all of these funds are invested in the Firm U:
• This is a gross return and does not factor in costs.
= ×
=
1,000,000Return $900,000
9,000,000
$100,000
The Arbitrage Process
FINM7402 16
CRICOS code 00025B
• Work out the net return:
• Return from unlevered firm $100,000
• less Interest on borrowings $ 30,000 ( 7.5%*400,000)
• less cost to L equity holders $ 60,000 ( 10%*600,000)
• Net return $ 10,000 p.a.
• This represents a riskless income of $10,000 per year.
The Arbitrage Process
FINM7402 17
CRICOS code 00025B
• As the arbitraging process goes, selling L to buy U, it eventually pushes
down the value of firm L and push up the value of firm U, until VL = VU
• Equity return on firm L increases to beyond 10% , and equity return on firm U
will be lower than 10%. Leverage increase equity risk and hence equity
return.
The Arbitrage Process
What does this imply for the equity return on levered
firms vs. unlevered firms?
FINM7402 18
CRICOS code 00025B
MM Proposition I
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Debt-to-equity Ratio
C
os
t o
f c
ap
ita
l:
R
(%
)
RU
E
D
• Recall that the value of the firm is
= �
=1

(1+)
• In a perfect market without taxes and other
frictions, a firm’s cash flows (CFs) only
divided between equity and debt holders.
Leverage won’t change the total amount of
CFs.
• The implication of MM Proposition I is that
or does not change with capital structure
choice in a perfect market.
= + + +
CRICOS code 00025B
Leverage increases the risk and return to stockholders
RD is the interest rate (cost of debt)
RE is the return on equity (cost of equity)
RU is the return on asset (can also be denoted as RA) / unlevered equity (cost of
capital)
D is the market value of debt
E is the market value of equity
MM Proposition II
( )DUUE RRE
DRR −×+=
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CRICOS code 00025B
The derivation is straightforward:
MM Proposition II
21
UED RRED
ER
ED
D
=×
+
+×
+ E
ED +by sidesboth multiply
UED RE
EDR
ED
E
E
EDR
ED
D
E
ED +
=×
+
×
+
+×
+
×
+
UED RE
EDRR
E
D +
=+×
UUED RRE
DRR
E
D
+=+× )( DUUE RRE
DRR −+=
FINM7402
CRICOS code 00025B
MM Proposition II
FINM7402 22
Debt-to-equity
Ratio
C
os
t o
f c
ap
ita
l:
R
(%
)
RU
RD
)( DUUE RRE
DRR −×+=
RD
E
D
= + + +
CRICOS code 00025B
• Changing proportion of equity vs debt change equity beta ( ) or levered beta ( )
• But asset beta ( ) or unlevered beta ( ) stays the same
• Hence equity premium increase as leverage increases. But required asset return
(determined by asset beta) does not change, so is the value of the firm.
• Purely financial transactions in a perfect capital market are zero NPV projects. Thus, they
neither increase nor decrease firm value.
From beta perspective …
DEA ED
D
ED
E βββ
+
+
+
=
= + −
FINM7402 23
(1)
(2)
CRICOS code 00025B
• Because (for essentially all firms) debt is safer than equity, investors demand
a lower return for holding debt than for holding equity. (True)
• So a firm can reduce its cost of capital by increasing leverage.
• What is wrong with this argument?
WACC Fallacy: “Debt is Better Because Debt Is
Cheaper Than Equity”
FINM7402 24
= = + + +
CRICOS code 00025B
• This reasoning ignores the “hidden” cost of debt:
Raising more debt makes existing equity more risky
• Note: Unrelated to default risk, i.e., true even if debt is risk-free.
WACC Fallacy
FINM7402 25
CRICOS code 00025B
• EPS can go up (or down) when a company increases its leverage. (True)
• Companies should choose their financial policy to maximize their EPS.
(False)
• What is wrong with this argument?
EPS Fallacy: “Debt is Better When It Makes EPS Go Up.”
FINM7402 26
CRICOS code 00025B
• LVI is currently an all-equity firm. It expects to generate earnings before
interest and taxes (EBIT) of $10 million over the next year.
• Currently, LVI has 10 million shares outstanding, and its stock is trading for a
price of $7.50 per share.
• LVI is considering changing its capital structure by borrowing $15 million at
an interest rate of 8% and using the proceeds to repurchase 2 million shares
at $7.50 per share.
• Assume that LVI’s EBIT stays the same in the future and that all earnings are
paid as dividends. Are shareholders better off with the increased leverage?
EPS Fallacy: Example
FINM7402 27
CRICOS code 00025B
• Suppose LVI has no debt. Since there is no interest and no taxes, LVI’s
earnings would equal its EBIT and LVI’s earnings per share without leverage
would be:
EPS Fallacy: Example
Earnings $10 million $1
Number of Shares 10 million
EPS = = =
FINM7402 28
CRICOS code 00025B
• If LVI recapitalizes, the new debt will obligate LVI to make interest payments
each year of $1.2 million.
• $15 million × 8% = $1.2 million
• As a result, LVI will have expected earnings after interest of $8.8 million.
• Earnings = EBIT – Interest
• Earnings = $10 million – $1.2 million = $8.8 million
EPS Fallacy: Example
FINM7402 29
CRICOS code 00025B
• LVI’s Earnings per Share (EPS) rises to $1.10
• $8.8 million ÷ $8 million shares = $1.10
• LVI’s expected earnings per share increases with leverage.
