*3.1. The Problem*

Shareholders, and also managers, analyze the company's performance from different viewpoints and use different indicators to measure it. This performance is the result of many different decisions, so the extraction of a single, unique, bad one, for analyzing its impact can be difficult. We have chosen the moment of the AGM for shareholders to simultaneously consider two issues: (1) deciding if the manager is maintained in function; and (2) deciding the amount paid as dividend.

We can present sequentially the series of decisions as:

$$\text{DECC}\_{t}\text{-}\_{t}\text{ DEC}\_{-t+1}\text{DEC}\_{-t+2}, \dots, \text{DEC}\_{0}\text{-DEC}\_{1}\text{DEC}\_{2}\text{-DEC}\_{3}, \dots, \text{DEC}\_{n}$$

The decisions made by the management (DECt) are right for the period [−t, 0]:

$$DEC\_{-t}, DEC\_{-t+1}, DEC\_{-t+2}, \dots, DEC\_{0\prime}$$

In the period [1, n], decisions are systematically wrong:

$$DEC\_1, DEC\_2, DEC\_3, \dots, DEC\_n$$

The problem is to find *n* (the moment in which the manager is switched). In other words, we estimate the *duration of making systematically bad decisions* (DSMBD) in setting one dividend policy. This duration expresses the length in time of making an inappropriate decision regarding dividend policy. This decision is supported by some agents (some shareholders which sustain this decision) even it is wrong. The supporters of the good decision are in minority (they do not reach more than 50% from the votes even they are right). The switch in sustaining the bad decision can be considered synonymous with a switch in power (Dragotă 2016). The manager is switched when the percent of shareholders that support them is lower than 50%. We consider four classes of shareholders, described in Section 3.2.

Dividend policy (respectively, the percent of the net earnings paid as dividend, or, alternatively, the percent invested in the company) is decided in AGM (at the moment *t* + 1), usually based on the manager's recommendation, only if *NEt* > 0. If *NEt* ≤ 0, we cannot discuss about a dividend policy.

The manager (supported by the controlling shareholders) (Class A agents in our model, see Section 3.2) proposes a dividend policy based on her or his expectations regarding the internal rate of return for the investment projects proposed to be financed from the retained earnings—*Et*−1(*IRRt*) and on their expectation regarding the evolution of the market—*Et*−1(*kMt*) (this is the market return for projects with a similar risk2):

If *E*1(*IRR*2) ≥ *E*1(*kM*2), then: *DIV*<sup>1</sup> = 0 If *E*1(*IRR*2) < *E*1(*kM*2), then: *DIV*<sup>1</sup> = *NE*<sup>1</sup> In other words, the dividend payout ratio (DPR) is:

$$DRR\_t = \begin{cases} \ 0\% \text{ if } E\_{t-1}(IRR\_t) > E\_{t-1}(kM\_t) \\ \ 100\% \text{ if } E\_{t-1}(IRR\_t) \le E\_{t-1}(kM\_t) \end{cases} \tag{1}$$

In our paper, this decision-making process is based on Walter (1956), sometimes defined as the "residual" dividend policy. This policy is widely recognized by practitioners, but also in the financial literature (Aivazian et al. 2006; Kim and Kim 2019).

In practice, the dividend payout ratio follows a Tweedie distribution (Dragotă et al. 2019). This distribution is characterized by a modal value of 0%. This modal value of 0% is confirmed by other

<sup>2</sup> It can be noted that this rate of return is not a realized one. Investors expect to record this promised rate of return, so an adequate notation is still Et−1(kMt).

studies (Denis and Osobov 2008; Fama and French 2001; von Eije and Megginson 2008; Fatemi and Bildik 2012; Kuo et al. 2013). In our paper, the option between 0% and 100% DPR is considered only for simplifications reasons. It is not the purpose of our paper to justify an optimal dividend policy, but to analyze the impact of a bad decision.

As long as the supporters of the power are dominant (respectively, more than 50% votes), the decision proposed by the management will be adopted.

The decisions made by the management (*DECt*) are right for the period [−*t*, 0]. They are determining a stock of wealth for shareholders, which can induce in shareholders a status of safety and also a state of trust for the manager's performance. A company's return is, to a large extent, the effect of some decisions made in the past. As an effect, investors can judge one manager's performance (the return in one year, source for dividend payments) even if this is the effect of the choices made in the past. Moreover, even the results of some projects are not desirable from a financial viewpoint, in real life their effects are combined with the other projects' effects, finally, the shareholders having access only to some synthetic indicators at the company's level (like cash flows, net earnings or return on equity). The initial stock of wealth allows the management to make some wrong decisions because their impact is not fatal for the company.

