corporate finance: asymmetric information and capital structure...

Corporate Finance:Asymmetric information and capital structure – signaling

Yossi Spiegel

Recanati School of Business

Ross, BJE 1977

“The Determination of Financial Structure: The Incentive-Signalling

Approach”

Corporate Finance 3

The model� The timing:

� Cash flow is x ~ U[0,T], where T ∈ {L,H}, L < H

� T is private info. to the firm

� The capital market believes that T = H with prob. γ

� In case of bankruptcy, the manager bears a personal loss C

� The manager’s utility: U = V – C x Prob. of bankruptcy

The firm issues debt with face value D

Stage 0 Stage 2Stage 1

The capital market observes D and updates the belief about the firm’s type

Cash flow is realized

Corporate Finance 4

The full information case� The value of the firm when T is common knowledge:

� With uniform dist.:

� The manager’s utility:

� The manager will not issue debt

T

DCxDFCxU TT −=×−= ˆ)(ˆ

( ) T

T

D

T

D

D

T xxdFDxxDdFxxdFV ˆ)()()(0

=−+

+= ∫∫∫

2/ˆ TxT =

Corporate Finance 5

Asymmetric information

� DT* is the debt level of type T

� B* is the prob. that the capital market assigns to the firm being of type T

� Perfect Bayesian Equilibrium (PBE), (DH*,DL*,B*):� DH* and DL* are optimal given B*

� B* is consistent with the Bayes rule

Corporate Finance 6

Bayes rule

� In our case, two levels of D are chosen. Suppose the probability that each type plays them is as follows:

� Having observed D1 the capital market believes that the firm is type H with prob.:

� In a sep. equil., h1 = 1 and l1 = 0. In a pooling equil., h1 = l1 = 1

( ) ( )( )BP

APABPBAP

)(|| =

l2l1Type L (1−γ)

h2h1Type H (γ)

D2D1

( ) ( )( ) )1(

)(||

11

1

1

11 γγ

γ−+

==lh

h

DP

HPHDPDHP

Corporate Finance 7

Separating equilibria: DH* ≠ DL*

� The belief function:

� In a separating equil., DL* = 0 because type L cannot boost V by issuing debt

� DL* = 0 ⇒ B*(0) = 0 ⇒ V(0) = L/2

=

=

=

wo

DD

DD

B L

H

/'

*0

*1

*

γ

Corporate Finance 8

Separating equilibrium� The IC of H:

� The IC of L:

� Indifference of type T between V and D:

{

0 Dwhen H of Payoff

D issuesit when H of Payoff

2

=

≥×−L

H

DCV43421

{ 43421

D issuesit when L of Payoff

0 Dwhen L of Payoff

2 L

DCV

L×−≥

=

{ T

DC

LV

T

DCV

L×+=⇒×−=

=

22

V valueinducesit ifD issuing when Payoff

0D ifPayoff

43421

Corporate Finance 9

The set of separating equilibria

D

L

DC

LV +=

2 H

DC

LV +=

2

2

HV =

2

LV =

V

D* D**

sep. equil.

D* is defined byL/2+CxD/L = H/2⇒ D* = (H-L)L/2C

Corporate Finance 10

The DOM criterion� D ≥ D* is a dominated strategy for type L: D = 0 always guarantees L a higher

payoff no matter what the capital market believes

� The DOM criterion:

� The idea: type L will never play D ≥ D* while type H might. Hence, if D ≥ D*, then the firm’s type must be H

� The DOM criterion still does not determine the beliefs for D < D* and D ≠ 0

� Under the DOM criterion: DL* = 0, DH*=D*

≥

=

=

=

wo

DD

DD

DD

BL

H

/'

*1

*0

*1

*

γ


Separating equilibria under the DOM criterion

D

L

DC

LV +=

2 H

DC

LV +=

2

2

HV =

2

LV =

V

D* D**

DL* = 0, DH*=D*


Pooling equilibria: DH* = DL* = Dp*

� The belief function:

� In a pooling equil., the choice of Dp* is uninformative; hence

=

=wo

DDB

p

/'

**

γγ

( )2

12

ˆ LHV ×−+×= γγ


The set of pooling equilibria

D

L

DC

LV +=

2 H

DC

LV +=

2

2

HV =

2

LV =

V

D* D**

poolingequil.

VV ˆ=


The DOM criterion

� The DOM criterion:

� The DOM criterion eliminates some pooling equilibria but not all

≥

=

=

wo

DD

DD

B

p

/'

*1

*

*

γ

γ


The set of pooling equilibria

D

L

DC

LV +=

2 H

DC

LV +=

2

2

HV =

2

LV =

V

D* D**

poolingequil.

