1

OPERATIONS

MANAGEMENT

*Break

Even

AnalysisTopic 5.3 (SL)

*Break-even Analysis

*Break-even analysis is a method

for finding out the minimum level

of sales necessary for a firm to just

start to make a profit

*Break Even Output*The level of output at which total

sales revenue is equal to total costs of

production

*When costs are greater than revenue

the firm makes a loss

*When costs are less than revenue the

firm will make a profit

*What happens when costs = revenue?

The firm will just break even

*Assumptions

*Fixed costs must be paid regardless of

the level of output

*Variable costs increase with output but

at a constant rate, so if 1 unit cost £5

then 10 units will cost £50

*Every Unit of output produced is sold

*Selling price remains constant

regardless of units sold

*Calculating Break Even

*3 Methods

*Using a table showing revenue and

costs over a range of output levels

*Using a formula

*Using a graph

*Table

0 0 50 0

1 15 50 5

2 30 50 10

3 45 50 15

4 60 50 20

5 75 50 25

6 90 50 30

7 105 50 35

8 120 50 40

9 135 50 45

10 150 50 50

11 165 50 55

12 180 50 60

Units of output Sales Revenue Fixed Costs Variable Costs Total Costs Profit

(000’s) (000’s) (000’s) (000’s) (000’s) (000’s)

*Formula

*Contribution per unit = selling price –

direct cost per unit

*This shows the amount that each unit

contributes towards fixed costs

*Break even = Fixed Costs $)

Contribution per unit ($)

*GraphSales Revenue/Costs

Units of output

00

50

100

150

200

2000 4000 6000 8000 10000 12000

Total Revenue

Total Costs

Fixed Costs

Break Even Point

Break even output

*Break-even analysis

Based on:

*costs

*prices

*production/sales levels

*Definitions

Break-even quantity (BEQ)

The level of sales or output where costs

equal revenue and the firm is therefore

making neither a loss nor a profit.

*Definitions

*Break-even revenue (BER)

The level of sales revenue being earned

by the firm at the break-even level of

output.

*Break-even point (BEP)

The position where TC and TR lines

cross.

*Note:

You need to be able to

draw on graph paper

*Drawing a diagram from scratch

Step 1 Extract the data

Step 2 Calculate the BEQ

Step 3 Fix the X Axis (quantity/capacity)

Step 4 Fix the Y Axis (revenue and costs)

Step 5 Plot the TR Axis

Step 6 Add the FC point

Step 7 Add the TC Line

*Step 1 Extract the data

FIRST – work out BEQ

*FC £480,000 per month.

*VC: £60 per unit

*Price: £120 per unit

*Total Revenue(TR) = Number of items

sold x their price

*Total costs (TC) = FC + VC(x)

*At break-even TR = TC or P(x) = FC +

VC(x)

*So BEQ = FC/(P - VC)

Note: P = price; x = quantity

*Step 2 Calculate the BEQ

*The equation BEQ = FC/(P - VC)

$480,000 per month / ($120 - $60

per unit)

= $480,000/£60 = 8,000 units per

month

*Step 3 Fix the X Axis (capacity)*If you are given a maximum capacity,

use that figure.

*If not, double the break-even quantity

is a good guide figure, or 16,000 units

in this case.

*Step 4Fix the Y Axis (revenue and costs) * In this case the maximum revenue is

16,000 x £120 = £1.92 million (price per

unit x maximum possible sales).

*Step 5 Plot the TR Axis

*Step 6 Add the FC point

FC

*Step 7 Add the TC Line

FC

*Remember

*Add labels to the two axes

and give the chart a title.

*Marks are awarded for this

finishing touch.