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Breakeven Analysis
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Objectives:
Determine the number of units sold to break even or toearn target profit
Use a CVP chart and a profit-volume chart todetermine the breakeven point and the volumenecessary to achieve a target profit
Explain the impact of changing variable on CVPanalysis
Calculate and interpret the impact of sales mixconsiderations in CVP analysis
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Cost-Volume-Profit Analysis
(CVP)
CVP analysis is also known as breakeven
analysis. It is a systematic examination of the inter-
relationships between selling prices, sales andproduction volume, costs, and profits
Fixed and variable costs need to be segregatedso that variable costs and volume can bemanipulated and changes in profit determined
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The contribution margin is an important
concept in CVP analysis. Fixed costs are incurred irrespective of sales, a
firm will make a loss if the contribution marginis insufficient to cover fixed costs
Breakeven point is the level of output at whichfirm makes zero profit, TC=TR
Cost-Volume-Profit Analysis
(CVP)
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Contribution
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Cost-Volume-Profit Analysis
(CVP)
Total variable costs increase proportionally with outputwhile unit variable costs are constant.
Total fixed costs remain constant but the unit fixedcosts fall as the output rises because the fixed costsare spread across more output.
40,000 20,000Unit sales
Total Unit Total Unit
Revenue 400,000 10.0 200,000 10.0Variable costs 160,000 4.0 80,000 4.0Contribution margin 240,000 6.0 120,000 6.0Fixed costs 150,000 3.8 150,000 7.5Net profit 90,000 2.2 (30,000) (1.5)
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Traditional Breakeven Chart
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Contribution Breakeven Chart
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Profit
Volume Chart
Profit (+)
0
Loss ()
Fixedcosts
()
BEP Volume of
activity (units)
Contribution
loss
profit
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Margin of Safety
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Breakeven Analysis
Assumptions made when using breakeven
analysis Fixed costs remain constant
Variable costs very proportionally with volume ofoutput
All other factors remain unchanged. E.g., sellingprices remain constant, methods and efficiency ofproduction unchanged, volume is the sole factoraffecting costs
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Breakeven analysisThe Equation Method
ExampleUnit sale price is 10, variable costs are 4 per unit, fixed costs
are 150,000 per year. Current output is at 40,000 units but can be
increased to 50,000 units.
How many units to be produced in order to break even?
Answer:Let x be the unit of production. The equation will be
10x = 4x + 150,000 + 0
6x = 150,000
x = 150,000/6 = 25,000 units
Sales = Variable costs + Fixed costs + Net profit
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Breakeven analysisThe Contribution Margin Method
This method uses contribution margin per unit ofoutput that is required to cover fixed costs
Alternative 1: Using Unit Contribution Margin
Example
Using the same values, calculate the break-even volume of sales.
Answer:
Let x be the unit required.Unit contribution margin = Unit sale price - Unit variable costs
x = (Fixed costs + Net profit) / Unit contribution margin
x = (150,000 + 0) / (10 - 4)
x = 25,000 units
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Breakeven analysisThe Contribution Margin Method
Alternative 2: Using Contribution Margin Ratio (P/V Ratio)
Example
Using the same values, calculate the break-even sales revenue
Answer:
We make use of the contribution margin ratio to calculate the
sales revenue required to cover fixed costs.
The contribution margin ratio is :
= (Unit contribution margin / Revenue per unit) %
= [(10 - 4) / 10 ] * 100%
= 0.6 * 100%
= 60% (P/V Ratio)
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Alternative 2: Using Contribution Margin Ratio (P/V Ratio)
Example
Using the same values, calculate the break-even sales revenue
Answer:
x= (Fixed costs + Net profit) / Contribution margin ratio(P/V Ratio)
x = (150,000 + 0 ) / 60%
x = 250,000
Breakeven analysisThe Contribution Margin Method
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CVP AnalysisChanges in Factors - Fixed costs
Example
Unit sale price is 10, variable costs are 4 per unit, fixed costs
are 150,000 per year. Current output is 50,000 units.
What is the consequential effect of an increase of 15,000 in
head office costs on the break-even level?
Original After increase in
fixed costs
Sales 500,000 500,000Vairable costs 200,000 200,000
Contribution margin 300,000 300,000
Fixed costs 150,000 165,000
Net profit
Contribution margin ratio
150,000
(6/10)*10060%
135,000
(6/10)*10060%
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Assuming all other things remain unchanged, a changein fixed costs will affect only the break-even point.
