Determining The Break-even Point

Using the TR = TC rule

The break even quantity can be calculated by comparing total sales revenue with total costs. Therefore:

$\begin{array}{l} Total variable cost = Average variable cost \times Quantity \\ Total revenue = Price \times Quantity \end{array}$

Using the contribution per unit rule

The quickest method

$Break-even = \frac{Fixed costs}{Contribution per unit}$

Interpretation of a break-even chart

Look at a chart and estimate the level of break-even.

Other uses of break-even charts include:

Target profit: how many units of output need to be produced to generate a certain level of profit?

$Q = \frac{Fixed Costs + Target Profit}{Contribution per unit}$

Break-even price: how much do we need to charge for out product in order to break-even?

$Break-even price = \frac{Total Cost}{Output}$

Price needed to reach a target profit: what price does a business need to charge in order to reach a target rate of profit?

Price = \frac{Profit Target + Total Cost}{Output}

Margin of safety

The margin of safety is the range of output between the break-even output and the current level of output (assuming this level of output is above the break-even point), over which profit is made. Business would want to calculate their margin of safety in order to know by how much sales could fall before a loss is made. Naturally, the larger the margin of safety the better. We calculate it by subtracting the break-even output from the current level of output.

Margin of safety = Current level of output − Break-even output