Repricing Alternatives, Optimal Repricing Policy, and Early Exercises of ESOs

Repricing Alternatives, Optimal Repricing Policy, and Early Exercises of ESOs

Jerry T. YangEller College of Business and Public Administration

University of Arizona

Willard T. CarletonEller College of Business and Public Administration

University of Arizona

First Draft: December 2001

Current Draft: 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 New Accounting rules

2 Repricing Alternatives

3 Brief Literature Review

4 Model

5 Results

6 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 pric

e 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 thepotential 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 Term. Principal's Agent'sValue Node Share Value Wealth

t = 0 t = 1 t = 2 t = 3 FV t=3 # f t=3 w t=3

H3 = (1+u)3 1 f 1, t=3 w 1, t=3

p(a hh )

H2

p(a h ) [a hh ]

[E hh ]

H2L = (1+u)2(1-u) 2 f 2, t=3 w 2, t=3

H

[a h ] H2L = (1+u)2(1-u) 3 f 3, t=3 w 3, t=3

[E h ] p(a hl+)p (a )

HL+[a hl+]

[E hl+]

HL2 = (1+u)(1-u)2 4 f 4, t=3 w 4, t=3

I

[a ] H2L = (1+u)2(1-u) 5 f 5, t=3 w 5, t=3

p(a hl-)

HL-

1-p(a) p(a l ) [a hl-]

[E hl-]

HL2 = (1+u)(1-u)2 6 f 6, t=3 w 6, t=3

L

[a l ] HL2 = (1+u)(1-u)2 7 f 7, t=3 w 7, t=3

[E l ] p(a ll )

1-p(a l )

L2

[a ll ]

[E ll ] 1-p(a ll )

where p(a) = q m + (1-q) a L3 = (1-u)3 8 f 8, t=3 w 8, t=3

or p(a) = a if q = 0 in some cases

Assumptions Agent’s Utility=U(w) = (w1-)/(1-), where [0,1)

The principal is risk neutral ( The agent is risk averse if 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 propertythat whatever the initial state and initial decisionare, the remaining decisions must constitute anoptimal policy with regard to the state resultingfrom 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 wealthThe 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 Agent's Exercise StrategiesStep 1: Contingent upon reaching the node H2, the agent

solves (Finding the optimal a )

(k is the coefficient in the disutility function (= ka ) resulting from the agent's effort (a).)

Let U(w) = (w1-)/(1-) Then the solution is

}2

1))(())(({max 2

11]1,0[

12

11

hhww

akaLpHp

hh

2

1

The Agent's Exercise StrategiesStep 2:

Determine the agent's exercise strategies at t = 2.

1 (EXERCISE) if EUhh > c Uhh

Ehh = 0 (HOLD) otherwise

• 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- )

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 4

HL+ HOLD 5 HOLD HOLD HOLD

L2 HOLD HOLD HOLD HOLD 6

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.Principal's Repricing Alternatives at node L

Share No Traditional Delayed Advanced

Value1 Repricing Repricing Repricing Repricing

( f i , t=3 ) (NR) 2 (TR) 3 (DR) 4 (AR) 5

f 1, t=3 H3 + + c (H2 -1) H3 + + c

(H2 -1) H3 + + c (H2 -1) H3 + + c

(H2 -1)1 + 1 + 1 + 1 +

f 2, t=3 H2L + + c (H2 -1) H2L + + c

(H2 -1) H2L + + c (H2 -1) H2L + + c

(H2 -1)1 + 1 + 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

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)

7

1 +

f 6, t=3 N/A 6 HL2 + L+ c (1-L) (HL - L) ] N/A HL2+ L+ c

(HL-L)

1 + 1 + f 7, t=3 N/A N/A N/A N/Af 8, t=3 N/A N/A N/A N/A

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 = 0 (risk neutral)

Nodes Agent's actions (a x' s) Exercise Strategies (E x' s)

X' s NR TR DR AR NR TR DR AR

H2 0 0 0 0 1 1 1 1HL+ 0.11616 0.11616 0.11616 0.11616 0 0 0 0HL- 0.11616 0 0.22176 0.49632 0 1 0 0

L2 0 0 0.09504 0 0 0 0 0H 0.626853 0.626853 0.626853 0.626853 0 0 0 0L 0.006747 0.1584 0.020072 0.123167 0 0 0 0I 0.203196 0.190674 0.198501 0.195634 0 0 0 0

