bep analysis

7/31/2019 BEP Analysis

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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


(CVP)


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Contribution


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(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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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



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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


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


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


= Fixed costs / Unit contribution margin

= 150,000 / 7.0 = 21,429 units



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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%



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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



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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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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



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Example


= 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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