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Table of Contents
Dynamics of depreciation and scrapping in
business economics’
Prof. Dr. Dr. Rainer Schwarz
Department Management, Management Accounting and Control Systems
Dipl.-Betriebswirt (FH) Peter Maybaum
Systems Engineer at the Department Management, Management Accounting and
Control Systems
Brandenburg University of Technology Cottbus
Faculty Mechanical Engineering, Electrical Engineering and Economical Engineering
PO-Box 10 13 44
03013 Cottbus / Germany
phone +49 355 / 69 2389
fax + 49 355 / 69 3324
e-mail: rasz@tu-cottbus.de
e-mail: maybaum@tu-cottbus.de
URL: http://www.wiwi.tu-cottbus.de/controlling/
Abstract
With the aim to bring in SD deeper into management education we compare the
concepts of depreciation and scrappage used in the literature of SD on one side and
business economics on the other. We demonstrate that the business economics concepts
of straight-line depreciation and of sudden scrappage can be formulated within the SD
methodology and software. The economic results are better in line with the textbooks of
business economics than those given by the current SD equations. As a result we
recommend using a pipeline delay instead of a third-order delay for modelling
scrappage. The concepts of straight-line depreciation and sudden scrappage are then
combined with the concepts of aging chains and co-flow in the framework of a simple
model of a firm. The simulation results are in line with fundamental expectations of
business economics. This will be the basis for our further work on a generic model of a
firm which could meet both the didactical challenges of management education and the
sophistication of modern System Dynamics.
' The authors wish so thank an anonymous referee for useful comments.
1. Introduction
One of the greatest goals of the founder of System Dynamics was to improve
management education. Almost 50 years after the expression of this aim only a small
minority of university professors or holders of a chair in Management are members of
the System Dynamics Society or otherwise actively involved in the field. In Germany,
less then 1% of the university professors in business economics are actively engaged in
the field of System Dynamics (SD) and the situation has not improved over the last
decade. We will not investigate the spectrum of reasons for this, but rather stress the
different terminology used in business economics on one side and in System Dynamics
on the other. For example, COYLE (1977, 248) writes that profit equals average income
minus average costs. For a well-known management accountant professor
(HORNGREN 1994, 61) operating profit and operating income are synonymous terms.
Of course even in business economics authors often use different words for the same
notion or concept. This complicates the introduction of SD into management education
even more.
It is one objective of this paper to build bridges between different terminologies. This is
a necessary precondition for our work on interactive learning environments (ILE) for
education in the field of management accounting and control systems. We will focus on
depreciation and scrapping. They are essential for the dynamics of investment and
equipment. At the same time, depreciation is one of the basic cost elements and
therefore an important determiner of profit. We try to understand these dynamics deeper
by using the ceteris paribus approach together with the vintage approach.
The understanding of investment in an asset, its depreciation and scrapping in
management literature can be summarised as stated below. Due to the investment of
some amount of money, a piece of equipment is obtained which has the following
attributes:
- an initial value equal to the price paid for the equipment,
- an economic life time during which the initial value depreciates,
- amaximal output per time unit called the capacity,
- atechnical life time during which the capacity is more or less constant,
- acertain input of labour to produce the output,
- acertain input of material to produce the output.
Therefore, through an investment decision, three main costs of the product are incurred:
depreciation, labour cost and material cost.
Therefore, through an investment decision, three main costs of the product are incurred:
depreciation, labour cost and material cost.
In textbooks and in management education these attributes are usually discussed
separately. The apparatus of co - flows known in SD is not applied. On the other hand,
there are only a few contributions from the SD field that investigate depreciation and
scrapping. Usually unit costs are applied. Through this approach, the value flows by
which they are generated are assumed away. In FORRESTER’s (1961) book and in
ZAHN’s (1971) book, which presents the first complex SD model of a growing firm,
depreciation and scrapping are not mentioned. In screening the papers from the last SD
society conferences, the word combination “capacity expansion” was only found in a
paper by LYNEIS (Quebec 1998) and in one by MOON, KIM and KIM (Wellington
1999), but the authors neither mentioned depreciation or scrapping. In other papers,
these words were sometimes present, but equations were not. In the SD literature, we
found clear statements about depreciation in the works of COYLE (1977), LYNEIS
(1980), STERMAN (1980, 2000), REPENNING and STERMAN (1994), and
SCHOENEBORN (2004). An explicit equation for scrapping is formulated by LYNEIS
(1980). SCHOENEBORN (2001, 2004) also considers scrapping in his models. Last but
not least we found an important contribution to the subject of linear depreciation in the
contribution of DINGETHAL (2004) to this conference. KEENAN and PAICH (2004)
also mention depreciation.