For simplification, in our paper, we assume that no agency problems occur in making the dividend payment decisions, even if they are documented in financial literature (Easterbrook 1984; La Porta et al. 2000a; Kim and Kim 2019) and they can be an interesting field of study. We also assumed that information is symmetrical (Dragotă 2016) and we ignored the impact of taxation3.

We assume, as in Dragotă (2016), that the decisions regarding dividend payments are made democratically, in AGM. The decisions are based on the principle one share, one vote4. The ownership structure is assumed to be dispersed. We consider that all the shareholders are exercising their vote. The dividend payout decision requires a simple majority (respectively, more than 50% votes). In our study, we consider that the decisions are made in each financial exercise and we consider in each financial exercise only one round of votes (we consider the final vote for each AGM).

For modelling reasons, we consider that the shareholders do not sell their shares in the considered period and, also, no new shares are issued in this period5. As an effect, the total number of shares and the initial number of shareholders remain constant.

## *3.2. Shareholders' Typology and Behavior*

We consider four classes of shareholders (agent types) (Dragotă 2016) (denoted A, B, C, and D), with *xt <sup>i</sup>* is the percent in total shares (which correspond to the voting power), with *xt <sup>A</sup>* + *xt <sup>B</sup>* + *xt <sup>C</sup>* + *xt <sup>D</sup>* = 1. Each of classes of shareholders (agents) is characterized by some features, described below.

**Class A** represents the decider (the power). In our study, they are the group of shareholders that make systematically bad decisions, until the power is switched. Agents from this class are overconfident in their decisions (De Bondt and Thaler 1995; Hirshleifer 2001), even if they are wrong. Due to the outputs produced, the behavior of this class of shareholders can be suspected by agency problems, even if they are not real. Additionally, it seems reasonable to anticipate that Class A will suggest that the other shareholders should support their decisions, probably insisting on arguments like *trust the expertise of the management which is acting in the benefits of the other shareholders*.

**Class B** represents the opposition, respectively, the group of shareholders that understand that the decisions of the Class A are bad, but are not in power. Their rationality is useless for convincing

<sup>3</sup> Taxation can have an impact on dividend payments (Dragotă et al. 2009). Walter (1956) analyzes the impact of taxation, too. <sup>4</sup> The model can be easily generalized for the case of multiple classes of shares, with different voting power, according to the

company's statute (see, for instance, (Nenova 2003), for the case of dual classes of shares).

<sup>5</sup> A similar result occurs if the new shareholders (the buyers) replicate the behavior of the former shareholders (the sellers).

agents from Class A, and even Class B can be associated with keywords like *financial rationality, abilities*, or *literacy*6.

As an observation, each rational agent probably knows that that the expected level of one indicator can be different from its realized level (see Figure 2). As an effect, it can be very difficult to argue that one forecast is, indeed, wrong.

**Figure 2.** Two forecasts for future level of cash flows–for each class of agents—A (with green) and B (with blue). The two classes estimate the level of indicator (the estimated cash flow) through its probability distribution. The forecast made by one class of agents (B—in the left, with blue) is better than the second one (A—in the right, with green). In (**a**), if the realized cash flow is N (from normal, very plausible for the first class of agents' forecast), it can be interpreted by the second class of agents as an unfavorable scenario of evolution (but still plausible, according to their forecast). A realized cash flow equal to O (from optimistic) should confirm the good forecast made by class A (even it is only a relatively unusual good performance based on the forecast made by class B). (**b**) depicts an even greater dissonance between the two forecasts. In this case, if the realized cash flow is N, class A can realize that the forecast was indeed wrong, but, also, they can consider that an extreme event occurred.

<sup>6</sup> As observation, when the impact of factors like financial literacy or education is discussed, it has to be interpreted cautiously. For instance, Mare et al. (2019) found that insurance literacy has an impact on financial decisions, but education (in general) does not.

**Class C** includes the shareholders that can change their decision. They can learn from past errors (for them, *evolution* is the keyword). Initially, *xt <sup>C</sup>* = 0. Firstly, they support the power (they are in Class D), but they change their vote.

**Class D** is a residual in this model: *xt <sup>D</sup>* <sup>=</sup> <sup>1</sup> − *<sup>x</sup><sup>A</sup>* − *<sup>x</sup><sup>B</sup>* − *<sup>x</sup>*<sup>t</sup> C. Initially, we assume that they support the power, but they can migrate to Class C.

According to these assumptions, *<sup>x</sup><sup>A</sup>* and *xB* are fixed (constant in time), with *xA* ∈ (0, 0.5) and *<sup>x</sup><sup>B</sup>* ∈ (0, 0.5), and *x<sup>C</sup>* and *xD* are variable. Initially, *x0 <sup>C</sup>* = 0.

