An Econometric Model of a Firm s Financial Statements. Otávio Ribeiro de Medeiros ABSTRACT

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1 An Economeric Model of a Firm s Financial Saemens Oávio Ribeiro de Medeiros ABSTRACT This paper repors he consrucion and esing of an economeric model designed o represen a firm s financial saemens. More specifically, he paper aims a showing how a firm s financial saemens can be empirically explained by means of a simulaneous equaions srucural model connecing macro and microeconomic (marke) variables wih accouning variables. We also presen forecass for he financial saemens. The firm o which he model is applied is a monopoly in he Brazilian domesic marke for peroleum producs and he larges Brazilian firm in operaion. The resuls obained are consisen wih he expecaions associaed o he srucural model. Applicaions semming from he sudy include financial analysis, forecasing and planning, as well as firm valuaion. Key words: economeric model, accouning, financial saemens, Brazilian firm. 1. Inroducion The relaionship beween economics and corporae finance is ofen recognized in he relevan lieraure. For insance, Ross e al. (1993) have argued ha financial planning requires sales forecass, bu ha i is impossible o make accurae forecass since sales depend on he uncerain fuure behavior of he economy. I is added ha, in order o reduce his uncerainy, firms can ge help from consulans specialized in macroeconomic and indusry secor forecasing. A consequence of his is ha i should be possible o capure he impac of macroeconomic and indusry secor or marke variables on accouning variables such as sales revenues. Because oher accouning variables such as curren and fixed asses depend on sales, as argued by Van Horne (197), he effec of economic variables mus also be noiceable in balance shees and income saemens. The economic variables mos likely o affec a firm s financial saemens are he GDP, inflaion, ineres and exchange raes, and exogenous commodiy prices. There are some empirical sudies explaining accouning relaionships. One example is Sowe e al. (1980), wih an empirical sudy using canonical correlaion o analyze he relaionships beween he wo sides of he balance shee, based on he hypohesis ha invesmen decisions are aken separaely from financing decisions. Their major resuls indicae ha he firms observed end o adjus he mauriy of heir asses o ha of heir liabiliies. In anoher example, Marsh (198) has shown in a sudy carried ou in he UK ha he firms are srongly influenced by marke condiions and by he hisory of sock prices, when choosing beween equiy and deb. I was found ou ha he firms seem o make heir choice of financial insrumens having in mind deb arges, which are esablished as a funcion of firm size, bankrupcy risk, and asse composiion. There is a differen kind of empirical sudy focusing paricular indusry secors or commodiy markes, which are a long radiion in applied economerics (Adams and Behrman, 1976; Banks, 1974; Fisher e al., 197; Wickens, 1980). In general, hese models Associae Professor, Universidade de Brasilia, Brazil. 1

2 show he relaionships beween exogenous economic variables, such as GDP, ineres raes, exchange raes, and so on, and endogenous variables such as supply, demand and price, besides he ineracions beween hese. I seems here is a gap beween hose economeric marke sudies and empirical analyses on he behavior of accouning variables belonging o firms ha operae in hose markes. Neverheless, we suppose ha sudies connecing economic marke variables o a firm s accouning variables, ogeher wih he re laionships beween he accouning variables, would be useful for explaining empirically a firm s financial saemens. For hese reasons, his paper is primarily concerned wih providing an empirical explanaion for he relaionships beween economic and accouning variables. A second purpose is o es empirically he causal relaionships beween variables inside he financial saemens, as menioned in he previous paragraph. Finally, here is also he objecive o es he use of economeric models as insrumens for he esing of hypohesis on accouning relaionships and for financial forecasing. To reach hese purposes, a simulaneous equaions model was developed, based on heoreical economic and accouning relaionships. The model is divided ino hree inerconneced subsysems or blocks. The firs one refers o a commodiy (peroleum) marke; he second one refers o he income saemen, and he hird one o he balance shee of a firm operaing in ha commodiy marke. In he income saemen, here are hree variables: gross revenues, oal coss, and ne earnings. The balance-shee variables are aggregaed ino blocks. In he asses side, here are he curren asses, long-erm receivables, and fixed asses. In he liabiliies side, here are he curren liabiliies, and he capial resources, composed by he long-erm deb and equiy. Balance shee and income saemen variables relae wih each oher and wih he marke variables demand, supply and price, which in urn are explained by exogenous economic variables: he counry s GDP, he exchange rae, and he price of an imporan inernaional commodiy, peroleum. The remaining secions of he paper presen model specificaion, daa descripion, empirical resuls, forecass, and conclusion.. Model Specificaion A srucural simulaneous linear-equaions model was developed, where he srucural equaions have he following general form: Y = + X + X + + X + u (.1) µ 0 µ 1 1 µ µ n n, where Y is he dependen variable, X i (i = 1,..., n) are independen variables, u is he error erm, µ i (i = 0,..., n) are coefficiens, and he subscrip refers o ime. Besides he srucural equaions, some oher equaions in he model are accouning ideniies or mahemaical relaionships. The model is composed of hree inerlinked blocks: a block explaining how he marke variables (demand, supply and price) inerac and how hey are affeced by exogenous variables; a second block showing he deerminaion of he income-saemen variables (gross revenue, coss and ne earnings); and a hird block demonsraing how he balance-shee variables are deermined. Afer a procedure where alernaive formulaions were esed, he equaions were finally specified as follows.