In the next section we compare these concepts with concepts of business economics,
which we express in terms of SD. We demonstrate that the basic business economics’
concept of straight-line depreciation can be captured in a SD equation. Then we
investigate the consequences of the different concepts of depreciation and scrapping on
profit and revenue. We compare the consequences of scrappage modelling by a third-
order delay (after LYNEIS) and by a pipeline delay. Finally, we investigate the
consequences of different time periods for depreciation and scrapping on the dynamics
of profits. In the third section, these results are used to demonstrate how capacity
expansion and the growth of a firm can be better understood within the perspective of
co-flows and vintages. We combine the concepts of straight-line depreciation and
instant scrapping with the vintage concept, which has been promoted in SD literature by
STERMAN (in his new book under the name ‘aging chains’), and with the concept of
co-flows. Finally, we discuss some possibilities for the introduction of our approach
into the generic model of a small firm.
Our intention in this paper is not to formulate a complex model that can be falsified in
an empirical context. We wish to introduce greater clarity about the dynamic properties
of basic management and accounting concepts which should be or are a part of any
management education and a part of business dynamics models that handle investment
and capacity expansion.
2. Depreciation and scrapping in business economics and in System Dynamics
We begin with a description of the business economics’ view on scrapping and
depreciation in the simplest possible way. We abstract from all complex and
sophisticated phenomena or complications and assume moreover that all other things
are equal (ceteris paribus assumption). In this paper we do not aim to completely
survey depreciation methods or phenomena (f.e. current versus historical costs, moral
obsolescence, and governmental regulations in different countries).
In business economics, the following concept for investment in equipment is used as the
normal one.” At a certain time t; the equipment is installed with a capacity of C
2 There can be types of equipment with declining capacity. We do not regard them here.
units/period. With this capacity, this equipment can produce during a period which is
called the technical life time (TL). At the end of this time (at ts =TL+ t)), the equipment
is scrapped and the capacity is zero. This concept can easily be transformed in a SD
picture (fig. 1) using two pulse rates at t; and ts. The equipment is installed at t; = 02
With TL = 10 (years), the equipment is scrapped at ts = 120 (months). An example for
this picture would be a taxi driver who buys a car and starts his business immediately.
After an incident the car is scrapped. Note that C=const over the period TL?
a
©
100-4
50+
capacity_be (prod/month)
O 12 24 36 48 60 72 84 96 108 120 132 144
Figure 1: Investment, capacity, scrapping and technical life time
Whereas in this simplest of cases investment and scrapping occur instantly, depreciation
is a more continuous valuation process. “In most cases, the amount allowable for
depreciation is the original cost of (initial investment in) the asset.”” In the case of the
straight-line depreciation method from this amount I and the computed book values BV
every year, an equal amount of depreciation D is deducted.
BV (t)=BV (t—1) -D,
where
D=I/TU, t= 2(1) TU and BV (1) =I.
TU is the useful life time of the asset or the depreciation period. For the moment, we
assume TU = TL = 10 (years). At the end of the depreciation period the terminal
disposal price should be zero (BV (TU) = 0).
This pulse rate cannot be seen because it overlaps with the ordinate in this figure and the other figures.
We abstract here from cases where the capacity is declining. In practise repairs can secure a constant
capacity or even increase it.
7 “ HORNGREN (1994, 721).
100.000
80.0004
(EUR)
60.000
40.0004
fixed_assets_be
20.000
0 12 24 36 48 60 72 84 96 108 120 132 144
Figure 2: Book value of fixed assets with the straight-line depreciation method
In the case of the double-declining balance (DDB) depreciation method the book value
BV of the previous year is multiplied by the DDB rate (= 2/TU):
BV (t) = BV (t— 1) *2/ TU,
where
t= 2(1) TU and BV (1) =I.
The DDB method never fully depreciates the existing book value. Therefore a firm has
to switch after a few years to the straight-line depreciation method.* In this sense it is
the more general depreciation method and teaching of depreciation in management
courses begins with this method. We simplify our analysis and restrict it to the usage of
the straight-line depreciation method. This is for teaching purposes. Firms prefer the
accelerated depreciation pattern in the first years and then switch to straight-line
depreciation in order to bring the book value to zero as it is demanded by law.
