Download LECTURE NOTES 3 and 4 EC 403

LECTURE NOTES 3 EC 403
BUSINESS AND ECONOMIC FORECASTING
A. DEMAND CONCEPTS FOR DECISION MAKING
Introduction
Firms are in business to make profits. When cost of production is increasing the firm may want to pass
the incremental cost on to the consumer by raising the price. Whether raising the price following the
rise in cost or otherwise- will prove beneficial or not depends on:
(a) the price elasticity of demand for the products.
(b) price elasticity of its substitutes, because when the price of a product increases, its substitutes
become automatically cheaper even if their prices remain unchanged.
Raising price will be beneficial only if
(i) demand for a product is less elastic and
(ii) demand for its substitute is much less elastic. Similarly, a firm not finding it feasible to increase the
price during a period of growth in consumers’ income would like to increase the production. The
additional production can be determined only through the income elasticity of demand for the product,
other factors held constant.
Elasticities of demand
The responsiveness of the quantity demanded to changes in own price (Own price elasticity), prices of
other goods (cross price elasticity), income (income elasticity), advertising (advertising elasticity).
The concepts of demand elasticities used in business decisions are:
(i)
Price elasticity.
(ii)
Cross elasticity.
(iii)
Income elasticity
(iv)
Advertising or promotional elasticity.
Price Elasticity
Determinants of price elasticity of demand.
(1) Availability of its (product’s) close substitutes. The higher the degree of closeness of the
substitutes, the greater the elasticity of demand for the commodity, If there are many good
substitutes for a product customers would tend to buy the substitutes even if the price of the
product rises only slightly. Conversely if it is only product in the market, no matter the change
they will still buy it.
(2) Nature of the commodity- luxuries, comforts and necessities. Demand for luxuries is more elastic
than demand for others in that their consumption can be dispensed with or postponed. Demand for
necessities is inelastic, their consumption cannot be postponed. Demand for durable goods is more
elastic than that of non-durable goods.
(3) Proportion of income spent on a commodity. If proportion of income spent on a commodity is
large, its demand will be more elastic and vice versa e.g. a small proportion of income is spent on
matches, salt. Demand for these goods is generally inelastic because increase in the price of such
goods does not substantially affect consumers’ consumption pattern. People continue to purchase
almost the same quantity when their prices increase. Goods that are low in price tend to be
unresponsive to price change. Conversely the purchase of expensive items tends to be very
sensitive to price changes.
(4) Time consumers take to adjust to a new price- the longer the time taken the greater the elasticity,
because over a period of time consumers are able to adjust their expenditure pattern to price
changes. For example if the price of TV sets is decreased demand will not immediately increase
unless people possess excess purchasing power. Over time the demand for the demand for an item
tends to become more elastic.
(5) Range of uses of a commodity- the wider the range of uses of a product, the higher the elasticity of
demand. As the price of a multi use commodity decreases, people extend their consumption to its
other uses, e.g. milk and electricity.
(6) Proportion of the market supplied at the ruling price. If at the ruling price, less than half of the
market is supplied, price –elasticity of demand will be higher than if the ruling price supplies more
than half the market.
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(Own) Price Elasticity of Demand
Is the proportionate change in Qd divided by proportionate change in price.
ED 
dQx / Qx dQx Px

=
.
dPx Qx
dPx / Px
We use point elasticity when changes in price is infinitesimal. For more substantial price changes we
use arc elasticity.
D
P
A (point elasticity)
D
Point price elasticity is the elasticity of demand at a finite point on a linear demand curve or demand
line or the elasticity at any one spot of the demand curve. Point elasticity is thus the product of price
quantity ratio at a particular point and the slope of the demand line.
Point elasticity = ED 
dQx Px

dPx Qx
Arc elasticity (Own price elasticity)
- Arc price elasticity of demand is the measure of elasticity of demand between two finite points on a
demand curve.
D
A
B
D
The problem in using arc elasticity is that the arc elasticity coefficients differ between the same two
finite points on a demand curve if direction of change in price is reversed. To avoid this we use the
arithmetic mean of the two prices and the average of the two quantities in the calculations. The
formula is expressed as
ED 
Q ( P2  P1 ) / 2 Q2  Q1 P2  P1



