A LIQUIDITY-PROFITABILITY TRADE-OFF MODEL FOR WORKING CAPITAL MANAGEMENT MIHIR DASH 1 RANI HANUMAN

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1 A LIQUIDITY-PROFITABILITY TRADE-OFF MODEL FOR WORKING CAPITAL MANAGEMENT MIHIR DASH RANI HANUMAN ABSTRACT This paper proposes a goal programming moel for working capital management. Goal programming is necessary to moel the working capital ecision, as a balance has to be achieve between the conflicting objectives of liquiity an profitability. The moel etermines, for given working capital turnover an fixe assets turnover ratios, how funs shoul be maintaine between working capital/current assets an fixe assets to achieve targete levels of liquiity an profitability, whilst minimizing the opportunity cost/loss of excess liquiity. INTRODUCTION Proper planning is necessary for the efficient working of any organization. This can be in terms of marketing, prouction/operations, human resource, an financial plans. There shoul be proper flow of funs for running any business. This fun is calle working capital. If at any point of time the organization oes not have sufficient funs to meet its short-term ebts such as creitors an salaries as well as ay-to-ay expenses it may become technically insolvent. On the other han, if it is very conservative it will have a surplus of working capital, which will aversely affect profits. The trae-off between profitability an risk is the key to working capital management. Too little working capital increases profit but reuces liquiity, as current assets are more expensive than fixe assets. For instance if a management feels that worker training is a cost they will apportion less funs for it. If on the other han a management sees it as an investment in manpower, the funs allocate woul increase substantially. It is applicable in any case either for procurement, inventory, storage, processing, istribution an human capital an other investment ecisions 2. Businesses must continuously innovate an transform themselves to stay ahea of competition in this fast growing worl. An efficient working capital management system has to be esigne to run the business an make profits in the long run. As costs are ever-increasing, companies have to make efficient use of funs in managing the procurement, inventory, processing an istribution of finishe prouct to the existing customers, an it is common in many business ecision-making situations that certain goals or objectives of the firm can only be met at the expense of other goals. If it is not possible to quantify the exact cost-benefit trae-offs among these goals, it may be necessary for ecision makers to rank orer the various goals so that the less important goals are pursue only after the more important goals are achieve or when no further progress towar goal achievement is possible. The first author is a senior faculty at Alliance Business Acaemy, 9 th Cross, 7 th Main, BTM Layout, II Stage, Bangalore , an can be contacte by phone on , or by at mihira@reiffmail.com. The secon author is a stuent at Alliance Business Acaemy, 9 th Cross, 7 th Main, BTM Layout, II Stage, Bangalore Electronic copy available at:

2 This paper formulates the working capital ecision as a goal programming moel, balancing the conflicting objectives of liquiity an profitability. The moel etermines, for given working capital turnover an fixe assets turnover ratios, how funs shoul be maintaine between working capital/current assets an fixe assets to achieve targete levels of liquiity an profitability, whilst minimizing the opportunity cost/loss of excess liquiity. REVIEW OF LITERATURE: Goal programming techniques have been wiely use in many iverse fiels, incluing operations, marketing, human resources, an finance. Aksoy (990) presente a bibliography of multiple objective ecision-making moels applie in various isciplines. He propose that there was a tren towars utilizing interactive techniques for solving the multiple objective ecision making problem, allowing the involvement of the ecision-maker throughout the ecision process. A variety of goal programming moels have been applie in the operations contexts, usually interlinking operations, marketing, human resource, an financial ecisions. Rees et al (984) analyze the multi-perio, multi-commoity network flow problem. They contene that cost minimization is not the sole or even the most important objective of the firm; other objectives often exist relate to preferre customer eman, inventory conitions, an shipping arrangements en contracts, necessitating a goal programming approach. Several commoities are istribute through a network of istribution points (i.e., stores, outlets, terminals, etc.) in orer to meet supply en eman constraints at these istribution points at the minimum shipping cost, an the moel is further complicate by the fact that shipments occur over several perios. Tabucanon an Estraza (989) evelope a goal programming moel base on several conflicting objectives of companies, incluing minimization of lea time/elay, maximization of revenue, minimization of prouction cost, an minimization of overtime. Their moel was applie to real ata from a company, an sensitivity analysis was performe to give insights to the ecision-makers regaring trae-offs between the conflicting objectives. Kim an Schnieerjans (993) formulate a linear goal programming moel for JIT prouction systems. They showe how the post-optimality analysis of the goal programming moel enables a ecision maker to examine the effects of prouction scheuling in a JIT mixemoel prouction environment. Khorram et al (994) propose a unique solution to resource allocation problems by combining goal programming with a qualitative forecasting moel (e.g. the Delphi metho) an a quantitative forecasting technique (e.g. the Poisson gravity moel). In their moel, the Delphi metho is use initially to elicit the experts' talents to erive the objectives to be consiere in resource allocation, an subsequently a quantitative forecasting technique is use to preict the future values for these objectives. This information is then was use to construct a goal programming moel. Rifai (996) iscusse the limitations of linear programming in ecision-making, an suggeste the use of goal to hanle problems with multiple objectives. He avocate caution in using the goal programming, since an improper structure of a goal programming moel can inuce misleaing results. Schnieerjans an Hoffman (999) propose a goal programming moel for ownsizing in orer to cut operation costs, base on a thorough analysis of the firm s prioritize opportunities Electronic copy available at:

