Econometric Modeling And Forecasting Companys FCF Components
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Published: Wed, 14 Mar 2018
Modeling of corporate financial activity is an essential part of financial analysis, budgeting and company valuation. A model, consisting of selected items from financial statements usually is constructed and used for forecasts without any specific techniques – simply predicting potential growth of a company’s income according to historical trends (adjusted by overall economic situation or intentions of management) and calculating other items, such as profit or working capital, using historical or desired ratios. Choosing assumptions for modeling and forecasting includes a high amount of subjectivity, caused by human factor. It could be reduced by using econometric techniques.
It is common knowledge that corporate activity is highly influenced by macroeconomic environment and econometric methods could be useful to incorporate both, endogenous financial statement (also called accounting) variables (e.g. sales, expenditures, investments, liabilities etc.) and exogenous macroeconomic (e.g. GDP growth, inflation, interest rates, etc.) ones.
As it was mentioned before, one of the purposes of financial modeling is company valuation (not only for companies listed on exchanges, but also for those involved in mergers and acquisitions (hereinafter – M&A) process), which can be performed using discounted cash flow (hereinafter – DCF) method. Due to this reason mainly items necessary for calculating free cash flow (hereinafter – FCF) and equity value will be modeled in the empirical part of the Thesis. These are: operating profit, depreciation and amortization, short-term assets and liabilities, long-term assets, financial debt and other auxiliary items.
The research problem is how to model and forecast items necessary to calculate a company’s FCF using econometric methods. From the problem definition the main aim to verify major hypothesis, whether financial statement items can be modelled using econometric techniques appears. The hypothesis can be split in three minor ones, which will be easier to verify:
There are “causal relationships between variables “ from financial statements (Medeiros, 2005);
Macroeconomic variables are useful for modelling company’s financial statement items;
Econometric models are useful for short-term (one year ahead) forecasting of financial statement items.
The objectives necessary to achieve the aim and to solve the problem will be:
Analyze the literature on the subject of econometric modelling of corporate performance;
Specify a theoretically reasonable model(s) to explain selected accounting variables using macroeconomic variables;
Choose some Lithuanian companies providing sufficient amount of data;
Estimate the model(s);
Test validity of the models in terms of goodness-of-fit criteria and forecasting performance.
All except one (Doornik, Medeiros and Oliveira (2009)) researches analyzed used structural simultaneous-equations models (SEM) estimating them by ordinary least squares (hereinafter OLS) or two-step least squares (hereinafter 2SLS) techniques. The major possible problem to encounter in the research can be insufficient amount of data available, as only companies listed on exchanges provide their financial statements publicly and for rather short period of time. In Elliott’s work (1973) such problem occurred and he said his “model is overidentified simultaneous system having a large number of exogenous and lagged endogenous variables relative to number of observations.” To tackle the problem “the structurally ordered instrumental variables [hereinafter – IV] approach” was used and this method will be possible (if necessary) in this Thesis.
Doornik et al. (2009) presented alternative way for modeling corporate activity: vector autoregression (hereinafter VAR) model, followed by vector error correction model (hereinafter VECM), mainly reasoning that “its forecasts are considered superior to simultaneous equation models”.
In order to get the most valid models for selected Lithuanian companies (in aspects of the best fitting to data and forecasting performance) all types of before mentioned methods will be used and conclusions, which of them are the most suitable (if suitable at all), will be provided.
In the Thesis secondary quantitative data will be used. It will include:
Official statistics, such as economical indicators (e.g., GDP growth, inflation and unemployment rates, growth of gross wage, interest rate, etc.) available through internet pages of state institutions (e.g. Department of Statistics to the Government of the Republic of Lithuania www.stat.gov.lt, The Ministry of Finance of the Republic of Lithuania www.finmin.lt, the Bank of Lithuania www.lb.lt.
