Table Of ContentStudies in Financial Modelling
Managing Editor
Jaap Spronk
Editorial Board
W. de Bondt
R. Flavell
P. Jennergren
H.Konno
B. Munier
D. Sondermann
G.P. Szego
Jaap Spronk· Benedetto Matarazzo (Eds.)
In Cooperation with the Editorial Board of the Rivista di
Matematica per Ie Scienze Economiche e Sociali
Modelling for
Financial Decisions
Proceedings of the 5th Meeting of the BURO Working
Group on ''Financial Modelling" held in Catania,
20-21 April, 1989
With 44 Figures
Springer-Verlag
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London Paris Tokyo
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Prof. Dr. Jaap Spronk
Erasmus University
P.O. Box 1738
NL-3000 DR Rotterdam
The Netherlands
Prof. Dr. Benedetto Matarazzo
Universita di Catania
Corso Italla 55
I-Catania
Italla
First published in "Rivista di matematica per Ie scienze economiche e sociali", Vol. 12, No.1, 1989
ISBN-13: 978-3-642-76763-0 e-ISBN-13: 978-3-642-76761-6
001: 10.1007/978-3-642-76761-6
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CONTENTS
pag.
Financial Modelling is Back in Town Benedetto Matarazzo, Jaap Spronk..................... 5
Inflation and Firm Growth: a Reassessment Daniel L. Blakley, Arne Dag Sti............... 7
Multi-factor Financial Planning Marc Goedhart, Jaap Spronk ...................................... 25
A Survey and Analysis of the Application of the Laplace Transform to Present Value
Problems Robert W. Grubbstrom, Jiang Yinzhong .......................................................... 43
Tax Effects in the Dutch Bond Market G.H.M.l Kremer ............................................... 63
The Continuous Quotations at an Auction Market Thomas Land/es, Otto Loistl ........ 73
A New Perspective on Dynamic Portfolio Policies Elisa Luciano................................. 91
The Splitting up of a Financial Project Into Uniperiodic Consecutive Projects
Paolo Manca...................................................................................................................... 107
Modelling Stock Price Behaviour by Financial Ratios Teppo Martikainen ................... 119
An Actuarial and Financial Analysis for Ecu Insurance Contracts Piera Mazzoleni..... 139
Multiperios Analysis of a Levered Portfolio Lorenzo Peccati ........................................ 157
The Time Series Characteristics of Quarterly Nominal and Real Lira/Pound-sterling
Exchange rate Movements, 1973-1988 Andrew C. Pollock............................................. 167
Exploring Efficient sets and Equilibria on Risky Assets with AP ABO DSS Prototype
Version 2.1 Francesco A. Rossi ....................................................................................... 195
A Stochastic Cash Model with Deterministic Elements Willem-Max Van Den Bergh,
Win/ried Hallerbach .......................................................................................................... 207
Utility of Wealth and Relative Risk Aversion: operationalization and Estimation
NicoL. Van DerSar................................................................................... ........................ 219
On the Robustness of Models of Optimal Capital Structure D. Van Der Wijst............. 229
3
FINANCIAL MODELLING IS BACK IN TOWN
In April 1989, the fifth meeting of the EURO Working Group on Financial
Modelling was held in Acireale, Sicily, organized by Benedetto Matarazzo of
the University of Catania. The meeting was attended by over 100 participants
from fourteen different countries. A large number of papers was presented and
dicsussed.
The Catania meeting clearly showed the right of existence of the working
group in which not only completed research projects but also ongoing research
can be discussed in a relaxed but constructive way. Apparently, there is a need
in Europe to strengthen the links between people working in the field of finan
cial modelling. Since 1989, a number of projects undertaken jointly by resear
chers in different countries have been set up. Since Catania other meetings
have been organized in Liege (Belgium), Sirmione (Italy), Groningen (The Ne
therlands) and Cura~ao (The Netherlands Antilles).
This volume was published earlier as a special issue of the Rivista di matema
tica per Ie scienze economiche e sociali.
Weare grateful to the editorial board of the Rivista for their kind willingness
to devote a special issue to this meeting. All papers were referred by two refe
rees. The final acceptance decision were made together with the editorial board
of the Rivista. We would like to express our gratitude to the referees for the
work they did.
The working group is mainly focussed on the development of tools which
support decision makers in the financial area, ranging from treasurers of firms
to professional investors (pension funds, mutual funds) and bank managers.