3 .1. The Brazilian peroleum marke The marke under analysis is he domesic marke for peroleum producs in a paricular counry, and he firm under sudy is a sae-conrolled monopoly wihin his marke. The marke variables are demand, supply, and he price of peroleum producs. The consumpion or demand for peroleum producs (DEMAND) was specified as a radiional demand funcion, deermined according o heory by he price of he produc, ha is, he domesic average price of peroleum producs (DPRICE) and by he counry s income level, represened by Brazil s GDP. The demand funcion mus be declining wih respec o he price and ascending wih respec o he GDP. Therefore DEMAND = α + α DPRICE + α GDP + u, α < 0, α > 0 (.) On he oher marke side, supply of peroleum producs (SUPPLY) is assumed o be a funcion which increases wih DPRICE and decreases wih he variable resuling from he produc IPRICE EXRATE. IPRICE sands for he inernaional price of peroleum and EXRATE for he exchange rae beween he US dollar and he Real. The firs economic reason for his formulaion is ha a monopolis firm faces a downward sloping demand curve and possesses an upward sloping supply curve, and i decides for he price supply combinaion ha maximizes is profi. The second is ha he firm adjuss supply and/or he domesic price of peroleum producs (DPRICE) according o movemens in he inernaional price of peroleum (IPRICE) and/or in he exchange rae (EXRATE): SUPPLY = β + β DPRICE + β ( IPRICE EXRATE ) + u, β > 0, β < 0. (.3) An ideniy is necessary for he equilibrium condiion, where supply equals demand: SUPPLY DEMAND (.4) This par of he model reproduces he basic relaionships in a supply-demand marke. This can be found abundanly in he economic and economeric lieraure (Wallis, 1973; Kmena, 1971; Dhrymes, 1970; Greene, 00), as well as in various empirical sudies dedicaed o specific commodiies markes (Adams and Behrman, 1976; Banks, 1974; Fisher e al, 197; Wickens, 1980). The deerminaion of demand, supply, and price is he resul of his block. These variables are essenial for he deerminaion of he income-saemen and he balance-shee accouns. The variables DEMAND, SUPPLY and DPRICE are endogenous, while GDP, IPRICE and EXRATE are exogenous... Income Saemen The nex sep is o deal wih variables and relaionships ha belong o he income saemen. The gross revenues (REVENUE) resul from he muliplicaion of he physical volume of sales (SUPPLY) imes he local average sale price (DPRICE) of he produc mix, ha is, he average price of all he peroleum producs consumed in he counry each year: REVENUE = DPRICE SUPPLY (.5) The variable COST, meaning oal coss and expenses, is a funcion of he oupu (SUPPLY) and of he cos of he inpus. Given he impossibiliy of obaining coss for he diverse inpus used in producion, he price of he mos relevan inpu, i.e. he inernaional price of peroleum (IPRICE), was used as a proxy. This is obviously an exogenous variable. In view ha such price has o be convered ino he local currency, is necessary o muliply i 3

4 by he real exchange rae (EXRATE), which is he exchange rae deflaed by he general price index: COST = γ + γ SUPPLY + γ ( IPRICE EXRATE ) + u, γ > 0, γ > 0. (.6) Ne earnings (EARNINGS) are obained by subracing oal coss and expendiures (COST) from gross revenues (REVENUE). EARNINGS = REVENUE COST (.7) The variables in his block are REVENUE, EARNINGS and COST, which are endogenous, besides IPRICE and EXRATE, which are exogenous..3. Balance shee Wih respec o he balance-shee variables, CURRENT ASSETS are assumed o keep a direc and posiive relaionship wih gross revenues (REVENUE), since he larger he revenue, he higher will be he invesmen in shor-erm asses (cash, invenories