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On productivity control in credit institutions
Engineering and Pwxess Economics, 4 (1979) 77-81 0 Elsevier Scientific Publishing Company, Amsterdam
77
~ Printed inTheNetherlands
ON PRODUCTIVITY CONTROL IN CREDIT INSTITUTIONS Maria Grazia De Angelis and Francesco Salvatore IliaAurelia, 424, Romn, Italy The
knowledge OF the factors that
the
productivity
for
the
deci.sions’
of
can
influence
directly
or
indirectly
a credit institution has a considerable Importance makers especially in order to decide the optimal
solution of management problems. This paper describes a methodology for a systematic approach to the problem of the business control. Particularly it is shown an operational model representing the business behaviour of a credit institution. This model allows an immediate evaluation of the productivity of a credit institution by some indexes drawn from the normal system of banking book-keeping. 1. INTRODUCTION Among various problems of management, the problem concerning the full utilization of productive factors,hence the maximisatian of their productivity, has always been a question o.ffundamental importance. Up to now such purpose has been attained by common sense and intuition of the managers; today the major costs of factors used and the consequent reduction of profit require a management policy characterized by a less subjectivity than in the past. Although an optimal solution of management problems has stimulated in almost all productive sectors the creation and use of quantitative methodologies, especially in the credit sector, the techiniques in use are absolete. The principals causes of apaty which has led to the particular delay in this field are the relatively modest competition within the banks and the very highy levels of profits which existed in the past as the result of remarkable difference between active and passive rates. The changed operative situation whereby the levels of interest which can no longer be controlled by credit institutions,the increase in management costs which are not completely absorbed in commissions and growth of financial intermediarieswhich reveal new methods of saving to the public, etc. have drawn the attention of credit insitutions to the control and optimisation of the factors of productivity. Tllisarticle, being a contribution to the
problem concerns the maximisation of productivity and after some references to different methods used for the quantification of bank productivity,willshow a mathematical model which should sufficiently represent the management situation in question. 2. ANALYTICAL DESCRIFTION OF PRODUCTION In order to optimise an economic system it is useful to outline the dynamics by which its most important elements are characterized. Generically we can state for a general productive condition the ratio of the quantity of the output (or product) Q obtained by means of quantity xi (i= 1,2,.. ..,n) of productive factors Xi: (2.1)
bi = Q/xi
(i = 1,2,...,n)
this represents the average yield of the output with respect to the factor in question, while its reciprocal: (2.2) l/hi =
Ci
=
Xi/Q
represents the average quantity of factor Xi employed for each product. On the other hand, if we consider, using the factor Xi, a variation from the quantity x'i to the quantity x'li,in the same period, the resulting product goes from Q' to the level Q" : then the effects connected with the variation of the product and/or with the investment of the productive factors can be examined with the following ratio:
78
(2.3)
di = (XT - x;)/(Qll- Q*) =
Xi/
z?
Q
this ratio similar to the ratio defined in (2.2) states an average variation of the productive factor Xi with respect to each unit of change of Q. The ratio: (2.4) exi = ((x~-x~)/x~)/((Q"-Q')/Q') = =
(
xi/x:)/( Q/Q’)
represent a measure of the sensitivity of a productive factor with respect to the produced quantity. That is to say this shows the degree by which a phenomenon reacts to changes of a productive factor. Seem suitable to note that the information which we obtain by previously defined index can be considered valid only in terms of preliminary approximation. In fact the quantity Q of the product is the resultant of all the productive factors which intervene in the productive process; therefore only the appreciation of the system regarding the correlative contribution of all the intervening factors can indicate with precision the most convenient investment of the productive factor Xi. The following functional relation express analytically the fact that Q is dependent on the quantities Xi (i = 1,2,...,n) of the factors of production: (2.5)
Q = F(X,,
X,,.....v$,)
Q is a function of the factors Xi and can be called the "production function". Giving Q a determined value, we obtain the following equation: (2.6)
q =
F(xl, x2>....., xn)
in the variables x. (i = 1. 2,..., n) whose solution depend onithe degree and on type of conditional interdipendencewhich occur during the productive process, namely on the fact, that such conditions are often complementary or at least, within certain limits, interchangeable. The interdipendenceof productive factors
becomes evident if we consider the factor X as a function of the production q and of Zmaining (n-l) factors; in this case we obtain the following equation: (2.7)
ts=g(x
1
,..,x
s-l
,x
s+1'
l.>+,
(1)
which, as a consequence of (2.2), can also be expressed in the following way: (2.8) cs=f(c,,..,cs_,,cs+,,.*cn, 1) and for s,=l, equations.
2,...,n,
we
obtain a system of
3. DETERMINING A CREDIT INSTITUTION'S PRODUCTION As we have seen, the indexes used for the examination of business productivity require the measurement of the quantities wherein they appear. If such necessity in productive activities of the industrial type does not show particular difficulties,regarding credit institutions the calculus of the final product constitutes one of the main problems in economic research and banking technique. Such measurement, being relevant for cost analysis and for proceeds of other results of bank management, becomes difficult due to the diversified business acttivities of bank itself as well as to close interrelations of individual activities or functions. In other areas, for instance in trasportation or manufacturing businesses, it is easy to identify units of measure: the number of persons transported in relation to the total kilometers traveled or the number of manufactured gloves, shoes, etc. For a bank we could use as a parameter the number of the book-keeping entrees or the average of the accounts treated for several type of banking operations during a unit of time. However the number of entries (as well as the number of the accounts) does not take into account the varying importance of the individual operations. Thus the entries of very large amounts or very small amounts are of equal weight. The principal defect of such method is the impossibilityof y$elding a global measure
79
of bank production. We do not want to add together non-homogeneous quantities concerning the measurement of the different types of bank operations. ?!Rnyeconomists (l), (2). (1), (4) affirm the necessity of employing a measurement in monetary units, whenever it is impossible to attain a measurement of physical units of output. Generally references to the physical units of production is difficult for institutions which represent a diversified production. In these cases it is necessary to evaluate the total products and services offered to the market by the institution. It seems evident that in this way we can make a mistake as it is difficult to distinguish the efficiency of the productive business services from the processes related to the determination of the selling prices of the outputs. In spite of such difficulties,severalmetho ds have been proposed for the quantification of the output where bank activities are concerned. Each of these methods present advantages and disadvantages,but are more or less apt to satisfy the given purposes de pending both on the bank activity in question and on the importance of the various bank functions. One of ttesimplestmethods proposed for the measurement of the product of bank activities is to consider the total resources of credit institutions.The relationship between the productive factors used and the total resources constitutes one of the methods used the main part of our analysis. However such methods easily lead to erroneo us results, since the resources composed of means and collected means (deposits), constitutes more of an indicator of bank poten tiality than an appropriate measurement of production. In fact it seems obvious that the transformation into products (loans and investiments) of raw material (resources) and the capacity of effecting a considerable volume of transformationsconstitutes a rather reliable index of bank efficiency. On this basis we can assume the sum of loans and of effected investments as a measure of bank production. Nevertheless, we have to state three inconvenienceswhen using the above method: 1) one does not take into consideration all
the so-called secondary services which the bank offers to its clients and which represent the main bank activities: 2) one uses the total of these activities which ,?ssumesa "level" to measure the pro ductive process includtnq a concent of "flux"; 3) one does not sufficiently consider the diversified importance, in order to determine the business income, of the active items of bank balance. In order to obviate such inconvenience it is proposed that a weighted index be adopted from the various active items of bank profit according to their relative importance. However, such method presents some difficulties in choosing proper weighting. Some prope the adoption of the interest rate used by the bank for the different types of operations; but others reveal the fact that the interest rate does not express the financial return of the operation because it is a function of competition and the different degree of managing efficiency. Another obviation,whichusually is made regaf ding the index in question, is the fact that resulting interest rates are influenced by inflation. For this reason it is necessary to cause a deflation with a fixed price of the weighted indexes. The method which at least partly allows the elimination of the inconveniencesmentioned would be based on the extension to credit institutionsof the added value method used in other business activities. By calculating the added value, in fact, we can consider both the returns derived from typical credit operations and returns derived from so-called secondary operations. The output is then measured by the size of "flux". This is, expressed by the difference between income and expenditure concerning the productive activity of the period in question plus the difference between the final and the initial remainders. As far as cost analysis is concerned we can say that the added value per unit of the productive factor used is a unit of measurement far more significant than the unit which results from the relationship of "loans and investments" or 'resources". 4. MODEL FOR AN ANALYSIS OF THE PRODUCTIVITY
80
a.
