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