# The Effect of the Subsidiary on the Ultimate Controller’s Private Benefits: Enlightenment to the Risk Management Challenges for Sustainability of the Corporate

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## Abstract

**:**

## 1. Introduction

## 2. The Design of The Ultimate Controller’s Private Benefits Model

#### 2.1. Model Assumptions

#### 2.2. Main Variables

- (i)
- a represents the autonomy of the subsidiary, which is granted by the parent company; the existence of autonomy will change the profitability of the subsidiary R(a).
- (ii)
- For the subsidiary profit function R(a), its relationship with subsidiary autonomy may have the following two situations. First, R′(a) > 0 means that the increase of autonomy will enhance the profitability of subsidiaries; second, R′(a) < 0, which means the increase of autonomy will weaken the profitability of subsidiaries.
- (iii)
- Under the condition that other factors, such as the scale of business and the main business remain unchanged: assuming that the autonomy of the subsidiary is 0, that is, R(0) = R, it indicates that when the subsidiary does not have the autonomy, the parent and subsidiary have the same profitability.

- (i)
- The value of the function f(a,n) is between (0, 1), which means that the basic coefficient of private benefits expropriation affects the expropriation;
- (ii)
- The independent variables a and n, respectively, represent the autonomy and self-interest demand of the subsidiary, which has an impact on the coefficient f(a,n) for the expropriation.

_{a}< 0, that is, the higher the autonomy, the larger the funds arranged in advance, and the smaller the basis of the ultimate controller’s expropriation.

_{n}< 0, that is, the larger the demand of the subsidiary’s self-interest, the smaller the expropriation basis of the ultimate controller. When ignoring the self-interest, demand and autonomy of the subsidiary, there is f(0,0) = 1, at this time the expropriation’s basis is the entire income. As shown in Figure 2:

## 3. The Model of Private Benefits under the Influence of Subsidiaries

- (i)
- The higher the ultimate controller’s equity ratio $\alpha $ in the parent company, the lower the proportion of expropriation from the parent company;
- (ii)
- The higher the product $\alpha \beta $ of the ultimate controller’s equity ratio to the parent company and the parent company’s equity ratio to the subsidiary, the lower the proportion of expropriation from the subsidiary.

## 4. Model Analysis

#### 4.1. The Influence of the Subsidiary’s Self-Interest Demand on Private Benefits

**Result 1.**

#### 4.2. The Influence of the Subsidiary’s Autonomy on Private Benefits

**Result 2.**

- (i)
- When R(a) is a monotonously decreasing function, there is$\frac{{R}^{\prime}(a)}{R(a)}<\frac{\left|{f}^{\prime}(a)\right|}{f(a)}$, this indicates that the greater the subsidiary’s autonomy, the smaller the ultimate controller’s private benefits.
- (ii)
- When R(a) is a monotonic increasing function, there are two situations. When$\frac{{R}^{\prime}(a)}{R(a)}>\frac{\left|{f}^{\prime}(a)\right|}{f(a)}$, the value of the function (9) is greater than zero. This indicates that the bigger autonomy of the subsidiary, the larger private benefits of control expropriated. When$\frac{{R}^{\prime}(a)}{R(a)}<\frac{\left|{f}^{\prime}(a)\right|}{f(a)}$, the value of the unction (9) is less than zero. This indicates that the bigger autonomy of the subsidiary, the smaller the private benefits of control expropriated.

**Result 3.**

- (i)
- When$f(a)R(a)\frac{{s}_{2}}{\beta}<R{s}_{1}$, that is to say,$R(a)<R(1-\alpha )\beta /\left[f(a)-f(a)\alpha \beta \right]$, let $R(1-\alpha )\beta /\left[f(a)-f(a)\alpha \beta \right]=M$. It shows that when the profitability of a subsidiary is $R(a)<M$, the greater the proportion of the subsidiary’s business scale, the smaller the private benefits expropriated by the ultimate controller.
- (ii)
- when$f(a)R(a)\frac{{s}_{2}}{\beta}>R{s}_{1}$, that is to say,$R(a)>R(1-\alpha )\beta /\left[f(a)-f(a)\alpha \beta \right]$, let$R(1-\alpha )\beta /\left[f(a)-f(a)\alpha \beta \right]=M$. It shows that when the profitability of the subsidiary is$R(a)>M$, the greater the proportion of the subsidiary’s business scale, the greater the private benefits expropriated by the ultimate controller.