prodActivity
b. a)
productivity point the ;>rodrctivity margin CXI be defined as a contri3Jtion margin expressed as a per-
margin
centage of the invested using the symho?s given VP = VA/L? hence fies der
r value
added/invested
a productivity
margin
of
Thus 1 : lic+uidity 20% si.gni-
that each 100 lire employed will re: 20 lire which can pay the management
and structural b)
liquidity. in table
costs
some profit. the productivity among the 1 ante
point three
as well
as to
obtain
is a point of bafollowing elements:
the amount of management and structural the productivity margin of invested costs, and the third element beying liqujdity, the amount of the liquidjty to be invested for covertng management costs. Meanwhile, returning to ( 1) we can see that the protudt’vity point is given by: PECS/VP= management and structural Costs invested
liquidity/value
added
X
81
Table
1
Elementary
variables
and aggregates
concerning
LC
Stock in hand: Rai - initial
assets
Raf - final assets Rpi - initial
liabilities
LI in hand
=
P
First costs of credit Work cost
operation
=
liouidity
=
cs
production
costs =
Gw + Ow
Management
and structural
costs =
=Gx+Ox+W+K VA
Gw - variables
Added value or contribution
margin
=
= LC + H - LI - CP - Zm
Gx - fixed Other organization OW-
Invested
CD Direct
of credit
G
liquidity
= P + Sp + Rpf + Rpi
operations
0
Created
= V + Sa + Raf + Rai
in hand
in hand
First profits
V
indicators
AGGREGATES
VARIABLES R
proposed
AC
costs
Current
activity
=
= F + Raf
variables AI
ox - fixed W
Various
and general
Z
Reserve
funds
Zg - quiescience
Invested
capital
EA
Interests,
provisions
active commissions
and ritirement
=
= F + Raf + B - Rpf
expenses
and
=
=Ia+Ia+Ia+Sa
funds Zm - amortization
office machines
Commissions
s
Sa - assets SP - Liabilities Other profits
H
Other costs
K B
Long term bank investiments
F D
Monetary Number
reserve
of employes
Dw - variables Dx - fixed Ia
Active
interests
Ia-
c/c credits
Ia-
bill portafolio
Ia-
stock portafolio
Ia-
advanced
For further
money,
on
contago,
information
etc
on the meaning
of same aggregetes
please refer
to Appendix
B.
82
The amount of
the
calculated
this
in
operating way,
point . In fact, if the are under the critical loss,
vice-versa
We want the
of
the
influence that
points
a pratical is
use
limited
of
to a
point of
the
index
ciency is following
compounded indi caters:
of
of the factor itself, calculated to case in a different way.
from case
One of the most simple proposal
is to relate
the average
such
a way
constitute a credit measure
organization
by the
effi-
product
of
the
an index
of
organization
of its production.
have an inefficiency,
enterprise, bank
to
cover
For VA>CS
we can begin
the management
The index
of
including
the indicator
productivity
the behaviour
we
is
not
costs. efficient.
efficiency,
activity
is the transformation
products
(loans and investment)
also
institutions cor-
margin with
generally
and major management
mean more
the
of work productivity
as a
in the bank
sector: amount of loans and investments/ of
employees
But this indicator has also its difficulties. It is the total movement of values, the interloocking, the succession of the costs and revenues average
of the period
credit
and not the
amount of loans and investements the work requirement
of a
institution.
Recapitulating could propose
the items of section the following
3. we
index of work
productivity:
index
With the work productivity
index we wish to
evaluate the productivity of each member operating within the institution. Index which express the efficiency of the work factor in credit institution are often and are continuosly
average number of employees/ contribution margin
and
values.
considered
of raw
of loans and
structural costs; therefore elevated movements must also to be cause of larger added
ii. work productivity
into
index has often been proposed
that determine
VP, emphasize
of the contribution
"movements"
it
proportionate
the "eleved" movements investements. personnel
call
of those credit
which do not mantain respondance
is CCS then
to
characterizing
average number
as production
sufficient
It seem obvious,
that the element
VA/L1
margin
of
and this goes for any producing
average
EO=T'.T"-((VA/CS)-1)
indicator
than an appropriate
material resources. On the grounds of such observation
efficiency:
Elevated
more a potentiality institution
following
contribution
of
They are
of the past and for a
measure
the
number
management.
T”=VP=VA/LI
If
with the averaqe
However, this method can easly give erroneous results because the administrative resources
T'=(L?-F'P)/PP:(VA/CS)-1
In fact we define
amount of administrative
employees
among branch-house.