and accouns receivable, ec): CURRENT ASSETS = δ + δ REVENUE + u, δ > 0. (.8) The specificaion of FIXED ASSETS is derived from he economic heory. More specifically, i comes from he heory of invesmen proposed by Jorgenson (1963), which is based on he neoclassical heory of opimal capial accumulaion. In his work, he parial adjusmen model is used in order o build a dynamic specificaion. The parial adjusmen model was firs applied in he mid-fifies by Cagan (1956), in his sudy of hyperinflaion, and by Nerlove (1958), in connecion wih he dynamics of agriculural supply. The parial adjusmen hypohesis saes ha he real invesmen is a fracion of he invesmen necessary o reach he sock of desired capial. If he real invesmen is given by I = K K, where K i is capial sock in period, hen 1 K K = (1 λ) ( K K ) (.9) * 1 1 * where K i is he desired capial sock. Assuming ha he capial-oupu relaionship deermines he desired capial sock, hen K * = α Y (.10) where α is he capial-oupu relaion (consan) and Y is oupu. I sems from equaions (.9) and (.10) ha K = α (1 λ) Y + λ K (.11) 1 whereα and λ are consan parameers. Therefore, capial sock in a cerain period is deermined by he oupu level (supply) and by capial sock in he previous period. Translaing ino accouning erms, his means ha FIXED ASSETS are an increasing funcion of he oupu (SUPPLY) and of lagged FIXED ASSETS. Thus, he equaion ha describes he deerminaion of he fixed asse is: FIXED ASSETS = χ + χ SUPPLY + χ FIXED ASSETS + u, χ > 0, χ > 0. (.1)

5 Long-erm receivables (LT RECEIVABLES) is he plug variable, being deermined by he difference beween oal liabiliies and curren plus fixed asses. Wih respec o he liabiliies side, several auhors (Giman, 1994; Ross e al., 1993; Van Horne, 197) have susained ha in general firms endeavor o mach he mauriy of heir liabiliies wih ha of heir asses. This is called he hedging approach o financing, in which each asse should o be mached by a financing insrumen wih he same approximae mauriy. Acually, he idea is ha firms use long-erm resources o finance no only heir fixed asses bu also he permanen porion of heir working capial, i.e. heir curren asses minus heir curren liabiliies. As menioned previously, Sowe e al. (1980) have shown evidence ha firms behave like his, in a sudy carried ou in he US. On he oher hand, despie Modigliani and Miller s (1958) proposiions, he saic rade off heory and he pecking order heory, a final word on which is he bes way o explain capial srucure has no been reached ye. Regardless of his, firms cerainly do no choose beween equiy and deb randomly, bu in accordance o cerain crieria. For simpliciy, insead of rying o model equiy and deb separaely, we ried o explain he dependen variable CAPITAL RESOURCES, which is he sum of equiy and long-erm deb as: CAPITAL RESOURCES = η + η FIXED ASSETS η CAPITAL RESOURCES + u, η > 0, η > (.13) For CURRENT LIABILITIES, he assumpion adoped was ha i is deermined by CURRENT ASSETS, reflecing he hypohesis ha he firm keeps a cerain proporion beween is shor-erm liabiliies and is shor-erm asses: CURRENT LIABILITIES = φ + φ CURRENT ASSETS + u, φ > 0 (.14) Besides he srucural equaions (.8), (.1), (.13) and (.14), here are inside he balance-shee block he accouning ideniies below: TOTAL ASSETS CURRENT ASSETS + LT ASSETS + FIXED ASSETS (.15) TOTAL LIABILITIES CURRENT LIABILITIES + CAPITAL RESOURCES (.16) TOTAL ASSETS TOTAL LIABILITIES (.17) LT ASSETS sands for he amoun of long-erm asses no belonging o fixed asses, and which is mainly made up of long-erm receivables. I is a plug variable, deermined by he difference beween oal liabiliies and he sum of curren asses and fixed asses. The endogenous dependen variables in he balance-shee block are CURRENT ASSETS, FIXED ASSETS, LT ASSETS, TOTAL ASSETS, CURRENT LIABILITIES, CAPITAL RESOURCES, and TOTAL LIABILITIES. 5

