Dr. Hassan, Y. – 91.380
•
Breakeven analysis is directed to the point at which operations merely break even (neither making nor losing money)
•
It focuses on cost-volume-profit relations that hold only over a short run
•
Cost-revenue-profit relationships can be understood by breaking down a unit of output into its component dollar values
Profit
Variable costs
Selling price
Fixed costs
1
One unit of output
•
Costs can be classified into two major categories:
Fixed costs ( FC ): are costs which remain constant regardless of the level of a firm’s activity
Variable costs ( VC ): are the unit costs that are proportional to output, n
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Profit ( Z ): is the difference between total revenue [ TR = n * SP ] and total cost [ TC = n * VC + FC ]
•
Selling price ( SP ): actual market price per unit
•
Revenue and variable costs are proportional to output
•
Conditions for linear breakeven analysis:
Income is only from operations under consideration
Fixed costs, variable costs per unit, and selling price are constant
All units produced are sold
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Breakeven charts can show the volume at which revenues and total costs exactly breakeven

Dr. Hassan, Y. – 91.380
Revenue and costs
TR
BEP
TC
FC
Units of output
Basic Relationships
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Total revenue/period = TR = n * SP
•
Total cost/period = TC = n * VC + FC
•
Gross profit/period = Z = TR – TC = n ( SP – VC ) – FC
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For BEP: Z = 0
∴
BEP
=
SP
FC
−
VC
•
The term ( SP – VC ) is called the contribution as it indicates the portion of selling price that contributes to paying off the fixed cost
•
At BEP, the contribution = FC
Breakeven Point Characteristics:
•
Sensitive to changes in costs or selling prices
•
A lower BEP means that fixed costs can be met at low n
•
Sales level well above BEP is good sign
•
To lower the BEP:
Reduce fixed costs
2

Dr. Hassan, Y. – 91.380
TR
BEP2 BEP1
Reduce variable costs
FC 2 < FC 1
TR
TC 1
TC 2
FC
TC
FC 1
FC 2
TC 2 < TC 1
Increase price of output
TR 2
TR 1
TC
3
FC
TR 2 > TR 1
Example:
An airline is evaluating its feeder routes. These routes connect smaller cities to major terminals. The routes are seldom very profitable themselves, but they feed passengers into the major flights which yield better returns. One feeder route has a max capacity of 1000 passengers/month. The contribution from the fare of each passenger is 75% of the $120 ticket price. Fixed costs per month are $63,000. Determine the breakeven point and net profit at full capacity when the effective tax rate is 40%.

Dr. Hassan, Y. – 91.380
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Example:
Sewing machines: $80 per unit [imported]
Fixed costs: $140,000 / year
40% commission
At what price should the machines be sold to allow the importers to breakeven on 5000 units?
Multiproduct Alternatives:
•
More than one product can be shown on a break-even chart
•
Allows decision maker to evaluate the combined effect of product mix on plant utilization, revenue, and costs
•
Use a “multiprtoduct profit” or “contribution” chart
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How?
Plot the FC as a loss on the vertical axis
Use the horizontal axis to denote sales revenue
The n at which loss = 0 is BEB
Profit
B
C
FC
C
Total profit
0
FC
A
A
FC
B
BEP
Total fixed cost
Loss
Multiple Alternatives:
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When choices are related to a number of alternative
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Frequently encountered in lease-or-buy decision
•
Similar to the sensitivity analysis of multiple alternatives

Dr. Hassan, Y. – 91.380
$
MC
TC
A
TC
B
FC
B
FC
A
Units of output
•
Costs and revenues do not always follow a linear pattern
•
Average fixed cost:
Declines as output increases
AFC = FC/n
•
Average variable cost:
Typically: saucer-shaped
First, declines as output increases until it reaches a minimum and then increases with the increase of output
AVC = VC/n
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Average total cost = AFC + AVC = TC/n
•
Marginal cost:
The extra increment of cost required to produce an additional unit of output
If the last increment of cost is smaller than the average of all previous costs, it will pull the average down
Thus, the average total cost declines until it equals the marginal cost
MC =
∆
TC/
∆ n
ATC
AVC
5
AFC

Dr. Hassan, Y. – 91.380
Marginal Revenue and Profit:
•
Additional money received from selling one more unit at a specified level of output
•
For linear revenue: MR = SP
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General: MR =
∆
TR/
∆ n
Example:
SP = 21,000 n
-0.5
MR
= d ( TR )
= dn d ( n*SP )
= dn d ( 21 , 000 n
0 .
5
) dn
MR = 0.5 [21,000 n
-0.5
] = 10,500 n
-0.5
Marginal Cost and Average Unit Cost
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As production increases the total cost per unit may increase due to:
Increase in maintenance cost
More overtime payments
Congestion leading to inefficiency
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Also, there will be an increasing marginal cost
TR
Z max
TC
BEP
BEP
•
To find the BEP, set the profit ( Z ) equal to zero
Z = n * SP – n * VC – FC
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To find the volume of output that produces maximum profit, set the first derivative equal to zero dZ dn
= d ( n * SP
− n * VC
−
FC )
=
0 dn d ( n * SP )
− dn d ( n * VC
+
FC ) dn
=
0
Or: d ( n * SP ) dn
= d ( n * VC
+
FC ) dn
∴
Marginal revenue = Marginal cost
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