. The value lies between the two values of the
P (Q2  Q1 ) / 2 P2  P1 Q2  Q1
point elasticities
In general, price elasticity of the demand curve that a firm faces is larger than the price elasticity of the
corresponding market demand curve because the firm faces competition from similar commodities
from rival firms.
Price elasticity of demand and total revenue
A businessman trying to maximise his total revenue or the total sale proceeds would like to know
whether raising or decreasing the price of a product will increase the revenue. The concept of price
elasticity of demand provides the answer to this query if the numerical value of the elasticity (its
magnitude)is known.
If ED = 0 an increase in price raises TR
2
ED<1 an increase in price raises TR
ED=1 increase in price maintains TR (no change).
ED >1 increase in price decreases TR.
ED=infinity. Increase in price decreases TR to Zero
Price Elasticity and Marginal Revenue
The relationship between price-elasticity and the total revenue (TR) can be more precisely known
through the relationship between price elasticity and the marginal revenue (MR).Price elasticity affects
the MR which affects the TR. TR = PQ, MR =
TR
. and MR  P(1  1 ) . Given this
ED
Q
relationship between MR and price elasticity of demand, the decision-makers can easily know whether
it is worthwhile to change price.
Derivation of the relationship between MR and e ( MR
 P(1  1
ED
))
TRx = Px .Qx……………………………………………………..(1)
Px  a  bQx ……………………………………………………..(2) Demand curve.
TRx  (a  bQx )Qx ….…………………………………………...(3)
 aQx  bQx ………………………………………………...(3a)
dTRx
MR x 
 a  2bQx ………………………………………..(4)
dQx
2
Equations (2) and (4) have the same Y intercept indicating both curves emanate from the same point on
the vertical axis of the graph and the slope of the MR is twice that of the demand curve expression (2).
TRx  Px .Qx ………………………………………………………(5)
MRx is the first derivative and can be found using the function of a function rule (since P x is a
function of Qx).
MR x  Px  Qx 
dPx
……………………………………………...(6)
dQx
Multiply and divide the last term by Px.
Qx
dP
Q dP
 Px  x  Px (1  x  x ) ………………………(7)
Px
dQx
Px dQx
dQx Px
1

)
but ED 
and therefore (7)becomes MRx  Px (1 
dPx Qx
ED
MR x  Px 
This relationship serves to specify the relationship that exists between MR, price and price elasticity of
demand at any particular price level on a given demand curve.
Assignment
NBA Corporation which had a monthly basketball shoe sale of 10 000 pairs (at $100/pair) before a
price cut by its major competitor. After this competitive price reduction, NBA’s sales declined to 8000
pairs per month. From the past experience NBA has estimated the price elasticity of demand too be
about –2.0 in this price-quantity range. If the NBA wishes to restore its sales to 10 000 pairs a month
determine the price that must be charged.
Cross Elasticity of Demand
Is the measure of responsiveness of a commodity X to the changes in the price of (its substitutes and
complementary goods). If cross elasticities between two goods are positive the two may be considered
as substitutes for each other. The greater the cross elasticity the closer the substitute. Similarly if cross
elasticity of demand for two related goods is negative, the two may be considered as complementary of
each other; the higher the negative cross elasticity the higher the degree of complementarity. As with
price and income elasticities we have point and arc cross price elasticity.
E X ,Y 
% in.demand of X
% in Pr ice of Y
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Point cross price elasticity of demand = E X ,Y 
Qx / QX QX PY
QX PY




.
PY / PY
PY QX
PY QX
Arc cross price elasticity of demand
% in.demand of X
gives different results depending on whether P Y rises
% in Pr ice of Y
( PY2  PY1 ) / 2
QX  QX 1
PY  PY1
QX
or falls, hence the need for formula E X ,Y 