6 3. Daa Descripion The model was applied o Perobras, a near monopolis firm in he Brazilian domesic marke for peroleum producs 1. The daa are annual and come from annual balance shees and income saemens from 1991 o 001. These saemens were obained from Economaica s daabase. The equaions were esimaed by wo-sage leas squares (SLS), in order o preven biased and inconsisen parameers due o endogenous explanaory variables. The daa referring o he inernaional price of peroleum is he Dubai price in US$/barrel, obained from he Briish Peroleum s websie. All he accouning daa were deflaed by he Brazilian general price index (IGP-DI) and ransformed ino index numbers (1991=100) prior o esimaion. The esimaed equaions are in he following secion. 4. Empirical Resuls This secion presens he resuls of he model esimaion. Prior o esimaing he sysem s equaions, he ADF Augmened Dickey-Fuller es for uni roos was applied o he series, wih he null of a uni roo being rejeced for all series. The esimaed equaions are shown ogeher wih heir R coefficiens and -saisics, wih he laer beween parenheses below each esimaed coefficien The marke The firs equaion in his sysem represens he naional DEMAND for peroleum producs: DEMAND = DPRICE + GDP R = (4.1) , 0.8 (1.0) (-4.67) (5.39) Equaion (4.1) is in oal agreemen wih he economic heory: he coefficien corresponding o DPRICE is negaive whereas he one corresponding o GDP is posiive. DEMAND is inelasic wih respec o price and income, as shown by he average priceelasiciy and income-elasiciy of and 0.157, respecively. This is an expeced oucome, since peroleum producs are essenial goods. The expression (4.) below is an equaion represening he SUPPLY of peroleum producs, wih he sale price of hose producs as he dependen variable, such as in Wallis (1973). This is done o preven mulicollineariy resuling from a high correlaion coefficien (0.87) beween he explanaory variable DPRICE and (IPRICE x EXRATE), which would cause loss of precision in he esimaion of he coefficiens. DPRICE = + SUPPLY + IPRICE EXRATE R = (4.) (. ), 0.71 ( 1.46) (1.67) (4.68) Equaion (4.) can be rearranged o have SUPPLY as he dependen variable: SUPPLY = DPRICE 1.40( IPRICE EXRATE ) (4.3) 1 Perobras is he larges Brazilian firm and i is ranked 160 in he Forune Global 500 (001). Economaica is a Brazilian firm mainaining a large daabase of accouning corporae daa. 6

7 Equaion (4.3) also maches he underlying economic heory. SUPPLY changes in he same direcion of he produc price. Besides, an increase in he inernaional price of peroleum or in he exchange rae causes an increase in he domesic price of peroleum producs (DPRICE) or in a reducion of SUPPLY. The -es null hypohesis ha he parameer associaed wih SUPPLY is equal he zero is rejeced a he level of This implies ha, alhough Perobras is virually a sae-owned monopoly, is prices have no been conrolled or fixed by he governmen, meaning ha i operaes as a privae monopoly. Oherwise, if he hypohesis ha he parameer referring o SUPPLY is equal o zero was acceped, hen DPRICE would be predeermined for he firm, meaning ha i had no monopoly power. 