Data from companies’ financial statements (income, profit, depreciation, liabilities, etc.) will be collected from internet page of exchange operator NASDAQ OMX Vilnius www.nasdaqomxbaltic.com. The companies that provided financial statements for the longest period of time (approximately for 10 years) will be selected.
The quantitative data analysis will be prepared with statistical / econometrical computer software, like R, EViews (Model object (Cuddington et al. (2008)), Gretl or / and simply Excel add-inn for data analysis.
The research was started carefully analyzing works previously done on similar topics. A summary of comprehensive literature analysis and evaluation is provided in Literature Review part. After discussing previous approaches on the topic Problem Definition part is provided. In the Methodological Approach part techniques chosen are justified and models specified. After this the most time consuming and various types of knowledge and skills requiring analytical part was performed. The results of it are summarized in Empirical Research Report. The last but not the least parts are Discussion and Conclusions, where literature review and findings of empirical research are integrated and everything summarized.
Application of econometric methods in corporate finance sphere is not very popular due to lack of data available and usually short time series. But there are some works devoted exactly to the econometric modeling of company’s financial statements incorporating macroeconomic variables. These are presented in section 2.1. and further research will based on theoretical framework constructed combining these works. Other literature, reviewed in section 2.2. …
Review and Analysis of Historical Researches on Econometric Modeling of Company’s Financial Activity
Saltzman (1967) was the first who broke the ice using econometric techniques to model a company’s financial statements. He constructed a simultaneous equation model consisting “of ten relational equations and five definitional equations” (p. 332). Endogenous variables, such as sales, production prices, amount of output, inventories, various costs and expenses, investments were taken from the company’s financial statements and other reports. The main exogenous variables, included into the model, were wage rates, raw materials prices and determinants of external demand. All the data used was quarterly, for nine years “allowing 35 observations for estimating purposes” (p. 339). The author chose to analyze a large US corporation’s subsidiary, working in oligopolistic market of manufacturing and selling home laundry appliances.
In order to get better interpretable results, theoretically specifying model it was divided into three parts:
Sales, prices, inventory and output
Investment and expenses
Cost and profit
Speaking about the first group of endogenous variables, Saltzman describes the company’s sales as demand function, depending on rather large amount of factors: sales in previous period; sales and product engineering expenses, “deflated by an appropriate average wage rate”; average price of products; interest rates, meaning “the cost and availability of credit” (p. 334); total potential market, estimated as “the sum of the total potential new market and the total potential replacement market” (p. 333) and income effects (personal disposable income divided by average price of the firms production). Also in the equation dummy or so called “shift” variables necessary to catch the effects of seasonality  were included. The production price equation was defined using economic theory, which states that company’s demand should be equal to its supply in order to maximize the profits. As data of other competitors were not available, in order to meet previously mentioned condition, one of the explanatory variables was the company’s average production costs. Also supply and demand influence on price was tried to capture using “the production capabilities and inventory position of the firm” (p. 335). Besides these variables lagged price term was included “to indicate the effects of expectations” (p. 335). The company’s output and inventory equations were defined in more simple way. The latter one was defined as function of inventory in previous period, the output and cost of sales, while the output was said to depend on output in previous period, production costs and inventory in previous period.
The second group of endogenous variables, investment and expenses, according to Saltzman, were even more difficult to define. The reason for problems defining expenses were that “management’s decisions in the area of expenses is assumed to be the current and anticipated rates of demand for the firm’s products in relation to the production capabilities and the inventory position” (p. 336) and a lot of these data were unavailable. The situation was tackled including in the expense equation difference between the company’s costs and inventories in previous period, as well as lagged and current sales and operating profit. Administrative expenses were assumed to be influenced by these expenses in previous period and sales.
