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Corporate Finance:Asymmetric information and capitalstructure the lemons problem
Yossi SpiegelRecanati School of Business
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Akerlof, QJE 1970
The Market for Lemons: QualityUncertainty and the MarketMechanism
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Corporate Finance 3
The lemons problem An entrepreneur establishes a firm
Cash flow is x ~ U[0,1]
The entrepreneur privately observes x
How much will investors pay for the firms equity?
Suppose the price is p should investors pay it?
The entrepreneur will agree to sell only if x p
Given p, investors should pay E(x|x p). With uniform dist.,
E(x|x p) = p/2.
It is impossible to sell the firm!
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Corporate Finance 4
Crucial assumptions for the lemons
problem The entrepreneur does not have to sell if he
does not want to sell
The entrepreneur knows x but investors donot and investors know this fact
The value of the firm is the same for theentrepreneur and the investors
The entrepreneurs willingness to sell impliesthat x p
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Corporate Finance 5
Overcoming the lemons problem Cash flow x is drawn from CDF F(x) on [0,)
The entrepreneurs payoff: p x
The buyers payoff is bx p, b 1 (the buyer can improvethe firm there are gains from trade)
A seller will sell iff p x
The buyer will buy iff
)(
)( 0
pF
xxdFx
p
=
x
pbpxb
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Myers and Majluf, JFE 1984
Corporate Financing and InvestmentDecisions when Firms have Information thatInvestors Do Not Have
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Corporate Finance 7
The model The timing:
Existing value, x, is drawn from somedist.
The mean of x is
A firm worth x caninvest I in a projectthat yields R > I
Stage 0 Stage 2Stage 1
The firm decideswhether or not totake the project and
how to finance it
Cash flow is realized
x
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Corporate Finance 8
The full information case Suppose that the firm issues equity
that gives investors of the firm
In order to raise I dollars:
The entrepreneurs payoff:
Rx
IIRx
+==+ )(
( )( ) ( ) IRxRxRx
IRxRxU +=+
+
+=+= 1
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Corporate Finance 9
Asymmetric information binary
case: x {xL, xH} Suppose we have a pooling equil. and
both type finance the investment
In order to raise I dollars:
The entrepreneurs payoff:
RxIIRx+==+
)(
( )( ) ( )RxRx
IRxRxU +
+
+=+=
1
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Corporate Finance 10
Will both types finance? The entrepreneur will invest iff U > x (value w/o investing)
Type L is subsidized by type H because
Both types invest only if U > x for type H
O/w only type L invests and type H forgoes the investmentalthough it has NPV > 0
( )( )( ) ( )
( ) ( )43421
mispricing
++=
+++=
+
+++=
++
+
=
RxRxIR
RxRxIRxR
Rx
RxxRxIRx
xRxRx
IRx
xU
HL xxx
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Corporate Finance 11
Asymmetric information:
continuous case: x ~ F(x) on [0,) Let be the highest x such that the entrepreneur invests
The expected value of the firm given :
In order to raise I dollars:
The entrepreneurs payoff:Rxx
IIRxx
+==+
)())((
( )( )( )
( )( )Rx
Rxx
IRxxRxU +
+
+=+=
1
x
( )xxxExF
xxdFxx
x
==
)(
)()( 0
x
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Corporate Finance 12
How is determined? The entrepreneur will invest iff U > x (value
w/o investing)
is determined s.t. the payoff U = x:x
x
045
x
( )( )
( )RxRxx
IRxxU +
+
+=
x
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Corporate Finance 13
How is determined? is determined by
Solving the two equations yield
( )( )
( )
( )
( ) xR
IIRxxxRx
Rxx
IRxx
xU
=+=++
+
444 3444 21
xx
( )xxxExx =)(
x
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Corporate Finance 14
Implications The entrepreneur will invest iff
If the entrepreneur uses safe debt:
This is also the payoff when using RE
Pecking order: RE Debt Equity
xx
IRxDRxU +=+=
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Corporate Finance 15
Price reactions Before investing, the expected value of the firm is
Conditional on passing on the investment project, themarket learns that hence, the expected value is:
Conditional on investing, the market learns that ;hence, expected value of the firm is
xx >
( ) ( )xxxExdFxF
xNE
x
>=
=
|)()(1
xx
( ) ( ) IRxxxEIRxdFxF
xYE
x
+=+= |)()(0
{ ( ) ( )IRxFxxdFxFx
xFIRxdFxF
x
xFE x
x
+=
+
+=
)()()(1)(1)()()(highisx
thatProb.0lowisx
thatProb.43421
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Corporate Finance 16
Price reactions to not investing
Not investing is good news
( )
( )
( )
( ) ( )( )
( )
( )[ ] 0|)(
|)(
||)(
)()(
)()(1
)(
)()()(1
)(
)()()(1
)(
ofdef.by the
0
0
>>>
>=
+>=
=
+=
=
xxxxExF
xRIxxxExF
IRxxxExxxExF
IRxdFxF
xxdF
xF
xxF
IRxFxdFxxF
xxxdF
IRxFxxdFxF
xENE
xxR
I
x
x
x
x
x
444 3444 21
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Corporate Finance 17
Price reactions to investing
Investing is bad news
( )
( )( )
( ) ( )
( ) ( ) ( ) ( )[ ]
( ) ( )
( ) ( )[ ] 0|)(1
|)(1
||)(1
)()(1
)()(
)(1
)(1)()(
)(
)()()(
)(
0
0
0
=
>+=
+
=
+
+=
+=
xxxExxF
xxxEx
R
IxF
xxxEIRxxxExF
IRxdFxF
xxdF
xF
xxF