The contents of this volume shows a broad variety of applications using techni
ques and methodologies from various fields such as econometrics, operations
research and financial mathematics. Those remembering the practice and theo
retical developments of financial modelling in the late sixties and during the se
venties and who have since then lost contact with the field may still be a little
5
bit sceptical. And not withhout reason. In the early stages of financial model
ling much went wrong. Enormous, complicated models were built with the
claim of «realism», requiring sophisticated information systems and access to
mainframe computers. As a consequence, financial modelling often was the bu
siness of «experts» far more than of decision makers. In fact, the whole ap
proach towards decision making was at the same time «hautain» and somewhat
naive. In addition, because of the experts being trained in fields generally diffe
rent from finance, many models neglected important results from develop
ments in financial theory. Looking backwards it is not much of a surprise that
the original optimism towards financial modelling very often turned into frusta
tion. Fortunately, much has changed during the eighties.
First of all, the philosophy and methodology with respect to tools for decision
making has been changed towards something which in the field of financial de
cision making might be labelled as «financial decision support systems». The
role of the decision makers has become dominant, both in the development and
in the use of the decision support systems.
The developments in both computer hardware and software for computers
made and still makes it much easier to individualise decision support systems.
In addition, as many of the contributions in this volume show, the results offi
nancial theory are much better taken into account than, say, ten years ago.
Ideally, financial modelling would function as a liason between financial theory
and practice.
Of course, much work remains to be done. We hope that international coope
ration within the framework of the EURO Working Group will contribute to the
required development.
Furthermore the editors, also on behalf of the publisher, would like to thank
the Editorial Board of the Rivista di Matematica per Ie Scienze Economiche e
Sociali for the kind willingness of transferring the copyright of material which
was earlier published in a special issue of the "Rivista".
Benedetto Matarazzo
Jaap Spronk
6
INFLATION AND FIRM GROWTH: A REASSESSMENT
DANIEL L. BLAKLEY, ARNE DAG STI
Bedriftsokonomisk lnstitutt
The Norwegian School ofM anagement
P. box 580
N-1301 Sandvika, Norway
Investigations into the impact of inflation on firm growth have resulted in ambiguous conclusions
within the economic growth and financial management literature. This paper will attempt to clarify
this situation and describe conditions under which rum growth will be helped or hindered by in
flaction. This is accomplished by constructing a financial modelling framework which incorporates
the findings of earlier research and allows the various effects to be contrasted and cum ulativel y asses
sed. Our findings suggest that conditions under which inflation may be beneficial to firm growth do
exist but are realistically improbable.
1. Introduction
Does inflation hinder or stimulate growth? The importance of this inquiry
to managers and policy makers has generated considerable research effort within
both the economic growth and finance literature. There has to date, however,
been little agreement either between or within these 2 scenes of academic inquiry
as to the overall effect of inflation. Indeed, positive and negative effects of infla
tion on growth have been identified in both schools leaving the net effect open
to debate and speCUlation.
The overall objective of this research effort is to develop a methodology for
analyzing the conflicting nature and cumulative impact of these accepted findings.
This will be accomplished via the construction of a modelling framework which
will unify micro and macro inflationary considerations. It is believed this is the
first attempt to consolidate the theoretical findings from these 2 distinct branches
of analysis. A secondary objective is to use the model to describe conditions
under which firm growth potential will be positively or negatively influenced by
inflation.
One well known result from monetary economic growth theory goes back
to James Tobin (1965). Tobin's point of possible non-neutral inflationary effects,
working through changes in capital intensity and interest rates, remains as a
7
corner stone finding in modern growth theory. In the literature this non-neutra
lity result has been termed the Tobin effect. As will be discussed below, increases
in capital intensity at the macro-level are analogous at the micro level to decreases
in the sales to asset ratio - e.g., the required investment in new assets necessary
to support a given increase in sales volume will increase. While this would be
expected, ceteris paribus, to decrease firm growth potential, the so-called Tobin
effect may have a secondary impact on the profit rate by lowering real interest
expense. This, on the other hand, would have a positive influence on firm growth.
Thus, the net effect of inflation on growth is open to debate in the macroecono
mic literature.
