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Agricultural & Applied Economics Association

A Model of Cooperative FinanceAuthor(s): John J. VanSickle and George W. LaddSource: American Journal of Agricultural Economics, Vol. 65, No. 2 (May, 1983), pp. 273-281Published by: Blackwell Publishing on behalf of the Agricultural & Applied Economics AssociationStable URL: http://www.jstor.org/stable/1240873

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A M o d e l o f Cooperative i n a n c eJohn J. VanSickleand GeorgeW. LaddTheuniquecharacteristics f cooperatives equire heybe analyzeddifferentlyrom hemore raditional oncooperativeirm.A modelof cooperative inance s developed hathas theobjectiveof maximizinghetotal,after-taxprofitsof thecooperativememberpatrons.A mathematicalnalysisderives herelationships mong hevarious inancialinstruments, nd anumerical nalysisderivesresults ora cooperativeundervarioushypothesized cenarios.Wesuggest hat a model ncorporatingheuniquecharacteristics f cooperativess the moreappropriateool for studying ooperativefinance han s the noncooperativemodel.Key words: cooperatives, inance, irm heory.

Cooperativesdiffer from noncooperativecor-porationsin at least five majorways:(a) A cooperative's customers also are itsowners. In the noncooperativefirm, custom-ers and owners are separated.(b) The price of a cooperative's commonstock is fixed by the articles of incorporation,and the stock is not traded n an open market.The price of a noncooperative irm'scommonstock is determined n the marketplace.(c) One source of capitalis availableto thecooperative that is not available to the non-cooperative irm-deferred patronage efunds.(d) Cooperativesmay operatewith a singletax on income. Noncooperativefirms do not.(e) The cooperative'sobjectiveis to benefitits member-customers. A noncooperativefirm'sobjective is to benefit its owners.The differences just listed require thatcooperative financial structure be analyzeddifferentlyfrom a noncooperative's financialstructure. Many textbooks and at least onejournalare devoted to the financialstructureof noncooperativefirms. The financialstruc-ture of cooperatives has received much lessattention.This paperanalyzes the economicsof a cooperative's financialstructure.

Cooperative ObjectiveThe relation of long-runcooperative financestudies (Sniderand Kohler,Nervik and Gun-derson, Korzanand Gray, Wilson, Coffman,BeierleinandShrader,Tubbs,Fenwick,Dahl)to typical short-runcooperativestudies (Bar,Helmbergerand Hoos, Phillips) significantlycontraststhe relationbetween-studiesof non-cooperative financial structureand short-runbehavior.

Researchdealingwith capital structureop-timization in corporations is exemplified inVickers' analysis. Vickers looked at twosources of capital, debt and owners' equity.He related equity cost to the coefficient ofvariationin total net operatingincome, totalcapital employed, and the leverage ratio(debt/total liabilities). He then developed adebt-cost function that stated the averageinterest rate of debt as a function-of thecoefficientof variation n the earningsstreamavailableto cover the intereston debtand theleverageratio. Vickerscomputedthe financialleverage,maximizing he rate of returnon thebook value of owner investment,an objectiveconsistentwith short-runprofitmaximization.He found that the optimum inancial everageoccurs where the marginalrate of returnonequity is equal to the marginalrateof intereston debt. In general, he concluded that theoptimumallocation of the firm's demandforcapital over alternative capital sourcesequates the cost of each capital source at themargin. This paper modifies Vickers' ap-proachto makeit applicable o a cooperative.The assumedobjectiveof the cooperative s to

John J. VanSickle is an assistant professor of food and resourceeconomics at the University of Florida; George W. Ladd is aprofessor of Economics at Iowa State University.Journal Paper No. J-10249 of the Iowa Agriculture and HomeEconomics Experiment Station.This research was partially financed by the Cooperative Man-agement Division of Agricultural Cooperative Service, U.S. De-partment of Agriculture.Ronald E. Raikes made valuable contributions to this research.The authors are grateful to the anonymous reviewers for helpfulcomments.

