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A MULTIPERIOD FIRM MODEL

A MULTIPERIOD FIRM MODEL. by Ralf Östermark. Firm plan model – Key elements. Input : Decision variables Sales volume Production volume New debt etc. Input : Given parameters Sales price/unit Production cost/unit Amortization ratio etc. Input :

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A MULTIPERIOD FIRM MODEL

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  1. A MULTIPERIOD FIRM MODEL by Ralf Östermark

  2. Firm plan model – Key elements Input: Decision variables Sales volume Production volume New debt etc. Input: Given parameters Sales price/unit Production cost/unit Amortization ratio etc. Input: Logical restrictions Inventory ≥ 0 Fixed assets ≥ 0 Debt ≥ 0etc. Computations/Output: Multi-period financial statements Balance sheet Statement of income Some elements of Cash flow statement Input: Historical accounts Balance sheet Output: Firm valuation: Sum of discounted future Net Income

  3. Firm valuation - Work schedule • Build a model for multi-period financial statements for the given case • Include the basic accounting logic • Link to the historical accounts • Link to the input elements (Decision variables, parameters) • Begin with the status quo i.e. no transactions • Check that the balance sheet is in balance • Add one decision/transaction at a time, link in all its effects and check the consistency of the balance sheet before continuing • Compute the company value as a sum of discounted net income over the planning period • Select a company to evaluate • Enter the historical accounts • Enter the parameters corresponding to the selected company • Fill in the decision variables according to your judgment as a company valuator • Compute the company value

  4. Large Scale Techno-Economic Firm Planning

  5. Key Features: • The necessary financial relations included • Free specification of planning horizon • Simulation and optimization combined • Guaranteed feasibility • A flexible optimization module written as a dynamic link libary (DLL) in strict ANSI C.

  6. Problem formulation:

  7. Strategic Firm Planning Model • Financial decision variables • Constraints on decision variables • Fundamental financial constraints • Balance sheet relationships • Goal functions • Multi-period optimization problem - solving in LINGO

  8. Decisionvariables • Sales volume (SALEVOL) • Production volume (PRODVOL) • New debt (NEWDEBT) • Repayment (REPAY) • Investments (INV) • New issues (NEWISSUE) • Dividends (DIV) • Depreciation (DEP)

  9. Deviation variables • Min dividend deviation (DIVDIFF) • Max dividend deviation (MAXDIVDIFF) • Equity deviation (EQUITYDIFF) • Debt/Equity deviation (DEDIFF) • Repayment deviation (REPDIFF)

  10. Fixed assets Value items Inventory Sales receivable Cash Other financial items Shareholders´equity Other restricted equity Net income of the year Other unrestricted equity Value items Accumulated depreciation difference Reservations Current liabilities Long-term debt Financialstatement

  11. Statement of income + Turnover - Operating costs - Changes in inventory - Depreciation - Interest expenses + Other financial income + Extraordinary income and expenses + Allocations - Taxes = Net income

  12. Constraints on decision variables 1. Turnover - upper bound = f(production capacity) Factor * FIXASSETS FIXED ASSETS

  13. 1. Turnover - upper bound (cont.) Factor * FIXASSETS

  14. Constraints on decision variables 2. Repayment level MINIMIZE

  15. Constraints on decision variables 3. New issues - upper bound MINIMIZE

  16. Constraints on decision variables 4. Dividends MINIMIZE

  17. Constraints on decision variables 5. Depreciation - lower bound

  18. Fundamental Financial Constraints Cash flow: + Turnover - Change in sales revenues - Costs - Change in other financial assets - Interest expenses + Change in current liabilities + Other financial income + New debt + Extraordinary income - Repayment - Dividends - Investments 1. Cash - nonnegative

  19. Fundamental Financial Constraints 2. Fixed assets- nonnegative

  20. Fundamental Financial Constraints 3. Long-term debt- nonnegative

  21. Fundamental Financial Constraints 4. Capital structure MINIMIZE

  22. Financial relationships Costs: c * TurnO Interests: i * DEBT Ot. fin. costs. o * OTH.FIN.ASS. Sales receivable s * TurnO Current liabilities cl * Costs