#### 4.3. The Influence of Subsidiary’s Self-interest Demand and Subsidiary’s Autonomy on Private Benefits

- (i)
- When the disposable funds owned by the subsidiary’s autonomy do not meet the funds that the subsidiary needs to retain for its own self-interest demand, two situations arise:Scenario 1: If the autonomy of the subsidiary is positively correlated with profitability, and $\frac{{R}^{\prime}(a)}{R(a)}>\frac{\left|{f}^{\prime}(a)\right|}{f(a)}$ is established: private benefits of control increase with the increase in autonomy;Scenario 2: If the autonomy of the subsidiary is negatively related to profitability, that is, $\frac{{R}^{\prime}(a)}{R(a)}<\frac{\left|{f}^{\prime}(a)\right|}{f(a)}$ is established: private benefits of control decrease with the increase of the autonomy.
- (ii)
- When the disposable funds of the subsidiary’s autonomy meet or even exceed the funds that the subsidiary needs to retain for its own interests, that is, the autonomy $a>{\phi}^{\prime}(n)$, the increase in autonomy no longer affects the number of funds in advance, so that the retained earnings remain unchanged. However, the autonomy of the subsidiary still has an impact on the profitability of the subsidiary, resulting in another two situations:Scenario 3: When R’(a) > 0: as the autonomy increases, the private benefits increase;Scenario 4: When R’(a) < 0:as the autonomy increases, the private benefits decrease.Result 4 can be inferred as the following.

**Result 4.**

**Result 5.**

- (i)
- When the funds that the subsidiary needs to retain are less than the subsidiary’s disposable funds within its autonomy: as the self-interest demand increases, the private benefits decrease;
- (ii)
- When the funds that the subsidiary needs to retain are greater than the subsidiary’s disposable funds within its autonomy: as the self-interest demand increases, the private benefits remain unchanged.

## 5. The Private Benefits Expropriation Proportion to the Public Parent—Subsidiary Company

**Result 6.**

## 6. Discussions

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 2.**Probability Distribution of Autonomy Difference Funds. The solid curve represents high autonomy. The dotted curve represents low autonomy.

**Figure 4.**The relationship between the ultimate controller’s private benefits and the subsidiary’s self-interest demand.

Notation | Definition |
---|---|

n | The self-interest demand of the subsidiary |

a | The autonomy of the subsidiary |

α | The shareholding ratio that the ultimate controller holds |

A | Parent company’s assets |

m | The subsidiary business scale coefficient |

β | The proportion of the parent company’s equity investment in subsidiaries |

R(a) | The profitability of subsidiaries |

R′(a) | The derivative function of profitability |

f(a,n) | the basic coefficient of the expropriation |

s | the proportion of the expropriation |

${s}_{1}$ | the proportion of private benefits that the ultimate controller derives from the parent |

${s}_{2}$ | the proportion of private benefits that the ultimate controller derives from the subsidiary |

$c(s)$ | the function of the private benefit ratio |

${c}_{s}$ | the first derivative of s |

${c}_{ss}$ | the second derivative of s |

k | the degree of the legal protection of shareholders |

P | private benefits |

U | The ultimate controller’s total revenue |

M | Abbreviated function of $R(1-\alpha )\beta /\left[f(a)-f(a)\alpha \beta \right]$ |

$\phi (a)$ | Subsidiary’s function of arranging funds in advance |

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**MDPI and ACS Style**

Cai, M.; Ma, Z.; Li, Y.
The Effect of the Subsidiary on the Ultimate Controller’s Private Benefits: Enlightenment to the Risk Management Challenges for Sustainability of the Corporate. *Sustainability* **2022**, *14*, 4837.
https://doi.org/10.3390/su14084837

**AMA Style**

Cai M, Ma Z, Li Y.
The Effect of the Subsidiary on the Ultimate Controller’s Private Benefits: Enlightenment to the Risk Management Challenges for Sustainability of the Corporate. *Sustainability*. 2022; 14(8):4837.
https://doi.org/10.3390/su14084837

**Chicago/Turabian Style**

Cai, Ming, Zhong Ma, and Youhua Li.
2022. "The Effect of the Subsidiary on the Ultimate Controller’s Private Benefits: Enlightenment to the Risk Management Challenges for Sustainability of the Corporate" *Sustainability* 14, no. 8: 4837.
https://doi.org/10.3390/su14084837