Cost estimating
in sawmilling
industries:
FAO
FORESTRY
PAPER
52/1
guidelines
FOOD
AND
AGRICULTURE
. ORGANIZATION
THE
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1984
Rome, 1984
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©FAO
FAO 1984
1984
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iii
PREFACE
This paper
paper deals
managerial decisions on profitability
This
deals with managerial
profitability assessments in
in sawmills.
sawmills.
target group
group is
is primarily
sawmill managers
and large
large companies
companies in
in
The target
primarily sawmill
managers in
in medium-sized
mediumsized and
different developing
developing countries.
countries.
Costing is
is a difficult field
field of
of study.
study. Even
introductory textbooks consist
consist of
of many
Even introductory
hundreds of
of pages.
pages. This paper explains the very core of managerial
managerial models for
for costing
and
assessments.
and profitability assessments.
These
valid for
for all
all kinds
kinds of
of companies.
companies. The
between
These models are valid
The main difference between
this booklet
booklet and
and an
an ordinary textbook
textbook is
is that
that almost
almost all
all examples deal
deal with sawmill
sawmill
this
problems. Although theoretical
theoretical models are
are general
general in
in nature,
nature, the
the sawmill
sawmill manager has
has
problems that
that are
are very
very specific
specific to
to his
his industry.
industry. Above
the sawmill's raw
raw material
material Above all,
all, the
log - ccreates
reates difficult
difficult problems.
problems. But there
there are
are also
also other
other problems
problems more
more or
or less
less
the log
typical for
for sawmills.
sawmills. A
A few
few of them
them are
are covered
covered in
in this
this paper.
paper.
typical
As
this paper
paper presumably will
be used in
in many countries,
countries, a Eictitious
fictitious currency
As this
will be
called the
the monetary unit
unit (MU)
(MU) has
has been
bee n used.
used. Any real
real currency would most
most likely
likely have
have
diverted
the readers'
readers' attention from
from the
the analyses to
to the
the realism
realism in
in chosen figures.
figures.
diverted the
With one exception - aa cash
f l ow budget - taxes
taxes have
have not
not been included
included in
in the
the text.
text.
cash flow
The
reason is
is that
that tax rules
rules are
are specific
specific to
to different
different countries and,
and, thereby,
thereby, impossible
impossible
The reason
treat in
in aa common
common way.
way.
to treat
In Chapter
Chapter 6 oon
n capital
capital budgeting,
budgeting, the
the inflation
inflation problems
problems might have
have been
been discussed,
discussed,
but inflation
inflation rates
rates vary
vary between countries and
and also
also differ
differ over
over time
time within any
anyon
country.
but
onee country.
Thus it
Thus
it is
is difficult
difficult to
to treat
treat the
the problem in
in aa manner suitable
suitable for
for all
all readers
readers and
and it
it has
accordingly been
been excluded
excluded from
from this
this study.
study .
and the subsequent
subsequent analyses
analyses - presented in
in this
this paper
pap er might
might look
look
The models - and
difficult,
especia lly for
for the
the first
first time
time reader.
reader. The model
is often
often defined
defined as
as
difficult, especially
model concept is
"a simplified picture
picture of
of reality".
reality". The
The models oE
of this
this paper
paper are also "simplified"
IIsimplified l l as
as
"a
compared to
to reality.
reality. However,
However, it
it is
is possible
possible to
to simplify
simplify them
them still
still further,
further, but
but then
then
there is
is a great
great risk that
that they
they will
will not contribute
contribute at
at all
all - or
or even
even negatively - to
to the
there
sawmill manager's
manager's endeavour in
in improving
improving his
his profitability
profitability assessments
assessments and
and costing
costing systems.
systems.
sawmill
This paper
paper is
is based on the work of Mr.
Mr. Bo
Bo L.
L. Eklund,
Eklund, Senior
Senior Lecturer
Lecturer in
in Business
Business
This
Forestry
Department.
Administration,
University
of
Karlstad,
Sweden
in
collaboration
with
the
Forestry
Department.
Administration,
Karlstad,
in collaboration
the
-- v
v -
TABLE
TABLE OF
OF CONTENTS
Page
Chapter 1.
1.
COSTING AS
AS A
A MANAGERIAL
MANAGERIAL TOOL
TOOL
COSTING
1.1
1.2
1.3
1.4
1.5
Chapter
2.
Chapter 2.
Chapter 3.
3.
Chapter
Chapter 5.
5.
33
44
5
5
66
22.1
.1
2.2
22.3
.3
.4
22.4
22.5
.5
22.6
.6
22.7
.7
6
6
The
of a conceptual
co nce ptual basis
basis
The value of
Variable and fixed
fixed costs
Traceable costs and common costs
cost s
Direct
indirect costs
Direct and indirecr
Opportunity costs and outlay costs
costs
Incremental
sunk costs
costs
Incremental costs and sunk
Sawmi
ll problems and solutions
solutions
Sawmill
77
10
10
12
12
13
13
14
14
14
THE SHORT TERM PROFIT
PROFIT PLANNING
PLANNING
18
18
3. 1
3.1
18
18
18
18
Company objectives
objec tiv es
c hart
The breakeven chart
Breakeven assumptions
Breakeven
assumpti ons
Breakeven aanalyses
Breakeven
nalyses and step-fixed costs
costs
Breakeven analyses
and
linearity
changes
a nalyses and linearity c hanges
20
20
20
20
25
25
BUDGETING IN
IN SAWMILLS
SAWMILLS
28
28
4.1
4.2
4.3
4.4
28
28
Budgets and budgetary
budgetary control
control
Budgeting sales
sales revenues
revenues
The sales revenues
The
revenues of
of the
the sawmill
sawmill
Budgeting
Budget
in g short-term
sho r t-term expenses
expenses
29
29
30
33
33
USING THE BUDGET IN
IN SENSITIVITY
SENSITIVITY ANALYSES
ANALYSES
52
52
5.11
5.
55.2
.2
5.3
52
52
5.4
5.5
5.5
5.6
Chapter
Chapter 6.
6.
11
2
2
CONCEPTUAL FRAMEWORK
FRAMEI,ORK
33.2
.2
3.3
3.4
33.5
.5
Chapter
Chapter 4.
4.
The
framework
The overall
overall framework
The
conc ept
The cost
cost concept
Cost
Cost objectives
Costing
Costing purposes
purposes
The plan
plan of
of this
paper
The
this paper
11
Sensitivity analysis
ana lysis
Breakeven volumes
volumes
Profitability
as aa function
of both
and
Profitabi
lit y as
function of
both CTP and
sales volumes
volumes
Production disturbance
disturbance and
and its
its economic
economic effects
effect s
The
CTP
in
price
negotiations
The CTP in price negotiati o ns
The cash flow
flow budget
budget
52
52
55
55
58
58
60
60
62
62
CAPITAL BUDGETING
BUDGETING
66
66
6.1
6.1
66
66
6.2
6.2
6.3
6.3
6.4
6.4
6.5
6.5
Decision character
Evaluating
Evaluating time-spread
time-sprea d money
Decision models
models
Sensitivity analysis
analysis in
in capital
capital budgeting
budgeting
investment decisions
decisions for
for the
the model
model company
company
Some investment
APPENDIX
APPENDIX 1:
1:
TABLES
TABLES FOR
FOR QUICK
QUICK ESTIMATIONS
ESTIMATIONS OF
OF
;', FUTURE VALUES
;', PRESENT
PRESENT VALUES
VALUES
;, ANNUITIES
66
66
72
72
79
79
81
81
89
89
90
90
92
92
- 1 -
1.
1.
1.1
1.1
COSTING
A GER I A L TOOL
COSTING AS
AS A ~lAN
MANAGERIAL
The overall
overa ll framework
f r amework
The
decision-makers, i.e.
i. e . their main role
role is
is to
to make
make sound
so und decisions
Managers are decision-makers,
decisions in
order
for their companies
compan ies to
to become
become -- or
or remain
r ema in -- prosperous.
pr os pero us. To do this
this the
t he manager
order for
needs
operational aspects
needs information
information about
about operational
aspects of
of his
his company
company as
as well
well as
as the
the environment
environment in
in
compan y operates.
operates . This
dea l s \.Jith
i ntern al aspects
aspects of
of the
the company's
company's
which his company
This paper
paper deals
with internal
costing
special reference
re fer enc e to
to costing
costing problems
problems in
in sawmills.
sawm il ls .
costing systems with special
The
' costing ' can
can be
be used
used in
in several
s everal ways.
ways. As it
it is
is used
used here,
here, it
it is
is fairly
fairly
The term 'costing'
closely
related to
to the
the modern
mode rn aspect
t acco
unting , which should
should be
closely related
aspect of
of coS
cost
accounting,
be separated
separated from
from
financial
financia
l accounting (bookkeeping,
(b9okkeeping, etc.).
etc.) . Cost
c an be
be described
described in
in the
the
Cost accounting can
fo
ll owing way:
way :
following
COST ACCOUNTING. Qua
n titative method that
tha t accumulates,
accumulates,
Quantitative
classifies,
interprets information
information for
for three
three
classifies, summarizes and interprets
major purposes:
purposes: (1)
i onal planning and
and control;
co nt rol;
(1) operat
operational
(2) special
special decisions,
deciSions, and (3)
(3) product
product costing.
costing. (Horngren
(2)
(Horngren,,
Charles T.,
T. , ed.,
ed. , Cost
Cost Accounting.
Account ing. A
A Managerial Emphasis,
Emphasis ,
Prentice/
Hall International editions, Englewood
Englewood Cliffs,
Cliffs, N.J..
N. J.,
Prentice/Hall
1982, p.
p. 967.)
967.)
1982,
The
accounting system
system of
of the
the company
company is
is described
described in
in Exhibit
Exhibit 1.1.
1.1.
The overall cost accounting
The system is
is based on three
three cornerstones - the
the financial
financial accounting
acco un ting system,
system, the
the profitThe
ability judgement
judgement system,
system, and
and the
the budget
budget system.
system. The dashed
dash e d line
line indicates
indicates that
that these
these
three cornerstones are internally
three
internally connected
connected and
and mutually
mutually supporting
supporting each
each other.
othe r. In
compiling the
t he yearly,
yearly, short-term budget of the
the company,
company , one must rely
r ely on information
information from
compiling
the financial
the
financial system.
system. The
budget, in
in its
its turn,
turn, is
is an
an important
important source
source of
of information.
information.
The budget,
At
the
same
time
product
costing
and
product
performance
reports
will
constitute
sources
At th e same time
pr oduc t
r e port s will constitute sources
of information
information in
in the
the budget
budget work.
work. In
In the
t he same
same way
way there
ther e are
are connections
connections between
bet,,,een the
the
financial
accounting
financial accou
n ting system
system and
and the
the profitability
profitability judgement
judgement system.
system.
In
In this
this paper we will concentrate on the
the budget and the
the profitability
profitability judgements
judgements
of the
of
the company. Financial accounting
accounting will
wi l l be
be regarded
regarded only
only as
as aa possible
po ssi ble source
so ur ce of
of
information.
focus on
on the
the following
fol lowing three
three aspects
aspects of
of cost
co st accounting:
accounting :
We focus
1.
fo r aa budget,
budget, budgetary
budgetary control
contro l and
and active
active use
use of
of the
the budget
budget for
for
The need for
various
var ious costing
costing purposes.
purposes.
2.
to estimate
es timate the
the cost of sawn
sawn timber,
timber, i.e.
i.e. how
how to
to measure the
t he performance
performance
How to
of the
the sawmill.
sawmill.
3.
to carry out capital budgeting
budget ing and how to
to use
use the
the information
informat i on from
from the
the
How to
budget system.
system .
- 2 -
External
AcExternal Account
ing
counting
Product
cost
ing
costing
internal
AcInternal Accounting
Pr
oduct perProduct
per-
Fin
ancia L
Financial
performance
performance
reports
budgeting
Capital budgeting
decisions
formance
r ts
formance repo
reports
F i-
\
I
\
I
\
COST
ACCOUNT ING
\
/
I
SYSTEM
/
\'---.-----'/,
\
I
\
I
\
-
"consist
"consist of"
of"
= "internally
"internally
connected
and
connected and
support
ing"
supporting"
I
Snort-term functional
functional budgets.
budgets
Short-term
Long-term
.g- market
market
Long-term budgets
oudgets (e
(e.g.
demand
demandand
andraw
rawmaterials
materials
forecasts)
1.1 -- The
The Cost
Cost Accounting
Accounting System
System and
and its
its three
three cornerstones.
cornerstone s .
Exhibit 1.1
1.2
The cost concept
The
In
the cost used for
for various decisions
decisions is
is often
often taken
taken for
for granted.
g rant ed.
In practice,
practice, the
Managers use,
use, uncritically,
uncritically, costs
costs taken
taken from
from the
the company's
company 's financial
financial accounting
acco unting system.
system.
In costing,
costing, however,
In
however, we need a clear definition
definition of
of what
what is
is meant
meant by
by the
the term
term 'cost'.
·c ost ' .
Let us,
us, therefore,
Let
therefore, define the
the cost concept in
in the
the following
following way:
way:
A
is aa gen
uine sacrifice
sacrifice made
for the
the goods
goods and/or
and/or
A cost
cost is
genuine
made for
services
se r vices provided by
by aa company
company to
to its
its customers.
customers .
In this
In
this definition we
we have
have underlined the
the expression "genuine
"genuine sacrifice".
sacrifice " . In
In order
order
co
produce aa product
product or to
to produce
to provide a service
service to
to somebody,
somebody, the
the company
company has
has co
to sacrifice
sacrifice
something. This
Thi s sacrifice
sacrifice can
can be
be measured
measurp.d in
in different
differ ent ways.
ways . This means that
that we
we will
will
most
most probably
probably get
get different
different evaluations
evaluations of
of the
the cost.
cost. We
We can
can measure
measure aa cost
cost as
as either
either
what
what we
we have
have paid
paid to
to somebody
somebody or
or what
what we
we have
have refrained
refrained from
from by
by using
using our
our resources
reso ur ces in
in
a certain
way.
(By
using
our
money
to
produce
a
product,
we
refrain
from
the
bank
ce rtain way. (By using our money to produce a product,
refrain from the
interest
got , if
if we had put it
it in
in aa savings
sav ings account.)
account.) In the
the first
first
interest that
that we
we would have got,
case we talk
talk about
about the
the sacrifice
sacrifice as
as an
an "outlay
" out lay cost",
cost", in
in the
the latter
l atter case
case we
we call
call the
the cost
cos t
case
an
an "opportunity
"opportunity cost".
cost". This will be
be explained
explained thoroughly
thoroughly in
in Chapter
Chapter 2.
2. Suffice
Suff i ce it
it to
to say
say
here
here that the
the size
size of
of aa cost
cost is
is obviously
obViously aa matter
matter of
of evaluation
eva luation and
and not
not merely
merely grabbing
grabbing aa
figure
figure from
from the
the financial
financial accounting
accounting system.
system.
In aa company's financial
financial accounting
accounting there
there might
might be
be sacrifices
sacrifices that
that will
will not
not be
be
In
considered
considered sacrifices
sacrifices in
in the
the costing
costing procedures.
procedures. A
A fire
fire in
in the
the sawmill
sawmill does
does not
not mean
mean
increased genuine sacrifices
sacrifices for
for the
the production
production of
of sawn
sawn timber,
timber, even
even if
if purchases
purchases of
of new
new
increased
- 3 -
At the
machines, etc.
etc. are "costs"
"costs" from
from the
the accountant's
accountant's point of view.
view. At
the same
same time,
time, there
machines,
are genuine
made in
producing and
and distributing
distributing the
the sa~n
san timber
genuine sacrifices
sacrifices made
in producing
timber that
that the
the
does not
not consider
consider "costs"
" costs " in
in his
his system.
system. Storing a
a m
m of
of sawn
sawn timber
accountant does
timber during
a year is
is a
a genuine sacrifice
sacrifice from
from the
the costing
costing point of view.
view. In this paper,
paper, when
a
referring
to "cost
s !!, we
those sacrifices
sacrifices recognized
in the
the sawmill's
sawmill's costing
referring to
"costs",
we mean
mean those
recognized in
costing
procedures.
procedures.
The
between various
various aspects of the
the cost concept in
in this
this respect
r es pe ct is
is
The difference between
illustrated in Exhibit 1.2.
1.2. There,
There, costs
costs according
accordi~g to
to both the
the financial
financial accounting
The dashed
the budget and profitability
profitability systems
systems have been "boxed".
"boxed". The
dash(:r~ lines
iines
system and the
the dashed
indicate
common to
to all
all systems.
systems . Those sacrifices
sacrifices falling
falling outsi:le
outsi:;;e the
indicate sacrifices common
lines are
as added
added costs
costs for
for the
the financial
financial accounting
accounting systiem
system and
lines
are considered as
and t~le
the two
two other
other
respe c tively.
systems respectively.
i,dded z':'(;
r i (iAdded
scrifices for
fo r costing
cost Inn
ces
purposes
EuLposes
J
Costs
to all
sil
Cos
ts common
comllion to
sub -s vs tems
sub-sl,stems
(E.g.
I E . g. labour
labour costs,
costs, costal
costsl
lof
l of raw
raw materials,
mate rials, and
03nd
:
trophies
:transportation
costs
Lt~'~O~P~hii;
·
;
'==rl~t
:
,~a:n~,~p=
o
=
'~t:a~t:io:n~c:o:'
:
t~'~--'~==~~===="h
\;;
:Capital
~:'The
The same
s.Jme examples
examples as
: Capital costs
costs ~
..
I above
I for invento+-- Sacrlf1ces in
in
Ifor
invento- / Ap____Sacrifices
Iabove
F,ncrifices
5.Jc
r ifi ce s in
in
{ Costs
costs due
due
to
the f in03nci .Jl ---..
to catascatas-
the financinl---,
nccounting
,Jccou
s:stemntinq
s:'stem
I
i
~
: r ies
:ries
costing systems
systems
costi n ~
"=====::;;;:::::::::==-::::7
Added sacr
isacribees in
1n the
the
fixes
Genu
ine sacr
i f ices inincosting
cos t i ng
s ystems
Genuine
sacrifices
sysi-fems
f InanCl<ll
financial
.Jccou ntln c
accountin7
Exhibit
Exhibit 1.2 - Sacrifices in
in different
different accounting sub-systems.
sub-systems.
Finally,
the cost concept
concept is
is always
always time-bound.
time-bound. Most expenses of a company will
will
Finally, the
be part
be
part of the
the total
total costs
costs of
of the
the year.
year. Labour costs,
costs, rents
rents paid
paid to
to house-owners,
hous e-owner s , fuel
fuel
and
le ctrici ty expenses
expe n ses will accrue during
during the
the year.
year. Accrued expenses will then
then be
be
and eelectricity
treated as costs for
for the
the year.
year. But,
e.g. the
the electricity bill,
bill, will
will once
once aa year
year represent
represent
treated
But, e.g.
consumption
eelectricity
lectri c ity cons
umption for
for a period that
that stretches over the
the end
end of
of one
one year and the
the
beginning of the
the other year.
year. In
suc h cases,
cases, the
the expenses must
must be
be allocated
allocated b2tween
between ~he
In such
years
to show each year's
year's cost.
cost.
years to
This problem of time-wise
time-wise allocation
allocation of
of expenses
expenses is
is especially
especially important
important for
for
This
capital investments in
capital
in machinery
machinery and
and buildings.
buildings. Each year's cost
c ost will
be measured
the
will be
measured as
as the
In actual
actual cost
costing
depreciations of machines and
and buildings.
buildings. In
ing the
the size
size of
of the
the depreciation
deprecia tion
will reflect
reflect estimated useful
life of machines
ma c hines and
and buildings.
buildings.
will
useful life
1.3
Cost
Cost objectives
the expression
expression 'cost
'cost objective'.
obj.ective'.
Now and then we use the
for which a cost estimate may
may be
be desired.
desired.
anything for
this term
term we refer
refer to
to
With this
-- 44-
numerous cost
cost objectives
objectives used
used in
in the
the costing
costing procedures
procedures of
of aa company.
company.
There are numerous
A product,
A
product, a
a product mix,
mix, or
or aa whole
whole production
production unit
unit might be
be considered
considered a cost objective.
objective.
We can also find
We
find the
the cost
cost objective
objective outside
outside the
the company.
company. We
We might
might be
be interested
interested
in
as a
a result
result of
of the
the fact
fact that
that the
the company
company serves
serves different
different
in comparing
comparing costs
costs accrued as
of customers.
customers.
customers or groups of
But cost objectives
objectives do
do not
not necessarily
necessarily have
have to
to be
be "physical
"physical units".
units".
Various kinds
kinds
But
Various
of activities
activities can
can also
also be
be used
used as
as cost
cost objectives,
objectives, e.g.
e.g. comparing
comparing one
one production
production system
system
of
with another system
system or
or comparing
comparing two
two different
different transportation
transportation routes.
routes.
We
are not
not interested
interested only
only in
We are
in costs
costs of
of various
various cost
cost objectives.
objectives. The
side
Ehe income side
must
must also be
be taken into
into account.
account. Therefore,
the following definition
definition of
of aa cost
cost objective
objective
Therefore, the
will
be used throughout
throughout this
this paper.
paper.
will be
A
is any
unit or any
any activity
A cost
cost objective
objective is
any physical
physical unit
activity
in
for a
a
in the
the companyts
company's operations
operations that
that can
can be
be examined for
profitability assessment.
assessment .
1.4
1.4
Costing purposes
There
are many costing
costing purposes
purposes in
in the
the company.
company. Different purposes might create
create
There are
different needs of costing
different
costing procedures.
procedures. This
in turn means that
that the
the costing
costing systems
systems must
must
This in
be flexible
be
flexibl€ enough
enoug~ to
to serve
serve different
different needs.
needs. Let
Let us
us look
look upon
upon the
the more
more important
important purposes
purposes
that
serves in
in aa company.
company.
that costing usually serves
Purpose 11
Cost estimates
estimates for
for various
various kinds
kinds of
of price
price assessments.
assessments.
In many managerial textbooks
textbooks one
one finds
finds that
that the
the main
main purpose
purpose of
of the
the company's
companyts
In
costing procedure is
is to
to serve
serve as
as aa basis
basis for
for price-setting.
price-setting. This
This is theoretically
theoretically
illogical. Pricing the
the products should
should be
be made from
from the
the point
point of
of view
view of
of the
the buyer.
buyer.
This will be developed
developed further
further in
in Chapter
Chapter 4.
4.
But still,
still, there
there are many situations
situations in
in which the
the company
company is
is faced
faced with aa customer
customer
But
In such
such aa situation the
In
the costing system
system should
should help in
in judging
judging whether the
the bid
should be
be accepted or rejected.
should
rejected. In
the full
full cost
cost of
of the
the product
product might
might be
be
In some
some situations the
a
a logical
logical measure to
to use.
use. On other occasions perhaps
perhaps some
some kind
kind of
of "reduced
t1 re duced cost"
cost tt will
will be
be
used.
Price
Price assessments call not only
only for
for flexibility
flexibility in
in the
the system
system as
as such.
such. They also
also
point
point to
to the
the need for aa theoretical
theoretical understanding
understanding of
of how
how different
different costs
costs influence
influence
profitability.
bid.
Purpose 22
Cost estimates are
are used
used for
Cost
for assessing the
the profitability
of special orders and/or different customers
customers or
or groups
groups
of customers.
customers.
orders, different
different customers
customers or
or customer
customer groups
groups usually
usually give
give rise
rise to
to
Special orders,
different costs.
costs. In order to
to assess the
the profitability the
the costing
costing system
system must be
be more
detailed than otherwise would
would have
have been
been necessary.
necessary. Providing
Providing aa customer
customer with
with dimensions
dimensions
that normally are not
that
not produced
produced will
will influence
influence costs.
costs. If
If these special
special orders
orders are
are produced,
produced,
the companyts
company's buffer
buffer stocks before the
the
the kiln and the
the trimmer
trimmer will
will have
have to
to increase
increase to
to avoid
drying and trimming of
of series
series that
that are
are too
too small
small to
to be
be profitably
profitably handled.
handled.
-- 5 --
Purpos e 33
Purpose
Cost
in g procedures serve
serve the
th e purpose
purpose of
of performance
performance assessments
assessments
Costing
ffor
o r the
y as
o l e as
for various parts.
part s .
the compan
company
as aa wh
whole
as wel
welll as for
Performance control
contro l is
i s an
an important
important task.
task.
to exert
e x ert control,
co ntr o l, we
we must
must
To be able to
cr
eate tools,
too l s, i.e.
i.e. costing
costi ng procedures,
proced u res , that
that are
are conducive
co nducive to
t o such
s uch aa task.
tas k. In the first
first
create
place , performance
perf ormance control
control always
always calls
ca ll s for
for some
some degree
degree of
o f sophistication
sophisticat ion in
in the
t he system.
syst em.
place,
All
th at can
ca n be
be influenced
i nflu enced should
shou l d be
be separated
separated in
in the
the budget.
budget . Secondly,
it is
is
All costs that
Secondly, it
sometimes
importance to
to clarify
c l a rif y where
where the
the cost
cost accrues.
~ccrues .
Who
n influence the
the
sometimes of
of utmost importance
Who ca
can
s ize of the
the cost
cost and,
and , thereby,
t here by, be
be made
made responsible
respo nsible -- or
or credited
c redited -- for
for the
the changes
c han ges that
that
size
occ
ur ?
occur?
1.5
1.5
The
this paper
pape r
The plan of this
To build up a costing
costi ng procedure
procedure in
in aa company
company is
i s aa difficult
difficult task.
task . There is
i s always
a l ways
To
aa risk
risk that
that too
too much
much is
is taken
taken for
for granted.
granted . Howeve
r, when
the system
system has
it
However,
when the
has been
been constructed it
sshould
hould also be possible
possible to
to use
use it.
i t. To
in profitability
profitability assessments,
ass essments,
To avoid
avoid common pitfalls in
aa theoretical basis
basis is
is needed.
need ed .
Chapter
Cha
pt er 2 gives aa conceptual
concept ua l framework
framewo rk for
for costing.
cost ing . The larger
larger part
part of
of this
this
chapter
va ri ous cost
cos t concepts
co nce pts from
from aa purely
purely theoretical
theoretical point
pOint of
of view.
view. The
chapter deals with various
concepts
di ed in this
t hi s chapter wi
ll be used
use d - often with
with cross
cross references
references -- in
l ate r
concepts stu
studied
will
in later
of the
the paper.
paper.
parts of
Chapter 3 also contains a theoretical
theo r etical basis,
basis , as short-term
s hort-term profit planning is
is
discussed.. The
The way basic
discussed
bas i c concepts such
s uch as
as variable and fixed
fixed costs are put
put together in
Th e most important
important message
message in
in this
this chapter
chapte r is
is that
that
break-even analyses is
is scrutinized.
scrutiniz ed . The
In practice,
however, problems are
a r e much
mu c h
profit planning
practice, however,
theory ! In
profit
plann ing is
is aa simple
s impl e task
task -- in
in theory!
more difficult.
difficult . Some difficulties of
of practical
pra ct ical profit
profit planning
planning are
are discussed.
discussed .
dea l s entirely
entire l y with
with sawmill
sawmill budgeting.
budgeting. With Chapters
Chapt ers 22 and 3 as aa
Chapter 44 deals
theoretical
theoretica l basis,
basis, the
the short-term
short - term budget
budget is
is compiled.
compiled . One
One company serves
se rves as aa "model
"mode l
compan
yt t throughout the
the whole paper except
except for
for one
one section
section in
in Chapter
Chapter 4.
4 . In discussing
d i scussing
company"
the
sawmill's
materialcosts
t he sawmi
llt s raw
raw ma
te rial cos ts (log
s), we
e another example
examp l e for
for reasons
r easons explained
exp l ained later.
l ater.
(logs),
we us
use
Chapter 55 treats
treats the
the concept
co ncept of
of sensibility
sensibility analysis.
analysis . In
In this
this chapter we return
return
to
to the
the budget to
to illustrate
illu strate how
how it
it can
ca n be
be used
used for
for various
various kinds
kinds of
of decisions.
decisions .
Chapter
6, finally,
fina ll y, introduces
introduces the
th e concept
co ncept of
of capital
capita l budgeting.
budgeting . The chapter
chapter
Chapt er 6,
sta
rt s with
short introduction
introduction to
to the
the theory
t heory of how to
to estimate
es t imate the
the time
t i me value of money.
starts
with aa short
money.
Thereafter,
There a ft er , we work through
through five
five models
models for
for capital
capital budgeting.
budgeting . At
At the
the end of the
the chapter
c hapt er
we return,
re t urn, for
for the
the last
la st time,
time, to
to our
o ur model
model company.
company. From the
the budget we analyze
analyze aa couple
co upl e
of possible
possib le decisions
de c i s i ons for
f o r capital
ca pital investments
investments in
in the
t he sawmill.
sawmill.
- 66 -
2.
2.
2.1
FRAMEWORK
CONCEPTUAL FRAMEWORK
The
lue of a
a conceptual
conce p tual basis
basis
The va
value
The
company is
is often
often faced
faced with the
t he problem
problem of
of making economic
economic
The manager of a company
decisions affecting
affect in g the
the profitability
prof it abi lity of
of his
his company.
company. Such decisions
decisions involve
involve both
bot h cost
cost
income aspects.
as pe cts . The result
re s ult of the
the manager's
is heavily dependent
dependent on how well
and income
manager's efforts is
well
he can assess
assess the economic
econom i c consequences
co nsequences involved
involved in
in decisions
decisions such
such as:
as:
he
i)
ii)
iii)
iv)
v)
vi)
Ca
n the
the compa
ny profitably
profitab l y sell
sell the
the product
product at the
the price offered by the
t he
Can
company
ccustomer?
us tomer?
the economic
economic effects
effects following
fol l owi ng aa decision
decision to
to add
add aa new
new product
product to
to
What are the
the compa
ny 's production
production programme?
programme?
the
company's
is preferable
preferable -- AA or
or BB -- if
if available
ava ilabl e machine
machine time
time is
is aa
Which product is
bottleneck?
IIs
s it,
i t, from
from an economic
economic point
point of
iew, justifiable
justifiab l e to
to repair a
a machine
of v
view,
machine now
oor
r should
i t be
until next
year?
should it
be postponed until
next year?
Does
it pay to
to hire
hire aa new
new production
production manager?
manage r?
Does it
Should depreciation costs
costs be
be considered
considered in
in calculating
calcu la ting the
the costs
costs of
of the
the products?
produc ts?
In
t his kind,
kind, the
the manager will meet problems both in
in
In answering
answering questions of this
the size
size of the
t he cost
cost as
as well
well as
as in
in deciding
deciding whether
whether or
or not
not there
there is
is aa genuine
genuine
assessing the
sacrifice to be evaluated.
eva luated. As a matter of fact,
fact, he will find
find that
that "the
"the cost
cost of something"
something "
is aa highly relative matter.
matter .
is
often happen
happen that
he will
will have trouble
.Additionally
Addit i ona ll y it
it will
tha t he
trouble in
in finding
finding the
the size
s i ze of
will often
the
cost . The only
onl y source
so urc e of
of information
information available
avai labl e -- without
witho ut effort
effort -- is,
is, in
in many
many cases,
cases,
the cost.
the financial accounts.
accou n ts.
Here
costs are
are measured in the
the conventional
co nventional way to
to serve
the
Here costs
s?ecific needs.
needs. However, the
the needs
needs in
in connection
connect i on with
with profitability
profitability judgements
judgements are
are
specific
often
often of
of such
suc h aa nature
na t ur e that other cost concepts
co ncepts and
and other
other assessments
ass ess me nts must
must be
be used.
used.
Sometimes
the manager
between different
diffe r ent cost
cost concepts.
concept~.
Sometimes the
manager has a difficult choice between
It is
is better to
to use a rough
ro ugh approximation of
of the
the concept
co ncept
It
of cost
cos t that
that is
is correct
co rr ect for
for a particular
par tic ular decision
decision than
than
to have an
an accurate
accurate estimate
estimate of
of an
an irrelevant
irre l evant concept.
co nce pt.
to
The unsophisticated
The
unsophi sticated executive is
is in
in danger
danger of
of taking
taking the
the
easier course of using
usin g conventional accounting
acco unting costs
costs as
as
they were
were appropriate
appropriate for
for all
all purposes.
purposes. Instead,
though they
it is
is better
bett er to
to modify reported
reported costs as
as necessary
necessary ro
to
it
the best
be st possible
pos sible guess
guess at
at the
th e concept
co ncept theoretically
theoretically
make the
relevant
r e levant for
for each
each decision.
decision. (Dean,
J., Managerial
Managerial
(Dean, J.,
Economics,
Economi
cs, Prentice-Hall,
Prentice-Hall, Inc.,
Inc., Englewood Cliffs,
Cliffs, N.J.,
N.J .,
1951. )
1951.)
Occas ionall y the
the income
income aspect
aspect might
might also
a l so create
create aa problem,
probl em, but
but in
in most
most situations
situations
Occasionally
the
y ' s income (for
(for a
a particular decision)
deci sion) will
wi ll be fairly
fairly easy.
easy.
the assessment
assessment of
of the
the compan
company's
True, the
True,
the size
size of the
the sales
sa le s income
income might be
be difficult
difficult to
to predict,
predict, but
but in
in most
most cases
cases there
there
--77 -
be no
no conceptual
co ncept ual confusion
confusion involved
involved in
in forecasting
forecasting the
the sales
sales income.
income. However,
However, in
in
will be
estimating costs
costs the
the conceptual
conceptual problem
problem almost
almost always
always turns
turns out
out to
to be
be the
the key
key task.
task. That
explains why this
this chapter puts
puts cost
cost concepts in
in focus.
focus.
2.2
2.2
Variable and
and fixed
fixed costs
costs
to describe costs is
is to
to study
study how a certain cost
cost reacts
reacts to
to
The most common way to
changes in
in company
company activity
activity level.
level. The activity may be measured as
as production
production or
or sales
volume, hours worked and
and so
so forth.
forth. In
the activity
activity level
level will
will be
be measured
measured as
as
volume,
In this
this ~aper
rper the
(m ) and
to - for
for short - as
as "volume".
I1vol ume rl.
production of sawn
and referred to
sawn timber
timber in
in cubic
cubic metres (m
)
If
If the
the total
total cost changes
changes with
with volume,
volume, the
the cost
cost is
is defined
defined as
as aa variable
variable cost.
cost.
The
such aa cost
cost is
is illustrated
illustrated in
in Exhibit 2.1.
2.1. The
The graph
graph shows
shows that
that the
the total
The pattern of such
cost changes in
cost
in direct
direct proportion
proportion to
to changes
changes in
in volume.
volume.
MU
200000
MU 20
per unit
150000
100000
50000
2000
4000
6000
8000
10000
units
Units
2.1 -- The
The proportional
proportional variable
variable cost
cost function.
function.
Exhibit 2.1
This
that the
the unit
unit cost is
is constant,
constant, assumed
assumed here
here as MU 20
20 per unit.
unit. This
This
This means
means that
is
the way
described in
in textbooks.
textbooks. There
for every
is the
way variable costs are mostly described
There are
are for
every company
company
l ots of examples
examp le s of
of proportional,
proportional, variable
variable costs.
costs. The
terials used in
in
lots
The cost of raw ma
materials
manufacturing often
often shows
shows this
this pattern.
pattern. Other examples are
are labour
labour costs,
costs, package
package costs,
costs,
sa le s commissions.
commissions.
and sales
However,
However, a
a realistic assessment of variable costs
costs is
is more complicated.
complicated. Depending
Depending
where, along
along the
the volume
volume axis,
axis, the
the cost
cost is
is studied,
st udied, one
one finds
finds changes
changes in
in the
the behaviour
behaviour
on where,
pattern. Besides
Besides proportional variable
variable costs,
costs, it
it is
is also
also possible
possible to
to discover
pattern.
discover both
both
and degressive
degressive variable
variable costs.
costs. The progressive
progressive cost
cost grows
grows at
at aa higher
higher rate
r ate
progressive and
than
increase in
in volume and the
the degressive
degressive at
at aa lower
lower rate.
rate. The
these
than the
the increase
The prinCiple
principle of these
two types
types of variable costs is
is illustrated
illustrated in
in Exhibit
Exhibit 2.2.
2.2. It
It is
is obvious from
from this
this graph
that the
the unit cost increases
increases for
for the
the progressive
progres~ive (Curve
(Ctirve I)
I) and
and decreases
dec reases for
for the
the
that
degressive (Curve
(Curve II)
II) variable
variable cost.
cost.
-- 8 --
MU
I
II
Volume
2.2 -- Graphical
G~aphical illustration
illustration of
of progressive
progressive (I)
(I)
Exhibit 2.2
and
(II) variable
variable costs.
costs.
and degressive (II)
not always find
find progressive
progressive and degressive variable
variable costs
costs
Unfortunately one will not
that
smoothly as
as in
in Exhibit
Exhibit 2.2.
2.2. Instead one usually finds
finds that
that these
these
that can
can be shown as smoothly
costs are
are composed of a series
series of
of proportional
proportional variable
variable costs
costs that
that will show
show a progressive
progressive
(degressive) behaviour pattern.
pattern.
(degressive)
Fixed
as costs
costs that
that remain
remain unchanged
u.nchanged with
with changed
changed volumes.
vo l umes .
Fixed costs
costs are
are defined as
As
As
can b2
bz seen from
from Exhibit 2.3,
2.3, the
the fixed
fixed cost
cost can
can be
be shown
shown as
as aa horizontal line
line parallel
paralle l
to
to the
the volume
volume axis.
axis. However,
However, for
for fixed
fixed costs
costs also,
also, reality
reality is
is more
more complicated.
complicated.
MU
Vo
l ume
Volume
2.3 -- The simple,
simple, fixed
fixed cost
cost curve.
curve.
Exhibit 2.3
be considered
considered when studying
studying the
the fixed
fixed costs.
costs. There
The volume range must always be
two aspects.
aspects . Firstly,
First l y, we must consider
consider where
where .on
the volume
vo l ume axis,
axis, the
the cost
cost studies
studies
on the
are two
made. The
horizonta l cost line
li ne presented
prese n ted in
in Exhibit 2.3
2 . 3 extends indefinitely
in defin i te l y from
The horizontal
are made.
zero and along the
no cost can remain
much
the volume
volume axis.
a x is . However,
However, ~
remain fixed regardless
regardless of
of how much
the
changes. Sooner or later
later aa cost
cost increase
increase must
must occur.
occur . Showing a fixed
fixed cost
cost
the volume changes.
as
a horizontal
horizontal line
line is
is valid only
on l y for
for aa part
part of
of the
the total
total range.
range. This part is
is called
called
as a
relevant range.
range. Secondly,
what happens,
happens, when the
the production volume
vo l ume
the relevant
Secondly, we must consider what
passes either of
o f the
the borderlines of the
the relevant
relevant range.
range .
passes
- 99 -
To study the relevant
To
relevant range
range we
we can
ca n use
use labour
labour costs
cos ts of
of supervisors
s upe rviso rs as
as an
an example
example
fixed cost.
cost. The
o f this cost
cost is
i s shown in
in Exhibit
Exhibit 2.4.
2 . 4. Here we can
can see
see that
that
of aa fixed
The graph of
the company can produce up
up to
to 10
10 000
000 units
uni ts with
with one
one supervisor.
s up e rvisor. In
to increase
increase
the
In order
order to
from 10
10 000
000 to
to 20
20 000
000 units,
units, another
a not her supervisor
s up ervisor must
must be
be employed.
emp loyed. Thus,
Thus, costs
costs
production from
for
been doubled.
doubled .
for supervisors have been
The company's
MU
I·r
elevan t rangt1
rang~
rirelevant
I
supervisors
I Three supervisors
,
i
75000
I
I
1
.
50000
I
I
supe rV lso r s ,
'Two supervisors',
One
supervisor I
One supervisorl
25000
produc Present produc-
~ tion
tion volume
vo lume
i__-10000
10000
20000
30000
Units
. Exhib
i t 22.4. 4 - Step-fixed
Step-fixed cost,
cost, supervisory
supervisory salaries
salaries at
at various
va riou s production
production
Exhibit
volumes.
vo
lumes .
This is
This
is shown
shown as
as a jump
jump to
to a higher level
level in
in one
one single
s ing l e step aalthough
lthough present
presen t
production remains
at
17
500
units.
remains at 17 500 units. If
If the
the pr
oduct i on increases
increases above
above 20
20 000
000 units,
units, aa
production
third su
supervisor
must
third
pervi sor mu
st be
be employed.
emp l oyed.
The stepwise
stepwise increase
inc r ease of
of certain
certai n costs
cos t s creates
crea t es some
some problems.
prob l ems . If an increase
in crease in
in
demand
demand of
of some
some 5 000 units
unit s is
is forecast
forecast for
for the
the coming
cornin g year,
year, the
t he company
company needs
nee ds to
to produce
produce
22
22 500 units.
units. To accomplish
accomp l ish this,
thiS, aa new
new supervisor
s uper visor must
must be
be employed.
emplo ye d. One supervisor
su perv isor
can handle
hf?d l e up
up to
to 20
20 000
000 units.
un its. The
s up e rv iso r is
is in
i n theory
theory needed
ne eded for
for only
on l y 22 500
500
The new supervisor
1/
units. Unfortunate
units-.
l y, the
the majority
maj or i ty of every
eve r y company's
comp an y ' s "fixed
" fixed costs"
costs" are actually stepstepUnfortunately,
fixed,
costs being fixed
fi xed , i.e.
i . e. costs
fixed only
on l y within certain
certain intervals
interva l s (relevant
(re l evant ranges).
ranges).
co ns iderat i on is
is to
to see
see what
what happens
happens when
when the
the production
prod uc tion volume
vo lume passes
passes
The second consideration
the
the borderlines of the
the relevant
r elevant range.
range. Increased production
pr oduct ion volume
volume is
i s followed
followed by
by
increased costs. But what happens
ha ppens to
to aa cost
cost when
when the
t he production
production volume
volume decreases?
decreases?
Supp
ose that
that the
the company
co mp a ny hired
hired aa third
th ird supervisor
supe rvi sor three
three years
years ago
ago due
due to
to increased
increased demand.
demand.
Suppose
What happens with
wi th the
the cost
cost of
of supervisors
supervisors if
if the
the production
production volume
vo lume shrinks
s hrinks to
to the
the previous
previous
level ((17
500 units)
units) or
level
17 500
o r lower?
l ower? From
From a principle
principl e point
point of
of view
view the
the last
last employed
emp l oyed supervisor
supervisor
can be
be fired.
fi red. If
so, labour
labo ur cost
cost for
for supervisors
superv i sors will
will go
go back
ba ck to
to the
the previous
previous level.
level.
If so,
1.1
1/
This is
i s aa principle
princ ipl e analysis.
a nalysi s . Such
Suc h objections
object i ons like
like "use
"u se overtime
overtime production"
production" or
or
"hire
"hire aa part-time supervisor"
s up erv i so r" are
are of
of no
no value.
va lue. There are
a r e always
always occasions
occasions in
in aa
compa ny, when the
the indivisibility
indivisibility of
of costs
costs creates
c rea tes problems
problems of
of this
this kind.
kind.
company,
- 10
10 -
then talk
talk of
of aa reversible,
reversible, step-fixed
step- fixed cost.
cost. If,
If, for
for one
one reason
reason or
or another,
another, the
t he
We then
su pervisor cannot be
be fired,
fired, the
the cost
cost of
of supervisors
supervisors will
will be
be unchanged
un c han ge d in
in spite
spite of
of the
the
supervisor
decrease in
in volume.
vo l ume .
A step-fixed
step- fixed cost
cost that
that tends
te nd s to
to remain
remain unchanged
un c hanged with
with volume
volume
decreases is
is called
called an
an irreversible
irreversible step-fixed
step -f ixed cost.
cost . Most
Most step-fixed
step-fixed costs
costs are
ar e partly
partly or
or
irreversible . Workers,
Workers , supervisors
su pervisors and
and even
even managers
managers can,
can , in
in principle,
prinCiple , be
be fired.
fired.
totally irreversible.
Mac hines and
and buildings
buildings cannot!
cannot~
Too
assumpt i o ns about future
future demand
demand might
might incur
incur
Too optimistic assumptions
Machines
step- fix ed costs
costs that
that with
wi th decreasing
decreasing demand
demand become
become devastatingly
devas tatingly high.
high.
irreversible step-fixed
Before
leaving the
the concepts
fixed costs
, aa certa
in mixtur
e of
Before leaving
concepts of
of variable
variable and
and fixed
costs,
certain
mixture
of them
them
will
will be
be commented
commented on.
on.
In some instances
instances a
a cost
cost can
can consist
cons ist of
of one
one fixed
fixed and
and one
one variable
variable
e l ement. Such
Su ch a
a cost
cost is
is called
called aa semivariable
semivariable cost
cost or
or aa mixed
mixed cost.
cost.
It
is e.g.
It is
e.g. common
element.
to
fixed amount p.a.
p.a. for
for electric
electric power
p ower installation
installation and
and aa variable
variable fee
fee for
for the
t he
to pay
pay aa fixed
actually used.
used.
Mixed
are generally
ge nerally of
of little
little interest,
interest, but
but
Mixed or semivariable costs are
power actually
from aa co
conceptual
from
n ceptual point
point of
of view
view it
it is
is important
important not
not to
to mix
mix these
these costs
costs with
wi th step-fixed
step-fixed
costs .
costs.
2. 3
2.3
Traceable
Traceable costs and common costs
A pair of cost concepts
concepts of
of great
great practical
practical use
u se in
in profitability
profitability assessments
assessments is
is
A
the
the constellation
constellat i on of
of traceable
traceable and
and common
common costs.
costs .
A cost
cost that
that can
ca n be
be indisputably
indisputably
traced
trac ed to
to a
a given
given cost
cost objective
objective is
is defined
defined as
as aa traceable
traceab le cost.
cost . Costs
Costs lacking
lacking this
this
as aa cost,
cost, the
the burden
a r e common
common costs.
costs. A
A common cost
cost is,
is, therefore,
therefore, defined as
traceability are
should be
be shared
shared by
by at
at least
least two
two different
different cost
cost objectives.
ob j ect ive s.
of which should
In using this
this cost
cost pair
pair the
the "traceability
" traceability aspect"
aspect" is
is crucial.
c rucia l. A
A cost
cost is
i s traceable
In
to
a
given
cost
objective,
if
the
elimination
of
the
cost
ob
jective
means
that
t h e cost
to a given cost objective, if the
the cost objective means that the
cost
disappears completely. In defining "traceability"
" traceability" the
the starting
starting point
p o int can
can also
als o be
be the
the
of aa new
new cost
cost objective.
objective .
If
object ive is
is added
added to
to aa company's
company's current
c urrent
If aa new cost
cost objective
addition of
activity,
activity, all
all costs
costs then
then accruing
accruing are
are traceable
tracea b le costs.
costs .
. The
traceabi lit y can
can be
be illustrated
illustrated by
by aa product-costing
product-costing example.
example.
The traceability
and sells
sells five
five different
different products,
products, A-E.
A-E .
company produces and
calculation s shown
shown in
in Exhibit
Exhibit 2.5.
