Double-principal Agent: False Accounting Information, Supervision Cost and Corporate Performance

2.1 Assumptions

It is worth studying how information sharing and decision-making cooperation between principals affect the outcome of the game in multiple-principal agent problem. Thus, this paper studies how cooperation on cash flow right and management supervision right between the controlling shareholder and the shareholder in power balance affect each party’s decision-making and the game’s equilibrium. Our research focuses on three conditions related to different degrees of cooperation, that is, complete cooperation (cooperation on both cash flow right and management supervision), supervision cooperation (cooperation on management supervision only) and complete non-cooperation. Intuitively, the condition of complete cooperation between multiple principals is similar to the single principal problem, while other two conditions lead to new games due to free-rider effect or supervision spill-over effect. This principal-agent is not uncommon: the corporate shareholders obtain return on equity according to reported profits prepared by the manager; when the manager is suspected of providing false accounting reports and giving false information on corporate performance, the shareholders fulfill the right of accounting information verification such as auditing by third-party CPAs to verify the fairness of accounting information^[30], then decide whether to impose a penalty on the manager and share supervision benefit; however, supervision generates certain amount^[2] of cost. Based on these analyses, the assumptions are as the followings.

2.2 Game process design

Game process Firstly, the controlling shareholder H₁ and the shareholder in power balance H₂ announce a mechanism of cash flow right and a management supervision scheme they choose, that is, they announce the return on equity function, accounting information verification probability and verification cost function, etc.; secondly, the manager has a trade-off between advantages and disadvantages in accordance with her own type θ which belongs to a certain type space Θ, then she discloses accounting information and pays θ^; finally, shareholders decide whether to audit according to the accounting verification probability p1(θ^)andp2(θ^).

Manager’s type parameterθ It is defined as supervision benefit^[3] transferred to shareholders or its increasing function, θ stands for the manager’s private information and its random distribution form is common knowledge. θ has a continuous distribution F(θ) on the interval [θ_,θ¯] where the lowest bound is θ_>0 and the highest bound is θ̅ < ∞, and its destiny function is ƒ (θ) > 0 for all θ. For technical reasons, assume a weakly decreasing hazard rate 1−F(θ)f(θ). The controlling shareholder and the shareholder in power balance do not know actual value of θ, but they can look into the value through supervision measures such as accounting verification at some cost. In the condition of complete information, that is, when shareholders know the manager’s actual θ, they can obtain complete benefit θ̅. However, if there exists information asymmetry and no supervision measures are taken, shareholders’ supervision benefit is θ_.

Verification cost Accounting verification comes at certain cost, for instance, audit fees paid to CPAs who are specialized in verification business. Denote verification cost for H_k by C(p_k). The cost function satisfies:

1) C(0) = 0;

2) Inada conditions C′(0) = 0, C′(1) = ∞;

3) C′(p_k) > 0 for p_k ∊ (0,1);

4) C″(p_k)> 0 for all p_k.

H₁ and H₂’s choices are to choose proper return on equity functions R₁(·) and R₂(·) in the decision of cash follow right and to choose proper accounting information verification probabilities p₁(θ) and p₂(θ) in the decision of management supervision in order to maximize individual utility function. We can assume that R_k(·) is a function of verification probability because return on equity depends on reported profits and the manager decides the falseness degree of accounting information according to shareholders’ supervision level.

After the manager discloses accounting information, two principals verify the reported accounting information according to their verification probability p_k^[4], review the reported accounting information, check the transferred profits and impose a penalty. Assume that p_k is common knowledge as long as accounting verification probability is given. Denote 1 – q = (1 –p₁)(1 –p₂), then q stands for the controlling shareholder and the shareholder in power balance’s joint verification probability.