Therefore
data cor-
and the volume
in order
useful, however, for a study management of a branch-house in time
a certain
them vaiid
consider
to make an analysis
in
between
with the efficiency,
resources
Too many variables
critical
we cannot
comparison
relationship related
invested liquidity point we have a
that
past.
the
(PP) a critical
a profit.
to emphaize
two critical
study
costs
becomes
calculated
(3). The gaeral principle for the construction of such indexes,consists of establishing a
Iiowever, if this indicator is used for a comparison in time and space, we could criti_ size the fact that a different qualitative composition of the productive units generating more or less work costs, will not change the index. In order to eliminate can add the following
such difficulties correction:
we
(average number of employees/ contribution margin) (work
costs/average
number of
employees)=
83
= work costs/contribution Utilising
the symbols
margin
of table 0.1 we can
write:
Dividing
thereafter
and the relative or variable
the number
components
of the employees
costs (in this connection B), we obtain
of empoyees
costs of either the fixed
a better
to read Appendix
specification
the index become more sensitive variations
and
to all We can obtain
of the fixed and variable
Utilizing
the representative
2nd
prices
+(Zg/D)+(D/VA) iii. capital
The index of organization
efficiency
to verify
typical of a
credit
if the activity
institution
manegement judging
the ability managing
them. The analysis capital
rates.
committed
to
trying
to obtain
for the attainment
itself and within
of the wole business
system.
of credit activity
(considered
to the invoice volume
industrial
enterprises),
the factor
compare
invested
level of the income rate of
capital
it is advisable
it into three significant a)Index
of credit
b)Index
of current
c)Index
of patrimonial
It is obvious
to divide
activity activity
jncome: rotation
property
in order to obtain
and with the contribut:on
VA/LC LC/AC
ration.
AC/AI
represents
that the income of the
of
it can be useful to
it both the total current
employed
from the development
ralationship:
of
Since the created liquidity is a typical expression of incomes derived from the equivalent
"capital".
of a
the constraints
common instrument utilized by the "top" management to measure the productivity of For a certain
of the
the capacity
result with a minimum1 investement
development
the most simple and
of analysis
judging
functions
of factor necessary the result
of the ecorosical
of income rate of the invested
represents
indexes means
certain
costs but without
the capital
above
the business
is apt to cover the
and structural
operators
helps
rates
ties possible; - or operating with high sales income rates To judge the efficiency
index
turnover
to the higer sales qu&ntita-
and very low turnover
productivity
sales in-
of applinq 1o.w
with elevated
in relation (Dw/VA)+(Gx,/Dx) (Dx,/VA)+
incone rates by:
with reduced
come as a consequence
symbol we
write: EL=CL/VA=(Gw/Dw)
satisfactory
- either operatinq
aspects of work factor.
The turnover
margin
of typical
rate of current
the business
activities
such quantity derived bank ope-
activities
capacity
of self
financig.
invested capital does not depend only on the relationship between selling price and total
In fact, quicker loans and investments turn into liquidity, the less heavy will be the
management activities sales.
problem
costs but also on the volume involved, that is to say on
The first two relation the following
of
emphs size separately
two facts:
first,
the income
rate of credit activity expresses the margin of "added value" and is therefore the real relationship between selling price and operating costs: second, the rotation rate
of temporal
dissolution
between
in-
come and expenditure, or better, the higer will be the amount of financial resources necessary to provide for the managing needs in relation to the payement series which anticipate the flow of correlated proceeds. Therefore we have better dynamics and consequently less financial costs compared to other conditions.
84
the
Consirierinq to note
current
of
the
total
branch-hnl>?e, and
index
the
component fixed
second
that
w;th
;i larger
a better
icteresfjng relevant
investmagt
ofcerS,
capital.
is
prof:t,
of
req?ect
a
to
of
rontrnl
in
acrellw-
tiw
turnover
of
tl-r
EN1 E A,k T= ( L(a,/I.I >+ { l*a,/L I ) -C( la/r.
This of
of
the
k;md,
express profit
at
jnstitutior
the
inrlcx
the
degree
the
disposal
mltir the
iti.
the
consideration
fol1owjr.o
of
of
the
tution.
the us to
for
5 of productivitv “rapi tall’:
index
flcqrae
the development o!- a credit
as an in-
urge
indicators
productivitv
incidefice
a credit
to
an;llvsi factor
the
derived fro% typ?c;il activities
i.mmobil:‘tv of
dex of flexibility in relation pocsibl? production. pore
T ) +
oF patrimonial of
and can be considered
Thp foreqning
i ) + ( fe3/1.,
7 j
incorres
the most
in:ti
otkrr
(
represrnts
v*ri ous
propertv
i:F!,/I
tot;??
investmen”.
On the
of
the
crder :A(
to
level
the
TP~~~T)PI~~Y :r.m m*rnir.
~os+ibi~i+v
which ‘rav have deterw
pro-
a sisSe-
cor.cerninq
1 i r~u
invested
i tv
The liouid
asset’.
stitution
could
ed productive productive institution: the
“r.a?ure” of
factor
“expenditures” of
economic
compared provisions
by a credit into
in-
so-call is power
(that
tke soil machinery) of the being a typical expression of
necessary
development This
‘nvested
be assim.ilated
credit
for
the
activit.{.
quantity
can usefully
assets. Therefore institution
realizes
by managing
the typical have been
such
liquid
derived
from
credits
derived derived derived
frorr from from
bills on hand; securities: active anticipations
research
into
the
the value
interpretation adviszble var?ations
of to of
the
identifv the
output the
cause
indic<3tnrs.
Meanwi1.p the input variables have be--n . agqregated into elementary indexes eti;tch one with a precise operational significance; the
propnsed
T, -EO-( (LT-PP)/PP)
model
is
the
following:
(VA/J,I)
Ip=EC=(VA/LC)(LC/AC)((F/AI)+(Raf/AI))
Tq=EN=(?a/LI)+(?a/LI)+(?a/LI)+(14a,~LI)+
in c/c;
cant ingenci es, etc ; 5 - active procisions and commissions. the systematic analysis That being stated, of the productivity index of invested the
is
= (D/VA)
2 - income 3 - income 4 - income
(and
of
it
T,-EL-(Gw/Dw)(Dw/VA)+(Gx/Dxj(Dx/VA)+(Zg/D)
income of a credit suhvided in five
classes: 1 - income
liquidities
e,~.si e-
infact,
he
with the complexity of interests, and active commissions which the
institution
To maitr the
cause
=+( Sa/LT) Althoug the model seem very simple, to advan_ tage of its rapid implementation, the result obtained by its correct use is most helpful. From a point of wiew of possible results, the model is considered both representative
and
prcdirtive.
- comparative
evaluation,
dicators
of
the
stitutions during Ye can consider the its -
use
cover
qlobd,l of
model
the
in;nif
followinq
cases: means of variations
hy
given
to
(vari.ations
businesses
on the
the time. model as oredict;ve
evaluation,
a value
based
same or more credit
input
variables
similar
tc
of
the
alternat:ve
politics);
sme modalities in order
to
as in
estimate
our
either
the
same credit
of
the
foregoinn
ro;nt,
t‘he business
more rredit
institutions
inst;tution
in
( a+dm+.b)/f;
be:*avi or
sqare
tempnrar/
intervals.
each with the
calculated
‘devi at ion 02 and the :nput VAT: able can be foilowinq tjro Eormulas:
6. S”OCt\STIC ‘WLEPENTATION OF TH% F!O!ZI.. However , the model presented, in spjte of
6,
its
Ve = (b - a) /6
easv
results certain ables.
construction only
if
it
and use is
levels assumed Suc:h deficiency
when such
model
with
in relati.on
global
Tn a predictive
by the input is especiallv
varivisible
is used as a predictTon model.
assume
the
input
deterministic
variables
values
but,
based on an expert manaqer’s knowledqe of the hehaviour of a single variable, the variables assume rather a series of values each possible of a certain verification, b!ore precisely, each input variable can be considered
as a random variable
distribuited
according to its probability function. In our context, a solution to this problem is given by the stocsstic implementation of the
model
of
business
operative point can be realised distribution which, tively
for
behaviour.
