Corporate Finance:Payout policies

Yossi SpiegelRecanati School of Business

Corporate Finance 2

A two-period model The timing:

Cash flow is distributed on [X0, X1] according to f(X)

The firm can always pay y

There’s a dividend tax t

The firm commits to pay dividend y in stage 2

Stage 0 Stage 2Stage 1

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

y is paid

Corporate Finance 3

The effect of dividend payments The value of the firm:

If t = 0, then V(y) is independent of y

If t > 0, the firm should pay no dividends

tyXXdFtyyXyVX

X

ˆ11

0

Bhattacharya, BJE 1979

“Imperfect Information, Dividend Policy, and "The Bird in the Hand" Fallacy”

Corporate Finance 5

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 market believes that T = H with prob.

If y > x, the firm bears a loss of b(y-x)

Dividend tax t

The manager’s utility: U = V + (1-)VT

The firm commits to pay dividend y in stage 2

Stage 0 Stage 2Stage 1

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

y is paid

Corporate Finance 6

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

With uniform dist.

The manager’s utility:

The manager will set y = 0

yT

T xdFxybxdFtyyxVV00

)()(1

TbytyTVV T 22

2

T

bytyTVVU TT 221

2

Corporate Finance 7

Asymmetric information yT* is the dividend of type T

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

Perfect Bayesian Equilibrium (PBE), (yH*,yL*,B*): yH* and yL* are optimal given B* B* is consistent with the Bayes rule

Corporate Finance 8

Separating equilibria: yH* ≠ yL* The belief function:

In a separating equil., yL* = 0 because type L cannot boost V by paying divided

yL* = 0 B*(0) = 0 V(0) = L/2

woyyyy

B L

H

/?*0*1

*

Corporate Finance 9

Separating equilibrium The IC constraint of H:

The IC constraint of L:

Indifference of type T between V and y:

0 y when H of Payoff

y dividend payingwhen H of Payoff

2

21

2221

HLH

bytyHV

TbytyLVTL

TbytyTV

21

221

2221

22

0 y when L of Payoff

y dividend payingwhen L of Payoff

2

21

2221

LLL

bytyLV

Corporate Finance 10

The set of separating equilibria

y

LbytyLV2

12

2

2L

V

y* y**

sep. equil.

HbytyLV2

12

2

2H

HbytyH22

2

Corporate Finance 11

The dividend of type H under the DOM criterion The DOM criterion eliminates all separating equilibria

except the Riley outcome:

Solving:

HLb

HLHLLHbLHttHLy

1

12*

222

L firmfor curve ceIndifferen

2

H is typesfirm' that thebelievsmarket when theValue

2

21

222

LbytyL

HbytyH

Corporate Finance 12

Bang-for-the-buck (the effect of y on the firm’s value)

LbytyLV2

12

2

2L

V

y*

2H

HbytyH22

2

Bang-for-the-buckwhen t

Bernheim and Wantz, AER 1995

“A tax-based test of the dividend signaling hypothesis”

Corporate Finance 14

An agency model of dividends -private info. about preferences The timing:

Cash flow before dividends is Y

The value of the firm is v(Y-y)

Cum dividend value of the firm: v(Y-y)+(1-t)y, (t is dividend tax)

The manager gets private benefits w(Y-y)

The manager’s utility: U = v(Y-y) + (1-t)y + w(Y-y),

The firm commits to pay dividend y in stage 2

Stage 1 Stage 2

y is paid

Corporate Finance 15

The manager’s problem The manager chooses y to maximize:

F.O.C:

S.O.C:

benefits Private valuedividend Cum

)(1 yYwytyYvU

0)(''1'dividends ofCost dividends ofBenefit

yYwyYvtU

0)("""assumptionby 0assumptionby 0

yYwyYvU

Corporate Finance 16

t y* (the benefits of y is smaller)

y* (the cost of y is bigger)

Illustrating the manager’s problem

yy*

1-t

v’(Y-y)+w’(Y-y)

Corporate Finance 17

Bang-for-the-buck The cum dividend value of the firm in equil.:

Suppose that is private info. for the manager. The ex. value of the firm before y is paid:

Effect of y on firm value:

Bang-for-the-buck:

*1** ytyYvV

*1** yEtyYvEVE

** VEVA

*'1*'*F.O.Cby

yYwtyYvy

VyA

Corporate Finance 18

Effect of t on bang-for-the-buck The effect of t on ∂A/∂y:

t ∂A/∂y

The effect of the opposite of what we had with signaling we have a test to discriminate between the two explanations for dividend payments

0**"

)()(

tyyYw

yA

t

Corporate Finance 19

An agency model of dividends –private info. about cash flows Consider the same model as before except that now Y =

and the manager chooses y to maximize:

F.O.C:

