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A MULTIPERIOD FIRM MODEL
Flerperiodisk företagsmodell
Fördjupad finansiell redovisning
Handelshögskolan vid Åbo Akademi
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Firm model – key idea
• The principal idea of the course is to learn how to connect corporate decision making to the financial statements of the firm through the use of fundamental accounting logic
• Corporate decisions typically span multiple accounting periods
• In order to evaluate the financial implications of corporate decisions, the latter must be connected through accounting logic
• The connection between T-accounts and their mathematical representation is of central importance
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Firm model - Work schedule
1. 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 all its effects and check the consistency of the balance sheet before continuing
– Evaluate the financial future of the firm as the sum of the discounted net income over the planning period
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Firm model - Work schedule
2. Add special features according to the separate case instructions
– Financial flow definitions
– Inflation
– Financial ratios
3. Select a company to model– Enter the historical accounts
– Enter the parameters corresponding to the selected company
– Specify the decision variables according to your judgment as a corporate key executive
– Estimate the financial strategy of the firm
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Practical Excel hints for entering
accounting logic
1. name the model variables for each accounting
period
Example:
TURNOVER_1 = SALES_PRICE_1*SVOL_1
OP_PROFIT_1 = TURNOVER_1 – OPCOST_1
Naming variables in Excel: Formulas -> define name
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Practical Excel hints for entering
accounting logic
2. Apply the good old T-accounts when defining
financial relationsExample:
The total sales of the firm year 1 is 10 units of
product 1 at sales price 5.
We assume that 20% of the sales is unpaid by the
end of the accounting year, hence 80% is paid in cash during
period 1. The initial balances (IB) for period 1 are:
Accounts receivable 15
Cash 20
To model these transactions mathematically, start
with writing them using ordinary T-accounts:
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Practical Excel hints for entering
accounting logic
2. Apply the good old T-accounts when defining
financial relations …
CASH_1 TURNOVER_1 ACCOUNTS_REC_1
IB 20 5*10 = 50
0.2*50 = 10
IB 15 15 cash payment
15
10 UB
75 UB
0.8*50 = 40
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Practical Excel hints for entering
accounting logic
mathematically:
Let s = credit proportion of turnover. Then
TURNOVER_1 = SALES_PRICE_1*SVOL_1 = 5*10 = 50
CASH_1 = CASH_0+ACCOUNTS_REC_0 +
(1-s)*TURNOVER_1 = 20 +15+40 = 75
ACCOUNTS_REC_1 = ACCOUNTS_REC_0+ΔACCOUNT_REC_1=
ACCOUNTS_REC_0+s*(TURNOVER_1-TURNOVER_0) =
15-5 = 15 +10-15 = 10
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Firm model - Practical Excel hints
The T-accounts and the mathematical relations are linked through the
following simple rules of thumb:
Assets increase on debit (+) / decrease on credit (-)
Debts increase on credit (+) / decrease on debit (-)
Revenues increase on credit (+) / decrease on debit (-)
Costs increase on debit (+) / decrease on credit (-)
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Practical Excel hints for entering
accounting logic
3. Continuous balancing of the accounts
• If the accounts do not balance after the accounting logic for a transaction has been entered into the system, it will not balance later on either
• Always ascertain that your system is in balance, before entering new accounting logic
• Otherwise, you will have big difficulties to identify your mistakes afterwards when debugging your system.
A system that does not balance will not be accepted.
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Practical Excel hints for entering
accounting logic
4. Conditional formatting for tracking exceptions
- for example, show negative cash with red font
to simplify problem identification
In Excel: Conditional Formatting Highlight Cells Rules
5. Use Deviation table(s) for tracking
constraint violations
If a constraint violation occurs, show it (in red
color) in the deviation table
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Firm model – Key elements
Input:
Decision variablesSales volumeProduction volumeNew debt etc.
