Download - Break even point(BEP)
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Applications of Linear EquationsApplications of Linear Equations
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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:
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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
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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
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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
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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
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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
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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
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AnalysisAnalysisCostCost
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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
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Terminology
Break Even Point
… is the point at which
neither
a Profit or Loss is made
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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
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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
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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 = $30 per unit.
Production Capacity per period = 900 units
Scenario 1
uestion: How much does the sale of an additional unit of a firm’s product contribute towards increasing its net income?
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Formulae Formulae
CM = SP - VC
CR = CM/SP * 100%
- To Find -
x = FC / CM$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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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?
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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 $
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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
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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
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This completes Chapter 5This completes Chapter 5