In SD literature depreciation is treated in various ways and different authors use
different equations. For a business economist, depreciation is a “non-cash cost”. In
contrast to this, COYLE (1977, 248) speaks of a depreciation cash flow’? and
formulates the equation:
DCFL.K = DR*WDV.K
with the depreciation fraction DR and the written down value WDV. Neither a technical
life time nor a useful life time nor scrapping is mentioned.
8
DINGETHAL (2004) considers this case.
9
HORNGREN (1994, 723)
'© On page 335 he asserts that depreciation is one source where cash comes from. However on the
diskette to COYLE’s (1996) book we find now the correct statement that depreciation does not involve
money.
LYNEIS (1980, 1988) and STERMAN (1980, 2000) are more explicit about
depreciation.
STERMAN (1980, 21) uses the equations
K.K=K.J + (DT)(KAR.JK-KDR.JK)
KDR.KL = K.K/ALK
with the capital arrival rate KAR (capital units/year), the capital discard rate KDR
(capital units/year)! ' the capital K (units) and the average life of capital ALK (years).
The outflow is a physical flow with the dimension “units”and not a value flow as with
depreciation and it is taken from the actual and declining level. As in the case of the
double-declining balance (DDB) depreciation method, a declining level is divided by a
life time. By multiplication with the price of capital PK ($/capital unit), STERMAN
(1980, 40) also formulates implicitly an equation for the depreciation D which
corresponds to the straight-line depreciation method:
D = PK.K*K.K/ALK
STERMAN (2000, 805) also uses a discard rate but now the capital stock is divided by
the average life of capacity. “Production capacity is the rate of output ...”.
Discard Rate = Capital Stock / Average Life of Capacity.
LYNEIS treats depreciation and scrapping in a more detailed way. He uses the
following equations for depreciation’:
BVFA.K=BVFA.J + (DT)(INVEST.J — DEPR.J)
BVFA=CE*CPUCE
where
BVFA = book value of fixed assets ($)
DT = delta time, simulation solution interval (days)
INVEST = investment ($/day)
DEPR = depreciation ($/day)
CE = capital equipment (units/day)
CPUCE = cost per unit of capital equipment ($/unit/day)
DEPR.K = BVFA.K / TDEPFA®
TDEPFA = 2400
where
DEPR = depreciation ($/day)
BVFA = book value of fixed assets ($)
TDEPFA = time to depreciate fixed assets (days)
The book value of fixed assets is initialized to equal capital equipment CE multiplied by
the price per unit of capital equipment CPUCE. Afterward, the book value is increased
by investment and decreased by depreciation. LYNEIS (1980, 1988, 264) states:
“Equation 117 approximates straight-line depreciation for the company that replaces
In our case the capital arrival rate is assumed to be a pulse and zero afterwards.
~ LYNEIS (1980, 1988, 264, 265)
8 SCHOENEBORN (2004, 94, 101) uses the same approach.
assets as they depreciate”.'* This is an important difference to the business economics
approach, which assumes investment to be a pulse in the beginning and zero afterwards
to get the pure behaviour of depreciation. In real companies, equipment is replaced only
if the life time has ended and if it is scrapped. Moreover, the equation of LYNEIS
computes depreciation from book value BVFA.K that is a declining variable.!°
SCHOENEBORN (2004) uses the same equation, which we will refer from now on as
the SD concept of depreciation. This is similar to the double-declining balance (DDB)
depreciation method. In contrast to this, the straight-line depreciation method gives a
constant amount of depreciation each year and uses only the original cost for
depreciation.
We compute now the resulting book value of fixed assets with this equation. In this
analysis we abstract from any new capital arrivals, i.e. we set STERMAN’s KAR.JK or
LYNEIS INVEST.J to zero in all subsequent time periods. We are interested only in the
effect of this depreciation concept on the book value of just one original investment. We
use an understanding that is known also as the net present value (NPV) concept in
business economics. NPV calculates for just one investment the sum of a single cash
outflow and the discounted cash inflows in all subsequent years. Figure 3 shows the
results of the SD concept of depreciation for the book value of fixed assets.
100.0004
80.0004
(EUR)
60.0004
40.0004
fixed_assets_sd
20.000
T ; T T
0 12 24 36 48 60 72 84 96 108 120 132 144
Figure 3: Book value of fixed assets with the SD concept of depreciation '°
Figure 4 shows the small models built in POWERSIM which were the basis for the
previous figures. In order to get an equal amount of depreciation using POWERSIM for
every period, we had to change the usual equation for straight-line depreciation. We
divide the book value by the remaining depreciation period.
