BREAK EVEN ANALYSIS

Break even analysis is the critical tool for determining the capacity a facility must have to
achieve profitability. The objective of break even analysis is to find the point in dollars and unit,
at which cost equal revenue. Break even analysis requires an estimation of fixed cost variable
cost, and revenue.

Fixed cost are cost that continue even if no units are produced. Example include
depreciation and debt. Variable cost are those that vary with the volume of unit produced. The
major component of variable cost are labor and materials. However, other cost, such as the
portion of the utilities that varies the volume, are also variable cost. The difference between
selling price and variable cost is contribution. Only when total contribution exceed total fixed
cost will there be profit.
Another element in break even analysis is the revenue function. In figure above revenue
begins at the origin and proceeds upward to the right. Increasing by the selling price of each
units. Where the revenue function crosses the total cost line, is the breakeven point, with a profit
corridor to the right and a loss corridor to the left.
A number assumption underlie the basic break even model. Notably, cost and revenue are
shown as straight lines. They are shown to increase linearly, in direct proportion to the volume of
units being produced. However, neither fixed cost nor variable cost need be a straight line. For

example, fixed cost change as more capital equipment or warehouse space is used; labor cost
change with overtime or as marginally skilled workers are employed; the revenue function may
change with such factors as volume discounts.
The first step in the graphic approach to break even analysis is to define those cost that
arefixed and sum them. The fixed costs are drawn as a horizontal line beginning at that dollar
amount on the vertical axis. The variable costs are then estimated by an analysis of labor,
materials, and other cost connected with the production of each unit. The variable cost are shown
as incrementally increasing cost, originating at the intersection of the fixed cost on the vertical
axis and increasing with each change in volume as we move to the right on the volume axis.
The breakeven point occurs where total revenue equals total cost, there for:
TR=TCPx=F+Vx
Solving for x, we get:
Breakeven point units

( BEPx)=

F
PV

And:
Brea even point in dollars

( BEPs )=BEPxP=

F
F
F
P=
=
PV
( PV ) (P) 1V /P

Profit: TRTC=Px( F+ Vx )=PxFVx=( PV ) xF

pricevariable cost

total
Break evendollars= cost

variable cost
1
selling price

Example of single product case

The firm first determines that it fixed cost of $10,000 this period. Direct labor is $1.50
per unit and materials is $75 per unit. The selling price is $4.00 per unit.
Solution:
F

BEPs =

( vp )

$ 10,000
$ 10.000
=
=$ 22,857.14
1.50+75
4375
1[
]
4.00

The BEP in units is :

F
$ 10,000
=
5,714
PV 4.00(1.5+75)

Note , that we use total variable cost (that is , labor and material)
Multiproduct case
Most firms, from manufacturer to restaurant have a variety of offerings, each offering
may have a different selling price and variable cost. We do this by weighting each product
contribution by its proportion of sales. The formula is then:

(1 VP 11 ) x (W 1)

BEPs=

Example of multiproduct case

Price

Cost

Sandwich
Drinks
Baked Potato

$5.00
1.50
2.00

$3.00
0.50
1.00

Annual

Forcasted

Sales unit
9000
9000
7000

With variety of offerings, we proceed with break-even analysis just as in a single product
case, except that we weight each of the product by its proportion of total sales

Solution:
Annual
Item

Sandwich
Drink
Baked
Potato

V/P

1-(V/P)

forecaste

of Weighted

sales

contribution

0.621
0.186

0.248
0.125

$5.00
1.50

$3.00
0.50

0.60
0.33

0.40
0.67

d Sales $
$45,000
13,500

2.00

1.00

0.50

0.50

14,000

0.193

0.096

$72,500

1.00

0.469

Revenue for sandwich is $45,000 (5.00 x 9,000), which is 62.1% of the total revenue of
$72,50. Therefore, the contribution for sandwiches is weighted by 0.621. The weighted
contribution is 0.621 x 0.40 = 0.248. In this manner, its relative contribution is properly reflected.
Using this approach for each product, we find that total weighted contribution is 0.469 for
each dollars of sales, and the BEP in dollars is $76,759
BEPs =

F
$ 3,000 x 12 $ 36,000
=
=
=$ 76,759
0.469
0.469
V1
[ 1
x ( w1 )]
P1

The information given in this example implies total daily sales (52 weeks at 6 day each) of :
$ 76,759
=$ 246.02
312 days
The management of Le bistro now knows that it must generate average sales of $246.02
each day to break even. Management also knows that if the forecasted sales of $72,500 are
correct, Le bistro will lose money, as break even is $76,759.
REDUCING RISK WITH INCREMENTAL CHANGES
When demands for goods and services can be forecast with a reasonable degree of
precision, determining a BEP and capacity requirements can be rather straightforward. But more
likely, determining the capacity and how to achieve it will be complicated, as many factors are
difficult to measure and quantify. Factor such as technology, competitors, building, restrictions,
cost of capital, human resource options, and regulation make the decision interesting. To
complicate matters further, demand growth is usually in small units, while capacity additions are

likely to be both instantaneous and in large units. This contradiction adds to the capacity decision
risk. To reduce risk, incremental changes hedge, demand forecast may be a good option.

Acquires capacity to stay ahead of demand, with new capacity being acquired at the
beginning of period 1. This capacity handles increased demand, until the beginning of period
2.At the beginning of period 2 , new capacity is gain acquired, which will allow the organization
to stay ahead of demand until the beginning of period 3. This process can be continued
indefinitely into the future. Here capacity is acquired incrementally at the beginning of period 1
and the beginning of period 2. But managers can also elect to make a large increase at the
beginning of period 1 an increase that may satisfy expected demand until the beginning of period
3.

Excess capacity gives operation managers flexiblelity. For instance, in hotel industry,
added extra capacity in the form of rooms can allow a wider variety of room option and perhaps
flexiblelity in room clean up schedules. In manufacturing, excess capacity can be used to be used
to be more setups, shorten production run, and drive down inventory cost.
Butin figure above shows an option that lags capacity, perhps using overtime or
subscontracting to accomodate excess deman. Straddles demand by building capacity that is
average, sometimes lagging demand and sometimes leading it. Oth the lag and straddles option
have the advantage of delaying capital expenditure.
In case where the business climate is stable, deciding between alternatives can be
relatively easy.The total cost of each alternative can be computed, and the alternative with the
least total cost can be selected. However , when capacity requirements are subject to significant
unknown, probabilistic models may be appropriate. One technique for making successfull
capacity planning decision with an uncertain demand is decision theory, including the use of
expected monetary value.