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.
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