break even point(bep)

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Page 1: Break even point(BEP)

Linear

Equations Apps.

Linear

Equations Apps.

©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved

5 - 1

Applications of Linear EquationsApplications of Linear Equations

Page 2: Break even point(BEP)

Linear

Equations Apps.

Linear

Equations Apps.

©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved

5 - 2

Learning Objectives

LO 2LO 2

LO 3LO 3 Solve two equations in two unknowns by the graphical method

Graph a linear equation in two variables

Express a linear equation in the slope-intercept form

LO 1 LO 1

AlsoAlso

After completing this chapter, you will be able to:

Page 3: Break even point(BEP)

Linear

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Linear

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5 - 3

Learning Objectives

Distinguish between fixed costs and variable costs

LO 5LO 5

LO 4LO 4

Perform linear Cost-Volume-Profit and break-even analysis employing:

AA

- The contribution margin approach

BB

- The algebraic approach of solving the cost and revenue functions

- A breakeven chart

CC

Page 4: Break even point(BEP)

Linear

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Linear

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5 - 4

Graphing a Linear EquationGraphing a Linear Equation

Graph the equation 3x – 2y = 8 over the range x=0 to x=8

Graph the equation 3x – 2y = 8 over the range x=0 to x=8

Rearrange the equation to solve for yRearrange the equation to solve for yStep 1Step 1

Substitute a few values for x, and calculate the corresponding values for y

Substitute a few values for x, and calculate the corresponding values for y

Step 2Step 2

Plot and connect the points on the xy graph

Plot and connect the points on the xy graph

Step 3Step 3

3x – 2y =83x – 2y =8

– 2y = 8 - 3x y = 8 - 3x

-2

y = 1.5x - 4y = 1.5x - 4x y0 -4

6 5

3 0.5

…continue…continue

LO 1LO 1

Page 5: Break even point(BEP)

Linear

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Linear

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0 1 2 3 4 5 6 7 8 9 10

7 6 5 4 3 2 1 0-1-2-3-4

X

Y

Plot and connect the points on the xy graph

Plot and connect the points on the xy graph

Step 3Step 3

y = 1.5x - 4y = 1.5x - 4x y0 -4

6 5

3 0.5

Graphing a Linear EquationGraphing a Linear Equation

y = 1.5x - 4y = 1.5x - 4

Page 6: Break even point(BEP)

Linear

Equations Apps.

Linear

Equations Apps.

©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved

5 - 6

Graphing a Linear EquationGraphing a Linear Equation

y = 1.5x - 4y = 1.5x - 4

This is called the slope–intercept form of this linear equation

This is called the slope–intercept form of this linear equation

Where 1.5 is the slope, and -4 is the y-intercept

Where 1.5 is the slope, and -4 is the y-intercept

0 1 2 3 4 5 6 7 8 9 10

1 0-1-2-3-4

X

Y

y = 1.5x - 4y = 1.5x - 4

LO 2LO 2

Page 7: Break even point(BEP)

Linear

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Linear

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5 - 7

Solving 2 equations in 2 unknowns graphically

Solving 2 equations in 2 unknowns graphically

LO 3LO 3

Rearrange each equation to solve for yRearrange each equation to solve for yStep 1Step 1

Substitute a few values for x, and calculate the corresponding values for y

in each equation

Substitute a few values for x, and calculate the corresponding values for y

in each equation

Step 2Step 2

Plot and connect the points on the xy graph – the point where the lines cross in

the point of intersection, your solution

Plot and connect the points on the xy graph – the point where the lines cross in

the point of intersection, your solution

Step 3Step 3

Find the point of intersection for the equations 3x – 2y = 8 and 4x+2y = 6

Find the point of intersection for the equations 3x – 2y = 8 and 4x+2y = 6

y = 1.5x - 4y = 1.5x - 4 4x+2y = 62y = 6- 4xy = 6 – 4x

2y = -2x + 3y = -2x + 3

y = -2x + 3y = -2x + 3x y0 3

2 -1

3 -3

Page 8: Break even point(BEP)

Linear

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Linear

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5 - 8

Solving 2 equations in 2 unknowns graphically

Solving 2 equations in 2 unknowns graphically

Find the point of intersection for the equations

3x – 2y = 8 and 4x+2y = 6

Find the point of intersection for the equations

3x – 2y = 8 and 4x+2y = 6

0 1 2 3 4 5 6 7 8 9 10

Y

7 6 5 4 3 2 1 0-1-2-3-4

3x-2y=83x-2y=8

0 3

2 -1

3 -3

4x+2y=64x+2y=6

(2, -1) or

y= 1.5x - 4y= 1.5x - 4

x yy = -2x + 3y = -2x + 3

y = -2x + 3y = -2x + 3or

Page 9: Break even point(BEP)

Linear

Equations Apps.