• But, are shareholders better off?
• Shareholders would be better off if the increased EPS for LVI can lead to an
increase in the share price.
EPS Fallacy: Example
FINM7402 30
CRICOS code 00025BFINM7402 31
CRICOS code 00025B
• Although LVI’s expected EPS rises with leverage, the risk of its EPS also
increases.
• While EPS increases on average, this increase is necessary to compensate
shareholders for the additional risk they are taking, so LVI’s share price does
not increase as a result of the transaction.
EPS Fallacy: Example
FINM7402 32
CRICOS code 00025B
Illustrate without formula…
FINM7402 33
• Unlevered LVI : V = 75m, expected EBIT = 10m, all goes to equity holders
• Levered LVI: V (75m) = E (60m) + D (15m), expected EBIT = 10m, 8.8m
goes to equity holders, and 1.2m goes to debt holders
• Suppose two state economy: good state (G) with 50% chance and bad state
(B) with 50% chance.
• Expected equity return for unlevered LVI: 0.5*20% + 0.5*6.67% = 13.33%
• Expected equity return for levered LVI: 0.5*23% + 0.5*6.3% = 14.66%
15m (G), Re = 15/75=20%
5m (B), Re = 5/75=6.67%
Unlevered LVI
13.8m (G), Re = 13.8/60=23%
3.8m (B), Re = 3.8/60=6.33%
Levered LVI
CRICOS code 00025B
• Dilution
• An increase in the total of shares that will divide a fixed amount of earnings
• It is sometimes (incorrectly) argued that issuing equity will dilute existing
shareholders’ ownership, so debt financing should be used instead.
• With new shares issued, the cash flows generated by the firm must divided
among a larger number of shares, thereby reducing the value of each share.
Capital Structure Fallacy: Equity Issuances and Dilution
FINM7402 34
CRICOS code 00025B
• Suppose Jet Sky Airlines (JSA) currently has no debt and 500 million shares
of stock outstanding, currently trading at a price of $16.
• Last month the firm announced that it would expand and the expansion will
require the purchase of $1 billion of new planes, which will be financed by
issuing new equity.
• How will the share price change?
• The current (prior to the issue) value of the equity and the assets of the firm
is $8 billion.
• 500 million shares × $16 per share = $8 billion
Equity Issuances and Dilution
FINM7402 35
CRICOS code 00025B
• Suppose JSA sells 62.5 million new shares at the current price of $16 per
share to raise the additional $1 billion needed to purchase the planes.
Equity Issuances and Dilution
FINM7402 36
CRICOS code 00025B
• Results:
• The market value of JSA’s assets grows because of the additional $1 billion
in cash the firm has raised.
• The number of shares increases.
o Although the number of shares has grown to 562.5 million, the value per
share is unchanged at $16 per share.
Equity Issuances and Dilution
FINM7402 37
CRICOS code 00025B
• As long as the firm sells the new shares of equity at a fair price, there will be
no gain or loss to shareholders associated with the equity issue itself.
• Any gain or loss associated with the transaction will result from the NPV of
the investments the firm makes with the funds raised
Equity Issuances and Dilution
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CRICOS code 00025B
• How does financial leverage affect firm value without taxes?
• If a change in leverage raises a firm’s EPS, should this cause its share price
to rise in a perfect capital market?
• True/False: When a firm issues equity, it increases the supply of its shares in
the market, which should cause its share price to fall.
Quick Quiz
FINM7402 39
CRICOS code 00025B
• M-M marks the beginning of the modern theory of corporate finance. Before
that, corporate finance was viewed as part of accounting.
• M-M is not a literal statement about the real world. It obviously leaves
important things out.
• But it gets you to ask the right question: How is this financing move going to
change the size of the pie?
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CIVL2010 ECMT2150 CS 333 CP1406 KIT308 Economics 701 ECON3740 ECE 5759 BFC3340 FINC2012 COMP4500 MATH3871 FIT3080 18-819C Economic ECO202Y5Y PHY100 FINC-780 Econ 100B EC602 IE582 EE450 COMP9517 WRDS 150B ECON 570 LECTURE 2 ECA5101 ECE 4420 ADAD9311 FIT3031 CS 544 MF 703 CS 6140 KIT501 ENGSCI 344 CSC171 IE 332 FINM8007 21S2 COSC 1114 FE545 E471 SIT102 CSC108 MAT301 IAE 101 COP3503 STAT2004 EC 303 CS1026 STAT1203 MATH3171 ISOM5160 IFN657 FIT2014 ACCT2102 DSCI550 STATS 330 ELEC421 COMP3670 QBUS6840 MEES:698B MAST30027 MIET1077 Economics IFT 6758 FIT5122 BUSN5101 CptS 111 HRMT5502 Math2018 PP 312 INFS3200 CZ3005 CSSE1001 SENG 2011 MKTG 553Q BUFN 640 COMP507 ETF5952 DATA 311 ECE4043 BANK3011 finance M3H623544 HW1 INFS 7410 AI6103 STAT3888 INFS3208 ACCT7103 ECOS3013 PSYCH 20B F79MA STAT3006 ENGG952 2X MGSC 7000 ECE4132 MSF 526 MATH 3033 CDS 511 EEEE4120 EEET2465 ECA5103 MATH2070 ELEC3104 BU51019 EEE8147 ENGR20003 COSC 1107 ETF3200 FNCE 435 MSFI 435 ISyE6420 GENG4405 HW ETC5523 IE 7315 MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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