The original work on the so-called sustainable growth problem in the finance
literature was put forth by Higgins (1977). In the absence of taxes, the firm's
sustainable growth is determined by additions to retained earnings (via undistri
buted profits) and the resultant allowable increase in debt to finance asset expan
sion and sales. Assuming a positive investment in net working capital and con
stant proportional relationships between sales to assets and profits to sales (both
of these factors, explicitly addressed in the growth literature, are assumed exo
genous in the sustainable growth formulation), Higgins (1977, 1981, 1984)
concludes inflation will reduce sustainable growth. The rational here is that in
creases in working capital must be financed regardless of whether the cause is
real or inflationary growth: to the extent that funds are diverted from invest
ment in productive (fixed) assets, inflation will hinder growth except in the
unusual situation where net working capital balances are negative. This intui
tively pleasing line of reasoning, however, is at odds with the findings of John
son (1981). Here, using the sustainable growth model, it is demonstrated that
inflation can increase firm growth even if working capital balances are positive.
Thus we observe conflicting evidence concerning the impact of inflation in
both the finance and economic growth literature. Furthermore, in economic
growth theory working balances and financial policies of the firm pay no role
while in the sustainable growth literature the effects of inflation on capital
intensity and profit are ignored. This ambiguity has resulted, perhaps not sur
prisingly, in many researchers simply assuming inflation has a neutral impact.
This view can be found in Donaldson (1983, 1985), Ellsworth (1983), Fmhan
(1984), Clark et. al. (1985), Harrington and Wilson (1983) among others.
In what follows below we will formulate a theoretical model designed to
identify and cumulatively assess the various effects briefly described above.
The method used will be to enhance the basic sustainable growth model to
include inflation effects on capital intensity and profitability. We will show
that by introducing the so-called Tobin-effects into the sustainable growth mo
del we are able to clarify the complex influences of inflation by separating and
identifying the different forces that operate on a firm's growth opportunities.
8
In the next section, we will develop the base model and identify the working
capital impact of inflation, which we refer to as the Higgins-effect, on firm
growth. Here we will also discuss the contrary results of Johnson and show
the dependence of such findings on a misspecification involving the choice of
a price deflator. In Section 3, the potential inflationary impact on profit rates
and capital intensity (which we refer to below as Tobin-effect 1 and Tobin
effect 2, respectively) is introduced. In the next section we consolidate and iso
late these 3 effects and define the sustainable growth equation. The following
section will focus on analyzing conditions under which we could expect the
positive effect to be outweighed by the negative and vice versa. We close our
analysis by discussing possible extensions and caveats and drawing some broad
conclusions.
2. Micro Inflationary Considerations
Based on the sustainable growth formulations developed by Blakley et al.
(1987), a set of difference equations will now be developed which capture the
dynamic relationship between the firm's balance sheet and income statement.
After specification of the equations, which reflect the assumptions and identities
inherent in standard sustainable growth formulations, a reduced form equation
will be derived which defmes the level of sales in a given time period. The real
rate of sales growth resulting from the solution of the reduced form equation
will then be calculated.
Assuming a constant capital structure with a long-run debt to equity ratio
of A, long-term liabilites in time t can be written as
(1)
where E is total equity at time t. Without issuing new equity any increase in
t
equity will be determined by the rate of increase in the firm's undistributed
profit. Defining 6 as the profit retention rate (Le., I-dividend payout ratio),
equity can be defined as
(2)
where lIt is total profit in time t. Assuming no taxes and a constant profit margin
on sales, total profit in time t is
(3)
where S t is total sales at time t and 1T is the profit margin.
Continuing with Higgin's assumptions that depreciation is sufficient to main
tain the replacement value of existing assets and that increases in real sales are
a constant proportion, (), of the increase in nominal assets, we can specify
9
and solving for St produces
St = e (ALTt -ALTt_,) + (1 +j)St_1 (4)
where j is the assumed constant, uniform and anticipated rate of inflation and
AL T t is the firm's net investment in long-term (i.e., productive) assets. (Note
the change in real sales has been defined using the current period as the base).
By further assuming current assets and current liabilities will have a constant
proportional relationship to nominal sales, we can write net working capital
in time t as
(5)
where </J is the assumed constant proportional relationship between working
capital and sales.
Lastly it is necessary to specify the balance sheet identities. Long-term assets,
A L T t' are the difference between total assets, AT t' and net working capital,
Wet' or
(6)
Further, total assets, AT t' are the sum of long-term liabilities and equity, or
(7)
We can now derive the reduced form difference equation for sales as a func
e,
tion of previous sales and parameters j, A, 0, 1r, and </J as (see Appendix 1).
l+e</J+j
S = . S
1-e{O+A)01r-</J}
t t-I
We solve this by using standard techniques to get (8).
(8)
where So is initial period sales.
The real sales growth can be defined as
1 +g*N
g* = - 1;
1 + j
where
lO