 2
 2
PY (QX 2  QX 1 ) / 2
PY2  PY1
QX 2  QX 1
The formula E X ,Y 
- If accurate measures of cross elasticities are available, the firm can forecast the demand for its
product and can adopt necessary safeguards against fluctuating price of substitutes and complements.
- Firms often use this concept to measure the effect of changing the price of the product they sell on the
demand of other related products that the firm also sells, e.g. a manufacturer of both razors and razor
blades can use cross price elasticity of demand to measure the increase in the demand for razor blades
that would result if the firm reduced the price of razors.
- A high positive cross price elasticity of demand is often used to define an industry since it indicates
that the various commodities are very similar.
- The value of the cross elasticity between two products allows us to specify the relationship between
the products as of either substitutability or complementarity.
- Concept of cross elasticity is of vital importance in changing price of products having substitutes and
complementary goods. If cross- elasticity in response to the price of substitutes is greater than 1 it
would be inadvisable to increase the price; rather, reducing price may prove beneficial. In case of
complementary goods, also reducing price may be helpful in maintaining the demand in case the price
of one of the complementary goods is rising.
Income –Elasticity of Demand
Is the responsiveness of demand to changes in incomes. NB income refers to the disposable income,
i.e. net of taxes. Income elasticity is always positive because of a positive relationship between income
and quantity of a product consumer buys. An exception is income elasticity of demand for an inferior
good is negative because of the income substitution effect.
Income Elasticity of demand
As with price elasticity we have point and arc elasticity.
EY 
dQx / Qx dQx Y

 for point elasticity and infinitesimally small changes.
dY / Y
dY Q
When changes in income are discrete we use arc elasticity which deals with average income and
average quantity demanded. As with arc price elasticity of demand, arc income elasticity of demand
gives different results depending on whether income rises or falls. To avoid this we usually measure arc
income elasticity of demand
EY 
Q (Y2  Y1 ) / 2 Q2  Q1 Y2  Y1



= Arc elasticity
Y (Q2  Q1 ) / 2 Y2  Y1 Q2  Q
For all consumer goods, income elasticity is positive though the degree of elasticity varies in
accordance with the nature of goods. Consumer goods are generally grouped under categories, namely
necessities, comforts and luxuries.
Use of income elasticity in business decisions
- Income elasticity of a product is of greater significance in production planning and
management in the long run, particularly during the period of business cycles.
- Concept can be used in estimating future demand provided the rate of increase in income and
income- elasticity of demand for the products is known. The knowledge of income elasticity
can thus be useful in forecasting demand for a commodity that a firm sells under different
economic conditions when changes in personal incomes are expected other things remaining
the same.
- It helps also in avoiding over production or underproduction.
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-
-
-
-
-
Demand for a commodity with low income elasticity will not be greatly affected as a result of
boom conditions or recession in the economy. Firms selling necessities may want to upgrade
their product to share in the rise of incomes in the economy over time.
Knowledge of elasticity is important for a firm in identifying more precisely the market for its
product and in determining the most suitable media for its promotional campaign to reach the
targeted audience.
If the income elasticity is very low for the firm’s product, management knows that the firm
will not benefit much from rising incomes and may want to upgrade the quality of its product
or move into new product lines with more income elastic demand. In forecasting demands
however, only the relevant concept of income and data should be used.
While it is generally believed that the demand for goods and services increases with increase
in GNP depending on the MPC, it is quite likely that increase in GNP flows to a section of
consumers, which does not or is not in a position to consume the product in which a
businessman is interested, e.g. if the major proportion of incremental GNP goes to those who
can afford a car, growth rates in GNP should not be used to calculate income elasticity of
demand for bicycles. Therefore, the income of only a relevant class or income group should be
used. Similarly, where product is of regional nature, or if there is a regional division of market
between the producers, the income –elasticity of only the relevant region should be used in
forecasting the demand.
Concept of income elasticity may also be used to define the normal ‘normal’ and ‘inferior’
goods.
Advertisement or promotional Elasticity of sales
The expenditure on advertisement and on other sales- promotion activities do help in promoting sales
but not in the same degree at all levels of total sales. The concept of advertisement elasticity is useful in
determining the optimum level of advertisement cost.
Reasons for Advertising
(1) Increasing shares and maximizing profits.
(2) Increasing the price if firm has market power.
D1
D2
(3) Strategic reasons-firms may advertise to discourage entry or retaliate against entry.
(4) Signal of product quality even if demand curve does not shift.
(5) As an investment- assumes impact is tied to long run as well.
Advertising Elasticity
Measures the responsiveness of the change in quantity demanded to a change in advertising budget
expanded for product X. We expect a positive relationship.
(Own) Point elasticity of advertising=E A 
dQx / Qx dQx Ax


