# Financial Sustainability Evaluation and Forecasting Using the Markov Chain: The Case of the Wine Business

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methods and Data

- C—the region characterizes the unstable state of the indicator,
- B—the region related to pre-crisis state of the indicator (preventive measures are required),
- A—characterizes the critical or crisis state of the indicator and requires the use of more radical activities to ensure financial security.

_{к}is the integral performance of financial security according to the k-th indicator; n is the number of periods; X

_{кt}is the k-th indicator value in the period t.

_{1}is the net working capital flexibility; X

_{2}is the current (total) liquidity ratio; X

_{3}is the quick ratio; X

_{4}is the absolute liquidity (solvency) ratio; X

_{5}is the financial autonomy ratio; X

_{6}is the current assets to equity ratio; X

_{7}is the capital productivity ratio; X

_{8}is the operating cycle duration; X

_{9}is the financial cycle duration; X

_{10}is the book debts repayment rate; X

_{11}is the owned capital turnover; X

_{12}is the total capital turnover; X

_{13}is the output profitability; X

_{14}is the activity profitability; X

_{15}is the return on assets; X

_{16}is the owned capital profitability. In such a case, indicators X

_{1}–X

_{4}form a group of liquidity indicators, X

_{5}–X

_{6}is the group of financial stability indicators, X

_{7}–X

_{12}is the business activity indicators and X

_{13}–X

_{16}is the profitability indicators.

_{j}is the integrated financial security indicator represented by the j-th group of indicators; m is the the number of indicators in the group. The above-mentioned measure identifies the most groups of indicators and the corresponding management measures.

_{t}is the integral indicator of financial security in the t period; f is the number of indicators (in the proposed system it equals 16).

_{1}); high level of financial security (s

_{2}); medium level of financial security (s

_{3}); low (pre-crisis) level of financial security (s

_{4}); crisis (critical) level of financial security (s

_{5}). Thus, the transition matrix has a 5 × 5 order with each element indicating the probability of transition from state s

_{i}to state s

_{j}. Moreover, the elements in each row of the matrix should add up to unity as each row represents a probability distribution.

_{i}to s

_{j}state during three paths: h

_{1}—increase of the financial security level; h

_{2}—stable financial security level; h

_{3}—decrease of the financial and economic security level. We will address the possible paths through the meso- and macro-economic conditions for the wine sector.

## 4. Results

- recovery periods: 2010, 2015;
- periods of stability: 2007, 2011, 2012, 2013, 2016, 2017;
- downturn periods: 2008, 2009, 2014.

- ▪
- in the recovery periods (2 periods), the number of periods with increasing financial safety indicators is 1 (thus, $P({h}_{1}|{a}_{1})=1/2$); the number of periods with stable level of the indicators is 1 ($P({h}_{2}|{a}_{1})=1/2$);
- ▪
- in the stability periods (6 periods), the number of business financial safety decreases is 1; the stationary level is 5;
- ▪
- in the downturn periods (3 periods), the number of business financial safety decreases is 2; the stationary level is 1.

_{2}to level s

_{1}(i.e., to improve financial security), the pre-set probability of increase in the financial security h

_{1}and probability a

_{1}for the meso- and macro-economic conditions of the sector functioning are multiplied:

_{2}will occur both in case of the increasing (a

_{1}= 0.5) and stable (a

_{2}= 0.5) level of the meso- and macro-economic conditions of the sector functioning:

_{2}to level s

_{3}is obtained residually as:

_{2}to levels s

_{4}and s

_{5}is zero as such cases are not observed during the training process.

