Practical Limitations of Break-Even Theory

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AU J.T. 11(1): 58-61 (Jul. 2007)
Practical Limitations of Break-Even Theory
Mohammed B. Ndaliman and Katsina C. Bala
Department of Mechanical Engineering, Federal University of Technology
Minna, Nigeria
<[email protected]>
A five-year expenditure profile of a company, ‘Buni Bricks and Blocks Industry
Nigeria Ltd.’, was studied alongside its incomes for the same period. The objective is to
determine the cost / revenue interactions on break-even charts. These charts were
obtained for the five years studied. Among the practical realities discovered include:
the sales revenue and total cost were not linear, two or more break-even points were
found to exist, some costs fall under both fixed and variable costs, and beyond certain
optimum production levels, sales revenue decreases sharply and total cost also

Keywords: Break-even analysis, marginal costing, fixed cost, variable cost, semi
variable cost, profitability, production level, profit margin.

The concept of break-even analysis is

dependant on the theory of marginal costing.
It has been stated that the break-even
Under this, the total cost of manufacturing or
point (BEP) is the production volume at which
producing products or services can be
a firm is neither making profit nor loss
segregated into two distinct parts: the fixed and
(Nwachukwu 2004). Any increase in the variable costs. Fixed costs are said to be
production from this level results in profit
remaining constant no matter the variation in
making, while any decrease would result in
the volume of products, while variable
losses. Industrial enterprises or firms therefore
(marginal) costs vary directly with production
strive to exceed this point so that they can
volume. However, difficulties do arise in
make profit. This point is normally illustrated
categorizing some costs as either fixed or
in cost/revenue (C/R) vs. production level (Q)
variable. Sinclair and Talbot (1986) stated that
charts as the position where the total revenue
most businesses have a combination of the two
(TR) line intersects the total cost (TC) line
resulting in semi variable costs.
(Fig. 1). The production level at the break-even
point is represented by QBE. Here
TC = vQ + F,

where Q is the quantity produced, v is the
variable cost per unit sold and F is the fixed
cost. Break-even analysis is often used as a
measure to determine general guidelines for
business decision making (Pollack 1995), to
evaluate the company’s desired profit levels, to
conduct cost reduction impact analysis
(Berryman and Nobe 1999), to evaluate the
potential prices, the impact of price changes
and fixed /variable costs on profitability

Fig. 1. One-product break-even analysis (BEA).
(Powers 1987).

AU J.T. 11(1): 58-61 (Jul. 2007)
Other costs are even questionable and
Table 1. Summary of cost items of Buni Co. Ltd.
cannot be easily classified. Haslehurst (1980)
Item Cost
gave an example of semi variable cost in press

work, where a reinforced plastic forming tool
-sharp sand
used for short runs can experience increase in
fixed cost. The continuous strengthening of the

plastic former by glass fibre addition can incur
addition cost. Thus, as the production volume
Variable & fixed
increases, the cost of glass fibre increases. As
Plant Expenses

such, fixed cost also increases by some factor.
-auto expenses
Variable & fixed
While making the assumptions of the
break-even theory, no consideration was made
Variable & fixed
for semi variable costs. It is this shortcoming
-miscellaneous expenses
Variable & fixed
and some others that led to this investigation.
-property taxes
In this write-up, the real characteristics of the

behavior of an enterprise is examined. The cost
General & Administrative
-Association dues
behaviors and revenues accruing to the firm
were studied and the results are reported in the
-Interest expenses
Variable & fixed
following paragraphs.
Variable & fixed

-Stationary & supply
-Travel & expenses
Case Presentation and Methods

Similarly, the sales recorded over the
In this study, an industrial establishment,
months for the production years were also
the ‘Buni Bricks and Blocks Industry Nigeria
obtained for analysis. The sales curves are also
Ltd.’, Yobe State, Nigeria, was investigated.
presented in the figures.
The company manufactures two types of

products: the fired clay building bricks and
cement blocks. Five years production activities
Observation, Interpretation and
and expenses were obtained for the study. The
period covered the years 1999 to 2003. The

items which constitute the expenditures of the
Figs. 2 to 6 represent the break-even
company are summarized in Table 1.
charts for five years production period of Buni
Within each year, production volumes
Bricks and Blocks Industry Nigeria Ltd.
vary from one month to the other. The sales
In Fig. 2, the chart presented is for two
also vary from month to month. The various
varieties of products. Cost accounting principle
production levels attained over the months
demand that each cost centre should have
were obtained. The expenses incurred in
distinct income and expenditure account.
achieving these levels of productions were
Therefore the true picture of each of the bricks
computed. As usual, these costs were classified
and the cement blocks were not revealed. Since
as fixed and variable costs. As can be seen
both the sales revenue and costs are lumped
from Table 1, some cost items come under both
together, the concept of break-even is of little
fixed and variable costs. These were arrived at
meaning in this case, unless a break-even chart
by using “high / low” method of Powers
is prepared for each of the products separately.
(1987). Summing up both cost components
This would be difficult because of costs
(fixed and variable); the total monthly costs of
allocation problems.
productions were obtained.
The company’s transactions for
The values of total costs obtained from
subsequent years as illustrated by Figs. 3 to 6
these computations are plotted in the graphs
are for one product only – the cement blocks.
shown in the various figures presented in the
In all the figures, the following general
following paragraphs.
observations can be made:

