Break-Even AnalysisUnit 5

Operations Management

Learning ObjectivesUse graphical and quantitative methods to calculate

the break even quantity, profit and margin of safetyHL – Use these methods to analyse the effects of

changes in price or cost on break even , profit and margin of safety

HL - Calculate the required output level for a given target revenue or profit

Analyse the assumptions and limitations of break even analysis

Break Even Point• The level of output at which total costs equal

total revenue

Break Even Total Costs = Total Revenue

No profit or loss is made

Calculating break even

• Can be done in 3 ways1. Table of costs and revenues method2. Graphical method3. Formula method

1. The Table Method

Quantity sold

Fixed cost ($) Variable cost ($)

Total costs ($)

Revenue (Price x Quantity) ($)

Profit / loss ($)

0 500 0 500 0 (500)

100 500 100 600 200 (400)

200 500 200 700 400 (300)

300 500 300 800 600 (200)

400 500 400 900 800 (100)

500 500 500 1000 1000 0

600 500 600 1100 1200 100

700 500 700 1200 1400 200

Hamburger StallStall has to pay $500 for each match day (fixed costs)Hamburger costs $1 (variable costs)Sold for $2

What is the break even?

2. The Graphical Method – The Break Even Chart

• Common to appear on exams (especially SL)

2. The Graphical Method – The Break Even Chart

• Break even chart requires a graph with these axes

Costs and sales revenue ($)

Units of output0

2. The Graphical Method – The Break Even Chart

• The chart itself is drawn showing 3 pieces of information1. Fixed costs2. Total costs3. Sales revenue

Break even chart – points to note• Fixed cost line is horizontal showing that fixed costs

are constant at all output levels• Variable cost starts at 0 and increases at a constant

rate• Total cost line begins at the level of fixed costs but

then follows the slope / gradient as variable costs • Sales revenue starts at 0, increases at a constant rate• The point at which total cost and sales revenue line

cross is the break even point, below this losses are being made and above profits are being made

Can you plot create a break even chart without even seeing one first?

Units of output

0

Cost

s and

sale

s rev

enue

Sales

Full Capacity

Margin of SafetyThe amount by which the sales

level exceeds the break even level of output

Margin of safety

Actual Sales – Break Even Output

• Useful indication of how much sales could fall without the firm falling into a loss

Units of output

0

Cost

s and

sale

s rev

enue

Sales

Full Capacity

Margin of safety

3. The Break Even Formula Method

If fixed costs are $200,000 and the contribution per unit of output is $50, then the break even level of production is….

200000 =

50

Exact answer therefore likely to be more accurate than many break even graphs

Read the case study thoroughly!!! They don’t just give you the figures you may need to do some basic maths first

fixed cost

X / 100 = 4.5 / 112.5 = 3.94 (This could be rounded to 4)