dAx / Ax dAx Qx
Q ( A2  A1 ) / 2 Q2  Q1 A2  A1



.
A (Q2  Q1 ) / 2 A2  A1 Q2  Q1
Advertising elasticity varies between EA = 0 to EA=  . When EA = 0, sales do not respond to
(Own) Arc elasticity of advertising=
EA 
advertisement. When EA = 1 sales increase in proportion to the increase in expenditure on
advertisement. When EA>1 sales increase at higher rate than the rate of increase in advertisement
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expenditure. A low advertising elasticity means that a firm will have to spend substantial sums to shift
demand for its product through advertising.
Determinants of advertising elasticity
(i)
Level of total sales – in the initial stages of sales of a product, particularly of one newly
introduced in the market, the advertising elasticity is greater than unity. As sales increase,
the elasticity decreases. This is because after the potential market is supplied the function
of advertisement is to create additional demand by inducing people to consume the
product, particularly those who are slow in adjusting their consumption expenditure to
provide for new commodities. Therefore demand increases at a rate lower than the rate of
increase in advertisement expenditure.
(ii)
Degree of competition- in a competitive market, the effectiveness of advertisement is also
determined by the relative effectiveness of advertisement by the competing firms.
(iii)
Cumulative effect of past advertisement- in case expenditure incurred on advertisement in
the initial stages is not adequate, enough to be effective, elasticity may be very low. But
over time continuing doses of advertisement expenditure may have cumulative effect on
promotion of sales and advertising elasticity may considerably increase.
(iv)
Advertising elasticity is also affected by other factors affecting demand for a product e.g.
change in product’s price, consumers’ income, growth of substitute and their prices.
Cross Advertising Elasticities
Measures the responsiveness of the quantity demanded (sales) of Product X, to a change in advertising
efforts directed at another product Y. We expect this to be negative between substitutes and positive
between complementary products.
E AX , Y 
dQx / Qx dQx Ay
= point cross advertising elasticity.


dAy / Ay
dAy Qx
Arc elasticity is a better concept for measuring the average elasticity over an extended range. It is
appropriate for incremental analysis.
E AX ,Y 
Q X ( AY 2  AY 1 ) / 2 QX 2  Q X 1 AY 2  AY 1



.
AY (Q X 2  Q X 1 ) / 2 AY 2  AY 1 Q X 2  Q X 1
Dorfman Steiner Conditions for profit maximisation
For profit maximisation the ratio of advertising expenditures to sales revenue should be equal to the
ratio of advertising elasticity of demand to price elasticity of demand. The model illustrates the
importance of advertising elasticity as a determinant of the profit maximising advertising budget.
E
A
 A
PQ E D
Given that Quantity sold is a function of the price and Advertising expenditure and also that cost is a
function of quantity.
  P  Q  CQ  A  P  Q( P, A)  C[Q( P, A)]  A
d
dQ dC dQ
First FOC : ..
 P


 1  0............................(i)( a)
dA
dA dQ dA
dQ
dQ
P( )  MC 
1
dA
dA
dQ
( P  MC )  1................................................................(ii )( a )
dA
A
Multiply both sides of (ii) by
PQ
dQ
A
A
( P  MC ) 

dA
PQ PQ
6
dQ A P  MC
A
 {
}
dA Q
P
PQ
P  MC
A
EA (
)
..........................................................(iii )( a)
P
PQ
P  MC
A 1

( )..........................................................(iv )( a)
P
PQ E A
Second FOC
d
dQ
dC dQ
 P
Q

.  0...............(i)(b)
dP
dP
dQ dP
dQ
dQ
P
 Q  MC 
 0.............................................(ii )(b)
dP
dP
Rearranging
dQ
dQ
P
 MC 
 Q.
dP
dP
divide both sides by P
dQ P  MC
Q
(
)   ...............................................(iii )(b)
dP
P
P
P  MC
Q dP
1
 

........................................(iv )(b)
P
P dQ
EP
P  MC
A 1

( )..........................................................(iv )( a)
But
P
PQ E A
P  MC Q dP
1
A 1
 

.
( ).....................................(iv )(b)
P
P dQ E P
PQ E A
P  MC Q dP
1
A 1
From this....
 


( )
P
P dQ E P PQ E A
FOC : ........