Copyright 1983 American Agricultural Economics Association

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274 May 1983 Amer. J. Agr. Econ.maximizethe total profits, after taxes, of thememberpatrons(Ladd).Thisobjectiveis sen-sible because it can be used in studies ofshort-runproductionandpricingandlong-runfinancial structure. In this paper we followTubbs, Fenwick, and Vickers and do not de-terminethe amountof capital.CooperativeFinanceModelThis paper studies financialstructureof Sec-tion 521 cooperativesthat use revolvingfundfinancing. This is done mainly for conve-nience. A qualitativemodel for cooperativesthat do not meet Section 521 criteriacan beformulated, but is much more complex.Hereafter, the word "cooperative" means"Section 521 cooperative." The cooperativemust determinethe total amountof debt andowners'equity. Owners'equityincludescapi-tal stock, deferred qualified patronage re-funds, and nonqualifiedpatronagerefunds.Supply of CapitalCooperativesorganizedas stock corporationscommonlyrequirea common stock purchasefor membership.Membershipallows the pa-tron to be involvedin the management f thecooperative. The price of common stock willbe assumed fixed to reflect point (b) in theopening paragraph.The numberof membersalso is assumed fixed in this paper. This isdone mainly for convenience. It is assumedthat the cooperative limits common stockownership to one share per member. Thissatisfies an early principleof cooperationes-tablishedby the RochdaleSociety (Abraham-sen, p. 48). Thecontributionof commonstockto the financialstructure hen may be written(1) CS = P - M.See table 1for definitionsof all symbolsused.The other formof memberequity, deferredpatronage refunds, is derived from thecooperative's net savings. Net savingsare al-located to dividends on capital stock and toqualified and nonqualified patronage refunds.Griffin et al. (p. 38) report that in 1976 only1.2%of the equity capital in cooperatives wassupplied by nonqualified patronage refunds.Because of their negligible use, nonqualifiedpatronage refunds are assumed to be zero.The capital supplied each year'by qualified

Table 1. Definitions of Symbols Used, InOrder of AppearanceSymbol Definition

CS Total value of common stock out-standingP Price per share of common stock(fixed)tM Number of members in the co-operative (fixed)7 Total number of years deferredpatronage refunds are deferreds Proportion of patronage refundspaid in cashQPR Amount of net savings allocated asqualified patronage refundsTKQP Total capital supplied by qualifiedpatronage refundsK Total capital employed by the co-operative (fixed)D Total debt employed by the co-operativeTr Members' total profits after taxesT,,, Members' total net revenues aftertaxes from products traded in-side and outside the cooperativeduring the current year (fixed).These net revenues represent allcurrent income and outlays ofmembers before allocations ofnet savings from the cooperativePVPR,m Present value of patronage refundspaid to membersDS,, Net (of income taxes) dividends oncapital stock paid to membersT Members' total net revenues be-fore taxes from products tradedinside and outside the coopera-tive during the current year(fixed). These net revenues rep-resent all current income andoutlays of the members beforeallocations of net savings fromthe cooperativet,M Members' average income tax ratep Ratio of member business to thesum of member and nonmemberbusinessd Members' discount rate defined asequal to the members' averagemarginal interest cost of debti,. Dividend rate on capital stock? Maximum allowed dividend rateon capital stock (fixed)DS Total (before income taxes) divi-dends on capital stock paid tomembersNS Net savings of the cooperativer Average interest rate on all currentand long-term debt used by thecooperative0 Net operating income of the co-

operative defined as equalingtotal receipts less all expendi-tures except the interest cost ofdebt (fixed)

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Van Sickleand Ladd A Co-op Finance Model 275Table 1. (cont.)Symbol DefinitionL Lagrange unction or determiningfinancial structure in coopera-

tivesX(i = 1, 2, 3, 4, 5) Lagrange multipliersE A smallpositive number fixed)MIC Marginalnterest cost of debtME1PV, Effect on the presentvalue of onedollarof deferredpatronagere-funds of varying7CL Total current liabilitiesemployedby the cooperative(fixed)LT Total long-term liabilities em-ployed by the cooperativer, Average nterestrateon long-termdebtpatronagerefundsdepends on the proportionof refunds paid in cash to the patrons. Thetotal capitalsupplied romqualifiedpatronagerefunds s equalto the capitalsuppliedby thatsource each year times the number of yearsdeferred,(2) TKQP= r(1 - s)(QPR).