Simply assume that yield from accounting information verification is qθ and it is divided equally between the two principals according to Assumption 4. q connects two principals’ verification probability and sets yield share. Because q is an increasing function of p_k, an increase in accounting verification by one principal would benefit another principal. However, because the second-order cross partial derivative of q is less than zero, the marginal benefit associated with an increase in accounting verification by one principal is decreasing. In this case, another principal would raise her verification probability in order to gain a matching benefit. Then it is likely to become wasteful in management supervision cost.

2.3 The Khalil-Martimort-Parigi model

Assume that shareholders and agent are risk neutral. The agent’s utility function is U = (1 – q)θ – R₁ – R₂ with a budget constraint U ≥0. Therefore, the agent’s decision is a trade-off between information rent (θ), return on equity payment (R₁,R₂) and verification yield (qθ). The utility function of H_k is Wk=Rk+qθ2−C(pk) where W_k ≥ 0 according to Assumption 5.

Khalil et al.^[31] provide an equilibrium solution theorem for their model. Regarding it as a theoretical foundation, the following part of this paper discusses how different degrees of cooperation affect principals’ decision-making and behaviors in the game.

In the following parts of this paper, the superscript “*” indicates an equilibrium function. And the superscripts m, c and d respectively stand for the condition of complete cooperation, supervision cooperation and non-cooperation in cash flow right and management supervision between the controlling shareholder and the shareholder in power balance.

3.1 Shareholders’ choice

The complete cooperation between the controlling shareholder and the shareholder in power balance on cash flow right and management supervision incorporate that they share a joint transfer payment R(·) and decide p₁and p₂ together, which results in a minimum cost (denoted by C~(q)) of joint accounting verification probability q, i.e.:

This optimization problem yields a unique solution when the condition C″(pk)>C′(pk)1−pk is satisfied^[31].

3.2 Manager’s choice

Because transfer payment R(·) is a function of q, the manager’s utility function can be denoted by:

Incentive constraints In reality, an increase in verification probability q(·) leads to a decrease in the manager’s information rent, which is what condition (3) stands for. And in order to discourage the agent from understating income, q(·)must be decreasing in θ, which satisfies condition (4). The condition (4) also results in principals’ decreasing marginal utility, and it means the total transfer payment from agent to principals is a concave function in θ.

3.3 Shareholders’ utility

Shareholders’ principal-agent problem is to choose R(·) and q(·)in order to maximize their net payoff anticipating the agent’s incentives:

Shareholders’ trade-off Shareholders’ decision is constrained by incentives, with a trade-off between R(·) and q(·). Actually, due to the fact that q is a decreasing function of θ and R(·) is an increasing function of θ or due to the first-order condition of (1), i.e. C θ = R′ (q(θ)), we can prove that R(·) is a decreasing function of q. Specifically, for all θ >x, an increase of q(x) units in principals’ marginal payoff equals to a decrease of 1 – F(x)units in agent’s information rent, costing an increase of f(x)C~′(q(x)) units in marginal cost.

A cut-off rule If the marginal verification cost were constant (c), q(θ) = 0 if and only if c>1−F(θ)f(θ);q(θ)=1 if and only if c≤1−F(θ)f(θ). In this case, shareholders’ verification decision is reduced to a simple comparison between the manager’s statement θ^ and a threshold value where no accounting verification occurs if θ^ exceeds the threshold and accounting verification must occur if θ^ is lower than the threshold. Such criterion is similar to the cut-off rule in single-principal model.

4.1 Shareholders’ choice

Shareholders only cooperate in management supervision, therefore we can still assume that the controlling shareholder and the shareholder in power balance bear a joint accounting verification cost C~(q) and share the yield from accounting information verification qθ. In this case, R_k(·) is a function of q. Apparently, due to non-cooperation in cash flow right, principals deem the manager as an intermediary, send decision-making signals to each other and improve their own utility. As will be clearer later, due to the positive externality in the process of cash flow right, supervision cost is bigger than that in the condition of complete cooperation. Therefore, contact between principal and agent should be constrained.

