## Methods to Determine the Break-Even Point

### Learning Outcomes

• Determine the break-even point using the equation method, the formula method, and in dollar sales and sales units

So the Minnesota Kayak Company has these awesome new kayaks they are going to introduce to the market. They are a new company and need help in determining pricing, costs and how many kayaks they will need to sell in a month to break even. They are looking to you to help them determine if the selling price and costs will help them to reach their goals. They give you the following information to work with:

 Price per kayak $500 variable costs per kayak$225 Contribution margin per kayak $275 Fixed costs/month$7,700

With this information, it is your task to find the breakeven point using the three different methods. Let’s look first at the equation method:

The equation method utilizes the profit equation introduced earlier.

$\text{Profit}=\text{Selling price}-\text{Variable Expenses}-\text{Fixed Expenses}$

Also, let’s revisit the contribution margin concept and some shortcuts.

• $\text{Contribution margin}=\text{Selling price}-\text{Variable expenses}$
• Profit= P
• Contribution Margin= CM
• Quantity= Q
• Fixed Expenses = F
• Variable Expenses = V

So in our kayak example we are looking for a break even point meaning that the profit = $0 We can then put together our break even point utilizing the equation method as follows: $\begin{array}{rcl}\0&=&\text{Unit CM}\times\text{Q}-\text{F}\\\0&=&\275\times\text{Q}-\7,700\\\7,700&=&\275\times\text{Q}\\\dfrac{\7,700}{275}&=&\text{Q}\\28&=&\text{Q}\end{array}$ Minnesota Kayak needs to sell 28 kayaks at$500 each to break even.

The formula method gets to the same answer in a different way. It is kind of a shortcut to the equation method:

$\begin{array}{rcl}\text{Unit Sales to Break Even}&=&\dfrac{\text{F}}{\text{Unit CM}}\\\dfrac{\7,700}{\275}&=&28\text{ kayaks}\end{array}$

So regardless of the method used, you get to the same result!

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