3 an their limite economic resources to achieve them. They provie a new methoological approach that can be use to etermine previously hien goals in a manufacturing linear programming moel of the ownsizing problem. Their moel illustrate how an optimal allocation of prouction resources can be achieve while proviing useful information in which to ensure other prioritize goals an their economic traeoffs. Coskun et al (2008) stuie integrative methos for improving business processes. Their approach involve etermining an analyzing the weak points an reucing the weakness egrees. They suggeste a four-phase business process improvement framework: start-up, self analysis, efining improvement strategy for making changes, feeback, an continuous improvement. They foun that ecision problems in process improvement coul be structure to provie input ata suitable for multi-criteria ecision making techniques. Lee an Kang (2008) evelope a moel for inventory management for multiple perios, consiering not only the usual parameters, but also price/ quantity iscounts, an storage an batch size constraints. The moel is formulate as a mixe binary integer programming problem minimizing the total cost of materials in the system, an the optimal solution etermines an appropriate inventory level for each perio an the optimal purchase amount in each perio. Several stuies have aresse the problem of working capital, an have evelope a variety of moels to assess the efficiency of working capital management. Jafar an Sur (2006) stuie the efficiency of the working capital management in the National Thermal Power Corporation (NTPC), an showe that the company achieve a higher level of efficiency in managing its working capital uring the post-liberalization era by aapting itself to the new environment which ha emanate from liberalization, globalization an competitiveness. They pointe out that, while many of the public enterprises are learning to survive an grow by aapting themselves to the new situation, a large group of public sector unertakings, significant both in number an investment, have been beset with serious problems like slow growth, low prouctivity, inaequate emphasis on research an evelopment, inefficient working capital management, an so on. Rafuse (996) argue that attempts to improve working capital by elaying payment to creitors are counter-prouctive, an that altering ebtor an creitor levels for iniviual tiers within a value system will rarely prouce any net benefit. He propose that stock reuction generates system-wie financial improvements an other important benefits, an suggeste that, to achieve this, companies shoul focus on stock management strategies base on lean supplychain techniques. Cote et al (999) explore the limitations of the traitional measures of working capital management an presente alternative measures base on earlier work in the finance literature. They also propose a new ratio, the merchanising ratio, which measure the net effect of a firm's working capital management strategy. Garcia-Teruel an Martinez-Solano (2007) stuie the effects of working capital management on the profitability of a sample of small an meium-size Spanish firms. They foun that managers can create value by reucing their inventories an the number of ays for which their accounts are outstaning. Moreover, shortening the cash conversion cycle also improves the firm's profitability. Filbeck an Krueger (2005) suggeste that firms shoul be able to reuce financing costs an/or increase the funs available for expansion by minimizing the amount of funs tie up in current assets. They foun significant ifferences in working capital measures between inustries Electronic copy available at:

