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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
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