E
A
 A ....................
PQ E D
B. COST CONCEPTS FOR DECISION MAKING
Information with regard to costs is required for 3 purposes:
(a) Financial reporting mainly for the benefit of the owners.
(b) Managerial control of current operations.
(c) Decision making on the part of managers with regard to future operations.
Costs vary with the circumstances in which they occur.
The most common source of cost information is historical accounting data. This however is of limited
use for decision making because present decision can only affect and be affected by future costs. Past
costs can be a very uncertain guide to the future due to inflation. Costing data involves both variable
and fixed costs and these may not be readily separable. Most decisions however have to be taken on the
basis of costs which are variable. Business managers must acquire knowledge of the way in which
costs behave in their firms with changes of output. The total output is among other factors affecting
costs per unit of output. Others are prices paid for factors of production employed, efficiency of
management, scale of plant constructed, level of technology attained and size of orders.
Costs may be controllable or uncontrollable. The degree to which any cost is controllable by a manager
depends on his position in the organization. Controllability of costs is related to a specific centre of
responsibility. All costs can be said to be controllable, in the sense that somewhere in the organization
there will be someone who is responsible for them.
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Total, Average and Marginal Cost
Total cost- the value of the total resource requirements for the total outlays of money expenditure,
both- explicit and implicit on the resources used to produce a given level of output. The total cost for a
given output level. The total cost for a given output is given output is given by the cost function. The
costs include all payments and contractual obligations made by the firm together with the book cost of
depreciation on plant and equipment. These costs are used in calculating the profits and losses in the
business, in filing returns for income tax and for other legal purposes. They include payment for labour,
materials, plant, building, machinery, equipments, traveling and transport etc.
Average Cost- is of a statistical nature rather than being an actual cost. It is obtained simply by dividing
the total cost (TC), by the total output (Q), i.e.
TC
 average cost.
Q
Marginal Cost- is the addition to the total cost on account of producing an additional unit of the product
or can be defined as the cost of the marginal unit produced. In reality an increment of 1 unit is often too
small to have any operational significance. MC 
TC TVC