AU J.T. 11(1): 58-61 (Jul. 2007)
i. Multiple points of intersections (BEP)
are found to exist except in Fig. 5.
ii both the total expenses and sales
income lines are not straight.
iii the revenue lines in Figs. 2, 3 and 5
tend to curve inward towards the extreme
levels of productions. This behavior is more

pronounced in Fig. 2.
Fig. 2. Break-even chart for production and sales of
From these observations, it is clear that
brick and cement blocks in the year 1999.
the “linearity” always assumed while
formulating the break-even theory (Adediran
2001; Degtiareva 2001) may not exist in
reality. This is because the demand for a
product normally changes with any alteration
in either selling price or even to the volume

The existences of multiple points of
Fig. 3. Break-even chart for Buni transactions for
intersections mean that it is possible to have
the year 2000.
more than one break-even point. Thus, the
likelihood of more than one area of
unprofitable operation exists. A Company
might choose to produce at a point so as to
maximize profit or to minimize loss.
In a simple break-even chart such as that
of Fig.1, the profit margin continues to widen
as the production level increases (Adediran
2001; Degtiareva 2001; Nwachukwu 2004).

However, the curve lines in Figs. 2, 3 and 5
Fig. 4. Break-even chart for the year 2001 Buni
shows that the two lines (total cost line and
revenue income line) do not diverge
indefinitely. This is because, at higher
production levels, there is tendency that the
selling price would decrease as the market
becomes saturated. This causes the sales
income line to drop downward.
In Fig. 2, the highest profit margin of
about N16,000 (US$126.4) is obtained between
production levels of 20 – 30 tipper trucks of the
product. Therefore, the optimum production

level should be between 20 and 40 tipper trucks
Fig. 5. Break-even chart for the year 2002 Buni
of the products with equivalent sales income of
between N30,000 (US$237) and N54,000
(US$426.6). It can be seen that further increase
in production above 58 tipper trucks results in
loss. This is because the total cost line rise
sharply possibly due to increasing extra
expenditures, and the total income line fall also
sharply possibly due to the increasing price of

products brought about by the extra costs.
Fig. 6. Break-even chart for the year 2003 Buni

AU J.T. 11(1): 58-61 (Jul. 2007)
Similar explanations can be given for the
iv. Economic factors such as demand,
other years as illustrated by Figs. 3, 4 and 6. In
supply and prices do affect the break-even
all these years the profit margins are small as
point and profitability.
can be seen from those figures. However, in
v. Actual sales determines the profit margin
Fig. 5, the profit margin is about N16,000 in
achieved by an enterprise
production range of 76 – 86 tipper trucks. The

optimum production is about 82 tipper trucks.
This is for only one product type – the cement

blocks. The equivalent sales income of
The authors wish to acknowledge the
N86,000 is accruable to the company at that
management of Buni Bricks and Blocks
level. Production beyond this level results in
Industry Nigeria Ltd. for allowing them access
income reduction. Further increase would
to their books of account.
ultimately result in losses.

Practically, the enterprise can not
influence sales level. It is the variation of the
sales level that determines the profit margin.

This is why different sales margins were found
Adediran, Y.A. 2001. Introduction to
for different years. This is one of the practical
engineering economics, 1st ed., pp. 4-10.
realities of markets.
Finom Associate, Minna, Nigeria.
This paper therefore tries to point out that
Amrine, H.T.; Ritchey, J.A.; and Hulley, O.S.
enterprises should not have the impression that
1983. Manufacturing organization and
break-even theory easily gives a point where
management. 4th ed., pp. 342-4. Prentice
the company earns profit. They should also not
Hall of India Private Ltd., New Delhi, India.
go by impression that the higher the Berryman, C.W.; and Nobe, M.D. 1999.
production, the more the profit. One of the best
Practical business application of break-even
ways to determine the break-even point by a
analysis in graduate construction education.
company is to accumulate historical costs and
J. Constr. Ed. 4: 26-37.
sales data for a number of accounting periods
Degtiareva, E. 2001. Minimizing risk by
and plot on a set of axes for each period
analyzing a lessee’s financial position:
(Amrine et al. 1983). In this way an optimum
Analysis of financial position and projected
production level can be obtained.
cash flow. Leasing-Courier 5(17): 1-5.

Haslehurst, M. 1980. Manufacturing
technology. The English Language Books
Society (ELBS) (Ed.), pp. 4-10. Hodder &

Stoughton, Bucks, UK.
The study revealed the following Nwachukwu, C.C. 2004. Management: Theory
practical realities associated with break – even
and practice, pp. 265-7. Africana First
Publishers Limited, Onitsha, Anambra State,
i. Semi variable costs do exist amongst the
cost components and must be considered for
Pollack, B. 1995. Break-even analysis: The
appropriate estimation (apportionment) into
third leg of the underwriting stool. Real
both fixed and variable costs.
Estate Review 25: 43-6.
ii. The sales revenue and total costs are not
Powers, L. 1987. Break-even analysis with
always linear in as normally assumed in the
semi-fixed cost. Ind. Market. Managemt. 67:
iii. Two or more break-even points may
Sinclair, K.; and Talbott, J. 1986. Using break-
exist for a particular industry depending on a
even analysis when cost behavior is
number of factors.
unknown. Managemt. Account. 68: 52-5.