'’ We have seen before that business economics has a different understanding of straight-line
depreciation.
'S STERMAN follows the same concept when computing the capital discard rate KDR in non-monetary
units.
‘© According to LYNEIS, STERMAN and SCHOENEBORN.
Model and equations in business dynamics
Model and equations based on SD-
literature
fixed_assets_bfpreciation_be
economic_life
ixed_assets_sgepreciation_sd
economic_life
init fixed_as' be = 100000
flow fixed_; be = -dt*depreciation_be
unit fixed_: be = EUR
aux depreciation_be = IF( fixed_assets_be>0,
fixed_assets_be / (economic_life - TIME) , 0 )
unit depreciatior EUR/month
const economic _|
unit economic _|
init
flow
unit Li
aux depreciation_sd =
fixed_assets_sd/economic_life
unit depreciatiot = EUR/month
const economic _lif
unit economic _life
fixed_assets_sd = 100000
Figure 4: Model structures in POWERSIM for the calculation of depreciation
The equations for scrappage are formulated by LYNEIS (1980, 1988, 327) as follows:
CES.KL = DELAY3] (CEA.JK, TSCE, CE.K, CEI)
TSCE = 2400
CEI = CCOR * (1 + CEGM)
where
CES = capital equipment scrappage (units/day/day)
DELAY3I = third-order delay with user-specified initial value
CEA = capital equipment arrivals (units/day/day)
TSCE = time to scrap capital equipment (days)
CE = capital equipment (units/day)
CEI = capital equipment, initial (units/day)
CCOR = constant customer order rate (units/day)
CEGM = capital equipment growth margin (dimensionless)
This approach means that in every period capacity is scrapped. Figure 5 shows the
results of a simulation with POWERSIM.
180,
150+
capacity_sd (products/month)
0 12 24 36 48 60 72 84 96 108
Figure 5: Scrapping on the basis of a third-order delay
120 132 144
At the end of this section we will compare scrapping on the basis of a third-order delay
and a pipeline delay in more detail. The simulation results for both approaches in terms
of revenue and profit are shown in the following figures 6 and 7.
15.0005 4-1
€ 10.000}
§
E
a
=|
w
5.0004
2
2S a
o
12-121 2-12- 12
—4—Tevenue_be
-y— Profit_be
0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 18
month
Figure 6: Revenue and profit based on the scrapping concept of business economics
15.000},
Ss
Ny
10.0004 tN
,
g ow
2 —
2 5.000] —
= aed ie ee _,_ revenue_sd
z ae 1 41
|
z ~ Profit_sd
of mw,
>
aes
-6.0004 225
2~p,
0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180
month
Figure 7: Revenue and profit with scrapping on the base of a third-order delay
Up to this point we assumed that TL = TU. This seems to be also the general
assumption in SD literature. In practical life we observe that TL can be much longer
than TU. Equipment is used for production even if it is fully depreciated and its book
value is zero. We assume now that TL is longer than TU and equals 15 years.
Depreciation is zero beginning with the month 120. By using such a policy after TU =
10 (years) the profit grows by 22%. In figure 8 this behaviour is compared to the profit
development according to the third-order delay equations of LYNEIS (in the lower
curve).
1
2425111 ait
2.5004 2
2.
a
Fs 4 Sy, 11111
5 \
= aN _,— profit_be
« -2.5004 Ds 1
u 2. 2 Profit_sd
2
-5.000} aN
ar)
a
-7.5004
0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180
month
Figure 8: Profit behaviour with a pipeline delay and usage of written off equipment
(upper curve) and with a third-order delay (lower curve)
Finally we compare the consequences of a pipeline delay and a third-order delay on
capacity in more depth. Every two years the equipment is scrapped and renewed. Here
scrappage and renewal have duration of | month each. After each period new capacity
is ordered which is equal to a changed product demand. For both cases (pipeline delay
and third-order delay) equipment with the same capacity is ordered. In the case of a
pipeline delay the capacity equals always the demand. In the case of the modelling with
a third-order delay capacity is scrapped continuously. Therefore the capacity does not
meet the demand in the first period (hence less revenue and profit). Then we have
overcapacity in the beginning of the second period and not enough capacity in the
second half of that period. Figure 10 is a zoomed part of figure 9. In our opinion, it
seems better to model scrappage with a pipeline delay.