From an
of Mew this implementation by fixing a probabjli.ty each
according (2.4) high values.
of
the
, supply
a)/6
with
generator. do not
(b -
=
input
variables
us with
rela-
To help the managers in estimating the values m, a and b we suggest supplyng them annually
with
lated
to
the most
the
ables
of
the model.
statistical
support
significant
input
revari-
CONCLUSrON The purpose
of
deterministic indexes, the insti.tuti.on. It
is
this
paper
is
to
propose
model that represent, business behaviour of
obvious
that
a such
model
a
by some a credit
could
help
the managers in the choice of the optimal management policy, In fact with the proposed that
model
mentary wale
is
a variation
possible of
variables
system
to
evalue
one or more of
considered
?nd at occourrence
leads
the the
variables, to
is
pointed out distribution
the probabilistic
After
this
proposed field.
to make
extension
that estiming of the input model
ele-
on the
quickly recours to instruments apt to or to hinder the development of such tendencGkes. Furthmore probability
effect
can
favour
the
be extended
and by means of
86
simulation utilized with
techniques to
put
respect
to
the
model. can
in order each
the
input
branch
variable
be
general
offices
subscri
consider
- d+rect oroductivjtv
ed.
the
profit
normal
for
their
movements
the
which
have
hand operations of
Is or could tion
Rianchi
“debit which
the
accounts
;
(CD),
period.
In
of
costs
for
reason
of
service
number
of
employees
As suggested
which
equili-
of bank management. At the same time financial and patrimonial equilibrium included.
costs
evidence
their
the
significance
4-n paragraph relationship
economical
of
so-
4 we shall here with the portions
account
reported
to
with
in appen-
di.x A.
as operation
costs
-- mana3_ement __.-- and costs
can be defined
generally
represent
between
for the persons
hi-person counters one of can be defined as fixed.
TotalJrofit _-_.-. __,-_. By this term. we intend
to
Specified
Final
reserve
(F),
read
change
after
an acquisition
therefore
the
different
during often
the both
the
occurs
and fixed
costs,
the will
financial
use,
cyclic
cessory expenses, machines, the installation and maintenance,as well as various
sum of
(R). the entity
the
initial to
of
and the
the
employed to
are can
an alienation, likely
to
not
between
represents case,
phenomenes
final
value,
due where being
same period,
are
scarcely
the
total
average
the
name
period
semi-annual, of
the
total
activities”
be
period
average
in nearly
character
two
balances
administratjve that
acti-
we intend
to
quarterly
or
activity. we define
the
quantity:
AC = F + Raf
we may consider costs (CS),all property and ac-
is
values
referred
refer
or
profit
and final
real the
total
“current
the following items: - management and structural costs regarding immovable
the
active
of deposits and credits variation. The fixed profits
to
and it
the
money,
subject
values
variable
define
(Raf) and Durable bank investment DurinS the administrative period
By term an analytic period bookkeeping a precise distinction between
supervisory executive:
-
monthly
volu
inter-
for large departments, besides the manager as a fixed cost an exerus, we CN? define t;ve for each principal. function;
do not
the
up to
correspond
mainly
in
of
in particuand structural
mainly
and those
When we
a variation
(6)
should
which
vities
durina
a minimal
the managers
representative.
change
opera-
department.
Chib
a direct dependance on the volume: on the other hand, we can define as management and structural costs those operation costs which me. In default of which permits
a fixed
the
-
to
which
level
a limit
initial
srect productivjma ----structural --_ _. costs _.._ The direct productivity
in each
as management
include
functions
of
me aggregates
to
and control,
by Arturo
- we can define
fica-
contribute
economic
according
concer-
lar:
bil
so-called
part
is ir;to
tjons of the different departments of a branch-hose. The bank organisation exceeds, for
mediate
examples
a clnssi
the
and a variable
identifi-
disconted
on the
factors
AS far as the costs of personnel ned, we till; subdivide the costs
on bills-on-
Yore
(5)suoqested
main weight
of
nor the such ope-
the of
maturity.
aSI those
APPEliDTX ---^..._-_.B In order to
the
permit value
determination
also
explain
re-
movements” and unspeci fi erl credits, permits putting into onl~.~ one contable
prospect brium their
the
deposit
gained
do not
the nomind
with
economical chLaracter.
the period, distinguished
profjts
their averaqe be added.
Tnncredi
to
the
indi cations
administrative
the
same way the
cation
forming
in
to
the mean cons!stency
dur:nq
during
contained
according
schematic
neither
operations
dates qeneral
onlv
acl:redited
illuminates
rations
that account
wd~ of
due to
such
out give
a possible
The interest
of
costs
articles, printed matter, elecenergy. telephone, postaqe, etc;
tric??
and loss
schemes
sults
are
puhhli ci ty,
statjonwrv
APPENT)TXA ---__ We want to point
to
expenses (purchasing, ( transport, etc.)
oti on
while
identify
the
term the
“invested
capital”
quantity:
AI = F + Raf
+ B + Rpf
intends
to
87
A number
of economists
contest
les in use for a correct the economical careful
quantity
of
8. For a further
study on the subject
rio Coda (81 and David
the princip-
determination
consult Vitto-
Calorrons (71).
BTBITOSRAPHY --------_ 1. Onida P., 1961. Econcmicita.
socialita
nell'amninistrazionr de' dottori
ed efficienza
d'impresa.
commercialisti,
Rivista
Gennaio-Feb-
braio. 2. De Luca H., 1955. Produttivita sul piano aziendale piano dell'economia
e sul
Annali
nazionale.
della Facolta di economia e commercio dell'TJniversit2 di Catania 3. Pagan0 S., 1955. Aspetti econoaico-tecnici vita d'impresa, 4. Dell'Amnre
della produtti
Pisa, pp. 20-60
G., 1971.
La banca: sparmio.
Cursi,
azienda
di produzione.
11 ri-
Gennaio.
5. Bianchi T. Costi, ricavi e prezzi delle banche di deposito. Giuffre Editore, pp. l-27, p". 181-197 6. Gli4 A., 1976. I1 costo unitario delle operazioni e la previsione di redditivita de1 servizio bancario.
Notizie
7. Coda V., Brunetti 1974. Indici di bilancio
Ipacri,
G., Bergamin
Lavoro Wet,
M. B.,
e flussi finanziari-
strumenti per l'analisi Etas lihri, pp. 1-79 9. Masini
Aprile-Maggio
della gestione.
C., 1976. e Risparmio
- eccnomia
di azienda,
pp. 483-468
10. Mackara
W. F., 1975.
What do banks produce?