Problems with modeling investment appeared it this case, as analyzed company was a subsidiary, thus investment decisions depended on parent company. Modeling total investment gave no satisfactory results, thus investments were divided in separate parts: capital expenditures, product engineering expenses and manufacturing engineering expenditures. Capital expenditures’ equation was defined as function of lagged capital expenditures, current sales, operating profit and dummy variable for periods, when there were no such investments. Other type of investments were product engineering expenses, which were assumed to depend on such type of investments in previous period, current sales, operating profit, “the firm’s percentage of the total industry sales” (p. 337) and the same dummy variable as in capital expenditures case. The author assumes that manufacturing engineering expenditures to be influenced by the lagged variable itself, sales and operating profit.
The cost and profit subsystem consists of the company’s manufacturing cost equation, while total and cost as well as profit were defined as identities. Manufacturing cost was assumed to be influenced by the same costs in previous period, the company’s sales, average price of materials, average wage rate. Moreover, “the firm’s efforts on behalf of cost reduction” (p. 338) were included in the equation in terms of production engineering, manufacturing, capital and administrative expenses divided by the firm’s average wage rate. Identity of total costs includes manufacturing cost, sales, product engineering, manufacturing engineering administrative and miscellaneous expenses. The company’s profit was defined as difference between sales and total costs and uncontrolled expenses.
An extremely large amount of exogenous and lagged endogenous variables and time series consisting only of 35 observations caused model overidentification problem. The equations were estimated using OLS and 2SLS methods. The results compared shown that “for this particular sample there was not a great deal of difference in the results of these alternative estimating procedures” (p. 332). After the estimation some variables, which signs were “contrary to theoretical considerations” (p. 332) were dropped from the equations and the model reestimated. Although nearly all coefficients were significant and R2 measures relatively good, multicollinearity could be the reason of these measures. This problem was tried to solve replacing some variables by others, but the results after this procedure were not commented.
Another research on the topic was performed by Elliott in 1973 with attempt to create “a simultaneous-equation model of major elements of overall corporate financial performance” (p. 1499). The main hypothesis the author tried to verify was “that many aspects of corporate financial performance are jointly determined and thus can only be reliably explained in the context of multiple-equation simultaneous model” (p. 1499). Elliott distinguished such joint relationships: sales – cash flows (hereinafter CF), CF – “strategic sales-generating expenditures” and sales – “strategic expenditures”. He also stated that these, as well as other relationships between accountant variables are influenced by “multiplier process” and some “fiscal and monetary policy variables” (p. 1500).
The author defined 11 relation equations and 10 definition identities. Using the equations such endogenous variables were modeled: real sales, production cost per dollar of real sales, marketing, research and development (hereinafter R&D) and capital expenditures (separately), fixed financial charges (mainly interest payments), depreciation, general, administrative and other expenses (as one variable), after-tax profit, inventory investment and new debt. As explanatory variables other accounting or lagged endogenous as well as macroeconomic variables were used. The latter were various combinations of money supply, high-employment government expenditures, yield on corporate securities, relative price movements (expressed dividing price index for company’s industry output by price deflator), shifts of industry demand (defined as index of physical output for company’s industry divided to Federal Reserve Board Index of Industrial Production). The other accounting variables were: firm dividend allocation, new capital raised issuing common or preferred shares, stock of marketing, R&D  , plant and equipment assets  , CF, ratio of costs of production unit to price, long-term debt. Also into some equations index of time was input.
The author introduced the idea that viewing to marketing, R&D and capital expenditures as investment it was possible to use “flexible accelerator mechanism” (p. 1504) for further analysis. Using this technique stocks of previously mentioned expenditures were changed by other variables, defined using respective expenditure in previous period and desired level of it. To define desired level functions depending on CF were used. There the author defined CF unconventionally. According to its approach, CF can be calculated summing up “discretionary internal funds”  (p. 1505), new debt and new funds, raised issuing common or preferred shares.
Some variables, e.g. money supply and high-employment government expenditures, were transformed using Almon-weight  technique with polynomial constraints, another were used as moving average.