2.5.
calculations
~
Products
A
Ass ume that
that aa
Assume
co mpany has
has made
made cost
cost
The company
B
C
D
E
625
740
480
810
405
460
320
500
180
10
10
200
20
110
10
10
265
25
25
15
10
10
20
30
30
30
15
15
35
(25
(25))
15
15
(35
(35))
Specification
Spe
cificat ion
Total revenues
r eve nues
700
raw matemateCost of raw
rials
435
of labour:
Cost of
labour:
Machine operators
opera t ors 190
Supervisors
15
Sales commission
14
Depreciations
20
20
Net income
income (loss)
(loss )
26
2.5 - Simplified example of product-costing
product-costing for
for
Exhibit 2.5
five products.
pr o ducts.
five
•
- 11 -
As can be seen from
fro m the
the figures,
figures, two
two products
pro ducts - B
~ and E
~ - have
have given
given aa negative net
net
As
in
income
come (loss)
( loss) during the
the year.
year. The
The question
questi on nnow
ow arises,
arises, whether
whether these
these two
two products
products should
should
b e deleted
del ete d from
from the
the production
production schedule
schedule or
or not.
not. To answer this
this question,
question, information
information is
be
f utur e demand,
demand, expected
expec t e d prices,
prices , the
the competitive situation in
in the
the future,
future,
needed on expected future
possible alternative
al ter na tive actions
act i ons and
and so
so forth.
forth. Let
us, to begin
beg in with, study
study the
the figures
figures
Let us,
to
t he y tell
te ll us.
us.
to see
see what
what they
If we
we stopped
stopped producing
producing these
these products,
produc ts , the
the following
fol l owing changes
changes would
would occur:
occur:
i )
ii )
iii)
iv )
v)
The
rev en ue s from
from products
products BB and
a nd EE will
will disappear.
disappear.
The revenues
Costs
ma t eria l will
will also disappear
dis a ppear given that
that this
this material
is
Costs of
of raw material
material is
indisputably
i ndisputably traceable
traceab le to
to the
the products.
products.
Cost
la bo u r will
will most
most probably
probab ly be
be reduced.
redu ce d. Machine operators
operators can
c an be
be
Cost of labour
dismissed. If
these costs
costs are
a re traceable.
t raceabl e . Supervisory salaries do
do not
not
If so,
so, these
cha nge. If
If there
there is
is only one supervisor,
supervisor, he
he is
i s needed
neede d for
for the
the
necessarily change.
rest of
the production,
production, and his
his salary is
is then
then to
to be
be regarded as
rest
of the
as aa common
common cost
cost..
If the
If
t he products are deleted,
deleted, the
the sales
sa l es commission
co mmiss io n will
will disappear,
dis a ppear, i.e.
i. e. this
this cost
cost
is
is traceable.
Years ago
ago machines
Depreciation cost
cost is
is nothing
noth ing but
but aa time-distributed
time-distributed cost.
cost. Years
we r e bought,
bo ught , the
the cost
cost of
of which
which now
now shows
shows as
as aa yearly
yea rly depreciation.
depreciation. If there is
is
were
use of
of the
the machines,
machines , the
the depreciation
depreciation must
must be
be regarded
re garded as a
a
no alternative use
cost .
common cost.
With
these possible
possible changes
cha nge s in
in mind,
mi nd, aa recosting
recosting of
o f products
products B~ and
and E~ has
has been
been made
ma de
Wi th these
in
2.6 . From this
th i s calculation
ca l c ula tio n we can
c an see
se e that
that both
both products give a surplus
surp lu s over
in Exhibit 2.6.
This surplus is
and above
above those
those costs that
that are traceable
traceable to
to the
the products.
produc ts . This
i s called
ca ll ed the
the
products'
contribution to
to profit.
pr ofit. If
her alternatives,
alternatives, it
it would
would be
be unwise
unwise
If there
there are
are no
no ot
other
products' contribution
t o cancel
cance l products
p roducts B
Band
des pi te the
t he "obvious
"obvious loss"
loss" according
acc ord ing to
to Exhibit
Exhibit 2.5.
2.5.
to
and EE despite
i
Products
Products
i
B
B
-
I
E
E
-
I
I
Specifi
cifications
I
I
I
I
I
1
625
Tota l revenues
revenues
Total
810
1
II
Traceable costs:
costs:
Traceable
materials
Raw materials
Operators' wages
wages
Sales commission
commission
Sales
Surplus above
traceable costs
:
I
Ii
405
405
185
185
14
I
I
I
599
I
1
I
500
500
265
265
20
20
785
1
26
26
I
1
25
25
Exhibit 2.6
2.6 - Recalculations of products B~ and
and EE from
fr om
2.5 using
using only
on ly traceable
traceable costs.
costs.
Exhibit 2.5
-- 12 --
Let
l ook at
at the
the labour
l abour cost
cost for
for supervisors.
superviso rs . We found
found that
that when
Let us
us have a look
when products
B and
the cost
cost objectives,
objectives , supervisory
su pervi sory salaries
salaries were
were treated
treated as
as aa common
common cost.
cost.
and ~
E were
were the
Changing perspective and
and making
making the
t he whole
wh o l e department
department the
the cost
co st objective
obj ect i ve would
would turn
t urn the
t he
supe
supervisory
r visory salaries into
into a traceable
t r aceab le cost.
cost. This
examp l e highlights a very
very important
importa nt
This example
character
characteristic
i st ic of this
this cost pair;
pair; a certain cost
cost may
may very
very well
well for
for one
one cost objective
o bjective be
be
characte
rized as a
a traceable
traceable cost,
cost , but
but for
for another
another cost
cost objective
objective the
the same
same cost may become
become
characterized
In other
aa common cost.
cost .
ot her words,
wo rd s, it
it iis
s the
nin g of
the cost
the defi
defining
of the
cost objective
objective that
that decides
decides whether
whether
aa cost
is traceable
traceable or
or common.
common. Ca
r e ful defining of
of the
the cost
co st objective
ob j ective becomes
becomes aa crucial
crucial
cost is
Careful
task
task wh
when
en using this cost
cost pair.
pair.
22.4
.4
Direct and indirect
Direct
indirect costs
costs
The cost pair
pair of
of direct
direct and
and indirect
indir ect costs
costs will
will be
be found
found in
in the
the accounting
accounting system.
sy stem.
The
It is
of very limited
It
is of
limited use
use in
in profitability
profita bility decisions.
decisions.
But the
the problem is
is how to find
fi nd
But
valid
in aa particular
particular situation.
situation . One source
source of
of information
information is
i s the
the
valid cost
cost estimates in
accounting system.
system . Cost
figur es , taken
taken from this
this system,
system, might sometimes
somet imes be
be the
the only
only way
way
Cost figures,
to
estimat e even
even if
if those
those are
are often
often constructed
constructed for
for highly
highly generalized
generalized purposes.
purpo ses .
to get
get aa cost
cost estimate
In
system the
the products
products usually
usually are
are cost
cost objectives.
objectives . All
All costs that
that
In the
the accounting system
can
traced to
to such
such aa cost
cos t objective
ob jective are
are direct
direct costs.
costs.
Examples
direct
can be
be directly
directly traced
Examples of direct
costs are
are raw material, labour
costs
labour costs
costs and
and sales
sales commissions.
commissions. Direct costs are
are traceable
traceable
to
bjective (Exhibit
(E xhibit 2.5).
2.5) , One
these two
two concepts
conce pts -- direct
direct costs
costs
to the
the cost
cost oobjective
One would expect these
and traceable
traceab l e costs -- to
to be
be synonyms.
synonyms.
Bu
t this
th i s is
i s not
not the
t he case!
case!
Direct
al l
and
But
Direct costs are all
those
h the
the accountant has chosen to
to treat
treat as
as directly
directly traceable.
traceable . Obviously,
ObVious l y,
those costs
costs whic
which
then,
indirect costs
those costs which the
t he accountant has
has chosen
c hos en to
to treat
treat as indirect
indir ect
then, indirect
costs are those
relative to
relative
to aa certain cost
cost objective.
objective .
Supervisory
salaries
(Exhibit
2
.
5)
are
usually
not
Supervisory
(Exhibit 2.5)
usually not
directly
directly traceable
traceable to
to one
one product
produ ct and
and therefore
therefore treated
treated as
as indirect
indirect costs.
cos t s . Rent
Rent paid for
for
an
depreciati on of factory
factory buildings,
buildings, and salaries
sa l aries to
to the
the management
management are
are ot
h er
an office,
office, depreciation
other
examples of
of costs
costs that the
examples
the accountant
accountant treats as indirect
indirect costs.
costs .
It is
It
is important to
to notice
notice the
the stress
stress that
that has
has been
been put
put here
here on
on the
the word
word 'treat'.
'treat'.
In
generall accounting
In the
the ' genera
accounting system
system it
it is
to identify
identify every single
Singl e cost in
in such
such
is impossible
impossible to
way that
aa way
that makes it
it possible
possible to
to classify
classify the
the nature
na tur e of
of the
the cost
cost for
for different
different situations.
situations.
There are thousands
thousands of
of small
s mall items
items used
used in
in production
prod uction and
and distribution
distribution of
of goods;
goods; pencils,
pencils,
erasers, staples,
sta ples, paper clips,
c l ips, lubricating
l ubricating oil,
o il , lubricating
lubr icating cans
cans and
and various
various minor
mino r
erasers,
tools, to
to mention
mention but
but aa few.
few.
There are services
services required
required like
li ke electric
electric power,
power, heating,
heating,
tools,
telephone
te l ephone ccalls,
a ll s , transportation,
transportation, mail
mail services,
services , insurance.
in s u rance.
It is obvious
ob vi ous that
th at it
it would
wo ul d
It
be too
be
too tedious
tedious to
t o trace such costs to
to individual cost objectives.
ob j ectives.
Instead
the accou
ntin g
Instead the
accounting
system is
built up
a way that
that fairly
fairly good estimates
estimates will
wi l l be
be achieved
achieved for
for each final
final
is built
up in
in such a
cost objective.
cost
objective . This may be
b e carried
carrie d out
out as
as shown
shown in
in Exhibit
Exhibit 2.7.
2 . 7 . Costs that
that are directly
dire ct l y
traceable to
to the
the cost
cost objective
ob je ctive will
wi ll be
traceable
be directly
directly applied.
applied . Indirect costs
costs will
wil l first
first be
be
allocated to
to different
different cost
cost centres.
centres . Such cost
cos t centres
centres may
may be
b e production
production or
or service
serv ice units.
uni ts.
From
From these
these cost
cost centres,
centres, indirect
indirect costs are applied to
to the
the cost objectives.
ob j ect i ves.
-
1313
-
Dire
c t costs
Direct
c os ts
Raw
t e ri a l s
Raw ma
materials
Sem
i-man u fact u red goods
Semi-manufactured
LLabour
abou r cos
costs
ts
Dir
ec tl y
Directly
app
li ed
applied
Indir
ect costs
Indirect
Supe
r viso r y saSupervisory
sa llaries
a r ies
Admini
stra ti ve
Administrative
expenses
F
ac t ory overhead
Factory
ove r head
Cost centre
ce ntr e
fo
r co
ll e cfor
collection
intion of
of in
d i re ct costs
co s t s
direct
Cost
aallol location
Cos
o bj ec Costt objecttive
i v e to
to
bea
r the
bear
t he
cos
ts
costs
Ind'
lre c tIndirectl y apply
li
ed
lied
Exh
i b i t 2.7
2.7 - Applying direct
direct and
and indirect
indirect costs
costs to
to cost
cost objectives.
ob j ectives .
Exhibit
2.5
2.5
Opportunity costs
costs and outlay costs
To
costs means
foc u s ing the
To classify
classify costs
costs as
as either opportunity costs or outlay costs
means focusing
the
nature of sacrifice.
sacrifice . Perhaps the
the most
most natural
natural .way
to measure
measure the
the sacrifice
sacrifice for
for aa certain
certain
way to
activity is
worker, another
another compa
activity
is to find
find out
out how much one has to
to ply
p~y somebody
somebody (a
(a worker,
ny or
or
company
an agency of any kind).
an
kind), \.Jages
salaries, vw materials and
and services
services paid
paid are
are all
a ll
Wages or salaries,
eexamples
xamples of
costs, i.e.
i.e. costs measured by the
the amount of money paid.
paid .
of outlay costs,
,aw
••
But there is a different
But
di f ferent way
way of
of measuring
measuring the
the sacrifice
sacrifice made,
made , namely
namely to
to see
see what
what
the company has
the
has to
to refrain
refrain from
from by
by choosing
choosing aa certain
certain course
course of
of action.
action. If
If a worker
wo r ker is
is
used for
activity A,
A, we can often find
out how
how much
much we
we have
have to
to refrain
refrain from,
from, when
when we
used
for activity
find out
we do
do not
n ot
use him
hi~ for
for activity
activity B.
B. Instead
the labour
labour cost
cost of
of activity
activity AA as
as the
t h e wage
wage
Instead of measuring the
actually paid to
to the
the worker,
worker, we
we can
can measure
measure the
the sacrifice
sacrifice in
in performing
performi ng activity
activity AA as the
t he
foregone net
net earnings
earnings by not letting
foregone
letting him perform activity B.
B. The cost measured
measured in
i n this
th is
way is
is called the
the opportunity cost.
cost.
A
A taxi-driver,
taxi-driver, who
who owns
owns his
his car
car has
has been
been requested
requested to
to drive
drive a
a customer
c u stomer to
t o aa place
p l ace
500 km away,
away, to
wait there while the
500
to wait
the customer
custome r attends
~ttends aa meeting
meeting and
and then
then drive
dr i ve the
th e customer
c u stomer
back again.
The total
again. The
tota l ride will
will amount to
to 11 000 km and the
the trip
trip will
wil l take
take aa whole
who l e day.
day .
The customer wants to
to have
have aa binding
binding offer
offer before
before he
he makes
makes up
up his
his mind.
mind . For
For the
the taxitax i the problem now is
is to
owner the
to decide
decide on
on the
the price
price to
to offer
offer the
t h e customer.
c ustome r . Let us simplify
s implif y
hi s problem
problem so
so that
that only
only two
his
two types
types of
of sacrifices
sacrifices will
will be
be involved,
~nvo l ved , namely
name l y the
t he cost
cos t of
of
gasoline
gasoline and
and the
the cost
cost of
of his
his own
own work.
wor k. The first
f i rst cost
cost can
can easily
easily be
be estimated
estima t ed as
as it
it is
is
an obvious outlay
outlay cost.
cost. Knowing the
the price
price of
of gasoline,
gasoline, MU
MU 44 per
per litre,
lit r e, and
and how
how much
muc h the
the
consumes, 0.18 litre
litre per
per km,
km, this
this cost
cost will
will be
be 11 000
000 xx 0.18
0. 18 xx 4,
4, which
which amounts
amo un ts to
to
car consumes,
MU 720
in
total.
720 i n total.
But
estimate the
the "labour
!!labour cost",
cost " , i.e.
Le . his
hi s own
own work?
wor k ? Here
He r e the
t he
But how should he estimate
opportunity
cost concept
concep t offers
o f fers aa way
way out.
out . From records
r ecords he
he knows
knows that
tha t during
du r ing this
thi s time
t ime
opportunity cost
of
of the
the year
year his
his average
average gross
gross earnings
earn i ngs amount
amount to
to MU
MU 804
804 per
pe r day
day and
a n d to
to achieve
ac hi e ve this,
t hi s , he
he
drives
dr i ves at an
an average
average 183
183 km
km per
per day.
day. In
In city-driving
City- driving the
the average
average gasoline
gaso li ne consumption
consumpti on
amounts
amounts to
to 0.22
0.22 litres
l itres per
per km.
km . With these
these figures
figures he
he can
can estimate
estimate his
his total,
tota l , net
ne t earnings
ea r nin gs
per
pe r day:
day :
+ Gross earnings
earni ngs per
per day
day
MU 804
804
MU
- Cost
Cost of gasoline per day
day 4x183x0.22
4x 183xO.22 = MU
MU 161
161
= Net
Net earnings
ea r nings per
per day
day
MU 643
643
MU
--14
14
from by
by not
not
This amount,
amount, MU 643
643 per
per day,
day, is
is what
what he,
he, at
at an average,
average, would refrain
refrain from
driving as usual.
usual.
This
is the opportunity cost.
cost.
If
720 (to
(to cover cost of
of
This is
If he
he demands MU 720
gaso
l ine) plus
(to cover
cover what
l d have
i.e. aa total
gasoline)
plus 643
643 (to
what he
he otherwise
otherwise wou
would
have earned),
earned), i.e.
total of
of
MU 11 343
343 for
for this
this special
special driving,
driving, he
he will
will be equally well off
off as
as compared
compared to
to "an
"an average
day".
22.6
.6
Incremental costs and
Incremental
and sunk
sunk costs
costs
in a
a company
company very often means
means adding
ad di ng new activities
act i vit i es to
to those
those
Making decisions in
performed. To perform the
the new
new activity,
activity, e.g.
e . g . taking
taking up
up aa new
new product,
product, means
means
previously performed.
that
two types
types of resources
resources will
will be
be used.
used.
Perhaps aa ne~
that two
Perhaps
new machine
machine must
must be
be bought
bought and
and aa new
new
operator employed.
employed . This
that the
the decisiOn
decisi6n wi
l l incur
these costs
This means that
will
incur added
added costs
costs,, and
and these
are
termed incremental costs.
costs .
However, the
the machine also
also demands
demands space
space in
in the
the factory.
factory.
If
are termed
However,
there
the f*tory
f9ftory floor,
floor, and
and there
there is
is no
no alternative
alternative use
use of
of this
this space,
space,
there is
is free
free space
space on
on the
We-term
the
of using
using it
it is
is zero..
zer~.
We term this
this cost a sunk
sunk cost,
cost.. This will
will be discussed
the cost of
further
numb~r of
of examples
examples in
in later
later chapters.
chapters.
further with a number
22.7
.7
Sawmill problems
problems and
and solutions
solutions
2.7.1
Problems
(a)
Give
examples of
of variable
variable and
and fixed
fixed costs
costs in
in aa sawmill.
sawmill. Comment also
Give some examples
on
variabi l ity different
different costs
costs might have
have and
and their
their degree
on what
what kind of variability
degree of
of
and/or reversibility.
reversibility.
fixedness and/or
(b)
In the
the discussion on "traceable and common costs" an example
example was
In
was given
given for
for
five
(cf Exhibit 2.5
2.5 and
and 2.6).
2.6).
five products (cf
Consider the
the various
various dimensions
dimensions of
of sawn
sawn timber
timber as
as different
different products.
p roducts.
Carry out
out a
a study for
for a
a sawmill,
sawmill, similar
similar to
to the
the one
one referred
referred to
to above,
above, under
under
the
that one
the products might
might be unprofitable.
unprofitable. The I
the assumption
assumption that
one or
or more
more of
of the
be regarded
regarded as
as traceable
traceable
will be
main question is:
i lf What costs in
in this
this situation will
0
costs?
(c)
A company is divided into two
two separate
separate production units - the
the sawmill
sawmill and
and
planing mill.
mill. Both units
units have the
the same,
same, overall
overal l management.
management.
the planing
How would you classify
claSSify the
the administrative
administrative cost
cost for
for this
this company?
company?
(d)
In our
the raw
raw materials
of the
the planing mill
mil l are
are all
all taken
taken from
In
our company the
materials of
from the
the
company's own sawmill.
sawmill. The
some 70
70 percent
percent of
of its
its production
production
The sawmill sells some
on
is used
used in
in the
the planing
p l aning mill.
mill.
on the open market. The
The remaining 30 percent is
has to
to decide
decide on
on the
the internal
internal price
price of
of the
the sawn
sawn timber.
timber. Use
The management has
the
the conceptual framework
framework presented
presented in
in this
this chapter
chapter to
to discuss
disc u ss different
different
ways of pricing the
the internally
internally delivered
delivered sawn
sawn timber.
timber .
Hints;
flints:
The
total production
productio n of sawn
sawn timber
timber on
the open
The sawmill can sell its total
on the
open
From
a
principle
point
of
view,
it
market because demand
demand is
is high.
high .
princip l e point
view, it
is
for the
the planing
planing mill
mi l l to
to buy
buy sawn
sawn timber
t i mber from
from open
open
is also
also possible for
suppliers.
market suppliers.
- 15
15 __
-
2.7.2
(a)
Solutions
In scrutinizing the
or any
any other
other industry
industry -- one
one finds
In
the cost
cost structure of aa sawmill
sawmill -- or
finds
very few
few costs
costs that
that easily
easily and
and indisputably
indisputably can
can be
be classified as proportional,
proportional,
Losts are
are vari
variable,
but degree
degree of
of variability
variability ~s
is difficult
difficult
variab le costs.
costs. Either
iither costs
able, but
variable
to
assess,, or
to assess
o r they
they are
are fixed.
fixed~
of aa proportional,
proportional, variable
variable cost
cost is
is the
the sales commission paid
paid to
to an
One example of
agent. If
If the
the agent's
is the
the same
outside agent.
agent's commission
commission is
same regardless
regardless of
of how
how much
much he
he
sells,
total commission
commission cost
cost will
will grow
grow at
at aa constant
constant rate,
rate, when
when the
the sales
sales
sells, the total
increases.
volume increases.
In
uct calcu
la tio ns, the
the cost
is often
used as
In prod
product
calculations,
cost of
of raw materials
materials is
often used
as an
an example
example of
aa variable cost,
cost , but
but this
this cost
cost cannot
ca nnot be
be treated
treated as
as aa proportional,
proportional, variable
variable cost
cost
all circumstances.
c ircumstances . For sawmills raw materials
materials cost
in most
under all
cost should in
most cases
cases be
as aa progressive,
progressive, variable
variable cost.
cost. As
the
raw
material
accounts
for a
classified as
As the
for
considerable part
can be
part of
of the
the total
total cost of
of sawn
sawn timber,
timber, misjudging this
this cost
cost can
expensive . A
A typical
typica l cost curve
c urve for
for the
the sawmill's raw materials
is shown
extremely expensive.
materials is
in
2.8 below.
below.
in Exhibit 2.8
MU
A
A
B
c
Units
Exhibit 2.8
2.8 -- AA typical
typical log
l og cost
cost curve.
curve.
~
•
t his sawmill
sawmill has
has aa normal
norma l production
p ro duction of
of A~ units
units per
per year
year but
but aa total
total capacity
Assume this
If the
increase
of
C units. If
the demand should ~
ncrease during
during one
one year
year to
to C£ units,
units, it
it is
is
of C
tempting
to try to meet
the demand.
demand . However,
However, we
we will
will find
find that
that the
the unit
unit cost
cost of
of logs
logs
tempting to
meet the
us say
increases sharply.
sharply. Reasonable
Reasonable increases
in creases in
in relation
relation to
to normal activity,
activity, let
l et us
increases
up to
B units,
up
to ~
units, will
will perhaps
perhaps not
not change
c hange the
the unit
unit cost too
too much, but
but marginal
marginal
quantities always do.
do. The danger is
i s that
that we never
never discover
discover the
the increase
increase in log
costs. If we use average figures
figures for
for the
the whole
who le period,
period, small,
sma ll, high-priced
quantities will not
not be
be observed.
observed . There are no
no costs
costs in
in the
the sawmill
sawmill that
that differ
differ
usually found
found in
in other
other industries.
industries. As an
an example
example of
of an
an important
important cost
cost
from costs usually
There are many ways of
that
is often fixed,
fixed, let
let us
us take
take labour
labour costs.
costs. There
of paying
paying aa
that is
worker,
so we
we will
will consider
consider one
one of
of these:
th~~e:
aa fixed monthly wage.
wage. With a strong trade
trade
worker, so
uni
on, there
there are very few
few possibilities
possibilities of
o f modifying
modifying total
total labour
labour cost,
cost, e.g.
e.g. in
in
union,
short recession.
recession.
connection with aa short
-- 16
16 -
Decreasing
in many cases that
that the
the labour
labour force
force will
will be
be occupied
occupied
Decreasing sales means in
with repair and maintenance work and
labour costs
remain at
and labour
costs will
will remain
at the
the same
same level.
level.
The
the sawmill
sawmill industry
industry also means
that either
The process structure in the
means that
either everybody
everybody
works or they
works
they do
do not.
not. As
As compared to
to a mechanical workshop
workshop with
with 10
10 lathes,
lathes, the
the
situation is
is different.
different. It
is
possible
to
stop
two
lathes
and
temporarily
It is possible to
lathes
their operators. In
sawmill it
it is
is more difficult to
to cut down the
the
dismiss their
In aa sawmill
attivity
a certain
certa i n percentage,
percentage, even though it
it is
is possible,
possible, e.g.
e.g. by stopping
activity by a
the
one day
day aa week.
week. Labour costs in
in the
the sawmill
sawmill industry
industry
the whole
whole production one
tendency to
to remain
remain unchanged,
unchanged, when
when the
the activity
activity level
level of
of the
the company
company
have aa tendency
goes
short periods
periods of
of time.
time.
goes down during short
(b)
The
to be
be taken
taken in
in this
this kind
kind of
o f problem
problem is
is to
to find
find both
both traceable
traceable
The decision to
revenues
traceable expenses for
for all products sold.
sold. There are many
many
revenues and
and traceable
costs that
that the
the sawmill
sawmill incurs
incurs whether
whether it
it sells
sells its
its products
products or
or not.
not. In the
the shortterm planning,
planning, machinery, buildings,
buildings, forklift
forklift trucks
trucks and
and administration
administration are
are
examples
of costs that
that the
the sawmill
sawmill has
has under
under all
all circumstances.
circumstances. We
to
examples of
We refer to
such
costs, and
and we
we do
do not
not take
take them
them into
into consideration
consideration for
for
such COSlS
costs as common costs,
Single
calculation.
single product calculation.
For
industri es , such
such costs
costs as
as direct
direct labour
labour and
and raw
raw materials
materials can
can be
be
For other industries,
classified as traceable
tracea b l e costs.
costs. If
to stop
stop production for
for
If management
management chooses to
aa certain product,
product, these
these costs
costs will disappear.
disappear. Cost of labour
labour in
in aa sawmill
sawmill
cannot
th a t easily.
easily. If
cide not to
to produce certain dimensions,
dimenSions,
cannot be
be reduced that
If we
we de
decide
need all
all production
production operators
operators for
f o r the
the remaining
remaining products.
products. This cuts
we still need
out labour
labour costs
costs as
as aa traceable
traceable cost
cost for
for the
the sawmill
sawmill and
and turns
turns it
it into
into aa
common cost.
cost.
the raw
raw materials
materials cost
cost gives
gives aa similar
similar result.
result. Whatever
Scrutinizing the
dimensions
raw
dimensions - profitable or non-profitable
non-profitable - the sawmill
sawmill produces,
produces, the
the raw
materials cost will
will be
be approximately
approximately the
the same.
same. If smaller
smaller dimensions
dimensions like
like
19x100 turn
turn out
out to
to be
be unprofitable,
unprofitable, the
the sawmill
sawmill still
still has
has to
to buy
buy the
the
19x75 or 19x100
whole log
log in
in order
order to
to get
get hold
hold of
of the
the material
material for
for the
the profitable
profitable part
part of the
the
production. It
is impossible to
to buy exactly
exactly what is
is needed
needed for
for each
each and
and
It is
every single product
product (dimension).
(dimension). This turns
turns the
the raw
raw materials
materials cost
cost into
into aa
variable, common cost.
variable,
cost. The sawmill's situation
situation is
is not
not unique
unique but
but fairly
fairly
unusual.
industries facing
facing this
this situation,
situation, profitability
profitability assessment
assessment
For all industries
for
for single products is
is aa difficult
difficult problem.
problem.
(c)
There are
are many
many possibilities
possibilities of
of classifying
classifying "administrative
"administrative costs".
costs". In the
the
first
first place,
place, administrative
administrative costs
costs are
are fixed
fixed costs
costs within
~ithin the
the relevant
relevant range
range of
of
the whole company.
company. Secondly,
Secondly, these
these costs
costs should
should be
be classified
classified as
as common
common costs
costs
the
for
the sawmill
sawmill and
and the
the planing
planing mill.
mill. There are
are few,
few, if
if any
any possibilities
possibilities
for both the
will,
allocating these
these costs
costs between
between the
the two
two units.
units. But, of course,
course, the
the company
company Will,
of allocating
in its
its product calculation, allocate
;llocate these
these costs
costs to
to both
both units,
units, e.g.
e.g. in
in relation
relation
in
to
to their respective
respectiv~ sales
sales volume.
volume.
(d)
be made between
between an
an outlay
outlay cost
cost and an opportunity
In this problem a choice will be
cost in
in order to
to estimate the
the sacrifice
sacrifice made by
by the
the sawmill.
sawmill. After having
haVing
cost
concept, company
company management has
has to
to estimate
estimate the
the size of
of the
the
chosen the cost concept,
sacrifice.
Choosing an outlay cost means that
that the
the company estimates
estimates what expenses
expenses accrue
accrue
from producing one
one cubic
cubic metre
metre of
of sawn
sawn timber.
timber. The estimate will
will contain
contain cost
cost
of raw materials, labour
labour and
and aa number
number of
of indirect
indirect production
production costs.
costs .
_ 17
17 __
_
probably this
this outlay
outlay cost will also
also contain
contain capital
cap ital costs,
costs, e.g.
e.g. depreciadepreciaMost probably
tion
tio n costs.
costs.
Choosing the
means estimating
option, i.e.
i.e. the
the opportunity cost
cost concept,
concept, means
the other option,
-- 3
what the
the sawmill
sawmill has
has to
t o refrain
refrain from
from when
when delivering
delivering one
one m3
m of
of sawn
sawn timber
timber
Assume the
the following data to
to be
be valid
valid during
to
planing mill.
mill . Assume
during the
the period:
period:
to the planing
3
3
market price of sawn
sawn timber
timber
Open market
MU 900 per m
m
Sales commission,
commission, 46
Sales
4%
MU
36 per m3
m
cost from
from the
the
Transportation cost
sawmill to
to the
the customer
sawmill
MU
3
3
88 per m
m
cost (of
(of production and
and
Total cost
except sales
sales
administration, except
commission and transportation
transportation
commission
costs)
costs)
MU 700 per m
m
3
3
3
tse
Choosing
the outlay
sawmi ll unit
unit will
will fix
fix the
Choosing the
outlay cost
cost concept
concept means
means that
that te sawmill
the
m3.
internal
price of sawn timber
timber at MU 700
700 per
per m
internal price
Choosing the
the opportunity
opportunity cost
ncept (cf.the
( cE . the taxi-driver's
taxi-driver's problem in
in
cost co
concept
section 2.5)
2.5) gives rise
rise to
to the
the following
following calculations:
c alculations:
33
m
MU 900 per m
Marke t price
price of sawn
sawn timber
timber
Market
Le ss : Sales commission
commission
Less:
MU 36
36
Transportation
Tra n spo rtati on costs
costs MU
MU
cost
Opportunity cost
8
MU
3
m
44 per m3
3
MU 856 per m3
m
Ther
e is
is quite a difference
diffe rence between the
the internal
internal price,
price, as estimated
There
estimated in
in
two different
differ e nt ways.
way s . But if
if there
there is
is aa real
real market
market demand
demand for
for sawn
sawn
these two
timber, large
large enough
e nough to
to cover
cover the
the total
tota l production,
production, then
then the
the opportunity
opportunity
timber,
is the
the only way to
to estimate the
the real
real sacrifice
sacr ifice (cost)
(cost) made
cost concept is
made by
by
If, at
at the
the sawmill. If,
th e same
same time,
time, there
there are
are possibilities
possibilities for
for the
the planing
planing
the
mi l l to
to buy
buy whatever it
it needs of sawn
sawn timber
timber from
from outside
outside suppliers,
s uppliers, the
the
mill
in a correct
correct way.
way. If
direct the
planing
cost will direct
the planin
g mill manager in
opportunity cost
market at
at a
a lower
lower price than
t han the
the sawmill's
he
he can find
find sawn
sawn timber
timber in
in the
the open market
will benefit
benefit from
from buying
buying this
this timber.
timber.
opportunity cost,
c ost, the
the whole
whole company
company will
-- 20
20 --
Estimating the
the breakeven volume is
is of
of great
great importance.
importance . We define the
the company's
company ' s
breakeven volume
volume as
as the
the volume
volume needed
needed to
to cover
cover total
tota l expenses.
expenses. Let XX be
be the
the breakeven
breakeven
volume and let
let all
a ll other
ot her variables
variables take
take on
on the
the same
same values
values as
as before.
before. We then
then get:
get:
8X
(total
reve(total sales
sales revenues
nues at
at the
the breakb r eakeven volume)
vo lume)
=
=
3X
2400
3X++ 2400
at
(total expenses at
th
e
br
eakeven
volthe breakeven volum
e)
ume)
Solving
So lvin g for
for XX gives
gives us
us the
the breakeven
br e akeven volume
volume as:
as:
X = 480
480 units
units
X
The
int ersection between the
the sales
sa l es revenues
revenues and the
the total
tota l expenses
expenses is
is aa point
in the
t he
The intersection
point in
diagram called
cal l ed the
the breakeven point
point or
o r the
the zero
ze ro profit
profit point,
point, and
and the
the breakeven
breakeven vo
l um e
volume
always corresponds
cor r esponds directly
directly to
to this
this point.
po int.
The
importance of the
the breakeven
breakeve n volume
volume is
is obvious,
obv i o us , as
as this
this is
i s the
t he lowest
l owes t acceptable
acceptable
The importance
As
is shown in
in the
the lower
l ower half
half of
of Exhibit
Exhibit 3.1,
3 . 1, the
t he company
company runs
runs at
at aa net
net loss
loss to
to
volume.
As is
the
left of the
the breakeven
brea keve n volume.
volume. To
the right
right ooff this
this volume,
volume, the
th e company's
co mpany's net
net income
income
the left
To the
starts growing.
g r ow ing .
3.3
Breakeven assumptions
In some
some textbooks
textbooks the
the breakeven
breakeven chart
chart is
is presented
presented in
in the
the same
sa me way
way as
as in
in the
the previous
previous
In
section
section..
There are,
are, however,
however, aa number
number of
of assumptions
assumptions that
that underlie
und er li e the
the breakeven
breakeven chart.
c hart .
First of
First
of all,
all, there
t he re is
is aa dispute
dispute about
about linearity
linearity versus
versus non-linearity.
non-linearity. In Exhibit
Exhibit
3.1
3.1 both the
the unit
unit price
price of
or the
the product
prod uct and
and the
the variable
variable expenses
expenses were
were supposed
supposed to
to increase
in creas e
proportionally.
However, for
However,
for the
the majority
majority of
of business
bu si ness companies,
companies, the
t he sum
sum of
of variable
variable costs
costs
(or
expenses) will
(or expenses)
wi ll include
include components
compo n ents growing
g rowing progressively
prog r essive ly and/or
and/or degressively.
degressively . The more
such components
compo nents are
are included
included and
and the
the higher
higher the
t he values
val ues of
o f these
these components
comp one nt s are,
are, the
the less
l ess
aaccurate
cc urate the
the breakeven
breakeven study
study becomes.
becomes .
c ha rt as presented
presented in
in Exhibit
Exhibit 3.1 covers the
the whole range
range from zero
zero
The breakeven chart
to 900
900 units.
uni ts . For
Fo r reasonably
r easona bly short
short periods
per i ods of
of time
time some
some fixed
fixed costs
costs might
might remain
remain fixed,
fixed,
even with considerable
co n s idera bl e changes
c han ges in
in volume,
volume, but
but over
over the
the whole
whole range
range we
we will get
get aa number
number
of step-fixed costs
of
costs that
that will
will change
c ha nge the
the fixed
fixed cost
cost curve.
c urve . Over the
t he whole
who l e range
range also
also rhe
t he
sales revenues and the
the variable
va ria ble expenses
expe n ses will
will look
l oo k different.
different . In order to
to simplify,
simplify, when
when
wide range
customary to cut
aa wide
range of volume is
is studied,
studied, it
it is
i s customary
c ut off
off a part of
o f the
the chart along
along
the
This
the volume
vo lume axis.
axis . Th
i s part
part is
is called
ca ll ed the
the relevant
rele va n t range.
range. (Cf.
(Cf. Section 2.2,
2.2, supervisory
supervisory
salaries
sa
larie s in
in Exhibit
Exhibit 2.4).
2.4) . The narrower
narr owe r the
the relevant
r elevant range
range is
is made,
made, the
the more
more trustworthy
trustworthy -aall
ll other
ot her things
t h ings being
being equale qual- the
the analysis
ana l ysis will
wi ll become.
bec ome.
There are also
a l so other
ot her assumptions
ass ump t i ons behind
behind the
the breakeven
breakeven chart.
chart. Volume is
is considered
considered
the company might
might
to
to be
be the
the one and only
on l y independent
independent variable,
variable, but the
the cost efficiency
efficiency of the
vary
with
other
factors
also.
vary
factors also. Different production
product i on methods,
methods, variations
vari ations in
in work
work hours,
hours,
fluctuations
fluctuations in
in sales and production during
during the
the year and so
so on are all
a ll examples
example~ of
possible cost
cost influencers
in fluence rs that
that are
are usually
usually not
not considered
considered in
in the
the breakeven
br ea keven analysis.
analysis!
3.4
3.4
Breakeven
Breakeven analyses
ana ly ses and step-fixed
ste p-fixe d costs
In Exhibit 3.2
3 .2 fixed
fixed and
a nd variable
variab l e expenses
expenses of
of the
the company
company have
have been
been plotted
p l otted for
for the
the
In
whole
whole volume
volume range.
range. We
We assume that
that the
the volume
vo lume interval
in terva l from
from AA to
to BB can
ca n be considered
co nsider e d the
the
- 2121 -
relevant range.
In deciding
deciding on
we have
relevant
range . In
on range
range limits
limi ts we
have considered
consi dered production capacity,
capacity, market
demands,
the smalle
s t volume that
that can
be accepted
accep ted without
without reducing the
the present
present labour
Labour force
demands, the
smallest
can be
and so
so on.
on.
MU
1111111111111
OMNI
I
I
A
A
=
= variable
expenses in
in the
the relevant
relevant range
expenses
range
=
= step-fixed
expenses
B
Units
Units
Exhibit
3.2
Exhibit 3.
2 The
Th e breakeven chart
chart for
for the
the relevant
relevant range
range from
from AA to
to BB
The relevant
The
re l evant range
range as
as in
in Exhibit
Exhibit 3.3
3 . 3 shows
shows aa rather
rather complicated
compl i cate d cost
cost structure.
st ructure.
Most of the
the so-called
so-calLed "fixed
I1fixed expenses"
expe nses" often
often turn
turn out
o u t to
to be
be step-fixed.
step-fixe d.
For
limited
For limited
relevant
rel
evant ranges
rang es and during short periods of time,
time, there
there are
are always
always some
some indisputably
indisputably fixed
fixed
eexpenses.
xpen ses. Administrative salaries
sal aries and depreciations
depreciations can
ca n serve
serve as
as examples
e xamples of
of such
such fixed
fixed
expenses.
Although
we choose
choose to study a limired
Al t hough we
limited volume
volume range,
range , we end
end up
up in
in aa fairly
fairly complicated
complicated
situation
situatio
n due
due to
to the
the step-fixed nature of the
the fixed
fixed costs.
costs. Showing revenues
revenues and
and expenses
expenses
in
in aa graph
gra ph is
is not
no t a practical
prac tica l way
way of
o f solving
solvi ng problems.
problems. There is
is aa need
need for
for aa simple,
simple,
mathematical
mathematical model
model that
t hat also
also covers
covers the
the srep-fixed
ste p-fixed functions.
functio n s . Consider
Co nsider the
t he following
following
example:
example :
--22
22 -_
/
MU
MU
I
I
I
o
Total expenses
Total
expenses
~
~I
~
Step-fixed
expenses
Step-fixed expenses
i
I
I
I
•
,I
I
I
,..:....J
I
I
,I
,•
Io
Totally
fixed expenses
·expenses
Totally fixed
a
6
,--- - - -
-
------------- --- -----
~4,~1~--------------------------A
B
Exhibit 3.3
3.3
Cost specification
seeciEication
Cost
relevant range
range
The relevant
range, units
units
Volume range,
Expenses
Exeenses in
in MU
MU
costs
Production costs
o0 -- 100000
100001 --
60000
60000
90000
Advertising
0
80000
o -- 80000
80001
80001 -- 140000
140001 --
0
25000
25000
35000
adminis Selling and administrative costs
costs
trative
the whole
Over the
volume range
range
40000
40000
-23
The cost
cost figures
The
figures given
given for
for this
this example
example can
can be
be explained
explained in
in the
the following
fo ll owing way.
way.
Costs
(machine operators'
operators' wages,
depreciation, etc.)
to MU
Costs of
of production (machine
wages, depreciation,
etc.) amount
amount ro
MU 60
60 000,
production of
of 100
100 000
000 units.
units . Increased production above 100
100 000
000 units
units is
is
allowing aa production
foll owed by
by a cost
cost. increase
increase of
of MU
MU 30
30 000,
000, totalling
totalling MU
MU 90
90 000.
000. The
pacity
followed
The production
production ca
capacity
will then
then exceed the
the most
most optimistic
optimistic forecasts
forecasts of
of company
company demand,
demand, which will then
then become
become
bottleneck.
a bottleneck.
It has
has been
been considered necessary to
It
to support personal
personal selling by advertising.
advertising.
Experience shows
shows that
that the
the company
company can
can sell
se ll up
up to
to 80
80 000
000 units
units without extra support.
support.
Advert.ising for
for MU
MU 25
25 000
000 will
will increase
increase the
the quantity
quantity sold
sold up
up to
to 140
140 000
000 units.
units . Above
Advertising
that
MU 35
35 000
000 are
are needed
needed to
to stimulate
stimulate demand.
demand .
chat volume another MU
Selling and
a nd administrative costs
costs amount
amount to
to MU
MU 40
40 000.
000.
fixed
for varying production
production volumes.
volumes.
fixed for
The
se costs are totally
t.otal ly
These
It
It is
is assumed that
that both
both sales
sa les revenues
revenues and variable
variable expenses
expense s are
are proportional
proportional to
the
The following
following estimates
estimates have
have been
been made.
made.
che volume.
The
Sales revenues
revenues
Variable expenses
expenses
margin
Contribution margin
MU 2.00 per unit
unit.
MU 0.70 per unir
unit
MU
unit
MU 1.30 per unit
In
unit wi
ll cont
ribu te MU
MU 1.30
1. 30 to
to cover
cover fixed
fixed expenses.
expen ses . This
In other
other words
words,, each
each unit
will
contribute
unit contribution will remain
remain unchanged
unchanged regardless
regardless of
of how
how many
many products
products the
the company
company sells.
sells.
unit
problem has
has been
been shown
shown graphically
graphically in
in Exhibit
Exhibit 3.4.
3.4. In
this example we have
have
The problem
In this
from picking
pi cki ng out
out aa relevant
relevant range.
range. Instead we study
study the
the whole range
range with
with the
the
refrained from
choosing aa relevant
relevant range
range later.
later. From
From the
the graph
graph we can
ca n see
see what
what might
might be
be called
aim of choosing
the
dilemma. Due to
to the
the stepfixed
step-fixed nature
nature of
of some
some of
of the
the company's
company's
the decision-maker's
decisionmaker's dilemma.
costs, the
t he sales
sales revenue
revenue function
function intersects
int ers ect s with
with the
the total
tota l expenses
expenses function
function repeatedly
repeatedly
costs,
giving " rise
rise not to
to one
one but
but a series
series of
of breakeven
breakeven volumes.
volumes. If
If we
we are
are in the
the net
net income
income
advertising for
another MU 35 000 means
means that
No.33 (NIA/3),
(N IA /3), advertising
for another
that the
the increase
inc rease in
in sales
sales
area No.
be large
lar ge enough
enough to
to cover
cover not
not only
only breakeven
breakeven volume
volume No.
No. 44 (BEV/4)
(BEV/4) but
but also
also exceed
volume must be
However, if
the profit gained
gai ned in
in NIA/3.
NIA/3. However,
if the
the new sales
sales volume just
just barely passes
pa sses 140 000
units, che
the decision to
to increase
increase advertising
advertising might
might throw
t h row the
the company
company from
from aa net
net income
income area
area
units,
into
a net
ne t loss
loss area
area - in
this case
from NIA/3
NIA/3 into
into NLA/4.
NLA/4 . In
In fact,
fact, every expansion in
in aa
into a
in this
case from
involves such
s uch aa risk.
risk.
company involves
in which we can
can use
use the
the breakeven
breakeven analysis.
analysis.
There are many ways in
To give a few
man y questions.
questions. To
few examples:
examples:
answering many
The model helps in
in
The
1.
How profitable is
is the
t.he company's
company 's present
present performance?
performance?
2.
What
happens co
to profit,
pr ofit , if
i f another machine is
is purchased
purchased in
in order
o rder to
to expand
e xpand
What happens
production volume?
volume?
3.
Can company profitability be enhanced
enhanced by
by aa change
change - upwards or downwards
downwards (!)
(!) in sales
sales volume?
volume? If
If so,
so, which of
of the
the two
two possibilities
possibilities is
is the
the more profitable?
profitable?
in
As was
was pointed out earlier,
The
tool, though,
th ough , is
is too
too awkward.
awkward. As
ear lier, there
there is
is
The graphical
graphical tool,
aa need for
for a simple mathematical model.
model. As long
long as
as both
both revenues
revenues and
and variable
variab l e expenses
expenses
are
proportional to
expenses create
create aa calculating
calculating
are proportional
ro volume
volume changes,
changes, only
only the
the step-fixed
stepfixed expenses
All that is needed is
problem. These
expe nse s, however,
however, can
can easily
easily be
be dealt
dealt with.
with. All
is an
an
These expenses,
problem.
First we
we calculate fixed expenses
of the
the fixed
fixed expenses
expenses for
fo r all
all possible
possible volumes.
volumes. First
estimate of
for
for different volumes.
vo lumes .
- 24 -
,o''"'>Oos_ _ ______ _ _, /
Sales revenues
MU
NIA/4 ----~:;~~~- !T~o~t:
a:;l~Sos
expenses
Total
NIA/4
NLA/4 - - -_ _~"
NLA/4
NIA/3
NIAI'
-----L
NLA/3
r_FT7
NIA/2
Selling and
and
administr a administrative expenzes
ext-'en !:('s
tive
NLA/2.
NIA/1
,A
.' .
NLA/1
Adverti.si n,;
Advertisind
expenses
>:.-'"
<,
-; "
Expenses
Expenses of
of
product
production
ion
~ ..
,~
~ <~
'.
Units in
in 1000
la O":
Units
140
100
100
BEVil
BEVI'
BEV/2
BEV/2
L~=k~~~ BEV/3
BEV/4
BEV/l
BEV/I
Exhibit 3.4
Vol,
Vol. range
range
No.
No.
--
11
The breakeven chart
The
chart with
with step-fixed
ste p-fixed expenses
expenses
Range
in units
units
Range in
--
80000
Fixed expenses
expenses
in preceding
in
range
o0
1Incremental
nc rementa 1
expenses in
in
present range
range
Total
-expenses
for
for diffediffe rent ranges
rent
ranges
+
+ 60000
40000
=
=
100000
22
80001
80001 -- 100000
100000
+
+ 25000
=
125000
33
100001 -- 140000
100001
125000
125000
+ 30000
+
=
=
155000
44
140001 --
155000
155000
++ 35000
=
190000
Having
this cost
structure, we can estimate the
the different breakeven
breakeven volumes.
volumes.
Having this
cost structure,
migh t be
be aa breakeven
breakeven volume
volume in
in each
each volume
volume range.
range. From Exhibit 3.4 we know
know that
that
This might
in
this example each
eac h range
range has
has its
its own
own breakeven
breakeven volume.
volume.
If
the breakeven
in this
If we
we denote
denote the
o f the
the i:th
~:th range
ran ge with
with BEV/i,
BEV!i, we
we find
find these
these volumes
volumes by
by equalizing
equalizing total
total revenues
revenues
volume of
with total
total expenses.
expenses . Using the
the contribution margin,
margin, i.e.
i.e. unit
unit revenue
revenue minus unit
unit variable
variable
expenses,
expenses, we get:
get:
(2.00
(2.00
(2.00
(2.00
-
0.70)
0.70)
0.70)
0.70)
0.70)
0.70)
0.70)
0.70)
(BEV/1) -- 100 000 = 0
o
(BEV/2) -- 125 000 = o
0
(BEV/3)
(BEV/3) - 155 000 = 0
o
(1)
(BEV/4) -- 190 000 = 0
o
(BEV/4)
(4)
(4)
(2)
(3
(3))
--25
25 -
Solving (1)
(1) through
through (4)
(4) we
we find
find the
the respective
respective breakeven
breakeven volumes
volumes as:
as:
BEV/1
BEV/l
BEV/2
BEV/2
BEV/3
BEV/3
BEV/4
BEV/4
76
76
96
96
. 119
= 146
=
.