4.. Income saemen The cos equaion shows ha he oal cos increases according o he level of SUPPLY and o he inernaional price of peroleum muliplied by he exchange rae, as expeced. COST = + SUPPLY + IPRICE EXRATE R = (4.4) ( ), 0.71 Equaion (4.4) is he only one ha needs o be esimaed in his block, since gross revenues (REVENUE) is a resul of PRICE muliplied by SUPPLY, and ne earnings (EARNINGS) are obained from REVENUE minus COST. A discussion is needed on he fac ha he sign of he inercep is negaive. As pu forward by Belkaoui (1987), alhough i migh be emping o inerpre he inercep as he oal fixed cos, his is no correc, unless he sample conains daa nex o he level of zero oupu, since he linear regression fi changes as he used sample is alered. Moreover, as shown by Baumol (1977) and Horngren (197), possibly he oal cos curves are no acually linear. Thus, anoher explanaion for he negaive inercep is ha by exending he esimaed regression line owards he origin a false negaive inercep is shown Balance shee The esimaed equaions relaive o he balance shee are shown below. CURRENT ASSETS = + REVENUE R = (4.5) , 0.65 ( 1.89) (4.5) According o equaion (4.5), CURRENT ASSETS can be explained by REVENUE, as previously specified. FIXED ASSETS = + SUPPLY + FIXED ASSETS R = (4.6) , 0.86 ( 1.75) (.57) (6.4) Equaion (4.6) confirms he hypohesis ha he capial sock in a cerain period is explained by SUPPLY and by capial sock of he previous period, as suppored by he applicable economic heory. CURRENT LIABILITIES = + CURRENT ASSETS R = (4.7) , (3.91) (.55) 7

8 Equaion (4.7) shows ha CURRENT LIABILITIES are deermined by CURRENT ASSETS, plus a consan erm. The problem here is ha alhough he esimaed coefficiens are significanly differen from zero by he -es, he R obained is low, which could be indicaing ha one or more explanaory variables are missing. The inroducion of a imerend variable raises R o 0.75, and produced a high value for he -saisic (.6), bu his was disregarded, due o he lack of a consisen economic jusificaion. Oher variables were esed (lagged curren asses and lagged curren liabiliies) wihou saisfacory resuls. CAPITAL RESOURCES = FIXED ASSETS + (-1.55) (1.8) 0.83 CAPITAL RESOURCES -1, R (3,95) + = (4.8) Equaion (4.8) suppors ha he long-erm capial resources used by he firm, i.e., he sum of equiy and deb, can be explained by FIXED ASSETS and lagged CAPITAL RESOURCES, which confirms he original specificaion. As menioned earlier, LT ASSETS is he plug variable, being deermined by he difference beween TOTAL LIABILITIES and he sum of CURRENT ASSETS and FIXED ASSETS. 5. Forecass An oucome of he regression resuls is he forecasing of he financial saemens. Forecass for he marke variables (DEMAND, SUPPLY and DPRICE) are obained hrough he soluion of he supply-demand block. The deerminaion of he oher endogenous dependen variables occurs sequenially, according o he esimaed equaions shown in he previous secion. For carrying ou he financial forecass, projecions of he exogenous variables are necessary. An economic scenario was adoped for he period In his scenario, he inernaional oil price (IPRICE) increases by 3% in 00 and by % in he subsequen years, in US$. The domesic GDP grows by 1.5% in 00,.5% in 003, and 4.0% in 004. The nominal exchange rae reaches 3.5 R$ per US$ in 00, and rises by 5.0% in 003, and by.0% in 004, respecively, in real erms. By subsiuing hese values ino he proper equaions, pro-forma balance shee and income saemen forecass referring o were obained. Such forecass are shown in Table 1, ogeher wih he 001 acual daa. Figures were convered ino US$ a he exchange rae of.3, which refers o 1/31/ Conclusion The economeric model here specified and esed looks saisically significan and, in general, is resuls seem o be in accordance wih he underlying economic and accouning heories. The relevan parameers obained in he regressions are significan by he Suden s -es, and have he signs foreseen in he model specificaion. The R coefficiens are saisfacory, ranging from 0.48 o Therefore, he resuls seem o poin ou ha i is possible o explain a firm s financial saemens by means of he impac of macro and microeconomic variables, ogeher wih he ineracion beween he accouning variables. The sudy also shows ha he firm analyzed 8