The total capitalemployedby the coopera-tive is the sum of equations (1) and (2), anddebt, i.e., total capital employedmay be writ-ten(3) k = PSI + r(1 - s)QPOR + D.CooperativeObjectiveFunctionThe assumedobjective for the cooperative isto maximizethe total, after-taxprofitsof themember patrons. The total, after-tax profitsof the memberpatronsareequalto the sumofthe members' total net revenues, after taxes,for products traded inside and outside thecooperativeduring he currentyear, the pres-ent value of patronage refunds paid to themembers, and the net dividends on capitalstock paid to members,is written(4) 7r = Tm + PVPRm + DSm.Members' total net revenues, after taxes,for products traded inside and outside thecooperative association may be specified as(5) Tm = (1 - tm)T.T is a fixed parameterbecause membershipand capitalemployed are fixed.PVPRm may be definedas(6) PVPRm = p s + (1-s) -td QPR].1[ (1 + d)T m J

Cooperativesare requiredby law to allocaterefunds to members and nonmembersalike.The capital which qualifiesfor dividends in-cludes common stock and equity suppliedbydeferredpatronagerefunds.Cooperativesarenot required o pay the same dividendrate oneach capitalsource, and mostcooperativesdonot pay dividends on equity suppliedby pa-tronagerefunds(Griffinet al., p. 85). We as-sume that the cooperative pays a dividendonly on membershipstock. The capital stockpatronshold in membership common) stockis equivalentto CS in equation(1). Dividendson members'capital stock are taxable to themembers so that the net dividends on themembers'capital stock may be stated(7) DSm = icPM(1

-tm).The objectivefunctionmay be rewrittenbysubstitutingequations (5), (6), and (7) intoequation (4),

(8) T = (1 - tm)T+ p s + (+ d)- tm QPR

+ (1 - tm)icPM.ilConstraintson CooperativesTheobjectivefunction s maximizedsubjecttoconstraints faced by cooperatives. The firstconstraintis that the cooperative employs Kamount of capital, equation (3). The secondand thirdconstraintsspecify that the propor-tion of qualifiedpatronage efundspaidincashwill be greaterthan or equal to 20%but lessthan or equal to 100%.(9) s - .2,(10) 1.0 - s.These constraints stem from the legal regula-tions governing cooperatives.The fourth constraint limits the dividendrate on capital stock. The cooperative ratecannotexceed 8%perannumor the limitspec-ifiedby stateregulations,whichever s greater.Thisupper imitvariesby states andis definedhere as i,(11) i > ic.The fifth constraintis that the net savingsmust be allocated. Thus, distributionof netsavings can be describedas(12) NS = DS + QPR.

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276 May 1983 Amer.J. Agr. Econ.Net savings can also be describedas the netoperatingincome of the cooperative less theinterest cost of debt,(13) NS = 0 - rD,where 0 is a fixedparameterbecause member-ship and capital also are fixed.Substitutingequation (7) for DS and equa-tion (13) for NS into equation (12) and rear-ranging,the constraintcan be written(14) 0 -rDO - icPM - QPR = 0.LagrangeanWith equation (8) as the objective functionand expressions (9) through(11) and (14) asconstraints,the Lagrangeanmay be stated(15) L = (1 - tm)T

+ pts + (1J- s) - tmIQPRI+P1s + d), ] J*+ (1 - tm)icPM+ h,[K - PMAi- (1 - s)QPR - D]+ X2[s - 0.2] + X3[1.0- s]+ X4[i- ic]+ X5[0 - rD- icPM - QPR].The variables that the cooperative decisionmakercan manipulate o achieve its objectiveare the proportionof qualifiedpatronagere-fundspaidin cash (s), the lengthof the revolv-ing fund (r), the dividend rate on commonstock (i,), the amountof net savingsallocatedas qualifiedpatronagerefunds(QPR), and theamount of debt to employ (D).EconomicAnalysisThe precedingmodel is incompletebecause itlacks the requirement hat s equals 1.0 if andonly if r equals 0.0. The lengthof the deferralperiod must be zero if all patronagerefundsare paid in cash. Adding constraints to themodel to incorporatethis restrictioncompli-cates the first-order onditions. As an alterna-tive we carryout two analyses. In this sectionwe requirethat(16) r > 0, and(17) s < 1.0.In a later section we require that s equal 1.0and 7 equal 0. Under assumptions (16) and(17) we can use qualitative analysis to deter-mine optimum values of s and ic, but not of D,7 and QPR.