Specified theoretical model was estimated using data of nine US corporations for 20 years (1948-1968). The companies were chosen from very different types of industries, such as drug producing, air transport, distilled beverages, building materials and heating, in order “to broaden the significance of observed trends and patterns and to provide a rigorous test of the general applicability of the model developed” (p. 1500).
In order to escape the overidentification problem, which appeared due to “simultaneous system having a large number of exogenous and lagged endogenous variables relative to the number of observations” (p. 1511), instead of 2SLS method Structurally Ordered IV were used. Multicollinearity was eliminated constructing and including into equations first and second stage variables and excluding some variables which “signs were not consistent with” (p. 1512) economic logic. Previously mentioned time index was included into some equations in anticipation of reducing autocorrelation problems. Moreover dummy variables, meaning merger of the firms, was included in two cases.
A lot of exogenous variables were found insignificant explaining modeled accounting variables, but the equations were not reestimated excluding these variables. Goodness-of-fit criteria also shown not very good results in every equation, but surprisingly the author concluded “the model fits the data of the individual firms quite well” (p. 1517). It was explained by rather high R2 measure.
The author tested the model using it for forecasts and comparing them with so called naïve  predictions. In nearly all cases both SEM (despite its overidentification) and instrumental model performed better.
Beedles (1977) research is quite similar to the ones, performed by Saltzman and Elliot, but Beedles himself stated the main difference that his work was devoted “for the study of firms with more than one  objective” (p. 1217). The author’s selected goals were sales, profit and stock price and they were modeled as endogenous variables. Besides these goals such called “policy variables” – investment, financing and dividend decisions – were selected. Investment decisions were split into smaller ones: working capital (as current ratio) and fixed asset (as level of fixed assets) investment decisions. Financing variable was measured as debt to equity ratio. Three more chosen exogenous macroeconomic variables were the Index of Industrial Production, interest rate (measured as yield on Baa corporate bonds) and the level of the stock market (measured as S&P 500 index). Specifying the model “endogenous goals [were] regressed on lagged goals, current and lagged policies, and current values of macro-variables” (p. 1223).
Three specified equations were estimated using OLS and 2SLS methods, but the latter was more appropriate as the system was overidentified using time series of three US companies for 45 years (the year 1929-1973). One more considerable difference comparing to other researches is that the author used relative variables, explaining that “percentage changes are not scale sensitive” (p. 1226) and such variables “eliminates such measurement sensitivity due to both firm size and time period” (p. 1226). Moreover, according to the author, the usage of variables in relative terms is more acceptable for managers, who want to see percentage changes and set goals in percentage terms.
To evaluate “quality” of the models evaluated by OLS and 2SLS techniques even five criteria were used: Theil’s U statistic measure, the covariance proportion of the mean square estimation error (MSE), the model’s ability to predict “turning points in actual data” (p. 1227) and not to predict when there are no such ones, and “an ex-post outside of sample simulation  has been conducted” (p. 1227), which was compared with naïve forecasts. According to these criteria, OLS and 2SLS models “consistently tracks [data] better than naïve model” (p. 1227), but the latter model performs better in out-of-sample forecasts. Comparing OLS and 2SLS “simulations”, 2SLS gives more accurate results, thus is more appropriate in corporate finance cases.
Medeiros in 2005 constructed and tested “an econometric model of a firm’s financial statements” also using SEM in order to connect market (micro and macroeconomic) variables with accounting ones. Medeiros, similarly as Saltzman, chosen one firm to apply the model, but differently the firm chosen was a Brazilian monopolist producer of petrol products. The author raised the purposes to explain “the relationships between economic and accounting variables” (p. 2) and “to test empirically the causal relationships between variables inside the financial statements” (p. 2) and in order to reach them divided the model into three parts. In the first one petroleum market, in the second – income statement, in the third – balance sheet was modeled. From the financial statements such variables were taken: gross revenues, total costs, net earnings, current assets and liabilities, long-term receivables and debt, fixed assets and equity. As market variables demand, supply, price, GDP and exchange rate were used.