Monthlv
review,
May 11. Salomons
D., 1965
Divisional control,
performance, Irwin, pp. l-54
mesurement
and
77
~ Printed inTheNetherlands
ON PRODUCTIVITY CONTROL IN CREDIT INSTITUTIONS Maria Grazia De Angelis and Francesco Salvatore IliaAurelia, 424, Romn, Italy The
knowledge OF the factors that
the
productivity
for
the
deci.sions’
of
can
influence
directly
or
indirectly
a credit institution has a considerable Importance makers especially in order to decide the optimal
solution of management problems. This paper describes a methodology for a systematic approach to the problem of the business control. Particularly it is shown an operational model representing the business behaviour of a credit institution. This model allows an immediate evaluation of the productivity of a credit institution by some indexes drawn from the normal system of banking book-keeping. 1. INTRODUCTION Among various problems of management, the problem concerning the full utilization of productive factors,hence the maximisatian of their productivity, has always been a question o.ffundamental importance. Up to now such purpose has been attained by common sense and intuition of the managers; today the major costs of factors used and the consequent reduction of profit require a management policy characterized by a less subjectivity than in the past. Although an optimal solution of management problems has stimulated in almost all productive sectors the creation and use of quantitative methodologies, especially in the credit sector, the techiniques in use are absolete. The principals causes of apaty which has led to the particular delay in this field are the relatively modest competition within the banks and the very highy levels of profits which existed in the past as the result of remarkable difference between active and passive rates. The changed operative situation whereby the levels of interest which can no longer be controlled by credit institutions,the increase in management costs which are not completely absorbed in commissions and growth of financial intermediarieswhich reveal new methods of saving to the public, etc. have drawn the attention of credit insitutions to the control and optimisation of the factors of productivity. Tllisarticle, being a contribution to the
problem concerns the maximisation of productivity and after some references to different methods used for the quantification of bank productivity,willshow a mathematical model which should sufficiently represent the management situation in question. 2. ANALYTICAL DESCRIFTION OF PRODUCTION In order to optimise an economic system it is useful to outline the dynamics by which its most important elements are characterized. Generically we can state for a general productive condition the ratio of the quantity of the output (or product) Q obtained by means of quantity xi (i= 1,2,.. ..,n) of productive factors Xi: (2.1)
bi = Q/xi
(i = 1,2,...,n)
this represents the average yield of the output with respect to the factor in question, while its reciprocal: (2.2) l/hi =
Ci
=
Xi/Q
represents the average quantity of factor Xi employed for each product. On the other hand, if we consider, using the factor Xi, a variation from the quantity x'i to the quantity x'li,in the same period, the resulting product goes from Q' to the level Q" : then the effects connected with the variation of the product and/or with the investment of the productive factors can be examined with the following ratio:
78
(2.3)
di = (XT - x;)/(Qll- Q*) =
Xi/
z?
Q
this ratio similar to the ratio defined in (2.2) states an average variation of the productive factor Xi with respect to each unit of change of Q. The ratio: (2.4) exi = ((x~-x~)/x~)/((Q"-Q')/Q') = =
(
xi/x:)/( Q/Q’)
represent a measure of the sensitivity of a productive factor with respect to the produced quantity. That is to say this shows the degree by which a phenomenon reacts to changes of a productive factor. Seem suitable to note that the information which we obtain by previously defined index can be considered valid only in terms of preliminary approximation. In fact the quantity Q of the product is the resultant of all the productive factors which intervene in the productive process; therefore only the appreciation of the system regarding the correlative contribution of all the intervening factors can indicate with precision the most convenient investment of the productive factor Xi. The following functional relation express analytically the fact that Q is dependent on the quantities Xi (i = 1,2,...,n) of the factors of production: (2.5)
Q = F(X,,
X,,.....v$,)
Q is a function of the factors Xi and can be called the "production function". Giving Q a determined value, we obtain the following equation: (2.6)
q =
F(xl, x2>....., xn)
in the variables x. (i = 1. 2,..., n) whose solution depend onithe degree and on type of conditional interdipendencewhich occur during the productive process, namely on the fact, that such conditions are often complementary or at least, within certain limits, interchangeable. The interdipendenceof productive factors
becomes evident if we consider the factor X as a function of the production q and of Zmaining (n-l) factors; in this case we obtain the following equation: (2.7)
ts=g(x
1
,..,x
s-l
,x
s+1'
l.>+,
(1)
which, as a consequence of (2.2), can also be expressed in the following way: (2.8) cs=f(c,,..,cs_,,cs+,,.*cn, 1) and for s,=l, equations.
2,...,n,
we
obtain a system of
3. DETERMINING A CREDIT INSTITUTION'S PRODUCTION As we have seen, the indexes used for the examination of business productivity require the measurement of the quantities wherein they appear. If such necessity in productive activities of the industrial type does not show particular difficulties,regarding credit institutions the calculus of the final product constitutes one of the main problems in economic research and banking technique. Such measurement, being relevant for cost analysis and for proceeds of other results of bank management, becomes difficult due to the diversified business acttivities of bank itself as well as to close interrelations of individual activities or functions. In other areas, for instance in trasportation or manufacturing businesses, it is easy to identify units of measure: the number of persons transported in relation to the total kilometers traveled or the number of manufactured gloves, shoes, etc. For a bank we could use as a parameter the number of the book-keeping entrees or the average of the accounts treated for several type of banking operations during a unit of time. However the number of entries (as well as the number of the accounts) does not take into account the varying importance of the individual operations. Thus the entries of very large amounts or very small amounts are of equal weight. The principal defect of such method is the impossibilityof y$elding a global measure
79
of bank production. We do not want to add together non-homogeneous quantities concerning the measurement of the different types of bank operations. ?!Rnyeconomists (l), (2). (1), (4) affirm the necessity of employing a measurement in monetary units, whenever it is impossible to attain a measurement of physical units of output. Generally references to the physical units of production is difficult for institutions which represent a diversified production. In these cases it is necessary to evaluate the total products and services offered to the market by the institution. It seems evident that in this way we can make a mistake as it is difficult to distinguish the efficiency of the productive business services from the processes related to the determination of the selling prices of the outputs. In spite of such difficulties,severalmetho ds have been proposed for the quantification of the output where bank activities are concerned. Each of these methods present advantages and disadvantages,but are more or less apt to satisfy the given purposes de pending both on the bank activity in question and on the importance of the various bank functions. One of ttesimplestmethods proposed for the measurement of the product of bank activities is to consider the total resources of credit institutions.The relationship between the productive factors used and the total resources constitutes one of the methods used the main part of our analysis. However such methods easily lead to erroneo us results, since the resources composed of means and collected means (deposits), constitutes more of an indicator of bank poten tiality than an appropriate measurement of production. In fact it seems obvious that the transformation into products (loans and investiments) of raw material (resources) and the capacity of effecting a considerable volume of transformationsconstitutes a rather reliable index of bank efficiency. On this basis we can assume the sum of loans and of effected investments as a measure of bank production. Nevertheless, we have to state three inconvenienceswhen using the above method: 1) one does not take into consideration all
the so-called secondary services which the bank offers to its clients and which represent the main bank activities: 2) one uses the total of these activities which ,?ssumesa "level" to measure the pro ductive process includtnq a concent of "flux"; 3) one does not sufficiently consider the diversified importance, in order to determine the business income, of the active items of bank balance. In order to obviate such inconvenience it is proposed that a weighted index be adopted from the various active items of bank profit according to their relative importance. However, such method presents some difficulties in choosing proper weighting. Some prope the adoption of the interest rate used by the bank for the different types of operations; but others reveal the fact that the interest rate does not express the financial return of the operation because it is a function of competition and the different degree of managing efficiency. Another obviation,whichusually is made regaf ding the index in question, is the fact that resulting interest rates are influenced by inflation. For this reason it is necessary to cause a deflation with a fixed price of the weighted indexes. The method which at least partly allows the elimination of the inconveniencesmentioned would be based on the extension to credit institutionsof the added value method used in other business activities. By calculating the added value, in fact, we can consider both the returns derived from typical credit operations and returns derived from so-called secondary operations. The output is then measured by the size of "flux". This is, expressed by the difference between income and expenditure concerning the productive activity of the period in question plus the difference between the final and the initial remainders. As far as cost analysis is concerned we can say that the added value per unit of the productive factor used is a unit of measurement far more significant than the unit which results from the relationship of "loans and investments" or 'resources". 4. MODEL FOR AN ANALYSIS OF THE PRODUCTIVITY
80
a.