Value of sMost cooperative associations use deferredpatronage refunds as a source of financing.Griffinet al. (p. 40) reportthat in 1976over84%of cooperatives used some form of de-ferredpatronagerefunds. Using deferredpa-tronage refunds allows a cooperative to ap-proach the principle of memberfinancinginproportionto use. We will assume deferredpatronagerefunds are used, so that expres-sions (16) and (17) must be satisfied. To de-termines we use proof by contradiction.Thatis, we show that the conjunctionof four rea-sonable assumptionsyields a conclusion thatcontradicts he assumptions.Oneassumption,therefore,mustbe discarded.Discardingonlythe unnecessary assumptionleads to a solu-tion for s. Expression(16) can be satisfiedbysettingthe Kuhn-Tucker onditionfor r equalto zero. Expression (17) is satisfiedif we re-state the constraintin equation (10) as(18) 1.0 - E _ s,where E is a fixed, small, positive number.The Kuhn-Tucker ondition for r is(19) aL (1 - s)ln(1 + d) QPR

-7 (1+ d)T+ X1[-(1 - s)QPR] = 0.

Equation(19)can be rearranged ndsimplifiedas(20) A = - In(1 + d)

The constraint in expression (9) dictatesthat s must be greaterthan or equal to 0.2.Because s must be greaterthan 0, the Kuhn-Tuckerconditionfor s is satisfiedas an equal-ity,(21) _L=pI 1 1QPRas Ll (1 + d)'] j+ Xh(7QPR) + 2 - 3 = 0.Assuming hat the solution ors is nota cornersolution (0.2 < s < 1 - e), then X2and X3areequal to zero. Substitutingequation (20) intoequation (21) and rearranging(22)

QPR-p 1- (1 + d)' ( 1 d) =0.If QPR is greater than zero, equation (22) re-quires that the bracketed expression be equalto zero. Assume

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Van Sickleand Ladd A Co-op Finance Model 277(23) d > 0.Expression (23) is logical because d is theaverage discount rate of the members. Theonly possible value for r that satisfies bothequation (22) and (23) is zero. To prove this,multiplythe expressioninside the bracketsofequation (22) by (1 + d)7and rewrite as(24) 1 = (1 + d)' - An(1 + d).Note that the series expansionfor (1 + d)T s(25) (1 + d)' = 1 + iln(1 + d)

+ I . [In(1 + d)]ij?2 j!Substitutingequation (25) into (24) yields(26) 1 1 + [n(1 + d)ySince d > 0, equation (26) is satisfiedif andonly if(27) 7= 0.But this contradicts he assumption n expres-sion (16). The conjunctionof the assumptionsexpressed in (10), (16), and (23), and the as-sumptionthat X,2 nd X3 equal zero, yields aconclusion that contradicts expression (16).Thus not all of the conditionscan be true. Theonly condition that can be droppedis the as-sumptionthat both X2and X3equal zero. Re-jecting this assumptionmeansthat either X,2snegative (implyingthat s equals .2) or X3 ispositive (implying hat s equals 1 - E).Royershowed thatfor constantannualpatronagere-funds and constant total capital supplied bydeferredpatronagerefunds,highervalues of sincreased the present value of patronagere-funds.Therefore,we conclude thats is greaterthan 0.2 and X2 quals zero. Then X3must bepositive, implying(28) s = 1 - Efor a maximum.Value of ieThe Kuhn-Tuckercondition for QPR will bean equality if the cooperative uses deferredpatronagerefunds in financing.That is,

(29) Q = ps + (1- ) -tmLQPR P (1+ d)T- X17(1 - s) - X5 = 0.