In the model the author constructed seven linear equations and nine “accounting identities or mathematical relationships” (p. 2). As was previously mentioned, “the model was applied to (…) a near monopolist firm in the Brazilian domestic market for petroleum products using its annual data from 1991 to 2001” (p. 6). For the estimation of the equations 2SLS method was chosen.
Before the system estimation all series were tested with Augmented Dickey-Fuller (hereinafter ADF) test for unit root, but the results were not commented. No special goodness-of-fit tests were performed. Such simple characteristics, as R2 and t-statistics shown the exogenous variables to explain endogenous rather well (nearly all coefficients significant, signs – as expected according to economic and accounting logic, R2 “satisfactory”), thus the model was used to forecast respective financial statement items for 2002-2004. But the forecasted numbers were not compared to the actual ones, thus it difficult to decide, if the model performed well.
New approach to econometric modeling of company’s activity was presented by Doornik et al. in 2009. It was offered to use VAR – VECM model instead of common SEM. The main motivation of such choice was that VAR – VECM’s “forecasts are considered superior to simultaneous equation models” (p. 2). The researchers, one of which performed previously discussed paper, selected to model the same Brazilian company in order to explain “the relationship among the accounting variables and the relationship of these variables with economic exogenous variables” (p. 2). From quarterly financial statements (1990-2006) such variables were chosen: current assets, fixed assets, current and long-term liabilities, equity, net revenue and net income. The accounting variables were adjusted by inflation. As exogenous economic variables were selected country’s interest rate  , country risk  , exchange rate, price of petroleum, Brazilian Wholesale Price Index (hereinafter WPI) and US Producer Price Index (PPI).
Before starting modeling specific data analysis, necessary “to support an appropriate model specification” (p. 5) was performed. Firstly ADF test for “the presence of unit roots in the variables” (p. 10) was carried out. The series were unit root appeared, were differenced and then first difference of them was included into the equations. After ADF test cross-correlation matrix was calculated and Granger causality analysis performed. This shown, which variables are related or influences each other. Later on carried out cointegration analysis “offered” constructing VECM instead of VAR model.
The best  estimated VECM had four lags, thus there were difficulties interpreting the coefficients “especially because the coefficient signals alternate over time” (p. 14). This problem was solved applying impulse response function “to verify how the dependent variables respond to a shock applied to one ore more system equations” (p. 14) and variance decomposition, “which decomposes the forecasted variance error for each variable in components which may be attributed to each of the endogenous variables” (p. 14-15).
Two types of forecasts were performed with selected VECM model. The first one – “ex-post” for 2002-2006 “with the objective of validating the predictive capacity of the model, comparing annual predictions with real data” (p. 15), the second one – “ex-ante” for 2007-2010. Doing ex-post forecast shown relatively good results for one year period (the largest deviation from real value was 1.37%), while for longer term periods the precision decreased. Ex-ante forecasts required to do predictions for macroeconomic variables and perform stochastic simulation. Of course, accuracy of the forecasts could not be measured.
Saltzman of course did a great job pioneering econometric modeling of financial statement, but his chosen exogenous variables, such as demand or supply, were rather difficult to measure, thus limited the model and made it imprecise. Lack of data and not solved problems with both multicollinearity and overidentification also made results to be not very reliable. Due to these reasons the model was not applicable for forecasts, although the author did not try to use it for this process. Also it is unclear, if exactly such way specified model would be applicable and explanatory to other firms, but some ideas of selecting variables can be taken.
Elliot, the second author, who attempted to model corporate performance with econometric techniques, took an advantage over Saltzman introducing different techniques of incorporating variables (e.g., almon-weights, accelerator mechanism, moving averages) with rather reasonable economic logic. On the other hand the economic and accounting logic of selecting variables and specifying equations was not confirmed, when a large amount of estimated coefficients revealed to be insignificant. Insignificance of coefficients does not allow using the models for other researches credibly, but not bad forecasting performance suggests taking into consideration some new concepts.
