1. Break-Even & Crossover Analysis
BASIC PROFIT MODEL
Chapter 2
Break-Even & Crossover Analysis

2. Relationships
Profit
Breakeven Point
Crossover Point

3. Breakeven Analysis Point where you are not making or losing money
Profit = 0
Revenue = Total Cost
Contribution Margin (CM)
Marginal profit per unit sale
Unit Revenue – Unit Cost
Price per unit – Variable cost per unit

4. Breakeven Analysis
You own a motel with a hundred rooms. Fixed daily cost is $1000 (includes mortgage, staff salaries, maintenance). Variable cost per room is $10 per room per day (includes extra utility cost, room clean-up, etc). You charge customers $50 per room.
Define the random variable X
Express Total Revenue, Fixed Cost, Variable Cost, Total Cost and Profit in terms of X.
Calculate Breakeven point.
Graph Revenue and Total Cost against the Number of Rooms rented.
Graph Profit against the Number of Rooms rented.

5. Breakeven Analysis
Let X be the number of rooms rented Revenue = 50X FC = 1000 VC=10X Total Cost (TC) = FC + VC = X Profit = Revenue – TC = 50X – [10X ] = 40X – 1000 At Breakeven, Profit = 0 therefore 40X – 1000 = 0

6. Spreadsheet Example Graphs
Breakeven Analysis
Spreadsheet Example Graphs

7. Crossover Analysis
Determining the point where two alternative yield equal results
Set two profit equations equal to each other

8. Crossover Analysis
You have the option of subcontracting to improve room quality and the surroundings, but that would increase fixed cost to $1800, with no change to variable costs. You will, however, be able to charge $70 per room per day. At what point will you be indifferent between your current mode of operation and the new option?
Option 1
Option 2
Price per Room 50 70
Variable Cost per room 10
Fixed Cost
1000
1800

9. Crossover Analysis Profit 1 = 40X – 1000 Profit 2 = 60X=1800
At Crossover, profits of both options are equal:
40X = 60X – 1800
20X = 800
X = 40 rooms
At 40 rooms, the profit is the same for both options.
What is the profit at that point? Which option is better below 40 rooms? Which option is better above 40 rooms?

10. Spreadsheet Example Graphs
Crossover Analysis
Spreadsheet Example Graphs

11. Maximize Price Let’s say demand now depends on price:
Demand = 200 – 3*Price
What price would you charge for a room?
Back to original problem FC = $1000 and VC = $10/unit
P = Price per room
D = Demand = 200-3p

12. Maximize Price
p = Price per room d = Demand = 200-3p Revenue = Price*Demand = p(200-3p) = -3p p FC =1000 VC = 10(200-3P) = -30p Total Cost (TC) = FC + VC = -30p Profit = Revenue – TC = [-3p p] – [-30p ] = -3p p

13. Maximize Price Profit = -3p2 + 230p – 3000 is a curve
Profit can be maximized when slope is zero
Slope is found by taking the first derivative of the profit function
Set the slope = 0 and solve for p.
-6p = p = $38.33

14. Spreadsheet Example Graphs
Maximize Price
Spreadsheet Example Graphs