Substitutingequation (20) and (28) into ex-pression (29) and rearranging ields(30) X5 = p (1 - ti)- E 1T- (1

1 d)n(30)(1 + d)(1 + d)'

The Kuhn-Tuckercondition for ic can bestated as(31) L _ (1

-tm)PMPR-

4 M-OP 0.icIf the cooperative pays a dividend on mem-bers' capitalstock, (31) is anequality.Assum-ing (31) is an equality, substituting(30) into(31) for X5yields

(32) Xh= PM (1 - tm)- p( - tm)A n ( I- E1 - (1 + d)' (1 + d)

Eand the expression multiplyingE n (32) arepositive. Because p is less than orequalto onethen X4must be positive. Consequently,(33) ic= i.Values of D, r, and QPRThe Kuhn-Tucker onditionfor D can be ex-pressed as(34) -- ,- r + D ?r0.aD [ aDThe bracketedexpressionin (34) is the margi-nal interestcost of debt (MIC)since the inter-est cost of debt is rD. Substitutingequation(20) for Xh nd (30) for X.into expression(34)and rearranging ields

(1(35) MIC 1 - (1 - tm)(1 + d)[ 1 _ rln(1 + d)-'- (1+ d)' (1+ d) "

Note from equation(6) that 1/(1 + d)' is thepresent value of one dollar of patronagere-funds deferred 7 years. And

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278 May 1983 Amer. J. Agr. Econ.d[1/ (1 + d) 7]/dr = - [n(1 + d)/(1 + d) ']which is the negative of the first right-hand-side term of equation(35). Thisis the effect ofvaryingr on the presentvalue of one dollar of

deferredpatronagerefunds. Labelit ME1PV,.If thecooperativeuses debtequation(35) is anequalityand implies that the cooperativewillemploy sufficient debt so that MICis greaterthan the negative of ME1PV,.(36) MIC (1 - t,,) - E 1i 1d)1+ d)T

rln(1 + d) -MEIPV,.(1 + d)7Finally, the Kuhn-Tucker onditions for X,

and X,can be writtenas(37) K --Ml -r(1 - s)QPR

- D = 0, and(38) = 0- rD - icPM - QPR = 0.dX5

Because MICis a functionof D, equations(36), (37), and(38)are threeequations n threeinstrumentalvariables:D, 7 and QPR. Theseeauations can be used to solve for D, 7 andQPR given values for s, d, K, P, M, p, 7, t,,,and an interestrate functionfor r.A numerical analysis was performed toevaluate the nature of the solutions. For theanalysis, the cooperative was assumed todefer payment of a small percentage of pa-tronagerefunds.The analysisconsidered val-ues for s from 0.2 through 0.99. Then, thevalues of D, 7, and QPR can be determinedfrom equations (36), (37), and (38).We assumed that the cooperative employscurrentand long-term iabilities as sources ofdebt. Hence, equation(37) maybe written as(39) R - PAf - r(1 - s)QPR- (CL + LT) = 0Because current iabilities(excludingthe cur-rent portion of long-termdebt) often can beused for financingwith relatively low or nointerest, we assumed that the average interestrate on current liabilities is zero. The averageinterest rate on long-term debt is assumed to bean increasing function of the permanent lever-age ratio [LT/(K - CL)], and is arbitrarilyspecified as(40) rL= 0.07 + O.OI[LT/(K - CL)]+ 0.03[LT/(K - CL)]'.

Table 2. Predetermined Variables for theCooperativeVariable ValueCL $775,000R $3,400,000P $500M 1200 members0 $400,000p 0.8t,,, 0.35With no interest on current liabilities, theaverage interest rate on debt may be written

r." LT(41) r = rLCL + LTBy using equations (33) and (41), equation(38) may be rewrittenas(42) 8 - r1 - LT - iPM - QPR = 0.