The power is switched democratically when the number of voters against the power is higher than 50% (respectively: *xB* + *xt <sup>C</sup>* > 50%). As in Dragotă (2016), the switch in power in AGM is determined exclusively by the changes in the voting preferences of Class C. Shareholders from Class C analyze the quality of decisions based on the results recorded by the company. As such, they do not evaluate the quality of the decision regarding the dividend payments made at the present moment (*t)* (see Section 3.1), but the quality of the decisions made in the past moments, as a proxy for the quality of the present decision (see also Table 2). The decision's quality is quantified comparing the recorded performance with the required one. We considered that the performance is proxied by the realized return of equity (*ROEt*). Similarly, the required level of performance is quantified through a required rate of return (*ROEt* \* ). The evolution of ROE is described in Section 3.3. In Section 3.4 we discuss how they estimate their required rate of return.

At each moment *t* (the annual shareholders' meeting), Class C agents: (a) analyze if the realized return of equity *ROEt* has an acceptable level (is higher or, at least, equal to the required rate of return, *ROEt \** ), deciding if they support the power; and (b) if they support the power, they vote for the recommended dividend policy. Additionally, the AGM is the moment when the agents from Class C can change their voting preference: (i) if *ROEt* ≥ *ROEt* \* , they are satisfied and keep their voting preference (they will continue to support the power); (ii) if *ROEt* < *ROEt* \* , they change their voting preferences, voting against the power. As a result, shareholders from Class A are imposing their viewpoint until: *xt <sup>B</sup>* + *xt <sup>C</sup>* > 0.5.

The changing preferences for Class C agents can be modelled through many different rules (Dragotă 2016). In this paper, we consider two cases. First, we assume that once an agent from Class D pass to Class C, his or her decision is irreversible (situation 1, S1). Secondly (situation 2, S2), we assume that:

$$\begin{array}{rcl} \text{if } \begin{cases} \text{ } ROE\_{t} \geq ROE\_{t'}^{\*} \ \text{ then } : & \mathbf{x}\_{t}^{\complement} \leq \mathbf{x}\_{t-1}^{\complement} \\ \text{ } ROE\_{t} < ROE\_{t'}^{\*} \ \text{ then } : & \mathbf{x}\_{t}^{\complement} \geq \mathbf{x}\_{t-1}^{\complement} \end{array} \end{array}$$

We consider that xt <sup>C</sup> is determined based on the rule defined in Dragotă (2016):

$$\mathbf{x}\_t^C = \mathbf{x}\_{t-1}^C + \alpha\_t \cdot \mathbf{M}\_t \cdot \mathbf{x}\_{t-1}^D \tag{2}$$

In this relation, the percent of shareholders which vote against the power (xt C) increase from financial exercise to financial exercise if they are unsatisfied by the level of the rate of return; however, they can change their opinion if the results are satisfying them, becoming more trustful in management's decision.

As such:

$$\alpha\_t = \begin{cases} -1, \text{ if } ROE\_t < ROE\_t^\* \\ -1, \text{ if } ROE\_t \ge ROE\_t^\* \end{cases} \tag{3}$$

Additionally, by definition, xt <sup>C</sup> should be at least equal cu 0: xt <sup>C</sup> <sup>≥</sup> 0.

*Mt* is a random variable uniformly distributed on [0,1], which can be interpreted as a magnitude of the interest to change the power (Dragotă 2016). If *Mt* = 0, this can be interpreted as a total indifference to the level of return, but also as a conservative attitude (Hirshleifer 2001). If *Mt* = 1, the entire population of agents from class D will change their voting preference, joining the class C of agents, immediately after the level of realized return is below the required rate of return. *Mt* is dependent of different factors that can have an impact on wealth and for this reason is not constant in time7.

*xt <sup>C</sup>* can be written as:

$$\mathbf{x}\_{t}\mathbf{x}\_{t}^{\complement} = \mathbf{x}\_{t-1}\mathbf{}^{\complement} + \boldsymbol{\alpha}\_{t} \cdot \boldsymbol{M}\_{t} \ (\mathbf{1} - \mathbf{x}^{A} - \mathbf{x}^{B} - \mathbf{x}\_{t-1}\mathbf{}^{\complement}) = \mathbf{x}\_{t-1}\mathbf{}^{\complement} \cdot (\mathbf{1} - \boldsymbol{\alpha}\_{t} \cdot \mathbf{M}\_{t}) + (\mathbf{1} - \mathbf{x}^{A} - \mathbf{x}^{B})\boldsymbol{\alpha}\_{t} \cdot \boldsymbol{M}\_{t} \tag{4}$$

As an observation, shareholders from Class D can migrate to Class C even in the case in which the company records a low performance, even if the dividend policy was correct.
