Course Title: Industrial and legislation regulating
Course Code: PRD 456
Course Coordinator: Dr. Omnia Osman Fadel
Sheet 2: Breakeven Analysis Solution
1- The fixed costs at Company X are $1 million annually. The main product has revenue of
$8.90 per unit and $4.50 variable cost. (a) Determine the breakeven quantity per year, and
(b)Annual profit if 200000 units are sold.
Solution:
(a) Breakeven quantity QBE
at breakeven: Revenue = Total Cost
8.9QBE = 1,000,000 + 4.5QBE
QBE = 1,000,000/ (8.90-4.50) = 227,272 units/year
(b) Annual profit if 200,000 units are sold
Profit = R – TC
= 8.90Q – 1,000,000 - 4.5Q
At Q= 200,000 units
Profit = 8.90(200,000) – 1,000,000 - 4.50(200,000)
= $-120,000 (loss)
2- It costs $1000 for hand tools and $1.50 labor per unit to manufacture a product. Another
alternative is to manufacture the product by an automated process that costs $15,000, with
a $0.50 per-unit cost. With an annual production rate of 5000 units, how long will it take
to reach the break-even point?
Solution:
Total Cost [by hand tools] = 1,000 + 1.5Q
Total Cost [by automated process] = 15,000 + 0.5Q
At breakeven:
Total Cost [by hand tools] = Total Cost [by automated process]
1,000 + 1.5Q = 15,000 + 0.5Q
Q = 14,000 units
Time to reach breakeven = QBE /Production rate
= 14,000/5,000 = 2.8 years
1-3
Course Title: Industrial and legislation regulating
Course Code: PRD 456
Course Coordinator: Dr. Omnia Osman Fadel
3- A product currently sells for $12 per unit. The variable costs are $4 per unit, and 10,000
units are sold annually and a profit of $30,000 is realized per year. A new design will
increase the variable costs by %20 and Fixed Costs by %10 but sales will increase to 12,000
units per year. (a) At what selling price do we break even, and (b) If the selling price is to
be kept same ($12/unit) what will the annual profit be?
Solution:
Old design
Revenue = $12/unit
Variable costs = $4/unit
Sales = 10,000 units/year
Profit = $30,000/year
New design
Revenue =??
Variable costs = 4+(0.2*4) = $4.8/unit
Fixed cost =??
Sales = 12,000 units/year
(a) Selling price for new design at breakeven (revenue per unit)
First, we calculate the fixed cost for old design
Profit = Revenue – Total Cost
30,000 = (12*10,000) – (4*10,000 + FC)
FC = $ 50,000
For new design:
Fixed Cost = 50,000 + (0.1*50,000) = $55,000
At breakeven:
Revenue = Total Cost
x * 12,000 = (4.8*12,000) + 55,000
x = $9.38/unit (selling price)
(b) Annual profit if selling price for new design is $12/unit
Profit = Revenue – Total Cost
= (12*12,000) – (4.8*12,000 +55,000)
Profit = $31,400/year
2-3
Course Title: Industrial and legislation regulating
Course Code: PRD 456
Course Coordinator: Dr. Omnia Osman Fadel
4- Indira Industries is a major producer of diverter dampers used in the gas turbine power
industry to divert gas exhausts from the turbine to a side stack, thus reducing the noise to
acceptable levels for human environments. Normal production level is 60 diverter systems
per month, but due to significantly improved economic conditions in Asia, production is at
72 per month. The following information is available: Fixed costs FC = $2.4 million per
month, Variable cost per unit v = $35,000, Revenue per unit r = $75,000
(a) How does the increased production level of 72 units per month compare with the current
breakeven point?
(b) What is the current profit level per month for the facility?
(c) What is the difference between the revenue and variable cost per damper that is
necessary to break even at a significantly reduced monthly production level of 45 units, if
fixed costs remain constant?
Solution:
Normal Production Level = 60 units/month
Improved Production Level = 72 units/month
FC = $2,400,000 /month
v = $35,000/unit
r = $75,000/unit
(a) At breakeven:
r* QBE = v* QBE + FC
(75,000* QBE) = (35,000* QBE) + 2,400,000
QBE = 60 units/month
(b) Profit = Revenue – Total Cost
= (75,000*72) – (2,400,000 + 35,000*72)
= +$480,000/month
(c) At Q = 45, find (r-v)
At breakeven
Revenue = Total Cost
45*r = 2,400,000 + 45*v
r-v = $53,333/unit
3-3