923
923
154
231
231
154
units
units
units
units
units
units
Let us
us also find
find out
out how
how large
large aa volume
volume is
is needed
needed to
to get
get aa profit
profit of
of at
at least
least
Let
MU 15
15 000.
000. The
on ly way to
to solve
solve this
t.his problem
problem is
is to
to study
study each
each volume
volume range
range separately.
separately.
The only
If
eded to
to get
the desired
profit from
from volume
If we
we denote
denote the
the volume
volume ne
needed
get the
desired profit
volume range
range ii by
by ~i'
X., we
we
-1
get
the following
following expression:
expression:
get the
(2.00 - 070) .
Xi
~l
15 000
-- 100 000 = 15
(5)
(5)
This
in words
words means:
means: The
times the
the volume
volume reduced
reduced by
This stated in
The contribution margin times
by
fixed expenses
expenses gives a profit
fixed
prof it of
of MU
MU 15
15 000.
000. Solving (5)
(5) gives
gives X1
~l == 88
88 462
462 units.
units. But
But the
first
range covers only
onl y up
up to
to 80
80 000
000 units.
units. Thereaft
e r, Yixed
take on
on aa
first volume
volume range
Thereafter,
Fixed expenses take
higher value. This means that
that it
it is
such aa high
high profit
pr of it within
within the
the first
first
is impossible to get such
volume range.
range. Instead,
to try
try with volume
volume range
range 2.
2. Denoting the
the needed
needed volume
volume
Instead, we
we have to
by
the fixed
fixed expenses
expenses value
value gives:
gives:
by ~2
X2 and changing the
(2.00 -- 0.70) • ~2
(2.00
- 125 000 = 15
15 000
000
X- -
(6)
(6)
Solving (6)
(6) gives X2
~2 =
= 107
107 692
692 units.
units. Once
again, we get an
an answer
answer outside
ou tsid e the
the volume
volume
Once again,
range for
range
for which the-fixed
t.he-fixed expenses
expenses are
are valid.
valid. Thus,
Thus, we have
have ro
t.o climb
c limb one
step further
further on
one step
the volume
volume axis,
axis, finding
X3 -- that
without Violating
violating
the
finding volume
volume -- ~3
that gives
gives the
the desired profit without
the
constraints.
the co
nstraints.
(2.00 -- 0.70)
0.70)
~3 --
-X-1
15 000
155 000 = 15
155
(7)
(7)
Solving
So lving (7)
(7) gives
gives X3
~3 == 130
130 769
769 units.
units.
3.5
Breakeven analyses and
and linearity
linearity changes
changes
So far
far we
we have considered sales
sales revenues
revenues and
and variable
variab l e expenses
expenses as
as strictly
strictly proporprop o rtional. In
In practice
pract.ice this
this assumption
assumption often
often makes
makes the
t.he problem
problem roo
too simplified.
simplified. Both may
may
change with changed
c hanged volumes.
volumes. As long
l ong aswe
get aa contribution
contribution margin
margin that
that is
is positive,
pOSitive,
aswe get
increased sales volumes
increased
vo lumes should
should improve
impr ove company
company profit.
profit. However,
pitfalls.
However, there are many pitfalls.
We will study two
two of them.
them.
Usually sales revenues
revenues sooner
sooner or
o r later
lat e r start
start growing
growing degressively
degressively and
and variable
expenses
expe nses start taking
taking on
on . aa progressive
progressive increase.
increase. It
It is
i s always
always possible to
to increase
increase sales
sales
by
prices. When sales
sales volume
volume increases,
increases, production
production volume
volume must
must follow.
follow. However,
by lowering prices.
an expansion
expansion will
will most probably create
an
create increases
increases in
in variable
variab l e expenses.
expenses. Labour costs might
change, costs
change,
costs of
of raw
raw materials may show
show aa progressive
progressive increase,
increase, transportation
transportation costs
costs may
increase as
as aa result of
increase
of higher
higher volume
volume and
and so
so on.
on. The effect
effect of
of expansive
expansive thinking
thinking
might be
might
be an increased
increased sales
sales volume
volume but
but with
with reduced
reduced profit.
profit. The
The economists
economists usually
usually
describe
this
as
shown
in
Exhibit
3.5.
describe this as
in Exhibit 3.5.
At
At first,
first, total
total revenues
revenues increase
increase more
mor e than
than total
total expenses
expenses do.
do. But
But soon
soon the
the
reversed process occurs.
occurs. The
The increase
increas e in
in revenues
revenues is
is reduced
reduced and
and the
the expenses are further
further
increased. This gives us
us two
two intersection
intersection points
points and,
and, thereby,
thereby, two
two breakeven
breakeven volumes.
volumes.
As long
As
long as
as production volume is
is to
to the
the left
left of
of BEV/L,
BEVIL, the
the company
company must
must strive
strive for
for increased
increased
production.
production. Obviously,
Obviously, optimal
optimal production
production volume
volume is
is where
where the
the distance
distance between
between the
t he sales
sales
-- 26 --
rrevenues
evenues and the
t h e total
total expenses functions
functions is
is as
as large
large as
as possible.
possible.
Every deviation - in
in
either direction -- from
from this
this volume
volume creates
creates aa lower
l ower profit.
profit. This volume,
volume, therefore,
therefore, is
is
cal
led the optimal
optimal production volume.
volume.
Increasing
sales) means that
that sooner
soone r
called
Increasing production
production (and sales)
will pass
or
a new breakeven
breakeven volume
vo lume -- BEV/U
BEV/U -- to
to the
the right
right of
of which
which is
is
or later the company will
pass a
net loss
aa net
1055 area.
area.
MU
Total
Total revenues
I
Total expenses
I
~
Optimal profit
BEV/L
Exhibit 3.5
3.5
Op
tima l
Optimal
producproduction
vo lume
volume
BEV/U
Units
economists breakeven
breakeven chart
c h a rt
The economists
In
In practice we do
do not
not believe
believe that
that we
we will
wil l find
find the
the optimal
optimal production
production volume.
vol ume.
The
The model,
model, however,
however, reflects
reflects reality
reality and,
and, thereby,
thereby , also
a ls o has
has aa certain
certain value.
value. The manager
manager
should realize
realize that
that he
he cannot
cannot expect
expect the
the same
same proportional
proportional change
c hange in
in revenues
revenues and
a nd expenses.
expenses .
However, there are no simple
However,
simple tools
tools that
that can
can help
help us
us analyse
analyse the
the change
change fn
i"n profitability
profit abil ity
that various decisions give
that
give rise
rise to.
to. For
For a
a running company
co mp any changes
c hanges in
in these
these functions
functions are
interactions of hundreds
hundreds of
of more
more or
or less
l ess important
important single
s ingle decisions.
decisions.
the relevant
relevant volume
vo lume range
range the
the business
business manager
manager might
might find
find at
at least
leas t approximate
approximate
Within the
shapes of
of his
his various
various functions.
functions. Perhaps his
his revenues
revenues and
and expenses
expenses will
wi ll not
not take
take on
on the
the
smoothed curveshape
curve shape of
of the
the economist's
economist IS breakeven
breakeven chart.
chart. The manager will rather
rather find
find
that
that the slopes
slopes change
cha nge frequently
frequently as
as is
is shown
shown in
in Exhibit
Exhibit 3.6.
3 . 6. Due
to the
the difficulty
difficul ty in
in
Due to
finding relevant
relevant data,
data, he will be
be forced
forced to
to accept
accept approximate
a pproximate estimations
estimations of
of revenues
revenues
and
a ll -- expenses.
expenses . Many managers consider
conSider"their
their cost
cost calciilaEion
ca l cu l ation very
very difficult,
difficult ,
and -- above all
but
it is
is better to
to use a rough
rough estimate
estimate than
than to
to refrain
refra in from
from even
even trying.
trying.
but it
-- 27
27 --
MU
Slope changes
changes in
in the
the total
total
revenues
-:;:'7-
Slope changes in the total
S lope chlia:n:g~e~st~~~:"'::~~__
expenses
expenses.
o
i
i
I
B
A
Units
Exhibit
Exhibit 3.6
The business
business manager's
manager'sbreakeven
The
breakeve n chart
chart
-- 2828-
4.
4.
4.1
4.1
BUDGETING IN
IN SAWMILLS
SAWMILLS
and budgetary
budgetary control
control
Budgets and
A budget
can be
defined as
as aa quantified
of classifying
class ifying aa budget.
budget. A
budget can
be defined
There are many ways of
compilation
com
pilation of
of the
the company's
company 1 s planned
planned actions
actions for
for the
the budget
budget period.
peri od. For every budget
budget
period, there
there are
are usually
usually aa number
number of
of plans
plans about
about whar
what to
to produce
produce in
in what
what quantities
quantities and
and
period,
for
staff needed and with what
what qualifications.
qualifications. The
rall aim of
of the
the
for what
what markets,
markets, staff
The ove
overall
budget is
is to
to quantify
quantify such
such plans,
plans, to
to compile
compile all
all estimations
estimations made
made and
and to
to control
control the
the
budget
feasibility
different plans.
plans . The
result of
of these
these activities
activities will
will be
be aa master
master budget.
budget.
feasibility of different
The result
A master budget
budget will consist
consist of
of aa series
series of
of sub-budgets.
sub-budgets. AA simple,
simple, annual
annual budgeting
budge ti ng
A
is shown
shown in
in Exhibit
Exhibit 4.1.
4.1 . Th~
point of
the work is
is to
to forecast
forecast the
the demand
demand
system is
The starting point
of the
ffor
or the year.
year. Estimated
Estima ted sales figures
figures will
will show
show how much the
the company needs co
to produce,
produce ,
which
in its
its turn
turn decides
de c ides labour
lab our and
and staff
staff needs.
needs. The
The compilation of
of sub-budgets
sub- budgets into
into aa
which in
master budget
budget is
is aa rather
rather tedious
tedious co-ordination
co-ordination task.
task.
1__J
1-------- -I
..
I
---I Co-or d lnatl on bebe---_,Co-ordination
I
Il
I
I
'
tween subun
subunits
I tween
i ts
I__
~---------
i
1__ _
...J
I
,
,
I
I
I
1
ISales Budget
IL-_~_---II
1
Sales Budget
I
Production Budget
Budget
I
Labour
Labour and Staff Budget F._
I
Budget
Financial Budget
~
r
4. 1
Exhibit 4.1
I
-
Company
Master
Budget
I-
Example
of a
a simple,
simp le, annual
annual budgetary
budgetary system
syst em
Example of
The budget is
is an important
important tool
too l in
in running
running the
the company.
company.
The
some important
important aspects
aspects of
of budgeting.
budgeting.
summarizes some
following quotation
quotation
The following
Budgets
formulate expected performance;
performance; they
they express managerial
Budgets formulate
targets
.
Without
targets,
lack direction,
direction, problems
prob l ems
Without
such
targets,
operations
lack
targets.
are not
not foreseen,
are
foreseen, results lack
lack meaning,
meaning, and the
the implications
implicati ons for
for
future policies are
are dwarfed
dwarfed by
by the
the pressure
pressure of
of the
the present.
present. The
The
future
planning
planning role
role of
of all
all levels
levels of management should
should be
be accentuated
accen tuate d
and
budgetary ,system.
will be
be compelled
comp e lled to
to
and enlarged by aa budgetary
system. Managers will
This forced
llook
ook ahead
ready for
for changing
changing conditions.
conditions. This
ahead and
and will
will be ready
i s by
by far
far the
the greatest
greatest contribution
contribu ti on of
of budgeting
budgeting to
to managemanageplanning is
(Horngren,
(Horngren, Charles
Char l es T.,
T., ed.
ed . Cost
Cost Accounting.
Accounting . A
A Managerial
Managerial
ment.
Emphasis,
editions, Englewood
Englewood Cliffs,
Cliffs,
Emphasis, Prentice/Hall
Prentice/Hall International editions,
N.J
•• 1982).
1982).
N.J.,
-- 29
29--
44.2
.2
sales revenues
revenues
Budgeting sales
4.2
.1
4.2.1
overall problem
problem
The overall
sales revenues
revenues ar
at least
lea st three
three aspects
aspects should
should be
be considered:
co nsidered:
When budgeting sales
1.
The price-setting
price-setting system.
system.
2.
demand for
for various
various products.
products.
Market demand
3.
Possible prices that
Possible
that can
can be
be achieved.
achieved.
The price
pri ce serting
setting system
system can,
ca n, roughly
roughly speaking,
speaking, be
be of
of two
two kinds.
kinds. Either the
the sawsawThe
mill
in an environment
environment where
where price
price setting
setting is
is completely
comp let ely free
free or
or in
in some
some kind
kind of
of
mill works in
price regulation
regulati on system.
system.
should be
be set
set in
in such
such aa way
way that
that the
the sawmill
sawmi ll will
will maximize
maximize its
its profit.
profi t.
Prices should
We
longer believe
believe in
in finding
finding an
an optimal
optimal price,
price, but,
but, of
of course,
course, we
we should
should pay
pay
We no longer
attention to revenues
revenues and
and expenses
expenses in
in aa way
way that
that improves
improves the
the situation.
situation.
In
In trying
trying to
create as
as large
large aa profit
pr ofit as
as possible,
possible, we
we should
should be
be aware
aware of
of two
two common
common mistakes.
mistakes .
Firstly, sales
sales volumes
volumes or
or sale
sale revenues
revenues as
as yardsticks
yardsticks for
for performance
performance cannot
ca nno t be
be
Firstly,
for profit
profit measurements.
measurements. A
l ook at Exhibit
Exhibit 3.5
3.5 proves
proves the
the statement.
statement. At
At
substituted for
A look
and sales
sales revenues
revenues are
are higher
higher than
than at
at the
the optimum
optimum volume,
volume, but
but
BEV/U both sales volume and
the company's profit
profit is
is lower.
l ower. True,
neve r be able
a ble to
to plot
pl ot down
down this
this curve for
for
the
True, we will never
our
ll, but the
the model still
still reflects
reflects reality.
reality.
our sawmi
sawmill,
Secondly, we must stop
stop believing
believing in
in cost
cost calculations
ca lculati ons as
as price-setting
price-setting tools.
tools. The
Secondly,
customer does
not
ask
for
the
supplier's
costs.
does not ask for the supp li er's costs . The
interest of
r
The one
one and
and only
only interest
of the
the custome
customer
is how competitive the
the supplier's
supplier's price
price is.
is. All
is
All other
ot her things
things being
being equal,
equal, the
the customer,
c ust omer,
in
ng between
sup pli ers, buys
buys the
the one
one that
that is
is cheapest!
cheapest!
in chOOSi
choosing
between products
products from different suppliers,
The
ta ken here is,
i s, therefore,
therefore, that
that the
the aim
ai m of
of product
product calculations
calcu l ations is
is not
not to
to get
get aa
The view taken
basis for
for product
product pricing.
pricing. Instead
Instead the
the reversed
reversed process
process should
should be
beemphasized;
emp haSized; the
the primary
p r imary
the product
product and
and then
then study
study whether
whether the
the product
product is
is profitable
profitable or
or not.
not.
task is to price the
4.2 .2
4.2.2
Forecasting procedures and techniques
Forecasting
techniques
If a manager is
is free
free to
to determine
determine product
product prices,
prices, he
he must
must consider
consider market
market prices
prices as
as
lf
The
prices
customers
are
willing
to
pay
depend,
inter
alia,
on
such
the
starting
point.
c
ust
omers
are
willing
to
pay
dep
end
,
inte
r
alia,
such
the
point.
factors as:
as:
1.
The overall competitive situation
situation in
in different
different markets.
mar ket s.
The
2.
The
The company's own
own offerings
offerings -- quality
quality and
and special
special features
features of
of its
its products,
products,
terms
ter ms of credit and
and so
so forth.
forth.
terms of
of delivery,
delivery, terms
3.
Pri ce sensitivity
sensitivity of
of customers.
c ustomers.
Price
these and
and similar
similar factors
fact o rs is
is always
always important
important in
in pricing.
pricing. Depending on
on
Judging these
prices chosen
~hose n we will
will get
g~t different sales
sales volumes
volumes and,
and, thereby,
thereby, variations
variations in
in company
prices
company
costs.
job is
is to
to try
try to
to find
find prices
pri ces that
that will
will give
give an
an expected
expected profit
profit that
that is
is as
as
costs. Our job
- and
high as possible.
pos sible. The
The interaction between
be twee n prices
prices"":
and their
their effects
effects on
on sales
sales volumes
volumes and
careful l y analyzed.
analyzed.
and costs
costs must
must be carefully
- 303 0
When
a forecasting
forecasting technique.
technique.
When studying market
market demand we need a
One
of the
the
One or more of
following techniques
techniques can
ca n then
then be
be used.
used.
1.
Sales
stafE judgements
judgements
Sales staff
the knowledge of
of the
the company's
company 's own
Using the
own sales
sales staff
staff is
i s perhaps the
the most common
common
technique
in sales
sales forecasting.
forecasting.
technique used in
Company salesmen
salesmen are
are familiar
familiar with
with both
customer wishes
wishes and
and the
the company's
company's own
own product
product assortment.
assortment.
2.
Internal
expert judgements
judgements
Internal and/or external expert
This
way of
of forecasting
forecasting means using
using knowledge
knowledge both
both inside
inside and outside
o ut side the
the
This way
company.
Company
the sales
sales staff
staff might
might have
have other
other views
views
Company executives outside the
than
the sales manager.
manager. It
uabl e to
i ons from
than the
It might
might also
also be
be val
valuable
to get
get expert
expert opin
opinions
from
i n various
various trade
trade and
and industry
industry associations.
associations.
people in
3.
Statistical demand
demand analysis
analysis
Statistical
from relatively
relatively simple
simple trend
tre nd analyses to
to aa variety
Statistical approaches vary from
of cause-effect
causeeffect studies.
of
studies. These
ll y part
These techniques
techniques are
are usua
usually
part of
of the
the forecasting
forecasting
procedures of large
large companies.
companies.
4.3
The sales
sales revenues
revenues of the
the sawmill
sawmil l
The
The
produce of
of the
the sawmill
sawmill can be
be studied
studied in
in different
d i fferent ways.
ways. One
is to
to consider,
conSider,
The produce
One is
for each
species, the
the output as
as one,
one, single
Single product
product - sawn
timber - plus
plus two
two by-products
for
each species,
sawn timber
byproducts
- chips or
or slabs
slabs and
and sawdust.
sawdust. Another
Another way
way is
is to
to consider the
the output as
as an assortment
assortment of
products.
produ
cts. In
In that
that case
quality, dimensions,
dimensions, and lengths
lengths are put in
in to
to split
split up
up the
the
case,, quality,
assortment into
assortment
into a
a number of individual
individual products.
products. For a sawmill
sawmill sawing
sawing 33 species
s pecies of
of wood
wood
in
different dimensions,
in 20
20 different
dimensions, 15
1 5 various
various lengths,
leng t hs, and
and 77 separable
separab l e qualities,
qua li ties, the
the total
total number
number
of products will
wi ll amount
amount to
to 66 300.
300. The
The addition of the
the tWo
two byProduCts.does,
by- products 'does, in
in this
this case,
case,
not in.crease
the compl
complexity
in.crease the
ex ity very much.
A
A look
look at how
how sawmills
sawmills budget
budget sales
sales revenues
revenues and
and expenses
expenses indicates
indicates that
that the
the first
first
method is
is the
the most frequently
frequently used.
used. One
finds, especially for
for small
small sawmills,
sawmil l s, that
that
One often finds,
one
one single
Single average estimation
est imat ion is
is used
used for
for both
both revenues
revenues and
and expenses.
expenses.
The opposite way,
way, considering
considering all
all possible
possible products,
products, is
is not
not feasible.
feasible. Most often
The
few combinations oE
of dimension
dimension and
and quality,
quality, all
all having
having the
the same
same sales
sales price
price per
per m3
m3
only a few
for all
all lengths
for
lengths are used.
used. To budget sales
sa l es revenues for
for all
all possible
pOSSible combinations
combinat i ons would
mean considerable extra work but
but with little
little or
or no
no information
information of
of value.
value. At
At the
the same
same
time, aa simple,
simple, overall
overall average figure
time,
figure does
does not
not suffice.
suffice. Therefore,
Therefore, we have
ha ve to
to find
find aa
compromise taking
taking the
the following
following aspects
aspects into
in to consideration:
considerat i on:
1.
The
of added information
information should
should exceed
exceed the
the extra cost
cost of
of data
data collection.
collection.
The value
value of
2.
The
inf ormation should
shou l d be
be of
of practical
p ra ctica l use
u se in
in directing
directing sales
sales efforts
efforts
The added
added information
and/or production scheduling.
and/or
sched uling.
The
need for
for separating various
various outputs
outputs from
from each
each other
other in
in the
the sales
sales budget
budget depends
depends
The need
on many factors.
on
factors. Most probably,
probably, this
this need
need differs
differs heavily
heavily from
from one
one sawmill
sawmill to
to another.
another.
Small
sawmills, perhaps with only local
local demand,
demand, may
may find
find that
that an
a n average
average estimate
estimate of
of sales
sa l es
Small sawmills,
revenues
re
ve nues per m3
m3 of
of sawn timber for
for all
all finished
finished goods
goods will
will suffice.
suff i ce. Most often,
often, however,
however, the
the
sawmill will
will benefit
sawmill
benefit from
from a more detailed
detailed budgeting.
budgeting . Sales prices
prices might vary
vary between
between
different
prices might
might differ
differ from
from domestic
domestic prices
pri ces and
and so
so forth.
forth.
different markets,
markets, export prices
-- 3131-
year.
yea r.
compiLing the
the sales
sales budget, we have
have to
to study
study the
the situation
situation for
for the
the budget
budg et
Before compiling
We
We must answer
answer at
at least
l east the
t he following
following questions:
questions:
1.
1.
demand fluctuate
f Luctuate during
durin g the
the budget
budget year?
year?
How will demand
2.
2.
With
With what
what certainty
certa in ty can
ca n demand
dema nd be
be predicted?
pre dict e d?
33..
ar e the
the expected
expected prices
pr ices for:
for:
What are
a.
b.
c.
D if E~rent dimensions for
for each
e ach species?
spe c ie s?
Different
Di fferent qualities for
for each
eac h species?
s pe c i e s?
Different
Diffe r e n t dimensions
a nd qualities for
for various markets?
markets?
Different
dimensions and
4.
4.
Does expected
ex pected log
log supply
suppLy meet demand
demand fluctuations?
fluctuations?
Does
5.
5.
Does expected log
log supply
s uppl y fluctuate
fluctuate in
in such
s uch aa way that
that the
the production
pr od uct i on might
mi ght be
be
Does
jeopardized?
jeopardized?
l ook more closely
close Ly into
into the
the sales
sales budget,
budget, the
the treatment
treatment of
of the
th e by-products
by-prod ucts
Before we look
must be
be commented
commented on.
on . Many
sawmi ll s take
tak e up
up sales
sales revenues
r e venues from
from their
t hei r by-products
by-products on
on the
the
Many sawmills
budget's revenue
revenue side.
side . Nevertheless,
Neverthe l ess , barks,
barks, chips,
chips, slabs,
s lab s, and
and sawdust
sawdust are
are all
all genuine
genuin e bybyproducts,
i.e . output
output from
from the
the sawing
sawing process
p r ocess that
that cannot
ca nn ot be
be dealt
dealt with
with as
as separate
separate products.
products.
products, i.e.
It
is not
n ot possible to
to trace
trace all
all costs
costs of
of handling
handlin g these
these by-products.
by-products. The handling
handlin g cost
cost
It is
will be
be part
part of
of the
the overall
overall costs
costs of
of the
t he sawmill,
sawmill, and
and only
only aa minor
minor part
part of
of these
these costs
co sts
In
such
a
case
the
most
logical
treatment
be indisputably
indisputably traced
traced to
to the
the by-products.
by-pr od ucts. In suc h a case th e most l ogical treat me nt
can be
of their
their sales
sa l es revenues
revenues is
is to
to deduct
deduct these
these revenues
revenues from
from the
t he sawmill's
sawmi ll' s expenses.
exp e ns es . This will
wi ll
of
referred to
to in
in section
section 4.4.2.
4. 4. 2.
be referred
Let
Let us
us introduce
introduce our model
mode l company,
company , which
which is
is aa sawmill
sawm ill in
in aa tropical
t ropi ca l country.
co untry. The
equipment consists
consists of
of two
two frame
frame saws.
saws . The
sawmil l has
ha s at
at most
production equipment
The sawmill
most produced some
3 (wi t hout overtime) during
11
during aa year.
yea r. The
The theoretical
t heoretica l capacity
capacity of
of the
the frames
frames is,
is,
11 200
200 m
m3 (without
according to
to the
the manufacturer,
manufacturer, some
some 20
20 000
000 m3.
m3 . The
The company saws
saws two species,
s pecies , which we
We wi
will
wi
LL call
caL L Species
Species AA and
and Species
Species B.
B. We
ll use this sawmill
sawmi ll as a model
model company throughout
thro ugho ut
will
this
th one exception
exception only.
only .
this paper wi
with
t h e next
ne xt year,
year, management has
ha s estimated
estimated the
the demand
demand for
for both
both species.
species. The
rke t
For the
The ma
market
is
that the
the management has
has decided
decided to
to work
work with
with single
single average
average prices
price s for
for each
each species.
spe c i es.
is such
such that
Management has arrived at
a t the
the sales
sa Le s budget presented
prese nted in
in Exhibit
Exhibit 4.2
s pe cies ,
4.2 For each species,
3 of
have been estimated
esti mated (first
(first row)
row) to
to 6 000 m
of sawn
sawn timber
d
yearly sales have
m3
timber for
for Species
Species A
A an
and
3
m for
for Species
Species B.
B. With an average price
pri ce of
of MU 900
900 and
and MU
MU 850
850 respectively
respectively for
for the
the
4 000 m3
two
two species,
spec i es, the
the company will
wiL L have
have a total
t otal cash
ca sh inflow
inflow over
over the
the year
ye ar of
of MU
MU 88 800
800 000
000
(5 400 000 ++ 33 400
400000).
cas h inflow
infl ow is
i s also
a l so shown
shown month
mont h by
by month,
month, which
which is
is important
important
(5
000). The cash
for
f l ow planning.
planning. As can be
be seen,
seen, the
the monthly
mont hly demand
demand fluctuates
flu ct uat es
for the
the company's cash flow
dur ing the
t h e year
year with
with aa minimum
minimum of
of 400
400 and
and 250
250 m3
m3 and
and aa maximum
max imum of
of 600
600 and
and 400
400 for
for Species
Species
during
A and BB respectively.
r espectively .
A
Forecasting sales
sa l es for
for various months
months reduces
reduces the
the risk
risk of
of not
not being
be ing able
able to
to meet
meet
in principle,
principle, sales
dema
nd . If
If demand
demand is
is not
not met
met the
the sawmil
sawmill
l loses,
loses, in
sa le s revenues minus
minus the
the
demand.
cost of
of raw
r aw material and
and some
some other
ot her minor
minor costs.
costs. However,
lmo st all
However, aalmost
all othercosts will
will reunchanged.
main unchanged.
~
1
1
2
2
33
-
4
4
5
5
6
6
7
7
Estimated demand
in
in m3
m3 of
of sawn
timber
tim
ber
600
600
600
400
400
400
400
Average
Ave rage price per
per
m3, MU
m3,
900
900
900
900
900
900
900
Month No.
No.
speci~
8
8
9
9
400
400
900
900
-
-10
-1111
12
__
500
500
600
600
66 000
900
900
900
900
900
Total
12
12 months
Specification
fica ti on
Species A
A
Cash inflow,
in flow,
MU 1 000
540 . 0 540.0
540.0 360.0
360.0 360,0
360.0 450,0
450.0 450.0
450.0 540,0
540.0 540.0
540 .0
540.0
540.0 540.0
360.0 360.0
360.0 360.0
360,0 360.0
5 400
400
1
Species 13B
Species
Est i mated demand
Estimated
in m3
in
m3 of sawn
timber
400
350
350
300
250
250
250
350
350
350
400
400
4 000
price per
per
Average price
m3,
m3, MU
850
850
850
850
850
850
850
850
850
850
850
850
850
Cash inflow,
in flow,
MU 1 000
340.0 297.5
297.5 297,5
297.5 255,0
255.0 212.5
212.5 212,5
212.5 212.5
212.5 297,5
297.5 297,5
297.5 297,5
297.5 340,0
340 .0 340,0
340.0
340,0
400
3 400
Tot al cash ininTotal
flow,
both
flow, both
species,
MU 1 000
880.0
7.5 837.5
1 5.0 572.5
572.5 572.5
572.5 572.5
572.5 657,5
657 . 5 747,5
747.5 747,5
747 . 5 880,0
880.0 880,0
880 .0
880,0 83
837,5
837.5 6615.0
88 800
1
1
~
----
Exhibit 4.2
4.2
Sales budget
budget
W
N
--33
33 -
sales budget
budget is
is an
an important
important tool
tool in
i n planning
planning the
the production
production over
over the
the year.
year.
The sales
It helps
in planning things
things like:
like:
It
helps the manager in
1.
I.
Raw material
over aa period.
period.
material purchases over
2.
size of
of buffer
buffer stocks.
stocks .
The size
3.
The
total production schedule
schedule taking
taking into
into account
account the
the choice
choice between
between overtime
overtime
The total
productioll
production for
for stock.
stock.
production and production
4.
The suitable time
time for
for repair
repair and
and maintenance.
maintenance.
sales budget
budget is
is aa pre-requisite
pre-requisite for
for the
the cash
cash flow
flow planning.
planning. This is
is especially
The sales
important for
for sawmills,
sawmills, as
as raw
raw material
material purchases
purchases and
and sales
sales are
are often
often unevenly
unevenly spread
spread over
over
important
the
year.
the year.
an annual
annual budget
budget subdivided
subdivided into
into months
months is
is the
the manager's
manager's tool
tool Eor
for control
control
Finally an
and
and correction purposes.
purposes.
4.4
short-term expenses
expenses
Budgeting short-term
4.4.1
sawmill's cost
cost centres
centres
The sawmill's
In some
some aspects sawmilling
sawmilling is
is aa fairly
fairly simple
simple type
type of
of industry.
industry. In most manuIn
facturing
industries, production flow
flow is
is divided
divided into
into departments
departments and
and sub-departments,
sub-departments,
facturing industries,
and
is separately
separately treated
treated in
in both
both budgeting
budgeting and
and calculating
calculating product
product costs.
costs.
and each unit is
separate estimations
estimations are then
then brought
brought together
together into
into one
one overall
overall cost
These separate
cost estimation
estimation for
for ,t
each product.
•
The main purpose
The
purpose in
in this
this section
section is
is to
to improve
improve the
the sawmill's
sawmill's budgeting
budgeting and
and cdst
cdst
For
this
reason
the
sawmill's
operations
will
be
divided
into
three
functions
control.
For
this
reason
the
sawmill
'
s
be
divided
into
three
functions
control.
described in
in Exhibit
Exhibit 4.3
4.3
as described
•
9
Altho
ugh a
a common way of
sawmill budgeting
bud~eting is
is to
to use
use overall
Although
of sawmill
overall average
average figures
figures (cost
(cost_
t imber), there
there are a number of reasons
reasons for
for acquiring
acquiring more
per m
m33 of sawn Limber),
more detailed
detailed information on
costs the
the sawmill
sawmill has
production or
tion
on what
what kinds
kinds of
of costs
has and
and where
where in production
or distribution
distribution these
accrue. Let
Let us
us look
look at some
some of
of the
the more
more important
important rationales
rationales for
for budgeting
budgeting and
and costing.
costing.
costs accrue.
Studying cost influencing
influencing activities
activities helps
~elps to
to discover
discover sacrifices
sacrifices made
wade in
in producproduction
tion and distribution.
distribution.
of storing.
storing.
cost of
The most important
The
important sacrifice
sacrifice that
that is
is usually
usually overlooked
overlooked is
is the
the
A systematic analysis
A
analysis of
of where
where costs
costs accrue
accrue is
is the
the only
only way
way to
to get
get aa proper
proper cost
cost
for various
various outputs.
outputs. The need for
for aa systematic
systematic approach
approach varies
varies from
from one
one sawsawestimation for
to another.
another. A
A small
smal l sawmill
sawmill producing only sawn Limber
(imber has
has aa quite
mill to
quite different
different costing
costing
situation
r ed to
to aa large
large sawmill
sawmill producing sawn timber,
timber, planed
situation as
as compa
compared
planed boards,
boards, and
and various
various
kinds of wood products,
products, perhaps
perhaps for
for different
different markets.
markets.
If somebody is
is aa pre-requisite
pre-requisite for
for managerial
managerial control.
control. If
is given aa
Information is
certain responsibility,
responsibility, he must also be
be equipped
equipped with proper
proper tools
tools for
for guidance and
performance control.
control. Take as
as an example
example costs
costs for
for repair
repair and
and maintenance.
maintenance. This can
can be
be
performance
treated as
as an overall
overa ll cost
cost for
for the
the whole
whole sawmill.
sawmill. However,
However, not
not budgeting
budgeting costs
costs of
of this
this
for different parts of the
the sawmill
sawmill means
that the
the manager cannot
cannot control
control where
kind for
means that
where costs
costs
budget each
each supervisor
supervisor should
should know
know what
what is
is expected
expecte d of
of him,
him, how
With aa proper budget
accrue.
he has
ha s consumed of his budget,
budget, and
and if
if and
and when it
it is
is time
time to
to point
pOint out
that he can
much he
out that
can no
no
longer keep costs within the
the budget.
budget. This in
in turn
turn probably
probably indicates
indicates that
that there
there is
is somesomelonger
thing
the management
management the
the possibility
possibility to
to react
react in
in time.
time.
thing wrong,
wrong, thus giving the
•
4
LOG HANDLING
I
Functional
costs
{tLog
~~~,:
costs log
r
SAWING PROCESS
I
liog
& log handling
I:"'" ·~~;;:Og
+Processing costs
Hwoo""ing
SELLING &&
STORING, SELLING
GENERAL ADMINISTRATION
+Selling & administration
costs
, rOi"".uoo
w
i=
=
Combined (accuLog &
(accu& log
log handling
handling
mulated)
mula
ted) cost
cost
{
concepts
Manufacturing costs
costs
costs
Full costs
Cost influeninfluencing activicing
ties
Debarking
Sawing
Green trimming
trimming
Drying
Final trimming
Work-in-process storing
storing
Internal transports
transports
storing
Finished goods storing
Selling activities
Shipments
Overall administration
Ç
Log purchases
purchases
Transportations
Measuring
Sorting
Caretaking
Storing
Storing
Internal transports
Exhibit 4.3
4.3
Cost concepts
concep ts and the
the sawmill's
sawmill's cost
cost influencing
influencing activities
activities
/
'
"
I
--35
35 --
4.4.2
Budgeting log
Log costs - integrated
integrated company
In this
t.his section we will deal
deal with budgeting costs
costs of
of logs
log s in
in a sawmill,
sawmi ll , and thereby
In
to decide
decide how
how to
to handle
handle rhe
the by-products
by -p roducts of
of the
the sawmill.
sawmill. We
two
we have to
We will
will discuss two
different
different methods used
used in
in practice.
practice. To
To show why one method is
is superior
superior Co
to the
the other,
other, we
have
t.o bring a
a planing
planing mill
mill into
into the
the picture.
picture.
In
this section
section we
Ur
have to
In this
we do
do not
not refer
refer to
to Oour
company.
model company.
Budget
ing log
l og costs
costs is
is aa controversial
controversial issue.
issue. They can
ca n be estimated gross,
gross, i.e.
i.e.
Budgeting
as
the actual cost paid
paid for
for purchased
pur chased logs.
logs. In
ts are
as the
In this
this case
case revenues
revenues from
from by-produc
by-products
put
on the
the revenue
revenue side of the
the budget.
budget.
put on
The
is to
t.o estimate
estimate log
log cost
cost net,
net, i.e.
The other way is
The following
following figures
figures
as
the actual
actual cost
cost paid for
for logs
Logs less
l ess revenues
revenues from
from by-producrs.
by-products.
as the
are
l assumed estimates per
per m3
m3 of
of sawn
~awn timber.
timber. 1/
!/
are al
all
Spe
cification
Specification
MU/m3
Sawn
timber, average
average sales
sa les price
price
Sawn timber,
Revenues
from by-products
by-products
Revenues from
Log costs
Sum of
all other costs
costs except
except direct,
direct,
of all
traceable
se lling costs
costs
traceable selling
1 000
000
1
200
200
500
400
The
types of
of cost
cost calculations
calculations have
have been
been shown
shown in
in Exhibit
Exhibit 4.4.
4 . 4. However,
the
The two types
However, the
gross
tota l revenues
revenues of
of MU
MU 11 200
200 while
while the
the net
net method
method gives
gives MU
MU 11 000.
000. The
same
gross method shows total
The same
difference,
difference, MU 200,
200, is
is also shown
shown on
on the
the expenses
expenses side
side of
of the
the income
income statement.
statement . Both
methods give
give the
the same
same profit
profit per
per m3
m3 oE
of sawn
sawn timber,
timber, i.e.
i.e. MU
MU 300.
300.
Adding revenues from
from by-products
by-products on
on one
one side
side of
of the
the income
income statement
statement (gross
(gross method)
method)
or deducting them
them from
from the
the other
other side
side (net
(net method)
method) might
might be
be viewed
viewed as
as aa quarrel
quarrel about
about
nothing, but,
but, in
in fact,
fact, the
the choice of method
is a
a matter
matter of
of avoiding
avoiding pitfalls
nothing,
method is
pitfalls in
in estimating
estimating
the
the result of various
various profit
profit centres
cent re s within
withi n the
the sawmill.
sawmill. Let
Let us
that there
there is
is also
als o
us assume
assume that
aa planing mill within the
the company.
company. For
For this
thi s profit centre,
centre, the
the following
fo ll owing figures
figures are
are
assumed:
Specification
MU/m
of
MU/m33 of
boards
planed boards
Planed boards,
boards, average sales
sales price
price
Revenues from
Revenues
from by-products of the
the
planing mill
mill
of al
alll other costs accruing in
Sum of
in
the planing mill
the
1 500
1
50
50
550
550
If
If the
the sawmill
sawmi ll and the
the planing
planing mill
mill are
are regarded
regarded as
as two
two different
different profit
profit centres,
centres,
we get various
various profits
profits in
in these
these two
two centres
cent res depending
depending on
on what
what cost
cost estimating
estimating method
method is
is
used.
1/
!I
Direct, traceable
traceable selling
selling costs/m3
costs/m 3 have
have been
been excluded
exc luded for
for simplification
simp lifi cation purposes.
purposes.
Direct,
They will be
be brought
brought into
into the
the picture
pi cture later
later on.
on.
- 36 -36-
Specification
in MU/m3 of sawn
sawn
Figures in
timber
Gross method
method
Revenues, sawn
sawn timber
timber
+ Revenues,
1
Revenues, by-products
by-products
+ Revenues,
= Total
Total revenues
Net method
000
1
a
200
1
costs, gross
Actual log costs,
+ Actual
0
200
1
500
200
300
Sum of
of all
all other costs excl.
excl.
+ Sum
of
of direct selling costs
Profit analysis
analysis
Total revenues
+ Total
revenues
Total
excl. of direct
Total costs excl.
selling costs
costs
per m3
m3 before de= Net
Net profit per
duction of selling
selling costs
costs
Exhibit 4.4
Exhibft.
4.4
000
500
Revenues
by - products
Revenues from by-products
net
costs, net
= Actua
Actuall log costs,
= Total
Total costs excl.
excl. of direct
selling costs
costs
000
400
400
900
==~~~
700
==Z~~
1
200
1
000
900
700
300
300
Comparison between the
Comparison
t.he gross and the
the net
net method
method in
in estimating
estimating log
l og costs per
per
3 of sawn timber .
m
m3 of
timber.
Let
assume the
the following
following production
production figures:
figures:
Let us
us assume
Specification
m3
Sawmill
Sawmill production:
Sales of
of sawn
sawn timber on the
Sales
the open
market
Inte
rnal deliveries ro
to the
the company's
company ' s
Internal
own
pLaning mill
mi ll
own planing
Planing
of planed
Planing mill
mill production of
77 000
3 000
2 650
boards
The
is estimated ro
to 85
85 percent
percent of
of sawn
sawn timber
timber inputs.
inputs.
The planing mill's recovery is
Furthermore,
Furthermore, we
we can
can assume that
that each
each m3
m3 of
of planed
planed boards
boards gives
gives 1.8
1 . 8 m3
m3 of
of by-products
by - products
(shavings).
Studying
the results of
of the two profit centres,
centres, we
we get
get the
the figures
figures given
g i ven in
in
Studying the
Exhibit 4.5.
4.5 . Internal
Internal deliveries
deliveries from
from the
the sawmill
sawmill to
to the
the planing
planing mill
mill have
have been
been shown
shown on
on
the
revenue
side,
estimated
at
manufacturing
costs.
The
two
of
course,
The
two
methods
give,
of
course,
the revenue side,
at
costs.
-- 37-
differ
e n t results.
result s . The
revenues of
of MU 22 700
700 000,
000, while the
the net
net method
different
The gross
gross method shows revenues
shows MU 2 100 000 for
for those
t hose 33 000
000 m3
m3 of
of sawn
sawn timber
timber internally
i nt ernall y delivered
del iver ed to
to the
t he planing
planing
shows
mil
l . Total
Total costs
costs have been
bee n estimated according
acco r ding to
to the
the figures
figure s used
used in
i n Exhibit
Exhibit 4.4.
4.4. The
mill.
gross
gives a
a profit for
f or the
the sawmill
sawmill that
that exceeds
exceeds the
the net
net method
met.hod profit
p r ofit by
by
gross method gives
MU 600 000.
000. Thi
s is
is due
t h e fact
fact that
that the
(.he sawmill
sawmill has been
been credited for
for all revenues
revenues
This
due to the
fr
om by-prod
ucts.
from
by-products.
Next
Next part
part of
o f Exhibit
Exhibit 4.5
4.5 shows
shows
method,
Usi
ng
the
gross
Using the
method,
it gets
gets
th
at is
than it
that
is MU
MU 600
600 000
000 higher
higher than
planing mill.
the eeffects
ffects of
the two
two methods
the resultsof
r esu l ~of the
the
of the
methods on
on the
the
plani
ng
mill
will
get
a
raw
materia
l s cost
the planing
will get
raw materials
the net
net method.
method.
with the
But
th e sawmill
sawm ill and
the planing mill are both sub-units
suh-un its in
in the
the same
same company and
But the
and the
profit
pr
ofit will
wil l be
be exactly
exact l y the
the same
same with
wit h both
both methods.
methods. However
,
this
profit,
752 000,
000,
However, this profit, MU 22 752
wi
l l be differently
diffe r ent l y distributed, depending
depending on
on what
what method
method is
i s chosen.
chosen . To choose
choose the
the net
net
will
method is
is important
important in
in large
large companies
companie s with
with several
several units,
units, such
s uch as
as aa sawmill,
sawmill, aa planing
planing
mi
l l, a mill for
for door-frames,
doo r -frames, window-frames,
wi nd ow-fr ames , etc.,
etc., and,
and, perhaps,
perhap s , an
an over-the-counter
over-t he-co unt er sales
sa l es
mill,
unit.
uni
t. In
it is
is important
important that
that the
the net
net method be
be adopted throughout
t hr o ughou t the
the whole
In this case, ir
whole
company,
be c ause management must
must know
know how
how much
much each
each unit
unit contributes
contributes to
to the
the overall
overall profit.
profit.
company, because
Another reason
reason is
is that
that rhe
the net
net method
me thod helps
helps motivate
motivate the
the staff
staff of
of different
different units.
units. The
The
ggross
r oss method obviously
obviou sly gives an
a n improper
improp e r advantage
advantage to
to the
the sawmill
sawmill unit
unit as
as compared
compared to
to those
t hose
units
uni
ts that
that internally
in terna ll y buy
b uy sawn
sawn timber.
timber. IItt is
to avoid the
the pitfall of closing
c l osing down,
down,
is important
important to
ee.g.
. g. a
a planing mill
mill unit due
due to
to "incorrect
"incor re ct loss
loss estimate".
estimate" . In
In the
the latter
latter case,
case, the
the overall
overall
analysis would
wou l d be extremely
extreme l y poor
poor for
for such
such aa decision.
decision.
Somet
Sometimes
imes object
objections
i ons against
against the
the net method are put forward
forward because
because the
t he manufacturing
manufacturi ng
costs are
costs
are not
not used in
i n the
the internal
i nt erna l pricing
pri cing of
of sawn
sawn timber.
timber. Opponents to
to the
the net
net methods
methods
like
like to point
point out
out that
that they
they use
use the
the opportunity
opportunity cost
cost in
in internal
internal pricing,
pricing, but
but their
their
objection is
is as
as illogical
ill og ical as
as the
the gross
gross method
method itself.
itself. To show
show this,
thiS, we
we will
will estimate
es timate the
the
cost of
of sawn
sawn timber
timber for
for our
o ur company
compan y itself.
itself. To do this,
this, we have
have to
to bring
bring the
the
opportunity cost
sawmill's direct,
direct, traceable
traceable selling
selling costs
costs into
into the
the picture.
picture. If
If these
t hese costs amount
amou n t to
to
MU 40
40 Per
~ er m3
m3 of
of sawn
saw n timber,
ti mb er, we
we find
find the
the opportunity
op portuni ty cost
cost of
of sawn
sawn timber
timber as:
as:
+ Sa
Sales
price of
+
l es price
of sawn timber
timber
- Direct,
Direct, traceable selling
selli ng costs
= Opportunity
Opportunity cost of sawn
sawn timber
ti mber
MU/m3
u
"
"
1 000
40
960
The opportunity
o pp ort unit y cost,
cost, MU
MU 960
960 per
per m3,
m3 , measures
measures what
what the
the sawmill
sawmill unit
unit will
will refrain
refrain
The
3
from
fr om by delivering
delive r ing internally
in te rn al l y one
one m3
m of
of sawn
sawn timber
timber (cf.
(cf. Section
Section 2.5).
2 . 5). To evaluate
eval ua te
"the
sac rifi ce" made
made by the
the sawmill
sawm ill in
in this
t hi s way
way is
is the
the only
onl y logical
logical approach,
approach, if
if the
t he
"the sacrifice"
following conditions
conditi on s prevail:
prevai l :
11..
The market demand
demand of
of sawn
sawn timber
t i mber must
must be
be at
at least
leas t equal
equal to
to the
the production
production
capacity of
of the
t he sawmill.
sawmill .
2.
2.
It
must be
be possible
It must
possib l e for
for the
the planing
pl a n i ng mill
mill to
to buy
buy sawn
sawn timber
timber from
from outside
o ut side agents.
age n ts.
38
- 38
SpeciflCoJti
on * )
Specification"
Gross
Gr oss method
method
:-Jet method
method
Net
MU
~
~,u
MU
Revenues from
(CO::1 sawn
s,Jwn timber:
ti mbe r:
(ope n market
market sales)
sales)
77 000 000
oao
000 (open
sx 1 JOe
** 1 22 700
700 000
000
900 (internal
deliveries), gross
gross method
method."
)3 000
900
(internal deliveries).
