A MULTIPERIOD FIRM MODEL

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A MULTIPERIOD FIRM MODEL
by Ralf Östermark
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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 0 etc.
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
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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

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Large Scale Techno-Economic Firm Planning
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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.

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Problem formulation
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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

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Decision variables

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

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Deviation variables

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

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Financial statement

• Shareholdersequity
• Other restricted equity
• Net income of the year
• Other unrestricted equity
• Value items
• Accumulated depreciation difference
• Reservations
• Current liabilities
• Long-term debt

• Fixed assets
• Value items
• Inventory
• Sales receivable
• Cash
• Other financial items

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Statement of income

• Turnover
• - Operating costs
• - Changes in inventory
• - Depreciation
• - Interest expenses
• Other financial income
• Extraordinary income and expenses
• Allocations
• - Taxes
• Net income

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Constraints on decision variables

• 1. Turnover - upper bound f(production capacity)

Factor FIXASSETS
FIXED ASSETS
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1. Turnover - upper bound (cont.)
Factor FIXASSETS
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Constraints on decision variables

• 2. Repayment level

MINIMIZE
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Constraints on decision variables

• 3. New issues - upper bound

MINIMIZE
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Constraints on decision variables

• 4. Dividends

MINIMIZE
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Constraints on decision variables

• 5. Depreciation - lower bound

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Fundamental Financial Constraints

• 1. Cash - nonnegative

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
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Fundamental Financial Constraints

• 2. Fixed assets- nonnegative

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Fundamental Financial Constraints

• 3. Long-term debt- nonnegative

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Fundamental Financial Constraints

• 4. Capital structure

MINIMIZE
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Financial relationships

• Costs c TurnO
• Interests i DEBT
• Ot. fin. costs. o OTH.FIN.ASS.
• Sales receivable s TurnO
• Current liabilities cl Costs

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Alternative Objective functions

• - Optimize discounted dividend

- Optimize discounted net income
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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 .8696Div(1)-10000.MinDivdiff(1)-
• 10000.EQUITYdiff(1)-10000.DEdiff(1)
• 15 -10000.REPdiffm(1)-30000.MAXdivdf(1)
• 16 !AMATRIX X lt b-vector
• 17 !Cash
• 18 3.135Oms(1).91Nylan(1)-.91Amort(1)-1.Inv
  (1)
• 19 1.Emiss(1)-1.Div(1).1Avskr(1)gt3137.551
• 20 !Turnover
• 21 1.Oms(1)-.5Inv(1).5Avskr(1)lt2950.4
• 22 !Fixed assets
• 23 1.Inv(1)-1.Avskr(1)gt-5900.8
• 24 !Long-term debt
• 25 1.Nylan(1)-1.Amort(1)gt-2353.9
• 26 !Minimal depreciation
• 27 -.03Inv(1)1.Avskr(1)gt177.024
• 28 !Debt-Equity ratio

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• 29 -2.375Oms(1)-1.09Nylan(1)1.09Amort(1)1.E
  miss(1)
• 30 -1.Div(1)-.9Avskr(1)1.DEdiff(1)gt-3012.849
  
• 31 !New Issues
• 32 1.Emiss(1)-1.EQUITYdiff(1)lt111.572
• 33 !Minimal Dividend
• 34 -.01Emiss(1)1.Div(1)1.MinDivdiff(1)gt13.77
  7
• 35 !Maximal Dividend
• 36 -.45Oms(1).09Nylan(1)-.09Amort(1)1.Div(1
  )
• 37 .9Avskr(1)-1.MAXdivdf(1)lt1450.449
• 38 !Minimal Debt Repayments
• 39 -.15Nylan(1)1.Amort(1)1.REPdiffm(1)353.0
  85

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Related Research
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 Conference in
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 Research 35, 1988, pp.
255-262. Östermark, R. and K. Söderlund "A
multi-period firm model for strategic decision
support", Kybernetes 285, 1999, pp.
538-556. Östermark, R., H. Skrifvars, and T.
Westerlund "A nonlinear mixed integer
multi-period firm model", International Journal
of Production Economics 67, 2000, pp. 183-199.

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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
Korhonens Bank Model EJOR, around 1989 The
derivative firm model (Choi et al, Man. and
Decision Economics 1993)

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