Expressions(39)and(42)providetwo equa-tions in the three unknownsLT, 7 and QPR.To obtainsolutions for all three,we combineda search method with the Gauss-Seidel al-gorithm.A numberof values of LTwere spec-ified. For each value of LT, the Gauss-Seidelalgorithmwas usedto solve (39) and(42) for 7and QPR. The values of LT, r, and QPR weresubstituted nto (8), alongwith(28)and(33)tocompute 7r - T,1. This combined search-Gauss-Seidelprocedurewas used for a num-berof valuesof s;' 7was required o be greaterthan or equal to 1.0 in each case.Table2 presentsthe assumed values for CL,K, P, M, 6, p and t,, that were used in thesolutionprocessto determinevaluesfor LT, r,and QPR. The values for CL, K, P, 0, and Mwere obtained rom datasuppliedby a market-ing and supply cooperative surveyed in July1979. The value d was assumed to be 12%,aroughestimate of members'marginal nterestcost for 1979,and i was set to 0.08.Each line of table 3 shows the combinationof valuesof LT, r, andQPRthat maximized rless T,, for the specifiedvalue of s. The com-putedvaluesof the objectivefunctionsupportthe earlier conclusion that highervalues of syieldhighermembers' otalnetrevenue,equa-tion (28). Values for s below 0.52 used theminimum amount possible for deferred

An alternative is the following: fix CL so that dD = dLT andar/8D= ar/aLT. Then substitute (40) into (41) and solve for MIC.Substitute this result, the definition of MEIPV,, and (1 - s) into(38) to obtain a third.equation to be solved with (41) and (44) bythe Gauss-Seidel algorithm. In using Gauss-Seidel for solvingfirst-order conditions, one needs to check that the solution is amaximum rather than a minimum.

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Van Sickleand Ladd A Co-opFinanceModel 279Table 3. Solutionsfor QPR, LT, and r forVarious Valuesof ss QPR LT 7T- T,,

(Years) -------- ($1,000)--------.2 1.0 176.8 1,883.5 111.0.3 1.0 175.1 1,902.5 111.7.4 1.0 173.3 1,921.0 112.4.5 1.0 171.7 1,939.2 113.1.51 1.0 171.5 1,942.0 113.2.52 11.98 352.0 0 113.8.6 14.38 352.0 0 123.7.7 19.17 352.0 0 139.4.8 28.76 352.0 0 160.1.9 57.52 352.0 0 186.5.99 575.28 352.0 0 211.41.00 0.0 352.0 2,025.0 113.4

patronage efunds.Valuesfors greater hanorequal to 0.52 used all deferredpatronagere-funds and no long-termdebt.However, in the previous model some con-straints that may be needed for practicalitywere omitted. The numericalanalysis showsthe maximumsolution to be where s equals0.99 and 7 equals 575years. A revolvingfundof 575years is not reallyfeasible. The numeri-cal analysis shows that for values of s below0.51the maximum olutionexists whereheavydebt financing is used, i.e., the permanentleverageratiorangesfrom0.71 to 0.74. Whileit is possible for cooperativesto have perma-nent leverageratiosthis high, it is quite likelythe lenders would impose severe operatingconstraintson such cooperatives.Further restrictions were added to themodel to evaluate the effect of limitationsonrevolvingfund length and debt. Addingtheserestrictions required adding two additionalconstraintsand Lagrangianmultipliers or themaximumallowed values of 7 and D. The re-sults of the mathematicalanalysis can beshown to indicatethat with these restrictionsthe cooperativemust eitherpay the maximumallowable cash patronagerefundrate, i.e., sequals 1 - E, or the cooperative must deferpatronagerefundsas long as possible, i.e., requals the maximum allowed value, or bothconditions must hold.The search-Gauss-Seidel algorithm wasmodified to incorporatethese additional re-strictions. Limits of four, eight, and twelveyears were considered for revolving fundlength and limits of $1,025,000 (a permanentleverage ratio of 0.39), $1,525,000 (a perma-nent leverageratioof 0.58), and$1,875,000(apermanentleverage ratio of 0.71) were con-