Beedles gave some critique on Saltzman’s and Elliot’s works, but did not provide any special improvement except of trial to use variables in relative instead of absolute terms  . The author clearly justified selection of endogenous variables (as firm’s goals), but he admitted himself, that “the specification of equations [was] difficult to find” (p. 1224) and “hundreds of other [macroeconomic] variables could be used to explain the selected objectives” (p. 1223). Moreover, possible multicollinearity was not tested.
The main limitation of last two in previous section presented researches is that the models where applied to only one monopolistic company. Especially it is important in the model presented by Medeiros, where such exogenous variables as supply and demand where used. These variables would be hard to evaluate for non-monopolist companies. Moreover, Medeiros used two little measures to verify “goodness” of the model: no goodness-of-fit tests were performed and although the model was used for forecasting, forecasting performance was not evaluated.
Doornik’s et al. presented VAR-VECM method, which allows not specifying every single equation a priori. Final selection of variables can be done after constructing cross-correlation matrix and performing Granger causality test. Due to this reason model specification becomes easier. On the other hand these methods do not allow explaining every coefficient, but provides a possibility to evaluate “the response of a variable with respect to a shock in another variable” (p. 5). Simplicity of specification and rather good the model’s forecasting performance suggests using the method for further research.
Review and Analysis of Other Literature in Relevant Area
Oxelheim in his working paper (2002) emphasized the importance of “macroeconomic fluctuations” on development of companies and gave some ideas on the choice of selecting macroeconomic variables possible to include in the model. The categories of indicators he pointed out were exchange, interest and inflation rates  as well as political risk premiums. He noticed that especially it is important to pay attention to the indicators in periods, when their volatility is high. According to him, exchange rates became extremely volatile and thus influential after collapse of Bretton Woods system in 1971 and since now (except cases when countries have pegged currency) it is essential to pay attention to exchange rate “evaluating foreign assets and liabilities in individual companies” (p. 5). The group of interest rate indicators usually was analyzed simultaneously with exchange rate, as it is mainly “concerned with debt, and its main focus is on translation of foreign debt” (p. 6). The impact of inflation was stated to be “closely linked to the problem of foreign investments and is concerned with differences in inflation between the countries in question” (p. 6). The last mentioned as important factor political risk premium was not analyzed in more details.
It is obvious that exact indicator should be selected individually. For example, analyzing the activity of Swedish car producer Volvo the author included Swedish real effective exchange rate, Producer prices in Germany (as the main competitors of the company are located in Germany) and Swedish short-term as well as world basket interest rates. Also the author stated, “The set of relevant variables may shift over time and the company should therefore follow up the process of identification continuously”.
Bezuidenhout, Hamman and Mlambo (2008) devoted their work to investigating causality between cash flow and earnings variables. They emphasized that it is very important to test stationarity, co-integration and causality between variables “before any attempt (…) to regress on variable on another” (p. 1-2). The authors used four earnings measures in the research: earnings before interest and tax (hereinafter EBIT), profit before tax, profit after tax and net earnings. As well three cash flow measures were used: cash generated from operations after adjustment for non-cash items, cash generated from operations adjusted for investment income received and working capital, and cash flow from operating activities after adjustments for interest and tax paid. The analysis was done with data of 70 companies from 16 sectors, thus credibility of the results is high. All the previously mentioned tests were performed in series. Firstly, stationarity was determined looking into the graphs, autocorrelation functions and correlograms as well as unit root tests  (ADF) of the time series. Secondly, the Johansen test for co-integration of the series, which were found to be non-stationary and integrated in the same order, was used. Thirdly, causality between variables, which were stationary, with Granger test was tried to determine, “th
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