000 xx
100
(int ernal deliveries)
700 (internal
deliveries),, net method
33 'J300
OO x)(
77 000
QilO
1
Revenues
fr om by-products:
by -pr od ucts:
Revenues from
IG 000 x)( 200
200
1G
Total revenues,
Total
revenu es , sawmill
sawmill
Tota
Totall costs (cf
(cC Exhibit
Exhi bi t 4.4):
4 . 41:
10 000
)( 900,
900. gross method
10
000 x
10
lC · OOO
000 x
)( 700,
700 . net
net method
Profit
fr om sawmill
sawmill
Profit from
7 000
000 000
000
2
100 000
100
9
9
000
100 000
22 000.000
000 ,000
11
11
700 000
700
99 000 000
000
7,000,000
7.000.000
_2_100
",€:.J~g .. ogg
~~~
A
100 000
.i.J22:2~~
000
3 975 000
000
3 975 000
Rev
enues from
fr om planed boards:
boa r ds :
Revenues
2 650
650 x)(
2
I 500...)
500 · · · )
1
Revenues
f r om by-products:
by -pr oduc t s :
Revenues from
470
50
4
7000 xx
50 ···* )
rev enues , planing
planing mill
mill
Total revenues,
To t al costs:
costs:
Total
Sawn timber
timber at
at manufacturing
manufacturing costs
costs
900, gross
g r oss method
method
3
900,
0000
00 xx
000 xx
700, net
net method
me thod
3
700,
Su
m of all other
othe r costs:
c os ts:
Sum
65 0 xx
2 650
550
550
Pr
of it from
from planing
plani ng mill
Profit
Profit
analys is, total
total company
company
Profit analysis,
Pr
of it from
fr om sawmill
Profit
Pr
of it from
[rom planing
planing mill
mill
Profit
Overall
profit
Overall company profit
.
..
)
235 000
4 210
21 0 000
000
4
2)5 000
000
235
4
000
210 000
700 000
000
2 700
22 100 000
457 500
~2..Q..Q.
1
52 500
.. ",="H~~Q~
22 700 000
000
1
, 457.500
457 , 500
652 SOO~
.. ""g~~,-~~
2 100 000
000
2
52
SOD
52 500
652 500
S0Q
2 752 500
_2
752_500
:=.;~
~~,j~~
NO account
account has
has been
been taken
taken to
to direct,
direct. traceable
traceable selling
selling costs
costs of
of the
the sawmill.
sawmill .
No
)
•• * )
***)
At
At manufacturing costs.
costs, Internal
Internal pricing
p ri c ing will
will most
most probably
prob;;Jbly be
be made
made with
with the
the opportuop~,o rtu­
cos t concept.
concept. This
Th is does
does not
not alter
alte r the
the difference
difference between
between the
the gross
g r oss and
an d net
net methods'
me thods '
nity cost
effects
effects..
One m3 of sawn
sawn timber
timbe r has
has been
been assumed
assumed to
to give
give .85
.85 m3
m3 of
of planed
planed boards
boards at
at an
an average
avera ge over
over
dimensions ,
all dimensions.
average figure
figure for
for planing
planing mill
mill by-products.
by - products . The
The size
size of
of this
this figure
figure does
does not
not InIn Assumed average
fluence the
the analysis.
analysis.
fluence
4.5
Exhibit 4.5
Comparison between
bet ween the
the effecrs
effects of
of gross
gross and
and net
net methods
method s in
in estimating
estimating the
t he
total
for
integrated
company
log
costs
l og cos ts - tota l for integrated company
Let us assume
willl then
then use
Let
assume that
that these
these conditions
cond ition s have
have been
be e nfulfilled.
fulfilled.The
Thesawrnill
sawmill wil
use the
the
opportuni
ty cost as a basis
basis for
for its
its internal
internal pricing.
pricing. Substituting MU 900
900 and
and MU
MU 700
700
opportunity
(reve
nues from
the sawmill's
sawmi llt s internal
internal deliveries
deliveries and
and the
the raw
raw materials
materials cost
cost of
of the
the planing
planing
(revenues
from the
respe c ively with
with MU
MU 960
960 gives
g iv es the
the profit
profit figures
figures for
for the
the two
two units
units as
as shown
shown in
in
mill) respecively
Exhib it 4.6.
4.6.
Exhibit
39-- 39
Specification
Total
Tota l estimates
est i ma t es in
i n MU
MU
(eq ual for
bot h methods)
me th o ds )
(equal
for both
Revenues from
from sawn
sawn timber:
timber:
77 000
(open mar
ket
000 xx 1 000
000 (open
market
sales)
33 000 x
960 (internal
( internal dede 960
liveries)
1
revenues, sawmill
sawmill
Total revenues,
(net method
method used):
Total costs (net
used) :
**))
7 000 xx
740*)
7404r
700
700)
3 000 xx
from sawmill
sawmill
Profit from
'
from planed
planed boards:
boards:
Revenues from
500
2 650 xx 1 500
Total costs:
costs:
**)
** )
Sawn timber,
timber, gross,
gross,
33 000 x
x 960
960
22 880 000
000
Revenues
by - proRevenues from by-products , 44 700
700 xx 50
50
ducts,
000
235 000
Sawn timber,
timber, net
net
22 645 000
000
Sum of all other
other costs:
costs:
1
22 650 x 550
550
Loss
planing mill
mill
Loss from planing
0 00
7 000 000
2 880 000
000
9 880 000
000
5 180
180 000
000
100 000
000
2 100
2
600 000
LgQQ"QQQ
000
3 975 000
645 000
22 645
457 500
1 457
500
127
500
==HL~QQ
1
Profit analysis,
Profit
analysis, total
total company
company
Loss
mill
Loss from planing mill
22 600
600 000
1127
2 7 500
500
profit
Overall company profit
2 472 500
§=~n,,
~QQ
Profit from sawmill
sawmill
**))
Total
in MU/m3
MU/m3 has been
been increased
increased by
by MU
MU 40/m3
401m3 as
as
Total cost
cost in
ddirect,
i rect , traceable
traceable selling
selling costs
costs have
have been
been added
added to
t o the
th e
previous cost used in
previous
in Exhibits 4.4
4.4 and
and 4.5.
4.5 . For
For interi nter deliveries the
al deliveries
the costs remain
rema i n at
at the
the level
lev el MU
MU 700/m3.
70 0/m3 .
nnal
**1
**)
'
Exhibit
Exhi
b i t 4.6
4.6
IIn
n this
this Exhibit the net method has
has been
been used
used for
fo r also
a l so
the
i.e. revenues
revenues from
from by-products
by- p r od uct s have
h ave
the planing
planing mill,
mill, i.e.
been deducted
deducted from
been
fro m costs
costs of
of sawn
sawn timber,
ti mber , gross.
g r o ss,
Profit analysis
analysis for
Profit
for the
the integrated
integrated company
company when the
t he opportunity
opport uni t y cost
cos t concept
co nce pt
is
for internal
internal pricing
pricing purposes.
purposes.
is used
used for
-- 40
_
40 -
As we
ar~ now
now u.sing
using the
the internal price
As
we are
the opportunity
opportunity cost
cost concept
concept in
in estimating
estimating the
of
, there
difference between the
the gross and the
the net
net methods.
of sawn
sawn timber
rimber,
there will
will be
be no
no difference
methods. However
However
the
shows that
that rhe
the planing mill
is no longer
longer profitable.
profitable. If,
on
the
the opportunity
opportunity cost
cost shows
mill is
If, on the other
other
hand,
we
measure
from
the
sawmill's
point
of
view
how
profitable
the
planing
mill
is as
hand, we measure from the sawmill's point of
the
mill is
a customer as compared ro open market customers, the
~a~c~u~s~t~o~m~.~r~a~s~c~o~m~p~a~r~.~d~t~o~~o~p~.~n~m~a~r~k~.~t~~c~u~s~t~o~m~.~r~s,
the two methods give
give different
different results
results as
3 for
is.shown
is
· shown ' in Exhibit 4.7.
4.7 . We
that the
the gross
od gives
results per
for
We find
find that
gross meth
method
gives different
different results
per m
m3
open marker
market customers and for
open
for deliveries
deliveri es to
to the
the planing
planing mill.
mill. Based
thiS, the management
management
Based on
on this,
could
at an incorrect
incorrect and economically devastating
devastating decision
decision to
to close
close down
down its
its own
could arrive
arrive at
own
planing mill.
mill.
Choosing the
Choosing
the net
net method,
method, we
we find
find a different
different pattern.
pattern. Both
types of
Both types
of customers are
equal
l y profitable,
Ilthe-profit-per-m 3 -of-sawntimber-figure lt , i.e.
i.e. both
both customer
c ust ome r
equally
profitable, based on "the-profit-per-m3-of-sawntimber-figure",
groups
of MU 260 per m3.
m3
This effect is
is important.
important. All
All "customers"
"customers l l -_
groups give
give aa profit
profit of
external
internal - should
shou ld be judged
judged in
in relation
relation to
to their
their actual
actual contribution
contribution to
to profit.
profit.
external or
or internal
Using
the net
the risk
risk of mis-judging
mis-judging the
the "internal
"internal customers".
customers!! . This
This is
is
Using the
net method
method eliminates the
also
if we
compare the
the overall
overa ll profit
profit of Exhibits
Exhibits 4.5
4.5 and
and 4.6.
4.6 . True,
True, there
there is
is aa
also obvious
obvious if
we compare
difference
in the
the two
two profit
profit figures,
figures, but
but this
this difference
difference is
is due
due to
to the
the traceable
traceable selling
selling
difference in
costs. These
These are
are not
costs.
not included
included in
in Exhibit
Exhibit 4.5.
4 .5. A
A quick analysis gives the
the following
following result:
Overall company
company profit,
profit, Exhibit
++ Overall
Exhibit 4.5
costs, 40
40 xx 77 000
000
- Traceable selling costs,
MU
22 752
752 500
280 000
profit, Exhibit
Exhibit 4.6
4.6
- Overall
Overall company profit,
""
22 472
472 500
Specification
Sawn timber
Sawn
timber revenues
in
Figures in
Gross method
Open
Planing
mill
market
mill
custocustomers
900
aoo
960
200
1
200
L~~~
500
1
Revenues, by-products
Revenues,
Total revenues
revenues
Actual log
log costs,
costs, gross
gross
Less by-product
Less
by- product revenues
revenues
Selling costs
Sum of all other costs
Total costs
costs
Profit analysis
anal:lsis
+ Total revenues
revenues
- Total costs
costs
=
Prof i t/m3, sawn timber
timber
= Profit/m3,
Exhibit
Exhibit 4.7
4.7
MU/m3
MU/m3
method
Net method
Open
Planing
Open
market mill
mill
custo customers
mers
000
960
0
0
0
0
0
0
960
==~g~
000
l=~~~
960
==~g~
500
500
500
500
-200
- 200
-200
- 200
1
1
40
40
400
400
400
400
400
400
940
==~i~
900
==~~~
740
==H~
700
==b~~
200
200
960
960
000
960
960
940
940
900
900
740
740
700
700
260
==~g~
60
===g~
260
==~g~
260
==~g~
1
1
Comparison between
between the
the effects
effects of
of the
the gross
gross and
and the
the net
net methods
methods in
in estimating
estimating
Comparison
profitability
profitability per
per customer
customer group.
group.
--41
41 --
44.4.3
.4.3
Budget.ing
tot a l expenses
expenses of
of the
t.he sawmill
sawmill
Budgeting total
Let us
us now
Let
n ow return
r et urn to
to our
o ur "model
"mode l company".
company ". With
the sales
sa l es budget
With the
budget as
as aa starting
starting pOint,
point,
our
next task
ou
r next
task is
is to
to budget
budget the
the company's total
totaL expenses
ex penses for
for the
the budget year.
year. This
mean
s to
to
This means
analyse
costs at
ot both logs
ana
l yse costs
logs and log
l og handling as well
wel l as costs accruing
acc ru ing trom
tr am sawing
~aw in g and
sto
ring, se
ll ing and
ist ra tion (cf.
(cE . Exhibit
Exhibit 4.3).
4.3).
storing,
selling
and general
general admin
administration
3 . Out
We
ve , in
in the
t he sales
saLes budget,
budget, assumed an overall
overall sales
sa l es figure
figure of
o f 10 000 m
of
We ha
have,
m3.
Out of
3
3
this,
forecasr for
for Species AA and
and 44 000
000 m3
m for
for Species
Species B.
B.
In
order
to
this, 66 000
000 m
m3 have
have been forecasr
In order to
es
timate the
rresponding ex
pen ses, we
ha ve to
to differ
differ between
between various
va ri ous costs.
costs. The
se costs
estimate
the co
corresponding
expenses,
we have
These
costs
can
be se
separated
ca
n be
para te d in
in four
f o ur main
main groups:
groups :
1.
Variable costs
co sts that
that can be estimated
estima ted per
per unit
unit of
of production,
production, for
for example
e xampl e log
l og
costs
costs..
2.
Costs that
that are variable but difficult
difficult or
o r impossible
imp ossible to
to estimate
estimat e per
pe r unit
uni t of
of
production.
Among these
pr
oducti on. Among
t hese costs we can find
find consumable items
items such
such as
a.s saw
saw blades,
conveyor belts
belts and
and the
the like.
like . W
e estimate these
these costs
co sts based
based on
on experience.
experience.
We
3.
Fixe d costs of
of the
t he sawmill
sawmill giving rise
rise to
to actual
actual payments
payments during
durin g the
the year.
year.
Fixed
These
ta ke on different values
values for
for different
different output
output levels,
levels, as
as many
many of
of them
the m
These may take
are of
are
o f a step-fixed
ste p-fixed nature.
nature . But if
ll out
put iis
s roughly
if we
we assume
assume that
that the
the overa
overall
output
roughly
the same
sa me from
fro m one year to
to another (cf.
(cf . the
the relevant
relevant range
range concept
concept in
in Section
Sect i on 2.2),
2.2),
the
also
the expenses
expe n ses will remain
remain fairly
fairly unchanged.
unchanged. Due
Due regard
regard must
be paid,
paid, though,
though,
also the
must be
to price changes.
c hanges . Among these cost items
items we find
find e.g.
e.g. labour
labour costs
costs (fixed
(fixed
to
t he relevant
relevant range,
ran ge , otherwise
ot her wise step-fixed)
step - fixed) and
and various
various administration
administ rati on
within the
( f i xed over
over aa series
se ri es of
of ranges,
ranges, or,
or , more
more correctly,
correctly , having
having aa wider
wider
costs (fixed
relevant
rel eva nt range
r a nge than
th an e.g.
e.g. labour
lab ou r costs).
costs).
4.
Finally, various
Finally,
var i o us kinds of capital
capita l costs,for
costs,for example,the
example, the costs
costs of
of depreciation.
depreciation.
As
As we now proceed into
into the
the actual
actual budget
budge~ construction,
c on struction , aa few
few things
t hin gs should
s h oul d be
be
kept in
kept
in mind.
mind . Firstly,
the
most
important
part
of
budgeting
is
to
identify
a
ll
sac
rifi ces
Firstly, the most important part of budgeting is to identify all sacrifices
made to
to produce
produce and
and sell
se ll the
t he desired
de si r ed output.
output. Secondly,
Second l y, it
i t is
is important
important to
t o analyse
analyse how
how aa
certain
ce rtain cost
cos t changes
changes in
in different
diff ere nt situations.
sit uati ons . Thirdly,
estimates are
difficult to
to
Thirdly, cost
cost estimates
are difficult
ma ke, and
a nd the
the responsible
res p ons ible manager
manager must,
must, therefore,
therefore , be
be careful
careful in
in his
his choice
choice of
of figures
figures to
to
make,
be put
put into
be
into the
t he budget.
budget. He
He must
a na ly se the
the effects
effects of
of possible
possible deviations
deviations from
from his
hi s
must analyse
budget. This means he
he has
ha s to
to carry
carry out
out proper
pr o per sensitivity
se nsi tivity analyses.
analyses .
Some
the problems mentioned here
h ere will
will be
be taken
taken up
up in
in this
this chapter.
chapter. Others will
will
Some of
of the
be
b e postponed
postpo ned until
un t il Chapter
Chapter 5,
5, which,
which, among
among other
other things,
things, brings
brings the
the sensitivity
sens it iv ity analysis
analysis
into
int
o the picture.
picture.
of aa sawmill
sawmill budget,
budget, showing
s h owing the
t he total
t ota l cost
cost of
of the
the company,
comp a ny, has
has been
been
An example of
given in
in Exhibit
Exhibit 4.10.
4.10 . In
this example,
e mph asis has
has been
been put
put on
on what cost
cost items
items to
to bring
bring
In this
example, emphasis
into the analysis.
into
analysis. Each
Ea c h cost
cost in
in the
th e budget
bud get has
ha s been
bee n given
give n an
an identification
identification code
code (Item
(Ite m No.)
No.)
and will be
be commented on
on in
in the
the text.
text . Before we look
l ook into
into the
the overall
overal l budget,
budget, we find
find
two more Exhibits,
Exhibits, 4.8
4.8 and
and 4.9,
4.9, treating
treating two
two important
imp ortant parts
parts of
of the
t h e budget.
budget. In commenting
commen ting
on the
t he overall
ove rall budget
budget references
refer e nces will
wil l be
be made
made to
to all
all three
three Exhibits.
Exhibits.
2 - 442-
Item No.
Comments
Comments
(Exhibit
4.10)
(Exhibit 4.10)
100
(log) costs.
costs.
This
is the
the sawmill's
sawmi ll 's cost
in other
Raw material (log)
This is
cost of
of what
what in
other
industries
is usually called
called direct
direct material.
material.
It includes cost items
items 101
101 -industries is
It
106.
101
a, b
101 a,b
Logs at
at buying costs
costs for
for species
species AA and
and BB respectively.
respectively.
have
Logs
Log costs have
been
been assumed to MU 250
250 and MU 225
225 for
for Species A
A and
and B
B respectively.
respectively.
Sawn
timber
timber recovery has been
been set
set. at
at 507
5010 for
for both
both species,
species, which gives
gives log
log
3
costs of
of MU 500
costs
500 and MU 450
450 for
for A
A and
and B
B measured per m3
m of sawn
sawn timber.
timber .
3
3
All
shown both
both in
in total
total and
and per
per m3.
m .
Log
m will be
be
All costs are shown
Log cost
cost per m3
known
to the
the sawmill
sawmill manager.
manager.
In
his log
log costs a weighted
known to
In budgeting his
average
of volumes and
and prices
prices could
could be
be used.
used.
average of
102
'!.'ransport.ation
by the
the sawmill
sawmill have
have been
been estimated
estimated to
to MU 222
222 000
000
Transportation costs paid by
for the whole year.
year.
for
The
total cost
the total
total number of
of m3:s
m3 :s bought gives a
a per
per unit
unit
The total
cost divided by the
cost
(MU 22).
22). This is
is multiplied with the
the forecast
forecast production volume
cost (MU
for each
species in
in order to
to get a
a figure
figure in
in the
the species'
species' total
total columns.
columns.
for
each species
103 a,b
are often
often overlooked
overlooked in
in budgeting.
budgeting. The
of tying up
Inventory costs are
The cost
cost of
capital
be estimated,
estimated, and
and this
this estimate
estimate will be
be made with the
the
capital must
must be
opportunity cost
cost of
of capital.
capital.
In
the amount
amount which
which the
the sawmill
sawmill
In other words, the
will lose,
will
lose, because
b e cause its
its money is
is tied
t ied up
up in
in a certain type
type of inventory.
In
order to
In order
to budget
budget the
the cost of
of log
log inventory,
inventory, it
it is
is necessary to
to estimate
estimate
how
it changes
the budget
budget period.
period.
This
in Exhibit
Exhibit 4.8.
4.8.
how it
changes over the
This has been done in
The
first row shows the
the starting inventory
inventory for
for each
each month.
month. The 13th
13th
The first
month is
is the
the first
first month
month of
of the
the next
next year.
year.
The
second row shows estimated
estimated
The second
production per month.
(Vacation
and 7).
7). Row
(Vacation periods
periods during months 66 and
In this
this e~a~~lc
examDle two
33 shows
ShO~3 forecast deliveries
deliveries of
of logs.
logs.
In
two periods
pe~iod5 through 66 and
and month
month 11
11 -- deliveries
deliveries have
have been
been put
put at
at zero,
zero, e.g.
e.g.
months 44 through
due
to blocked roads.
roads.
due to
The commencement
commencement point
point for
for analysing
analysing the
the figures
figures in
in Exibit
Exibit 4.8
4.8 is
is the
the
The
1, estimated
estimated production figures,
starting inventory for
for Month
Month No.
No.1,
figures, and
and
starting
forecast log deliveries.
The beginning inventory
forecast
The
inventory for
for Month
Month No.
No. 2 is
estimated as:
as:
4 040 -- 1I 080 + 1I 320 = 4 280
280
The important
important figure
obtain
is
during the
the
is the
the average
average log inventory during
The
figure to
to obtain
This is
is estimated
estimated as
as the
the sum
sum of
of all
all 13
13 inventories
inventories (38
(38 120
120 m3)
m3 )
year.
divided
13, which gives an average inventory
inventory of
of 22 930
930 m3.
m3 .
divided by
by 13,
aa capital
tied up in
in log
log inventory
inventory of
of MU
capital tied
250 = 732
732 500
500
2 930 x 250
This means
This
Month No.
~th
NO.,
2
2
1
33
44
55
66
77
88
9
9
10
10
1111
1122
13
13
Total
Spec
iSpecification
Species A
A
Beginning inin ven
t ory
ventory
Production
Product ion
Log deliveries
040 4 280
44 040
280 44 160
980 22 800
800
160 33 380
I
1
080
1
320
1
080
960
1
080
800
1
080
1
00
1
720
1
120
120
1
080
600
600
1
00
00
800
1
320
1
440
300 22 320
320 38
38 120
1 20
440 4 360 3 880 22 300
080
1
080
200
000
200 4 000
1
080
1
600
080
1
00
Average log
of beginning
beginning inventories
over 13
months divided
Average
log inventory
inventory ~= Sum of
inventories over
13 months
divided by 1133
22 930 m3.
m3.
080
600
=
38
120/ 13
38 120/13
=
~~~~~ ~~ ~~~~~~~~l~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~============================ = ==========
Species BB
Beginning ininventory
Production
Production
Log deliveries
2 360
360 2 520
520 22 440
440 22 120
120 1 400
2
1
I
680
280
280
200
320 1 000
280
280 2 360 22 040
040 1 320
000 19
1 9 000
000
1
1
720
720
720
720
720
720
400
400
720
720
720
720
720
720
720
720
880
640
400
0
0
00
00
320
320
800
800
800 2 800
400
0
0
400
Average log
log inventory
inventory == Sum of
of beginning
beginning inventories
inventories over 13
13 months divided
divided by
by 13
13
460
m3.
1
m3.
=
=
19 000/13
000/13 =
19
=
1
Costs of
Costs
of capital tied up at
at 10
10 per
per cent
interest: 2 930x250x0.1
930x250xO. 1 = 73
73 250
or MU 12.20 per
cent interest:
250 or
per m3 of
of sawn
sawn
timber,
timber, Species
Species A.
A.
Costs
of capital tied up
Costs of
up at
at 10
10 per
per cent
cent interest:
intere st: 1 460x225xO.1
460x225x0.1 = 32 850
850 or MU
timber,
timber, Species
Species B.
B.
1
Exhibit 4.8.
4.8.
Exhibit
8.20
8.20 per m3 of
of sawn
sawn
Estimates of
of capita
capital
costs for
of Species
A and B,
Estimates
l costs
for log
l og inventory
inventory of
Species A
B, opportunity cost at 10
10 percent interest.
interest.
-"
w
-- 44
~ -
Comments
IItem
tem No.
No. (Exhibir
( Exhi bit 4.10)
4 . 10)
103
103 a,b
cont.
It
oughout this
this example,
that tthe
he sawmill'
s cost
Ir has,
has, thr
throughout
example, been
been assumed
assumed that
sawmill's
cost of
of
capital is
is 10
10 percent
percent p.a.
p.a. Thi
s gives a capital
capita l cost of
of MU
MU
capital
This
732 500 x 0.1
732
0. 1 = 73
73 250
250
which
shows up
up in
in the
the budget
budget as MU 73
73 000
000 (cf.
(cE . Exhibit
Exhibit 4.10).
4 . 10).
which shows
in
This in
turn
of MU 12.20
12 . 20 per
per m3
m3 of
of sawn
sawn timber.
timber.
turn gives
gives aa cost
cost of
The
The lower
l owe r part
part of
o f Exhibit
Exhibit 4.8
4.8 shows
s h ows the
the same
same estimations
estimations for
for Species B.
B.
capital tied
capital
He
re we
at aa capital
t i ed up
up of
of MU 328 500,
500, aa ca
pi t al cost
cost of
of
Here
we arrive at
32 850.
850. The
The cost
cost per
per m3
m3 of
of sawn
sawn timber
timber amounts
amounts to
to MU
MU 8.20.
B. 20.
MU 32
104
This sum
The sum
s um of the
the costs
costs so
so far
far gives
g ives the
the gross
gross log
log cost.
cost . This
s um shows
shows what
wh at
The
tthe
he sawmill
ll y has
to pay
pay to
to buy
buy and
store its
its logs
l ogs during
th e year.
year .
sawmill actua
actually
has to
and store
during the
105
next procedure is
is to
to deduct
deduct estimated
estimated revenues
r evenues from
from by-products
by-products in
in
The next
The
o rd er to
to arrive at
at the
the net
net cost
cost of
of logs.
logs. Estimating this figure
figure is
is
order
on experience.
experie nce .
always based on
We
the quantity
quant i ty of
of chips,
chips, slabs,
s l abs , sawdust
sawdust and
and bark
bark that
that we
we obtain
obta in
We must
must kn3w
knw the
With these
prices
we can
can
for
h m
m of timber
timber sawn.
sawn.
With
t hese figures
figures aand
nd their
t he ir pr
i ces we
for eac
each
These have
est
imate the
th e total
total revenue
revenue from
from by-products.
by-products. These
have been estimated
est i ~ated to
estimate
MU 212
MU
212 000 for
for a
a production
pr oduct ion of
of 10
10 000
000 m3
m3 of
of sawn
sawn timber.
tim ber. It
been
It has been
assumed
that all
all by-products,
by-p r oducts , regardless
regardless of
of species,
speC i es , are equally
equally valuable.
va luabl e .
assumed that
In
for by-products,
by-p roducts , we
put either
lin e
In case
case there
there is
is no
no market
market for
we put
either aa zero on line
105
r aa positive
i.e. aa cost
of disposing
disposing the
t he by-products.
by-products.
105 oor
positive amount,
amount, i.e.
cost of
106
Summing up
the figures
figures so far
far presented
presented gives
g ives log
l og cost
cost net.
net. This is
is the
th e
Summing
up the
value o
of
material,, when the
value
f the
the raw material
the log
log enters
ente r s the
the debarking
debarking process.
pr ocess .
107
107
Log handling costs.
costs . These costs are indirect,showing
indirect, showing up
up as the
the same
same per
unit
cost for
for both
both species.
s pecies.
unit cost
108
La
bour costs
quite eaSily
be estimated from
from the
th e company's
company's payroll.
payr o ll.
Labour
costs can quite
easily be
Account
be made for
for staff
staff insurances,
insurances, pension
pe ns i on costs,
costs , etc.
etc . and
and
Account must
must be
estimated wage increases.
increases. However there
the r e is
is often
ofte n no need (in
(in a sawmill)
sawmill) to
aallocate
llocat e labour
labo ur costs on various
vario us parts
parts of
of production.
pr od uct i on . The
reason for
for this
th is
The reason
is
ll ccan
an be
be looked
looked upon as
as a process industry.
industry. No worker
is that
that the
the sawmi
sawmill
can
be eliminated without disturbing
ca
n be
d i sturbi ng the
the whole
whole production
production system
system
(cf
. Example
21 and
a nd its
its solution
solution in
i n Section
Section 2.7).
2.7). For
r easons,
(cf.
Example 21
For cost
cost control reasons,
though , labour
l abo ur costs have been
be en split
s pli t on
on all
all three
three cost-centres.
cost -centres. This offers
o ffers
though,
the
ibility of
kee ping control
co n t r o l of
of the
t he amount
amount of
o f such
s uch labour
labour input
inpu t
the poss
possibility
of keeping
as
r t ime and shift
shift work.
wor k.
as ove
overtime
109-111
Costs of
of wateri
watering
Costs
ng repair and maintenance,
maintenance, fuel
fu el and
a nd miscellaneous
mi scel laneous consumpconsumpttion
ion have
in as examples of
of cost
cost items
items that
t ha t might show
show up
up in
in this
th is
have been
been put
put in
the budget.
budget. Watering
Wa tering is
is definitely
definitely part
par t of
of the
t he log
log handling.
hand l ing.
part of the
Other costs
co sts, such
such as
as fuel
fuel consumption,
consumption, do
do not
not necessarily
ne cessar ily have
have to
to be
be brought
brought
int o this
this part of the
the budget.
budget . Fuel expenses
ex penses for
for aa forklift
for k l ift truck,
truck, used
us e d
into
the whole sawmill,
sawm ill, can
ca n also
also be
be taken
ta ken up
up elsewhere.
elsewhere . However,
However, ifthe
if the truck
truc k
over the
is
i n log handling,
hand ling , its
its fuel
fuel expenses
e xpense s should
should be
be allocated
allocated to
to the
the
is only
only used
used in
llog
og handl
ing cost centre.
ce ntre.
handling
,
-_ 45
45 -_
112
Costs
lump sum
the
Costs of
of depreciation are
are often
often treated
treated as
as aa lump
sum at
at the
the end
end of
of the
budget. But
if machines and buildings
buildings can be
be traced
traced to
to a certain cost
But if
centre,
this should
should be
be done
done also
also in
in the
the budget.
budget. There are at least
least two
two
centre, this
for this.
this.
reasons for
If
If logs
logs for
for some
some reasons
reasons are sold,
sold, without being
being sawn,
sawn, it
it is suitable to
to
kn
ow the
the actual handling
handling cost.
cost.
know
Another
that depreciation rates
rates may vary
vary for
for machines/buildings
ma c hines / buildings
Another reason is that
used
in different parts
parts of
of the
the sawmill.
sawmi ll. Putting all
all depreciations
depreciations in
in one
used in
lump
the risk
risk of
of poor
poor analyses
analyses of
of actual
actual costs.
costs.
lump sum
sum increases the
113
Adding
Adding cost
cost items 101-112
101-112 gives the
the full
full cost of logs
l ogs and log
log handling.
handling.
200
200
Sawing costs
costs show all costs from
from the
the start
starr of production
production - in
in most cases
the debarking station - up
up to
to the
the point where sawn
sawn timber
timber is
is stored.
stored.
the
201
Labour
costs include all operators from
from debarking
debarking to
to trimming.
trimming. RepairLabour costs
men,
drivers, etc.
etc. can be
be included
included in
in the
t he overall costs for
for repair
repair and
and
men, drivers,
maintenance. It
It has
has been assumed that
that the kiln drying capacity suffices
suffices
for
ly Species
Spec ies A.
A. Species B,
B, though,
though, is
is assumed to be
be naturally dried.
dried.
for on
only
The
is operated by
by one man,
man, and out of
of his
his time
time only
is
The kiln
kiln is
only 20 percent is
estimated for
for running
running the
the kiln.
kiln. During the
the remaining 80 percent
percent he is
occupied in
in the
the sawmill.
sawmill. Therefore,
Therefore, the
the labour
l abou r cost
cost for
for this
this operator,
operator,
p.a., has
has been
been distributed
distributed accordingly:
accordingly:
totalling MU 40 000 p.a.,
Work
Kiln operation:
40 000
000 ==
0.2 xx 40
Sawing:
0.8
0 .8 xx 0.6 xx 40
40 000
000
40 000
000
0.8 x 0.4 xx 40
Eleven remaining
remaining workers:
workers:
11 xx 40 000 xx 0.6
0.6
11
11 xx 40 000 xx 0.4
0.4
11
A
B
88 000
200
19 200
12
12 800
000
264 000
176
176 000
200
291 200
188 800
188
=========
202
202
Repair
include labour
labour costs
costs for
for repairmen
repairmen and
and costs
costs
Repair and maintenance costs include
of
spare parts, etc.
etc. The
part of
of repair
repair and maintenance expenses
The major part
of spare
traceable to
to the
the sawing
sawing process.
process. Allocation of
of
will most probably
probably be
be traceable
these expenses
be based
based on
on capacity
capacity demand
demand from
from various
various parts
parts of
of
these
expenses should be
the
the mill.
203
203
Heating
for artificial
artificial drying,
drying, might
might be
be difficult
difficult to
to estimate.
estimate.
Heating costs,
costs, mainly for
If
the sawmill
sawmill buys the
the needed
needed energy
energy from
from outside
outside suppliers,
suppliers, there
there are
are no
no
If the
problems in
problems
in cost
cost estimating.
estimating.
But
if the
the sawmill uses
uses its
its own
own by-products,
by-products, e.g.
e.g. bark,
bark, slabs
slabs or
or sawdust,
sawdust,
But if
then
be made
made on
on the
the basis
basis of
of the
the opportunity
opportunity cost
cost
then cost
cost estimates must be
In other
other words,
words, the
concept. In
the cost
cost of
of heating must be estimated as
as the
the
foregone
foregone opportunity of not
not selling
selling the
the by-products.
by-products. If,
lf, on
on the
the other
hand, there
there is
is no
no market
market for
for by-products,
by-products, there
there will
will be
be no
no cost
cost involved
involved
hand,
__ 46
46 -
203
cont..
cont
for
these by-products in
in heating
he ating the
the kiln.
kiln. (There
be other
ot her
for using
using these
(There might be
costs
o~ course!).
cou rs e!) . Fina
ll y, if
t of
wmill's
costs,, of
Finally,
if there
there is
is aa cos
cost
of disposing
disposing the
the sa
sawmill's
by
- ;Jroducrs ~ these
thesE" disoosal
(-li.sposal costs
costs wil
•...,il 1 show'
s aa cost
by-products.
show' up
up a as
cost reduction
reduction for
heating the
the kiln,
kiL n, when by-products
by-pr od ucts are
are used.
used. The
thing is
i s that
that the
The main
main thing
ove
rall budget
lanc ed, i.e.
i.e. not
influence d by
the
overall
budget will
will be
be ba
balanced,
not influenced
by the
the revenues
revenues of
of the
by-products
these are
a r e positive,
positive, zero,
zero, or
or negative.
negative.
by-products whether these
matrix shows what
what happens.
happ ens.
Revenue
s,
Revenues,
by-products
by-products
Log
Log costs
costs
Heating
costs
Posit
i ve
Positive
Zero
Ze r o
Decrease
Unc.hanged
Unchanged
IIncrease
ncrease
Increase
Increase
Unchanged
De c rease
Decrease
Negat
ive
Negative
The
f o llowing
The following
Tota
cost
Totall cost
ba
l ance
balance
Zero
Zero
Zero
Zero
Ze
ro
Zero
204
Costs
esti ma te. A
A source
source of
of
Costs of
of consumption
consumption artic.les
articles are
are fairly
fairly easy
easy to estimate.
information wil
l be
be the
the costs
of previous
prev i ous co
n s umptions adj
u sted for
for price
information
will
costs of
consumptions
adjusted
changes.
cha nges .
205
CE
. comment
Item No.
No . 111.
111.
Cl.
commentss on Item
206 a,b
a ,b
206
As species
s pecies A
A and BB are differently
differently dried,
dried, we
we also
a l so get
get different
diff ere n t work-inwo rk-inAs
inventory costs.
costs . The
p roduction of
of 6 000 m3
m3 of
of Species
Species AA means
means
process inventory
The production
an average production
production of
of 66 000/50
000/50 == 120
12 0 m3
m3 of
of sawn
sawn timber
timb er per
per week.
wee k.
an
If
t he drying process
pr ocess to
to rake,
ta ke, as
as an
an average,
average, seven
seve n days,
days,
If we
we consider rhe
3
it
that we
we always have
have aa process
pr ocess inventory
inventory of
of 120
120 m3
m measured
measured as
as
it means
means that
sawn timber.
t imber. In
to get
co n t inuous flow
flow of
of production,
p rod uction , aa buffer
buf f e r
In order
order to
get a continuous
stock of 80 m3
m3 of
of sawn
sawn timber
tim ber has
ha s been
bee n assumed
assumed necessary.
necessary. For Species
Spec ie s A
we then
then get:
get:
Work-in-process,
Wo
rk-in-pr ocess, flow
f l ow inventory
inv.entory
Work-in-process,
Wo
rk-in-pr ocess , buffer inventory
inve n tory
12 0 m3
m3
120
Work-in-process,, total
Work-in-process
total
200 "
Capital
Cap
i ta l tied up,
up, 200
200 x 536
536
Capital
Ca
pital cost,
cost, toral
tota l
3 of
Capita
st per m
of sawn
sawn timber
timber
Capitall co
cost
m3
80
80
II
MU
MU
107 200
72 0
10 720
MU
1.80
MU
In estimating the
t he capital
ca pital tied
tied up
up we have
have here
here used
used the
the log
log and
a nd log
log
In
handling costs (Item
(Ite m No.
No. 113
113 in
in Exhibit
Exhibit 4.10).
4.10).
handling
For Species BB the
For
t he situation
situat i on is
i s slightly
s lightly different.
different. As this
this species
s pec ies is
is
open
ope n air dried,
dri ed , no
n o buffer
buffer stock
stock is
i s required.
required. Average
Average drying
drying time
ti me has
has
been set
set at
at 18
18 weeks.
wee k s . With a production
production of
of 44 000/50
DOD/SO == 80
80 m3
m3 of
of sawn
sawn
3
timber
timbe r per
per week,
week, an
an inventory
in ve ntory of
of 80
80 xx 18
18 == 1 440 m3
m must
mus t be
be built
buil t up,
up,
it is
is possible
possible to
to take
take anything
anyt hing out
out as
as finished
finish ed goods.
goo ds. Obviously,
Obviously,
before it
the inventory
invent o ry will vary
vary during
during the
the year,
year, but
bu t an
an average
average of
of 11 440 m3
m3 is
is
the
good enough for
f or estimating
est imat ing capital
ca pital costs.
costs.
Work-in-process
Work-in- proces s inventory
invent ory
Capital
Capita l tied
482
tied up,
up, 1 440 x 482
Ca pital cost,
tota
l
Capital
total
cost ,
Capital
Ca pi ta l cost per m3
m3 of sawn
sa wn timber
timber
440 m3
1 440
m3
MU
694 080
MU 694
080
MU 69
69 408
408
MU
MU
MU 17.35
17.35
1
--47
47 -_
207
CE.
Item No.
No. 112.
112.
Cf. comments on Item
208
Adding together
cost items
manufacturing costs on
Adding
together cost
items 101-207
101-20 7 gives
gives the
the total
total manufacturing
on
full cost basis.
basis.
aa full
300
In the
the last
last function,
function, storing finished
finished goods,
selling, and
In
goods, selling,
and general
general administrationare
the sawmill's
sawmi l l ' s overall
overall costs.
costs .
stration
are brought
brought into
into the
the budget
budget to
to give
give the
301
301
Labour
for one storekeeper.
storekeeper.
Labour costs for
302
Cash discounts
might vary
vary from nothing up
perhaps 5 percent
percent of
of the
Cash
discounts might
up to
to perhaps
the
price. In
disco unt s have
have been
been assumed
assumed to
to be
be
In this
this budget cash discounts
sales price.
CE. comments on Item
Item Nos.
Nos. 108
108 and
and 201.
201 .
Cf.
2 percent
percent of
This means,
means,for
Species A,O.02
A,0.02 xx 900
900 :::= MU
MU 18
of the
the sales
sa l es price.
price. This
for Species
18
3
3
per
for Species 8,0.02
B,0.02 xx 850
850 == MU
MU 17
17 per
per m3.
m .
per m
m3 and for
303
303
/
A sales
sales commission of
of 33 percent
perc ent of
of the
the sales
sales price
price has
has been
been assumed.
assumed .
A
27 and
and MU
MU 25.50
25.50 for
for Species
Species AA and
and BB respectively.
respectively.
gives MU 27
This
304
costs always
always accrue
accrue in
in connection
connection with
with sales.
sales. A
probab l e source
Travelling costs
A probable
of information
information is
is last
last year's
year's costs,duly
costs,duly adjusted for
for price increases.
increases.
of
305
305
Sawmills usually
Sawmills
usually have aa very
very small
small sales
sales staff;
staff j in
in our case one
one sales
sales
manager, as
as it
it has
has been assumed that
t hat the
the company also
also sells
sells through
th rough outout manager,
side agents.
agents. The
salary on a
a yearly
yearly basis has
has been
The sales manager's salary
estimated at
at MU
MU 105
105 000,
000, all
all costs
costs included.
incl ud ed.
306
306
Estimates of
of finished
finished goods
goods inventory
inventory costs
costs are
are made
made in
in Exhibit
Exhibit 4.9.
4.9.
first row
row shows
shows beginning
beginning inventory
inventory each
each month.
month. The
row gives
gives
The Eirst
The second row
production figures
figures of
of sawn
sawn timber
timber in
in m3.
m3 . Since
Since the
the recovery
recovery is
is 50
50 percent,
percent,
they
the corresponding
correspo nding production
pr oduction figures
figures in
in
they are
are half
half the
the size
size of
of the
4.8 . Finally,
Finally, the
sales.
Exhibit 4.8.
rhe third
third row
row gives
gives estimated monthly sales.
inventories are estimated in
in the
the same
same way as in
in Exhibit
Exhibit 4.8.
4 . 8.
Beginning inventories
the second
second month,e.g.,
month,e.g., we
we find
find the
the beginning
beginning inventory
inventory as:
as:
For the
1 700 +
+ 540
540 - 600
600 == 11 640
640
1
of average
average inventory
inventory capital
capita l tied
tied up,
up, and
and capital cost follow
follow
Estimates of
the same
same pattern
pattern as
as for
for Exhibit
Exhibit 4.8
4 . 8 (cf.
(cf . Item
Item No.
No. 103).
103) .
the
307
Cf. comments on
on Item
Item No.
No. 112.
112.
Cf.
308
Our company has
has one general manager at
at aa yearly
yearly cost
cost of
of MU 127
127 000,
000, all
costs included.
included.
309
One
c lerk has
has been assumed for
for the
the sawmill.
sawmill.
One office clerk
per year.
year.
310
310
Mi sce ll aneous office
office expenses
expenses can
can rather
rather easily
easily be
be estimated
estimated from
from last
last
Miscellaneous
accounts.
year's accounts.
311
Adding together
together all
all cost
cost items
items gives
gives the
the total
tota l cost
cost for
for the
the company
company as
as aa
whole as
as well as
as for
for different
different species.
species.
Total
: MU 62
Total cost
cost:MU
62 000
Month No.
2
2
1
3
3
5
5
4
66
7
7
88
10
99
12
12
1111
13
Total
Specification
flcation
Species A
A
Beginning ininventory
1
700
1
640
1
580
520
1
1
660
800
1
1
700
1
600
1
740
1
780
1
820
1
760
1
700
22 000
Production,
Production, m3 of
timber
sawn timber
540
540
540
540
540
540
300
300
540
540
540
540
540
540
6
6
Demand, m3 of
of
Demand,
sawn timber
timber
600
600
600
400
400
400
400
400
500
500
500
600
600
66 000
800
000
Average, finished
finished goods inventory =
= Sum of
beginning inventories over
over 13
13 months divided by 13
13 =
Average,
of beginning
22
700 m3
m3 of
of sawn timber.
22 000/13
000 / 13 == 1 692 or approximately
approximately 11 700
timber .
1
~
==================~=================================== ==================================================
Species BB
Beginning ininventory
1
Production,
Production, m3 of
of
timber
sawn timber
Demand, m3
m3 of
of
Demand,
sawn timber
timber
100
1
060
1
070
080
1
1
140
250 1 200
1
1
1
150
1
160
160
1
170
1
180
1
140
140
1
100
100
14 800
360
360
360
360
360
360
200
200
360
360
360
360
360
44 000
400
350
350
300
250
250
250
350
350
350
400
400
44 000
Average, finished
finished goods
inventory == Sum
inventories over
13 months
13 =
Average,
goods inventory
Sum of
of beginning
beginning inventories
over 13
months divided
divided by
by 13
14 800/13 == 1 138
138 or
or approximately 1 140
140 m3
m3 of sawn timber.
14
timber.
1
1
Cost of
tied up
up at 10
10 per
per cent
cent interest:
interest:
of capital tied
timber,
timber, Species
Species A.
A.
1
700x679.70xO.1
11 5 549
549 or MU
MU 19.25
19.25 per
per m3
m3 of
of sawn
sawn
700x679.70x0.1 == 115
140x624.30x0.1 =
Cost of capital tied
tied up at 10
10 per
per cent interest:
interest: 1 140x624.30xO.1
timber, Species
Species B.
B.
1
Exhibit 4.9
Exhibit
71
71
170
170 or
or MU
MU 17.80 per
per m3
m3 of sawn
Estimates of
of capital
capita l costs
costs for
for finished
finished goods
goods inventory
inventory of Species
Species A
A and B;
B: opportunity
opportunity cost
cost at
at · 10
10 percent
percent interest.
interest.
Estimates
co
-- 49 --
4.4.4
to budget
budget
Profit according to
Let us now
now put
put together
together the
t he sawmill's
sawmill ! s sales
sales budget,
budget, which
which we
we find
find in
in Exhibit
Exhibit 4.2,
4.2,
Let
the budget expenses
expenses according
accordi ng to
to Exhibit
Exhibit 4.10.
4.10. The
resulting analysis
analysis is
is shown
shown in
in
with the
The resulting
4.11.
Exhibit 4.11.
The first
first two
two rows
r ows are
are taken
ta k e n from
from the
the sales
salesbudget
budgeta and
nd they
they show
show tota
total
l revenues
revenues as
as
Row 33 we find
find the
t he total
tot al sales
sales revenues,
revenues, MU
MU 88 800
800 000 for
for the
the
On Row
p rev i ous l y estimated.
esti mated.
previously
budget year.
year.
Tota l expenses
ex penses are
a r e shown
shown on
on Rows
Rows 4-6.
4-6 . The average
ave r ag~ expense
expense of
of MU
MU 792.75
792.75 and
and
Total
MU 733.40
733.40 for
for Species
Species AAand
and BBrespectively
respectivelyare
are extracted
extracted from
from Exhibit
.1 0. Multiplying
MUltiplying
Exhibit 44.10.
3 respectively
them for
for the
the forecast
forecast
sa
sales
les vo
volumes
lumes of
of 6 000
000 and
and 4 000 m
m3
respectively gives
gives total
tor :l1
expe
expenses
nses of MU
MU 77 960
960 100 (figures
(fig ures being
being rounded
rounded off).
off).
To
arr ive at company profit,
profit, subtract
subtract Row
Row 66 from
from Row
Row 3.
3. We
fi nd that
he two
To arrive
We find
that tthe
two species
co
ntribu te MU
643 500 and
and MU465 500
500 to
the overall company profit
profit of
of MU
MU 11 109
109 000.
000 . The
to the
contribute
MU 643
last
4.11, profit
profit per m3
m3 of sawn
sawn timber,
tim ber, is
is obtained by dividing the
t he profit
last row
row of
of Exhibit
Exhibit 4.11,
3
figures of
of Row 77 by
by the
the sales
sales volumes,
volumes , i.e.
i.e. 66 000,
000, 44 000
000 and
a nd 10
10 000
000 m3
m respectively.
respectively.
figures
Being presented
pre se nted with the
the overall
overall budget
budget figures,we
figure s ,we can
ca n state
state that
that the
the company
company as
as
aa whole,as
well as each
each of
of the
the two
t wo species,will
s pe cies,wi ll give
g i ve aa profit
profit for
for the
the budget
budget year.
year . But
whole,as well
ch can we rely
rely on
on these
these figures?
figures? After
After all,
all, they
they are
are but
but estimates
est imates based
based on
on assumpassumphow mu
much
tions, information about
about price
price changes
cha nges that
that might
migh t occur,
occur, approximations,
approximations, and
and perhaps
perhaps even
even
tions,
guesses. No budget figure
figure shows
s hows what
what will
will actually
actua ll y happen.
happen. Instead,
s how what
wha t
Instead, budgets
budgets show
happen, given
given that
that all
all forecasts,
forecasts, assumptions,
ass umpti ons , etc.
etc. underlying
underlying the
the budget
budget will
wi ll occur
occur
will happen,
during the budget
budget year.
year .