4 across time, an significant changes in these working capital measures within inustries across time. Chakraborty (2008) evaluate the relationship between working capital an profitability of Inian pharmaceutical companies. He pointe out that there were two istinct schools of thought on this issue: accoring to one school of thought, working capital is not a factor of improving profitability an there may be a negative relationship between them, while accoring to the other school of thought, investment in working capital plays a vital role to improve corporate profitability, an unless there is a minimum level of investment of working capital, output an sales cannot be maintaine - in fact, the inaequacy of working capital woul keep fixe asset inoperative. Chakraborty an Banopahyay (2007) stuie strategic working capital management, an its role in corporate strategy evelopment, ultimately ensuring the survival of the firm. They also highlight how strategic current asset ecisions an strategic current liabilities ecisions ha multi-imensional impact on the performance of a company. Singh (2008) foun that the size of inventory irectly affects working capital an its management. He suggeste that inventory was the major component of working capital, an neee to be carefully controlle. Singh an Paney (2008) suggeste that, for the successful working of any business organization, fixe an current assets play a vital role, an that the management of working capital is essential as it has a irect impact on profitability an liquiity. They stuie the working capital components an foun a significant impact of working capital management on profitability for Hinalco Inustries Limite. Agarwal (988) formulate the working capital ecision as a goal programming problem, giving primary importance to liquiity, by targeting the current ratio an quick ratio. The moel inclue three liquiity goals/constraints, two profitability goals/constraints, an, at a lower priority level, four current asset sub-goals an a current liability sub-goal (for each component of working capital). In particular, the profitability constraints were esigne to capture the opportunity cost of excess liquiity (in terms of reuce profitability). The literature of goal programming in operational/financial ecisions is quite extensive, though only a few stuies have irectly focuse on working capital ecisions. Agarwal s (988) stuy was a step forwar, but no further refinements to his moel have been propose. This paper proposes certain moifications in Agarwal s (988) moel. LIQUIDITY-PROFITABILITY TRADE-OFF MODEL: The goal programming moel propose in this paper examines the trae-off between liquiity an profitability. Goal programming is appropriate because liquiity an profitability represent conflicting objectives of a firm. The ecision variables for the moel are the usual components of working capital, viz. cash, marketable securities, accounts receivable, inventory, an current liabilities, an fixe assets, sales, an profit. Each of these variables is assume to have well-efine target levels. Aitionally, the current ratio, profit margin, working capital turnover ratio, an fixe assets turnover ratio are assume to have stable target levels. These variables an targets are represente in Table.

5 Table : variables an target parameters VARIABLE CASH x MARKETABLE SECURITIES x 2 ACCOUNTS RECEIVABLE x 3 INVENTORY x 4 CURRENT LIABILITIES x 5 TARGET FIXED ASSETS f FA SALES y S PROFIT π P CURRENT RATIO θ PROFIT MARGIN m WORKING CAPITAL TURNOVER RATIO ω FIXED ASSETS TURNOVER RATIO Highest priority is given to maintaining liquiity, turnover, an profitability, built into the moel via the current ratio, the working capital an fixe assets turnover ratios, an the profit margin, followe by the targete levels of each of the variables. The ifferent priority coefficients (P i ) assigne to each of the ifferent goals are represente in Table 2. Table 2: priority levels assigne to constraints CONSTRAINTS PRIORITY DEVIATION VARIABLES LIQUIDITY P, WORKING CAPITAL TURNOVER P 2 2, 2 FIXED ASSETS TURNOVER P 3 3, 3 PROFIT MARGIN P 4 4, 4 OPPURTUNITY COST P 5 5, 5 CASH P 6 6, 6 MARKETABLE SECURITIES P 7 ACCOUNTS RECEIVABLE P 8 INVENTORY P 9 CURRENT LIABILITIES P 0 FIXED ASSETS P SALES P 2 PROFIT P 3 x 7, 8, 9, 0, ,,, 2 3 C MS AR I CL φ

6 The goal programming formulation for the problem is given below: 3 min w = P j ( j j ), subject to the constraints: () Total assets: x x2 x3 x4 x5 x f = C MS AR I CL FA (2) Liquiity: x x2 x3 x4 = θ. CL (3) Working Capital Turnover: y wx ( x2 x3 x4 x5 ) 2 2 = 0 (4) Fixe Assets Turnover: y φ x f 3 3 = 0 (5) Profit margin: π my 4 4 = 0 (6) Opportunity cost: π mφ[ x x2 x3 x4 x5 y/ w] 5 = P (7) Cash: x 6 = C (8) Marketable securities: x = MS (9) Accounts receivable: x3 = AR (0) Inventories: x4 9 = I () Current liabilities: x = CL (2) Fixe assets: x f = FA (3) Sales: y 2 2 = S (4) Profit: π 3 3 = P (5) Non-negativity: x, x 5, x f, y, π, ±, ± 3 0 j = The moel formulate above aresses a few limitations of Agarwal s (988) moel. Agarwal s moel has an inbuilt over-emphasis on liquiity, through its liquiity goals an once again through its current assets an current liabilities sub-goals; in fact, the profitability goals also have an inbuilt liquiity target. Also, the profitability goals in Agarwal s moel are somewhat ambiguous: profit as a variable seems to be unrelate to the other (working capital) variables, an the cost of capital term in the profitability goals is not very clear. The propose moel tries to aress some of the limitations of Agarwal s moel. In orer to relate the profit variable with working capital variables, the moel introuces variables for fixe assets an sales, an interlinks the variables via the working capital turnover ratio, the fixe assets turnover ratio, an the profit margin goals. Liquiity remains as a major goal, an Agarwal s profitability goal is replace by a profitability goal which functions to balance funs between working capital an fixe assets, in accorance with the targete turnover ratios. The resulting opportunity cost is the profit forgone by excess/eficiency of liquiity (as etermine by the turnover ratios). APPLICATION OF THE MODEL: The goal programming moel presente in preceing section was applie to the input ata of the firm Vijaya Krishna Spice Farms Pvt. Lt., a foo-processing company mainly involve in the storage of ifferent varieties of chilly an the processing of the same into chilly paste. The financial ata require for analysis was obtaine from the company, for the five year span from

