#### Transcript Break-Even Analysis

```Break-Even Analysis
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:
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:
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:
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.
EXERCISE
• The company QUEENS is
producing 5 different
products(A,B, C,D, E). The total
estimated revenues are given
for A, B, C, D, E 180000, 200000,
395000, 500000,140000 TL
respectively. The total
estimated fixed costs are
538000 TL.
• Unit prices and VC for products
A, B, C, D and E are :
PRODUCT
Unit Price (TL)
UVC(TL)
A
235
120
B
150
63
C
425
195
D
175
68
E
420
210
•A)Calculate the
percentage sales rate for
each product
• B) Calculate the ratio of UVC to
the unit price for each product
• C) Calculate the Break-even
quantities and revenues for each
product
• D) If the income tax rate= 23%,
and net income= 200000 TL,
what should be the gross
income and break even revenue
Product
Revenues
S.Ratio
(%)
Unit
Price
UVC
UVC/P Weighed
%
A
180.000
12.7
235
120
0.511
0.065
B
200.000
14.1
150
63
0.42
0.059
C
395.000
27.9
425
195
0.459
0.128
D
500.000
35.4
175
68
0.389
0.138
E
140.000
9.9
420
210
0.50
0.050
SUM
1.415.000 100.0
0.44
• BER= FC/ (1-UVC/P)
• BER= 538.000/(1-0.44)=960.714
TL
PRODU
CT
Sales
percent
Sales
revenue
Unit
Price
BEQ=
R/P
A
12,7
122.011
235
519
B
14,1
135.461
150
903
C
27,9
268.039
425
631
D
35,4
340.093
175
1943
E
9,9
95.110
420
226
• D) Tax rate=23%
• Gross income= Net income/ (10.23)= 259.740 TL
• BER for the company= (538.000
+ 259.740)/ (1-0.44)=1.424.535
TL
```