In
the
In other
other words,
words, the
This means
means that
This
that we have
have to
to
tions . This means in
in turn
t urn
tions.
in order to
to use
use the
t he budget
budget
in
this concept is
is treated.
treated.
this
budget is a conditional tool
tool and
and should
shou l d be
be used
used accordingly.
accord ingly .
budget
prepare
prepare for
for possible
possible deviations
deviations in
in our
our forecasts
forecasts and
and assumpassump that we
we have
have to
to carry
carry out
out various
various kinds
kinds of
of sensitivity
se nsitivity analyses
analyses
that
efficient l y. For this
th is purpose,
purpose, we turn
turn to
to Chapter 5,
5, in which
efficiently.
-- 50
50 --
Total
Total both
species,
:o;eccics,
MU I 000
MU
UOO
Sp{,Lli ication
SpeLification
No.
Item No.
1
100
101a
lOla
1016
101b
C(\~l~
Log costs
Logs
I.o~~ at buying
Sp ('cics A
A
cost.
cost . Species
buying
Logs
Lop at buying
Spcc[cs B
COSt. Species
cost,
."
3 000
,
"
1
102
Transportation
Triln~r " rlOlt inn
IO)a
101a
IIH"'nlor~'
Log
I.o~ inventory
tor Species
coq"
Spl'Cics AA
cost, tor
IIn'cn lory
Log
I.o~ inventory
I", Species
co~ 1 ~
costs
lor
,
10)b
1036
Species
S~ccics
A,
A.
Species
5~l'cics 8,
H.
to t a 1 ,
total,
toti!. 1 ,
total,
MU I 000
MU
000
MU I 000
1
1
Species A,
Seccics
A.
Ecr m3
m~ of
per
of
sa
... n timsawn
t Imber, ÑU
ber,
MU
800
800
800.
800
132
IJ2
))
73
))
73
J)
33
ecr
ber, MU
MU
ber,
SOO.OO
500.00
)1 000
222
SEccics B,
Species
B.
m) of
per m3
of
t Im_
sa ... n timsawn
4')0.00
450.00
22.00
12.20
12.20
90
'0
»33
-
22.(10
22.00
II. 20
8.20
FI
104
10'
105
106
10'
(O "tS, both
both
Log
LoS! costs,
species,
spcci\'~' gross
~ros 5
Hy-pnHI\l c t revenu'es
revenue s
- By-product
-
.-
(S,
101
107
108
109
10'
110
,
( OS t ~ , both
Log
Lo~ ,o,ts,
both
Spec
spc< ;I " S ,
112
II)
113
-
,
"
212
212
127
127
'"
40
40
24
24
25
45
)0
30
15
21
27
18
18
90
'0
54
54
.
10, handling
handl i ng
Log
I.o,'! S log
3 205
3 078
.
cos t
128
128
4 916
ON
net
handl InB costs
c osts
Log handling
LabOllr costs
Labour
cos t s
Watering
+ Repair
Repair P.
& maintenance
maintenance
Fuel &
.!. miscellaneous
miscell aneous
Fuel
Depn' c l ilt ions
Depreciations
Ill
III
5
5
'"
146
)3
216
1
1
'"
923
534.20
480.20
85
21.20
21.20
838
51).00
513.00
459. 00
459.00
"
4.00
2.50
2. SO
4.50
4.00
2.50
4.50
16
10
18
12
12
1
J,OO
3.00
3.00
36
)'
9.00
9.00
930
536.00
536.00
482 . 00
482.00
47.25
47.25
200.Sas-i
Sawing
200
201
202
202
20)
203
204
204
205
20001
206a
20bb
2066
201
207
.
.
.
.
.
20R
208
)00
300
)01
301
)02
302
)0)
303
)04
304
)05
305
306
)0'
)01
307
)08
308
309
)0'
Labour
LabC"ur costs
costs
6 mllinten<lnCC
Repair
maintenance
Rep" i r P.
Ileal i 11~ costs
c osts
Heating
Con
intip
innmal
material
Clln~\I
ml'l r
i'''1
•.' ria!
'Il.
I-'ul·1 ('ls.
Fuel
Work-in-process
Work- in-process inil1vent (l ry . Species AA
ventory,
Wnrk- i n-proc['ss in10Work-in-process
Vcnl(lry.!ipccies B
ventory,Species
Uepfl'ciatiolls
Depreciations
,
M"nU!.l<
rurin~
Manufacturing
cos t s
costs
Sto
ring. selling,
sc 1 Ling, &&
Storing,
general
administration
is;cncral administration
costs
Labour costs
Cash discounts
discountS
Sa
Sales
l. ·~ commission
c ommiss ion
Travelling
Tr"v"
1 1 i IlA
Sa
I 11 ry. sales manager
manager
Salary,
finished goods
goods
Finished
inventory costs
inventory
Dcpr['ciations
,
Depreciations
Salary, general
Salary,
genera 1 manager
manager
SaL,...y. office clerk
c I c rk
Salary,
.
,
310
.
)11
311
,
Of
c, ml
011t ic
ice,
miscellaneous
scc Ilaneous
Fu
\1 cost
of sawn
sawn
Full
cost of
ttimber
i mbr r
123
121
.,
"
14
74
49
"
"II
"
480
480
291
189
189
48.50
48.50
,.
49
))
33
8.20
8.20
15.70
15.70
82
94
94
-
"
43
72
11
II
-
11
"
69
69
69
-
f,
2 1., to
\(l
624.
4 0,"
078
'"
40
24
16
16
176
116
108
162
162
20
63
63
115
68
108
108
"
"
71
11
44.00
. 00
18.00
21.00
27.00
3.40
10.50
I q. 2 5
19.25
29
7. 20
7.20
",
186
17.
'j '.
17.3.
07Q,7 0
679.70
, 577
105
-
2 499
200
200
)4
34
7.2('1
7.20
;0.00
50.00
)00
300
270
210
12. )(1
12.30
50.00
500
6 577
12.)0
12.30
7.20
1.80
29
8.20
-
14
42
4.00
17.00
25.50
25.50
3.40
10.50
10.50
17.80
17.80
72
"
43
127
121
76
16
"
51
51
12.70
12.70
"
62
31
37
25
25
48
"
"
0.20
6.20
4.80
7.
20
7.20
12.70
12.70
6.20
6.20
4.80
4.80
1 697
691
7
44 755
155
7Q2.75
792.75
7)3
. 40
733.40
29
,h.
19
'"
2 942
2
overa ll budget
£u II cost
cost
sawmill ' 5 overall
budget at full
Exhibit 4.10 Compilation of
of the sawmill's
Exhibit
"
Specification
1. Sales
6 000
2. Sales
4 000
3. Total
per m3
m3
Total in
in MU
MU for:
for:
Species A
A
Species
Species BB
in
in MU
iinn MU
~3
per m3
m3
per m3
900
.00
900.00
5 400 000
Prices/
Costs
in MU
~
revenues/Species
revenues/Species A,
A,
m3
m3
revenues /S pecies B,
B,
revenues/Species
m3
m3
revenues
revenues
850.00
850.00
-
5 400 000
000
-
;::;::;::;:::;:::;,;::.:;;
4. Expen
Expenses/Species
ses/Species A,
A,
m3
6 000 m3
792.75
5. Expenses/Species B,
B,
4 000 m3
m3
Total expenses
6. Total
733.40
44 756
756 5500
00
-
Total
for
Total in MU for
the whole company
the
in
in MU
5 400 000
000
3 400 000
3 400 000
000
3 400 000
8--------800 000
==;:::;;;= =::::;::
-
=====::;::::-==
4 756 500
1
600
2 933 600
600
2 933 600
4 756 500
500
2 933 600
600
100
7 690 100
643 500
500
400
466 400
-
,'"
u,
~
1
-
•
•
Total profit (Row
7. Total
(Row 3-Row 6)
6)
8. Profit
Profit per m3
m3 of sawn
sawn
sawn timber
timber
=:::;:: ======
=======
107.25
107.25
=:::;=;::===
116.60
===::;:::::=
= =;::;::;;:;:::; :::;:::;
1 109 900
1
110.99
=;::====
Exhibit
Profit according
according to
Exhibit 4.11
4.11 Profit
to budgets
budg ets -- total
total and per m3
m3 of sawn
sawn timber
timber
..
' .,-.) ~
•
=
- 52-
5.
5.
5.1
5.1
USING THE BUDGET
BUDGET IN
IN SENSITIVITY
SENSITIVITY ANALYSES
ANALYSES
Sensitivity ana
analysis
Sensitiviti
ly sis
All
ageria l decisions
dec i sions can
can be
be divided
divided into
into three
three different
different sub-groups:
sub-groups:
All man
managerial
1.
und er risk.
risk.
Decision-making under
2.
Decision-making under
under certainty.
certainty.
3.
under uncertainty.
uncertainty.
Decision-making under
Under
first group
find decisions,
for which
the outcome
is known
Under the
the first
group we
we find
decisions, for
which the
outcome is
known with
with aa
certain probability.
In
it is
is however
however unusual
unusual that
that the
the
In managerial
managerial decision-making it
manager of a company knows
knows the
the probability
probability of
of occurrence
occurrence of
of an
an event.
event.
Decision-making
sure about
the outcome
Decision-making under
under certainty
certainty means
means being
being absolutely
absolutely sure
about the
outcome of
of
3
3
the
the decision.
If
a
customer
If a
offers a price
price of
of MU
MU 860
860 per
per m3
m and
and wants
wants to
to buy
buy 200
200 m3,
m , we
we
will
for sure
sure what
what economic effects will follow
follow this
this decision.
decision. With knowledge
knowledge of
of
will know for
the
cost situation,
the cost
situation, we can estimate "how profitable"
pr ofitab Le" the
the offer
offer is.
is. Although it
it looks
looks like
like
aa decision under
under certainty,
certai n ty, it
it is
is not.
not . We
lves what
what long-term
long-term effects
We must,
must, e.g.,
e.g., ask
ask ourse
ourselves
effects
t he price
price will
have, if
if it
it is
is lower
l ower than
than the
the company's ordinary price.
price.
the
will have,
The
The majority of
of decisions,
decisions, however,
however, belongs to
to the
the third
third group -- decision-making
under uncertainty.
uncertainty. This
This is
is difficult
difficu l t because there
there are such
such aa huge
huge number
number of
of possible
outcomes and so
so many
many variables
variables that
that it
it is
quite
impossible
to
make
a
quantitative
analys is
is quite
to
a quantitative analysis
of them
of
them all.
a ll. It
It is
is in
in this
this context
that the
the sensitivity analysis becomes
becomes a means in
in
context that
helping us to
to improve
improve our
our judgements.
judgements.
It
It is
is fairly
fairly easy
easy to
to calculate
calculate the
the cost of
of a product,
product, to
to construct an overall
was maae
made in
budget (as
(as was
in Chapter
Chapter 4),
4), or
or ro
to carry out an investment
investment analysis.
analysis.
It is more
It
difficult to
interpret
the
result
of
the
initial
work.
t o interpret the result of the initial work . It is
is often
often rather
rat~er uninteresting
uninteresting
to know
know what
what the
cost is
to
the product
product cost
is or how profitable an investment
investment might be.
be . Instead, we
we
want to
to know what will
will happen,
happen, if
if one
one or
or more
more variables
variables take
take on
on other
other values
values than
t han those
those
we have
carrying
have put
put in.
in. In
In car
rying out
out a
a sensitivity analysis,
analysis, we start
start varying one or more
variables,
variables, in
i n order to
to find
find boundaries
boundari es within
wi thi n which
w~ich we
we have
have good
good reasons
reasons to
to believe
believe that
that
the future
the
future outcome might fall.
fall. Even if
if this also is
is some kind of guesswork,
guesswork, we have at
at
least
more enlightening
l east aa more
en li ghtening picture
picture of
of what
what might
might happen.
happen.
In trying
trying to
In
to find
find the
the boundaries
boundaries we look
look for,
for, we might vary one variable
variable at a time,
time,
or we
we might
might vary combinations
combinations of
of variables.
variables. We then
then try
try to
to identify
identify key
key variables
variables that
that
we know will
will have a decisive
we
dec is ive influence
influence on
on the
the outcome.
outcome . Among
Among key
key variables
variables product
product prices
prices
and sale
sale : volumes
vo l umes always
always occur.
occur. In
In specific
specific cases,
cases, though,
though, other
other variables
variables might also
have a status of a key variable. In
In sawmill
sawmill costing
costing the
the sawn
sawn timber
timber recovery
recovery might
might be
be such
such
a
a key variable.
variable.
5.2
volumes
Breakeven volumes
In discussing
discussing the
In
the short-term profit planning
p~anning in
in Chapter 3,
3, the
the breakeven-volumebreakeven-volumeconcept was introduced.
introduced. It
It was defined
defined as
as the
the lowest
lowest volume
vo l ume needed
needed to
to cover
cover the
the company's
com pany's
In ot
other
overall expenses.
expe n ses. In
her words,
words, we have
have to
to find
find aa volume
volume that
that equates
equates total
total revenues
revenues
of the
of
t he sawmill
sawmi ll with
wit h its
i ts total
tota l expenses.
expe n ses. Trying to
to find
find this
this volume
volume for
for our
our model
model company,
company,
we run into
we
i nto difficulties.
diffic ulti es . First
First of
of all,
all, the
the company has two
two different products,
products, Species
Species A
and
a nd B,
B, which means that
that we
we will
will get
get aa mixture
mixture of
of revenues
revenues and
and expenses
expenses for
for two
two different
different
•
_ 53
51 -_
-
products.
products.
Secondly,
Secondly , the
the overall
overall budget
budget (Exhibit
(Exhibit 4.10)
4.10) has
has been
been built
built up in
in such
such a way
that we
nn ot take
xpenses estimates
estimates out
out of
of the
the budget
budget and
that
we ca
cannot
take eexpenses
and put
put these
these expenses
expenses into
into the
the
Before we
we do
must split
formulas for
for breakeven
breakeven calculations.
calculati ons . Before
do so,
so, we must
split our expenses into
into
formulas
variab
l e and fixed
fixed costs.
costs. To
still better
better picture
picture of
the sawmill's
itability
To get
get aa still
of the
sawmill's prof
profitability
variable
under
different
circumstances,
we
might
have
ro
study
expenses
in
terms
of
traceable
under different
we
have to study expenses in terms
traceable and
and
co mmon costs
co sts (cf.
(cE. Section
Section 2.3).
2 .3 ) . But let
let us
us start
start with
with the
the overall
overall picture.
picture.
common
In
defined the
the breakeven
breakeven volume
volume in
in the
the following
following way:
way:
In Section 3.2
3.2 we defined
where
where
(Price/
un i') . X
X .= (VC/unit)
(VC/uni') • X
X + FC
(Price/unir)
X
volume
X = breakeven volume
VC . variable costs and
Fe . fixed
fixed cosrs
cost"s
FC
'0
unit" concept
concept for
for our
our product
product mix.
mix. Let
Our first
task is
is to find
find aa "price
"price per
per unit"
Let us
Our
first task
between the
the species'
spec.ies ' sales
sa l es volumes,
volumes, 60
per ce nt for
for Species
assume
relation between
60 percent
Species AA and
and
assume that
that the
'he relation
will remain
remain the
same, even
even if
if changes
changes occur
occur in
in the
the forecast
forecast ·
40 percent
percent for
for Species B,
B, will
'he same,
for the
prod uct mix of
of MU 880 per m3.
m3 .
We can then
then use
use an
an average
a verage price
the product
volumes. We
Erice for
sales volumes.
Average price
price (A,
(A, B)
8) == 900
900 xx 0.6
0 .6 ++ 850
850 xx 0.4
0.4
per m3
m3
= MU 880 per
To
next problem,
problem, dividing
dividing the
the company's
company ' s costs
costs into
into variable
variable and
and fixed
fixed
To solve our next
In the
costs , we
we make use
use of
of our
our budget
budget in
in Exhibit
Exhibit 4.10.
4.10. In
the present analysis
analysis ir
it is
is quite
quite
costs,
imp oss ible to
- in
in advance -- how
how the
the sawmill's
sawmill's cost structure
structure will change
impossible
to decide
decide precisely volumes . Therefore,
focus our interest
interest towards
towards those
those costs that
that are indisputably
indisputably
with volumes.
Therefore, we focus
traceab
l e to
c hanges, i.e.
i . e. traceable
traceab l e costs.
costs .
traceable
to volume
volume changes,
In
5.1 the cost structure
structure has
has been
been shown.
shown. Costs have
hav e been identified
identified with
with
In Exhibit
Exhibit 5.1
the
used in
in the
the overall
overall budget
budget in
in Chapter
Chapter 44 (Cf.
(Cf . Exhibit
Exhibit 4.10).
4.10).
the same
same item
item Nos.,
Nos., as we used
As
As can be seen from
fr om Exhibit
Exhibit 5.1,
5.1, all
a ll costs
costs up
up to
to Item
Item No.
No. 106
106 have
have been
been considered
considered
traceable ; i.e.,
i . e., in
in case
case the
the sawmill's
sawmill ' s production
production is
is zero,
zero, these
these costs
costs will
will not
not accrue.
accrue.
traceable;
inventory costs
costs have
have been
been considered
cons idered traceable,
traceab l e, as
as large
large volume
volume reductions
reductions
Also various inventory
should
followed by a cut down
down in
in the
the sawmill's
sawmi ll's inventory.
inventory.
should be
be followed
Labour costs,
Let us
us look
look at some
some of
of the
the costs
costs in
in the
the "common
"common costs
costs column".
co lumn". Labour
costs, e.g.,
Let
will,within
changes,remain unchanged.
unchanged. (As
(As long
long as
are paid by
as workers
workers are
will,
within reasonable
reasonable volume
volume changes,remain
The same
the week or the month). The
same statement can be made
mad e about staff
staff salaries
salaries and depreciadeprecia the
Will they
tions . But
about such
such expenses
expenses like
like fuel
fuel and
and electricity?
electricity? Will
they not
not decrease?
de c rease?
But how about
tions.
The answer is
is that
that there
there will
wi ll most
most probably
probably be
be aa change,
cha nge, but
but it
i t is very difficult to
to
E.g., take
take fuel
fu el expenses.
expenses. True,
True , aa lower
l ower volume
volume means
means less
le ss transportation
transportation work,
work,
estimate.
E.g.,
The number of actual
but the
the reduction in this work can
can be
be made
made in
in two
two ways.
ways. The
ac.tual transports,
transports,
but
e.g . from
fr om the
the saw
saw to
to the
the kiln,
kiln, might
mi ght decrease.
decrease. But,
But, as
as a
a lower
lower volume
be transported,
e.g.
volume will be
it is
is also
t he actual
actual load
load is
is decreased
decreased each
eac h time
time the
the fork
fork lift
lift truck
truck
it
also possible
possible that the
the goods.
goods . The same
same type
type of
of argument
argument can
can be
be used
used to
to defend
def end electricity
electricity expenses
expenses
transports the
l ess fixed.
fi xed. Both the
the saw
sa w and the
the trimmer
trimmer will
will work
work all
all day
day long
long but
but at a lower
lower
as more or less
The kiln is
is heated
heated but
but perhaps
perhaps without
without being
being fully
fully loaded.
loaded.
The
pace.
Let
those costs
costs we
we call
ca ll traceable
traceab l e will
will vary
vary with
with the
the production
production and
and
Let us
us assume
assume that those
sales
t hose called common
common costs
costs will
w_ill remain
remain unchanged.
un c hanged. Let
Let us
us term them
them
sales volume
volume and those
fixed costs
costs and
and estimate
estima te the
the contribution
co ntribution margin.
margin. This margin is
is defined
defined as
as
variable and fixed
the
sales price
price and
and those
th ose variable
variable costs
costs that
that are
are relevant
relevant for
for aa
the difference
difference between the sales
decision. This
in covering
covering the
the company's
company 1 s common
common costs
costs and
certain decision.
This margin will contribute in
in creating profit.
profit. We
us e the
the expression
expression contribution
contribution to
to profit,
pr of it, CTP.
CTP.
We will
will here use
in
-- 54-
Item No
costs in
Traceable costs
in MU:
MU :
Species AA
Spec
ies B
Species
*)
*)
**))
1 06
106
5513.00
13. 00
Common costs
in
1 ,000
in MU 1,000
**)
**)
459.00
107
1 07 - 112
11 2
230
201
656
-- 203
204 204
- 205
205
206
119.20
9.20
19.20
1.80
1 .80
17.25
207
500
301
40
303
302 -- 303
45.00
42.50
304 304
- 305
305
306
306
139
19.25
117.80
7.80
307 - 310
310
Total
309
598.25
.~~~=~~
555.85
~~~=~~
874
l=~H
1
**)) Costs
for which traceability
traceability has been assumed
assumed to
Costs for
'
he
he rouahly
rou gh l y proportional
proportional to
to larger
larger volume
volume changes
changes
over the
over
the budget
budget year.
year .
**)
**)
'
Costs that have
Costs
have been
been assumed
assumed constant
constant even
even for
for
rather large changes
changes in
in volume.
volume . Some
Some of
of these
these
rather
costs will
on l y after aa decision
decis i on to
to cut
cut
will change only
do.wn (temporarily)
(temporar ily) the
the production
p r oduction time
time has
has been
been
down
taken.
Exhibit 5.1.
5 . 1..
Analysis of
of the
the traceability
traceability of
of various
various costs
costs inin tire
th-e budget
budget
If
that also
the traceable
traceable costs
costs of
of Exhibit 5.1
5.1 change
change proportionately
If we
we assume
assume that
also the
to
get the
the following
following CTP estimate:
estimate:
to the
the product
product mix,
mix, we
we get
CTP =
= 880 - (598.25
(598 . 25 x 0.6 + 555.85
x
x 0.4)
0.4) = mu
MU 298.71
We can safely round
We
round off
off this
this figure
figure to
to CTP
CTP == MU
MU 300.
300 . To check the
the correctness of
of this
this
figure, we can
ca n estimate the
the overall
overall profit
profit of
of the
the sawmill
sawmi ll at
at 10
10 000
000 m3
m3 as:
as:
figure,
Profit (10
(10 000 m3)
m3 ) = 10
10 000 x 298.71
298 .71 -- 11 874 000
Profit
which
whi
c h gives a profit of MU 11 113 100.
100.
Exhibit 4.11.
4.11.
This is
to the
is close enough to
the figure
figure given in
in
Let
us now use the
the value of
of CTP
CTP == MU
MU 300
300 to
to estimate
estimate the
the breakeven
breakeven volume,
voLume, but
but let
let
Let us
us also
also put
Such changes can
us
put in
in possible changes in
in CTP
CTP per
per m3
m3 of
of sawn
sawn timber.
timber. Such
ca n occur
because of price and/or
and/or cost
cost changes.
changes. In
5.2 breakeven volumes have been
been shown
shown
In Exhibit
Exhibit 5.2
based
decreases of
of five
five percent
percent in
in each
each step.
step. The breakeven
based on the assumption of price decreases
volumes(BEV.)have
volumes (BEVil') have
been
beenestimated
estimatedininthe
thefollowing
following way,
way, where
where "OV
"O'iV ' indicates
indicates the
the
budget
pri ce for
for our
our product
product mix.
mix.
budget price
-- 55
55 --
300 . BEVO%
BEV07, = 11 874 000
.
3 of
which gives
gives BEV07.
BEVO% =. 66 247
of sawn
sawn timber.
timbe r.
247 m
m3
calculated in
in the
the same
same way.
way.
Price change
Price
%
0
-- 55
-10
-15
Exhibit 5.2
5. 2
Exhibir
Actual price
price
in MU
in
880
836
792
792
748
748
remaining breakeven
breake ve n volumes
volumes have
have been
The remaining
reduction
CTP reduction
in
in MU
CTP00
CTP
i "I.
per m3
m3
BEVi%
BEV i %
in m3
m3
247
6 247
0
0
300
44
256
256
7 320
88
88
212
840
8 840
132
132
168
168
11
11 155
Changes
in breakeven volumes
volumes as
as aa function
function of
of price
pri ce changes
c han ge s
Changes in
ll picture looks,
l ooks, at
at first
first glance,
g l ance, very
very good.
good. There is
is aa budget
budget profit
profit
The
The overa
overall
3
of
s
l
ightly
more
than
MU
1
100000
and
a
of
6
247
m
.
This
means
a
100
000
and
a
breakeven
volume
of
6
247
m3.
of slightly
than
1
safety
safety margin,
margin, i.e.
i.e . difference
difference between
between budget
budget volume
volume and
a nd breakeven
breakeven volume,
volume, oof
f roughly
roughly
33 750 m3.
m3
Let
us now see
see under
under what
what circumstances
circumstances these
these estimations
est imati o ns are
are valid.
valid.
Let us
First of
of all,
all, we
This means that
First
we have used
used the
the sawmill's
sawm ill' s full
fu ll cost.
cost . This
that breakeven
breakeven
vo
l ume, as
l ong as
structure does
does not
is va
lid in
in the
th e long-term
long-term
volume,
as long
as the
the cost
cost strucrure
not change,
change, is
valid
perspective. IIn
n other
if both revenues
revenues and
and expenses
expen ses repeated
r e peated year
year after
after year,
year,
other words,
words, if
we would
would get
get the
the profit
profit estimated
estimated for
for this
this budget
budget year,
year, given
g iven an
an average
average production
prod uct i on and
and
3
sales volume of
10
000
m3.
In
this
perspective
the
profit
does
not
impress
too
much.
of 10 000 m . In this
the profit does no t impres s to o much.
If
If the
the budget
budget year is
is an unusually
unusually good
good year,
year, the
the expected
expected profit
profit also has,
has, in
in part,
part,
to
to cover the
the overall,
overal l, fixed
fixed costs
costs of
of less-profitable
less··profitable years.
years. What
What kind of
o f aa year
year is
is the
the
budget year budget
- a "good one",
oneil, "a
"a normal
normal year",
yea r".' or
or "a
lI a bad
bad one"
one" ??
Second
l y, looking
l ooki ng into
into Exhibit 5.2,
5.2 , we find
find that
that price
price decreases
decreases rather
rather quickly
quickly
Secondly,
turn
turn the
the sawmill
sawmi ll into
into less
less impressing
impressing profitability.
profitability. As
As "price
Itprice changes"
changes" in
in Exhibit
Exhibi t 5.2
5.2
is aa combinat
combination
of .both
both price
price aand
cost cchanges,
we realize
of
is
i on of
nd cost
hanges, we
realize that
t hat a
a negative
negative change
change of
15 percent is
is not
not an
an unrealistic
unrealistic figure.
figure. In
In ot
her words,
rather limited
li mited downward
downward cchanges
hanges
other
words, rather
in pri
ces-costs will
will increase
i ncrease the
the overall
ove rall breakeven
br eakeve n volume
volume rapidly.
rapidly . In spite of
of the
the
in
prices-costs
promising
pr omising profit
profit figure
figure for
for the
t he budget
budget year,
yea r, we
we cannot,
ca nnot , in
in the
the long
l ong run,
run, afford
afford too
too large
l arge
price-cost
pri ce-cost deviations.
deviations.
Thirdly, how
how realistic
realistic are
are the
the cost
cost estimates
est ima tes made
made in
in the
t he budget?
budget? Depreciations
Deprecia t ions Thirdly,
cost Item
I tem Nos.
Nos. 112,
112, 207
207 and
and 307
307 -- have
have not
not been
been commented
co mme nted on
on so
so far.
far. Capital costs are
are
often underestimated.
unde r estimated. The depreciation
depreciation figure
figure is
i s put
put into
into the
the budget
budget in
in order
order to
to show
show
tthe
he need for
for profit
profit accumulation
ac c umul atio n over
over time.
time . How realistic
realistic are
are these
these figures?
figures? Assume
Assume
that
they represent
represent 10 percent of actual investment
investment costs.
costs . In
In that
that case
case they
they will most
that they
probably
p ro babl y be
be a heavy
hea vy underestimate
underestimate of
of the
the actual
act ual capital
ca pi ta l cost.
cost . If
If they
they are
are doubled,
doubled, more
more
than half
half of
than
of the
the estimated
estimated profit
profit disappears.
disappears. It
It is
is important,in
important,in the
the long-term
long-term sensitivity
analysisIto
an a ly sisJ to make realistic
realistic assumptions
assumptions about
about capital
capita l costs.
costs.
5.3
Profitability as aa function
functi on of
of both
bot h CTP
CTP and
and sales
sales volumes
vo lumes
In the
the preceding section
section we made use
use .of
of only
only the
the price-cost-variable,
price-c ast-variable, i.e.
i.e. the
the
sawmill's CTP.
CTP. Changes
Changes in
in prices and/or
and/or costs
costs mostly
most l y occur
occur together
together with
with changes
changes in
in sales
sales
volumes. When market demand
demand for
for one
one reason
reason or
o r another
anot he r goes
goes down,
down, customers'
customers' price
price awareawar eness tends
tends to
to increase.
increase. The supplier,
supplier, facing
faCing decreased
decreased demand,
demand, has
has aa tendency
tendency to
t o lower
lower
56 --- 56
in order
order ro
to elicit
elicit demand.
Qemand.
Costs,
however, have a
a tendency
tendency to
to remain
remain unchanged.
unchanged.
Costs, however,
his prices in
In
5.3 the
the CTP
eTP and the
the sales
sales volumes
volumes have
have been put
put together in a
a combined
In Exhibit
Exhibit 5.3
combined
sensiti
v ity analysis
of profit
profit changes
changes as
as a
a result
result of
of combined changes
changes in
in the
the two
two ab
o vesensitivity
analysis of
abovementioned variables.
variables .
;~
.
The
The figures
figure s in
in Exhibit
Exhibit 5.3
5.3 have
have been
been estimated
estimated in
in the
the following
following way:
way:
Profit
CTP
i
Volo
= CTP i ° volo j - 1874
874 000
000
Vol.--CTP..V01..-1
j
The first
first profit figure,
figure, MU
MU 11 113
is rhe
the profit actually budgeted
budgeted for
for the
the year.
y ear.
The
113 000,
000, is
If
t he CTP
to Mu
Nu 250
250 per m3
mJ of
of sawn
sawn timber,
timber, the
the sales volume still
still remaining
If the
CTP decreased to
3 , we
aat
t 10 000 m
t~e would get:
get:
m3,
Profit
250
10 000
= 250
874 000
000 =
- MU 626 000
250 x10
xl0 000
000 -- 11 874
3 , gi
Letting
at the
the MU 300 level,
level, when sales volume goes down
down to
to 9 000 m
ves ;
Letting our
our CTP
CTP remain at
m3,
gives:
Profit
Profit
300
=
= 300 xx 9 000 -- 11 874
874 000
000 == 826
826 000
000
99 000
00 0
For
c h ccombination
ombination of
of chosen
c hosen CTP and sales
sales volume,
volume , estimated profits
profits have
have been
been calculat
ed
For ea
each
calculated
in the same
same way.
way.
in
Exhibit 5.3
5.3 shows
shows that
that when the
the CTP
CTP decreases
decreases to
to aa certain
certain level,
level, the
the sawmill
sawmi l l
Exhibit
The actual,
starts
loss.
The
actual, critical
critical CTP is
is MU 187,
187, when the
the sales
sales volume
volume is
is
starts running at aa loss.
3
10 000 m3.
m • It
It should
should be
be kept
kept in
in mind
mind that
that the
the CTP-values
CTP-values used
used are
are all
all hypothetical
hypothetical figures.
figures.
In
should, based on experience,
experience, be able to
to judge
judge what values
values to
to choose.
choose.
Each
In reality
reality we
we should,
step
50\
by
which the
the CTP-values have been decreased,
decreased, corresponds to
to a
a combined
step of MU 50,
price-cas t -change
negative price-cost-change
base the price-cost-change
to aa
CTP-value corresponds to
p e rcentage figures
figures seem
seem to
to
percentage
of 5.7
5.7 percent
p e rcent based
based on
on the
the sales
sales price
price of
of MU
MU 880.
880. Or, if
if we
of
3
on the
the combined
c ombined per-m3-cost,
per-m -cost, we
we find
find that
that each
each step
step of
of MU in
in
on
cost increase
increase of
of 8.7
8.7 percent.
percent. Over a
a spectrum
spectrum of years,
years, these
these
cost
be fairly
fairly realistic.
realistic.
be
return ro
to Exhibit
Exhibit 5.3.
5.3.
Lowering the sales
sales volumes
volumes also
also reduces
reduces profits.
profits.
Let us return
But
that even
in CTP
CTP and
and sales
sales volumes
volumes give
give drastic
drastic
But we
we see
see that
even limited combined changes in
A 10
10 percent cut
cut in
in the
the CTP
CTP and
and sales
sales volume
volume variables,
variables, i.e.
i.e . CTP
CTP == MU
MU 200
200 and
and
effects. A
3 , throws the
sales
the budgeted profit into
into the
the loss
loss area
area giving
giving rise
rise to
to a
a
sales volume
volume == 99 000 m
m3,
loss of
of MU 74
74 000.
000.
So,
all, the
the budgeted
budgeted profit
profit is
is one
one thing.
thing. The actual
actual
So, after all,
net loss
profit according to
to the
the post-analysis
post-analysis at
at the
the end
end of
of the
the budget
budget year
year might
might be
be quite
qUite
profit
different.
Finally,
let us
us look
look at
at the
the fixed
fixed costs
costs or
or common
common costs
costs in
in Exhibit
Exhibit 5.2.
5.2.
Finally, let
Changes
in the
the CTP
influence any costs
costs other than those indisputably
indisputably traceable,
traceable,
in
CTP do
do not
not influence
among those
those costs
costs that
that we
we have
have considered
considered to
to be
be common
common costs,
costs, i.e.
i.e. not
not influenced
inf l uenced by
by
but among
changes, we might find
find minor errors
errors in
in our
our judgements.
judgements.
For
limited volume
For very
very limited
volume changes,
changes, the
the so-called common costs
costs will
wi ll remain
remain unchanged;
unchanged;
but if
changes,
but
if we
we find
find that
that demand
heaVily, we must make aa more thorough
thorough study.
study.
decreases heavily,
First of
of all,
all, large
large decreases
decreases in
in sales
sales volume
volume will
of those
those
First
will probably affect part of
that we have
have termed
termed common
common costs.
costs.
Many
these are
are in
in fact
fact variable,
variable, but
but it
it is
is
Many of
of these
costs that
difficult
to analyse how
how these
these costs
costs will
will change.
change.
Therefore, we
we can
can say
say that
that the
the analysis
analysis
difficult to
Therefore,
is
in a
a slightly "pessimistic"
tlpessimistic" way.
way.
should be
be aa positive
positive "error
"error margin".
margin".
There should
is made
made in
Sales
CTP
voluCTP ~mes
per m3
m3
mes
per
in MU
MU
Profits in
10
10 000
99 000
88 000
1
000
000
7 000
6 000
~ =
profit
prof it combinations
*)
113*
113 )
826
526
226
250
626
376
126
-- 124
124
200
126
- 74
74
-
-- 274
150
-- 374
374
300
1
'
-- 74
74
~ ,~
loss
ti o n s
loss combina
combinations
V>
"
*)
*) Profit according to
to budget,
budget, i.e.
i.e. CTP
CTP == MU
MU 298.71.
298.71.
All other
figures on this
this row are
are based on a CTP
All
other figures
of MU
MU 300.
300.
'
Exhibit
5.3
Exhibit 5.3
Profits in
MU 11 000 as
as a
Profits
in MU
a function
function of
of changes
in CTP
CTP and sales
in
sales volume
volume
-- 58-
Th
e r e is
i s another possible
possibl e cost
cost change
c hang e that
t hat we should
should study.
study. We
tima ted the
There
We have
have es
estimated
"common
S" according
to the
the budget
b udg et as
as MU
to1U 11 874 000.
000 .
Par
t oof
f this
this amount
amo unt can be
be
"common cost
costs"
according to
Part
in
f lu enced by our
o ur decisions.
decisions . In
i on with
c rease in
in demand,
to
influenced
In aa situat
situation
with rapid
rapid de
decrease
demand, we
we have
have to
study
f our
our fixed
fixed costs (cf.
(ct. Section 2.2,
2.2, especially Exhibit 2.4).
2.4) .
study the
the step-fixed
step-fixed nature
nature o
of
We
l l find that
that the
the following
following costs are
a r e of
of step-fixed
ste p-fixed character:
character :
We wi
will
Cost
Cost
Item No.
108
Labour,
l og handling
Labour, log
110
Repair
(at least
l east the
the labour
Repair & maintenance
maintenance (at
compo
nent and
se rvi ces purchased
from
component
and services
purchased from
ou
t side)
outside)
201
201
Labour,
sawi ng process
Labour, sawing
202
Repair
(cE. Item
Item No.
No . 110)
11 0)
Repair &
& maintenance (cf.
203
Heat ing (If
(If the
the sawmill
sawmill has
than one
Hearing
has more
more than
kiln,
one can be
be closed,
c l osed, at
at least
least
kiln, perhaps one
te mp o rarily. Or one
one chamber
chambe r can
ca n be
be
temporarily.
blocked
depending on
on the
the technical
techn i cal construcco n st ru cblocked depending
t i on of
of the
the kiln).
kiln).
tion
301
301
Labour, storing
Labour,
305
305 & 310
Sa larie s , sales
sa l es manager
c l e rk
Salaries,
manager and
and office
office clerk
Besides
step -fixed costs we must
mu st also
a l so analyse
ana l yse those
those costs
cos ts that
that are
are variable
variab l e or
or
Besides step-fixed
f i xed and
a nd variable
variable costs
costs (semi-variable)
(semi-variable) to
to see
see how
h ow they
t hey will
will change
cha nge with
with various
va ri ous
mixes of fixed
decisions.
decisions. What
do, if
if we believe
believe that
that aa decrease
decrease in
in demand
demand will
will last
l ast over
ove r aa long
l ong
What we
we can
can do,
period, is
is to
to decide
decide on
on aa temporary
temporary shut-down
shut -down of
of rhe
the whole
who l e mill
mi ll either
eit h er for
for an
an extended
extended
period,
period or by
by reducing
reducing the
the number
number of
of work-days
work-days per
per week.
week. The two
two possibilities
possibil i t i es will
will to
to
some extent
extent have
some
have different
diffe ren t effects on
on costs.
costs. Reducing
the number
number of
work-days per
per week
wee k
Reducing the
of work-days
will,
will, e.g.,
e . g . , have
have no
no effect
ef fe ct on
on such
such costs
costs as
as drying
drying costs,
costs , as
as the
the kiln
ki ln cannot
ca nn ot be
be shut
s hut off.
of f.
5.4
Production disturbance
Production
disturbance and its
i ts economic
economic effects
effects
In pproduction
one always
In
r oduct i on one
a l ways has to
to be
be prepared
prepared for
for various
various kinds
kind s of
o f unforeseen
unf oresee n or
or
unplanned
unplann ed production
product i on disturbances.
disturbances. Some
possible ro
to influence,
influe nce , like
lik e
Some of
of them are possible
s t ops due to
to poor
poo r maintenance,
maintenance, poor
poo r planning
planning of
of raw
raw materials
materials inflow,
inflow, or
or
production stops
careless operation
operat i on of
of machinery.
machinery. Others we cannot
canno t influence,
influence, such
such as
as defective
defective
parts
parts in
in machines,
machines, strikes
strikes or
o r various
various kinds
kind s of
of catastrophe.
catas trophe.
But
Bu t whatever
whate ver rhe
the reason,
reason, all
all
disturbances have
hav e one thing
thing in
in common:
co mmo n: they
they are
are extremely
e x t r emely expensive
expensive to
to the
the sawmill.
sawm ill.
Let us
us once
once more
more return to our budget
Let
budget in
in Exhibit
Exhibit 4.10
4. 10 to
to study
st ud y the
the economic
economic effects
effects
of
of production disturbances.
dist urban ces . Str
ikes , fires,
fires, catastrophes
catas tr ophes and
and the
the like
like can
can be
be long
l o ng lasting.
las t ing.
Strikes,
Othe
r disturbances might vary
vary from
from minute-long
minute-long stops
stops to
to stops
stops of
o f several
several days.
days . Very few
few
Other
costs
are changed
cha ng ed during
during these
t hes e temporary
tempora r y stops,
sto p s , but
but one
one thing
thing we
we know
know for
for sure
sure is
i s that
t hat the
the
costs are
m3
m3 nor
not produced
produced during
during aa stop
stop will
will never
neve r be
be produced.
produced. For our
our company,
company, every
every stop,
sto p, long
l ong
eenough
nough to
to eliminate
el imina te production of
of one
one m3
m3 of
of sawn
sawn timber,
timber, reduces
r educes the
the revenues
revenues by
by MU
MU 880
880
as an
as
a n average.
average .
We also
We
a ls o know that
t ha t the
t h e m3
m3 we
we do
do not
not produce
produce will
wi ll save
save us
us the
the raw
raw materials
materials cost,
cost,
th e cash
cas h discount,
discount, and the
the sales
sales commission,
commission, but
but no
no other
ot her costs
cost s of
of significance
sig ni ficance will
wi ll be
be
the
reduced.
red uced. Our average
average inventories
in ve n to ri es will
wi l l not
no t be
be affected
a ffe cte d by
by aa minute-long
minute-l ong -- not
not even
even aa few
few
days'
days ' long
l ong -- production
production stop.
stop . The very
very few
few traceable
traceab le costs
costs for
for this
t hi s kind
kind of
of disturbance
disturbance
have
have been
bee n summarized in
in Exhibit 5.4
5.4 As can be
be seen
see n from
from this,
this , the
t h e raw
raw materials
mater ial s costs
costs
_ 59
59 -_
-
calculat.ed
in Exhibit 4.10
4.10 have
have been
been reduced
reduced by
by the
the raw
raw materials
materials inventory
inventory costs
costs
calculated in
(Item
No. 103).
103).
Deducting these
these costs
price, gives
gives us a CTP that
that
(Item No.
costs from the average sales price,
is
f o r rhis
this profitability
profitability estimate.
estimate. As
As an average
average the
the sawmill
sawmi ll will
lose MU 355.40
355.40
is relevant
relevant for
will lose
3
for
each m
m3 of
timber not
for each
of sawn
s~timber
not produced.
produced.
importance of this
this CTPreduction
CTP-reduction becomes
becomes obvious,
obvious, if
if we
we calculate
calculate what
what it
The importance
it means
means
per day.
day.
If
50 working
weeks per year less
less 15
15 legal
legal holidays,
holidays, we
we arrive
arrive at 235
235
If we
we assume
assume 50
working weeks
wo
rking days.
days. With a normal
normal daily
daily production
pr od uc t ion of
of 10
10 000/235
000/235 == 42.6
42.6 m3
m3 of
of sawn
sawn timber,
timber, the
the
working
reduction in
in the
the sawmill's
sawmill's CTP
CTP will be
be 42.6
42.6 xx 355.40
355 . 40 == MU
MU 15
15 140
140 for
for one
one day's
day's breakdown.
breakdown.
With an
working day
day we
we get
get aa CTP
CTP drop
drop of
of MU
MU 11 893
893 per
ur or
With
an 8-hour
8hour working
per ho
hour
or MU
MU 31.55
31.55 per
per minute.
The cost
cost estimates
estimates made
made here
here are
are based
based on
on the
the opportunity
opportunity cost
cost concept.
conce pt.
It is
is
The
It
important
to find
find out
o ut the
the actual costs of
of production
production stops,
stops, but it
it is
to
important to
is also
also important
important ro
instruct
the ooperators,
perato rs, especially those
those in
in key
key positions,
posit ions, what
what even
even short
short stops
stops mean
mean
instruct the
econom i cal ly to
to the
the sawmill's
sawmill's profit.
profit.
economically
in MU
MU per
per m3:
m3:
Costs in
Spec
ies A
A Species BB
Species
Specification
5 13.00
513.00
costs, net
net
- Log costs,
method
12.20
Log inventory
+ Log
costs
18.00
- Cash discounts
commis27.00
- Sales
Sales
commis-27.00
s
ion
sion
459.00
545.80
492.80
= Relevant cost
per m3
per
price , m3
m3
Ave rage price,
+ Average
rage, relevant
- Ave
Average,
cost m3
= Relevant CTP per m3
Relevant CTP per day
Weighted
average
in MU
in
8.20
17.000
17.0
25.00
25.~0
880.00
524.60
355.40
======
15 140
140
per hour
Relevant CTP per
hour
1
pe r minute
Relevant CTP per
31. 55
31.55
Exhibit 5.4
5.4
893
for evaluating
evaluating production
production stops
stops
Different CTP:s for
_ 60
60 _
5.5
5.S
The
The CTP in price
pri ce negotiations
Customers
try to
to negotiate for
for aa lower
lower price.
price.
Customers always try
have
the following
following possibilities:
possibilities:
have the
In
situation mee
we will
In such aa situation
1.
Demand
is good
and we
find other customers,
customers, if
if our refusal
refusal to
to cut the
the price
price
Demand is
good and
we can find
means aa lost
lost customer.
customer.
2.
Demand
is bad
cut is
is necessary ro
to get the
the customer
custome r to
to buy now.
now.
Demand is
bad and
and price
price cut
We leave
We
leave longterm
long-t e rm effects
effects out,
out, e.g.
e.g. the
the influence
influence that
that aa price
on
price cut
cut might
might have on
the customer's future
future expectations.
expectations. We
do not
not consider
the possibility
possibility of
of losing
the
We also
also do
consider the
losing
the
the customer permanently.
perman ently. lnstead
interest on
on what
CTP we
use
Instead we
we concentrate
concentrate our
our interest
what CTP
we will
will use
in
-term effects
effects on
on profit.
proEit.
in the
the two
two situations
situations described
described above
above in
in order
order to
to estimate
estimate short
shortterm
To
simpl ify, we take
take only
on l y species
species AA as
as an
an example.
example.
To simplify,
The
The first
first case
case is
is simple:
simple :
If
is good,
good, and the
the sawmill
sawmill can
can sell
sell its
its product
product
If demand
demand is
without cutting the
without
the price,
price, rhere
there is
is no
no need
need for
for aa price
price cut
c ut at
at all.
all.
But if
the price is
is
if the
cut,
the consequences will
will be
be a
a reduction
reduction in
in CTP.
CTP . Let
Let us
us assume
assume aa price
price cut
cut of
of MU
MU 25,
25,
cut, the
i.e.
MU 900
i.e. from the
the price
price ~U
900 to
to MU
MU 875
875 per
per m3.
m3 .
Specification
Ordinary
price
Price
m3
Price per m3
Cash discount
Sales commission
Sales
900 . 00
900.00
18.00
18.00
27.00
27 .00
875.00
875.00
17.50
17.50
26.25
CTP per m3
m3
855.00
831.25
Reduced
price
The
The price difference
difference of
o f MU
MU 25
25 will
wi ll be
be reduced
reduced to
to aa difference
difference of
of MU
MU 23.75
23.75 after
after having
having
taken changes
~ha nges in
in cash
cash discount
discount and
and sales
sales commission
commission into
into consideration.
consideration .
But what
what economic effects will accrue
But
accrue in
in the
the second
seco nd case?
case? We assume that
that the
the sawsawinventory of
of finished
finished boards
boards has
has piled
piled up,
up, and
and that
that one
one possibility
possibility of
of selling
selling the
the
mill's inventory
boards is
is to
to cut
cut the
the price.
price.
In
In this
this situation there
there are
are two
two possibilities.
possibilities.
Let us
us call them
them C1
C1 and
and C2:
C2:
Let
Cl:
C1:
We try
try to
to maintain the
the ordinary
ordinary price.
price.