sidered for long-termdebt. The optimumre-sults from all combinationsfor these restric-tions are listed in table 4. In every case theresultsshow that the cooperativeshoulddeferpatronage refunds the maximum allowabletime. The results also indicate that solutionsfor long-termdebt depend on the maximumallowedvalueof 7. As 7is allowedto increase,the optimumvalue of long-termdebt gener-ally decreases. Also, for some prespecifiedmaximum orvaluesof 7, the optimum evel oflong-termdebt is less than the allowed level.For instance, when r is restrictedto twelveyears, the cooperative should employ$1,146,645 of long-term debt. Restrictinglong-termdebt to an amountthat is less thanthe optimumamountleads to long-termdebtbeing used at the maximum allowed amountand s decreasing to allow substitution ofequitycapitalfor debtcapital.The results alsoshow thatin six of the eightfeasiblesolutionsswas approximatelyequal to 0.7. In the caseswheres was less than0.7, no feasible solutionexisted forvalues of s greater han those in thetable.Analysis TwoThe previousanalysisassumed(16) and (17).We now assume s equals 1 and r equals 0.Underthis assumption here is only one solu-tion. Long-termdebt is derived from (39) as(43) LT = k- PMf.If p is less thanone, the solution for i, is (33).And QPR is obtained from (42) as(44) QPR = 0 - rLLT iPM.Table 4. OptimumSolutionswith RestrictedLevelsof 7 andLT

Optimum Solution forMaximum Allowed LT/r LT s LT (K - CL) 7r T,,(Years) ($1,000) ($1,000) ($1,000)4 1,025 a a a a4 1,525 .43 1,520. .58 109.54 1,875 .72 1,816. .69 113.08 1,025 .54 1,025. .39 112.88 1,525 .71 1,507. .57 116.38 1,875 .72 1,554. .59 116.412 1,025 .69 1,011. .38 122.712 1,525 .72 1,147. .43 123.612 1,875 .72 1,147. .43 123.6a No feasible solutionexists when7 is constrained o be less thanfour yearsand LTis constrained o be less than$1,025,000.

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280 May 1983 Amer. J. Agr. Econ.The last line of table 3 presentsthe resultsforthis solution. This value of -r - T,,, almostequals the value when s equals .52 and 7equals 11.98. Values of 7 - T,,, n table 4 aregenerallylarger(up to $9,100 larger)thanthelast value in table 3.Conclusions and ImplicationsWe have studieda cooperativewhose objec-tive is to maximizethe after-taxprofitsof itsmemberpatrons.Ourresultsshow that for theconditions studied here a cooperativecan dobetter for its memberpatronsif it pays about70%of its patronagerefunds n cash than if itpays all in cash or only 20% in cash. Ourresultsalso show that if a cooperativepays adividend on commonstock, it shouldpay themaximumallowablerate.Griffin et al. (p. 32) showed that in 1976cooperatives' permanent everage ratio aver-aged approximately 0.33. Our analysisyielded optimumvalues for the leverageratiofrom 0.39 to 0.69. Haugen's sample ofcooperatives showed their average leverageratio to be 0.54 in 1974and 0.71 in 1980.Theresults in table 4 show that shortening he de-ferralperiodforpatronagerefunds eads to thecooperativeusingmoredebt andpaying ess ofthe patronagerefunds in cash. These resultscoupled with the recent pressure to shortendeferralperiodsmayexplainwhy Haugenwit-nessed the increase in debt use. Our resultsare consistent with those of Snider andKohler, Nervik and Gunderson,KorzanandGray, Tubbs, Fenwick, and Dahl, who con-cluded that cooperatives have in the past re-lied too heavilyon deferredpatronagerefundsas a source of financing.

Haugen argues that the leverage ratio forcooperatives moved in a dangerousdirectionbetween 1974and 1980. The maximum ever-age ratio in our study nearly equals the 1980average in Haugen's paper. Our results sug-gest that he may be correct in arguingthatcurrent everageratios aretoo high.The ques-tion is, how do we test this hypothesis?Andwhat can be prescribed if the hypothesis isaccepted? We suggest that the responsibleindividuals operate with inappropriate mod-els-cooperative decision makers and coop-perative creditors use the familiar nonco-operative finance model typified by Vickers.We maintain that a noncooperative financemodel is an inappropriate tool to use for study

of cooperative inance. A studyof cooperativefinance must incorporatethe uniquefeaturesof cooperativeslisted at the beginningof thispaper. Our study is an effort to incorporatethese unique features into a practical modelfor analyzing cooperativefinance. The modelcould become more useful by developingap-propriate nterest rate functionsand discountrates for the membercustomers and consider-ing the dynamic aspects of variableearningsand interest rates, and growth.[Received May 1981; revision acceptedSeptember 1982.]

