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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

10

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])