Repricing Alternatives, Optimal Repricing
Policy, and Early Exercises of ESOs
Jerry T. Yang
Eller College of Business and Public Administration
University of Arizona
Willard T. Carleton
Eller College of Business and Public Administration
University of Arizona
First Draft:
Current Draft:
December 2001
June 2002
Repricing Alternatives, Optimal Repricing
Policy, and Early Exercises of ESOs
Reporters
892630 Hui-hus Huang
892633 Huai-min Xie
892641 Po-xuan Yin
Outline of Presentation
1
2
3
4
5
6
New Accounting rules
Repricing Alternatives
Brief Literature Review
Model
Results
Conclusion
1. New Accounting Rules
• New accounting rules took effect in July
2000 and were imposed by FASB.
• The accounting penalty applies only if
companies issue lower-price replacement
stock options within six months after initial
options are canceled.
1. Repricing Alternatives
Repricing involves the lowering of the exercise price
of a stock option usually when the current exercise
price is above the market value of underlying
shares.
(0) NR: No Repricing
(1) TR: Traditional Repricing
(2) DR: Delayed Rrepricing
(3) AR: Advanced Repricing
(4) Others (See Table 1 for details)
(1) TR: Traditional Repricing
Change the exercise price of the underwater
options to current market value.
but
The repriced options are subject to
variable award accounting.
(2) DR: Delayed Rrepricing
Cancel underwater options and reissue them six
months and one day later.
(a.k.a. the "6&1" Method)
but
Employees will be "out-of-the-market"
for 6 months without knowing the
future exercise prices.
(3) AR: Advanced Repricing
Grant new options at market price up front in
return for surrender of old grants by the
employees after six months and one day.
but
Shareholders' concern is the
potential double dilution.
(4) Other Alternatives
• Truncated Options:
The exercise period is automatically reduced and the
options expire w/o cancellation if the stock price falls
below a predetermined level.
• New Grants:
Hand out more options at a lower exercise price while
leaving underwater options outstanding.
• New Shares:
Grand certain amounts of restricted stocks while
leaving underwater options outstanding.
• Share Swap:
Grant restricted stock of like value in exchange for the
submission of underwater options
3.
Brief Literature Review
[Empirical Papers]
Repricing has been studied empirically since the early 1990s.
However, to our best knowledge, there is no study on repricing
using post-1998 data to reflect the accounting rules changes
since December, 1998. For example,
•
•
•
•
Gilson and Vetsuypens (1993) study repricings by financially
distressed firms during 1981- 87.
Saly (1994) examines repricings following the stock market crash of
1987.
Chance, Kumar, and Todd (1997) and Brenner, Sundaram, and
Yermack (2000) use repricing data up to 1998 to characterize the
repricing incidence by firm-specific factors and market conditions.
They find that repricing is more likely to occur for firms with
insider-dominated boards.
Chance, Kumar, and Todd (1997) examine the incidence of "direct
repricing" -- corporations lower the exercise prices of existing stock
options.
[Analytic Papers]
•
Acharya, John, and Sundaram (2000) study the dymanic
optimality of repricing executive stock options and characterize
the conditions that affect the relative optimality of repricing.
•
Yang and Carleton (2002)
•
Hall and Murphy (2002) study stock options for undiversified
executives.Use a certainty-equivalence framework to distinguish
"executive value" from "company cost".
•
Ingersoll (2002) study the subjective and objective evaluation of
incentive stock options. Use the agent's marginal utility function
as a martingale pricing process to compute the subjective value.
The main focus of this paper is
• to assess the ex-ante optimality of the repricing
strategies mentioned above in terms of
protecting shareholders’ interests while facing
the challenge of invigorating executive moral
deflated as a result of plunging stock prices.
Figure 1:
A three-period binomial model and distribution of terminal cash flows.
Firm
Value
t = 0
t = 1
t = 2
t = 3
Term .