The discussion can be made in the vicinity of equilibrium solution, hence we might as well assume that the controlling shareholder H₁ has already observed the shareholder in power balance’s optimal cash flow function R2∗c(q), then we see how the controlling shareholder would choose R₁(·).

4.2 Manager’s choice

The manager’s utility function is as the following:

With R2∗c(q) given, this utility function resembles (1), and constraints similar to (2)(3)(4) exist where (3) can be obtained using the envelope theorem. In this case, the first-order condition of q associated with (5) becomes:

The positive externality (6) demonstrates that on one hand an increase in q leads to a decrease in the marginal yield of H₁ when θ is constant. It can be proved that R2∗c(q) is a decreasing and convex function^[31], which is different from the complete cooperation condition. On the other hand, an increase in q results in a partial marginal yield transfer from H₂ to H₁ by the agent. In other words, shareholders increase verification probability and gain positive externality benefits from the shareholder in power balance’s cash flow, so they have incentive to improve supervision.

4.3 Equilibrium analysis

The controlling shareholder’s behavior pattern can be analyzed intuitively. Because verification probability q*^c(θ) is a decreasing function of θ, the manager knows that a higher verification probability is associated with a lower transferred supervision payoff to shareholders, which the shareholder in power balance (H₂) knows; H₂ also knows that a higher verification probability is related to truthful statement by the manager; the controlling shareholder knows that H₂ knows, therefore he tries to mislead if H₂ by claiming a higher verification probability and makes H₂ believe in a lower transfer yield from the manager, leading to a lower transfer payment from H₂ and an extra positive externality benefit for himself.

Excessive monitoring The behavior pattern described above is also the one for the shareholder in power balance. Consequently, the equilibrium outcome of the game is an increased verification probability resulting from the positive externality effect dependable on another shareholder’s cash flow right scheme adjustment, which is different from the complete cooperation condition. Considering principals and agent’s total welfare and when the manager’s payoff is exogenous, the lower accounting verification cost is, the higher total welfare is. Therefore, cooperation in supervision only between shareholders results in relatively excessive monitoring and a higher supervision cost.

To sum up, when the shareholders only cooperate in supervision, one shareholder tries to use the manager as an intermediary, sends signals and obtains partly another shareholder’s yield. The specific method is that the shareholders propose to increase the joint accounting verification probability. On one hand, this method increases shareholders’ own verification cost. On the other hand, this method brings positive externality benefit, which is a dominant factor for shareholders’ total benefit. As a result, compared to the condition of complete cooperation, the joint accounting verification probability is higher in equilibrium, which means shareholders’ larger tendency to supervision and leads to excessive monitoring. Using the equilibrium solution theorem we find that the equilibrium of the manager’s utility in this condition is lower than that in the complete cooperation condition, that is, U*^c(θ) < U* ^m(θ); we also find that shareholders and manager’s total welfare is lower while shareholders’ welfare is higher.

5.1 Shareholders’ choice

Under this condition, the controlling shareholder and the shareholder in power balance cooperate in neither cash flow right nor management supervision. Hence it is acceptable to define that the controlling shareholder and the shareholder in power balance provide their own cash flow function R_k(·) and accounting verification probability p_k independently where R_k(·) is a function of p_k, and that they bear their own accounting verification cost C(p_k) independently.

The discussion can be made in the vicinity of equilibrium solution, hence we might as well assume that the controlling shareholder has already observed the shareholder in power balance’s optimal cash flow function R2∗d(p2) and then we see how the controlling shareholder would choose R₁(·)·

5.2 Manager’s choic

Define the agent’s earning function before deducting the payment of controlling shareholder H₁as the following:

This facilitates our discussion: treating v(p₁,θ) as the manager’s initial earning, we can consider the problem of controlling shareholder H₁as a “one principal-one agent” problem. Denote p₂ in equilibrium by p2∗(p1,θ).

