COMPANY’S VALUE EVALUATION THROUGH MODIFYING ITS CAPITAL STRUCTURE WITH BONDS AND STOCKS ISSUANCE SIMULATION USING MACHINE LEARNING AND STATISTICAL ANALYSIS APPROACHES

: the present financial landscape is complexly woven with the interplay of financial instruments and technologies, reshaping the way companies manage their value. Financial instruments act as the cornerstone of capital structure, influencing cash flows and overall valuation. Meanwhile, financial technologies introduce innovation and efficiency via presenting unprecedented capabilities in assessing and forecasting the impact of these instruments on a company's worth. The ability to make timely decisions on resource allocation and capital raising is a key determinant of success in a rapidly evolving business landscape. Thus, the financial sector undergoes transformative changes, reshaping how companies navigate complexities and make informed decisions in an increasingly dynamic environment. The symbiosis of these elements is reshaping the future of finance, offering new avenues for creating and managing value in an interconnected world.


General assumptions, data, and methodology.
Financial data of Berkshire Hathaway was selected for this investigation due to its robust track record of successfully issuing substantial bonds, reflecting the company's financial strength, thus possibility to handle huge issuances.With over 2 billion stocks outstanding, Berkshire Hathaway presents a unique opportunity for in-depth analysis of stock dynamics.Additionally, the company's commitment to transparency provides easy access to coherent financial data, a crucial factor in accurate forecasting.This is why the company is an ideal subject for comprehensive financial modeling, offering valuable insights into the intricate interplay of capital structure, stock dynamics, and overall financial performance.
Forecasting time series data involves predicting future values based on historical observations.For this purpose, the often choice is ARIMA [4], exponential smoothing [5], gradient boosting (in our case, XGBoost [11]), linear regression [9], trivial forecast (in our case, mean of three previous observations for prediction), and an annual growth model.Thus, Berkshire Hathaway's financials from 2007 to 2022 are used as an initial data set [1][2].To assess model accuracy, each financial indicator undergoes rigorous backtesting, evaluating performance over the last five periods of known data using MAPE metric.Such an approach with accuracy evaluation with MAPE on basis of known data ensures robustness in model selection [6, p. 121] and sets the stage for forecasting the company's financial trajectory from 2023 to 2027.
The ultimate objective of forecasting Berkshire Hathaway's financials lies in simulating the potential impact of issuing bonds and stocks on its financial results.By utilizing these forecasts, various scenarios may be simulated, exploring how different levels of bond and stock issuances might influence the company's overall financial health.This simulation approach allows for strategic planning and risk management, aiding in decision-making related to capital structure, financing options, and potential implications for shareholders.
The investigation introduces simulations of bond and stock issuances at varying levels, conducted separately to analyze their distinct impacts.Stock issuance levels are set at 0.05%, 0.1%, 0.3%, and 0.5% of existing shares, equivalent to 1.1kk, 2.2kk, 6.6kk, and 11kk shares, respectively.Similarly, bond issuances are simulated at levels of 300k, 700k, 2000k, and 3500k pieces.To maintain comparability, all bonds have a 5-year maturity, a face value of 1000, and a coupon rate of 2%.The chosen numbers facilitate a comprehensive analysis, allowing for a straightforward comparison between stock and bond issuances.Stocks and bonds are issued once, in the year 2023.These specific quantities were selected to ensure that issuing 300k bonds results in a comparable increment in total assets to issuing 1.1kk stocks.This equality is maintained across various levels, providing a consistent basis for evaluation.Coupon payments associated with bond issuances are considered liabilities and influence total assets.However, dividend payments are not factored into the analysis, aligning with Berkshire Hathaway's policy of not paying dividends.
The simulation incorporates the nuanced impact of issuing bonds and stocks on the company's financials.Since issuing bonds introduces additional debt, it affects both Liabilities and Total Assets.Concurrently, issuing stocks adds to equity, influencing Total Assets [8].These dynamics are seamlessly integrated into the forecasted financials, ensuring a comprehensive representation of the company's evolving capital structure.To derive Revenue, a sophisticated approach is employed, utilizing weighted rates of Revenue to Assets, Revenue to Debt, and Revenue to Equity which show how dependent one variable is on another and are calculated as dividing the first specified variable by the second.Further those are also used to calculate Free Cash Flow and Net Content is licensed under the Creative Commons Attribution 4.0 license (CC-BY 4.0) income that occur when bond and stock issuing scenarios are deployed.Both while issuing bonds and stocks, forecasted rates associated with dependence on debt were used to make results comparable.This approach is used because pure forecasting of Net Income is only applicable for estimating algorithms accuracy, while running scenarios is a more complicated task.Thus, this method considers the diverse effects of financial instruments on the various components of the company's structure.