Linear

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5 - 9

AnalysisAnalysisCostCost

Page 10: Break even point(BEP)

Linear

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Linear

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TerminologyFixed CostsFixed Costs

Business Costs

Business Expenses

Variable CostsVariable Costs

…do NOT change if sales increase or

decreasee.g. rent, property taxes, some

forms of depreciation

…do change in direct proportion to sales volume e.g. material costs,

direct labour costs

LO 4LO 4

Page 11: Break even point(BEP)

Linear

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Linear

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©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved

5 - 11

Terminology

Break Even Point

… is the point at which

neither

a Profit or Loss is made

Page 12: Break even point(BEP)

Linear

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Linear

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5 - 12

TerminologyContribution Margin

…is the dollar amount that is found by deducting ALL Variable Costs from Net Sales and ‘contributes’ to meeting

Fixed Costs and making a ‘Net Profit’.

…is the dollar amount that is found by deducting ALL Variable Costs from Net Sales and ‘contributes’ to meeting

Fixed Costs and making a ‘Net Profit’. Contribution Rate

…is the dollar amount expressed as a percent (%) of Net Sales

…is the dollar amount expressed as a percent (%) of Net Sales

A Contribution Margin statement

LO 5CLO 5C

Page 13: Break even point(BEP)

Linear

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Linear

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$ %Net Sales(Price * # Units Sold) x 100

Less: Variable Costs x x

Net Income x x Less: Fixed Costs x x

Contribution Margin x x

TerminologyA Contribution Margin Statement

Page 14: Break even point(BEP)

Linear

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Linear

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5 - 14

Market research for a new product indicates that the product can be sold at $50 per unit. Cost analysis provides the following information:

Fixed Costs per period = $8640

Variable Costs = $30 per unit.

Production Capacity per period = 900 units

Scenario 1

uestion: How much does the sale of an additional unit of a firm’s product contribute towards increasing its net income?

Page 15: Break even point(BEP)

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Linear

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Formulae Formulae

CM = SP - VC

CR = CM/SP * 100%

- To Find -

x = FC / CM$x = (FC / CM)* SP

* At Break Even, Net Profit or Loss = 0

Applying Formulae Formulae

Contribution Margin

Contribution Rate

*Break Even Point: ...in Units (x)

...in Sales $

...in % of Capacity BEPin Units/PC*100

Page 16: Break even point(BEP)

Linear

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Linear

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As in the previous scenario, the new product can be sold at $50 per unit. Costs are as follows: Fixed Costs are $8640 for the period , Variable Costs are $30 per unit, and the Production

Capacity is 900 units per period.

Applying the Formulae Formulae

CM = SP - VCCR = CM/SP * 100%

Units x = FC / CMBreak Even Point:

In $ x = (FC / CM)* SP

= $50 - $30 = $20 = $20/$50 * 100 = 40%

= $8640/$20 = 432 Units

= ($8640/$20)* $50 = $21,600= 432/ 900*100 = 48% of

CapacityBEPin units / PC*100

Page 17: Break even point(BEP)

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Linear

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The Lighting Division of Seneca Electric Co. plans to introduce a new street light based on

the following accounting information:

Scenario 2

FC = $3136 VC = $157 SP= $185 Capacity = 320 units

uestion: Calculate the breakeven point (BEP) …in units …in dollars …as a percent of capacity

Page 18: Break even point(BEP)

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Linear

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Scenario 2 FC = $3136 VC = $157 SP= $185 Capacity = 320 units

Break Even Point…in units

…as a percent of capacity

…in dollars

= FC / CM

= (FC / CM)* SP

= BEPin units/PC*100

= $3136/

SP – VC = CM$185 – 157 = $28

SP – VC = CM$185 – 157 = $28

28 = 112 Units

= ($3136/ 28) * $185 = $20720

= 112/320 * 100 = 35% of Capacity

Page 19: Break even point(BEP)

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FC = $3136 VC = $157 SP= $185 Capacity = 320 units

Scenario 2 -1$2688

Determine the BEP as a % of capacity if FC are reduced to $2688.

=BEPin units/PC*100 FormulaFormula

Step 1… Find CM Step 2… Find BEP in units

SP = $185VC = - 157CM $ 28

= FC/CM

=

= $2688/ $28= 96 Units

=BEPin units /PC*100

Step 3… Find% of Capacity

= 96/320*100= 30% of Capacity

Page 20: Break even point(BEP)

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FC = $3136 VC = $157 SP= $185 Capacity = 320 units

Scenario 2 -2$4588

Determine the BEP as a % of capacity if FC are increased to $4588, and VC reduced to 80% of SP.

= BEPin units /PC*100 FormulaFormula

Step 1… Find CM Step 2… Find BEP in units

SP = $185VC = - 148CM $ 37

= FC/CM= $4588/ $37= 124 Units

=BEPin units /PC*100

Step 3… Find% of Capacity

= 124/320*100= 39% of Capacity

VC =SP*80% = $148

$148

Page 21: Break even point(BEP)

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FC = $3136 VC = $157 SP= $185 Capacity = 320 units

Scenario 2 -3

Determine the BEP as a % of capacity if SP is reduced to $171.