prodActivity
b. a)
productivity point the ;>rodrctivity margin CXI be defined as a contri3Jtion margin expressed as a per-
margin
centage of the invested using the symho?s given VP = VA/L? hence fies der
r value
added/invested
a productivity
margin
of
Thus 1 : lic+uidity 20% si.gni-
that each 100 lire employed will re: 20 lire which can pay the management
and structural b)
liquidity. in table
costs
some profit. the productivity among the 1 ante
point three
as well
as to
obtain
is a point of bafollowing elements:
the amount of management and structural the productivity margin of invested costs, and the third element beying liqujdity, the amount of the liquidjty to be invested for covertng management costs. Meanwhile, returning to ( 1) we can see that the protudt’vity point is given by: PECS/VP= management and structural Costs invested
liquidity/value
added
X
81
Table
1
Elementary
variables
and aggregates
concerning
LC
Stock in hand: Rai - initial
assets
Raf - final assets Rpi - initial
liabilities
LI in hand
=
P
First costs of credit Work cost
operation
=
liouidity
=
cs
production
costs =
Gw + Ow
Management
and structural
costs =
=Gx+Ox+W+K VA
Gw - variables
Added value or contribution
margin
=
= LC + H - LI - CP - Zm
Gx - fixed Other organization OW-
Invested
CD Direct
of credit
G
liquidity
= P + Sp + Rpf + Rpi
operations
0
Created
= V + Sa + Raf + Rai
in hand
in hand
First profits
V
indicators
AGGREGATES
VARIABLES R
proposed
AC
costs
Current
activity
=
= F + Raf
variables AI
ox - fixed W
Various
and general
Z
Reserve
funds
Zg - quiescience
Invested
capital
EA
Interests,
provisions
active commissions
and ritirement
=
= F + Raf + B - Rpf
expenses
and
=
=Ia+Ia+Ia+Sa
funds Zm - amortization
office machines
Commissions
s
Sa - assets SP - Liabilities Other profits
H
Other costs
K B
Long term bank investiments
F D
Monetary Number
reserve
of employes
Dw - variables Dx - fixed Ia
Active
interests
Ia-
c/c credits
Ia-
bill portafolio
Ia-
stock portafolio
Ia-
advanced
For further
money,
on
contago,
information
etc
on the meaning
of same aggregetes
please refer
to Appendix
B.
82
The amount of
the
calculated
this
in
operating way,
point . In fact, if the are under the critical loss,
vice-versa
We want the
of
the
influence that
points
a pratical is
use
limited
of
to a
point of
the
index
ciency is following
compounded indi caters:
of
of the factor itself, calculated to case in a different way.
from case
One of the most simple proposal
is to relate
the average
such
a way
constitute a credit measure
organization
by the
effi-
product
of
the
an index
of
organization
of its production.
have an inefficiency,
enterprise, bank
to
cover
For VA>CS
we can begin
the management
The index
of
including
the indicator
productivity
the behaviour
we
is
not
costs. efficient.
efficiency,
activity
is the transformation
products
(loans and investment)
also
institutions cor-
margin with
generally
and major management
mean more
the
of work productivity
as a
in the bank
sector: amount of loans and investments/ of
employees
But this indicator has also its difficulties. It is the total movement of values, the interloocking, the succession of the costs and revenues average
of the period
credit
and not the
amount of loans and investements the work requirement
of a
institution.
Recapitulating could propose
the items of section the following
3. we
index of work
productivity:
index
With the work productivity
index we wish to
evaluate the productivity of each member operating within the institution. Index which express the efficiency of the work factor in credit institution are often and are continuosly
average number of employees/ contribution margin
and
values.
considered
of raw
of loans and
structural costs; therefore elevated movements must also to be cause of larger added
ii. work productivity
into
index has often been proposed
that determine
VP, emphasize
of the contribution
"movements"
it
proportionate
the "eleved" movements investements. personnel
call
of those credit
which do not mantain respondance
is CCS then
to
characterizing
average number
as production
sufficient
It seem obvious,
that the element
VA/L1
margin
of
and this goes for any producing
average
EO=T'.T"-((VA/CS)-1)
indicator
than an appropriate
material resources. On the grounds of such observation
efficiency:
Elevated
more a potentiality institution
following
contribution
of
They are
of the past and for a
measure
the
number
management.
T”=VP=VA/LI
If
with the averaqe
However, this method can easly give erroneous results because the administrative resources
T'=(L?-F'P)/PP:(VA/CS)-1
In fact we define
amount of administrative
employees
among branch-house.
Therefore
data cor-
and the volume
in order
useful, however, for a study management of a branch-house in time
a certain
them vaiid
consider
to make an analysis
in
between
with the efficiency,
resources
Too many variables
critical
we cannot
comparison
relationship related
invested liquidity point we have a
that
past.
the
(PP) a critical
a profit.
to emphaize
two critical
study
costs
becomes
calculated
(3). The gaeral principle for the construction of such indexes,consists of establishing a
Iiowever, if this indicator is used for a comparison in time and space, we could criti_ size the fact that a different qualitative composition of the productive units generating more or less work costs, will not change the index. In order to eliminate can add the following
such difficulties correction:
we
(average number of employees/ contribution margin) (work
costs/average
number of
employees)=
83
= work costs/contribution Utilising
the symbols
margin
of table 0.1 we can
write:
Dividing
thereafter
and the relative or variable
the number
components
of the employees
costs (in this connection B), we obtain
of empoyees
costs of either the fixed
a better
to read Appendix
specification
the index become more sensitive variations
and
to all We can obtain
of the fixed and variable
Utilizing
the representative
2nd
prices
+(Zg/D)+(D/VA) iii. capital
The index of organization
efficiency
to verify
typical of a
credit
if the activity
institution
manegement judging
the ability managing
them. The analysis capital
rates.
committed
to
trying
to obtain
for the attainment
itself and within
of the wole business
system.
of credit activity
(considered
to the invoice volume
industrial
enterprises),
the factor
compare
invested
level of the income rate of
capital
it is advisable
it into three significant a)Index
of credit
b)Index
of current
c)Index
of patrimonial
It is obvious
to divide
activity activity
jncome: rotation
property
in order to obtain
and with the contribut:on
VA/LC LC/AC
ration.