Q
Q
-measurement of marginal cost is simplified when the firm/plant produces a single homogeneous
product by the use of facilities which are devoted solely to that product. In practice products require the
use of both specialist and multipurpose machinery and share use of the latter with other products. This
shows that it is difficult (or near impossible to calculate marginal cost. (NB. Marginal costs are
different from incremental costs.).
Variable and Fixed Costs
Fixed Costs Fixed costs do not vary with the variation in output between zero and a certain level of
output and include (1) cost of managerial and administrative staff. (2) Depreciation of machinery,
building and other fixed assets and (3) maintenance of land, etc. Concept of fixed cost is associated
with the short run. Some costs may be fixed in the short period but can be varied. Over longer periods
of all costs can be varied since the business can be discontinued. In the long run even fixed costs
become variable costs as the size of the firm or scale of production increasers. Long run costs are by
implication the same as fixed costs.
Variable Costs- are those costs which vary with the variation of output. They include cost of raw
materials, running cost of fixed capital such as fuel, ordinary repairs, routine maintenance expenditure,
direct labour charge associated with the level of output and the costs of all other inputs that vary with
output. Short run costs vary with the variation of output, size of the firm remaining the same. They are
the same as variable costs. Variable costs are subject to different patterns of variations. In some cases a
variation is direct such as doubling of activity leading to doubling of cost. In other cases the
relationship is more complex e.g. the costs of machine maintenance in the factory, may consist of a
fixed element-preventive maintenance and a variable element arising from use.
Cost concepts-the cost concepts which are relevant to business operations and decisions can roughly be
grouped on the basis of their purpose under two categories: (i) concepts used in economic analysis of
the business activities and (ii) concepts used for accounting purposes.
Actual Costs- are those which are actually incurred by the firm in payment for labour, material, plant,
building, machinery, equipment, traveling and transport, etc. The total money expenses recorded in the
books of accounts are, for practical purposes, the actual costs. The actual cost comes under the
accounting concept.
Explicit Costs (also called out of pocket cost or expenses). –these fall under actual or business costs
entered in the books of accounts. They are items of expenditure which involve cash payments or cash
transfers, both recurring and non-recurring. They include wages, rent, interest, transport expenditure,
utility expenses, payments for materials, licence fees and insurance premium. The explicit costs are
clearly reflected in the normal accounting practices.
Implicit Costs-these are costs which do not take the form of cash outlays and they do not appear in the
accounting system. They refer to the value of the inputs owned and used by the firm in its own
production activity Implicit costs include the highest salary that the entrepreneur could earn in his or
her best alternative employment (say in managing another firm for somebody else). Thus implicit
wages or salary, implicit rent, implicit interests are the highest wages/ salary, rents and interest which
8
labour building and capital can respectively earn from their next best use. Implicit costs are not taken
into account while calculating the loss or gains of the business, but they form an important
consideration in business decisions. In assessing the alternative costs, both explicit and implicit costs
are taken into account.
Direct and Indirect Costs
Direct Costs- These costs are called direct costs or prime costs. These are costs incurred and can be
directly attributed to the production of a particular unit of a given product. The use of raw materials,
labour inputs, and machine time involved in the production of each unit can usually be determined. The
costs include direct materials e.g. wood in furniture and direct labour that is labour that is physically
traceable to the finished goods in an economically feasible way.
Indirect Costs- The costs are also called overheads costs or factory burden. These are costs which
cannot easily and accurately be separated and attributed to individual units of production except on an
arbitrary basis.. The factory overheads have a variable element e.g. power supplies and most indirect
labour and a fixed element e.g. supervisors salaries, property taxes, rent, insurance and depreciation of
plant and buildings.
RELEVANT AND IRRELEVANT COSTS
Relevant costs
These are costs that will be incurred as a result of a decision and are relevant costs for decision making.
When a manager would like to make a decision, and as a result of that decision, costs may or may not
be earned. Relevant costs are those that will be incurred as a result of a decision.
Sunk costs are those costs which cannot be altered, increased or decreased by varying the rate of
output. For example, once it is decided to make incremental investment expenditure and the funds are
allocated and spent, all the preceding costs are considered to be sunk since they accord to the prior
commitment and cannot be revised following the change in the market conditions. Sunk costs should
therefore not be included in the decision.
Irrelevant Costs
Costs that have been incurred already or which will be incurred in any case are irrelevant costs as far as
current decision making is concerned.
INCREMENTAL COSTS
Also called differential costs or avoidable costs. They refer to the change in total costs from
implementing a particular management decision, such as the introduction of a new product line, the
undertaking of a new advertising campaign, or the production of a previously purchased component.
Although closely related to the concept of marginal cost, this concept has a relatively wider
connotation. The costs are the increases or decreases in total costs or the changes in specific elements
of cost that result from some variations in operations or the aggregate change in costs that result from a
decision.Incremental costs may therefore be either fixed or variable, since a new decision may require
purchase or additional capital facilities plus extra labour and materials.
The concept of incremental cost is based on the fact that, in the real world, it is not practicable for lack
of perfect divisibility of inputs to employ factors for each unit separately hence incremental cost refers
to the total additional cost associated with the marginal batch of output. In the long run firms expand
their production; hire more men, materials, machinery and equipment. The expenditure on these is
incremental cost. The incremental costs arise also owing to the change in product lines, addition of new
product or introduction of a new product., replacement of worn out plant and machinery, replacement
of old technique with a new one or opening of a new channel of distribution.
If for example a new channel of distribution is opened up, many elements of cost will remain