C2:
C2 :
We cut
cut the
the price
price ro
to the
t he extent
extent that
that the
the new
new price
price elicits
elicits an
an immediate
immediate sale.
sale.
We
We now
now have
have to
to see
see what
what will
wil l happen
happen when
when choosing
choosing either
either of
of the
the two
two alternatives.
alternatives.
If
If we decide
decide to
to maintain present
present price
pri ce (C1),
(C 1 ), we
we can
can have
have the
the following
following expectations:
expectations:
1.
We will
will get
We
get this
this price sooner
sooner or
or later.
later.
2.
The
boards will
remain in
in stock
stock and
and thereby
thereby give
give rise
rise to
to inventory
inventory costs
costs during
during
The boards
will remain
the waiting
waiting time.
time.
3.
demand increases
increases in
in the
the future,
future, we
we can
can sell
sell the
the boards
boards tor
tor the
the ordinary
ordinary
When demand
price (assumption),
(assumption), but there
there is
is aa possibility
possibility that
that the
the boards
boards have
have deteriorated
deteriorated
during storage
storage (cracks,
(cracks, discoloration,
discoloration, stains,
stains, etc.).
etc.).
how long
long will
will it
it take?
take?
But how
3
_ 61 -_
-61
If we
to cut
cut our
our price
price (C2),
(C 2 ), the
the boards
boards will
will be
be sold
sold immediately.
immed iat e ly.
If
we decide to
that the
the price
pri ce cut
cut will
will be
be large
large enough
enough ro
to elicit
elicit immediate
immediate demand.
demand.
presumed that
It is
is
It
Let
us use the
the following
following denotations
denotations to
to quantify
quantify the
the required
required decision:
decision:
Let us
Let :
Let:
xX
= the
the waiting time,
time, expressed
expressed in
in months,
months,
y = the
the lower
lower price needed to
to elicit
elicit an immediate
immediate demand,
demand ,
Y
the mathematical
error, if
if we do not
not take
take possible deterioration into
mathematical error,
ee = the
and
consideration and
ii
cost , i.e.
i.e. the
the interest
interest we have
have to
to pay
pay on
on capital
capital tied
tied up.
up.
= our capital cost,
not taken
taken into
into consideration
conside ra tion any
any other
other cost
cost than
than deterioration
deterioration (e)
(e) and
and
We have not
capita l cosrs
costs (i).
(1) . All
like manufacturing costs
costs and company
company ove
rheads, are
are
capital
All other
other costs,
costs, like
overheads,
eq ual for
for both
both courses
cou r ses of
of action.
action.
In
sunk costs,
costs, and
and they
they should,
should,
equal
In other
other words
words they are sunk
therefore,
not influence
influence our
our decision.
decision.
costs, though,
though, are
are
therefore, not
Deterioration and capital costs,
incremental
to CI
C (cf.
(cf. Section
Section 2.6).
2.6). There
are two more incremental
in cre mental costs,
costs, namely
namely
incremental costs to
There
are
1
ca sh discounts and
and sales
sales commissions.
commissions . But if
if we define
define the
the present
present (ordinary)
(ordinary) price
price as
as
cash
well
as the
the variable
variable YY as
as the
the net
net price
price we
we get
get after
after deduction
deduction of
of cash
cash discounts
discounts and
and sales
sa l es
well as
commissions,
have taken
taken these
these incremental
increment.al costs
cost.s into
int.o consideration
co nsideration as
as well.
well.
commissions, we have
What
What are the
the unknown
unknown variables
variables in
in this
this problem?
problem? Y
Y is
is the
the dependent
dependent variable
variable that
that
we
are supposed ro
to estimate.
estimate . The waiting time
time -- XX -- must
must be
be assumed.
assumed.
Finally,
the capita
we are
Finally, the
capitall
cost
(i) must be
be decided.
decided.
But
this is
is the
the opportunity
opportunity cost
co st concept
co n cept that
that we
used many
cost (i)
But this
we used
many times
in
in Chapter
Chapter 4,
4, and
and we
we will
will probably use
use the
t he interest
interest the
the sawmill
sawmil l has
has to
to pay on
on its
its credit
credit
account
account..
The
for Species
SpeCies AA is
is MU
MU 900.
900 . Most probably
probably the
the boards
boards show
show aa much
much
The average price for
lower
us sayMU
700per m3.
m3 . We
state our problem
problem as:
as :
lower price,
price, let
letus
sayMU70Cper
We can
can now state
consequences: Cl
C
Economic consequences:
1
700 -
Y •
Y
i
.- X
X
100
-1 2
100-12
- ee
Economic
consequences: C2
C
Economic consequences:
2
yY
The formula
formula reads:
reads:
If
C , we
get the
the desired (ordinary)
(ordi n ary) price
price minus
If we
we choose
choose C1,
we will
will get
l
the interest
interest we
we would
would have
have earned
earned at
at i
i percent p.a.
p.a. during
during XX months
months minus
minus the
the costs
costs of
of
the
deterioration that
that will
will accrue.
accrue .
The
The economic consequences of
of C2
C are
aremerely
merely the
the price
price we
we get
get today,
today , after
after having
having
2
accepted a
a price
price cut.
cut . Equating the
the two
two courses of
of action and
and solving
solVing for
for Y gives
g iv es the
the
price
that is
is economically justified.
justified .
price that
r
Let us
us assume that
that it
it will take
take at
at least
least nine
nine months
months (X)
(X) before
before the
the customers
customers are
are
Let
to pay
pay MU
MU 700
700 for
for these
these boards.
boards.
the costs of
of deterioration
deterioration (e)
(e) and
willing to
Disregarding the
using
the 10 percent
per ce nt interest,we
interest,we can
can solve
solve for
for Y:
Y:
using the
700-700
Y
Y
10 -- 9
9
- 10
-
Y
Y
100-12
MU 651.16
651 . 16 or
or rounded
rounded off
off to
to MU
MU 650.
650.
which gives YY == MU
We did
did not take
take the
the cost
cost of
of deterioration
deterioration into
into consideration
consideration because
because it
it varies
varies from
from
one place to
to another depending
depending on
on climate
climate factors,
fa cto rs, storing
storing resources
resources and
and so
so forth.
forth.
Let us
us
estimate the
the average
average cost
cost per
per m3
m3 of
of a anine
ninemont,.
mont~. wait,
wait, added
added storing
storing as,
as - MU 35.
35. All we have
have
to
this figure
figure in
in our formula
formula which
which means
means that
that the
the ordinary
ordinary price
price will
will be
be
to do
do is
is to
to enter
enter this
3•
Solving for
MU 618.60 ora rounded-off
of MU
620 perm3.
reduced
to 700
700 - 35
35 == 665.
665.
Solving
for YYgives
givesMU618.600ra
ro und ed"Off price
priceof
MU62Qperm
reduced to
_ 62 __
_62
we have
have calculated
What
have done
done here
here is
is not
not to
to estimate
estimate aa certain
certain CTP.
eTP. Instead
Instead we
What we have
o ur present
present CTP
eTP will
will be
be reduced in
in order to
to elicit
elicit an
an immediate
immediate demand.
demand.
how much our
5.6
5.6
The
flow budget
budget
The cash flow
In doing
doing so,
so, we
we fo
focus
cash
Let
Let us now
now construct
construct aa cash
cash flow
flow budget
budget for
for our
our company.
company.
In
cus cash
inflows
during the
the budget
budget year.
year. The
starting point
inflows and cash outflows during
The starting
point for
for this
this is
is to
to study
the sawmill's revenues
revenues and
and expenses.
expenses. The
The budgets presented in
in Exhibits
Exhibits 4.2
the
4.2 and 4.10 are
important sources
sources of
of information.
information. These
These two budgets, however,
however, do
do not
not necessarily
necessarily tell
tell
the whole truth
truth about
about cash
cash flows.
flows . Log purchases,
purchases, e.g.,
e .g., do not
not always
always coincide
log
coincide with
with log
the
We mus
must
also remember
remember that
that there
there ca
can
consumption, causing
causing changes
c hange s in
in inventory
inventory balances.
balances.
We
t also
n
payments during
during the
the year
year that
that havenothing
have nothin g to
to do
do with
with either
either sales
sales revenues
r eve nues or
or
be many payments
As
an example,
example, we can mention
men tion interest
interest and amortization
amortization payments on
o n loans.
loan s.
expenses.
As an
In planning the
the cash flow
flow we have
have to
to consider
cons ider not
not only
only the
the total
tota l amount of
of cash
cash
In
The primary aim
flows but
but also how they
they are
are distributed
distributed timewise
timewise during
during the
the year.
year. The
aim is
i s to
to
flows
make sure
sure that
that cash
cash is
is available,
available, when
when payments
payments are
are due.
due.
To build up
up a
a cash flow
flow budget
budget we turn
turn to
to the
the expenses
expenses budget
budget in
in Exhibit 4.10,
4.10,
which is
is the
the most
most complicated
comp li cated of
of our
ou r two
two main
main sources
sources of
of information.
information. The expenses
expe nses budget
much of
of these
shows the
shows
the overall costs that
that the
the company
company will
will have
have during
during the
the year.
year. But
But hhow
ow much
create corresponding
corresponding cash
cash outflows?
outflows? To
this question,
to
To answer
answer this
question, we
we will
will have
have to
costs will create
scrutinize each cost item,
item, check
check whether aa corresponding
corresponding payment
payment will
will accrue,
accrue, and,
and, finally,
finally,
see
the payments
payments will
wi,ll be
during the
the year.
year.
To
let us
us leave
leave the
the raw
raw
see when the
be due during
To begin with,
with, let
materials costs
costs out
out and
and instead
instead start
start with
with log
log handling
handling costs
costs (Item
(Item No.
No. 108
108 in
in Exhibit
Exhibit 4.10).
4.10).
To
get a
a somewhat realistic
realistic example,
example, we
we have
have to
to make
make some
some assumptions
assumptions about
about how
how
To get
are spread
spread during
during the
the year.
year . This has
has been
been made
made in
in Exhibit
Exhibit 5.5.
5.5. Some expenses
expenses
expenses are
others quarterly.
quarterly.
In
Item No.
No. 205,
205, it
it has
has been
been assumed
assumed that
that
are paid monthly, others
In one
one case,
case, Item
are made
made once
once every
every six
six months.
months. All
All these
these expenses are supposed to be paid
payments are
but in
in every company there
there will be
be aa great
great number
number of
of payments
payments that
that accrue
accrue more
more
regularly
but
or less
less irregularly
irregularly over
ove r the
the year.
year . One can,
can, of course,
course, not
not take
take into
into consideration every
every
sum that
that might
might flow
flow in
in or
or out,
out, but
but more
more important
important payments,
payments, showing
showing an
an irregular
irregular
petty sum
pattern, must be
be studied.
studied. Examples
shown on
on the
the right
ri g ht in
in Exhibit
Exhibit 5.5.
5.5.
pattern,
Examples of
of such payments are shown
In Exhibit
Exhibit 5.5 we recognize the
the items
items from
from Exhibit
Exhibit 4.10.
4.10. Some
them, however,
howev er,
In
Some of
of them,
show
in these
these two
two exhibits.
exhibits. Most items
items have been placed in
in the
the "monthly
show different
different amounts in
No. 109,
109, watering costs,
costs, has
has been
been placed
placed in
in the
the "quarterly
"quarterly column",
co lumn", i.e.
i.e.
column".
Item No.
it
has been assumed that
i~ has
that the
the electricity
elect ricity and
and water
water bills
bills are
are paid
paid every
every three
three months.
months.
Item
fuel expenses
expe nses of
of 20,
20, paid
paid every
every month,
month, and
and electricity
electricity of
of 8,
8, paid
paid
Item No.
No. 111 contains fuel
Item
total value
of 94 in
in Exhibit
Exhibit 4.10
4.10 and has here been
been estimated
quarterly.
Item No.
No. 203
203 had
had aa total
value of
at
only 20.
20. The
74, is
the value
by-products used
used for
for hheating,
eating , and
they
at only
The difference, 74,
is the
value of
of by-products
and they
do not give rise
The aamount
might be
rise to
to cash
cash outflows.
outflows. The
mount in the
the monthly column might
be costs of
of
oil and the
the amount
amount in
in the
the quarterly
qu arterly column
column can
can be
be electricity
electricity costs
costs (fans).
(fans).
oil
No. 304
304 is
is travelling
trave lling costs.
costs. These have been
been assumed
assumed evenly spread over
over the
the
Item No.
year (22)
(22) plus
plus extra
extra expenses
expenses during
dur ing intensive
intensive selling
se llin g periods
periods (months
(months 8,
8, 99 and 10).
10). The
manager is
is assumed
assumed to
to have
have aa yearly
year ly salary
salary of
of 116.
116. In addition to
to this he gets
gets aa premium
premium
of one per cent
cent of
of achieved
achieved profit
pr ofit to
to be
be paid
paid in
in the
the 6th
6th and
and the
the 12th
12th month
month with
with half
half of
of
of
the
amount each
each month.
month.
the estimated amount
To get aa rough
rough "estimate
estimate of
of the
the cash
cash outflow,
outflow , the
the totals
totals have
have been
been spread
spread out
out
to the
the estimates
estimates shown
shown in
in the
the footnotes.
footnotes.
This does not
not give exact amounts
amounts but
but
according to
good enough approximations.
approximations.
- 63
63 -_
-
There are still
still a number of
of cost
cost items
items in
in Exhibit
Exhibit 4.10
4.10 that
that are
are missing in
in
Exhibit 5.5.
5.5 . Log
depending on
on inventory.
inventory. They
therefore, treated
Log costs
costs fluctuate depending
They are,
are, therefore,
separately.
costs and,
and, therefore,
therefore, part
part of
of Exhibit
Exhibit 4.10,
4.10, but the
the
Depreciations are costs
corresponding expenses must be found
found elsewhere,
elsewhere, and
and they
they will be
be discussed
discussed later.
later. Cash
Cas h
discounts and sales
discounts
sa l es commissions vary with the
the sales
sales volumes
volumes and
and have been treated together
together
with the
the cash
cash inflows
inflows from
from sales.
sales.
Item
No.
in Exhibit
Exhibit 4.10
4.10
Expenditures taken
taken from
from the
the budget
budget in
regularly per:
per:
irreguAccruing irreguAccru ing regularly
Accruin2
Accruing
Total
Total
larly:
Month
108
Quarter
Half
Half--yea r
year
No. Amount
Amount
Month No.
40
109
40
25
25
11
1100
45
1111
11
20
201
4480
80
480
202
82
82
203 1 )
2031)
12
204
1123
23
205
50
301
40
304
22
45
8
8
28
20
8
8
123
123
1188
40
304
' 304
305
105
308
116
11 6
72
4
4
(8 )
22
24
(9 )
44
44
( 10 )
66
6
6
105
308
(6)
(6 )
5.5
5.5
5.5
(1
2)
(12)
5.5
5.5
5.5
309
62
62
310
48
48
1_2472)
Total l~§~Z2)
~~3)
593)
~4)
44)
§~5)
235)
333
L~~~
1
1) Deviates from
from budget
budget figure
figure because
because all
all bark
bark and
and most
most of
of the
the
slabs
for heating the
the kiln.
kiln.
slabs and
and chips
chips are used for
2)
Spread evenly over
over 12
12 months
months by
103 900
900 p.
p . m.
m.
by MU
MU 103
3)
14 800,
800, mon
ths Nos.
3 , 6,
9, & 12.
12.
Spread by
months
6, 9,
by MU
MU 14
Nos. 3,
4)
000, months
months Nos.
12 •
Spread by MU 22 .000,
Nos. 66 & 12.
5)
indications above.
over the year
yea r according
according to
to indications
above.
Spread over
Exhibit 5.5
5 .S
of how actual expenditures
expenditures (payments)
(payments) are
are spread
spread over
over the
the year.
year.
Analysis of
000)
(Amounts in MU 11 000)
_ 64 _
_64
Let us
us now compile the
the cash
cash flow
flow budget,
budget, which
wh i ch is
is shown
s hown in
in Exhibit
Exhibit 5.6.
5.6 . From
From
Let
Exhibit 4.2
4 .2 we
the estimated
estimated sales
sa le s volumes.
volumes. To simplify
si mplif y the
the procedure,
procedure, it
i t has
has been
been
we find the
assumed that
that the
the sales
sales recorded
recorded each
ea c h month
month also
also give
give rise
rise to
to cash
cash inflow
inflow for
for that
that month.
month.
On the
the first
fi r st row
row we find
find the
t he sales
sa l es revenues
revenues for
for both
both species
sp ec i es multiplied
multipli ed by
by 0.95.
0.95.
That
revenues have
ha ve been
been reduced
redu ced by
by cash
cash discounts
discounts (2
(2 percent)
percent) plus
plus sales
sa l es commissions
commi ss i ons
That means
means revenues
(3 percent).
(3
per cent). Thereby we have
hav e taken
taken also
also cost
cost Items
Ite ms Nos.
Nos . 302
302 and
and 303
303 into
int o consideration.
co nsiderat ion.
On
the second row
row we find
find revenues
revenues from
from by-products.
by-pr od ucts. Summing
Summi ng together
toget her we get total
tota l inflow
inf l ow
On the
for each month,
month, which,
which, on
on the
the fourth
fourth row,
r ow, has
has been
been accumulated
accumulated month
month by
by month.
month.
for
Cas h outflows start
start with payments
payments for
f o r logs.
l ogs. Our
source of
of information is
is Exhibit
Exhibit 4.8.
4 .8 .
Cash
Our source
Thereafter transportation
transportation expenses
expenses have
have been
been estimated.
estimated. For
transportaFor raw materials
materials and transportation expenses we must take
take into
int o account
account that
that we
we do
do not
not always
always consume
consume the
the same
same amounts
amo un ts as
as
tion
have purchased.
purchased .
we have
Next row shows the figures
figures estimated
estimated in
in Exhibit
Exhibit 5.5.
5 . 5.
Next
upon earlier.
earlier .
These have
have been commented
comme n ted
These
Finally, we have assumed bank loans
loans due
due ro
to previous
previous investments
investments that
that give
give rise
rise to
to
Finally,
quarterly payments
payments of
of MU
MU 550
550 000.
000. To get
get a realistic
realistic picture
picture of
of the
the overall
overa ll cash
cash flow,
fl ow ,
also consider
co nsider company
comp any taxes.
taxes. They have
have been
been assumed
assumed to
to be
be paid
paid monthly.
monthly. We have
have
we must also
accounted
for the
the toral
total tax
tax expenses
expenses during
during the
t he budget
budget year.'/
year.!/
accounted MU 45 000 per month for
Summing up
up all
all expenses gives the
the total
tota l cash
cash outflow,
o u tflow, which
which has
has been
bee n accumulated
acc umul ated
mon th by
by month.
month. Comparing
Compa ring accumulated cash inflow
infl ow and
and cash
cash outflow
outflow gives
g i ves the
t he balance
balance
month
month by
by month.
month. We see from
from this
this last
la st line
line in
in Exhibit
Exhibit 5.6
5.6 that
that the
the cash
cash flow
flow situation
s ituat ion
varies during
varies
duri ng the
the year.
year. In the
the beginning of
of the
the year
year the
the balance
balance is
is rather
rather small
s mall but
but
positive,
increasing up
up to
to more than
than MU
MU 11 000
000 000
000 in
in the
the 8th
8th month.
month. Durin
g the
the
positive, thereafter increasing
During
9th
however, we
face aa negative
negative balance
balance of
of over MU 600
600 000.
000 . This is
is due
due to
to the
the
9th month,
month, however,
we face
fore
cast purchase
purchase of
o f logs
l ogs which is
is extremely
extremel y high
high during
during the
the 9th
9th month.
month .
forecast
Studying the
the cash flows
flows gives rise
rise to
to many questions.
questions. Would
it be
be possible to
to
Would ir
influence
purchases of
of logs
logs and spread
spread them
them more evenly
evenly during
dur i ng the
the year?
year? If
I f not,
not , how
how to
to
influence purchases
solve
cas h flow
flow ·problem.
loan s be
be taken?
taken? How will this
t hi s influence
influe n ce the
t he overall
ove rall
solve the cash
problem. Must
Must new loans
cost
a l so the
the profit
profit of
of the
the company?
compa n y? If
If log
l og purchases cannot
cann ot be
be
cost picture
picture and thereby also
changed
to do
do something
somethi ng else.
e l se. Is
Is the
the pattern shown
shown here
here typical
ty pi ca l also
a lso
changed,, we
we obviously
obviously have to
for other years?
If so,
so, can
can the
for
years? If
the overall
overa ll cash
cas h outflow
outf l ow be
be restructured?
restr ucture d? There
i s one heavy
heavy
There is
payment,
in terests and amortization,
amortizat i on, that
that also
also accrues
accrues in
in the
the 9th
9th month.
month. Perhaps
Pe rhap s the
the
payment, interests
bank
bank re-payments
re-payments can be
be changed to
to give
give aa more even
even pattern
pattern over
over the
the years.
years.
!/
1/
do not
n ot analyse
ana l yse how
how this
this amount
amount is
is estimated.
esti mated.
We do
country
taxes actually
act ually paid.
paid.
country to another as do taxes
Tax-paying systems vary from
from one
one
./
,-----_. -..
_.
------ -_._... .... - -----_... _. _.._-_..
__ ..
--_. - - --
3
44
5
6
77
88
9
10
'0
795.6
20.
20.11
584.3
584.3
14.8
14.8
543.9
543 . 9
5430
543.9
.9
13
.8
13.8
543.9
13
.8
13.8
624.6
15.9
710.1
710.1
710.1
18
.0
18.0
18 . 0
18.0
836.0
836.0
21.2
21.2
836.0
21.2
557.7
557.7
4 760.8
857.2
857.2
7 714.7
857.2
8 571.9
11
11
Cash inflow
inflow
(Species AA ++ B)
B) xx 0.95
0.95
(Species
by-p r oducts
by-products
795
.6
795.6
20.1
20.1
836
836.0
.0
21.2
Total inflow
inflow
857.2
Accumulated inflow
inflow
Accumulated
857.2
~~~=~
13.8
815.7
815
.7
815.7
599.
599.11
557.7
557.7
557.7
557.7
627.9
~=~~~=~
2 488.6
~=~~~=~
3 087.7
~=2~;=~
3 645.4
~=~~~=~
4 203.1
~=~2~=!
240 . 0
240.0
144.0
17.6
17
.6
103
.9
103.9
200.0
90.0
90.0
13.2
13
.2
118.7
118
.7
550.0
(,5.0
45.0
1
640.5
640.5
728.1
728
.1
~=~~2=~
5 401.3
~=~2~=~
6 129.4
728.
728.11
6857.5
200.0
300.0
1 000.0
150 . 0
150.0
72 . 0
72.0
12.3
12 . 3
180.0
180.0
22.0
105.9
105.9
630.0
74.8
74.8
90.0
11.0
11.0
109.9
109.9
103 . 9
103.9
45.0
45.0
45.0
45.0
45.0
405 . 9
405.9
7 202.0
~=!~~=~
~=~~~=~
;=n~=;
12
"
~=~~L~
Cash outflow
outflow
Cash
Log purchases,
purchases , Species
Species AA
Log
Log purchases,
purchases , Species
Species BB
Log
Transpo r tation
Transportation
From Exhibit
Ex hibit 5.5
5. 5
From
Interests
Interests &
& amortizations
Taxes
330.0
330.0
198.0
198.0
24.
24.22
103
.9
103.9
Total outflow
outflow
Total
Accumulated
Accu~ulated outflow.
outflow,
701.1
550.5
1 016.9
016.9
1(,8 . 9
148.9
148.9
148.9
721.2
721.2
433.2
433.2
652.9
2 422.5
422.5
2
701.1
~g!=l
251.6
~=~~~=~
2 268.5
~=~~~=~
2 417.4
~=~H=~
2 566.3
~=~~~=~
3 287.5
~=~~;;~
3 720.7
~=;~2=;
4 373.6
~=H~
=~
6 796.1
~=;?~=~
Cash balance end of month
156.1
H~=l
421.3
~~!=~
220.1
~~2,;l
670.3
~;g=~
079.1
L,2;~=!
915_6
~!~=~
040.1
l=2~2=1
027.7
J=2~;=;
-666.7
;~~~=;
45.0
45.0
45.0
t.~.0
1
1
103.9
103.9
45,0
45.0
45.0
1
126.2
550.0
45.0
45.0
103.9
103.9
122.7
122.7
150 . 0
150.0
90.0
550 . 0
550.0
45.0
45.0
1
(000 MU)
f'!U)
exhibit 5.6 The
The Cash
Cash Flow
Flow Budget
Budget (000
Exhibit
45.0
45.0
1
148.9
;=~2~=g
7 350.9
;=~~2
=~
-344.5
;~~~
=~
363.8
~~~=~
11.0
126.2
550.0
45.0
45
.0
972.2
972.2
8 323.1
~=H~=~
248.8
~~~=~
I
cr-
cs,
Ln
'-"
I
_- 66_
66-
6.
6.
6.1
CAPITAL
BUDGETING
CAPITAL BUDGETING
Decision
Decision character
In
In the
the previous
previous two
two chapters
chapters we
we have
have worked with
with budgeting
budgeting and cost
cost calculation
calcu l ation of
routine
routine operations,
operations , i.e.
i.e. more
more or
or less
l ess daily
daily operations
operatio ns of
of the
t he sawmill.
sawmi ll.
In
t h is chapter,
In this
we
change the
the perspective into
into various
various kinds
kinds of
of long-term
Long-term decisions
decisions within
within the
the field
field
we will
will change
of capital budgeting.
of
budgeting. We
define capital
capital budgeting as "long-term
"l ong-term planning decisions
decisions for
for
We define
investments
financing" (Horngren,
(Horngren, Charles
Charles T.,
investments and
and their
their financing"
T., ed.,
ed., Cost
Cost Accounting.
Accounting. A Managerial
Emphasis,
International editions,
editions, Englewood
Englewood Cliffs,
Cliffs, N.J.,
N.J., 1982,
1982, p.
p. 404).
404).
Emphasis, Prentice/Hall International
Capita
l budgeting differs in
in many respects
respects from
from short-term
short-term cperating
c perating decisions.
decisions.
Capital
Let
us point
point out
out the
the main characteristics of capital
ca pital budgeting
budgeting as compared
compared to
to the
the company's
company' s
Let us
shor
t-term decisions.
decisions.
short-term
1.
In
pital budgeting
he time
explicitly .
In ca
capital
budgeting tthe
time span
span has
has to
to be
be taken
taken into
into account
accountexplicitly.
used in
in aa cap
i tal budgeting can vary
vary from
from more
more than
than one
one year
year up
The
t ime span
The time
span used
capital
to time
time periods of
of 10,
10, 15,
15, or
or even
even more
more years.
years.
to
2.
Due to
to the
Due
the expanded time
time span
span of
of the
the decision,
decision, "the
"the money
money concept"
concept" changes.
changes.
A monetary unit
unit received
received (paid)
(paid) today
today is
is worth
worth more
more than
than the
the same,
same, nominal
nominal
A
amount received (paid)
(paid) in
in aa more
more or
or less
les s remote
remote future.
future.
amount
3.
Some -- but
but far
all -- capita
capitall budgeting decisions
Some
far from
fr om all
decisions have
have enormous
enormous impacts
impacts on
a company's
abilit y to
to survive
su rvive in
in the
the long
long run.
run. When
When chis
this is
is the
t he case,
case , the
the
a
company's ability
ca
pital budgeting decision
decision involves
involves heavy
heavy risk-taking.
risk-taking.
capital
4.
Capital
is of non-routine
non-routine character,
c haracter, i.e.
i.e. decisions
decisions are
are made
made
Capital budgeting is
intermittently.
5.
Capital
focuses cash
cash flows,
flows, some
some of
of which do
do not
not necessarily
nece ssar ily have
have to
to
Capital budgeting focuses
co
rrespond to the company's revenues
revenues and/or
and/or expenses.
expenses.
correspond
6.
Due to
Due
to long time
ti me spans normally involved
involved in
in capital
cap it al budgeting,
budgeting, the
the degree
degree of
of
uncertainty is
is often extremely
extremely high.
high.
There
Th
e re are
are numerous examples of
of capital
capital budgeting
budgeting decisions.
decisions. Investing money
money in
in
new production
product ion equipment
eq uipment and/or
and/or buildings
buildings is
is undoubtedly
undoubted ly acapital
a capital budgeting decision,
deCision, while
while
the
the purchase
purchase of
of a
a new electric pencil-sharpener
pencil-sharpener is
is not.
not. Obviously,
Obviously, there
there is
is no
no easily
eaSily
identified line
line of
of demarcation
de marcation between
between capital
ca pital budgeting
budgeting and
and operational
operational decisions.
decisions.
In assessing the economic consequences
consequences of
of aa certain
certain decision,
deCiSion, the
the time
time span
span and
and
In
its
influence
can
be
taken
as
something
typical
for
capital
budgeting.
its influence
be
something typical for capita l budgeting. True,
True, as
as we will
see
see later,
later, there
t here are
are models of capital budgeting
budgeting that
that do
do not
not consider
consider the
the difference
difference
between the
the present
present and
and the
the future
future value
value of
of money.
money. But it
it is
is always
always possible
possible to
to change
change
such
models into
models, in
such models
into new models,
in which
which this
this difference
difference is
is regarded.
regarded. So let
let us start
start with
the
the task of
of comparing present and future
future values
values of
of money.
money.
6.2
Evaluating time-spread money
Evaluating
The models
models and
and some
The
some of
of the
the concepts
co n cepts used
used in
in capital
capital budgeting
budgeting originate
originate from
from the
the
field of banking.
banking. Assume
Ass um e aa person
person who
who wants
want s to
to put
put in
in MU
MU 100
100 in
in his
his savings
savings account.
account.
He knows that
that he gets 88 percent
percent interest
interest p.a.
p.a. on
on money
money saved.
saved. How much does
does his
his capital,
capital,
due to
to the
the bank interest,
interest, increase
increase during
during one
one year?
year? Let
Let us
us use
use the
the following
follOWing denotations:
denotations:
- 67
67--
Co
Co
= capital value now,
now, also
also called
ca lled present
present value.
value.
C
C1
capital value
value at
at the
the end of
of the
t he first
fir st year,
year, aalso
ls o called
called
1 = capital
va lue.
future value.
r
r
= rate
of return,
bank interest
rate of
return, i.e.
i.e. in
in this
this case
case the
the bank
interest
(8 percent).
W
e can now show
show his problem graphically.
graphica ll y. We
s kind
We
We will
will use
use thi.
this
kind of
of graph
graph throughout
this
this chapter,
chapter, letting
lett.ing upwards directed
directed arrows
arrows show
show cash
cash inflows
inflows and downward directed
directed
arrows cash outflows.
outflows. Putting the
the money into
into his savings
savings account
account is
is a
a cash outflow (even
(even
if the
the money is
is still his own,
own, being just
just temporarily
temporari l y lent
lent to
to the
the bank) and the
the collection
collection
if
it (after
(after one
on"e year)
year) is
is aa cash
cash inflow.
inflow.
of it
= ??
C
C11
to
I
money value
value increases
increases
The monev
at 88 %
% interest
r
PI
~I
iat
C
;= 100
100
The designation
designation to
t
indicates "time
"time zero",
zero", i.e.
Le. "now"
"now" or the
t h e starting point
point for
for a
a project.
project.
indicates
-0
We will use
use this
this designation
aesignation occasionally.
occ asionally.
We
The
of the capital after exactly
exactly one
one year
year is
is 100
100 xx 1.08,
1.08, which will be
be the
the
The value
value of
This, in
will grow
grow by
by 8 percent
to aa
capital value
value for
for the
the second
second year.
year. This,
in turn,
turn, will
percent to
beginning capital
future capital,
capital, at the
the end of the
the second
second year,
year, which
wh i ch amounts
amounts to
to 1.082.
1.08 2 . This ending capital
future
the second
second year
year becomes
becomes beginning
beginning capital
capital the
the third
third year.
year. In the
the same way,
way, the
the beginning
beginning
of the
capita l oE
of the
the last
l ast year
year will be
years, the
the capital
capita l has
has grown
After exactly ~
n years,
be 1.08(n-1).
capital
to:
to:
C
C
n
;
n
rr
n
C . (1 +
+ 100
Co-(1
100)
o L
.
t
t
( 1)
)
•
L.1----
= Compound interest
interes t
value
Present value
;
;
Future value
value
In
(1) we
the general formula
formula for
for' the
the compound
compound interest,
interest, with which
which the
the present
present
In (1)
we have
have the
into aa higher,
higher, future
future value.
value.
value grows into
-- 68
68 -
In capita
capital
budgeting we
we do
In
l budgeting
do not
not very often use
use the
the compound
compound interest
interest formula,
formula, but
but
we
l ways need to know the
the reverse
reverse process,
proc e ss, i.e.
i.e. how
how to
to convert
convert a known,
known, future
future value
value (Cn)
(C n )
we aalways
present value (C0).
iinto
nto aa present
(Co ), Assume
the person in
in our example knows that
that he
he will
wi ll get
get
Assume that
that the
exactly MU 108
108 in
in exactly
exactly one
one year's
yearts time.
time.
His
oblem is
is to
to find
find out the
the present
present value
value
His pr
problem
(Ço) of the
(~o)
the future
future value
value (C1
(f1)) tthat
hat is
is known
known to
to him.
him.
If
is still
still 88 percent,
percent,
If the
the interest
interest is
wecann graphically
we-ca
gra phically state
state hi
his problem
in the
the following
fol l owing way:
way:
problem in
c,
C1
The money value decreases
dec reases
The
Pe at
at 88 per
per cent interest
interest
1
C01=
= 108
' 08
1
?
Putting the figures
figures into
into formula
f ormu la (1)
(1) gives:
g i ves:
108 = Co
1.
08
1.08
This
is equivalent
fo rmul a (1)
(1) only
on l y that
that ~o
is the
th e unknown aand
nd
This expression
expression is
equivalent to formula
Co now is
Ci the
fl
the known
known variable.
variab le. Solv
i ng for
for Co
fa and,
and, at
at the
the same
same time,
ti me, putting
putting in
in the
th e general
ge n era l
Solving
eTcpression for
for the compound
expression
compoun d interest
interest-a-ccording
a ccording to
to (1)
(1) we
we get:
get:
c,
C=
o
(2
(2))
1
,n
100'
r
(1
4.
Here n
Here
n = 1,
1, and the
th e answer
answer becomes
becomes
C
oo
108
10°=10
0
1.08
~
100
This is
is clearly
clear l y the
the reversed
reversed process.
process. The
Th e factor
factor 1/(1
called the
th e compound
compound
1/(1 ++ l~O
L )n) nisiscalled
100
di s count, as we have discounted
discounted (diminished)
(di minish ed) the
the future
future value
value in
in estimating
estimating its
it s present
presen t
discount,
value, i.e.
i . e. we have "diminished"
"diminished" the
the future,
f utur e, nominal
nominal value
value in
in order
o rder to
to make
make the
the two
two amounts
amounts
value,
equally
equal
l y large
large in
in real
real terms!
terms !
We do not have to
to calculate
ca l cu la te these
these factors
factors every
every
(1
(1 + r/100)n,
r/100)n, and the
the compound
compo und discount
discount factors
factors 1/(1
1/(1 ++
Appendix
Appendix 1).
1). In
In Table
find the
the compound
compound interest
interest
Table A we find
of
r
and
nvalues.
of r - and n-val u es . The
The compound
compound discount
discount factors
factors are
are
time.
t ime. The compound interest
interest factors,
factors,
r/100)n,
r /100) n, are found
found in
in tables
tab l es (see
(see
factors for
for various
various combinations
combinations
factors
shown
shown in
in Table
Table B.
B.
A
A person, who puts
puts in
in an
an amount
amount of
of MU
MU 500
500 in
in his
his savings
savings account
account at
at an
an interest
in te rest
of 12
12 percent
percent p.a.
p.a . will,
will, after
after 10
10 years,
years , have
have aa capital
cap it a l that
that has
has grown
grown to:
to :
10 years
500 • Table AA ~ ~%years = 500
500 • 3.1058
3.1058
C10 = 500
12%
552. 90
= 11 552.90
--69
69 -
If
we know the
to,' in
If we
the initial capital at £0
in this
this case Co
fa = MU 500,
500, we multiply this
this
capital by the
Tale AAfor
the interest
interest factor
factor found
found in
in Taole
for the
the pertinent
pertinent r~- and
and n-values,
~-valuesl in
in this
this
case 3.1058,
3.1058, to
to ger
get the
the future
future value
value Cid.
~10'
To save some
some work we use
use the
the abbreviated
abbreviated form:
form:
10
TA12
This
is read
read "Table A
A for
for 10
10 years and 12
12 percent".
percent".
This is
In
In the
the same way we
we can
can use
use the
the discount
discount factors
factors of
of Table
Table B.
B. Assume aa person,
person, who
who
bas a life
life insurance
insurance that
that will
will be
be paid
paid in
in exactly
exactly seven
seven years.
years. Its future value
value is
is
has
If he
he wants
wants to
10000.
If
t .o get
get his money now,
now, he can do
do so by accepting a
a lower,
l ower, nominal
nominal
MU 10
000.
than what he
he would get,
get, if
i f he
he wair
ed until the
the insurance
insurance ·pe
ri od expired.
expired_ If
the
amount than
waiteduntil
Teriod
If the
insurance
company discounts the
insurance company
the future
futu r e value
value by
by an
an interest
interest rate
rate ot say
say 8 percent,
percent, he
get :
will get:
7
Co == C7
C7 .TB
TB; == 10
10 000
000 • 0.5834 = 55 384
8
If
interest of
of 10
10 percent
percent he
he wo
uld have
have got:
got:
If the
the insurance
insurance company had used an interest
would
C = 10
10 000 • TB7
TB 7
C7
7
10
IO
10 000
000 • 0.5131 == 55 131
131
= 10
From
learn that
that the
the higher the
the interest
interest rate,
rate, the
the lower
lower is
is the
t he
From this
this example
example we
we learn
compound discount
discount factor
factor and,
and, thereby,
thereby, also
also the
the present
present value.
value.
,
So
of single cash flows
flows along the
the time
ti me axis.
axis. In
So far
far we
we have
have studied movements of
capital budgeting,
budgeting, however,
however, we
we very
very often
often want
want to
to discount
discount the
the sum
s um of
of equally
equa lly high,
high, nominal
nominal
amounts
that are earned (e.g.
(e.g. net
net income
income figures)
figures) or
or saved
saved each
each year
year during
during aa series
series of
of
amounts that
for which it
it has
has been
been estimated
est imated that
that net
net earnings
earnings per
per year
year will
wiil
years. Assume
Assume aa company,
company, for
amount to
amount
to MU 22 000 for
for the
the next
next five
five years
years to
to come.
come. To illustrate
illu st rat e this
this problem,
problem, we
we can
can
once again make use
use of a graphical
gral-'hical model,
model, which
which has
has been
been shown
shown in
in Exhibit
Exhibit 6.1.
6.1.
22
22
22
2
2
2
2
000,0.5674
000-0.5674
000·0.6355
000-0.6355
000,0.7 11 7
000.0.7117
000·0.797 1
000-0.7971
000-0.8928
000.0.8f8
-=
=-
----------------------------------1
I
-------------------------1
I I
- --- -------------------------~
i
----------::---1i tt tt t
- --------------------[
=
---
I
t
1
I
1
I
to
lr
'It
Discount
facto
rs
factors
for
for the
yea
rs 1
years
to 55 for
io
-rr = 12%.
12 %.
tI
1
1
t
t
i
t
t
I
~I----+I----~I----~--~~--~,
I
t
4
4
55
33
1
2
2
Each
----O.= MU
MU 2
2 000
Each-+=
000
1
Exhibit 6.1
6.1
Discounting
Dis
co un ting a series of equally
eq uall y high,
high, nominal
nominal amounts
amounts
Each
amount of
Each amount
of MU 2 000 is
is spread
spread out
out during
during each
each year.
year . For computational
reasons,
reasons, it
it is
is easier to place each
each amount
amou n t at
at the
the end
end of
of its
its year.
year . This slight
sl ight error
error
into the
the analysis
analysis is,
is, however,
however, negligible
negligible in
in capital
capita l budgeting.
budgeting.
brought into
-- 70
70-
To find the
the present
present value
value or
or Co,
fa' we
we multiply
multiply and
and add
add together:
together:
2.000.TB 1 ++ 2
2 000TB12
000·TB 22 +
+ 22 000.TB
Co = 2.000.T132
000-TB3312
12
12
12
1
+
4
5
22 000.TB
=
000-TB12
000-TB12
12 + 22 000·TB
12 =
000[0.8928 ++ 0.797
22 000·[0.8928
1 +
0.7117 + 0.6355
0.6355 +
+
0.7971
+ 0.7117
00.5674)
. 5674] = 22 000-3.6045
000·3.6045 =
= 77 209
209
(3
(3))
sum of
of the
the parenthesis
parenthesis becomes
becomes 3.6045,
3.6045, or,
Of, after
after rounding,
rounding, 3.605.
3.605. If
The sum
If we
5
compare
this figure
figure with the
the figure
figure in TC12,
TCI2J which is
is 3.602,
3.602, we find
find a
a difference
difference of
of
compare this
0.0025.
sum and
and the
the cable
table value
value is
is due
due to
to rounding
rounding off.
off.
0.0025. The difference between our sum
This
that in
in Table C
C we find
find the sum
sum of compound
compound discount
discount factors
factors for
for various
various
This means
means that
combinations of rcombinations
r- and
and n-values.
n-values. When the
the amount
amount received
received (paid)
(paid) is
is equally
equally high
high each
each
year -- then
then and
and only
only then
year
then -- we do not have to
to make separate
separate calculations of each amount.
amount.
Instead
Instead we
we just
just use
use Table
Table C
C and
and multiply the
the yearly
yearly (equally
(equally high)
high) amount
amount by the
the factor
factor
sums
find in
in the
the table.
table.
sums we
we find
Let
new concept,
concept, the
the annuity.
annuity. In
In taking a loan
l oan in
in a bank,
bank, there
there
Let us
us introduce aa new
are two different ways of paying
are
paying the
the money
money back.
back. Either
choose to amortize the
the loan
loan
Either we
we choose
by
the help of equal amortization amounts
amounts every
every year
year (flat
(flat amortization).
amortization). In
case,
by the
In this case,
the
the interest paid will vary over the
the years
years and
and so
so will
will the
the combined
combined amount
amount of
of interest
interest
and amortizations.
amortizations. Or,
Or, we
we ask
ask the
the bank to
to find
find an equally high amount
amount to be
be paid each
year,
year, estimated
estimated in
in such
such aa way
way that
that it
it covers
covers both
both re-payments
re - payments on
on the
the loan
loan (amortizations)
(amortizations)
and the
th~ bank's
bank's interest.
interest. This amount is
is called
called the
the annuity.
annuity.
Assume a company taking
taking aa loan
loan of
of MU
MU 100
100 000
000 at
at an interest
interest of
of 10
10 percent
percent p.a.
p.a.
loan is
is to
to be
be paid
paid back
back in
in five
five years.
years . The
The payment series
series for
for this
this flat
flat amortization
amortization
The loan
loan will be
be as
as follows:
follows:
End of
of
year No.
No.
11
22
3
3
4
55
Debt before
before
amortization
100
80
60
40
20
000
000
000
000
000
Interest
for the
the
year
Amorti Amortization
Total
amount
amount
paid
10
8
6
4
2
20
20
20
20
20
30
28
26
24
22
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
This
shows a
a maximum financial
financial burden
burden of
of MU
MU 30
30 000
000 (first
(first year)
year) and
and aa
This series
series shows
minimum
Suppose the
minimum financial
financial burden
burden of
of MU
MU 22
22 000.
000. Suppose
the borrower finds
finds it
it inconvenient
inconvenient with
with
s uch varying financial
financial burdens.
burdens . Instead,
Instead, he asks the
the bank for
for an annuity loan,
loan, i.e.
i.e. a
such
loan
which wi
will
loan which
ll be
be repaid with the same,
same, nominal
nominal amount
amount every
every year.
year. Graphically,
Grap hi cally,
_ 71_
71_
_
the
l em can be described
described as
as follows:
follows:
the prob
problem
100 000
000
Co =~ 100
iIli
IS
1
1
IA
4
A
l\
A
A
A
A
He wants
pay, in
in the
the future,
future, MU AA per
per year
year to
to cover both interest
interest and
and amortizaamortizaHe
wants to pay,
The
present value
val ue of
of this
this series
ser i es of
of five
five payments
paymen t s of MU AA shall
sha ll be
be exactly
exact l y
The present
100 000.
000. How much does
does he
he have
have to
to pay?
pay?
MU 100
tion.
Let
us go back to
to Exhibit
Exhibit 6.1.
6.1. There,
Let us
There, we
we estimated
estimated the
the present
present value
value of
of aa series
of
payments , equally high
high each
each year.
year. Now we know the
the present
present value,
value, which
which is
i s MU
MU 100
100 000,
000,
of payments,
and
and we
we want
want to find
find a
a series of equally high,
high, nominal
nominal amounts paid
paid every year,
year, the
the present
present
value of
of which shall
shall be
be exactly
exactly MU
MU 100
100 000.
000. We
present the
the prob
l em in
in a
a similar
similar way
We can present
problem
as
6 . 1 and just
just reverse
reverse the
the process.
process. This
This is
is shown
shown in
in Exhibit
Exhibit 6.2.
6.2.
as was
was done in Exhibit 6.1
000
100 000
Co =~ 100
Table B,
B,
discount
factors
factors
for
~ 10%
for rr =
A·0.9090
A-0.9090
A-0.8264
A0.75 13
A-0.7513
A-0
_6830
A-0.6830
A0.6209.;
,A-0_6209
4,2 i
_ __ ____ _ _ _ _ _ ~ _ _ ~ 2 t
1
I
1
i~
1
33
!
I
I
I
1
5
~
I
I
I
I
= - - ----- -- ---- -- ---- --~1
I
I
- - --- - - - - - - - - -_ -- - - -- -I
____
__
__________
____
____________
I
- _ ___ __ __________ _ ___ __ ____ _ _________ _ _ J1
I
I
4
4
I
~
1
1
1
1
1
~
1
~
•
Each
ThiJ
sum
This sum
equals Co
6.2
Exhibit 6.2
--+
the annuity
an n u it y
i. e . the
= A,
A, i.e.
Discounting
annuities to
Di
scounting the
the annuities
to present
present value
value
Putting these
these figures
figures into
into formula
formula (3)
(3) we
we get:
get:
100
100 000
000 =~ AA • [0.9090 + 0.8264
0 . 8264 ++ 0.7513
0.7513 ++ 0.6830
0.6830 ++ 0.6209]
0.6209]
= A.3.7906
A·3 . 7906
By
for AA we get:
get:
By solving for
A =
100 000
3.7906
381
- 26 381
(4)
(4)
The
The annuity
annuity estimation is
is the
the reversed
reversed process
process of
of estimating
estimati ng the
the factors
factors found
found in
in
Tab l e C.
C. Al
l we
is to multiply
mu l tiply the
the present
present value
va l ue (MU
(MU 100
100 000)
000) of
of our
our loan
l oan
Table
All
we have
have to do is
the annuity factor
factor in
in Table
Table D,
D, which
whi c h is
is calculated
calculated as
as the
the inverted
inverted values
values of
of the
the
by the
C values, and
and we
we get
get the
th e annuity.
annuity .
corresponding Table C
72 - 72
We have
have now two
We
two payment series - for
he flat
flat amortization loan
loan and for
for the
the
for tthe
annuity loan.
Both series are equally valuable
loan. Both
valuable in
in real
real terms.
terms. To
To prove
prove this
this statement
statement
we
through the
the following
following two
two calculations:
calcu lations:
we can carry through
Year No.
No.