_{3}–s

_{4}:

_{5}, it is only possible to consider the probability of a rise to the financial security level s

_{4}, which is equal to 0.25. In other cases, the probability of staying in level s

_{5}in crisis is 0.75. Thus, we obtain a probability matrix of the transition among the financial security levels for the PJSC Artwinery taking into account the meso- and macro-economic conditions and the internal financial management possibilities. The transition matrix for the optimistic scenario takes the following form:

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Shewhart charts for liquidity indicators of PJSC Artwinery. (

**a**) Dynamics in X

_{1}; (

**b**) Dynamics in X

_{2}; (

**c**) Dynamics in X

_{3}; (

**d**) Dynamics in X

_{4}.

**Figure 2.**Shewhart charts for the financial stability indicators of PJSC Artwinery. (

**a**) Dynamics X

_{5}; (

**b**) Dynamics in X

_{6}.

**Figure 3.**Shewhart charts for business activity indicators of PJSC Artwinery. (

**a**) Dynamics in X

_{7}; (

**b**) Dynamics in X

_{8}; (

**c**) Dynamics in X

_{9}; (

**d**) Dynamics in X

_{10}; (

**e**) Dynamics in X

_{11}; (

**f**) Dynamics in X

_{12}.

**Figure 4.**Shewhart charts for profitability indicators of PJSC Artwinery. (

**a**) Dynamics in X

_{13}; (

**b**) Dynamics in X

_{14}; (

**c**) Dynamics X

_{15}; (

**d**) Dynamics in X

_{16}.

**Figure 5.**Probability of change of financial security level of PJSC Artwinery according to the optimistic scenario.

**Figure 6.**Probability of change of financial security level of PJSC Artwinery according to the baseline scenario.

**Figure 7.**Probability of change of financial security level of PJSC Artwinery according to the pessimistic scenario.

Informal Description of Graduations | Numerical Value |
---|---|

Very high financial security level | 0.8–1.0 |

Sufficient financial security level | 0.64–0.8 |

Medium financial security level | 0.37–0.64 |

Low (pre-crisis) financial security level | 0.2–0.37 |

Crisis (critical) financial security level | 0.0–0.2 |

Indicator | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 |
---|---|---|---|---|---|---|---|---|---|---|---|

