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Break Even Analysis
Lecture 5This lecture is part of Chapter 2:
Budgets, Running a Company
Today’s Lecture
Fixed versus Variable Costs
Break Even Analysis
Learn how to use the Solver in Excel
Break-Even Analysis
An important part of running a company is the determination of how the company should be financed and how the prices of the products the company sells should be set.
Clearly, in order to do this properly a sound financial analysis is necessary.
Types of costs
It is essential to realize that there are two basic types of costs a company incurs.
• Variable Costs• Fixed Costs
Variable costs are roughly proportional to a company’s sales. I.e. the cost per unit remains roughly constant.
Fixed costs remain roughly the same regardless of sales. I.e. the cost per unit is inversely proportional to sales.
Types of costs
Total Costs
Variable Costs
Fixed Costs
Sales
Sales Value
A simple graph but important to understand!
Break-Even Analysis
Commonly, the Break-even point is defined to be the level of sales where:
Revenues = Expenses
Let us have a look at a simple example.
Aunt Petunia opens a flower shop.
Break-Even Analysis
Fixed Costs:
• Rent: 5,000• Utilities: 300• Helper: 1,500
Variable Costs:
• Flowers: 40% of selling price
So we know that: Selling price – cost of flowers – rent – utilities
– helper = 0when she breaks even
Break Even Analysis
A B C D E F G H I23456 Sales Cost as percentage of7 Cost of Sales 0 sales 40%8 Rent 50009 Utilities 30010 Helper 150011 Net Income -680012
Auntie Petunia Flowers - Break even Analysis
Let’s enter the last line into the spread sheet
We learned something in the last lesson. It’s good to put the assumptions separately.
=E6*$H$7But!!!?? I’m not a Mathematician!How am I going to find the value for E6 so that E11 = 0?
=E6-E7-E8-E9-E10
Break Even Analysis
A B C D E F G H I23456 Sales 12600 Cost as percentage of7 Cost of Sales 5040 sales 40%8 Rent 50009 Utilities 30010 Helper 150011 Net Income 76012
Auntie Petunia Flowers - Break even Analysis
Piece of cake! Trial and error!
Oops! Not as easy as I thought.Especially if H7 is not a nice number like 40%. Is there a better way?
The Solver
We could cave and write down the equation. That would, in fact not be such a bad idea since equations are really not as difficult to understand when one knows what they are supposed to mean.
But *** RELIEF *** Excel has an incredibly useful function called the solver. It will solve equations without giving it the equations!
That was close ….
The Solver
The Solver can be found in the Tools menu of Excel. If it’s not there, it can be installed by going to the “Add-ins” menu item and selecting the Solver Add-in.
This is really quite self-explanatory!
Enter the appropriate values for “Set target cell”, “Equal to” and “By changing cells”, and click Solve.
Break Even Analysis
A B C D E F G H I23456 Sales 11,333 Cost as percentage of7 Cost of Sales 4,533 sales 40%8 Rent 5,0009 Utilities 30010 Helper 1,50011 Net Income 012
Auntie Petunia Flowers - Break even Analysis
Let try out the Solver!
Incredible!Like this anyone can do Math!
The break even point is 11,333
An Equation
The Solver is a fabulous tool, but really in business it is beneficial to at least be open-minded about equations.
Let’s give it a try! We know that:E11=E6-E7-E8-E9-E10(Income = Sales – Cost – Rent – Utilities – Helper)
At the break even point, Net Income = 0 and hence E11 = 0
Inserting this we obtain:0 = E6-E7-E8-E9-E10
An Equation
We want to change E6 such that0 = E6-E7-E8-E9-E10
is true.
Ah, if we just set E6 to the other values together the above equation is true. Or,
E6 = E7+E8+E9+E10is the solution to our problem.
Let’s try it and go back to the situation before we used the solver:
Break Even Analysis
A B C D E F G H I23456 Sales 0 Cost as percentage of7 Cost of Sales 0 sales 40%8 Rent 50009 Utilities 30010 Helper 150011 Net Income -680012
Auntie Petunia Flowers - Break even Analysis
Let’s fill the equation into cell E6
Oops!
What went wrong?
=E7+E8+E9+E10
An Equation
May be Math isn’t as easy as I thought…
But wait, doesn’t E7 depend on E6? Yes indeed, we have defined E7 = E6 * H7 (cost of product).
Let’s put this into our equation:
E6 = E7+E8+E9+E10 => E6 = E6*H7+E8+E9+E10
Or: E6 - E6*H7 = E8+E9+E10E6 * (1 - H7) = E8+E9+E10E6 = (E8+E9+E10) / (1 - H7)
Break Even Analysis
A B C D E F G H I23456 Sales 11,333 Cost as percentage of7 Cost of Sales 4,533 sales 40%8 Rent 5,0009 Utilities 30010 Helper 1,50011 Net Income 012
Auntie Petunia Flowers - Break even Analysis
Yosh! Let’s try that again.
Yatta! It works
After all, this was quite easy wasn’t it?And now we can change H7 to play out scenarios. Very useful indeed!
(E8+E9+E10) / (1 - H7)
Break Even Analysis
A B C D E F G H I23456 Sales 9,714 Cost as percentage of7 Cost of Sales 2,914 sales 30%8 Rent 5,0009 Utilities 30010 Helper 1,50011 Net Income 012
Auntie Petunia Flowers - Break even Analysis
If Aunt Petunia raises the price so that the cost is only 30% of sales ….
… she can break even already at 9714. Of course now she may be so expensive that no one wants to buy her flowers anymore.
The other way around
There may be times when it is betterto turn things around.
Just now, Aunt Petunia found how much she needs to sell in order to break even given certain cost as percentage of sales. This is in general a good idea since for many products the profits are more or less set.
In order to see how feasible a business is one could also enter an expected sales amount and then see how much the cost of the product can be in order to break even.
Break Even Analysis
A B C D E F G H I23456 Sales 12,000 Cost as percentage of7 Cost of Sales 5,200 sales 43%8 Rent 5,0009 Utilities 30010 Helper 1,50011 Net Income 012
Auntie Petunia Flowers - Break even Analysis
With our nice equation, it’s fairly easy to accomplish this:
E6 * (1 - H7) = E8+E9+E10(1 – H7) = (E8+E9+E10)/E6H7 = 1 - (E8+E9+E10)/E6
Cool! And I thought that Financial Analysis is only for … others
Key Points of the Day
The Solver is a great tool
But Math can be very useful as well
There are two types of costs:
– Variable Costs
– Fixed Costs
Break Even Analysis is a snap with Excel