## Break-even Point – Definition

The **break-even point** is that volume of activity at which total revenue equals the sum of all variable and fixed costs. The activity can be expressed in unit or in dollar sales. This break-even is the point at which there is no profit or loss.

Break-even Point is a point where the total cost and the selling price are equal and at this point, the firm neither gains nor loses. At this point, the income of the business exactly equals its expenditure. This point is also referred to as the minimum point of production when total costs are recovered.

## Explanation

The break-even point can be calculated for an entire organization or for individual projects or activities that an organization undertakes.

The basic objective of break-even point analysis is to find out the number of units of product that must be sold if a company is to operate without loss. In other words, the no-profit-no-loss point is the break-even point. Sales below the break-even point mean a loss. While at sales above the break-even point, profits begin.

## The break-even formula

We know that profit can be calculated as sales revenues minus costs and those expenses consists of variable and fixed costs.

**Profit = Sales revenue – variable costs – fixed costs **

where sales revenue at break-even point = Fixed Cost + Variable Cost

This equation can be restated as follows:

**Profit = (unit sales price x sales volume in units) – (unit variable cost x sales volume in units) – fixed costs**

## Methods to calculate Break-even point

The Break-even point can be determined by the following methods.

**(1) The Algebraic/Equation method**

The following equations leep in finding the break-even point as per the algebraic method.

SP = VC + FC **where** SP = Sales Price, VC = Variable Costs, FC = Fixed cost

SP – VC – FC = 0 (Break-even Point)

We can determine the break-even point in units and dollar by using algebraic or equation method as illustrated below:

### Example (Equation method)

Suppose a company ABC manufactures and sells a single product. The different per units costs are as under:

S.P per unit = $25

V.C per unit = $15

The total fixed costs of the product are $30,000. Calculate the Break-even point in units and dollar using the equation method.

**Solution**

The following formula can be used to calculate the sold number of units at the break-even point:

SP x Y = VC x Y + FC (Y is the number of units sold to break-even)

25 x Y = 15 x Y + 30,000

25Y = 15Y + 30,000

25Y – 15Y = 30,000

10Y = 30,000

Y = 30,000/10

Y = 3,000 units

Now, as we have calculated the Break-even point in units, we can easily compute the break-even point in dollars using the following equation:

B.E point in dollars = B.E point in units x SP

= 3,000 x 25

= $75,000

### 2. Contribution margin method or Unit Cost Basis

We can also compute the break-even point by using contribution methods. Let’s consider the same figures for the ABC company used in equation method.

C.M = SP – VC

C.M = $25 – $15

C.M = $10

Use the following formula to calculate the break-even point in sales units:

B.E Point = Fixed Costs / C.M per unit

= 30,000 / 10

= 3,000 units

Now, calculate the break-even point in sales dollars by using the below fomula:

B.E point (dollars) = Fixed Cost / C.M (expressed as a percentage of sales revenue)

= 30,000 / 40%*****

B.E Point (dollars)= $75,000

*** **C.M in percentage

### 3. Budget Total Basis

**Brek-even Point = Total Fixed Cost X (Sales / Contribution Margin)**

(In Value)

If, the same (as in I) cost data is available;

Then, Contribution is the same, i.e. $16.

And, Break-even point = 40,000 x (20/16)

25,000 x 20 = $50,000

### 4. Graphical presentation method ( Break-even chart or CVP graph)

Break-even point or Cost-volume-profit relationship can also be presented through the use of graphs.

## Importance of break-even point analysis

The following are some of the more important applications of the break-even point analysis:

**(1)** What is the sales volume required to produce desired profits?

**(2)** What is the minimum level of sales needed to avoid losses?

**(3)** What will be the effect on profits of changes in fixed costs and valuable costs?

**(4)** How will the change in sales mix in the context of a multiproduct firm, affect profits.

**(5)** What is the sales level required to earn a target profit?

**(6)** Which product is most profitable?

**(7) **What will be the effect of a simulations change in prices, costs and volume on profits?