The first-order condition of (7) with respect to p₂ satisfies:

Furthermore,

In the symmetric equilibrium, there exists p1∗d=p2∗d=p2∗andp2∗ is a non-increasing function of θ according to the equilibrium solution theorem, therefore R2d(⋅) is a convex function; and 0<∂p2∗∂p1<1.

The free-rider problem Because ∂2q∂p1∂p2, management supervision effects from the controlling shareholder and the shareholder in power balance are complementary, but such complementarity is incomplete due to 0<∂p2∗∂p1<1. Different from the condition of supervision cooperation where ∂p2∗∂p1=1 and the complementarity is complete, incomplete complementarity leads to a free-rider phenomenon in supervision: when one shareholder increases one unit of accounting verification p_k, the other principal increases less than one unit of accounting verification p_j. Furthermore, we can prove that ∂p2∗∂p1<1 also undermines the positive externality benefit from cash flow right. Ultimately, management supervision is inadequate and even no management supervision occurs when the manager’s transfer payment is high.

The agent’s utility function is as the following:

Constraints similar to (2)(3)(4) exist: (4) still holds according to the equilibrium solution theorem, with a marginal probability rather than a joint probability; the following similar to (3) can be obtained using the envelope theorem:

In this case, it depends on p2∗(p1(θ),θ) then on R2d(⋅) indirectly.

5.3 Equilibrium analysis

Using the first-order condition of the utility function of the controlling shareholder H₁, we obtain the following:

Closely look into (11). ① The terms in the square brackets on the right side of (11) consist of the total effect on the increase in joint verification probability q resulting from an increase in the controlling shareholder’s verification probability p₁. The total effect includes a direct effect (1−p2∗) and an indirect effect via p2∗, i.e. ∂p2∗∂p1(1−p1∗d), which is undermined by the free-rider effect considering 0<∂p2∗∂p1<1. ② The direct outcome of an increase in q is a decrease by 1−F(θ)f(θ) in agent’s rent. θ2 of the decrease are transferred to the shareholder in power balance H₂. ③ −∂p2∗∂p1R2∗d′(p2∗) is the positive externality benefit of H₁ gained from H₂. Compared to the condition of supervision cooperation, the positive externality benefit is lower due to ∂p2∗∂p1<1.

Equilibrium analysis In the state of equilibrium holds p1∗d=p2∗. Then we rewrite (11) using (9):

Firstly, we discuss the case of no monitoring when the manager’s transfer payment is relatively high. In the analysis of (12), shareholders’ marginal benefit from accounting verification is negative when the manager’s transfer payment θ exceeds a certain level. Therefore, the shareholder in power balance’s verification probability is insensitive to the controlling shareholder’s, that is, ∂p2∗∂p1 is relatively small. In this case, the value of the right side of (12) is relatively small, and no monitoring occurs when it is smaller than that of the left side, that is to say, when marginal benefit is small than marginal supervision cost.

Secondly, we discuss the case of excessive monitoring when the manager’s transfer payment is relatively low. When ∂p2∗∂p1 approaches 1, the case is similar to the condition of supervision cooperation and the value of the right side of (12) is relatively large. When it is larger than that of the left side, excessive monitoring occurs.

To sum up, consistent with what is described in the equilibrium solution theorem, either no monitoring or excessive monitoring comes up in the condition of non-cooperation. And which phenomenon occurs depends on which effect plays a dominant role, the positive externality effect or the free-rider effect. When the manager is honest and the transfer payment is high, the case is similar to the complete cooperation condition and there exists a cut-off rule that no monitoring occurs when a threshold is beaten. When the manager’s transfer payment is low, the case is similar to the condition of supervision cooperation and it leads to excessive monitoring. In addition, the minimization of verification cost results in the maximization of shareholders and manager’s total welfare. In this aspect, no monitoring is better than monitoring and less monitoring is better than more monitoring. It is obvious, however, that the manager will take advantage of tunneling shareholders’ interest.