Principal's
Node Share Value
FV t=3
#
f t=3
Agent's
Wealth
w
t=3
H3
=
(1+u)3
1
f
1, t=3
w
1, t=3
H2L
=
(1+u)2(1-u)
2
f
2, t=3
w
2, t=3
H2L
=
(1+u)2(1-u)
3
f
3, t=3
w
3, t=3
HL2
=
(1+u)(1-u)2
4
f
4, t=3
w
4, t=3
H2L
=
(1+u)2(1-u)
5
f
5, t=3
w
5, t=3
HL2
=
(1+u)(1-u)2
6
f
6, t=3
w
6, t=3
HL2
=
(1+u)(1-u)2
7
f
7, t=3
w
7, t=3
L3
=
(1-u)3
8
f
8, t=3
w
8, t=3
p(a hh )
p(a h )
H2
[a hh ]
[E hh ]
H
[a h ]
[E h ]
p(a hl+ )
p (a )
HL+
[a hl+ ]
[E hl+ ]
I
[a ]
p(a hl- )
1-p(a)
p(a l )
HL[a hl- ]
[E hl- ]
L
[a l ]
[E l ]
p(a ll )
1-p(a l )
L2
[a ll ]
[E ll ]
where p(a) = q m + (1-q) a
or p(a) = a if q = 0 in some cases
1-p(a ll )
Assumptions
 Agent’s Utility=U(w) = (w1-g)/(1-g), where g  [0,1)
The principal is risk neutral (g = 0)
The agent is risk averse if g
0
 All payoffs are assumed to be received at the terminal date t = 3
 No layoff and bankruptcy will occur throughout these three
periods.
 Discount rate is zero to simplify the notation.
 The agent is compensated with stock options only.
 FV0 is normalized to unity on the only share.
 Homogeneous expectation:
 Only the tax benefit (or liability) resulting from the new
accounting rulings has an economic impact on firm value.
 All options are granted at the money.
Model (Figure 1)
A three-period binomial model and distribution of terminal cash flows.
Model (Figure 1)
A three-period binomial model and distribution of terminal cash flows.
Bellman's Principal of Optimality
"An optimal policy has the property
that whatever the initial state and initial decision
are, the remaining decisions must constitute an
optimal policy with regard to the state resulting
from the first decisions."
(Page 15, Applied Dynamic Programming by Richard E.
Bellman and Stuard E. Dreyfus, 1962)
The agent’s terminal wealth
The agent's terminal wealth if the agent holds and cashes in his/her
options until t = 3.
The agent’s terminal wealth
The agent's terminal wealth if the agent holds and cashes in his/her
options until t = 3.
The agent’s terminal wealth
The agent's terminal wealth if the agent holds and cashes
in his/her options until t = 3.
The principal's share value
The principal's terminal share value if the agent holds and cashes in
his/her options until t = 3.
The principal's share value
The principal's terminal share value if the agent holds and cashes in
his/her options until t = 3.
The principal's share value
The principal's terminal share value if the agent holds and cashes in
his/her options until t = 3.
The principal's share value
The principal's terminal share value if the agent holds and cashes in
his/her options until t = 3.
The Agent's Exercise Strategies
Step 1: Contingent upon reaching the node H2, the agent
solves (Finding the optimal a )
max { p ( H )(
a h h[ 0 ,1]
w11g
1g
)  p ( L)(
w12g
1g
1
2
)  kahh
}
2
(k is the coefficient in the disutility function (=
the agent's effort (a).)
Let U(w) = (w1-g)/(1-g)
1
2
ka ) resulting from
Then the solution is
The Agent's Exercise Strategies
Step 2:
Determine the agent's exercise strategies at t = 2.
1 (EXERCISE)
if EUhh > c Uhh
0 (HOLD)
otherwise
Ehh =
• where cUhh is the agent's expected continuation utility
from the node H2 given by
c Uhh = [ahh ][U1] + [1 - ahh][U2] - 1/2k[a hh ]2
• where EUhh is the agent's expected terminal utility
if the agent choose to exercise his/her options at node H2:
EUhh = U (whh ) = (whh )/(1- g)
The Agent's Exercise Strategies
The agent's terminal wealth if the agent holds and cashes
in his/her options until t = 2.