7 The target values of the current ratio, working capital turnover ratio, fixe assets turnover ratio, an net profit margin were set approximately at their five-year averages, to eliminate chance fluctuations for a particular perio. The optimal working capital position (assuming equal priorities of all goals an sub-goals) of the firm for the year is etaile in Table 3: Table 3: results of the two moels TARGETS DATA AGARWAL S SOLUTION SOLUTION CASH 3,72, ,72, ,72, MARKETABLE SECURITIES 33,098, ,098, ,098,6.00 ACCOUNTS RECEIVABLE 89,86, ,86, ,86,27.00 INVENTORY 5,884, ,884, ,9,465.2 CURRENT LIABILITIES 33,433, ,433, ,433, FIXED ASSETS 20,265, ,238,84.79 SALES 322,370, ,582, PROFIT 3,782, ,809, ,858, (opportunity cost) 3,026, ,075, CURRENT RATIO WORKING CAPITAL TURNOVER RATIO FIXED ASSETS TURNOVER RATIO PROFIT MARGIN The results from Agarwal s moel inicate a Rs. 3,026, opportunity loss ue to excess liquiity, while the results the propose moel inicate a Rs. 3,075, opportunity loss. The results of the propose moel suggest that excess liquiity (in the form of Rs. 2,973,8.79 of inventory) be converte to fixe assets in orer to improve profitability. It is observe that, in the solution, while the working capital turnover ratio, the fixe assets turnover ratio, an the profit margin are close to their targete values, the current ratio is not. The eviation variables in the optimal solution are presente in Table 4 (for simplicity, only non-zero values are isplaye). Table 4: eviational variables in the optimal solution CONSTRAINTS DEVIATION VARIABLES LIQUIDITY = 08,050, WORKING CAPITAL TURNOVER = 5,26, FIXED ASSETS TURNOVER PROFIT MARGIN OPPURTUNITY COST CASH MARKETABLE SECURITIES ACCOUNTS RECEIVABLE INVENTORY = 9 2,973,8. 79 CURRENT LIABILITIES FIXED ASSETS = 2,973,8. 79 SALES = 2 26,22,02.88 PROFIT = 3,075,

8 The eviation variables inicate over-achievement of liquiity far in excess of the targete level, uner-achievement of working capital turnover, an over-achievement of sales. Further, the eviation variables an inicate excess liquiity (inventory) that is to be converte to 9 fixe assets. The sensitivity analysis of the moel to ifferent parameters is presente in Table 5. Table 5: sensitivity analysis of the optimal solution OPPORTUNITY COST %CHANGE ELASTICITY CASH 5% 3,0, % % 3,093, % -2.50% 3,058, % -5% 3,040, % MARKETABLE SECURITIES 5% 3,386, % % 3,230, % -2.50% 3,230, % -5% 2,765, % ACCOUNTS RECEIVABLE 5% 3,9, % % 3,493, % -2.50% 2,657, % -5% 2,239, % INVENTORY 5% 3,562, % % 3,39, % -2.50% 2,832, % -5% 2,589, % CURRENT LIABILITIES 5% 2,762, % 2.50% 2,99, % % 3,232, % -5% 3,389, % FIXED ASSETS 5% 3,265, % % 3,70, % -2.50% 2,980, % -5% 2,885, % It is observe that the results of the propose moel are highly sensitive to changes in accounts receivable (with elasticity ), followe by inventory (with elasticity 3.629), current liabilities (with elasticity ), marketable securities (with elasticity 2.077), fixe assets (with elasticity.2354), an, least of all, cash (with elasticity ).