_ii
Flat payment
Flat
Eayment
each year
each
11
22
33
4
4
55
Discount
Present
Present
factors,
values
i
TB 10
TBin
___
30
28
28
26
26
24
24
22
22
000
000
000
000
000
0.9090
0.8264
0 .7513
0.7513
0 .6830
0.6830
0 . 6209
0.6209
27 270
270
139
23 139
534
19 534
16
16 392
660
13 660
Sum oof
f present values
val ues over
over 55 years:
years:
99 995
========
rrounded
ounded off
off
oorr
100 000
========
The present value
val ue of
of the
the annuity
annuity series
series we
we get
get by
by multiplying
multiplying the
the annuity,
annuity, MU
MU 26
26 380
380
The
5
by reio
TC10,! whic
which
by
h gives aa present
present value
value of
of MU
MU 100
100 007.
00 7. Also
i n this case aa small
s mall rounding
rounding
Also in
difference appears.
a ppear s .
6.3
Decisio
n models
mode ls
Decision
66.3.1
.3.1
The basic
basic example
examp le
Let
Let us
u s turn
tu rn to the
the decision models used
used in
in capital
ca pital budgeting.
budgeting. To compare difEerent
different
models as
well
as
the
results
of
our
decisions,
we
will
use
the
same
basic
example
as
as the results of o ur deC isions, we will use the same basic example through
through
all five
all
five methods presented.
presented. We
We will focus
f oc us on
on the
t he methods
met hods as
as such,
such, leaving
leaving for
for the
the moment
moment
all practical considerations
all
considerations aside.
aside .
Ler us
us study a company planning to
Let
to invest
invest in
in aa new
new machine,
machine, e.g.
e.g. aa lathe.
lathe.
nneeded
eeded to carry out
out the
the analyses
analyses are
are as
as follows:
follows:
The amount
amount to
to be invested,
invested , the
the price
price of
of
The
the lathe,
lathe, all
all costs
costs included.
incl ud e d.
Estimated
Est imated net
net earnings per
p er year
year as
as a
a result
result
of the
t h e investment.
investment.
of
Scrap value
value of
of the
the lathe
l at he at
at the
the end
end of
of its
its
useful
us ef ul life
life (in
(in this
this case
c ase 10
10 years).
yea rs).
MU
MU
Figures
100 000
"
20 000
"
10 000
Finally,
i n t erest rate
rate to
to be
be able
able
Finally, we
we need an interest
to discount future
future cash
cash flows
flows to
to rheir
their present
present
to
values.
This rate
values . This
rate is
is the
the company's
companyts required
~equired
rate
of
return,
RRR.
When
referring
~ate
~eturn, RRR.
referring to
to the
the RRR,
RRR,
we will
will denote
denote it
it ~r'
r. In
we
t his example we use
use
In this
10 percent.
r
6.3.2
6.3.2
The Net Present Value model
The
ide a behind
behind the
the Net
Net Present
Present Value
Value method
(NPV-method) is
i s that
that all
al l cash
cas h flows,
flows,
The idea
method (NPVmethod)
being traceable
traceab l e to
to the
the investment
investment decision,
dec ision, will
will be
be moved
moved to
to to
£0 find
find the
the NPV.
NPV . The model
uses different
time axis
axis cash inflows
uses
diffe r ent time
t ime value
value of
of money
money depending
dep e ndingononwhere
wherealong
alongth-ethe time
inflows
and cash
cash outflows
outflows accrue.
accrue . The time
time value
value of
of money
money is
is estimated
estimated by
by help
help of
of the
the company's
company 's RRR.
RRR.
- 73 -
Our basic
basic example
example can
can be
be shown
shown in
in the
the following
following way:
way:
---------------------h
r
E
20 000
E = 20
E = 20
20 000
000
5
10
t1S10
t
to
22
11
=
110
0 000
---)1
~~----4----+--1ll
~
=
I
I
n=10
n= 1 0
33
= 100
II =
1 00 000
000
where
I . the
the investment
investment expense
expe ns e
where I
= net
net ea
earnings
E =
rnin gs per
per year
year
scrap value
the end of
of the
the 10th
10 th year
s10 = scrap
value at
at the
510
The
The dotted
dotted line
line indicates
indicates that
that the
the amount
amount EE == 20
20 000 accrues every year.
year .
present
value at
prese
nt value
at the
the RRR of
of 10
10 percent,
percent, NPV10,
NPV 10 ' is
is found
found by
by the
the formula:
formula:
10
10
NPV10 = E.TC10 + S10.11310
The net
( 5)
(5)
This formula
formula reads
reads in
in words:
words: The net
ne t present
present value,
value, all
all amounts
amounts discounted
d i scounted at
at
10 percent,
percent, is
is found
found as
as the
the sum
sum of
of the
the net
net present
present values
values of
of yearly
yearly earnings
earnings plus
plus the
the scrap
scrap
value
value minus
minus the
the investment
investment expense.
expense. The designations
designations TC
Te and
and TB
TB stand,
stand, as
as before,
before , for
for
Tables
Tabl
es CC and
and B.
B.
Let
Let us now put in
in the
the assumed figures
figures for
for this
this investment
investment together
together with
with the
the values
va lues
found in
in Tables CC and
and B.
B. We get:
get:
NPV10 = 20
20 000 • 6.145 + 10 000 • 0.3855 - 100 000
NPV10 = 26
26 755
755
This NPV of
This
of MU 26 755
755 tells
tells us
us that
that the
the investment
investment gives
gives aa rate
rate of
of return
ret urn that
that is
is
higher than
than the
the RRR
RRR of
of 10
10 percent.
percent. As all future
future cash
cash flows
flows have
have been
bee n discounted
discou n te d by
by the
t he
RRR,
RRR, aa NPV
NPV of
of exactly
exact ly zero
zero would
would have
have yielded
yielded exactly
exact ly 10
10 percent.
percent. But
as the
the sum
s um of
of the
t he
But as
discounted
future
cash
flows
is
larger
than
the
investment
expense
that
the
company
has
discou nt ed future cash flows is larger than the investment expense that t he company has
to
pay now,
to pay
now, the
the investment
investment obviously must yield
yield more
more than
than 10
10 percent.
percent.
For
NPVmethod we
For the
the NPV-method
we get
get the
the following
following decision
decision rules:
rules:
1.
If the
the NPV
NPV for
If
for aa single
singLe investment
investment is
is equal to
to or
larger
larger than zero,
zero, the
the investment
investment is
is profitable.
profitable.
2.
In comparing two or more investment
In
investment alternatives,
aLternatives,
the one
one with
with the
the largest
the
largest NPV is
is the
the most profitable
one.
- 7474 -
It is
is important to
to learn
l earn to
to interpret
interpret the
Fir st of all,
all, the
the NPV
NPV
Ir
the NPV one gets. First
is aa function of the
t he figures
figures we
we put
put into
into formula
formula (5).
(5). These
The se amounts, in
in their
their turn,
t urn, are
are
is
estimat
i ons. The
the estimations,
est i mat i ons , the
the less
less trustworthy is
is the
the NPV.
NPV.
is
The poorer the
estimations.
There is
always
alway s aa degree
degree of
of uncertainty
uncertainty in
in our
our estimates.
estimates. But
But this
t his we will take
take care
ca re of
of later
later on,
on,
bring the
the sensitivity
se n s it ivity analysis
analysis into
into the
the picture.
picture.
when we bring
As was
was pointed out earlier,
Th e NPV
NPV is
is also
a l so aa function
fun c tion of
o f the
t he chosen
chose n RRR.
RRR. As
earlier, the
the
The
pre se n t value
value diminishes
diminishes with
wit h higher
higher interests.
intere sts . In Exhibit 6.3,
6.3 , NPV.s
NPV . s have
have been
been shown
shown
present
for
values of
of RRR.
RRR. If
take any
interest into
in to consideration,
for various values
If we
we do not
not take
any interest
consideration, we
we get
get the
the
nominal
n ominal difference
difference between
between cash
cash inflows
infl ows and
and cash
cas h outflows
outfl ows as:
as :
10
NI'V,
NPV,
• 20 000 + 10 000 - 100
100 000 = 110
110 000
000
~j U
11
0 000
aDO
110
100
100 000
000
80
tlOCl
80 000
660
0 000
000
40
000
40 000
,
20 000
DOD
20
2
6
R
10
12
14
16
RRR,
RRR ,
6.3
Exhibit 6.3
"
The
as a
a function
fun ct ion of
o f the
t he company's
company ' s RRR
The NPV as
This
the intercept
in terce pt with
with the
the vertical
vertical axis
axis in
in Exhibit
Exhibit 6.3.
6 . 3 . The more we
we
This corresponds
corresponds to the
t he RRR,
RRR, the
the lower
l ower the
the NPV
NPV becomes.
becomes . At a RRR
RRR of
of slightly
s lightly less
l ess than
tha n 16
16 percent,
percent,
increase the
the
becomes zero.
zero .
the NPV becomes
6.3
.3
6.3.3
The Annuity
Annuity M
Method
The
e thod
The annuity
ann uity concept
conc ept was introduced
intro du ce d in
i n Section
Sec ti on 6.2
6.2 and
and defined
defined as
as an
an equally
equally high
high
amount
to be
l arge enough
enough to
to cover
cover both
both amortizations
amortizatio ns and
a nd yearly
yearly interest
interest
amount to
be paid each year and large
on a loan.
l oan . We can
can use
use this
this concept
co nce pt also
also when
when analysing
ana ly sing the
the profitability
profitability of
of an
an investment.
investment.
Th
e an
nuity then becomes
beco mes an equally
equa lly high
h ig h amount
amo un t needed
needed each
each year
year to
to cover
cover depreciations
de pr ec iati ons and
and
The
annuity
RRR. From a
a computational point of
of view,
view , depreciations
deprec iati ons are
are substituted
subst itut ed for
for amortizations.
amortizations.
It
should be
in mind,
though, that
that depreciations
depreciati ons and
and amortizations
amortizati on s are
a r e two
two different
different
It should
be kept
kept in
mind, though,
thi
ngs. A
A yearly
year l y depreciation is
is aa measure
measure of
of the
the company's
comp a ny ' s sacrifice,
sacrifice, i.e.
i.e. cost,
cost, when
when
things.
The amortization,
us
ing the
the machine
bu il d i ng that
t ha t it
it has
has invested
invested in.
in. The
amo rtizati on, on the
t he other
other
using
machine or
or building
hand, is
hand,
is just
just the
the re-payment
re - payment the
the company has
has ro
to do,
do, in
in case
c ase it
it takes
takes aa loan,e.g.
l oa n, e . g . from
from aa
bank
bank..
I
--75
75 -
Let us now go back
back to
to our basic
basic example.
exampl e. We
that year
l y net
(~) have
have
Let
We know
know that
yearly
net earnings
earnings (E)
been estimated
estima ted to
to MU
MU 20
20 000.
000 . When using
using the
the Annuity
Annuity Method we ask
ask ourselves,
ourselves, how much
much the
the
Still
using
as the
annuity, we
we
investment cost is
is per year and compare
compa r e this
this with
with E.
E. Stil
l us
i ng A as
the annuity,
find
find A
~ with the
the following
fo llowing formula:
formula:
10
10
(6
(6))
(I -- S10.TH10)*TD10
A == (I
A
t
t-----
annuity factor.
factor.
- The annuity
The present
p resent value
--The
the scrap
scrap value
value
of the
in 10
10
to he paid in
y ears time.
time .
years
= The
The amount to
to he
be inin ves t ed
vested
be
I
ot her words, we
we find
find the
the annuity
annuity as
as the
the annuity
annuity factor
factor in
in Table
Table D,
0, multiplied
multiplied by
by the
the
In other
differ e nce between
between the
the investment
investment amount
amount and
and the
the present
present value
value of
of the
the scrap
scrap value.
value . Putting
difference
in
figures we
we get:
get:
in our
our figures
A = (100
(100 000 -- 10
10 000
000 • 0.3855) • 0.1627
A
A = 15
15 643
643
In
s, we
to earn the
t he amount
amount MU
643 in
in order
In other
other word
words,
we need,
need, each
each year,
year, to
MU 15 643
order to
to be
to depreciate
depre ciate and
and pay
pay interest
interest on
on (the
(the company's
co mp any 1 s RRR)
RRR) this
this investment.
investment. According to
to
able to
will get
get an
an E-value
E-val ue of
of MU
MU 20
20 000
000 per
per year,
year, i.e.
i.e. MU
MU 44 357
357 more
more than
than is
is
the example we will
Obviously, this
this investment
investment is
is profitable.
profitable .
required. Obviously,
Fo
r the
the Annuity Method we get the
the following
following decision
dec i sion rules:
rules:
For
•
1.
If the
the yearly
earnings accruing from
from the
the investment
investment are larger
larger than or equal to
to
If
yearly earnings
the annuity required,
r equired, aa single
sing l e investment
investment is
is profitable.
profitable.
the
2.
In compar
ing two
two or
or more investment
investme n t alternatives,
alternatives, the
the one with the largest
largest
In
comparing
between yearly net earnings and the
the annuity is
is the
the most
difference between
most profitable
one .
one.
If
l oo k closer at
at the
the results
results we
we have
have got
got from
from the
the NPV-Method
NPV-Method and the
the Annuity
If we
we look
Method,
Method, we will find
find that
that they
they give
give exactly
exact l y the
the same
same results.
r esults . In
In the
the Annuity -Method
Method we
that the
the required
required annuity
annuity was
was MU
MU 15
15 643.
643. At
the same
sa'me time
time we know that
that we will
will
At the
found that
20 000
000 yearly.
yearly. If
If we
we now take the
the difference
difference between
between these
these two
two amounts and estimate
earn MU 20
th e present value
va lue of
of this
this difference,
diffe ren ce, we
we get
get the
the following
following result.
result.
the
NPV
NPV _ =
E-A
E A=
10
(20 000
000 -- 15
15 643)
643) • TC10
Tcig = 26
26 744
744
(20
In
6.3.2 we
found the NPV10
NPV 10 as
as MU
MU 26
26 755.
755. The small
small difference
difference between
betwe en
In Section 6.3.2
we found
If we
we had
had calculated the
originates from
tab le roundings.
roundings. If
the two
two NPV,s
NPV,s without
these NVP.s originates
fromtable
using table
tab l e values,
values, we
we would
would have
have found
found that:
that:
NPV10 = NPVE-A
Mathe
matically, the
the NPV-Method
NPV-Method and
and the
the Annuity
Annuity Method
Method are
are identical.
identical. The difference
d iff erence between
between
Mathematically,
is that
that we get
get the
the results
results in
in slightly
slightly different
different ways
ways depending
depending on
on how
how the
the initial
initial
them is
va
l ues are
are introduced.
introduced.
values
f
76-- 76
6.3.4
The
Internal Rate
Rate of Return
Return Method
Method
The internal
Let
at the
the Internal
Internal Rate
Rat e of
of Return
Return (IRR)
(IRR) that
that we
we will
will denote
denote with
with i.
~i
Let us
us now look at
-1
in our
our formulas.
in
formulas. The
IRR- concept has
ha s actually already
already been mentioned
in Section 6.3.27
The IRR-concept
mentioned in
We define the
We
the i.
.-1
!.i as
that interest
int e r est rate
rate which
which gives
gives aa NPV
NPV that
that is
i s exactly
exac tly zero.
zero. In Exhibit
Exhibi t
as that
6.3
fo und th,it
that our
e would
the comp
a ny 's RRR was
6.3 we found
our basic
basic exampl
example
would yield
yield aa NPV
NPV of
of zero,
zero, when
when the
company's
increased
increa
sed to
t o slightly less
less than
t han 16
16 percent.
percent. This
Th i s perce
ntage is
i s the
the internal
interna l rate
rate of
of return
r eturn
percentage
that
t ha t our
o ur basic
basic example
example gives.
g ives.
When using the
the Internal
Internal Rate of
o f Return
Return Method,
Method, we define the
the desired NPV as zero
zero
and put
and
put in our
ou r figures
fi gures in
in formula
formula (5).
(5). The
The unknown variable
variab le is
i s ii
!i and
and we
we denote
denote the
the net
ne t
pres
e n t value
value by NPVii,
NPVii, which we
we put equal
equal to
t o zero.
zero. We
the n get:
get:
present
We then
o0 == 20
000
as
defi ned NPV.
NPV.
as we have defined
L.
10
10
10
TB . - 100
100 000
000
10 000
TB.
1. + 10000.
'i
TC.
(7)
(7)
O.
O.
'i
The unknown
unknown variable
va ria ble is
is our
our IRR.
IRR. But
interest rate has been
been hung
hung upon
upon two
two different
di ff erent
But this
this interest
table
t hat we
we actually
actua ll y have two
two unknown variables,
variab l es , TC
Te. and
and TB.
TB . .
table values,
values, which means
means that
1·
1·
We
sol ve aa single
Single equation
eq uation with
with two
two unknown
unknown variables.
variables. There
differ~nt
We cannot solve
There are
are tQo
to differ6nt
techniques
to solve
solve our
our problem.
problem.
techniques to
.
Sometimes there
there is
is no scrap
scrap value.
va lue. In
ld have
have had only
on l y one
one
In such
such aa case
case we
we wou
would
variab l e - the
the table
table value for
f or TC.
Te. Let
unknown variable
that the
t he scrap
scrap value
value is
i s so
so small
sma ll
Let us
us assume
assume that
that
we can overlook
that we
overl ook it
it to
to get aa rough
ro ugh estimate
estimate of
o f the
t he ii.
li' In
In such
s uch a
a ccase
ase the
t he second
second
term will
will become zero,
zero, and we can solve
solve equation
eq uation (7)
(7) for
for-rei.'
1
10
20 000 • TC.
o0.20000..TC.+0
- 100000
000
1. + -0 100
10
'i
1
I- Because
{Be CaUSewewehave,
have, temporarily,
tempora ri ly,
the effect
effect of
of the
the
overlooked the
va lue.
scrap value.
We then
then get:
get :
10
10
1100
00 000
000
'i
20 000
TC.1.
-5,
5,
which we interpret
interpret in
in the
the following
following way.
way. Find
, in
in Tabl
e C,
e, a
a compound
co mp ound discount
discoun t sum
sum that
that
Find,
Table
is equal
equal to
when
we know that
is
to 5,
5, wh
en we
that the
the discount
di sco un t process
process will
will be
be made
made over
over 10
10 years.
years. Looking
Looking
into Table
Table C,
C, we
we find
on the
into
find on
the row for
for 10
10 years
years the
the following
fo ll owing discount
discount sum
sum factors:
factors:
15%
16%
55.019
. 0 19
4.833
Obviously,
t he TC~O of
5 .000
must
veryclose
c l osetot o1515percent.
percen t. But,
over l ooked
Obviously,theTC.of
5.000
must
be be
very
But, we have overlooked
the
value. If
if this
this value had been
been taken
tak en into
int o account,
acco unt, we
we would
would have
have got
got aa figure
figure
the scrap value.
close to
Now, when we have aa first,
to the
t he quotient
quotient for
for 16
16 percent.
pe rce nt. Now,
first, rough
rough estimate
estimate of
of our
our
i., we
we can
can find
i.,
find aa better
better eestimate
stimate by solving
solving the
the whole
wh o l e formula
formula (7)
(7) by
by using
using this
t his rough
rough
-l
So let
e~timate.
let us
us put
put in
in our figures
figures as
as well
well as
as the
t he table
ta ble values
values for
for 16
16 percent
percent to
to see
see
es-timate.
In othe
orher
words,
we estimate
what we get.
get. In
r wo
rds , we
est imate the
t he NPV for
for exactly
exact ly 16
16 percent to
to get:
get:
10
,.
__ 77
77 _
20000
100000
NPV16 = 20
000 • 4.833 + 10
10 000 • 0.2266 -- 100
000
which gives NPV16
== -- 11 074
NPV
074
16
It
is clear
th at the
the investment
investment yields almost
almost 16 percent,
percent, which we
we also found
found in
in Exhibit
It is
clear that
6.3
6.3..
1
The
tech niqu e of
of estimating
estimating the
the i.
i. value
value is
is simple.
simple. Sometimes
The second technique
Sometimes there
there are
are many
many
-1
""unknowns"
unknowns" involved
. when
here are
ar e different
different net
net earnings
earnings for
for different
involved as
as is
is the
the case
case e.g
e.g.
when tthre
It
then, to
to temporarily
temporarily overlook
overlook the
the scrap
scrap value.
va lue . Instead one can
can
years.
It is
is no
no help,
help, then,
ju st make
trial and errors put
put in
in various percentage
percen tage figures,
figures,
just
make aa pure
pure guesswork and by trial
un
t il one
NPV that
that is
is equal
equa l to
to zero.
zero.
until
one reaches aa NPV
For
For this
this meth
method
od we get
get the
the following
following decision
decision rules:
rules :
1.
is lar
larger
or equal
If
the estimated i.
~i is
ger than
than or
equa l to
to the
the ir,
!rl aa single
Single investment
investment is
is
If the
profitabl e .
profitable.
2.
In
two oor
r mo
re investment
investment alternatives,
alternatives, the
the one
one with
the highest
In comparing
comparing two
more
with the
highest !i
ii
is
one .
is the
the most
most profitable one.
taken in
in this
this paper
paper is
is to
to use
use the
the Internal
Internal Rate
Rate of
of Return
Return Method only
only as
as
The course taken
par t of the
the sensitivity
sensitivity analysis.
analys i s . But,
for all
all major investments
investme nt s the
the IRR
IRR should
should be
be
part
But, for
estimated.
6.3.5
The Simple Pay-Off
Pay-Off Method
Simp l e Pay-Off
Pay-Off Method differs
differs from
from the
th e previous
previous methods
methods described
described in
in two
two ways.
ways.
The Simple
not use
use any
any interest
interest rate
rate and
and it
it does
does not
not require
require decisions
decisions on
on the
the investinvestThis method does not
ment's useful
is supposed that
ment's.
useful life.
life. Instead
Inst ead it
it is
that the
t he company
company has
has aa pre-determined
pre-determined pay-off
pay-off
period,
peri od, within which the
the investment
investment must
must pay
pay back
back the
the money
money being
being invested.
invested. Let us
us use
use
the following
following denotations
denotations in
the
in addition
addit ion to
to those
those we have
have used
used before.
before .
pay-off time
time
POTr = restricted pay-off
POT
time
POT,
actuall pay-off time
a == actua
Using this method,
method, we will compare
compare POT,
POTa with
with POTr
POTr to
to see
see if
if the
the former
former is
is shorter
shorter
than the latter.
In our
our basic
than
latter. In
basic example, we
we have
have to
to add
add aa value
value for
for POTr.
POT r . Let us
us assume
assume
than the
t he company requires
requires that
that investments
investments of
of this
this type
type must
must be
be paid
paid back
back in
in less
l ess than
than
eight years,
years, i.e.
i. e. we
we put
put POTr
POTr == 8.
8.
the Simple
Simp l e Pay-Off
Pay- Off Method we
we get
get the
the following
following formula
formula for
for our
our estimations:
estimations :
In the
I -- E·POT
I
EPOT,a == 00
(8)
(8)
The initial
earnings times
The formula
formu l a reads:
reads: The
initial investment
investment is
is subtracted
subtracted by
by the
the yearly,
yearly , net
net earnings
times
the
the actual
actual pay-off
pay- off time
time in
in years
years until
until the
the difference
difference becomes
becomes zero.
zero.
Putting our values into
into (8)
(8) we
we get:
get:
100
100 000
000 -- 20
20 OOO-POT
000.POTa = 00
=
giving
giving POT,
POT a = 55 years.
years.
78
78
In othe
other
I/E, which is
In
r words,
words, we look
look for
for the
the value
value of
of liE,
is expressed
expressed in
in years.
years.
is
than the
the restricted
restricted pay-off
pay- off time,
time , POTr,
POTrl the
the investment
investment is
is pr
o fitable.
is less
less than
profitable.
If
If this
this
We
We get
get the
the following
following decision
decision rules:
rules:
1.
If
If POTr
POTr is
is larger than or equal to
to the
the POTa',
POTi, aa single
single inve
investment
stme nt is
is profit
profitable.
able.
2.
In
two or more
investmen t alternatives,
alternatives, the
the one
one with
with the
t h e shortest
shortest
In comparing
comparing two
more investment
POTa
is the
the most
most profitable
profirable one,
one, ggiven
POTa
is
less
than
the
company's
POT,.
POT
a is
iven its
it s POT
is
l
ess
than
the
company's
POTro
a
In
ng the
the Simple Pay-Off
Pay-Off Method,
Method, no
no regard
regard has
has been
been taken
taken of
of the
time value
value of
of
In usi
using
the time
money. In
a l l cash
c ash flows
flow s are
are regarded
reg a rded as
as equally
equally valuable.
valuable. This
This is
is the
the main
In other words,
words, all
main
that has
has been
been put
put forward
forward in
in criticizing
criticizing tthismethod.
hi s method. To
To set
set aside
aside this
this criticism,
criticism,
objection that
the
has been
been developed
developed into
into the
the next
next method.
met hod.
the method has
66.3.6
. 3.6
The
Modified Pay-Off
Th
e Modified
Pay-Off Method
The
Pay-Off Method differs
differs from
from the
the previous one
one
The Modified
Modified Pay-Off
the time
the
time value of money is
is treated.
treated. The modification
modifi c ati on means that
that
brought into
into the
the picture.
picture. This
This is made
made simply by putting in
in the
t he
according to
to Table
Table CC in
in formula
formula (8).
(8).
only in respect
respect to
to how
only
the
company's
interest
the
interest is
discount sum
compound discount
For
the Modified Pay-Off Method
Method we
we get
ge.t the
th e following
following formula:
formula:
For the
POT
POT
II -- EE • TC
TC10
IO a = 0o
((9)
9)
The
differenc e , as compared to
to formula
formula (8),
(8), is
is that
that the
the TC-value
TC-va lue is
is put
put in.
in. The
The
The only difference,
company's
company
' s ir .
= 10
10 percent in
in our basic
basic example,
example, but we do
do not know for
for how
how many
many years
years we
we
will make our
calculations.
our ca lcul at ions. The unknown
unknown variable,
variable, therefore,
t herefore, becomes
be comes "the
" the year
ye[).r denotation
denotation
for
for Table C".
C". The number of years
years we put
put in
in is
is the
the actual
actual pay-off
pa y-off time,
time. POTa,
POTa , that
that we
we will
estimare. Solving this
estimate.
this by
by putting
pu tti ng in
in our basic
basi c example
example figures
figure s we
we get:
get:
100 000
POT
I/
TC10
TC
10 aa -=---.
-E-;:0"'0-5.0
= 5.0
E - -;;-:20::-;:0'
20 000
The quotient
quotien t I/E
liE is
is no
no longer
l onger "years"
"year s" as
as it
it was
was in
in formula
formula (8).
(8 ). Instead
Ins tead the
the figure
figure 5.0
5.0
the Table
Table C-value
C-value for
for aa certain
certain number
number of
of years,
yea rs, i.e.
i. e . the
the unknown
unknown variable
variabl e to
to
represents the
be found
found for
for 10
10 percent.
percent. Checking the
the "10
"10 percent
per ce nt column"
co lumn" we
we find
find the
t he following
following table
table
values:
7 years
8 years
4.868
4.868
5.335
5.335
this we
we can
can conclude
conclude that
that POTa
POT must
must be
be somewhere
somewher e in
in between
between 77 and
and 88 years.
years .
From this
a
polation we
we find
find aa more
more exact
exa c t estimate.
estima te .
7
7
interBy inter-
+ 5.000
5.000 -- 4.868
4.868 . 7.28
7.28 years
years
+
5.335
5 . 335 - 4.868
decision rules
rules for
for the
the Modified
Modified Pay-Off
Pay-Off Method
Method will
will be
be exactly
exactly the
the same
same as
as those
those
The decision
for
for the
the Simple
Simple Pay-Off
Pay-Off Method.
Method. The difference
difference is
is found
found only
only in
in the
the way
way we
we estimate
estimate the
the
POTa.
POT •
a
_ 79 _
_79
6.4
Sensitivity analyses in capital budgeting
has been
been pointed
pointed out
out before,
before, all
all economic
economic decisions
decisions are
are made
made under
under uncertainty.
uncertainty.
As has
Obviously, the
the degree
degree of
of uncertainty
uncertainty increases
increases when
when we
we have
have to
to make
make decisions
decisions with
with aa time
time
Obviously,
we can
can get
span of many years.
years. We cannot reduce
reduce the
the uncertainry
uncertainty as
as such.
such . But
But we
get a
a feeling
feeling
happen, if
if we
we have
have made
made mistakes
mistakes in
in estimating
estimating the
the figures
figures put
put into
into our
our
about what will happen,
show how we carry out
out aa sensitivity
sensitivity analysis
analysis we
we will
will put
put in
in some
some further
further
formulas.
To show
about our
our basic
basic example.
example. Let
Let us
us assume the
the following:
following:
information about
1.
this new lathe
lathe will
will increase
increase the
the company's
company's fixed
fixed costs
costs by
by MU
MU 88 000
000 per
per
Buying this
year.
2.
The sales
sales price of
of the
the product
product produced
produced on
on this
this lathe
lathe has
has been
been estimated
estimated to
to
The
12 per
p e r unit.
unit. Variable
costs have
have been
to MU
8, i.e.
i.e. the
the product
MU 12
Variable costs
been estimated to
MU 8,
is supposed to
to give aa CTP
CTP of
of MU
MU 44 per
per unir.
unit.
is
3.
The sales
sal e s volume has
has been
been estimated
estimated to
to 77 000
000 units
units per
per year
year as
as an
an average
average for
for
The
the
period.
the whole period.
these figures
figures as
as the
the only
only ones
ones that
that might
might fluctuate
fluctuate during
during the
the period.
period.
Consider these
We
We find,
find, if
if we put
put them
them together,
together, that
that they
they give
give the
the overall
overall figures
figures that
that we
we have
have used
used
so far.
far.
revenues, 7 000
Sales revenues,
costs, 7 000
Variable costs,
per year
Fixed costs
costs per
year
12
8
8
(E)
earnings per
per year
year (E)
Net earnings
MU
MU
MU
84 000
++ 84
56
- 56 000
-- 8 000
20 000
MU = 20
========
will always be
of making
making aa sensitivity
sensitivity analysis.
analysis. But
But there
there will
be
There are many ways of
uncert~inty about two
two things
things -- the
the sales
sales volume
volume and
and our
our CTP
CTP per
per unit.
unit. The
The CTP/unit may
uncertainty
fluctuate
result of
of price
price changes
changes or
or as
as aa result
result of
of variations
variations in
in costs,
costs, or,
or,
fluctuate either
either as
as aa result
as a combined result
result of
of both.
both.
as
At this
this stage
stage the
the decision-maker
decision-maker might
might ask
ask himself
himself questionssuch
questions such as:
as:
At
1.
How
large deviations in
in my
my sales
sales forecast
forecast can
can I1 accept?
accept?
How large
2.
does a
a price fluctuation
fluctuation of
of plus/minus
plus/minus 10
10 percent
percent affect
affect my profitability?
profitability?
How does
3.
How does
does aa combined negative
negative change
change in
in both
both prices
prices and
and sales
sales volumes
volumes affect
affect
profitability?
my profitability?
As a matter of
of fact,
fact, we
we recognize
recogniz e this
this type
type of
of question
question from
from Chapter
Chapter 5,
5, when
when the
the budget
budget
As
of
used for
for sensitivity
sensitivity analyses.
analyses.
of our model
model company was used
Let us
us now assume that
that the
the price
price per
per unit
unit or
or the
the variable
variable cost
cost per
per unit
unit might
might
Let
fluctuate in
in such a way that
that the
the CTP
CTP per
per unit
unit will
will take
take on
on values
values between
between MU
MU 3.00
3~00 (lowest)
(lowest)
fluctuate
and
MU
5·00
(highest).
Assume
further,
that
,
these
II
fe
figures",
i.e.
Assume
further,
that
these
are
"safe
figures",
i.e.
are
possible
sa
and
5.00 (highest).
extreme figures.
figures. In
In the
the same way we estimate
estimate sales
sales volumes.
volumes. The
The maximum sales figure
figure is
is
9 000 units.
units. Perhaps
Perhaps this
this is
is the
the maximum
maximum capacity
capacity of
of the
the lathe.
lathe. At a minimum, total
total
sales
be at
at least
least 55 000 units
units per
per year.
year. Re-writing formula
formula (5)
(5) gives:
gives:
sales will
will be
NPV
= (y.X
Y.X -- 8
8 000)
NPV10
10 (
l10O - 10 000 • TB
IO
10
Te
TB 10
-- 100 000
O
TC l10
__80
80 _
Y . achieved
ac hi eve d CTP per
per unit
un it and
a nd
X
X = achieved sales
sales volume
volume per
per year.
year .
where
where::
10
10
The
f i rst term
te r m in
in this
this equation
eq uation is
is equivalent
eq uiva l e n t to
to E.TC10
E. TC10 in
in formula
formula (5).
(5). Before
st art i ng
Before starting
The first
the sensitivity
sensitiv i ty analysis
ana l ysis we simplify
simplify the
the formula
formula further
further by
by finding
finding the
t he values of
of those
those
the
terms that
that will
remain the
the same
same through
through the
the whole process.
process. We get:
get:
terms
will remain
000·6 . 145 - 10 000·0
NPV10 = Y·X·o.145
Y'X5.145 - 88 000-6.145
0000.3855
. 3855 -- 100
100 000
000
or
Y·X·'.145 -- 145
145 305
305
NPV10 = Y'X'5.145
Holding XX constant at
at 7 000
(our origina
l estimate
of the
the sales
sales volume)
000 units
units (our
original
estimate of
volume) we
we change
change Y
Y
successively . Then the
the process
process is
is repeated
repeated for
for XX holding
ho l ding YYconstant.
constant . Fi
nally, we combine
successively.
Finally,
changes in
in both variables
var i ables and
and register
register the
the resulting
resulting NPV:s.
NPV : s. The
results are
are shown in
in
The results
Exhibit 6.4.
6.4.
In Exhibit
Exhibit 6.4 we recognize the
the NPvIO,
calculated , at
at the
the intersection
intersection
In
NPV10, previously calculated,
between the
the row for
for CTP 4.00
4.00 per
per unit
unit and
and the
the column
column showing
showing aa volume
volume of
of 7 000 units per
year. Lowering the
the sales volume to
to 66 000 units,
units, still
still gives
gives aa positive
positive NPV
NPV (2
(2 175).
175). But
But
at
a sales volume of
of 55 000
the NPV becomes negative
negative (-22
(-22 405).
405) . We
We can easily find
find
at a
000 units,
units, the
that
911 units per
per year,
year, the
the NPV becomes zero.
zero. This means that
that 55 911
that at
at exactly 55 911
911 units
yields
percent, given the
the estimated
estimated CTP
CTP remain
remain at
at MU
MU 4.00
4.00 per
per unir.
unit.
yields exactly 10 percent,
Keeping the
the volume constant,
constant, allows the
the CTP
CTP to
to decline
decline to
to MU 3.20
3.20 per unit
unit before
before
the
negative. The CTP
CTP per
per unit,
unit, which
which results
res u lts in
in aa NPV
NPV == 0,
0 , iis
s found as
the NPV becomes negative.
3.38. In
In other words,
long as
as the
the estimated
estimated sales
sales volume
volume remains
remains at
at 77 000
000 units,
units,
words, as long
MU 3.38.
the
3·38 without violating
violating the
the company's
company 1 s RAP.
RRR.
the CTP
CTP may
may shrink to MU 3.38
from Exhibit
Exhibit 6.4
6.4 that
that the
the investment
investment is
is very
very sensitive
sensitive ro
to volume
vo l ume
We can notice from
decreases
A decrease
decrease to
to 55 000
000 units
units must
must be
be compensated
compensated with
with high
high increases
increases in
in the
the CTP
CTP
decreases.. A
per unit. Combining - even moderate -- decreases
decreases in
in both
both CTP
CTP and
and volume
volume results
resu l ts in
i n aa
negative NPV.
NPV.
c---------,---- .. -.- - - - , - - - - -I - , - - - - - Sales
volumes
CTP s
1
000
5 000
1'")
I
I
I
I
77 000
000
000
6 000
1
88 000
000
000
99 000
1
1
I
I
-7 657
657
I -7
I 2 175
-7
657 I, 12
12 007
007
-7 657
I
946 I 21
21 839
839
99 549
549 I 3311 761
76 1
2.60
-1 512
5 12
1
2.80
2.00
1
3.00
3.00
1
3.20
3.20
3.40
3.60
3.00
3.80
44.00
. 00
4.20
4.20
44.40
. 40
44.60
. 60
4. 80
4.80
1
549
99 549
610
20 610
20
3311 671
42
42 732
732
793
53
53 793
_ _ _ _ _ _ --5
_5 _
_ ...JI 18,152
L
_ _64
_ 854
_
199
I 4_41
1_
503
199
64
85 _
4
18 152 L_I
--22
22 405
405
175
26 755
755
51
2 175
26
51 335
335
75 915
9 15
75
1
- 16 260
--,
-10
-1 n 115
1 15
I
- -16
- --260
- -- -
I
1
1
--
.11 970
')70
I
2 . 175
2.175
I
-- - ,-T
1
1
1
1
1
I
1
Exhib
i t 6.4
6.4
Exhibit
Changes
10 percent as aa function
function of
of combined
combined
Changes in NPV:s at 10
changes
changes in sales volumes
vol umes and CTP:s
CTP : s
81
81
6.S
6.5
investment decisions
decisions for
for the
the model company
company
Some investment
Let us now return
return to
to our
o ur model company
company budget
budget that
that we introduced
introduced in
in Chapter 4.
4 . The
Let
budget
for this
this company, was
was aa short-term
short - term budget.
budget. But we
this for
for
we can also use this
budget presented for
longterm capital budgeting.
budgeting. Let
Let us
us consider two
two different
different types
types of
of decisions.
decisions.
long-term
6.5.1
6 . 5.1 Improving
Improving the
the production
production output
output
in Chapter 4,
4, the
the production
production capacity
capac it y of
of our model company
company is
is
As was mentioned in
approximately 20
20 000 m3
m3 of sawn
sawn timber.
timber. Despite
Despite this,
this, the
the sawmill
sawmi ll has
has not
not produced
produced more
more
3
than 11
than
11 200 m3
m during
during aa single
single year.
year.
could be
be improved,
improved, if
if production
production stops
stops could be
be reduced.
reduced.
The production capacity could
There are three
three major
major problem
problem areas:
areas:
1.
by poor maintenance.
Many stops
stops are
are caused by
by defective
defective parts
parts or by
preventive maintenance should
should bring
bring down
down the
the number
number of stops.
stops . •
preventive
2.
Other stops
stops are
are caused by
by problems
problems with the
the electronic
electronic equipment,
equipment, which
is due
due to
to the
the tropical
tropical climate.
climate. To
set aside
this problem increased
increased
To set
aside this
obviously is
supervision (one
(one or two
two operators)
operators) is
is required.
required.
3.
A
for numerous
numerous machine
machine stops
stops is
is the
the log
log quality.
quality. At
al l
A third cause for
At present all
log
is made directly
directly on
on the
the ground.
ground . Especially during the
the rainy
rainy
log storing is
periods,
periods, logs
logs are muddy and
and stones
stones and
and other
other particles
particles give
give rise
rise to
to many stops.
stops.
these stops the
the storing
storing ground
gro und could
cou ld be
be covered
covered with tarmac.
tarmac .
To avoid these
Improved
suggested measures
measures are
are costly.
cost l y. To get
for possible
possible decisions,
decisions, the
the
The suggested
get a ground for
sawmill manager
manager has,
has, during the
sawmill
the past year,
year, recorded
recorded number
number of
of stops
stops in
in the
the sawmill,
sawmill, length
length
and main cause
cause for
for each
each stop.
stop. A
farily correct
correct estimate of stop-times
stop-times and their
their causes
causes
A farily
wi
l l be
be as
as follows:
follows:
will
Stop cause
Electronic errors
Stones
etc. on logs
logs
Stones etc.
Poor maintenance
Poor
(the cause
cause has
has not
not been
been
Miscellanous (the
clearly identified)
identified)
No. of
of hrs
hrs during
during
No.
the
the year
86
86
152
166
220
sto p time
time
Total stop
624
====:=
Total, theoretical
theoretical production
production time
time
Total,
2 000
stop-time
Relative stop-time
31.2%
If all
all stops
stops could
cou l d be eliminated,
elim inated, total
tota l production,
production, based
based on
on last
last year's
year ' s production,
production,
If
3
could be increased
increased up
up ro
to 10
10 000/0.688
000/0 .688 == 14
14 535
535 m3.
m • Even if
if this
this is
is a highly
highly theoretical
theoretical
figure, the
the manager realizes
realizes that
that the
the present
present situation
situation is
is unacceptable
un acceptable in
in the
the long
long run.
run.
figure,
All recorded
record ed stops
stops have accrued
accrued in
in the
the sawing
sawing process.
process. The
The trimming capacity will
All
suffice for an increased
increased output even
even up
up ro
to 15
15 000
000 m3.
m3 . The kiln capacity is
is aa bottleneck
bottleneck
suffice
that
that must be
be dealt
dealt with.
with . This will be
be discussed
discussed in
in the
the following
following section.
section.
_ 81
82 -
To
cover the log
log ground with tarmac
tarmac is
is aa difficult
difficult task.
task.
To cover
The
space is
is now fully
fully
The space
utilized. During the
the work the
the stock of
of logs
logs must be cut down ro
to give sufficient
sufficient work
utilized.
surface for
for the
the tarmac
tarmac machines.
machines. The
the r efore, has
to be
The ground,
ground, therefore,
has to
be covered
covered and
and the
the process
be extended
extended over
over more
more or
or less
less aa whole
who l e year
year before
before log
log handling
handling can
can be
be normalized.
normalized.
will be
This
result in
in a reduced
reduced production
production volume
volume during
during the
the year,
year, estimated at roughly
roughly
This must
must result
20 percent - equally
equally spread
spread on
on both
both species.
species.
Furthermore, two
two more
more men
men in
in the
the production
production process
process can
can be
be justified.
justified. One
Furthermore,
One worker
for manual
the electronic equipment,
equipment, the
the other
other mainly for
for repair
repair and maintenance
maintenance
for
manual support of the
work.
tvork.
The sawmill
The
sawmill manager has carried out some
some preliminary
preliminary cost estimation for
for the
the improved
improved
programme. He
He has
has got
a tender
tender from
from the
the tarmac
tarmac company,
company, which
which shows
shows the
the total
tota 1
got a
production programme.
will be
be MU
MU 420
420 000.
000. Two
cost MU
MU 80
80 000
000 per
per year.
year. In
l, MU
cost will
Two more
more workers will cost
In al
all,
MU 500 000
for the
the first
first year.
year. The figure
figure is
is frightening.
frightening.
for
On the
cost savings side,
On
the cost
side, the
the manager has
has made a
a round
round estimate.
estimate. For
For the
the first
first year
by
hopes to
to reduce
reduce production
production stops
stops
50 percent
as compared to
to last
last year's
yea r ts records.
records.
50
percent as
he hopes
For the
the second
second year
year and
and onwards,
onwards, he
he estimates
estimates aa reduced
reduced stop-time
stop-time of
of 75
75 percent.
percent. This
figure is based on
on aa planned
planned training programme for
for the
the workers.
workers.
Let us
us base
base the
figure
Let
the economic
on these
these figures.
figures.
analysis on
We
into two
two parts.
parts. Employing two more workers will
We can
can now separate his problem into
affect
stop-times caused by electronic errors
errors and
and poor
poor maintenance.
ma in tenance. This will increase
increase
affect stop-times
as production
production volume.
volume.
In Exhibit
Exhibit 5.4
5.4 we estimated the
the lost
lost CTP/hour
erP/hour
labour costs as well as
In
that the
the sawmill
sawmill loses as
as a
a result
result of a production
production stop.
stop. We arrived at
at aa figure
figure of
of
that
893 / hour.
If
will reduce
reduce production stops as planned,
planned, the
the
If hiring two more
more workers will
MU 11 893/hour.
following
effects will
will occur.
occur.
following economic effects
year:
First year:
(86
166)
(86 + 166)
0.8 • 0.5
0.5 • 11 893 =
MU
MU 190 814
Second year and
and onwards
onwards per
per year:
year :
(86
166)
(86 + 166)
1).75
0.75 • 1 893 -=
MU 357 777
777
we have
have the
the recorded
recorded stop-times
stop-times during
during the
the last
l ast year.
year . If
If we
do
Within parentheses we
we do
in the
the production
production process,
process, we
we will
will have
have (roughly)
(roughly) the
the same
same stop-times
stop-times also
also in
in
nothing else in
If
we
cover
the
log
ground
with
tarmac,
the
overall
production
volume
will
future.
If we
the log ground
tarmac, the overall production volume will
the future.
20 percent during
during the
the first
first year,
year, which
whi ch explains
explains the
the factor
factor 0.8.
0 . 8 . Before the
the
decrease by 20
training programme has
has been
been carried
carried through,
through, the
the manager
manager has
has estimated
estimated the
the reduced
reduced stopstopto 50
50 percent.
percent. Each hour of reduced
reduced stop-time
stop-t i me will
will increase
increase the
the result
result of
of the
the sawmill
sawmill
time to
by MU 1 893 per hour,
hour, or,
o.r, in
in total
total for
for the
the first
first year,
year, MU
MU 190
190 814.
8 14. For
second and
and
by
For the second
following years,
years, stop-times
stop-times will
will be
be reduced
reduced by
by 75
75 percent.
percent. At
At the
the same
same time
time the
the sawmill
sawmill
following
will
at the
the same
same total
total capacity as
as during
during the
the last
last year.
year . Yearly improvements
improvements of
of
will produce at
the
the result
result will
will amount to
to MU
MU 357
357 777.
777.
Let us,
make a
These estimates are extremely uncertain.
uncertain. Let
us, therefore,
therefore, make
a simple
simple sensitiThese
vity analysis. Let
Let X
X be
be the number of
of hours
hours of
of reduced
reduced stop-times
stop-times in
in case
case two
two more
more
workers are
are employed.
employed. Without bothering about
about the
the first
fi r s t year's
yearts reduced
redu ced production,
production, we
we
ask: How many hours of
of reduced
reduced stop-time
stop-time must
must we
we have
have per
per year,
year, in
in order
order to
to justify
justify
economically the
the decision
de c ision to
to hire
hire two
two more
more labourers?
labourers? The answer
answer is:
is:
gives
which gives
11 893 • X
X = 80 000
000
X =
42.3 hours.
83
_83
126 hours
hours for
for the
the first
first and
and 189
189 hours
hours for
for the
the second
second year.
year.
Even
The
The original estimate was 126
Even
if
figures are
incorrect, the
the actual
actual stop-time will most
most probably be reduced by more
more
if these
these figures
are incorrect,
than
hours . Employing two
two more
more workers
workers seems
seems to
to be
be aa wise
wise decision.
decision.
than 42.3 hours.
But
this is
is actually not
not aa capital
decision, as
there is
is no
no capital
But this
capital budgeting decision,
as there
capital
investment
involved. But
the
training
programme
for
the
workers
will
cost
the
investment involved.
But the training
for the workers will cost the sawmill
something.
wil l , of
of course,
course, be
be directed
directed towards
towards the
the whole staff.
staff. Assume
something. This programme will,
that
that a
a very serious
serio us programme,
programme, bringing
bringing in
in technical
technical consultants
consultants for
for teaching
teaching and
and demonstrademonstrations, is
is planned.
planned. Consultancy
costs and cost
cost of
of stopping the
the production during teaching
tea c hing
tions,
Consultancy costs
days
be high.
high. Let
us estimate the
the total
total cost
cost to
to MU
MU 300
300 000.