115
104
Hl ~capacity_ppl
products/month
al —o~ capacity_inf
i) 12 24 36 48 60 72 84 96 108 120 132 144
Figure 9: Consequences of a pipeline delay and a third-order delay on capacity
11
_ ~~ capacity_ppl
al ~~ capacity_inf
products/month
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48
month
Figure 10: Consequences of a pipeline delay and a third-order delay on capacity (detail)
3. Capacity expansion in a vintage perspective
After having analysed the concept of pure depreciation of an initial piece of capital
equipment we now turn to capacity expansion again in the simplest possible way. This
means we now introduce investment in new equipment during the lifetime of the old
one. LYNEIS (1980, 1988, 265) already saw the possibility of a more detailed model
with “individual asset levels for each different age category of fixed assets”. This is
exactly what bookkeeping in a normal company does register. But up to now we find in
companies no mathematical models of these dynamics. Vintage models have been
developed within macroeconomic literature.'’ Some authors in System Dynamics
literature have adopted that approach.'* The interest in vintage models for firms was
only recently refreshed by STERMAN (2000) and supported by the possibilities of
software packages like POWERSIM® and VENSIM°. STERMAN now uses a different
terminology. He speaks of aging chains. At the same time System Dynamics has
developed the modern concept of co-flows.'? Based on both concepts we formulate a
model the structure of which is described in figure 11. This model was constructed only
for management education purposes and does not claim broader empirical relevance.
The equations are noted in Appendix A. We use the following assumptions:
- The firm already exists and has a small capacity in the at the start.
- The policy of the firm requires minimisation of order backlog. This means that the
firm invests in new capital equipment if the capacity reaches its upper limit.
- Every vintage of capital equipment is connected with a certain capacity, a given
price or book value and a given amount of personnel to operate the equipment.
- The orders grow as linear functions.
- New equipment is immediately available, there are no delivery times.
- When a vintage of equipment is scrapped its capacity will be replaced by new
equipment. Non-essential members of the workforce leave the firm.
- One machine needs one worker and produces one product per hour (velocity of the
machine).
- The capacity results from this velocity and the available working time.
- The available working time is 173 hours per month.
- New personnel is immediately available
- Personnel costs grow in one year by 2 %.
- Maintenance times grow with the age of the equipment.
- Material is delivered just in time.
- One unit of material is needed for one product.
Each vintage of machines (respective equipment) is characterised by a certain book
value, a given capacity and a given number of workers to operate the equipment. It is
connected with a co-flow of these attributes. In general, there is also a certain amount of
material input to the machine which can be modelled as a co-flow. In this paper we
abstract from this attribute and model it as an input of material needed for one product.
We use in the model | array for every month in order to register the aging of vintages.
‘7 STERMAN (1980) gives a short survey.
'8 STERMAN (1980), MATTHES und SCHWARZ (1982), MATTHES und SCHWARZ (1983),
KOZIOLEK, MATTHES und SCHWARZ (1988).
"See again STERMAN (2000).
With TL = 10 (years) we have 120 arrays for capacity and workforce each. The
depreciation period TU is 5 years. So we have 60 arrays for the book value of fixed
assets.
The simulation with this model gives a behaviour which a business economist is
familiar with (figure 12). We assume that the already existing firm has a certain
capacity in the first two years. Then the demand reaches the limit of the capacity and the
firm invests in equipment. This brings an immediate increase in capacity. The same
happens in the years 2011 and 2018. The upper curve has some jumps because we
assume there are some smaller repairs during the lifetime of the equipment. The lower
curve shows the assumed linear growth of demand (orders) and the resulting growth of
the production output.
period order backlog sales
Oo.
chance customers
orders
‘average order
regular customers wag or
time for average revenue labor costs
order backlog .
repair costs
investment aasets
expansion
‘material costs
total depreciation
sitet eet)
repbscement J” ps acaets total deprecation
cajoaly nat
ees
purchase value of mela Banke workers for new
machine
ew machine
naman
startup machines 7
=—— [Lmenes
expansion
hourly wage rate
repair
total capacty of
machines,
capacity new
pectine replacement
4 mater pce metal requked pee
C7 rater costs
roduction
Z
hiring
finished inventory sales
worker per machine
nanberotworkes
working time
production capacity
workers for new
machine
labor costs
expansion average order
backlog
hourly wages
wage rise
Figure 11: System Dynamics model of an aging chain of equipment connected with co-
flows for every vintage.