unaffected. The sales manager may not get any increase in salary and most of costs of operating the
sales department will remain unaffected. On the other hand it may be necessary to engage additional
salesmen and management will need to compute the additions to costs which will result from the
decision, in order to compare these with the additions to revenue which are expected to accrue.
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INCREMENTAL REVENUES
This is the change in total revenue that occurs as a result of a decision. When incremental costs are
compared with incremental revenues, it is possible to see whether a proposed decision is likely to be
profitable or not. If incremental revenues exceed incremental costs, then the proposed decision will add
to total profits.
Contribution Analysis
This is the analysis of incremental revenue and incremental cost of a business decision or business
activity. The contribution of a decision is defined as the incremental revenues of that decision less the
incremental costs of that decision.
Breakeven charts can also be used in measuring the contribution made by the business activity towards
covering the fixed costs. For this purpose variable costs are plotted below the fixed costs. In this
context, the contribution is the difference between total revenue and variable costs.
At the breakeven level of output Q, there is a contribution towards profits. Only decisions that have a
positive contribution should be undertaken; and where decisions are mutually exclusive, the one with
the larger expected contribution is to be preferred.
Costs
TR
and
Breakeven point
revenue
contribution
Profit
FC
Loss
O
VC
Q
Output
Common types of decision Problems
(a) Mutually Exclusive Projects. Project A promises sales of 10 000 units at $2 each with materials,
labour, variable overheads and allocated overhead costs as shown below. Project B promises sales
revenues of $18 000 with materials, direct labour, variable and allocated overheads as also shown
below:
Project A
Project B
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Revenue $10000@ $2
Cost
Materials
$2 000
Direct labour
$6 000
Variable O/head
$4 000
Allocated O/head
$6 000
Profit
$20 000
Revenue $6000@$3
Cost
Materials
Direct labour
Variable O/head
Allocated O/head
$18 000
$ 2 000
$18 000
$5 000
$3 000
$3 000
$3 000
$14 000
$ 4 000
The apparent profit from B is $4 000 and it would seem that B is preferable to A by virtue of its higher
profitability but when contribution analysis is applied to the above decision problem a different result is
obtained. Project A is selected using contribution analysis (see table below)
In the table below incremental costs are subtracted from the incremental revenues to find the
contribution of each project. Since the allocated overheads were not a cost incurred as a result of this
particular decision they are excluded from the contribution analysis, and it can be seen that A
contributes more to overheads and profits than does B.
Project A
Revenue $10000@ $2
Incremental Costs
Materials
$2 000
Direct labour
$6 000
Variable O/head
$4 000
Contribution
$20 000
$12 000
$ 8 000
Project B
Revenue $6000@$3
Incremental Costs
Materials
Direct labour
Variable O/head
$18 000
$5 000
$3 000
$3 000
$11 000
$ 7 000
(b) Make or Buy Decisions
Company X manufactures high quality power tools. All these tools require the same
roller bearing units, which the company manufactures in its own bearing department.
Pertinent cost data for the past year of operations in that department are shown below:
X Tool Company: Bearing Department Costs
Total
$ 38 640
$126 390
$252 780
$417 810
Direct Materials
Direct labour
Allocated overhead
Total Cost
The company could produce these in its bearing department but is considering having the additional
units supplied by a specialist bearing firm. Company X anticipates that it will require an increase of
15% in total direct labour costs and 12% in total materials costs, to produce these additional units inhouse. No additional capital expenditure will be necessary, since some machines currently have idle
capacity. A specialist bearing producer has been approached, and after considering the specifications
has offered to supply the 7500 bearing units at a total cost of $30 000 or $4 per unit. Should company
X make or buy the additional bearing units?
The answer to the above question, compare the incremental costs of the two alternatives facing X. The
incremental costs of buying them from the specialist come to $30 000, since this is the dollar amount
that X must outlay to obtain the additional units. To calculate the incremental costs of making the units
in-house, we calculate the increases in materials and direct labour costs that would be occasioned by
the manufacture of those units. The 12% increase in the total material cost would imply an incremental
material cost of $4 637 and a 15% increase in total direct labour costs would imply a $$18 959 increase
in that cost category. The total cost of these figures is $23 596 is less than the $30 000 outlay by $6 404
(company X saves by making the units itself) (see table below).
Incremental Cost of making the bearing units
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Direct Materials
Direct labour
Total Incremental Cost
Total
$ 4 637
$ 18 959
$ 23 596
The total of $23 596 is less than the $30 000 outlay by $6 404 (company X saves by making the units
itself).
NB. The above analysis however does not consider the possibility that some part of overhead expenses
may vary with the level of production of the bearing units. It is conceivable that some overhead cost
components expense and cafeteria expense might vary to some degree as a result of producing these
units in-house. If however overheads vary more than $6 404, as a result of this decision would have
been to buy the product from the outside supplier.
A number of other considerations should also enter the decision:
(a) The issue of long term supplier relations. X may need a specialist producer some time in the
future when it may be unable to produce the bearings from within due to capacity limitations
by giving this contract it could establish itself as a customer of the supplier.
(b) The issue of quality of the bearing units supplied by the outside firm as compared with those
produced in-house. Decision maker would have to be assured that the quality matches that
standard desired, at least.
(c) Issue of labour relations – the decision to make the units involves an increase in labour force,
which may lead to crowded working conditions and overtaxed washroom and cafeteria
facilities. It is conceivable that the hiring of additional labour units and the resultant increased
congestion and reduced efficiency could cause a lowering of employee morale with
subsequent longer term disadvantage to the profitability of company X.
(d) Accuracy of the estimations that are involved in the decision making. If the demand for tools
does not increase as predicted and company X purchased the roller bearing units from outside,
this would be an irreversible commitment involving considerable expense whereas the
decision to make the units in-house could soon be suspended.
(e) Whether the quoted price is in fact the lowest
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