000. Here
Here the simple pay-off
pay-off
days will be
Let us
could be
be used.
used. But
But now we must decide
decide on
on aa probable
probable reduction
reduction in
in stop-times.
stop-times. To be
be
method could
very
conservative, let
let us
us assume 75
75 hours
hours per
per year
year in
in reduced
reduced stop-times.
stop-times. How
long will
very conservative,
How long
it
such aa training programme
has payed back?
back?
it take
take before
before such
programme has
The answer is
is obviously:
obviously:
300 000
(75 .1 893)
(75.1893)
=
2.11 years
2.11
Let
us now deal
deal with
with the
the tarmac
tarmac problem.
problem. We
need precise
for the
Let us
We need
precise cost
cost estimates
estimates for
reduced production during
during the
the first
first year.
year. In
we studied the
the sawmill's
sawmill ' s cost
cost
In Section 5.2 we
struct
ure. We
found that,
that, based on the
the budget
budget figures,
figures, average
average variable costs for
for both
both
structure.
We found
species amount to
species
to MU
MU 580
580 per
per m3.
m3 . This
is, of
of course,
course, an
an approximate
approximate figure.
figure. The
The split up
up
This is,
of total
total costs
costs in
in variable
variable and
and fixed
fixed components
components varies,
varies, among
among other
other things,
things, for
for what
what
the analysis
analysis is
is made.
made. In
this case,
case, however,
however, variable
variable costs
costs might
might be
be higher.
higher.
purpose the
In this
The reason
reason is
is that
that this
this is
is aa very
very special
special cut
cut in
in the
the production.
production. Perhaps disturbances
disturbances will
will
occur that
that increase
increase some
some of
of the
the costs.
costs. We
We cannot totally
totally rely
rely on
on the
the estimated
estimated figure,
figure,
but this
this uncertainty
uncertainty can
can be
be dealt
dealt with
with in
in aa sensitivity
sensltlvlty analysis.
analysis. So,
So, for
for the
the moment
moment
3
let
us
accept
a
variable
cost
of
MU
580
per
m3.
let us
a variab l e cost of MU 580 per m .
Costs of
of reduced production
Costs
300
2 000
600 000
000
MU 600
=
The figure
f igure 300
300 is
is the
the CTP
CTP per
per m3
m3 estimated
estimated in
in Section
Section 5.2
5.2 and
and 22 000
000 is
is the
the planned
planned producproduction decrease.
decrease . This cost will
will occur
occur during
during the
the first
first year
year only.
on l y.
For the
the second
second year,
year, as
as well
well as
as the
the following
follOWing years,
years, the
the production
production volume
volume will
will
increase as
as aa result
result of
of improved
improved log
log quality.
quality. Let
Let us assume that
that stop-times
stop-times will
will be
be
reduced by
by 75
75 percent.
percent.
Increased CTP
CTP due
due to
Increased
to improved log
log quality
quality
893
152 -0.75
·0.75 -.1
·: 1893
=
215 802
802
MU 215
The
sawmill manager estimates
estimates aa useful
useful life
life for
for the
the tarmac
tarmac ground
ground of
of 15
15 years.
years.
The sawmill
During this
this period,
period, he considers
considers it
it necessary
necessary to
to make
make imporvements
imporvements in
in the
the surface
surface every
every
five years
five
years at
at a cost of MU 50
SO 000
000 each
each time.
time .
_ 84 __
_84
The capital
capital budgeting
can
way:
The
budget ing problem
pr o bl ~ m c
an now
now be
be shown
s hown graphically
graphi c all y in the
t he following
f o ll owing wa
y:
2 1 5 802
802 - - - - - - - - - - - - - - - 21
215
5 802
8 02
215
I
t
0
to
I
1
I ti
I
I
111
22
3
3
1
420
420 000
000
4
4
5
5
r
50 000
000
I
8
9
9
10
10
jr
l
r
,
l 1_4I
~
15
15
50
5 0 000
000
600 000
600
The investment
The
investment expense
expense is
is MU 420 000,
000, placed
pl aced at
at co.
~o .
Th
e first
f ir st year's
yea r ' s production
pro du ct i on
The
cut, MU 600
600 000,
000, is
is placed
pla ce d at
at the
the end
end of
of the
t he year.
year . Also
t he CTP-increases,
eTP- i ncreases, MU
MU 215
215 802
802
cut,
Alsothe
during 14
14 years,
years, as
as well
well as
as the
the maintenance
mai n te nance costs,
costs, MU
MU 50
50 000,
000, are
a r e placed
p l aced at
at the
the end
end
yearly during
of
of each
each year.
year.
NPV will
will be:
be :
The estimated NPV
14
14
215 802
TC 10
802 TC10
NPV10 = 215
11
1
10
1
55
10 - 420 00010
- 420 000
10
TB 10 -- 600 000 TB10
TB
50 000 TBio
TB 10 -- 50
50 000
000 TT
TBio
-- 50
445 140 - 545 400 - 31 045 -- 19
19 275
275 -- 420
420 000
NPV10 = 1 445
NPV10 = 429 420
The yearly increase
incre ase in
in CTP,
CTP, MU
MU 215
215 802,
802, has
has been
bee n multiplied
mu l ti pli ed by
b y two
two table
ta bl e values.
va lues.
The
1
The
E~rst value,
value, TC14
Tci4 discounts
discounts the
the sum
sum of
of the
the yearly
year l y CTP:s
CTP:s to
to the
the beginning
beginning of
of year
year 2,
2,
The first
is equivalent
eq uivalent to
to the
the end
end of
of year
year 1.
1 . From there,
there, the
the amount
amount is
is discounted
d i sco un ted one
one year
yea r
which is
11
by T1310.
by TB 10 '
~.,re have
have used,
used, as before,
before, aa RRR
RRR of
of 10
10 percent.
percent . We get a positive
p os i t i ve NPV, which
whi c h actually
act ual ly
We
represents an IRR
IRR of almost exactly
exact l y 17
17 percent.
pe r cent . True,
True , there
there are
are uncertainties
un certai nti es in
in our
ou r cost
cost
represents
estimates. These
The se can be handled
hand l ed in
in the
the same
sa me way
way as
as before,
before , i.e.
i. e. by
by means
mea n s of
of aa sensitivity
sens i t i v i ty
analysis
In lack of
of real
real data,
data, we refer
re f er back
bac k to
to the
th e description
desc rip t i on in
in Section
Sect i on 6.4.
6 . 4 . But
to
In
analysis..
But to
indicate
for such
such an
an analysis,
a na l ys i s, it
it can
ca n be
be pointed
pai n ted out
out that
t h at if
i f only
on l y 50
50 percent
pe r ce n t of
of
indicate the
the need
need for
the estimated stop-time can be
be reduced,
reduced , the
the NPV10
NPV 10 becomes
becomes negative.
negat i ve . But at the
the same
same time,
ti me,
the
it
hat there
there is
is aa high "profit
" profit potential"
potential " in
in measures
me a sures that
t hat bring
bri ng down
down the
t he
it is
is obvious
obvious tthat
sawmill's stop-time.
stop-time .
6.5.2
Building a new
new kiln
k il n
In
Chapter 4 we
we learnt
In Chapter
learnt that
that Species
Spec i es BB is
i s open
open air
air dried.
dri ed . The
The average
ave r age work-in-process
wo rk-i n-process
for Species BB was estimated
est imated to
to 11 440 m3.
m3 . Thi
s inventory
inve n tory tied
t i ed up
up aa total
t ot al capital
ca pi ta l
inventory for
This
694080,
the cost
cost of
of which
which amounted
amo unted to
to MU
MU 69
69 408
408 or
or MU
MU 17.35
17. 35 per
per m3
m3 of
of sawn
sawn timber.
ti mber .
of MU 694
080, the
that the
the sawmill
sawmill manager
ma n ager wants
wa n ts to
to bring
br ing down
down this
t hi s capital
c apit al cost
cost by
by building
bu i lding
Assume that
kiln. Cost estimates have
have shown
shown that
t hat the
the type
ty p e of
of kiln
ki l n suitable
su i tab l e for
f o r the
t he model
mode l
one more kiln.
cost MU
MU 400
400 000.
000.
company will cost
__ 85
85 _
To
estimate the
the profitability
To estimate
In doing so,
S0, we have
have to
to make
make certain
certain
In
much
to the
the figures
fig u res used.
used.
much attention to
kiln, we have to
to study
study all
al l consequences.
consequences.
of a new kiln,
assumptions about
about the
the situation.
situation. We do not pay too
too
assumptions
Instead
we
concentrate
on
principles.
Instead we
on principles.
Let
l ist, without detailed
detai l ed comments,
comments, what costs will be changed in
in case a
a kiln
kiln
Let us
us list,
is built.
built.
is
1.
Work-in-process inventory,
invento r y, Species
Species B,
B, will
will decrease.
decrease.
2.
cannot be
be run
run without
without an
an operator.
operator .
The kiln cannot
3.
Costs of
Costs
of heat and electricity
electricity will
wil l increase.
increase.
4.
Artificial drying gives
gives improved
improved product
product quality,
quality, which
which will reduce
redu ce costs
costs of
of
Artificial
refund
c laims.
refund claims.
5.
will be
be reduced
reduced due
due to
to the
the smaller
smaller inventory.
inventory.
Handling costs will
Labour costs will
will increase.
increase.
Let
c hanges as a result
result of
of the
the decsion
decsion to
to build a new kiln.
kiln.
Let us
us check possible
possible cost changes
Reduced
costs
Reduced inventory costs
The revenues
The
revenues will be
be unchanged.
unchanged. Economically aa new
new kiln
kiln can
can be
be justified
justified only
only by
by
the
cost reduction
reduction that
that will
will accrue.
accrue . The
most
important
factor
is
the
reduction
in
the net
net cost
The most important factor is the reduction in
inventory costs.
co sts . We
assume the
the following
following situation.
situation.
We will assume
1.
A
buffer stock of 50
50 m3
m3 of
of undried
undried timber
timber will
will be
be needed.
needed. The
possible
A buffer
The possible
inventory
inventory reduction
reduction will be
be 1 440 -- 50
50 .= 1 390
390 m3.
mi.
(Cf.
for
(Cf. Chapters 44 and 55 for
information on
on average
average inventory).
inventory) .
2.
The reduced
The
redu ced inventory
invent ory will increase
increase the
the sawmill's
sawmill's sales
sales volume,
volume, when
when the
the present
present
inventory can
c an be
be sold
sold out.
out. Thereafter,
the sales
sales volume
volume will
wi l l remain
remain the
the same
same
Thereafter, the
order to
will be
be
IIn
n order
as before.
to facilitate
facilitate increased
increased sales,
sa l es, the
the inventory
inventory will
reduced
reduced by
by only 800
800 m3
m3 during
during the
the first
first year.
year. The remaining 590
590 m3
m3 will
will be
be sold
so ld
during the
the second
second year.
year.
The
value of this
this inventory
inventory for
for this
this decision
decision will
will be
be based
based on
on the
the opportunity
opportunity cost
cost
The value
concept. The sawmill
the
kiln.
sawmil l will
wi ll not
not get
get this
this money
money at
at all,
a ll , unless
un l ess it
it builds
bui l ds the kiln. Each
3 will
sold
m3
will increase the
so l d m
the cash
cash inflow
inf l ow by:
by:
Average sales
sales price
price
Cash discounts
Sales commissions
Opportunity cost
cost
MU/m3
"
"
"
+ 850.00
+
850·00
17.00
17·00
25.50
25·50
. 807.50
Reduction in capital tied
tied up
up (cash
(cash inflow):
inflow):
First
First year,
year, 807.50 . 800
Second year,
year, 807.50
807 . .50 • 590
590
-
MU
"
646 000
425
476 425
86
Labour costs
for kiln operations for
for Species
Species AA was estimated to MU 8 000 per year
year
Labour costs for
(CE. Item No.
No. 201
201 and
and comments
comments in
in Chapter
Chapter 4).
4). We
that the
(Cf.
We assume
assume that
the operator
operator can
can handle
handle the
new kiln
less simultaneously
simultaneously with the
the old
old one.
one. An increased
increased labour
labour time
t ime of
of
kiln more
more or less
25
been assumed
assumed for
for additional
additional work.
work.
25 percent has been
Year
Yearly
l y cost
cost increase,
inc r ease, labour
labo u r
MU 22 000
Heating
Heating and
and electricity costs
The
l y heating and electricity costs
costs have
have been estimated.
estimated. Joint
Joint heating with
wit h
The year
yearly
improve the
the
will improve
the overall efficiency.
efficiency. Total
Total costs for
for heating will
amount to
the old kiln will
will amount
MU 121
121 000 per
per year,
year, after
after the
the new
new kiln
kiln has
has been
been built.
built. (CE.
5.S and
MU
(Cf. Exhibits
Exhibits 4.10
4.10 and
and 5.5
comments
comments to Item
I te m No.
No . 203).
203).
Increased, yearly cost
cost (121
(121 -- 94)
94)
Increased,
27 000
MU 27
Improved
Impr
oved product quality
quality
Ana l yzing refund
refund claims
claims during
during last
l ast year
year has
has shown
shown that
that these
these costs
costs are
are 0.1
0 . 1 percent
percent
Analyzing
less
less for
for Species AA than
than for
for Species
Species B.
B. This
This difference is
is assumed
assumed to
to be
be assigned
aSSigned to
to
differ ent drying
drying techniques.
techniques.
different
refund claims,
claims, 0.001
0.001 • 850 • 4 000
000
Reduced, refund
per year
MU
3 400
Handling costs
Cost reductions have been
been considered
considered too
too difficult
difficult to
to estimate
estimate and,
and , in
in addition,
addition,
Cost
i~significant.
too insignificant.
Only one more decision
decision must be
be made,
made, before
before we
we put
put our
our figures
figures together
together -- to
to
estimate
life of
of the
the new
new kiln.
kiln . Let
that this kiln can
ca n be
be used
used for
for
estimate the useful life
Let us
us assume
assume that
years . The
described.
The problem can now be graphically described.
20 years.
000 476 425
646
646 000
425
3
3 400
3 400
400
400
649
649 400 479 825
825
33 400 ----------------- 33 400
1,
r
t
I
12
to
to
/
2
2
!
2
33
i
Il ~
I
4
4
I
19
19
000
27 000
29 000 - - -- -- --- --- --- -- ----------- -
400 000
20
1
29
29 000
1
122 425
122
425
--87
87 -
recognized all
all figures
figures except
except the
the last,
last, downward
downward directed
directed arrow
arrow of
of MU
MU 11 122
122 425.
425.
We recognized
This amount is
i s the
the sum
sum of
of the
the sold
sold out
out inventories
inventories during
during years
years 1 and 2.
2. How come
come we have
ha ve
this in
i n as aa cash
cash outflow?
outflow?
put this
If -- and
if - the
the kiln is
i s built,
buile, we will get during years 11 and 22 (646
If
and only if
(646 000 ++
425) i.e.
i.e . 11 122
inflow . But what
the company
l onger
122 425 as a cash inflow.
what will
will happen,
happen, when
when the
company no
no longer
476 425)
Either the
sawmill goes
goes back
back to
to natural
natural
use the
the kiln?
ki ln? There are two
two possibilities.
possibi l it.ies. Either
the sawmill
can use
In
a new buffer
buffer stock must be built up again,
again, which means
means lost
lost sales
In that
that case,
case, a
drying.
MU 11 122
in current prices.
prices. lf,
If, on the other hand,
hand, a
a new kiln is
is built
built again,
again, this
thi s
of MU
122 425
425 in
buffer stock
stock does
does not
not have
have to
to be
be built
built up.
up. But that
that is
is aa new
new decision.
decision. We
do
not
know
We do not know
today
today what will
wil l happen
happen 20
20 years
years from
from now.
now. To simplify things
things aa bit,
bit, as
as we
we have
have not
not
discussed the
the theoretical
theoretical basis
basis for
for this
this decision,
decision, we
we choose
choose to
to treat
treat the
the problem
problem as
as if
if
the comapny
Species BB naturally
naturally again.
again. As
be shown
shown later
later on,
thi s
the
comapny should start drying Species
As will
will be
on, this
significant effect
effect on
on our
our estimates.
estimates.
amount has no significant
Let
the NPV in
in the
the usual
usual way,
way, still
still using
using the
the same
same RRR:
Let us
us now estimate the
i·
i.e-e·
i i
-r
.
percent .
10 percent.
22
1 + 479 825TB10
2 + 3 400TC10-TB10
18
. 400TB
+ 479 825TB
+ 3 400TC
NPV10 =~ 649 400TB1
10 ·TB 10
10
0
10
1
20
20
122 425TB20
425TB 10 -- 400
400 000
000
- 29
29 000TC10
000TC
- 11 122
10
23 045
590 305
305 +
+ 396
396 527
527 ++ 23
045 -- 246
246 906
906
= 590
- 166
400 000
000
166 792
792 -- 400
NPV
10 =
~
NPV10
196
179
196 179
We find
find that building aa new
new kiln
kiln is
is most
most probably
probably aa profitable
profitable measure.
measure . As
ter
As aa mat
matter
of
fact, all
all measures that
that can
can be
be taken
taken in
in aa sawmill
sawmill to
to reduce
reduce various
various kinds
kinds of
of buffer
buffer
of fact,
should be
be carefully
carefully analyzed.
analyzed. Especially
interest periods,
periods, the
the capital
stock should
Especially during high
high interest
in buffer stocks
stocks is
is very
very costly.
costly.
tied up in
We assume in
in our estimates
estimates that
that we
we will
will have
have to
to build
build up
up aa new
new buffer
buffer stock,
stock, when
when
We
This is
But checking
out. This
is of course
course not
not too
too realistic
realistic an
an assumption.
assumption. But
the kiln has worn out.
the present
present value
va l ue of MU
MU 11 122
122 425,
425, we
we find
find that
that it
it amounts
amounts to
to "only"
"only" 166
166 792.
792. Let us
us
the
assume
increase the
the useful
useful life
life of
of the
the kiln
kiln by
by another
another 10
10 years.
years. The present
present
assume we
we could increase
value
of this
this future
future amount
amount would
would then
the n be
be reduced
reduced to
to MU
MU 64
64 314.
314. This
This illustrates
illustrates the
the time
time
value of
value of
of money.
money.
- 88 _
APPENDIX 1:
1:
TABLES FOR
FOR QUICK
QUICK ESTIMATIONS
ESTIMATIONS OF
OF
.'. FUTURE VALUES
VALUES
.'. PRESENT VALUES
.'. ANNUITIES
COMRlUNDED
A: CONPOUIED
TABLE A:
TABLE
T<,.,
Yen j,,,,,,,,,,sI
10
Inl
1
2
3
4
5
,,
••
6
7
8
9
to
10
11
11
"
12
13
13
l'
l'
l'
17
14
15
1.().400
.0400
1,08
16
1.0816
1.1249
1.1
249
1,1699
1.1699
1.2157
1.2157
1.0600
1.0600
1.1236
1.1910
1.2625
1.3382
1.265]
1.2633
1.3159
1.3159
1.]686
.3686
J .4233
,4233
J ,4802
,480~
1.4185
1.5036
1.7908
1.5869
1.7138
1.7118
1.8509
1,9990
2.J~89
2.1589
1.5395
.5395
1,6(UO
.6010
.6651
1.6651
.7317
1.7317
.8009
1.8009
20
25
2,6658
2,6658
17
I'I'
"
"
18
19
.""
66%
'i(
1,8730
IJI1l0
.9479
1.9479
2.0238
2,0258
,1068
2,1068
2.1911
2,1911
16
I
It
(,1
..4 %
8%
1.0800
1.1664
1,1664
1.100
1.100
1.1:!OO
LINO
1.1400
1.1400
I.l~OO
1.1500
1.~100
1,2100
1.2996
1.1996
1.3226
1.J~~6
1.2597
1.3310
1.4641
1.6105
1.~j44
1.2544
I.J{)49
1.4049
1.5735
IJ73S
1.7623
1.7623
1.4815
1,4815
1.6890
1.6S90
1.9254
1.9254
1.5109
1.5209
1.7489
1.7489
]1.9738
,9738
2.2107
2.2107
2,4760
~.476O
2.
]950
2.1950
U023
2.5023
~.1
,4]b
2.1436
~.JS79
2.3579
2.59]7
2.5937
3.1058
1,3605
1.3605
1,4693
1.4693
1.77
16
1.7716
1.9487
<;f
%
~.77]1
2.7731
"'"
%
U~~6
2.8526
].2519
3.2519
3.7072
3,7072
2.01
])
2.0113
2.31)2
2.3132
2.660]
2.6603
].0590
3,0590
LSI7
3.51744
4.04~3
4,0453
166%
'7r
%
18""
10
o/r
N%
25 'Ii
25
10 %
"
.\~
q
35%
4093
45 'it
45%
SO '7t
5093
1,1600
1.1600
]1.3456
. .\456
1.1800
1.1
800
1.3924
1.3924
1.60430
1.6430
1.2000
1.2000
I.~~OO
1.2500
lJOO
1.300
IJ~()O
1.3500
11.4400
..wOO
U625
1.5625
1.6900
1,6900
I.Ir:!:~j
1.8225
2.4b(1.t
2.4604
3,3215
3.3215
4.41UO
4.4840
J.40CX1
1.4000
1.9600
1.9600
2.7440
2,7440
.l.S416
3.8416
5.3782
I1.4500
4500
2.1025
3.0486
4.4205
4.4205
6.4097
6,4097
l,jOOO
1.5000
2. 2500
2.2500
3.3750
1.31~O
5.0625
5.0625
., ,5938
7.5938
7.5295
10.5414
10.5414
14,7579
14.7579
~0,6610
20.6610
9.2~1
9.2941
D,·06.5
13.4765
19,~409
19.5409
18,D41
28.3343
~1I.91~~
28,9255
41.0S.t7
41.0847
11.)906
11.3906
17.()859
17.0859
~5,n289
25.6289
3i'1,44]4
38.4434
S7,66~0
57.6650
40.49H
40.4957
56.6939
79,]715
;91195
]111.1201
11.1201
.~9.~n8
59.5728
39.37]8
~ 1:1834
1.1859
3597
27 . 1439
27.1439
36.604.42
49.4697
66.711.40
66.7840
90, 1.~85
90,1585
1.5609
1.5609
1.8106
1.8106
2.100)
2.1003
1.9388
1.7280
2,0736
2.0736
2.287M
2,2878
2.488]
2.4883
2.6996
],1855
3,1855
2.9860
2.9860
2.11262
2.8262
].~784
3.2784
].7~R9
3,7589
3,8030
3.8030
4,4114
4.4114
4,43B
4.4355
,UD8
5.2338
4,2998
4.2998
5.1598
"'.1917
6.1917
6. 1759
7,2876
' 1.1278;:
8,5994
8,~994
10.1472
]0,1472
11.9737
11.9737
7.4301
7.4301
8,9161
8.9161
10.6993
12.8392
12.11]92
15.4070
15.4070
2.4364
USJ2
3.5832
1.9~31
1.9531
2.1970
2.4414
3.05111
3.0518
2.8561
1.8561
.l.1I1H
3.8147
44,7684
.761U
5,9605
5.9f.O~
7,4~06
7.4506
9,)
132
9.3132
4.8268
6.2749
8.1573
3.7 129
3,7129
10,6045
10.6045
lJ.7I1~~
13.7858
h.O~J4
6.0534
118.1722
.1722
II ,03~4
11.0324
14,!$937
14.8937
20,1066
20.1066
'0 "
4.69]
4.6533
5.]505
5.3505
6,1538
6.1538
5.4736
5.4736
4.2~62
4.2262
4.8
179
4.8179
5.4924
56196211
6.2613
7,1]79
7,1379
8,1367
8.1367
S,1173
5.1173
5.9360
6.88511
'f;:119:5785
7.9875
9.2655
9.2655
4.5950
U950
5.0545
~.O545
5,5599
5,5599
6,1159
6.1159
6,7275
6.727S
6.1304
6.1304
6.8660
6,8660
7.6900
7.6900
8.6128
8.6128
9.6463
9.6463
8.1372
8. 1372
9.2765
9,2765
9.3545
9J545
10.7643
12.3762
12.]762
14,2248
14.2248
16.3666
10.7480
10,7480
12,4677
12.4677
14,462~
14,4625
]6,776
16.7765~
19,4608
19,4601\
14.1290
16.6722
16.6722
19.6733
19.673]
23 .2144
23.2144
27,3930
27.3930
18,4884
18.4884
2J:.I!I61
22.1861
26.62]]
26.6233
]31.9480
1.9480
38.3l76
38.3376
35.5991
3~.~991
44.4089
44,4089
55 ,5 111
55.5112
69.3889
86,7362
66.5417
66,~4t7
86.5042
116.5042
121.7119
121.7139
164.3118
164 .3138
217 ,7953
217.7953
304.9135
304.9I3S
10.5752
12,0057
12.0057
13.7435
13.1435
112.4554
112.4554
146.192:0
146,1920
190.0496
221.11236
221.8236
299,4619
404,2736
404.2736
426,8788
426,8788
597,6]04
597.6304
836,61125
836.6825
10,83047
10.8347
17.0001
26.4619
32,8947
32.8947
40,8742
40,
8742
62.66&6
62.6686
95.)962
95.3962
264.6978
70 j,6410
705.6410
1812 .7762
1812.7762
4499.8793
4499,8793
1.8983
2.3]16
2.3316
2.~18J:
2.5182
2.8531
].IJ8-I
3.1384
],4785
3.4785
],8960
2,1329
2,mY
2,2609
2,3966
2.3966
2.7196
2,7196
2,9]7~
2.9372
3.1722
3.4523
3.452]
],7975
3.7975
4,1772
4.1772
U6]~
3418375
2,54()4
2.5404
3,0256
3.2071
3,2071
3,4259
3.4259
3.7000
1.
_
3.9960
4,)157
4.3157
4,6610
4.2919
6,8485
6.8485
2.8543
2.854]
<;t%
I~
""
2.0122
~.0122
2.6928
1~
M%
1.- 1.1.~9]8
1.5938
1.6895
1 ,00
MU 1,00
1 , 00 ,1,00,
i. e.i.e.
the
AMOUNTS
of MU
thefuture
future value ofofMU
AMOUNTS of MU
4,8871
4.8871
7.0771
7.0771
J11.6415
1.641.~
14J~19
14.5519
18,1899
18.1899
22,7]74
~1I,4217
;.8:7
4327147
17.9216
17,9216
23.2981
]0.2117~
30.2875
:469;
1~,~5681
155,5681
86JS06
86.497n
86,4976
129.7463
129,7463
12~,2SI8
(651,6511581
194.619~
12:41::129953
1111.615 I
26),)419
263.3419
291.9293
437,8939
437.8939
381.8458
381.8458
~53, 6764
553.6764
802,8308
802.8308
1164.1047
16117.9518
1687,9518
656,840t1
656,08
84
985,2611
985.2613
1477,89]9
1477.8919
2216.8387
2216,11387
]325,1567
3325.2567
10819,3217 25251.1681
B251.IbIIl
10819.3217
1
'"
'"
C0
1
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TABLE C:
SUM of
of MU
MU 1,00
1, 00 paid
paid each
each year
year (a
(a se
ri es of
equa ll y large
l arge amounts)
amounts)
C: THE PRESENT VALUE SUM
,.,,"
'"'
Int.-'
.,~.
11 1
11?(
11%
I~ %
,"
1]9(
13 %
14 %
"'"
150?(
15%
16
16 ?(
%
\7%
17
%
lSI](
18%
19q
19
%
:!O'i;
%
25'-,
%
JOr;;.
30%
.\51",;,
35%
40"-(
40%
.s st;:(
45%
ÇØ%
~O'7r
0.917 0.909
0.909
0.917
1.759
1.736
1.759 1.736
2.5]1
2.531 2.487
3.240 3.170
3.170
3.240
3.890 3.791
3.79 1
3.890
0,901
0.901
1.713
1,713
2.444
0.885
1.668
2,361
2.361
2.974
2.974
3.517
O.K77
0.877
LbJ7
1.647
2.322
1.32'
2.91-1
2.914
3AH
3.433
0.870
1.626
2.283
2.855
1.855
U52
3.352
0.862
0.862
1.605
2,246
2.246
2.798
0.1W7
0.847
!.!I66
1.566
2.174
2.690
3.127
1.127
0.840
0.840
1.546
2.140
2. 140
2.639
2.639
3.058
3.058
0.800
1.440
1.440
1.951
1.952
2.362
2.362
2.6K9
2.689
0.769
1,361
1.361
1,816
1.81(,
2.166
2.166
2.·06
2.436
0.741
0.741
1.281J
1.289
1.696
1.696
0.714
0.714
1.224
1.224
1.589
1.589
1.997
2.220
IJU9
1,849
2.035
2.0).'
0.690
0.690
1.165
1.493
1.720
1,876
1.It76
0,667
0.667
3.274
0.855
1.585
2.210
2.743
1.743
3,199
3.199
0.833
0.833
],102
3.102
3,696
3.696
0,893
1.690
1.690
2.399
],0]5
3.035
3.602
4,623
5.206
5.747
6.247
6.110
6.710
4.486 4.355
4.355
4.486
5.033
4.868
5.033 4.868
5.535
5.)]5
5.535 5.335
5.995 5.759
5.995
5.7.59
6.418
6.145
6.418 6.145
4.231
4.712
5.146
5,146
5.537
5.889
4.109
4.56
4.5611
4,965
4.965
5.326
5,648
5.648
3.998
3.998
4.423
4.423
4,799
4.799
5.132
5,426
5.426
3.I!IK9
3.889
4.288
4.639
4.946
!I.216
5.216
3.7K4
3.784
4.160
4A87
4.487
4.172
4.772
~.019
5.019
3.685
3,685
4.039
4.344
4.607
4.833
3.589
3,589
3.922
4,207
4.207
4.451
4.451
4,659
4.659
3,-198
3.498
3.812
4.078
4.303
4.494
4.494
3,-110
3.410
3.706
3.706
3.954
3,954
4.163
4.339
4.3W
3.326
3.326
3.605
3,837
3.837
4.031
2.951
3.
161
3.161
2.385
2.3K~
2.168
2.IM
2.508
2.50K
2.263
2.)3
2.331I
4.192
4.11J2
3.329
1.329
3.463
3.570
~U70
2.643
2.K02
2.802
2.'lI25
2.925
3.019
.\.019
3,091
HWI
1.983
2.057
2.0n
2. ](W
2.109
2,144
2.144
2.168
2.16K
1.824
1.883
1.922
1,948
1.948
1.965
1.%5
7,139
7,536
7.536
7.904
6.805
6.495
6.805 6.495
7.16
7.1611 6.814
7.487
7,10)
7.487 7.103
8.061 7,606
5.23 4
5.234
!I.421
5.421
5.583
5.124
5,724
5.&47
5.847
4.836
4.988
4.988
5,1
UI
5,118
55.229
..229
5.324
4.656
4.656
4.793
4,9 10
4,910
5.008
5.092
5,092
4.487
4.411 7
4,611
4.611
4.715
4.7\5
4.802
4.802
4,876
4.tl76
4.327
4.439
4.533
4.610
4.610
4,675
4.675
3.656
1.656
3.725
3.125
3.780
1.780
3.824
3.859
1.85'l1
3.147
3,190
3.190
3,223
3.223
3.249
3.268
1.752
2.752
2.779
2.179
2.799
2.814
8.5.59
8.559
5.687
5.687
5.918
5.918
6.
122
6.122
6.302
6.302
6.462
5.029
7,786
7,367
7.786 7.367
5.935
5,935
6,192
6.192
6,421
6.626
6.808
6.808
~.-I~3
5.453
8.244
8,244
6.207
6.492
6.750
6.750
6.982
7.
191
7,191
2.185
2,196
2.196
2.204
2.210
2.214
1.977
1.977
1,985
1.985
1.990
1.990
1.993
1.993
1.995
1.995
7.963
7,467
7.841
7.&41
8.051
8.053
8.174
8.242
8.n:!
8.304
7,025
7.025
7.330
7,497
7A97
7,588
7.588
7.638
7.675
5.628
5.766
5.829
5.859
5,873
5.873
5.353
5,467
5.467
5.517
5.539
5.548
5,548
5.554
5.101
5. 101
4.870
4.948
4.979
4.992
4,997
4.997
4,999
4.999
3.954
3.98!1
3.985
3.995
3.999
1.999
4.000
4.000
3.316
3.129
3.329
3.332
U12
3.333
3.333
L\33
3.333
3.3JJ
2.850
2.856
2.857
2,221I
2.22
2.222
1,999
1.999
2.000
2.000
2.000
2.000
2,000
2.000
44%
~
55%
c;;:
6 '7i
6%
71>
7%
81>
%
9?(
9%
00.962
.962
1.886
2.n~
2.775
3.630
3,630
4.452
0.9!\2
0.952
1.859
1.859
2.723
3.546
4,329
4.329
0.94~
0.943
1.833
2.673
2.673
3.465
4,212
4.212
0.935
0,935
1.808
1.808
2.624
2.624
3.]87
3.387
4,100
4.100
0.926
0.926
1.783
1.783
2.577
2.577
],]
12
3.312
3,993
3.993
5.242
6.002
6.733
7.435
7,435
8.111
5.076
5.786
5,786
6.463
7. IOS
7.108
7.722
4.917
4,917
5.582
5.582
6.210
6.210
6.802
6,802
7.360
4.767
5.389
55.971
.97 1
6.5 15
6.515
7.024
""
"
8.306
8.863
9,]94
9.394
9,899
IO.~63
10.563 9.899
11.118 10.380
10.380
7,887
7.887
8.184
8,384
B.B.H
8.853
9.295
9.712
7,499
7.94]
7.943
8.358
8.358
8.745
8.745
9.108
9. 108
20
Jl
35
"
1l.590
13.590
15.622
17.292
17.292
18.664
18.664
11.470
12.783
13.765
13.765
14.498
\4.498
40
lO
50
17.159
15.046 13.332 11.925 10.757
10.757 9.779
19.793
159 15.046
19.791 17.
21.482
9.9 15
15.762 n.wl
13.801 12.233 10.962
10.962 9.915
21.482 18.256 15.762
111
1
3
4
4
l
5
tOlK
10 %
1.52K
1,528
2.106
2.106
2.589
2.589
2.991
1. 11 1
1.111
1.407
1.407
1.605
1,605
1.737
1.737
-0
66
77
88
99
1
0
10
11
12
Il
13
14
15
15
25
30
8,760
8.760
9.385
9,385
9.986
12.462
14.094
14
.094
Is
.n'!
15.371
16,374
16.374
10
..594 9,818
129 8.514
8.5 14
9.129
10.594
9.818 9.
9.823 9.077
11.654 10,67S
9.823
9,077
10.675
12
,409 11.2.58
10.214 9,426
12,409
11.258 10.274
12.948 11.654
11.654 10.566
12.94S
10,566 9.644
9.64-1
8.422
8A22
8.694
8,855
8.855
8,951
8.951
9.042
9.042
5.660
HI60
5.1W2
5.842
6.002
6.002
6,142
6.142
6,623
6.623
6.873
6.873
7.003
7.070
77.105
. I O~
7,
7.133
133
6.259
6.464
6.5M
6.565
6.616
6.642
6.660
-.
5.197
5,197
5.342
5A68
5.468
5.575
5.929
6.097
6.
178
6.178
6.216
6.235
6.215
6.246
,
5,880
5.880
5.195
5,234
5.234
5.251
5.258
5.258
5.262
2.598
2.665
2.715
2.71!1
2.825
2.857
2.1157
2.857
2.1157
2.857
2.379
2.414
2.414
2.438
2.43K
2.456
2.469
2.478
2.484
2.4R4
2.497
2.497
2,499
2,-199
2.500
2.500
:2:.500
2.500
2.500
2.222
2.2 22
2.222
2,222
:'..222
2.222
TABLE
i.e. the
the yearly
amount to be paid in
in order
order to
to amorTABLE D:
D: THE
THE ANNUITY
ANNUITY FACTORS,
FACTORS, i.e.
yearly amount
tize
tize (depreciate)
(depreciate) an amount
amount of
of MU
MU 1,00
1,00
Y
.. ~.
Yen(
fnl
'"'
Interr.t.,
ir
I,,, ,·,,· s' I'.'
9C
9C
5~ %
I
44
6%
69>
7%
'0;;
%
89>
•9%
'if
10,"
10%
1153
II'/(
12%
I~'ifo
13%
13'it
14~
1453
I~<;t15
%
16?i
1653
17 %
?r
181](
18 %
19?(
19 %
20
?(
20%
2~ O;(
2551
.\01(
30%
J~q.
3551
40%
40'1
4551
.t5 %
~50%
O q
5
5
1.0400 1.0500
1.0600 1.0700
1.0700 1.0800
1.0800 1.0900
1.1000 1,1100
1.1100 1.1200 1.1300 I.I-lOO
1.1500 1.1600
1.1600 1.1700
1.\700 1.1
800 1.1900
I.~OOO L!~OO
1.:\000 1.3500
U500 1.·1(100
UOOO
1.0400
1.0500 1.0600
1,0900 1,1000
1.1400 1.1500
1.1800
1.1900 1.2000
1.2500 1.3000
1.4000 IA:'iOO
1.4503 1.5000
0.5)02
a.D78 0.5454
0,5454 0.5531
0.5531 0.5608
0,5608 0.5685
0,5685 0.5762
0.5762 0.5839
0.5839 0.5917
0.5917 0.5995
0.5995 0.6073
0.6073 0.6151
0.6151 0.6230
0.6230 0.6308
0,6308 0.6387
0,6387 0.6466
0.6466 0.6545
0,6545 0.6944
O,b9+a 0.7348
0.7348 0.7755
0.7755 0.8167
0.8167 0.8582
0.8582 0.9000
0.9000
0.5302 0.5378
0,3603 0,3672
0.3810
0.4021 0.4092
0,3603
0,361"1 0,3741
0.3741 0.]8
10 0.3880
0.3880 0.3951
0,3951 0,4021
0,4092 0.4164
0,4164 0.4235
0,4235 0.4307
0.·1.107 0.4380
0.4380 0.4453
0,4453 0,4526
0.4526 0.4599
0.4599 0.4673
0.467) 0.4747
0.4747 0.5123
Ojl~3 0.5506
O..~506 0.5897
0.5897 0.6294
O,62~ 0.6697
0,6697 0.7105
0,7 105
0.2755
0.2886 0.2952
0.3019 0,3087
0,3087 0,3155
0,3155 0,3223
0.3223 0,3292
0.)292 0.3362
0.]]62 0.3432
a.H):! 0,3503
O.HOJ 0.3574
0,3574 0.3645
0.36045 0.3717
0,371 7 0,3790
0,3790 0,3863
0.]86] 0,4234
0,4234 0,4616
0,46\6 0.5008
0.5008 0.5408
0.5408 0.5816
0.58 16 0.6231
0.6231
0.2755 0.2820
0,2820 0,2886
0.2952 0,3019
0,2246
0.2310 0.2374
O,B74 0.2439
0.2439 0.2505
0,2505 0,2571
O.2~i7l 0
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0.2774 0,2843
0.291] 0,2983
0.2983 0.3054
0,3054 0,3126
0.3126 0.3198
0.3198 0.3270
0.3270 0,3344
0.3344 0.3718
0.371H 0.4106
0.4 106 0,4505
0,4505 0.4914
0.49 14 0,5332
G.~]]2 0.5758
0.~751S
0.2246 0.2310
0.2638
0.2706 0.2774
0.2843 0.2913
6
77
88
9
10
10
0.1908
0.~098 0,2163
0.2~~9 0.2296
0.2364 0.2432
0.2432 0.2502
0.2~02 0.2572
0.25n 0.2642
0.2642 0.2714
0.27 1.1 0.2786
0,2786 0.2859
O,21J59 0.2933
0.2933 0.3007
0.3007 0.3388
0.]]88 0,3784
0.)71(.4 0.4193
0.4193 0.4613
OA613 0.5043
O.~043 0.5481
O.~·UII
0.1908 0,1970
0.1970 0.2034
0.2034 0.2098
0.2163 0,2229
0.22% 0,2364
0,1666
0,1728 0.1791
0.179 1 0,1856
0 . l8~6 0.1921
0,192 1 0.1987
0.1987 0,2054
0.20~4 0.2122
0,2122 0.2191
0,2191 0,2261
0.2261 0.2332
0,2332 0,2404
0.2404 0,2476
0,2476 0.2550
0.25~0 0.2624
0,2624 0.2698
O,26~ 0.2774
0.2774 0,3163
0,3163 0,3569
0.3569 0,3988
0.)9K8 0.4419
0,4419 0,4860
0.4860 0,5311
0.~311
0,1666 0.1728
0.1485 0.1547
0.1547 0.1610
0. 16 10 0.1675
0,1675 0.1740
0, 1740 0,1807
0.1807 0,1874
0,1874 0.1943
0,1943 0.2013
0.2013 0,2084
0,2084 0,2156
0.2156 0.2229
0.2229 0.2302
0,2302 0.2377
0,2377 0.2452
O,24~2 0.2529
0. 2529 0.2606
0,2606 0.3004
0.3004 0.3419
0.3419 0.3849
0.3849 0.4291
0.4291 0.4743
0.4743 0,5203
0,5203
0.1485
0,1345
70 0.1535
1601 0,1668
0,1806 0,1877
0.1877 0,1949
0.1949 0,2022
0.W2:? 0.2096
0.2096 0,2171
0,2171 0,2247
0,2247 0.2324
0,232.1 0,2402
0.2402 0,2481
0.2481 0.2888
0.2888 0.3312
0.3312 03752
0.3752 0,4203
0,4203 0,4665
0.4665 0.5133
0.5133
0,1345 0,1407
0.1407 0,14
0,1470
0.1535 0,
0,1601
0,1668 0.1736
0,1736 0.1806
0.
12 33 0.1295
1490 0,1558
0.1558 0,1627
0,1698 0.1770
0.1770 0,1843
0.1843 0,1917
0,1917 0,1993
0,1993 0.2069
0.2069 0,2147
0.2147 0.2225
0.2225 0.2305
0,2305 0.2385
O, B8~ 0.2801
0.l801 0.3235
0.323~ 0.3683
0.3~3 0.4143
0,4143 0,4612
0.4612 0,5088
0.5088
0.1233
0.1295 0.1359
0.1359 0,1424
0.1424 0,
0.1490
0.1627 0.1698
11
11
12
12
J3
13
14
14
15
15
0,2068 0.2148
0,2229 0,2311
0.4577 0,5058
0.1141 0.1204
0.1204 0.1268
0,1268 0.1334
0,1334 0.1401
0,1401 0.1469
0.1 4690,15400,1611
0.1684 0.1758
0.1758 0,1834
0,1834 0,1911
0.1911 0,1989
0.19890.2068
0.21480.2229
0.l311 0.2735
0,2735 0,3177
0.3177 0.3634
0.3634 0.4101
0 ..1101 0,4577
0.5058
0.1540 0.1611 0.1684
0.1065
0.1327 0.13%
0.1396 0,1468
0. 1468 0,1540
0,1540 0,1614
0,1614 0,1690
0, 1690 0.1767
0. 1767 0.1845
0.1845 0,1924
0, 1924 0.2005
0,2005 0.2086
0.101S6 0.2169
0.1 169 0,2153
0.2253 0.2684
0.2684 0,1134
0. 3134 0.3598
0. )598 0,4072
0.40n 0,4553
O ,4~5) 0.5039
0,5039
0.1065 0.1128
0.1128 0.1193
0.1193 0.1259
0.1259 0.1327
0,1001 0,1065
0. 1065 0,1130
0.1130 0.1197
0.1197 0.1265
0.1265 0.1336
0.1336 0,1408
0,1 408 0,1482
0,1482 0.1557
0,1557 0.1634
0,1634 0.1712
0,1712 0.1791
0.1791 0.1872
0, 18720.1954
0. 19540.2037
0.20370.2121
0,1121 0.2206
0.2206 0.2645
0.264~ 0.3102
0.3102 0.3572
O.Hn 0.4051
0.4051 0.4536
0.4536 0.5026
0,5026
0,09470.10100.10760,11430.\213
0.1284 0.1357
0,1432 0,1509
0, 1509 0.1587
0.1~87 0,1666
0.1666 0.1747
0.1747 0,1829
0.1829 0.1912
0.1912 0,1997
0, 1997 0,2082
0.2082 0,2169
0.2169 0.2615
0.261~ 0,3078
0,3071J 0.3553
0.3553 0,4036
OAO)6 0.4525
0,4S25 0.5017
0.50 17
0.0947 0,1010 0.1076 0.1143 0.1213 0.1284
0.1357 0,1432
0.0899
0.096] 0.1030
0 . 10)0 0,1098
0,1098 0,1168
0 . 1168 0.1241
0.1241 0,1315
0,\315 0,1391
O,I3,}1 0,1468
0, 1468 0.1547
0.1547 0,1628
0.1628 0.1710
0, 1710 0.1794
0.1794 0.1878
0,1878 0,1964
0,1964 0.2051
0,2051 0,2139
0.2139 0.2591
0,2591 0.3060
0,3060 0.3539
0,]5]9 0.4026
0.4026 0,4517
0,4517 0.5011
0.5011
0.0899 0.0961
20
20
25
0.1~8 0.1960
0.1960 0.2054
0.2054 0,2529
0.2529 0.3016
0,]016 0.3509
0,)509 0,4005
0,4005 0.4503
OA503 0,5001
05001
0,1777 0.1868
0.16M7 0,1777
0.1339 0,1423
0.1423 0,1510
0,1510 0,1597
0.1597 0.1687
0,0736 0.0802
0.0802 0.0872
0.0944 0.1018
0.1256 0,1339
0,0872 0.0944
0.1018 0.1095
0.1095 0.1175
0.11 75 0,1256
0.0736
0,1829 0.1925
0.1925 0,2021
0.2021 0,2510
0,2510 0,3004
0.3004 0.3502
0,]502 0.4001
0.4001 0.4500
0.4500 0.5000
0.5000
0,1734 0,1829
0.1640 0.1734
0,1215 0.1364
0,1364 0.1455
0,1455 0.1547
0,1547 0.1640
0,1 187 0,1275
0, 1102 0,1187
0,0640 0,0709
0,0858 0.0937
0.1018 0,1102
0.0937 0,1018
0,0640
0,0709 0.0782
0.0782 0.0858
0.\813 0.1910
0,1910 0.2008
0,2008 0.2503
0.250) 0.3001
0.3001 0.3500
0.3 500 0.4003
0.4000
0.1619 0.1715
0,1428 0,1523
0.1715 0.1813
0.1241 0.1334
0.1334 0,1428
0.1523 0.1619
0, 106 1 0,1150
0,0578 0,0650
0,1150 0,1241
0.0973 0,1061
0,0806 0.0888
0.0888 0,0973
0,0578
0,0650 0.0726
0.0726 0.0806
0,)000
0. 1805 0,1904
0,1904 0,2003
0,2003 0.2501
0.2501 0.3000
0,1707 0.1805
0,1609 0.1707
0,1223 0,1318
0,1318 0,1414
0.1414 0.1511
0.1511 0.1609
0,10)7 0.1129
0,1129 0,1223
0,0536 0.0611
0,0611 0.0690
0,0946 0.1037
0,0772 0.0858
0,0690 0.0772
O,08.~8 0,0946
0,0536
0,18020.1901
0.\90\ 0.2001 0.2500
0,170]0.1802
0.160.1 0.1703
0.09)0 0.1023
0, 12 13 0.1310
0.1310 0,1407
0.1407 0.1506
0,1506 0.1604
0,1023 0,1117
0,1 11 1 0,1213
0,0505 0.0583
0,0839 0,0930
0.0150 0,0839
0,0505
0,0583 0.0665
0.0665 0,0750
1800 0,1900
0.1900 0.2000
0.2000
0,1701 0.
0.1800
0.1601 0.1701
0.1204 0.1303
0.130] 0,1402
0.1402 0.1501
0,1501 0.1601
0,1106 0.1204
0, 1009 0.1106
0,0912 0.1009
0,0634 0.0725
0,0725 0.0817
0,0466 0.0548
0.0817 0.0912
0,0466
0.0548 0.0634
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