IRxFxdFxxF
xxxdF
IRxFxIRxdFxF
xEYE
x
x
x
x
x
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Yosha, JFI 1995
Information Disclosure Costs andthe Choice of Financing Source
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Corporate Finance 19
The model The timing:
The entrepreneurs type is F()
is disclosed if the entrepreneur raises funds from the capital market but not if heborrows money from a bank
The rivals payoff: R = R(x) - c(x) R(x) > 0 > R(x), c(x) > 0, c(x) > 0
The entrepreneurs payoff: E = (x(),) Ex < 0,
E > 0 (higher means a higher type)
An entrepreneurneeds to raisefunds to invest: Bank Capital market
Stage 0 Stage 2Stage 1
A rival observes theentrepreneursdecision and takesaction x, that hurtsthe entrepreneur
Cash flow is realized
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Corporate Finance 20
The rivals action given The rivals chooses x to maximize
xx()
R(x)
c(x)
x()The entrepreneuris better off if the
rival believes that is low
)()( xcxRR
=
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Corporate Finance 21
Bank debt vs. capital market Bank debt: the rival does not know and hence uses his belief ;
hence the rival takes an action
Capital market: the rival observes and takes an action x();the firm incurs an issuing cost
The effect of on E with bank debt (holding fixed):
The entrepreneurs payoff (the positive sign is by assumption):
0,,
>
=
x
d
xd EE
)(x
( )( ) ( )( ) ( ){
( )( ) 0,',,
)(
)(
)(
>
+
=
++
44 344214434421
xx
x
x
d
xd EEE
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Corporate Finance 22
The rivals action given
Av. quality of firms that work with banks:
,xE
( )( ) ,xE
Capital market Bank
*)(1
)( *
F
dF
=
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Corporate Finance 23
Implications Good firms work with banks, firms which raise
funds in the capital market are less good
pecking order
* The av. quality of firms which issuein the capital market
Positive price reactions to private placements
The literature on info. revelation shows howeverthat info. revelation can lead to either positive ornegative reactions by 3rd parties (e.g., rivals)
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Rock, JFE 1986
Why New Issues are Underpriced
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Corporate Finance 25
Stylized facts about IPOs Short-run equity underpricing: The closing price on the first day of
trading is on av. above the offering price
Weiss, Hanely and Ritter, Going Public,The New Palgrave Dictionary(Table 1), reports that the av. increase in the stock price shortly afterIPOs is 16.4% in the U.S. during the period 1960-1987 31.9% in Japan during the period of 1979-1989 79% in Korea during the period 1984-1990
149.3% in Malaysia during the period 1979-1984
Long-run equity overpricing: For several years following the IPO,the returns on IPOs are on av. lower than those on comparable stocks the av. cumulative matching firm-adjusted return 36 months after the IPO
is -15.08% (Ritter,JF1991)
Oversubscription: IPOs are typically oversubscribed and eachparticipant receives just a fraction of his order
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Corporate Finance 26
The model The timing:
The firms value, x, is drawn from CDF F(x) on [0,)
The mean of x is
Each investor has K to invest
Investors have enough to invest but one investor is notenough:
An entrepreneurgoes for an IPO
Stage 0 Stage 2Stage 1
N+1 investors decidewhether or not toparticipate
Cash flow is realized
x
KxNK >>
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Corporate Finance 27
All N+1 investors are uninformed The value of equity is
Each investor has K to invest and hence demands
There is oversubscription:
Since total supply is 1, investors are rationed and each one gets:
( ) { 1
1
1
1
demandIndividual
investoreachofShare
+=
+ Nx
K
xKN
43421
)
xE =
xK /
32143421assumptionBydemandAggregate
1
)1( >>+x
NK
x
KN
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Corporate Finance 28
N uninformed investors and 1
informed investor The informed investor participates in the IPO iff E x
Uninformed investors do not observe the informed investors
decision (if they could they would infer x)
If uninformed investors participate, they get: 1/(N+1) if E x (the informed investor participates) 1/N if E > x (the informed investor does not participate)
The net expected payoff of an uniformed investor:
In a competitive capital market, YU = 0
( ) ( )
+
+=E
E
U xdFEx
N
xdFEx
N
Y )(
1
1)(
1
0
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Corporate Finance 29
Underpricing in IPOs The condition for a competitive equilibrium:
Rewriting:
Multiplying by N and rearranging:
Less underpricing as N gets large
( ) ( ) 0)(1
1)(
1
0
=+
+=
E
E
UxdFEx
NxdFEx
NY
( )
( )( )
=
+=
++
E
E
xdFExNNN
Ex
xdFExNNN
Ex
0)(1
1
)(1
1
1
xxdFN
ExxEE
)(1
ngUnderprici
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Corporate Finance 30
Post IPO share price After the IPO the market observes the participation and
learns whether the informed investor participated or not
If the informed investor did not participate then x < E new value of equity
If the informed investor participated then x > E newvalue of equity
ExdF
EF
xE
E
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