*3.4. Required Rates of Return*

In our paper, we consider in the same model two of the investor's statuses. On the one hand, investors are making their analysis from a portfolio management's perspective, being interested about characteristics like return<sup>13</sup> and risk of their portfolio, making their judgments in estimating a required rate of return, etc. (Markowitz 1952). On the other hand, they are shareholders and they participate in AGM, being implied in making decisions at the corporate level, like adopting the dividend payout ratio.

In our model, two required rates of return appear as benchmarks, respectively, *Et*−1(*kMt*) and *ROEt* \* .

The first indicator is related to the expectations regarding the capital market. We assume that this indicator is estimated by the shareholders. In our study, we consider that, when proposing a dividend policy, the management compares the expected IRR with *Et*−1(*kMt*) and decides to pay dividends only if *Et*−1(*kMt*) > *Et*−1(*IRRt*).

<sup>8</sup> This statement is formalized in the corporate finance literature through classical selection criteria, like the net present value (NPV) > 0 and IRR > the required rate of return (Ross et al. 2010; Dragotă et al. 2013).

<sup>9</sup> Theoretically, the realized IRR can take values in the (−∞, <sup>∞</sup>) interval. <sup>10</sup> Some readers can have objections to this manner of formulation, considering that the expected rate of return is a function of the realized rate of return, and not vice versa. In our simple formulation, if we consider *Et*−*1(IRRt)* as function of *IRRt*, *IRRt* should be generated randomly.

<sup>11</sup> Similar to the formulation of IRRt, if we consider *Et*−*1(kMt)* as function of *kMt*, *kMt* should be generated randomly. <sup>12</sup> Shareholders' wealth at moment *t (Wt)* is structured in two components: the initial capital invested in company and the capitalized dividends.

<sup>13</sup> In the entire paper we consider the real rates of returns, even it is not specified expressly. In a more general context, we can assume that it is not important if we prefer real or nominal rates of returns as long as all the comparisons and considerations regarding these rates are consider the coherence between rates (e.g., compare real rates of returns with real rates of return, and nominal rates of returns with nominal rates of returns).



**Table 4.** Numerical simulation for the financial indicators (example).


Regarding the second indicator, the required ROE (*ROEt \** ), investors can consider different benchmarks (Dragotă et al. 2013). However, basically, all of these benchmarks can be reduced to two fundamental approaches. On the one hand, they expect a rate of return, related to the characteristic of the project (for instance, in CAPM they require a rate of return higher than risk-free rate and they claim also a risk premium—otherwise they will reject the project) (Ross et al. 2010). On the other hand, investors analyze the alternatives available on the capital market (if they do not invest in the proposed project, what alternatives are available?).

First (but not necessary in this order), they require an acceptable rate of return14. It can be considered that they consider as normal to record (at least) a level for return equal to a benchmark assumed to be normal (this can be considered as an "anchor"). It can be considered that the rate of equity return recorded in the past can be considered as a proxy for future performance. As such, in this study, we assumed, conventionally, that investors consider an average for the past five financial exercises as a first proxy for the required rate of return (noted APROE).

Secondly, shareholders require a rate of return related to IRR (a function of the risk of the investment project). Finally, they accept renouncing dividends in exchange for an acceptable estimated IRR for the projects adopted.

Thirdly, investors analyze the capital market conditions. They compare their return with the returns recorded by other investors, for other investment projects. In our model, we consider that they compare their performance with the capital market return (*kMt*).

Finally, we can assume that all these benchmarks can be adjusted for some extraordinary events. Shareholders can have a relative tolerance before dismissing their management15. We introduce a coefficient of intolerance for the manager's performance—τ, with τ ∈ [0, 1]. If this tolerance is maximal, that means that τ = 0. In other words, shareholders do not require a rate of return (however, they require that their wealth to be maintained at the same level, so min (*ROEt* \* ) = 0). If shareholders decide to maintain the management in function only if the company records a level of ROE higher than *ROEt \** , we can state τ = 1 (they are totally intolerant in the case of a lack of performance). This coefficient can be related to some socio-cultural factors (e.g., Schwartz 2006).

Thus:

$$ROE\_t^\* = \pi \cdot \max(APROE\_t; E\_{t-1}(IRR\_t); kM\_t) \tag{9}$$