Example
The new break-even point is= Fixed costs / Unit contribution margin
= 165,000 / 6 = 27,500 units
CVP AnalysisChanges in Factors - Fixed costs
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CVP AnalysisChanges in Factors - Variable Costs
Example
A 10% increase in raw materials is necessary to improve the
quality of the products. Will there be an effect on the break-even point?
Original After increase in
variable costs
Sales 500,000 500,000Vairable costs 200,000 220,000
Contribution margin 300,000 280,000
Fixed costs 150,000 150,000
Net profit
Contribution margin ratio
150,000
(6/10)*10060%
130,000
(5.6/10)*10056%
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All other things equal, a change in the variablecosts will have the immediate effect onchanging the contribution margin ratio, and thebreak-even point.
CVP AnalysisChanges in Factors - Variable Costs
Example
The new break-even point is
= Fixed costs / Unit contribution margin= 150,000 / 5.6 = 26,786 units
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CVP AnalysisChanges in Factors - Selling Price
Example
Assuming that the company decided to increase the selling price
by 10%. This resulted in a 10% reduction in the sales volume. Otherthings equal, what will be the consequential effect?
Original After increase
in selling price
Sales in units 45,000Sales revenue
50,000500,000 495,000 45,000 @ 11
Variable costs 200,000 180,000 45,000 @ 4
Contribution margin 300,000 315,000
Fixed costs 150,000 150,000
Net profit 150,000 165,000
Contribution margin ratio 60% 63.6%
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When selling price changes, the effect it has onthe sales volume depends on the priceelasticity of demand
Example
The new break-even point is
= Fixed costs / Unit contribution margin
= 150,000 / 7.0 = 21,429 units
CVP AnalysisChanges in Factors - Selling Price
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In this example, we assumed that the elasticity
of demand is unity, that means a 10% changein selling price will lead to the same percentagechange in volume
If the demand is elastic, i.e. >1, then 10%change in price will lead to large change involume, i.e., 20%
CVP AnalysisChanges in Factors - Selling Price
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If the demand is inelastic, i.e.,
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When the demand is elastic, a 10% increase inprice will lead to sharp fall in net profit
For unity and inelastic demand, a 10% increase inprice led to increase in net profit
Elastic Unity Inelastic
Sales units 40,000 45,000 47,500Sales revenue (11) 440,000 495,000 522,500
Variable costs (4) 160,000 180,000 190,000
Contribution margin 280,000 315,000 332,500
Fixed costs 150,000 150,000 150,000
Net profit 130,000 165,000 182,500
CVP AnalysisChanges in Factors - Selling Price
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Besides making ST profit decision, CVP
analysis also helpful in selecting the best salesmix
Firms can use CVP to help in altering theexisting sales mix by selling more of the product
which has highest contribution margin, and theoverall contribution margin and break-even pointmight improve
CVP AnalysisThe Sales Mix
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CVP AnalysisThe Sales Mix
Example
Assuming that Company X sells the following 3 products. If the
firm could switch its sales to sell more of product B, reduce the 50% saleson product A & C, and assuming that the firm is able to maintain the same
total sales 250,000. What effect it has on the contribution margin ratio
and break-even point?
Before Product A B C
Selling Price 10 10 10Variable Costs 5 3 4
Units 10,000 10,000 5,000
Fixed Costs 150,000
After Units 5,000 17,500 2,500
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Product A B C Total
Sales 50,000 175,000 25,000 250,000
Variable costs 25,000 52,500 10,000 87,500
Contribution margin 25,000 122,500 15,000 162,500
Fixed costs 150,000
Net profit 12,500
Contribution margin ratio 50% 70% 60% 65%
Product A B C Total
Sales 100,000 100,000 50,000 250,000
Variable costs 50,000 30,000 20,000 100,000Contribution margin 50,000 70,000 30,000 150,000
Fixed costs 150,000
Net profit NIL
Contribution margin ratio 50% 70% 60% 60%
Before
After
CVP AnalysisThe Sales Mix
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CVP AnalysisThe Sales Mix
Example
The new break-even point is
= Fixed costs / Unit contribution margin= 150,000 / 6.5 = 23,077 units
Alter the sales mix will increase the contribution margin ratio by
5%, leading to a profit of 12,500 and lowering the break-even point from
250,000 to 230,770
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CVP AnalysisBenefits vs. Costs
Benefits
Enriches theunderstanding of therelationship between costs,volume, and prices asfactors affecting profit
Enables management tomake assumptions whichwill assist in ST decisionmaking
Costs
Assume that fixed costsare constant, variable costand revenue curves arelinear
Assume that volume is theonly factor affecting costs,price of cost factors and ofproduct produced/soldremain unchanged
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