= BEPin units /PC*100 FormulaFormula

Step 1… Find CM Step 2… Find BEP in units

SP = $ 171VC = -157CM $ 14

= FC/CM = $3136/ $14= 224 Units

=BEPin units /PC*100

Step 3… Find% of Capacity

= 224/320*100= 70% of Capacity

$171

Page 22: Break even point(BEP)

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FC = $3136 VC = $157 SP= $185 Capacity = 320 units

Scenario 2 -4

Determine the NI if 134 units are sold!

Step 1… Find CM Step 2… Find BEP in units

SP = $185VC = - 157CM $ 28

= FC/CM= $3136/$28= 112 Units

UnitsSold 134BEP 112 Over BEP 22

CM of $28 per unit Company had a NI of 22* $28 = $616.

NI = #Units above BEP*CM FormulaFormula

Page 23: Break even point(BEP)

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FC = $3136 VC = $157 SP= $185 Capacity = 320 units

Scenario 2 -5

What unit sales will generate NI of $2000?

#Units above BEP = NI/CM FormulaFormula

Step 1… Find CM Step 2… Find BEP in units

SP = $185VC = - 157CM $ 28

= FC/CM= $3136/$28= 112 Units

NI/CMNI/CM

CM of $28 per unit

= $2000/$28 per Unit

= 72 Units above Break Even

72 Units + 112 BEP Units = Total Sales Units = 184

72 Units + 112 BEP Units = Total Sales Units = 184

Page 24: Break even point(BEP)

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FC = $3136 VC = $157 SP= $185 Capacity = 320 units

Scenario 2 -6

# Units below BEP = (NI)/CM FormulaFormula

Step 1… Find CM Step 2… Find BEP in units

SP = $185VC = - 157CM $ 28

= FC/CM= $3136/$28= 112 Units

(NI)/CM(NI)/CM

CM of $28 per unit

= 12 Units below Break Even

What are the unit sales if there is a Net Loss of $336?

= ($336)/$28 per Unit

112 BEP - 12 Units Below = Total Sales Units = 100

112 BEP - 12 Units Below = Total Sales Units = 100

Page 25: Break even point(BEP)

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Scenario 2 -7

Step 1… Find CM Step 2… Find BEP in units

SP = $185VC = - 157CM $ 28

= FC/CM= $3136/$28= 112 Units

CM of $28 per unit

The company operates at 85% capacity. Find the Profit or Loss.

FC = $3136 VC = $157 SP= $185 Capacity = 320 units

320*.85= 272

320*.85= 272

UnitsProduction 272BEP 112 Over BEP 160

UnitsProduction 272BEP 112 Over BEP 160

# units above BEP *CM = NIFormulaFormula

160 Units * $28 = Profit $4480160 Units * $28 = Profit $4480

Page 26: Break even point(BEP)

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CaseThe Marconi Co. year end operating results were as follows:

Total Sales of $375000

Operated at 75% of capacity

Total Variable Costs were $150000

Total Fixed Costs were $180000

What was Marconi’s BEP expressed in dollars of sales?

Page 27: Break even point(BEP)

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CaseThe Marconi Co. year end operating results were as follows:

Total Sales of $375000 Operated at 75% of capacity

Total Variable Costs were $150000 Total Fixed Costs were $180000

What was Marconi’s BEP expressed in dollars of sales?

What information is needed to calculate the $BEP?What information is needed to calculate the $BEP?

2. VC per

Unit

2. VC per

Unit

1. Number of

Units sold

1. Number of

Units sold

3. CM3. CM 4. BEP

in $

4. BEP

in $

Page 28: Break even point(BEP)

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The Marconi Co. year end operating results were as follows: Total Sales of $375000

Operated at 75% of capacity Total Variable Costs were $150000

Total Fixed Costs were $180000 What was Marchoni’s BEP expressed in dollars of sales?

Case

2. VC per

Unit

2. VC per

Unit

1. Number of

Units sold

1. Number of

Units sold

3. CM3. CM

Let SP = $1 and X be the Number of $1 Units soldSales of $375 000 = 375000 Total Units sold

$150000 375000

Total VCTotal Unit Sales

= = $0.40perunit

SP $1.00VC .40 CM $ .60

Page 29: Break even point(BEP)

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The Marconi Co. year end operating results were as follows: Total Sales of $375000

Operated at 75% of capacity Total Variable Costs were $150000

Total Fixed Costs were $180000 What was Marchoni’s BEP expressed in dollars of sales?

Case

4. BEP

in $

4. BEP

in $

$BEP = (FC/CM)*SP= ($180000/0.60)*$1.00= (300000)*1.00# Of Units# Of Units

= $300 000 $BEP

Page 30: Break even point(BEP)

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This completes Chapter 5This completes Chapter 5