### Break-even

```Operations Management
Dr. Ron Lembke
BREAK-EVEN ANALYSIS
BREAK-EVEN ANALYSIS
Given a fixed cost, how many do we have
to make to break even?
 A: buy units @ \$200
 B: Make on lathe: \$80,000 + \$75 each
 C: CNC Machining Center:
 \$200,000 + \$15 each
Which is the cheapest way?
BREAK-EVEN ANALYSIS
 If we only sell 1, which is cheapest?
 If we sell a gazillion, which is cheapest?
Total Costs
BREAK-EVEN
Outsource
Draw Lowest
Fixed Cost Line
Volume
Total Costs
BREAK-EVEN
Outsource
Machining
Center
Volume
Total Costs
BREAK-EVEN
Outsource
Lathe
Machining
Center
Volume
Total Costs
BREAK-EVEN
Outsource
Lathe
Machining
Center
Volume
BREAK-EVEN ANALYSIS
Total Costs
Cost of 1,000 units
A: 200 * 1,000 = 200,000
B: 80,000 + 75*1,000 = 155,000
C: 200,000 + 15*1,000 = 215,000
300k
C
A
200k
B
100k
Volume
0
1,000
BREAK-EVEN ANALYSIS
Cost of 2,000 units
A: 200 * 2,000 = 400,000
B: 80,000 + 75*2,000 = 230,000
C: 200,000 + 15*2,000 = 230,000
A
Total Costs
400k
300k
B
C
200k
100k
0
2,000
Volume
BREAK-EVEN ANALYSIS
Cost of 3,000 units
A: 200 * 3,000 = 600,000
B: 80,000 + 75*3,000 = 305,000
C: 200,000 + 15*3,000 = 245,000
A
Total Costs
600k
500k
400k
B
C
300k
200k
100k
0
3,000
Volume
BREAK-EVEN ANALYSIS
 When does Lathe become cheaper than
Outsourcing?
 80,000 + 75*x = 200*x
 80,000 = 125*x
 x = 640
BREAK-EVEN ANALYSIS
A
600k
Total Costs
500k
Outsource
400k
Lathe
Machining
Center
B
C
300k
200k
100k
0
640
3,000
Volume
BREAK-EVEN ANALYSIS
 When does Machining Center become cheaper
than Lathe?
 80,000 + 75*x = 200,000 + 15*x
 60*x = 120,000
 x = 2,000
BREAK-EVEN ANALYSIS
A
600k
Total Costs
500k
Outsource
Lathe
Machining
Center
400k
B
300k
C
200k
<= 640 Outsource
640-2000 Lathe
>= 2000 Mach Ctr
100k
0
640
2,000
3,000
Volume
BREAK-EVEN PROFIT QUANTITY
How much do sales have to grow to make
an investment pay off?
 Fixed costs = \$10,000
 Direct labor = \$1.50 / unit
 Material = \$0.75 / unit
 Sales price = \$4.00
 How many units must sell to break even?

BREAK-EVEN PROFIT QUANTITY

Gross Profit per unit
= \$4 – (\$1.5 + \$0.75) = \$1.75
How many units to sell to offset Fixed
cost?
 \$10,000 = \$1.75 * x
 X = 10,000/1.75 = 5,714.3 = 5,715 units

SUMMARY

Break-even quantity calculations
 Cheapest
for one unit, and a gazillion
 Accurate drawing
 Find break-points algebraically

Break-even profit quantity
 fixed
cost to develop a product, how many must sell
to be profitable?
```