If options
Repricing Alternatives at node L
exercised
No
Traditional
Delayed
Advanced
and cashed in
Repricing
Repricing
Repricing
Repricing
at t = 2
(NR)
1
(TR)
2
(DR)
3
(AR)
4
Agent's Terminal Wealth ( w t=3 ) if options are exercised at t = 2
H2
 (H2 -1)(1 - tc)
 (H2 -1)(1 - tc)
 (H2 -1)(1 - tc)
 (H2 -1)(1 - tc)
HL-
HOLD
 (HL - L)(1 - tc)
HOLD
 (HL - L)(1 - tc) + HOLD
HL+
HOLD 5
HOLD
HOLD
HOLD
L2
HOLD
HOLD
HOLD
HOLD 6
4
The Agent's Exercise Strategies
The principal's terminal share value(t=3) if the agent
holds and cashes in his/her options until t = 2.
Repricing Alternatives at node L
Principal's
Share
Value1
No
Repricing
Traditional
Repricing
Delayed
Repricing
Advanced
Repricing
( f i , t=3 )
(NR) 2
(TR) 3
(DR) 4
(AR) 5
f 1, t=3
H3 +  + c  (H2 -1)
1+
H2L +  + c  (H2 -1)
1+
H3 +  + c  (H2 -1)
1+
H2L +  + c  (H2 -1)
1+
H3 +  + c  (H2 -1)
1+
H2L +  + c  (H2 -1)
1+
H3 +  + c  (H2 -1)
1+
H2L +  + c  (H2 -1)
1+
f 3, t=3
N/A 6
N/A
N/A
N/A
f 4, t=3
N/A 6
N/A
N/A
N/A
f 2, t=3
The principal's share value above is the same for every repricing pocily implemented at node L.
f 5, t=3
N/A 6
H2L+ L+ c   (1-L)  (HL-L)]
N/A
H2L+ L)+c   H2L -1)+ (HL-L) ]
1+
1 + 2
or
H2L+ L+ c  (HL-L)
1+
f 6, t=3
f 7, t=3
f 8, t=3
N/A 6
HL2 +  L+ c   (1-L)  (HL - L) ]
N/A
N/A
1+
N/A
N/A
N/A
HL2+ L+ c  (HL-L)
N/A
N/A
1+
N/A
N/A
7
The Agent's Exercise Strategies
Step 3:
Repeat Steps 1,2 until we determine the agent's
expected actions (a's) and exercise strategies
(E's) at t = 1, and t =0.
The Optimal Repricing Policy
Let C is the probability of no repring , the agent’s expected utility at
node L( given a triggering policy (C)) :
Finding the optimal a :

The agent’s expected utility at t=0 :
The Optimal Repricing Policy
Let C is the probability of no repring , the principal’s expected payoff
at node L( given a triggering policy (C)) :
Finding the optimal C :
The principal’s expected payoff at t=0 :
Table 6 所需之前提要素
• Agent’s utility fn：，
當γ=0 －＞表示 risk neutral
當γ越大 －＞ 越 risk averse
• 先決給定的條件：
α=0.3，k=0.3，u=0.4
Table 6:
The agent's chosen actions and exercise strategies
(A) When g = 0 (risk neutral)
Nodes
X' s
2
NR
Agent's actions (a x' s)
TR
DR
AR
Exercise Strategies (E x' s)
NR
TR
DR
AR
1
0
0
1
0
0
H
HL+
HL-
0
0
0
0
0.11616 0.11616 0.11616 0.11616
0.11616
0
0.22176 0.49632
L2
H
L
I
U0
0
0.626853
0.006747
0.203196
0.0062
V0
0.372171 0.408025 0.393365 0.42148 0.372171 0.408025 0.393365 0.42148
0
0.626853
0.1584
0.190674
0.009217
0.09504
0.626853
0.020072
0.198501
0.007326
1
0
1
1
0
0
0
0
0
0
0
0.626853
0
0
0
0
0.123167
0
0
0
0
0.195634
0
0
0
0
0.008016 0.0062 0.009217 0.007326 0.008016
Table 6:
The agent's chosen actions and exercise strategies
(B) When g = 0.5
Nodes
X' s
Agent's actions (a x' s)
TR
DR
AR
Exercise Strategies (E x' s)
NR
TR
DR
AR
NR
H2
HL+
HL-
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0
0
0
0
0
0
0
0
0
0
0
0
1
L2
H
L
I
U0
0
0.8
0.676
0.8
0
0.8
0.8
0.8
0.8
0.8
0.475
0.8
0
0.8
0.8
0.8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.461407 0.499608 0.489318 0.5307 0.461407 0.499608 0.489318 0.5307
V0
1.73111 1.74839 1.71935 1.67509 1.73111 1.74839 1.71935 1.67509
Table 6:
The agent's chosen actions and exercise strategies
(C) When g = 0.9
Nodes
X' s
Agent's actions (a x' s)
TR
DR
AR
Exercise Strategies (E x' s)
NR
TR
DR
AR
NR
H2
HL+
HL-
0.8
0.8
0.8
0.8
0.8
0
0.8
0.8
0.8
0.8
0.8
0
0
0
0
0
0
1
0
0
0
0
0
1
L2
H
L
I
U0
0
0.8
0.8
0.8
0
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0
0.8
0.8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7.06441
7.34456
7.3459
10.3013
7.06441
7.34456
7.3459
10.3013
V0
1.75111
1.68017
1.75651 0.479188 1.75111
1.68017
1.75651 0.479188
Table 7 所需之前提要素
• Wo是〝 t=0時agent的wealth 〞
是由
，γ [0,1) 而解出的。
•
w0
：an incentive measure for the agent.