AC/AI
represents
that the income of the
of
it can be useful to
it both the total current
employed
from the development
ralationship:
of
Since the created liquidity is a typical expression of incomes derived from the equivalent
"capital".
of a
the constraints
common instrument utilized by the "top" management to measure the productivity of For a certain
of the
the capacity
result with a minimum1 investement
development
the most simple and
of analysis
judging
functions
of factor necessary the result
of the ecorosical
of income rate of the invested
represents
indexes means
certain
costs but without
the capital
above
the business
is apt to cover the
and structural
operators
helps
rates
ties possible; - or operating with high sales income rates To judge the efficiency
index
turnover
to the higer sales qu&ntita-
and very low turnover
productivity
sales in-
of applinq 1o.w
with elevated
in relation (Dw/VA)+(Gx,/Dx) (Dx,/VA)+
incone rates by:
with reduced
come as a consequence
symbol we
write: EL=CL/VA=(Gw/Dw)
satisfactory
- either operatinq
aspects of work factor.
The turnover
margin
of typical
rate of current
the business
activities
such quantity derived bank ope-
activities
capacity
of self
financig.
invested capital does not depend only on the relationship between selling price and total
In fact, quicker loans and investments turn into liquidity, the less heavy will be the
management activities sales.
problem
costs but also on the volume involved, that is to say on
The first two relation the following
of
emphs size separately
two facts:
first,
the income
rate of credit activity expresses the margin of "added value" and is therefore the real relationship between selling price and operating costs: second, the rotation rate
of temporal
dissolution
between
in-
come and expenditure, or better, the higer will be the amount of financial resources necessary to provide for the managing needs in relation to the payement series which anticipate the flow of correlated proceeds. Therefore we have better dynamics and consequently less financial costs compared to other conditions.
84
the
Consirierinq to note
current
of
the
total
branch-hnl>?e, and
index
the
component fixed
second
that
w;th
;i larger
a better
icteresfjng relevant
investmagt
ofcerS,
capital.
is
prof:t,
of
req?ect
a
to
of
rontrnl
in
acrellw-
tiw
turnover
of
tl-r
EN1 E A,k T= ( L(a,/I.I >+ { l*a,/L I ) -C( la/r.
This of
of
the
k;md,
express profit
at
jnstitutior
the
inrlcx
the
degree
the
disposal
mltir the
iti.
the
consideration
fol1owjr.o
of
of
the
tution.
the us to
for
5 of productivitv “rapi tall’:
index
flcqrae
the development o!- a credit
as an in-
urge
indicators
productivitv
incidefice
a credit
to
an;llvsi factor
the
derived fro% typ?c;il activities
i.mmobil:‘tv of
dex of flexibility in relation pocsibl? production. pore
T ) +
oF patrimonial of
and can be considered
Thp foreqning
i ) + ( fe3/1.,
7 j
incorres
the most
in:ti
otkrr
(
represrnts
v*ri ous
propertv
i:F!,/I
tot;??
investmen”.
On the
of
the
crder :A(
to
level
the
TP~~~T)PI~~Y :r.m m*rnir.
~os+ibi~i+v
which ‘rav have deterw
pro-
a sisSe-
cor.cerninq
1 i r~u
invested
i tv
The liouid
asset’.
stitution
could
ed productive productive institution: the
“r.a?ure” of
factor
“expenditures” of
economic
compared provisions
by a credit into
in-
so-call is power
(that
tke soil machinery) of the being a typical expression of
necessary
development This
‘nvested
be assim.ilated
credit
for
the
activit.{.
quantity
can usefully
assets. Therefore institution
realizes
by managing
the typical have been
such
liquid
derived
from
credits
derived derived derived
frorr from from
bills on hand; securities: active anticipations
research
into
the
the value
interpretation adviszble var?ations
of to of
the
identifv the
output the
cause
indic<3tnrs.
Meanwi1.p the input variables have be--n . agqregated into elementary indexes eti;tch one with a precise operational significance; the
propnsed
T, -EO-( (LT-PP)/PP)
model
is
the
following:
(VA/J,I)
Ip=EC=(VA/LC)(LC/AC)((F/AI)+(Raf/AI))
Tq=EN=(?a/LI)+(?a/LI)+(?a/LI)+(14a,~LI)+
in c/c;
cant ingenci es, etc ; 5 - active procisions and commissions. the systematic analysis That being stated, of the productivity index of invested the
is
= (D/VA)
2 - income 3 - income 4 - income
(and
of
it
T,-EL-(Gw/Dw)(Dw/VA)+(Gx/Dxj(Dx/VA)+(Zg/D)
income of a credit suhvided in five
classes: 1 - income
liquidities
e,~.si e-
infact,
he
with the complexity of interests, and active commissions which the
institution
To maitr the
cause
=+( Sa/LT) Althoug the model seem very simple, to advan_ tage of its rapid implementation, the result obtained by its correct use is most helpful. From a point of wiew of possible results, the model is considered both representative
and
prcdirtive.
- comparative
evaluation,
dicators
of
the
stitutions during Ye can consider the its -
use
cover
qlobd,l of
model
the
in;nif
followinq
cases: means of variations
hy
given
to
(vari.ations
businesses
on the
the time. model as oredict;ve
evaluation,
a value
based
same or more credit
input
variables
similar
tc
of
the
alternat:ve
politics);
sme modalities in order
to
as in
estimate
our
either
the
same credit
of
the
foregoinn
ro;nt,
t‘he business
more rredit
institutions
inst;tution
in
( a+dm+.b)/f;
be:*avi or
sqare
tempnrar/
intervals.
each with the
calculated
‘devi at ion 02 and the :nput VAT: able can be foilowinq tjro Eormulas:
6. S”OCt\STIC ‘WLEPENTATION OF TH% F!O!ZI.. However , the model presented, in spjte of
6,
its
Ve = (b - a) /6
easv
results certain ables.
construction only
if
it
and use is
levels assumed Suc:h deficiency
when such
model
with
in relati.on
global
Tn a predictive
by the input is especiallv
varivisible
is used as a predictTon model.
assume
the
input
deterministic
variables
values
but,
based on an expert manaqer’s knowledqe of the hehaviour of a single variable, the variables assume rather a series of values each possible of a certain verification, b!ore precisely, each input variable can be considered
as a random variable
distribuited
according to its probability function. In our context, a solution to this problem is given by the stocsstic implementation of the
model
of
business
operative point can be realised distribution which, tively
for
behaviour.