F.O.C determines – y. Hence, – y = const. and

benefits Private valuedividend Cum

)(1 ywytyvU

0)(''1'dividends ofCost dividends ofBenefit

ywyvtU

1*

y

Corporate Finance 20

Effect of dividend on the firm’s value The cum dividend value of the firm in equil.:

Suppose that is private info. for the manager. The ex. value of the firm before y is paid:

Effect of y on firm value:

*1** ytyvV

*1** yEtyvEVE

** VEVA

Corporate Finance 21

Bang-for-the-buck Suppose ; then A and y change. We can define

bang-for-the-buck as:

The effect of on A:

*yin Changein value Change

y

A

B

yV

y

V

y

Ay

yVVA

B

*

*

*

****

Corporate Finance 22

Effect of t on bang-for-the-buck Computing bang-for-the-buck:

B is decreasing with t

tyvtyvy

V

yVB

yVyV

11

*'1*'*

**

***

Allen, Bernardo, and Welch, JF 2000

“A Theory of Dividends Based on Tax Clienteles”

Corporate Finance 24

The model The timing:

Cash flow is V ~ N(,2)

There are institutional investors and retail investors

Monitoring by institutional investors adds ln(M) to the cash flow

The cost of monitoring is cM

Dividend taxes: tR > tI

The firm sets its dividend y

Stage 0 Stage 2Stage 1

The capital market determines the value of the firm

Institutional investors monitor the firm and cash flow is realized

Corporate Finance 25

Payoffs Wealth of institutional and retail investors:

The expected payoff of type t = I,R investors:

EWt is equal to Wt except that replaces V

Var(Wt):

)(2 t

ttt WVarEWWEU

monitoringofCost

sharesfor Payment

wealthInitial taxDiv.Stake

ln cMpwytMVW IIIII

222 tttt EWWEWVar

sharesfor Payment

wealthInitial taxDiv.Stake

ln RRRRR pwytMVW

Corporate Finance 26

Institutional investors: monitoring and demand for equity Institutional investors choose M and I to maximize:

F.O.C for M and I:

Using F.O.C:

Ambiguous price effect:

)(

22

2ln

II WVar

II

EW

IIIII cMpwytMWEU

cMc

MII

*0

0ln 2 III pytM

pytc II

II

ln2

21 I

II

p

Corporate Finance 27

Retail investors: demand for equity Retail investors choose R to maximize:

F.O.C for R:

Using F.O.C:

Downward sloping demand

)(

22

2ln

R

R

WVar

RR

EW

RRRI

RR pwytc

WEU

pytc RI

RR

ln2

2ln RRRI pyt

c

Corporate Finance 28

Equilibrium Demands:

Market clearing:

The equil. is given by the sol’n to the system of 3 equations (demands + market clearing) in 3 unknowns: I, R, p, given y

The owners choose y to maximize p

pytc II

II

ln2

pytc RI

RR

ln2

supplydemand

1 RI

Corporate Finance 29

Characterizing the equilibrium Rewriting the demand equations:

From the 2 demand equations:

In equilibrium, I = I and R = 1-I (using market clearing)

We found I and R as functions of y. We now must determine y

The owners of the firm will set y* to maximize p

pc

yt

pc

yt

IRRR

IIII

ln

ln

2

2

2

222 *1

IR

IRRIRRIIII

yttytytR

Corporate Finance 30

The effect of y on p: p is determined by the equil. system:

To find the effect of y on p we must differentiate the equil. system w.r.t. y

yp

ytp

ytp

RI

RRRII

IRIII

0011

11

101

2

2

1

ln

ln

2

2

RI

RRRI

IIII

ytpc

ytpc

Corporate Finance 31

The comparative static matrix: Writing the system in matrix form:

Using Cramer’s rule:

ytt

pR

I

R

I

RI

II

0011

11

101

matrix statics eComparativ

2

2

2

2

IR

RIIRI

IR tttt

yp

Corporate Finance 32

The optimal y The owners of the firm set y to maximize p:

y* is chosen so that I = I

We found earlier that in equil. :

22

2

*0

RIIR

IRI

IR

RIIRI

IR

tttt

tttt

yp

2

2

*

IR

IRRI

ytt

Corporate Finance 33

Solving for y*

The optimal dividend:

y* when 2 and tR-tI

2*

RIIR

IRI tt

tt

2

2

*

IR

IRRI

ytt

IR

R

IIRR

IR

tttty

2

*

yy*

Corporate Finance 34

Bang-for-the-buck The value of the firm is:

From before we know that:

yc

yV

cVV I

I

I

**

**ln*

0** 22

2

IR

IRI

IR

IRRI

tty

ytt

**

***

22

2

2

22

ytt

cytt

ttc

ttytt

cttcy

V

IR

RIRR

IR

IR

IR

IR

IRRIR

IR

I