9 seems o pursue a financial equilibrium siuaion, using long-erm capial resources o finance is permanen asses. The main resricion o he sudy migh be he degree of aggregaion adoped. As seen, we have no aimed a explaining more deailed accouning variables inside he blocks. This was done deliberaely for he sake of simpliciy and o avoid dealing wih a model ha would be oo large for handling and inerpreing. Balance Shee Asses Curren Asses 14, , , ,74.79 Long-Term Asses 5, , , , Fixed Asses 1, ,1.7 11, , Toal Asses 3, , , ,59.46 Liabiliies Curren Liabiliies 9, , , , Capial Resources 3,08.3 3, , ,48.15 Toal Liabiliies 3, , , ,59.46 Income Saemen Gross Revenues 34, , , , Coss & Expenses (30,334.48) (33,404.79) (35,475.60) (37,48.36) Ne Earnings 4,73.7,360.77, , Table 1: Financial saemens: acual (001) and forecass (00-004) in US$ million. I should also be aken ino accoun ha since he chosen firm is a monopoly, i has cerain peculiariies, which make he sudy in quesion a singular case. Therefore, i becomes necessary, in due ime, o expand and es he mehodology using oher kinds of firms, in order o achieve more generalized conclusions. Finally, we expec ha he resuls here obained migh inspire he developmen of furher empirical research on he relaionships beween economics and accouning. 7. References ADAMS, F. G and BEHRMAN, J.R. Economeric Models of World Agriculural Commodiy Markes. Cambridge, Mass.: Ballinger, BANKS, F.E. An Economeric Analysis of he Copper Marke. Cambridge, Mass.: Ballinger, BAUMOL, W. (1977). Economic Theory and Operaions Analysis. Englewood Cliffs, NJ: Prenice-Hall, BELKAOUI, A. (1987). Quaniaive Mehods in Accouning: A Procedural Guide for Professionals. New York: Quorum Books, BRITISH PETROLEUM. CAGAN, P. (1956). The moneary dynamics of hyperinflaion. In: FRIEDMAN, M. ed. Sudies in he quaniy heory of money. Chicago: The Universiy of Chicago Press (1956). DHRYMES P. J. Economerics. New York: Harper, ECONOMATICA. Brazilian corporae daabase. FISHER, F. M., COOTNER, P. H. and BAILY, M. N. An Economeric Model of he World Copper Indusry. Bell Journal of Economics and Managemen Science, 3(), ,

10 GITMAN, L. J. Principles of Managerial Finance. 7 h Ed. New York: HarperCollins, GREENE, W. H. Economeric Analysis. 5 h Ed. Upper Saddle River: Prenice Hall, 00. HORNGREN, C. T. (197). Cos Accouning. 3 rd Ed. London: Prenice Hall Inernaional, 197. JORGENSON, D. W. Capial Theory and Invesmen Behavior. American Economic Review, 53, 47-59, May KMENTA, J. Elemens of Economerics. New York: MacMillan, MARSH, P. The Choice Beween Equiy and Deb: An Empirical Sudy. The Journal of Finance, Vol. XXXVII, No. 1, March 198. MODIGLIANI, F. and MILLER, M. H. The Cos of Capial, Corporaion Finance, and he Theory of Invesmen, The American Economic Review, 48, 61-97, NERLOVE, M. (1958). Disribued Lags and Demand Analysis. Washingon, DC. US Deparmen of Agriculure, Agriculure Handbook, No. 141, ROSS S.A., WESTERFIELD R.W., and JAFFE, J.F. Corporae Finance, 3 rd Ed. New York: McGraw-Hill, STOWE, J. D., COLLIN, J. W., and ROBERTSON, T. D. Relaionships beween he Two Sides of he Balance Shee: A Canonical Correlaion Analysis, The Journal of Finance, vol. XXXV, No. 4, Sepember VAN HORNE, J.C. Financial Managemen and Policy. nd ed. Englewood Cliffs, N.J.: Prenice-Hall, 197. WALLIS, K. F. Topics in Applied Economerics, London: Gray-Mills, WICKENS, M. R. An Aggregae Economeric Model of he World Copper Marke. Meals and Mineral Research. London,