Models evaluation and financials forecasting.
Backtesting process is shown on example of Revenue forecasting in Figure 1.As it can be seen, gradient boosting encounters challenges in predicting this specific financial metric, primarily due to limited training dataset.Expanding the dataset by incorporating quarterly financials may be a potential solution, providing machine learning algorithms with a richer context.This allows the algorithms to identify subtler patterns, leading to more accurate predictions.Extending to big data opens opportunities of using neural networks which unlocks additional opportunities in enhancing prediction capabilities.In Table 1, the results of backtesting are provided.Notably, dependencies of one variable on another were more challenging for prediction than pure financials, which highlight either vulnerability of such dependencies or lack of data available [7].All in all, these results underscore the importance of choosing models tailored to specific financial indicators, as each of them has own characteristics in patterns.(compiled by the author based on data from [1][2]).
It is noteworthy that the simple trivial model often outperforms complex models in forecasting time series data, making it a tough competitor to beat.Despite its simplicity, it is really effective when there is no access to large datasets that ML algorithms thrive on.Forecast example is depicted in Figure 2 and shows the prediction of Revenue for 5 years.(compiled by the author based on data from [1][2]).
Thus, for getting accurate predictions diverse models were employed and rigorously backtested, so that the chosen models serve as a robust foundation for forecasting the company's trajectory for future periods.It is important to mention that an ultimate forecasting model does not exist, thus testing and evaluating the most suitable one for specific characteristics of dataset is crucial.This forward-looking exercise provides a strategic outlook for simulating the impact of issuing financial instruments.

Simulation modeling.
Dynamics of the most important results of all simulations is shown in Figure 3.  Analyzing absolute total figures presents challenges, emphasizing the importance of examining relative dynamics, as depicted in Figure 5.The data is normalized to the initial forecast, revealing non-linear impacts of stocks and bonds, contrary to initial perceptions of previous figures.Distinct patterns emerge; early Revenue growth is predominantly influenced by bonds issuance, with equity financing proving more profitable in the long run.In contrast, debt borrowing yields a more substantial initial jump in profitability.Net Income is more significantly impacted by bonds issuance than stocks, while Total Assets experience a greater increase with stocks issuance due to its non-obligatory nature [10].WACC follows the trend discussed earlier, rising with larger stock issuance, and dropping with increased bond issuance.This nuanced perspective provides a more comprehensive understanding of the complex dynamics between stock and bond issuance, profitability, and the overall financial structure of Berkshire Hathaway.Moreover, the average growth rates for Revenue and Net Income are higher in scenarios involving bonds issuance, along with an increase in Total Assets.These findings align with the earlier-described patterns.The Total Valuation in the DCF model, considering the Terminal Value (Table 6), illustrates that bonds have a more pronounced impact on total valuation compared to stocks.This is attributed to the fact that bonds generate a more substantial revenue, influencing both the TV and Present Value of TV.The percentage variations in the total valuation for different scenarios of stock and bond issuance, relative to the initial forecast, show that bonds, especially at higher levels, contribute more significantly to the total valuation.(compiled by the author based on data from [1][2]).

Those include changes in
Overall, in the DCF valuation of Berkshire Hathaway, different scenarios show that bonds have a more pronounced impact on Total Valuation than stocks.This analysis, using Free Cash Flow dynamics, indicates that bond issuances, by lowering WACC and altering the capital structure, lead to a higher valuation.This effect is evident when considering both the Terminal Value and its Present Value.The comparison of various stock and bond issuance scenarios reveals that bonds, especially in larger quantities, significantly enhance total valuation relative to the initial forecast.

Conclusion.
The analysis from 2007 to 2022 involves diverse models, backtested with MAPE.

Fig. 3 .Fig. 4 .
Fig. 3. Results of simulations.Dynamics of Revenue, Total Assets, Debt-to-Equity, and WACC correspondingly for 2023-2027 (compiled by the author based on data from [1-2]) Dynamics of Business Value and Market Capitalization are depicted in Figure 4. Thus, stocks issuance contribute more both Business Value and Market Capitalization in comparison to bonds.

Table 1
Backtesting results for each financial

Table 2
lower paces, while predicted Share Price is quite vulnerable.As for dependencies, those are expected to stay almost unchanged.
. According to the forecast, Revenue is expected to grow, as well as Total Liabilities.Total Equity is about to increase with Content is licensed under the Creative Commons Attribution 4.0 license (CC-BY 4.0)

Table 3
presents the specific variations in simulation results compared to the initial forecast.It's important to note that each simulation value represents the mean of all forecasted years for the corresponding indicator.All percentage values are additional (or subtractive) percentages relative to the initial forecast.In general, the table reaffirms the empirical observations mentioned earlier.Notably, contrary to stocks, bonds exhibit minimal impact on Market Capitalization.Additionally, bonds tend to have a negative effect on a company's Business Value, decreasing it as more bonds are issued.

Table 3
Content is licensed under the Creative Commons Attribution 4.0 license (CC-BY 4.0)

Table 4
showcases average changes in ROS, D/E, and WACC, which are absolute, and EPS, which is normalized to initial forecasting.D/E logically decreases with stock issuance, in contrast to bonds, with almost identical paces.Although WACC changes are relatively insignificant, the table confirms earlier statements about dependence of WACC and introducing debt or equity.It is important to mention once more that simulating Net Income and Free Cash Flow required weighted calculations, as in the case of Revenue.ROS experiences a more substantial decrease with stock issuance compared to the growth observed in bonds ROS, which is, thus, due to patterns of Net Income simulated.The decrease in EPS for stocks is attributed to the slower pace of revenue growth relative to the rapid increase in stock issuance.It's essential to note the interconnected nature of ROS and EPS with revenue, where bonds issuance exhibited higher revenue growth, influencing these results.

Table 5 .
The results reflect the impact of various scenarios on FCF, in percentages relative to the initial forecast.This disparity suggests that bond issuances contribute more significantly to the increase in the DCF valuation of Berkshire Hathaway compared to stock issuances.Lower costs of capital through bond issuances lead to a higher valuation in a DCF model because of lower WACC and shifts in capital structure[3, p.

Table 6
Total Valuation using DCF model for each scenario, 2027