X_{1} | 0.67 | 0.50 | 0.31 | 0.19 | 0.15 | 0.08 | 0.12 | 0.15 | 0.20 | 0.23 | 0.41 |

X_{2} | 3.16 | 2.08 | 1.54 | 1.25 | 1.17 | 1.09 | 1.13 | 1.17 | 1.25 | 1.30 | 1.69 |

X_{3} | 3.13 | 1.99 | 1.52 | 1.22 | 1.15 | 1.07 | 1.09 | 1.06 | 1.14 | 1.22 | 1.46 |

X_{4} | 0.03 | 0.07 | 0.02 | 0.02 | 0.01 | 0.01 | 0.05 | 0.11 | 0.10 | 0.09 | 0.22 |

X_{5} | 0.72 | 0.61 | 0.55 | 0.49 | 0.40 | 0.36 | 0.38 | 0.40 | 0.42 | 0.41 | 0.55 |

X_{6} | 0.79 | 0.65 | 0.36 | 0.25 | 0.26 | 0.16 | 0.22 | 0.26 | 0.35 | 0.44 | 0.58 |

X_{7} | - | 4.38 | 2.70 | 1.98 | 2.22 | 2.14 | 2.19 | 2.24 | 2.42 | 1.64 | 2.59 |

X_{8} | - | 359.66 | 343.16 | 270.22 | 340.45 | 392.01 | 423.28 | 427.83 | 756.42 | 510.34 | 525.26 |

X_{9} | - | 293.83 | 278.03 | 156.89 | 149.81 | 168.86 | 191.90 | 235.77 | 473.85 | 305.85 | 315.84 |

X_{10} | - | 0.30 | 0.35 | 0.33 | 0.41 | 0.45 | 0.52 | 0.41 | 0.56 | 0.61 | 0.55 |

X_{11} | - | 1.47 | 1.48 | 1.78 | 1.81 | 1.93 | 1.78 | 1.68 | 1.02 | 1.43 | 1.24 |

X_{12} | - | 0.97 | 0.86 | 0.92 | 0.79 | 0.73 | 0.66 | 0.66 | 0.42 | 0.59 | 0.59 |

X_{13} | 26.10% | 35.59% | 33.37% | 19.85% | 25.19% | 28.70% | 28.70% | 32.89% | 53.70% | 44.28% | 47.53% |

X_{14} | 7.08% | 7.57% | 4.75% | 2.03% | 4.47% | 2.91% | 2.91% | 6.17% | −2.46% | 1.95% | 2.42% |

X_{15} | 5.82% | 5.90% | 3.40% | 1.46% | 2.85% | 1.92% | 1.94% | 4.22% | −1.01% | 1.17% | 2.97% |

X_{16} | 8.87% | 10.19% | 6.57% | 3.35% | 7.57% | 5.17% | 4.97% | 10.33% | −2.43% | 2.46% | 5.44% |

Indicator | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | IP_{к} | IG_{j} |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

X_{1} | 1 | 1 | 1 | 1 | 1 | 0.5 | 1 | 1 | 1 | 1 | 1 | 0.95 | 0.88 |

X_{2} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1.00 | |

X_{3} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1.00 | |

X_{4} | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1 | 0.55 | |

X_{5} | 1 | 1 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1 | 0.68 | 0.68 |

X_{6} | 1 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1 | 1 | 0.68 | |

X_{7} | 1 | 1 | 1 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.70 | 0.76 | |

X_{8} | 1 | 1 | 1 | 1 | 1 | 1 | 0.25 | 0.5 | 0.5 | 0.5 | 0.78 | ||

X_{9} | 1 | 1 | 1 | 1 | 1 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.80 | ||

X_{10} | 1 | 1 | 1 | 1 | 1 | 0.5 | 0.5 | 1 | 0.5 | 0.5 | 0.80 | ||

X_{11} | 1 | 1 | 1 | 1 | 1 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.80 | ||

X_{12} | 1 | 1 | 1 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.70 | ||

X_{13} | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1 | 1 | 1 | 1 | 0.68 | 0.70 |

X_{14} | 1 | 1 | 0.5 | 1 | 0.5 | 0.5 | 1 | 0.5 | 0.5 | 0.5 | 1 | 0.73 | |

X_{15} | 1 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 1 | 0.5 | 0.5 | 0.5 | 1 | 0.68 | |

X_{16} | 1 | 1 | 0.5 | 1 | 0.5 | 0.5 | 1 | 0.5 | 0.5 | 0.5 | 1 | 0.73 | |

I_{t} | 0.90 | 0.94 | 0.81 | 0.84 | 0.78 | 0.69 | 0.78 | 0.61 | 0.66 | 0.66 | 0.81 | 0.77 |

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## Share and Cite

**MDPI and ACS Style**

Rekova, N.; Telnova, H.; Kachur, O.; Golubkova, I.; Baležentis, T.; Streimikiene, D.
Financial Sustainability Evaluation and Forecasting Using the Markov Chain: The Case of the Wine Business. *Sustainability* **2020**, *12*, 6150.
https://doi.org/10.3390/su12156150

**AMA Style**

Rekova N, Telnova H, Kachur O, Golubkova I, Baležentis T, Streimikiene D.
Financial Sustainability Evaluation and Forecasting Using the Markov Chain: The Case of the Wine Business. *Sustainability*. 2020; 12(15):6150.
https://doi.org/10.3390/su12156150

**Chicago/Turabian Style**

Rekova, Nataliya, Hanna Telnova, Oleh Kachur, Iryna Golubkova, Tomas Baležentis, and Dalia Streimikiene.
2020. "Financial Sustainability Evaluation and Forecasting Using the Markov Chain: The Case of the Wine Business" *Sustainability* 12, no. 15: 6150.
https://doi.org/10.3390/su12156150