V 0
V 0
w0
：the principal’s decision-making criterion
for choosing a repricing strategy at node L.
Table 7:
Measure of the incentive provide by each repricing strategy
(A) When g = 0 (risk neutral)
NR
TR
DR
AR
U0
0.0062
0.0092
0.0073
0.0080
w0
0.0062
0.0092
0.0073
0.0080
V0
0.3722
---
0.4080
0.0841
11.8843
0.3934
0.0531
18.8291
0.4215
0.0368
27.1485
w 0 / V 0
V 0 / w 0
Table 7:
Measure of the incentive provide by each repricing strategy
(B) When g = 0.5
NR
TR
DR
AR
U0
0.4614
0.4996
0.4893
0.5307
w0
0.0532
0.0624
0.0599
0.0704
V0
1.7311
---
1.7484
0.5311
1.8828
1.7194
-0.5641
-1.7727
1.6751
-0.3068
-3.2595
w 0 / V 0
V 0 / w 0
Table 7:
Measure of the incentive provide by each repricing strategy
(C) When g = 0.9
NR
TR
DR
AR
U0
7.0644
7.3446
7.3459
10.3013
w0
0.0310
0.0457
0.0458
1.3456
V0
1.7511
---
1.6802
-0.2074
-4.8207
1.7565
2.7406
0.3649
0.4792
-1.0336
-0.9675
w 0 / V 0
V 0 / w 0
Table 8:
The agent's expected actions and exercise strategies
Nodes
X' s
2
H
HL+
HLL2
H
L
I
U0
w0
V0
w 0 / V 0
+.
NR
Agent's actions (a x' s)
TR
DR
AR
0.3688
0.3394
0.3394
0
0.7175
0.2501
0.6452
1.3613
0.3688
0.3394
0.1699
0
0.7175
0.5680
0.6245
1.4805
0.3688
0.3394
0.6055
0.4880
0.7175
0.3629
0.6319
1.4698
0.3688
0.3394
0.2743
0
0.7175
0.5608
0.4643
1.7567
(1.9322)*
(2.1026)
(2.1012)
(2.7202)
0.1359
0.1524
0.1490
0.2772
(0.2230)
(0.2288)
(0.2265)
(0.5240)
1.2665
1.2783
1.2841
1.1582
(0.7267)
(0.7383)
(0.7304)
(0.7734)
--
1.4020
0.7450
-1.3039
Exercise Strategies (E x' s)
NR
TR
DR
AR
52.68%
0
0
0
1.22%
0
0
52.68%
0
78.75%
0
1.22%
0
0
52.68%
0
0
0
1.22%
0
0
52.68%
0
63.56%
0
1.22%
0
0
The number in parentheses is the standard error of the
variable above.
CONCLUSION
• 以〝provide most incentive〞觀點言：
w0
最好的是 TR。(由 V0 觀察出)
• For principal：
DR ＞ TR ＞ NR ＞ AR
• For agent：
AR ＞ TR ＞ DR ＞ NR