= production capacity
production
= orders
0
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023
Figure 12: Growth of demand and the resulting expansion of capacity and output
The next figure 13 depicts important economic results. Assuming a constant product
price we get linear growth of sales. The cost of material is a unit cost per product and
grows, therefore, in a linear way too. Because of the discrete investments, we have
jumps in the workforce which are needed for the operation of new equipment. This is
accompanied by jumps in the labour costs and to the same effect the profit declines in
these years. The book value of the equipment is decreased by straight-line depreciation
and increased by investments into new vintages of equipment (figure 14).
EUR/mo
60,000 -
50,000 ,
40,000, -
ye — = profit
30,000 en st — material costs
labor costs
20,000
10,000
‘2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023,
Figure 13: Behaviour of important economic variables
EUR/mo
200,000
150,000
100,000
total book value
50,000 \ |
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023
Figure 14: Book value of equipment
4. Discussion and proposals for further work
We have seen that basic concepts of business economics, especially depreciation and
scrapping can be expressed in small SD models. This can help to introduce the SD
methodology into management courses. Here it is appropriate to use the terms and
concepts of basic business economics textbooks within SD models. The paper
demonstrated this for the straight-line depreciation method. It is the basic depreciation
method in two senses. First, teaching in management accounting usually starts with this
method. Secondly, it is more general than the DDB method which cannot depreciate the
existing book value fully. Therefore a firm must always switch to the straight-line
depreciation method.”° Unlike this usage in business economics, depreciation equations
similar to the DDB method are preferred in SD literature. This reflects the well-known
observation that most firms use accelerated depreciation (DBB) in the beginning. One
should at least add the SD view on the straight-line depreciation method which we
propose in this paper in SD models for management education.
Whereas depreciation diminishes the value of equipment over the whole depreciation
period (the useful life time TU) scrapping affects the equipment only at the end of its
technical life time (TL). It destroys (or sells) the equipment and brings the capacity
almost instantly to zero. A good example for this is a blast furnace which is destroyed.
Scrapping is rarely mentioned in SD literature. In the few cases which handle scrapping,
it is modelled with a third-order delay. This has the effect of continuous scrapping
which begins shortly after the installation of new equipment. Any buyer of a new car
would eventually find that this is complete economic nonsense. Besides this we find
with a third-order delay a remaining capacity even at the end of the technical life time.
This concept resembles accelerated (DDB) depreciation and it leads to a missing
capacity even before the end of the technical lifetime (and despite continuous repairs).
20 See also DINGETHAL (2004).
16
In the equations of STERMAN and LYNEIS (in section 2 above) this permanent
scrapping is compensated with permanent investment into new equipment.?! This
approach does not correspond to the business economics understanding of scrapping
and we cannot recommend it for management education. In contrast to a third-order
delay, the application of a pipeline delay mirrors the understanding of business
economics completely. The contrast between both delays can be seen in their
consequences to revenue and profit.
In business economics and in SD literature it is often assumed that the depreciation
period TU and the technical lifetime of equipment are identical or equal. Business
practise knows otherwise. Sometimes equipment is scrapped even if it is not written off
and in some cases it is advisable not to scrap equipment even if it is written off. The
latter policy brings an immediate jump in the profit because the capacity is used and
depreciation does not diminish the profit anymore. Under our assumptions this effect
leads to a profit growth by 22%.
The concepts of straight-line depreciation and pulse-like scrapping also allow a
convenient combination of the vintage concept (or aging chains) and the concept of co-
flows. Both concepts are well known in the SD community but rarely used in
management courses. Capacity expansion and the bookkeeping of equipment are fields
where vintage thinking is common to business economics. Here one can open a door to
bring more SD into management education. In section 3 we formulated a simple model
which combines all the four concepts mentioned: straight-line depreciation, pulse-like
scrapping, aging chains and co-flows. The simulation with this model gives a behaviour
which a business economist is familiar with. Therefore it seems to be suited for
adoption in management teaching or in high schools with a specialization in business
economics. It also could be a module in an interactive learning environment (ILE) for
courses in management or management accounting and control.
However we regard the model effort in this paper only as a starting point. The
combination of the four concepts should be elaborated in greater detail. With concern
for high school and management education we see the need for an interactive learning
environment. A necessary step in that direction would be the introduction of the basic
concepts outlined in this paper into a generic model of a firm. This model should depict
the main concepts and causal loops that are taught in business economics, but usually
without the SD approach. Our further work will combine the results of this paper with
the generic model of SCHONEBORN and SCHWARZ (2002).
2! See also SCHWARZ and MAYBAUM (2000) for a detailed analysis of LYNEIS’ model.
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