9 DISCUSSION: Several stuies have stresse the importance of effective working capital management. Agarwal (988) ha formulate a goal programming moel for working capital ecisions, but it ha some serious limitations, especially its over-emphasis on liquiity. The moel propose in this paper extens the scope of Agarwal s moel, whilst retaining the concept of a liquiityprofitability trae-off. The results of the moel suggest that working capital, an inventory in particular, shoul be streamline to profitability. This approach is thus in conformance with the stuies of Rafuse (996), Cote et al (999), Garcia-Teruel an Martinez-Solano (2007), Filbeck an Krueger (2005), Singh (2008), an Singh an Paney (2008). In particular, the relationship between ifferent components of working capital, fixe assets, sales, an profits nees to be examine in greater epth an moele accoringly. There is vast scope for extening the moel propose in this paper. The propose moel is a static, aggregate-level moel; a ynamic/multi-stage micro-moel, with appropriate interlinkages between the ifferent variables, incorporating the working capital cycle concept an time value of money, woul give more etaile results. Also, the propose moel has some limitations: it consiers a specific form of liquiity an profitability goals/constraints, which may not have taken some other relevant parameters into consieration; an it assumes stable turnover ratios, which may limit its applicability in practice. Further, the propose moel is a linear programming moel, an thus eals only with the linear behavior of working capital; nonlinearities are not taken into consieration. BIBLIOGRAPHY:. Agarwal, J.D. (988), A goal programming moel for working capital management, Finance Inia, Vol. 2, Issue Aksoy, Y. (990), Interactive Multiple Objective Decision Making: A Bibliography ( ), Management Research News, Vol. 3, Issue Chakraborty, K. (2008), Working Capital an Profitability: An Empirical Analysis of Their Relationship with Reference to Selecte Companies in the Inian Pharmaceutical Inustry, The Icfai Journal of Management Research 4. Chakraborty, P.K. an Banopahyay, K. (2007), Strategic Working Capital Management: Case of a Turnaroun Company, ICFAI Reaer 5. Coskun, S., Basligil, H. an Baracli, H. (2008), A weakness etermination an analysis moel for business process improvement, Business Process Management Journal, Vol. 4, Issue Cote, J.M. an Latham, C.K. (999), The Merchanising Ratio: A Comprehensive Measure of Working Capital Strategy, Issues in Accounting Eucation; Vol. 4, Issue 2 7. Filbeck, G., Krueger, G. an Krueger, T.M. (2005), An Analysis of Working Capital Management Results across Inustries, Mi-American Journal of Business, Vol. 20, Issue Garcia-Teruel, P.J. an Martinez-Solano, P. (2007), Effects of working capital management on SME profitability, International Journal of Managerial Finance, Vol.3, Issue Jafar, A. an Sur, D. (2006), Efficiency of Working Capital Management in Inian Public Enterprises uring the Post-liberalization Era: A Case Stuy of NTPC, The Icfai Journal of Management Research

10 0. Khorram Shahgol, R. an Okoruwa, A. (994), A goal programming approach to investment ecisions: A case stuy of fun allocation among ifferent shopping malls in Atlanta, Operational Research, Vol. 73, Issue.. Kim, G.C. an Schnieerjans, M.J. (993), A Multiple Objective Moel for a Just-in- Time Manufacturing System Environment, International Journal of Operations & Prouction Management, Vol.3, Issue Lee, A.H.I. an Kang, H.-Y. (2008), A mixe 0- integer programming for inventory moel: A case stuy of TFT-LCD manufacturing company in Taiwan, Kybernetes, Vol. 37, Issue. 3. Rafuse, M.E. (996), Working capital management: an urgent nee to refocus, Management Decision, Vol. 34, Issue Rees Loren., P.; Clayton, Ewar R.; Taylor, III, Bernar W (987), A linear goal programming moel of a multi-perio, multi-commoity network flow problem, Business Logistics, Vol. 8, Issue. 5. Rifai, A.K. (996), A note on the structure of the goal-programming moel: assessment an evaluation, International Journal of Operations & Prouction Management, Vol.6, Issue. 6. Schnieerjans, M.J. an Hoffman, J.J. (999), Downsizing prouction/operations with multi-objective programming International Journal of Operations & Prouction Management, Vol.9, Issue. 7. Singh, J.P. an Paney, S. (2008), Impact of Working Capital Management in the Profitability of Hinalco Inustries Limite, The Icfai University Journal of Financial Economics 8. Singh, P. (2008), Inventory an Working Capital Management: An Empirical Analysis, The Icfai University Journal of Accounting Research 9. Tabucanon, M.T. an Estraza, M.D.E. (989), Multi-objective prouction planning moel for a garment factory, International Journal of Clothing Science an Technology, Vol., Issue 3.