Input:
Given parametersSales price/unitProduction cost/unitAmortization ratio etc.
Input:
Logical restrictionsInventory ≥ 0Fixed assets ≥ 0Debt ≥ 0 etc.
Computations/Output:
Multi-period financial statementsBalance sheetStatement of incomeSome elements of Cash flow statement
Output:
Firm valuation:
Sum of discounted future Net Income
Input:
Historical accountsBalance sheet
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Large Scale Techno-Economic
Firm modelling
Key elements
Optimal Firm Design
Dynamic Firm Models
(Monetary Process)Real Process
Forecasting
Neural Nets
Nonlinear Models
Optimization
Fuzzy Sets
Genetic Algorithms
Computation
PC-applications (interface)
High Performance CPU (CSC)
Parallel Processing
(1) MIMD / SUPER machines
(2) Joint research
CSC - support:
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Key Features:
• The necessary financial relations included
• Free specification of time 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:
mn
t
m
t
n
tt
tttt
T
t
t
Abcx
bxAxcx
MAX
,,
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Strategic Firm 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
• Fixed assets
• Intangible assets
• Inventory
• Sales receivable
• Cash
• Other financial items
• Shareholders´equity
• Other restricted equity
• Net income of the year
• Other unrestricted equity
• Accumulated depreciation difference
• Reservations
• Current liabilities
• Long-term debt
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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)
1
1
_
_*
tt
tt
tt
InventoryprogceMachinepri
progPFactorFIXASSETTurnO
InventoryCapacityTurnO
FIXED
ASSETS
Factor * FIXASSETS
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Factor * FIXASSETS
UNIT
PRICESALES
UNIT
COSTMACHINE
FIXASSETSFactor
VOLUMEPRODUCTIONOFVALUESALES
capacityoductionUNIT
COSTMACHINECOSTPURCHASEMACHINE
*
Pr*
1. Turnover - upper bound (cont.)
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Constraints on decision variables
2. Repayment level
MINIMIZE
h
1h
1t
t
h
1t
t0
hhh
REPAYDIFFREPAYNEWDEBTDEBTrep
REPAYDEBT*repREPAY
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Constraints on decision variables
3. New issues - upper bound
MINIMIZE
tt EQUITYDIFFEQUITYnNEWISSUE 0*
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Constraints on decision variables
4. Dividends
MINIMIZE
→< 1hh TR.EQUITYFREE.UNRESDIVUpperbound
h
h
tth
hh
MINDIVDIFFNEWISSUEEQUITYdivDIV
div*EQUITYDIV:Lowerbound
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h
h
t
t
h
t
th MAXDIVDIFFDIVNETINCOMET.EQUITYFREE.UNRESDIV ++< ∑∑1
1=1=
0
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Constraints on decision variables
5. Depreciation - lower bound
h
t
h
ttt
hhh
DEPINVFIXASSETdep
DEPFIXASSETdepDEP
1
1
10
*
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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
h
tth CashCashCash
00 00
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Fundamental Financial
Constraints
2. Fixed assets- nonnegative
001
0
h
ttth DEPINVFIXASSETSFIXASSETS
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Fundamental Financial
Constraints
3. Long-term debt- nonnegative
001
0
h
ttth REPAYNEWDEBTDEBTDEBT
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Fundamental Financial
Constraints
4. Capital structure
MINIMIZE
hh
h
tttt
hh
DEDIFFLIABdeDIVNETINCOMENEWISSUE
EQUITYLIABdeEQUITY
*
*
1
0
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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
Max w
DIV
rDIFF
tt
t
h
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Max w
NETINCOME
rDIFF
tt
t
h
11
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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 = +.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;
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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;
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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 28:5, 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…
Östermark, R: Incorporating asset growth potential and bear market safety
switches in international portfolio decisions. Forthcoming in Applied Soft
Computing (2012) (http://dx.doi.org/10.1016/j.asoc.2012.03.052)
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])