VV ˆ=


The intuitive criterion� Due to Cho and Kreps, QJE 1987

� Fix a equilibrium (DL*, DH*) and consider a deviation from this equilibrium to D’. If the deviation never benefits type x (even if it induces the most favorable beliefs by the capital market) but can benefit type y, then the deviation was played by type y

� The intuitive criterion:

� The intuitive criterion still does not determine the beliefs everywhere

=

=

wo

DD

DD

B p

p

/'

*by dominated is 1

*

*

γ

γ


The set of pooling equilibria under the intuitive criterion

D

L

DC

LV +=

2 H

DC

LV +=

2

2

HV =

2

LV =

V

D* D**

poolingequil.

VV ˆ= The intuitive criterion eliminates all pooling equil.


Conclusions

� The only equilibrium which survives the intuitive criterion is DL* = 0 and DH* = D*

� This equilibrium is the Pareto undominated separating equilibrium and it is called the “Riley outcome”

� Debt can be used as a signal of high cash flow

� The debt of type H:

� D*↑ when L↑, H-L↑, and C↓, D* is independent of γ!

( )C

LLHD

H

L

DC

L

2*

22

−=⇒=+

Leland and Pyle, JF 1977

“Informational asymmetries, financial

structure, and financial intermediation”


The model� The timing:

� Cash flow is x ~ [0,∞), with Ex = xT and Var(x)=σ2, where T ∈ {L,H}, xL < xH

� T is private info. to the firm

� The capital market believes that T = H with prob. γ

� The entrepreneur’s expected utility:

An entrepreneur sell a fraction 1-α of the firm to outside equityholders

Stage 0 Stage 2Stage 1

The capital market observes 1-α and updates the belief about the firm’s type

Cash flow is realized

( ) ( )VxWWVarb

EWWEU TTTT αα −+=×−= 1)(2


The full information case� The variance of WT:

� The entrepreneur’s expected utility:

� Under full info., V = xT:

⇒ α* = 0 ⇒ The entrepreneur will sell the entire firm

� Why? Because the entrepreneur is risk-averse and the capital market is risk-neutral

( ) ( )( )( )( ) 222

21

σαα

αα

=−=

−−+=

T

TT

xxE

EWVxEWVar

( ) ( ) 32144 344 21)(

22

21

xVarEW

TT

bVxWEU

T

σααα ×−−+=

( ) 22

2σα×−=

bxWEU TT


Asymmetric information

� αT* is the equity participation of type T

� B* is the prob. that the capital market assigns to the firm being of type T

� Perfect Bayesian Equilibrium (PBE), (αH*, αL*,B*):� αH* and αL* are optimal given B*

� B* is consistent with the Bayes rule


Separating equilibria: αH* ≠ αL*� The belief function:

� In a separating equil., αL* = 0 because type L cannot boost V by keeping equity

� αL* = 0 ⇒ B*(0) = 0 ⇒ V(0) = xL

=

=

=

wo

B L

H

/'

*0

*1

*

γαααα


Separating equilibrium� The IC of H:

� The IC of L:

� Indifference of type T between V and α:

( ){

0 when H of Payoff

firm theof fraction a keeps he when H of Payoff

22

21

=

≥−−+

αα

σααα LH xb

Vx4444 34444 21

{( )

4444 34444 21firm theof fraction a keeps he when L of Payoff

22

0 when L of Payoff

21

αα

σαααb

Vxx LL −−+≥

=

{( )

αασ

αα

σααα

αα

−×+

−−

=⇒−−+=

=

12121

22

V valuea inducesit if firm theof fraction a keeping when Payoff

22

0 ifPayoff

bxxV

bVxx TL

TL

4444 34444 21


The set of separating equilibria

α

αασ−

×+=12

22b

xV L

HxV =

LxV =

V

α* α**

sep. equil.

αασ

αα

−×+

−−

=121

22bxx

V HL

( )2

* 2σ

αb

xxZZZZ LH −≡++−=


The Riley outcome� Using L’s IC, the ownership share of type H is:

� α* increases with Z which � increases with the extent of asymmetric info., xH-xL� decreases with risk aversion, b� decreases with the variance of cash flows, σ2

� Using H’s IC:

� α** < 1 iff 2(xH–xL)< bσ2; otherwise, type H prefers every α > 0 over α = 0

provided that he convinces outsiders that the firm’s type is H

{( ) { ( )2*

21

2

H is typehis that believesmarket theandfirm theof fraction a keeps he when L of Payoff

22

0 when L of Payoff

++−=⇒−−+=−

=

ZZZb

xxx

b

xx

HLL

LH

σαα

ασααα4444 34444 21

{( ) ( )

2

H is typehis that believesmarket theandfirm theof fraction a keeps he when H of Payoff

22

0 when H of Payoff

2**

21

σασααα

αα

b

xxbxxx LH

HHL

−=⇒−−+=

=4444 34444 21

corporate finance: asymmetric information and capital structure...

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