  23. Alternative Objective functions - Optimize discounted dividend - Optimize discounted net income

  24. Example: optimization in LINGO The optimization module of the firm planning system is written as a dynamic link library (DLL) in strict ANSI C by the author. However, in smaller optimization formulations like the one in analys.xls, the optimization can be carried out by Excel. We illustrate the solution process by a small system written for LINGO: 13] ! Objectivefunction 3 ; 14] MAX = +.8696*Div(1)-10000.*MinDivdiff(1)- 10000.*EQUITYdiff(1)-10000.*DEdiff(1) 15] -10000.*REPdiffm(1)-30000.*MAXdivdf(1); 16] !AMATRIX * X < b-vector; 17] !Cash; 18] +3.135*Oms(1)+.91*Nylan(1)-.91*Amort(1)-1.*Inv(1) 19] +1.*Emiss(1)-1.*Div(1)+.1*Avskr(1)>3137.551; 20] !Turnover; 21] +1.*Oms(1)-.5*Inv(1)+.5*Avskr(1)<2950.4; 22] !Fixed assets; 23] +1.*Inv(1)-1.*Avskr(1)>-5900.8; 24] !Long-term debt; 25] +1.*Nylan(1)-1.*Amort(1)>-2353.9; 26] !Minimal depreciation; 27] -.03*Inv(1)+1.*Avskr(1)>177.024; 28] !Debt-Equity ratio;

  25. 29] -2.375*Oms(1)-1.09*Nylan(1)+1.09*Amort(1)+1.*Emiss(1) 30] -1.*Div(1)-.9*Avskr(1)+1.*DEdiff(1)>-3012.849; 31] !New Issues; 32] +1.*Emiss(1)-1.*EQUITYdiff(1)<111.572; 33] !Minimal Dividend; 34] -.01*Emiss(1)+1.*Div(1)+1.*MinDivdiff(1)>13.777; 35] !Maximal Dividend; 36] -.45*Oms(1)+.09*Nylan(1)-.09*Amort(1)+1.*Div(1) 37] +.9*Avskr(1)-1.*MAXdivdf(1)<1450.449; 38] !Minimal Debt Repayments; 39] -.15*Nylan(1)+1.*Amort(1)+1.*REPdiffm(1)=353.085;

  26. Östermark R: "Pitkän tähtäyksen strateginen tilinpäätössunnittelumalli" (A long term strategic planning model). Presented at European IFPS User's Group Meeting, Amsterdam 1983. In: European IFPS User's Group Proceedings, 11, 1983, 14 p. Östermark, R. and E. Kasanen: "A graphical decision support system for multi-objective financial modeling", Turku School of Economics, 1985. Presented at the EURO VII Conferencein Lisbon, Portugal 09/1986. Östermark, R.: "A graphical DSS for conflict zone analysis of commercial bank environment", In: DSS Transactions 1987, 15 p. Presented at the DSS-87 Conference in San Fransisco, California. Östermark, R.: "Optimal compromising within a multi-criterial conflict zone", European Journal of Operational Research35, 1988, pp. 255-262. Östermark, R. and K. Söderlund: "A multi-period firm model for strategic decision support", Kybernetes28:5, 1999, pp. 538-556. Östermark, R., H. Skrifvars, and T. Westerlund: "A nonlinear mixed integer multi-period firm model", International Journal of Production Economics67, 2000, pp. 183-199. Related Research

  27. Related Research… Booth, Bessler, Foote.”Managing interest-rate risk in banking institutions” European Journal of Operational Research 41(1989) 302-313. Reid, Bradford.”A Farm Firm Model of Machinery Investment Decisions” American Journal of Agricultural Economics (1987) 64-77. Bessler, Booth. “An interest rate risk management model for commercial banks” European Journal of Operational Research 74 (1994) 243-256 Korhonen’s Bank Model [EJOR, around 1989] The derivative firm model (Choi et al, Man. and Decision Economics [1993])

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