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An Innovative Applied Theory on Principal-Agent Problem
HU Zuguang Abstracts Normal 0          false  false  false    EN-US  ZH-CN  X-NONE

The paper puts forward an innovative method of setting profit target. In the traditional method, the board of directors (the principal) of a corporation always suggests a high profit target for the CEO (the agent) and the CEO always emphasizes the difficulty of fulfilling the target set by the board. They often bargain over the problem the concession of the board and a low profit target. But by the end of the year the CEO can usually far surpass the low profit target and earn a big bonus. The new method (“HU’s theory”) put forward in the paper opened a completely new vision. In the author’s practice of using “HU’s theory” in Chinese corporations, the CEO will automatically raise the profit target to the maximum level he can reach. So by applying “HU’s theory” the trouble of bargaining over the profit target between boards and CEOs has been eliminated.

The core of “HU’s theory” is that the final profit target should be jointly decided by boards and CEOs. Usually it is an arithmetic average of profit targets separately suggested by boards and CEOs. As usual, when a CEO over-fulfills the final profit target, he can get a certain percentage of the over-fulfilled amount as his bonus. But a special feature of “HU’s theory” is that the CEO will be fined for the difference between his actual profit and his self-offered profit at the beginning of the year. The paper proves mathematically that by fining the CEO for the difference between his actual profit and his self-offered profit at the beginning of the year, the CEO will automatically suggest a maximum profit target which can fulfill in a year, thus eliminated the time consuming bargaining.

There is a true story here. The Reebok International Company is an American company. Its board of directors discussed with Paul Fireman, the CEO of the company, the problem on setting up profit targets for 1985-87. After repeated bargaining both agreed that the profit targets for 1985-87 should be $20 million each year. If Fireman fulfills the $20 million target he can get base salary of $350,000. If he over-fulfills the target, he can get 5% of the over-fulfilled amount as a bonus. Guess what were the actual results? The actual results are shown in Table 1.

Table 1 Some financial data of the Reebok International Company (in $)

Years

Profit targets

Actual profits

Base salary

Fireman’s bonus

1985

20,000,000

130,000,000

350,000

5,500,000

1986

20,000,000

282,000,000

350,000

14,000,000

1987

20,000,000

321,334,000

350,000

15,066,700

From Table 1 we can see that the profit targets are small as compared with the actual profits, so Fireman got huge bonuses in the three years. (Ramirez, 1988)

The above story told us in the bargaining between principals (usually the board of directors) and agents (CEOs) for setting up profit targets the information processed by the two sides are asymmetric, the agents side usually have more information. The CEOs know how much profit their companies can make. But they usually hide the information. In the bargain between the principals and agents the latter tend to lower the target so that he can over-fulfill more and get more awards. Harris and Raviv pointed out that if principals cannot observe the behaviors of agents, the best way for the principals is to demand a fixed “rent” from the agents. (Harris and Raviv, 1979), but they failed to pointed out how to decide the amount of the “fixed rent”. Maskin and Tirole discussed the bargaining process between principals and agents with agents possessing private information (Maskin and Tirole, 1992), but they also failed to point out how to set up the target. Weitzman had suggested theoretical incentive models (Weitzman, 1976 and 1980), but his models cannot be used in practice.

How to solve the problem of asymmetric information between boards and CEOs in deciding profit targets? According to my research (The research is funded by NFNSC-National Foundation for Natural Science of China) there is a way out-just call it “HU’s theory” for the time being. Here I would like to use the above Rebook example to explain the advantages of “HU’s theory”. if I were the board chairman of Reebok, I would suggest the following profit target decision method to Reebok’s CEO in 1985:

\1.       The profit target for a year should be jointly decided by the board and the CEO, that is, the final

Contracted profit target is a weighted average (for simplicity here we use an arithmetic average) of the board Demand D and the CEO’s Self-offered quota S:

C=WS+(1-W) D=0.5S+0.5D

2.        If the actual profit A reaped by the CEO in a year surpasses the contracted target C, the CEO will be awarded by 8% of the surpassed amount, i.e.

Bonus=0.08(A-C)

Now the board is required to put forward its profit target demanded D and the CEO is required to give his self-offered quota S. If I were the board chairman I would demand for a profit target as the same as in the above Reebok example, i.e., $20million for 1985. once this is set, we can see that the contracted profit target C is decided by the CEO’s self-offered quota S:

C=0.5D+0.5S                         =0.5*20+0.5S                         =10+0.5S

Suppose the CEO makes his self-offered quota S=0, then the contract quota is only C=$10million. It would be too low! But do not worry; “HU’s theory” has the third stipulation.