From an
of Mew this implementation by fixing a probabjli.ty each
according (2.4) high values.
of
the
, supply
a)/6
with
generator. do not
(b -
=
input
variables
us with
rela-
To help the managers in estimating the values m, a and b we suggest supplyng them annually
with
lated
to
the most
the
ables
of
the model.
statistical
support
significant
input
revari-
CONCLUSrON The purpose
of
deterministic indexes, the insti.tuti.on. It
is
this
paper
is
to
propose
model that represent, business behaviour of
obvious
that
a such
model
a
by some a credit
could
help
the managers in the choice of the optimal management policy, In fact with the proposed that
model
mentary wale
is
a variation
possible of
variables
system
to
evalue
one or more of
considered
?nd at occourrence
leads
the the
variables, to
is
pointed out distribution
the probabilistic
After
this
proposed field.
to make
extension
that estiming of the input model
ele-
on the
quickly recours to instruments apt to or to hinder the development of such tendencGkes. Furthmore probability
effect
can
favour
the
be extended
and by means of
86
simulation utilized with
techniques to
put
respect
to
the
model. can
in order each
the
input
branch
variable
be
general
offices
subscri
consider
- d+rect oroductivjtv
ed.
the
profit
normal
for
their
movements
the
which
have
hand operations of
Is or could tion
Rianchi
“debit which
the
accounts
;
(CD),
period.
In
of
costs
for
reason
of
service
number
of
employees
As suggested
which
equili-
of bank management. At the same time financial and patrimonial equilibrium included.
costs
evidence
their
the
significance
4-n paragraph relationship
economical
of
so-
4 we shall here with the portions
account
reported
to
with
in appen-
di.x A.
as operation
costs
-- mana3_ement __.-- and costs
can be defined
generally
represent
between
for the persons
hi-person counters one of can be defined as fixed.
TotalJrofit _-_.-. __,-_. By this term. we intend
to
Specified
Final
reserve
(F),
read
change
after
an acquisition
therefore
the
different
during often
the both
the
occurs
and fixed
costs,
the will
financial
use,
cyclic
cessory expenses, machines, the installation and maintenance,as well as various
sum of
(R). the entity
the
initial to
of
and the
the
employed to
are can
an alienation, likely
to
not
between
represents case,
phenomenes
final
value,
due where being
same period,
are
scarcely
the
total
average
the
name
period
semi-annual, of
the
total
activities”
be
period
average
in nearly
character
two
balances
administratjve that
acti-
we intend
to
quarterly
or
activity. we define
the
quantity:
AC = F + Raf
we may consider costs (CS),all property and ac-
is
values
referred
refer
or
profit
and final
real the
total
“current
the following items: - management and structural costs regarding immovable
the
active
of deposits and credits variation. The fixed profits
to
and it
the
money,
subject
values
variable
define
(Raf) and Durable bank investment DurinS the administrative period
By term an analytic period bookkeeping a precise distinction between
supervisory executive:
-
monthly
volu
inter-
for large departments, besides the manager as a fixed cost an exerus, we CN? define t;ve for each principal. function;
do not
the
up to
correspond
mainly
in
of
in particuand structural
mainly
and those
When we
a variation
(6)
should
which
vities
durina
a minimal
the managers
representative.
change
opera-
department.
Chib
a direct dependance on the volume: on the other hand, we can define as management and structural costs those operation costs which me. In default of which permits
a fixed
the
-
to
which
level
a limit
initial
srect productivjma ----structural --_ _. costs _.._ The direct productivity
in each
as management
include
functions
of
me aggregates
to
and control,
by Arturo
- we can define
fica-
contribute
economic
according
concer-
lar:
bil
so-called
part
is ir;to
tjons of the different departments of a branch-hose. The bank organisation exceeds, for
mediate
examples
a clnssi
the
and a variable
identifi-
disconted
on the
factors
AS far as the costs of personnel ned, we till; subdivide the costs
on bills-on-
Yore
(5)suoqested
main weight
of
nor the such ope-
the of
maturity.
aSI those
APPEliDTX ---^..._-_.B In order to
the
permit value
determination
also
explain
re-
movements” and unspeci fi erl credits, permits putting into onl~.~ one contable
prospect brium their
the
deposit
gained
do not
the nomind
with
economical chLaracter.
the period, distinguished
profjts
their averaqe be added.
Tnncredi
to
the
indi cations
administrative
the
same way the
cation
forming
in
to
the mean cons!stency
dur:nq
during
contained
according
schematic
neither
operations
dates qeneral
onlv
acl:redited
illuminates
rations
that account
wd~ of
due to
such
out give
a possible
The interest
of
costs
articles, printed matter, elecenergy. telephone, postaqe, etc;
tric??
and loss
schemes
sults
are
puhhli ci ty,
statjonwrv
APPENT)TXA ---__ We want to point
to
expenses (purchasing, ( transport, etc.)
oti on
while
identify
the
term the
“invested
capital”
quantity:
AI = F + Raf
+ B + Rpf
intends
to
87
A number
of economists
contest
les in use for a correct the economical careful
quantity
of
8. For a further
study on the subject
rio Coda (81 and David
the princip-
determination
consult Vitto-
Calorrons (71).
BTBITOSRAPHY --------_ 1. Onida P., 1961. Econcmicita.
socialita
nell'amninistrazionr de' dottori
ed efficienza
d'impresa.
commercialisti,
Rivista
Gennaio-Feb-
braio. 2. De Luca H., 1955. Produttivita sul piano aziendale piano dell'economia
e sul
Annali
nazionale.
della Facolta di economia e commercio dell'TJniversit2 di Catania 3. Pagan0 S., 1955. Aspetti econoaico-tecnici vita d'impresa, 4. Dell'Amnre
della produtti
Pisa, pp. 20-60
G., 1971.
La banca: sparmio.
Cursi,
azienda
di produzione.
11 ri-
Gennaio.
5. Bianchi T. Costi, ricavi e prezzi delle banche di deposito. Giuffre Editore, pp. l-27, p". 181-197 6. Gli4 A., 1976. I1 costo unitario delle operazioni e la previsione di redditivita de1 servizio bancario.
Notizie
7. Coda V., Brunetti 1974. Indici di bilancio
Ipacri,
G., Bergamin
Lavoro Wet,
M. B.,
e flussi finanziari-
strumenti per l'analisi Etas lihri, pp. 1-79 9. Masini
Aprile-Maggio
della gestione.
C., 1976. e Risparmio
- eccnomia
di azienda,
pp. 483-468
10. Mackara
W. F., 1975.
What do banks produce?
Monthlv
review,
May 11. Salomons
D., 1965
Divisional control,
performance, Irwin, pp. l-54
mesurement
and