Introduction to Management Science
Topic: Breakeven Analysis
By Omar Abou Kasm
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Breakeven Analysis
Example: Suppose that to develop a new product, we must pay a fixed cost of $100,000 for equipment
plus $3.50 per unit (variable cost) for labor and materials. Each unit can then be sold for $6.
Should we develop this product? If yes, how many should we produce?
We need a tool to help us in making this decision.
Let x be the number of units (quantity)
Total cost: C = Fixed cost + (variable cost)(number of units) = 100,000 + 3.5x
Total revenue: R = (unit price)(number of units) = 6x
Profit: P = Total revenue – total cost = R – C = 6x – (100,000 + 3.5x) = 2.5x – 100,000
We are interested in making a profit, so we want Profit > 0
Profit > 0
2.5x – 100,000 > 0
x > 100,000/2.5
x > 40,000 units (We need to sell more than 40,000 units to start making profit)
Note: x = 40,000 units is the breakeven quantity
(The quantity that makes the Profit = 0; we start making profit beyond this point)
In general: Breakeven quantity = (Fixed cost)/(unit price – variable cost)
Here we can assess the market: can we sell more than 40,000 units?
If no, then investing in this product is not a good idea!
Example: if we can only sell 30,000 units, then Profit = 2.5(30K) – 100K = -$25,000 (a loss!)
How much profit do we make if the actual demand was 80,000 units?
x = 80,000 units
Profit = 2.5x – 100,000 = 2.5(80,000) - 100,000 = $100,000
What if we want to make a profit of 25% of the investment (fixed cost)?
Profit = 0.25(100,000) = $25,000
Replace in the profit equation: 2.5x – 100,000 = 25,000
x = 125,000 /2.5 = 50,000 units (We need to sell 50,000 units to make a profit of 25% of the investment)
In general: Required number of units = (Target profit + Fixed cost)/(unit price – variable cost)
Graphical representation: Similar information can be seen in the graph below.
Break-even point = 40K units
In Excel: We can create an excel model to help us make this analysis
Additional Exercise: In the previous example, our variable was the number of units -- What if we are
interested in another variable?
For example, what if we know that the demand is 70,000 units, the fixed and variable costs are the
same, and we are interested in finding the selling price that will make us break-even. What changes in
the model?
Number of units = 70,000
Let p be the selling price (unit price)
Total Cost = Fixed cost + (variable cost)(number of units) = 100000 + 3.5*70000 = $345000
Total Revenue = (number of units)(unit price) = 70000p
Profit = Total Revenue – Total Cost = 70000p – 345000
To breakeven: Profit = 0
→ 70000p – 345000 = 0
→ p = 345,000/70,000 = $4.93, The selling price should be $4.93 to breakeven.
In general: Break-even price = (Total cost)/(number of units)
In Excel:
Additional Qs:
In the previous exercise we saw that the break-even unit price if $4.93. Should we proceed with the
production if people are willing to pay $2 for our product?
No, $2 is less than the breakeven price ($4.93); so, we will not make profit. Any price above the breakeven unit price will start generating profits.
What if you were asked to calculate the breakeven unit cost and you found that it is $3. Should we
proceed with the production if we saw that the actual unit cost is $5?
No, $5 is more than the breakeven unit cost ($3); so, we will not make profit. Any unit cost less than the
breakeven unit cost will start generating profits.
Notice the difference between considering the unit price versus considering the unit cost of an item?
Why is it this way? Hint: Think of how the Profit is calculated.