3.        If the CEO’s self-offered quota S (Which is put forward in the beginning of the year) falls short of the Actual profit A by the end of the year, the CEO will be fined for the shortage.

The amount of the fine is 6% of the shortage:

Fine=0.06(S-A)          (When SA or S=A, he will neither be fined nor awarded.

What will the CEO do in 1985 when facing with the above 3 stipulations of “HU’s theory”? He will ponder the question: What should be my self-offered quota in order to get maximum net gain? He may calculate his prospective net gains for 5 cases (5 different self-offered quotas) as Table2 shows.

Table2 A comparison among 5 cases (in $ millions)

Case1

Case2

Case3

Case4

Case5

S (The CEO’s Self-offered quota)

D (Board Demand)

C (Contracted target) =0.5S+0.5D

A (Actual Profit reaped in the year)

Award=0.08(A-C)

Fine= 0.06(S-A) (When S<A) Net gain=Award+ Fine

0

20

10

130

9.6

-7.8

1.8

110

20

65

130

5.2

-1.2

4

120

20

70

130

4.8

-0.6

4.2

130

20

75

130

4.4

0

4.4

140

20

80

130

4

0

4

From Table 2 we can see that in case 1 the CEO’s self-offered profit quota S=0, so the contracted profit target is only 10. In that case, the CEO surpassed the contracted target by 130-10=120. So he can get an award of (130-10)*0.08=9.6 ($million). But don’t forget that the CEO will also be fined for discrepancy between his self-offered profit quota S and the actual profit A. The fine=0.06(S-A)=0.06(0.130)=-7.8. So the CEO’s net gain is 9.6+(-7.8)=1.8 (million). Now let’s look at case 4. In that case, the CEO’s self-offered quota S=130 million, (From the Reebokexample we can see that he can reap that much profit in 1985), the contracted profit target is therefore (20 + 130)/2=75, so the CEO over-fulfilled the contract by 130-75=55. He can therefore get an award of 0.08*(130-75)=$4.4 million which is the largest among all cases.

Our conclusion: HU’s theory can make the CEO honestly offer a profit quota up to his ability.

Now let’s compare the result of “HU’s theory” in Table 2 with the actual result of Reebok example in Table 1. In Reebok example, the board only promised to give the CEO 5% of the over-fulfilled amount as bonus, but in “HU’s theory” the board promise to give the CEO a bonus of 8% of the over-fulfilled amount. Obviously, “HU’s theory” is more powerful in motivating the CEO to over-fulfill the profit target. In Reebok example, the board spend $5.5 million to award the CEO as bonus but in “HU’s theory”, the board only spends $4.4 million to award the CEO. In Reebok example the profit was only $20 million but in “HU’s theory” the profit target is $75 million (Case 4 in table 2), Obviously, HU’s Theory has a stronger constraint on the CEO. In a word, “HU’s theory” has the advantages of higher incentive, lower cost and stronger constraint. In addition, the CEO will willingly offer a maximum profit uota he can realize. That saves a lot of bargaining time.

In the above example we can see that the most salient feature of the “HU’s theory” is that it can make the CEO willingly offer a maximum profit quota he can realize. Now let’s prove it mathematically.

First, repeat the meaning of letters:

D: The profit target demanded by principals

S: The agents’ self-offered profit quota

C: The contracted profit target: C=wS+ (1-w) D

w: The weight for agent’s self-offered quota (In Table 2, w=0.5)

A: The actual profit reaped in a year

P: The awarding percentage (coefficient). In Table 1, Q=0.06, meaning a punishment of 6% of the shortage between the agent’s actual profit by year end and the agent’s self-offered quota at the beginning of the year.

Now let’s prove that under “HU’s theory” the agent will always make S=A, i.e., he will always offer a maximum profit quota S which equals the actual profit A he can reap in a year.

Proof: The agent’s net gain is

N= Bonus + Fine (The base award is a fixed number and does not appear here for simplicity)

=P (A-C)+Q(S-A)

Here S<=A. It means that the agent’s self-offered profit quota will not surpass his actual ability A.