ReferencesAbrahamsen, Martin A. Cooperative Business Enterprise.New York: McGraw-Hill Book Co., 1976.Bar, Josef. "'AMathematical Model of a Village Coopera-tive Based on the Decomposition Principle of Linear

Programming." Amer. J. Agr. Econ. 57(1975):353-57.Beierlein, James G., and Lee F. Schrader. "Patron Valua-tion of a Farmer Cooperative under Alternative Fi-nance Policies." Amer. J. Agr. Econ. 60(1978):636-41.Coffman, Dick L. "Alternative Long-Run Financial Im-plications for the Local Multi-Enterprise Farmers

Cooperative Elevator under Varying Levels ofGrowth and Capital Rationing." M.S. thesis, IowaState University, 1976.Dahl, Wilmer A. "An Analysis of Financial ManagementPractices and Suggested Alternative Strategies inWisconsin Local Supply Cooperatives." Ph.D.thesis, University of Wisconsin, 1975.Fenwick, Richard A. "Capital Acquisition Strategies forMissouri Farm Supply Cooperatives." Ph.D. thesis,University of Missouri, 1972.Griffin, Nelda., Roger Wissman, William J. Monroe,Francis P. Yager, and Elmer Perdue. The ChangingFinancial Structure of Farmer Cooperatives. Wash-ington DC: USDA ESCS Farmer Coop. Res. Rep.No. 17, Mar. 1980.

Haugen, Rolf E. "Financing Growth While Coping withInflation--A Financial Perspective.' Coop. Accoun-tant, no. 4(1981), pp. 68-74.Helmberger, Peter G., and Sidney J. Hoos. CooperativeEnterprise and Organization Theory." J. Farm Econ.46(1964):603-17.Korzan, Gerald E., and Edward L. Gray. "Capital forGrowth and Adjustment of Agricultural Coopera-tives." Oregon Agr. Exp. Sta. Bull. No. 596, 1964.Ladd, George W. "The Objective of the Cooperative As-sociation." Development and Application of Coop-erative Theory and Measurement of Coopera-tive Performance. Proceedings of a symposium at theannual meeting, 27 July, 1981, Clemson, SC. Wash-ington DC: USDA ACS Staff Rep., Feb. 1982.

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Van Sickle and Ladd A Co-op Finance Model 281Nervik, Ottar,and RobertGunderson."FinancingCoop-eratives." South DakotaAgr. Exp. Sta. Bull. No.434, 1954.Phillips,Richard."Economic Nature of the CooperativeAssociation." J. Farm Econ. 35(1953):74-87.Royer, JeffreyS. "DistributingCooperativeBenefits to

Patrons." Coop. Accountant, in press.Snider,Thomas E., and E. Fred Koller. "The Cost ofCapital in Minnesota Dairy Cooperatives." Min-nesota Agr. Exp. Sta. Bull. No. 503, 1971.Tubbs, Alan Roy. "CapitalInvestments n AgriculturalMarketingCooperatives: mplicationsor FarmFirm

and Cooperative Finance." Ph.D. thesis, CornellUniversity,1971.VanSickle,JohnJay. "The DevelopmentandAnalysisofa CooperativeDecision Model for ProductPricingand FinancialStructure."Ph.D. thesis, Iowa StateUniversity,1981.Vickers, D. The Theory of the Firm: Production, Capitaland Finance. New York: McGraw-HillBook Co.,1968.Wilson, E. Walter."An EconomicAnalysisof Alterna-tive FinancingPlansfor AgriculturalCooperatives."Ph.D. thesis, Universityof Georgia,1974.