U 0 0.0062 0.009217 0.007326 0.008016 0.0062 0.009217 0.007326 0.008016

V 0 0.372171 0.408025 0.393365 0.42148 0.372171 0.408025 0.393365 0.42148


(B) When = 0.5



H20.8 0.8 0.8 0.8 0 0 0 0

HL+ 0.8 0.8 0.8 0.8 0 0 0 0HL- 0.8 0.8 0.8 0 0 0 0 1

L20 0 0.8 0 0 0 0 0

H 0.8 0.8 0.8 0.8 0 0 0 0L 0.676 0.8 0.475 0.8 0 0 0 0I 0.8 0.8 0.8 0.8 0 0 0 0

U 0 0.461407 0.499608 0.489318 0.5307 0.461407 0.499608 0.489318 0.5307

V 0 1.73111 1.74839 1.71935 1.67509 1.73111 1.74839 1.71935 1.67509


(C) When = 0.9



H20.8 0.8 0.8 0.8 0 0 0 0

HL+ 0.8 0.8 0.8 0.8 0 0 0 0HL- 0.8 0 0.8 0 0 1 0 1

L20 0 0.8 0 0 0 0 0

H 0.8 0.8 0.8 0.8 0 0 0 0L 0.8 0.8 0.8 0.8 0 0 0 0I 0.8 0.8 0.8 0 0 0 0 0

U 0 7.06441 7.34456 7.3459 10.3013 7.06441 7.34456 7.3459 10.3013

V 0 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。

• ： an incentive measure for the agent.

： the principal’s decision-making criterion for choosing a repricing strategy at node L.

0

0

V

w

0

0

w

V

Table 7: Measure of the incentive provide by each repricing strategy

(A) When = 0 (risk neutral)

NR TR DR AR

U 0 0.0062 0.0092 0.0073 0.0080

w 0 0.0062 0.0092 0.0073 0.0080

V 0 0.3722 0.4080 0.3934 0.4215w 0 / V 0 -- 0.0841 0.0531 0.0368V 0 / w 0 -- 11.8843 18.8291 27.1485


(B) When = 0.5

NR TR DR AR

U 0 0.4614 0.4996 0.4893 0.5307

w 0 0.0532 0.0624 0.0599 0.0704

V 0 1.7311 1.7484 1.7194 1.6751w 0 / V 0 -- 0.5311 -0.5641 -0.3068V 0 / w 0 -- 1.8828 -1.7727 -3.2595


(C) When = 0.9

NR TR DR AR

U 0 7.0644 7.3446 7.3459 10.3013

w 0 0.0310 0.0457 0.0458 1.3456

V 0 1.7511 1.6802 1.7565 0.4792w 0 / V 0 -- -0.2074 2.7406 -1.0336V 0 / w 0 -- -4.8207 0.3649 -0.9675

Table 8: The agent's expected actions and exercise strategies

+. The number in parentheses is the standard error of the variable above.


X' s NR TR DR AR NR TR DR ARH2 0.3688 0.3688 0.3688 0.3688 52.68% 52.68% 52.68% 52.68%

HL+ 0.3394 0.3394 0.3394 0.3394 0 0 0 0HL- 0.3394 0.1699 0.6055 0.2743 0 78.75% 0 63.56%

L2 0 0 0.4880 0 0 0 0 0H 0.7175 0.7175 0.7175 0.7175 1.22% 1.22% 1.22% 1.22%L 0.2501 0.5680 0.3629 0.5608 0 0 0 0I 0.6452 0.6245 0.6319 0.4643 0 0 0 0

U 0 1.3613 1.4805 1.4698 1.7567

(1.9322)* (2.1026) (2.1012) (2.7202)w 0 0.1359 0.1524 0.1490 0.2772

(0.2230) (0.2288) (0.2265) (0.5240)V 0 1.2665 1.2783 1.2841 1.1582

(0.7267) (0.7383) (0.7304) (0.7734)w 0 / V 0 -- 1.4020 0.7450 -1.3039

CONCLUSION

• 以〝 provide most incentive 〞觀點言：

最好的是 TR 。 ( 由觀察出 )• For principal ： DR ＞ TR ＞ NR ＞ AR• For agent ： AR ＞ TR ＞ DR ＞ NR

0

0

V

w

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Repricing Alternatives, Optimal Repricing Policy, and Early Exercises of ESOs