MIHAELA GHICAJANU, MANUEL-VIOREL SEMEN *
ABSTRACT: This paper presents some significant aspects regarding the break-even analysis of an economic organization. The analysis will consider a case study for a company which produces a certain production volume, considering a certain value of its sales and determining its Break-Even Point, under two possible hypotheses: the first case by only operating with a normal profit, and the second one by considering a requested profit (opportunity cost) of 3%.
KEY WORDS: sales, activity level, relevant range, profit/loss, break-even point, fixed cost, variable cost, semi-variable cost, profitability, efficiency, contribution.
1. INTRODUCTION
The analysis based on the study of the Break-Even Point has some strong roots in, and tight theoretical connections with the fundamental concept of Cost-Volume-Profit (or CVP) analysis.
Before a closer approach of the typical for the break-even analysis problems and themes, one should first clarify some of the basic concepts related to its stipulations, such as:
Behavior of costs
Relevant range
Activity level
Fixed cost
Variable cost
Semi variable cost
Behavior of a cost – represents the way in which this cost will react (increase, decrease or remain constant) to changes (increases or reductions) in the level of activity.
* Lecturer at the University of Petroşani, Romania Assist. Prof. at the University of Petroşani, Romania
100 Ghicajanu, M.; Semen, M.
Relevant range – the range (interval) of the activity level within whose boundaries the hypotheses regarding the linear behavior of the cost are verified.
Activity level – a decisional indicator and the cause and reason for the actual magnitude (value) of the variable costs. (The term “activity level” is here preferred to
“production”, in order to extend the applicability of the following considerations, not strictly for actual production, but to other industries as well – we could here name services and any further industries which don’t necessarily produce physical, tangible goods).
Fixed costs – costs which remain constant in total value; they don’t react to changes in the activity level.
Variable costs – costs which modify in total value in direct proportion to changes in the activity level.
Semi variable costs – costs which have a fixed and a variable component, i.e. a part of such a costs has a fixed behavior, and the other one a variable behavior.
The analysis model Cost-Volume-Profit considers a number of restrictive hypotheses, such as:
- costs and sales incomes have a linear behavior over the studied relevant range;
- all costs are separated into their fixed and variable component;
- the combination of types of products which are sold remains constant;
- the level of stocks remains unchanged (the manufactured quantity equals the sold quantity);
- the productivity remains constant;
- inflation is not taken into consideration.
2. BREAK-EVEN POINT
The Break-Even Point represents the activity level (e.g. production quantity) at which the value of costs equals the value of the revenues caused by the sales of the company products.
In an alternative statement, the Break-Even Point represents the exact level of the company activity, where no profits are registered, but no losses either.
This critical point of any firm’s profitability called Break-Even Point can be determined through either analytical, or graphical methods.
In order to build an equation for determining the Break-Even Point, one should start from clarifying the relations or functions for total costs and total revenues. The calculation elements contained in the equations have been symbolized as shown below:
sp – Selling Price per Unit;
vc – Variable Costs per Unit;
TC – Total Costs;
FC – Total Fixed Costs;
Break-even analysis of the enterprise… 101 VC – Total Variable Costs;
TR – Total Revenues;
Q – Activity Level;
Q* - Activity Level at Break-Even.
Considering the notations from above and the definition of costs, revenues and break-even point, this critical point called Break-Even Point can be determined according to the following steps:
Q sp
TR= × (1)
VC FC
TC = + ; TC =FC+vc×Q (2)
By definition, at Break-Even Point, the costs become equal to the revenues, which means that:
vc sp Q FC Q
vc FC Q
sp TC
TR= ⇒ × * = + × * ⇒ * = − (3)
vc sp Q FC
= −
* (4)
In order to a achieve a better clarification of the content, and to exemplify the actual use of the fundamental concept Break-Even Point , a case study with two particular situations will be presented below.
3. CASE STUDY
A company which produces and sells textile products recorded the following situation regarding its production, operating costs and revenues at the end of one the years of its economic life:
Indicators Measure Units Value
1. Production Units 92.000
2. Operating revenues 000.000 ROL 13.892
3. Operating costs - Variable costs
- Fixed costs 000.000 ROL 14.100
3.300 10.800
4. Operating profit / loss 000.000 ROL 208
5. Production capacity Units 150.000
6. Selling price per unit ROL / unit 151.000
102 Ghicajanu, M.; Semen, M.
The actual determination of the Break-Even Point of the company will have to be done according to the following steps:
ROL per unit Selling Price
151.000 ROL per unit
45.652,17 40.217,40 Variable Costs
Raw Materials Labor Costs
Other Variable Costs 31.521,74
Total Variable Costs 117.391,74
Fixed Costs 000.000 ROL
Administration Salaries 1.500
Overheads 910
Depreciation 780
Interest 110
Total Fixed Costs 3.300
Units Production Capacity
150.000 Units Units Units Units Units Units Output
- 50.000 80.000 90.000 100.000 150.000 000.000
ROL 000.000
ROL 000.000
ROL 000.000
ROL 000.000
ROL 000.000 ROL Sales
Potential
- 7.550 12.080 13.590 15.100 22.650 Costs 000.000
ROL 000.000
ROL 000.000
ROL 000.000
ROL 000.000
ROL 000.000 ROL
Fixed Costs 3.300 3.300 3.300 3.300 3.300 3.300
Variable
Costs - 5.869,6 9.391,3 10.565,2 11.739,1 17.608,7
Total Costs 3.300 9.169,6 12.691,3 13.865,2 15.039,1 20.908,7 000.000 ROL Calculation of Break-Even Point
Fixed Costs 3.300
Contribution per Unit 000.000 ROL
Sales Price per Unit 151.000
Variable Cost per Unit 117.391,31
Contribution per Unit Sold 33.608,69
Units Sold 98.189
% Capacity Break-Even Point
65,46 %
Break-even analysis of the enterprise… 103 The analysis of the Break-Even Point can also be performed under another hypothesis: the management of the company requests a minimal accepted profit of 3 % as an opportunity cost for the use of the capital. A comparative presentation of the two cases is shown below:
CASE I CASE II
Indicators Measure
units Value Indicators Measure
units Value
1.Fixed Costs 000.000 ROL 3.300 1.Fixed Costs 000.000 ROL 3.300
2.Selling Price ROL 151.000 2.Selling Price ROL 151.000
3.Variable Costs per
Unit ROL 117.391,3 3.Variable
Costs per Unit ROL 117.391,3
4.Production Units 92.000 4.Production Units 92.000
5.Contribution per
Unit ROL 33.608,6% 5.Contribution
per Unit ROL 33.608,6%
6.Production Capacity
Units 150.000 6.Production Capacity
Units 150.000
7.Break-Even Point (BEP)
Units 98.189 7.Requested profit
ROL / Unit 4.530
8.Position of BEP to Production Capacity
% 65,46 8.Break-Even
Point (BEP) Units 113.485
9.Position of BEP to Production Capacity
% 75,65
9. Position of BEP
to Production % 106,72
10. Position of BEP to Production
% 123,35
104 Ghicajanu,M.; Semen, M.
CASE I – The company operating with a normal profit, without considering any opportunity cost of its invested capital;
CASE II – The company operating with a minimal accepted profit (opportunity cost of