Break-Even Analysis
Greg Hiatt
May 5, 2002
Defined:
Break-even analysis examines the
cost tradeoffs associated with
demand volume.
Overview:
Break-Even Analysis
•
•
•
•
Benefits
Defining Page
Getting Started
Break-even Analysis
– Break-even point
– Comparing variables
• Algebraic Approach
• Graphical Approach
Benefits and Uses:
• The evaluation to determine
necessary levels of service or
production to avoid loss.
• Comparing different variables to
determine best case scenario.
Defining Page:
• USP
= Unit Selling Price
• UVC
= Unit Variable costs
• FC
= Fixed Costs
• Q
= Quantity of output units
sold (and manufactured)
Defining Page:
Cont.
• OI
= Operating Income
• TR
= Total Revenue
• TC
= Total Cost
• USP
= Unit Selling Price
Getting Started:
• Determination of which equation
method to use:
– Basic equation
– Contribution margin equation
– Graphical display
Break-even analysis:
Break-even point
• John sells a product for $10 and it
cost $5 to produce (UVC) and has
fixed cost (FC) of $25,000 per year
• How much will he need to sell to
break-even?
• How much will he need to sell to
make $1000?
Algebraic approach:
Basic equation
Revenues – Variable cost – Fixed cost = OI
(USP x Q) – (UVC x Q) – FC = OI
$10Q - $5Q – $25,000 = $ 0.00
$5Q = $25,000
Q = 5,000
What quantity demand will earn $1,000?
$10Q - $5Q - $25,000 = $ 1,000
$5Q = $26,000
Q = 5,200
Algebraic approach:
Contribution Margin equation
(USP – UVC) x Q = FC + OI
Q= FC + OI
UMC
Q= $25,000 + 0
$5
Q= 5,000
What quantity needs sold to make $1,000?
Q = $25,000 + $1,000
$5
Q = 5,200
Graphical analysis:
Dollars
70,000
60,000
Total Cost
Line
50,000
40,000
30,000
20,000
Total Revenue
10,000
Break-even point
Line
0
1000 2000 3000 4000 5000 6000
Quantity
Graphical analysis:
Cont.
Dollars
70,000
60,000
Total Cost
Line
50,000
40,000
30,000
20,000
Total Revenue
10,000
Break-even point
Line
0
1000 2000 3000 4000 5000 6000
Quantity
Scenario 1:
Break-even Analysis Simplified
• When total revenue is equal to total
cost the process is at the break-even
point.
TC = TR
Break-even Analysis:
Comparing different variables
• Company XYZ has to choose
between two machines to purchase.
The selling price is $10 per unit.
• Machine A: annual cost of $3000 with
per unit cost (VC) of $5.
• Machine B: annual cost of $8000 with
per unit cost (VC) of $2.
Break-even analysis:
Comparative analysis Part 1
• Determine break-even point for
Machine A and Machine B.
• Where: V =
FC
SP - VC
Break-even analysis:
Part 1, Cont.
Machine A:
v = $3,000
$10 - $5
= 600 units
Machine B:
v = $8,000
$10 - $2
= 1000 units
Part 1: Comparison
• Compare the two results to
determine minimum quantity sold.
• Part 1 shows:
– 600 units are the minimum.
– Demand of 600 you would choose
Machine A.
Part 2: Comparison
Finding point of indifference between
Machine A and Machine B will give
the quantity demand required to
select Machine B over Machine A.
Machine A
FC + VC
$3,000 + $5 Q
$3Q
Q
=
Machine B
=
FC + VC
= $8,000 + $2Q
= $5,000
= 1667
Part 2: Comparison
Cont.
• Knowing the point of indifference we
will choose:
• Machine A when quantity demanded
is between 600 and 1667.
• Machine B when quantity demanded
exceeds 1667.
Part 2: Comparison
Graphically displayed
Dollars
21,000
18,000
Machine A
15,000
12,000
9,000
Machine B
6,000
3,000
0
500 1000 1500 2000 2500 3000
Quantity
Part 2: Comparison
Graphically displayed Cont.
Dollars
21,000
18,000
Machine A
15,000
12,000
9,000
Machine B
6,000
3,000
Point of indifference
0
500 1000 1500 2000 2500 3000
Quantity
Exercise 1:
• Company ABC sell widgets for $30 a
unit.
• Their fixed cost is$100,000
• Their variable cost is $10 per unit.
• What is the break-even point using
the basic algebraic approach?
Exercise 1:
Answer
Revenues – Variable cost - Fixed cost = OI
(USP x Q) – (UVC x Q) – FC
$30Q - $10Q – $100,00
$20Q
Q
=
=
=
=
OI
$ 0.00
$100,000
5,000
Exercise 2:
• Company DEF has a choice of two
machines to purchase. They both
make the same product which sells
for $10.
• Machine A has FC of $5,000 and a
per unit cost of $5.
• Machine B has FC of $15,000 and a
per unit cost of $1.
• Under what conditions would you
select Machine A?
Exercise 2:
Answer
Step 1: Break-even analysis on both
options.
Machine A:
v = $5,000
$10 - $5
= 1000 units
Machine B:
v = $15,000
$10 - $1
= 1667 units
Exercise 2:
Answer Cont.
Machine A
FC + VC
$5,000 + $5 Q
$4Q
Q
=
Machine B
=
FC + VC
= $15,000 + $1Q
= $10,000
= 2500
• Machine A should be purchased if
expected demand is between 1000
and 2500 units per year.
Summary:
• Break-even analysis can be an
effective tool in determining the cost
effectiveness of a product.
• Required quantities to avoid loss.
• Use as a comparison tool for making
a decision.
Bibliography:
Russel, Roberta S., and Bernard W.
Taylor III. Operations Management.
Upper Saddle River, NJ: Pentice-Hall,
2000.
Horngren, Charles T., George Foster,
and Srikant M. Datar. Cost Account.
10th ed. Upper Saddle River, NJ:
Pentice-Hall, 2000.