# Break-Even Analysis

Break-even analysis is a method of determining the break-even point for a business. The break-even point is the sales level at which neither a profit nor a loss is made. At this point, total revenue and total cost are equal. Mathematically, profit is zero, i.e. the difference between the total revenue and the total cost is zero. If a firm produces below the break-even point, it makes a loss; it makes a pofit if it produces above it. Break-even analysis can help a business to determine how much sales it has to make in order to achieve a profit target.

**Margin of safety**

The actual sales unit minus the break-even sales unit is the margin of safety. It shows the amount by which sales will reduce before the business starts making a loss. The margin of safety can be given in units or in percentages. To obtain the breakeven in percentage, the breakeven sales unit is subtracted from the current sales unit and divided by the current sales level; the result is then multiplied by 100. For example, if the break-even sale is 1000 units and the actual sales level is 1500 units, the margin of safety is 500 units or 33.3% (500/1,500).

**Determination of break-even point**There are two methods of determining the break-even point, namely the graphical and formula methods.

**Graphical method**

A break-even chart is drawn and the break-even point is gotten from where total revenue and total cost curves intersect. There is an assumption that costs are either fixed or variable. The fixed cost is drawn as a straight line as it does not change in response to output change. The total cost curve is the addition of the fixed and variable cost curves. It slopes upwards.

**Formula method**

total fixed cost

Break-even point = ———————————

contribution per unit

Break-even point when there is a target price:

total fixed cost + target profit

Break-even point = ——————————————————–

contribution per unit

N.B.: Contribution = selling price minus variable cost

Numerical example of break-even point determination

Fixed cost is $10,000 per annum

Variable cost is $5 per unit of output

Selling price is $15 per unit

Maximum capacity is 2,000 units.

**(a) Graphical method**

0 units | 500 units | 1,000 units | 1,500 units | 2,000 units | |

Total fixed cost | $10,000 | $10,000 | $10,000 | $10,000 | $10,000 |

Total variable cost | $0 | $2,500 | $5,000 | $7,500 | $10,000 |

Total cost | $10,000 | $12,500 | $15,000* | $17,5o0 | $20,000 |

Total revenue | $0 | $7,500 | $15,000* | $22,500 | $30,000 |

Profit | -$10,000 | -$5,000 | $0* | $5,000 | $10,000 |

The points for total revenue and total costs are plotted on the graph as follows.

Figure 1: Break-even chart for numerical example 1

**Break-even point = 1,000 units** (traced from where total revenue and total cost are equal)

N.B. :

Total variable cost = Variable cost per unit x quantity

e.g. total variable cost for 500 units is $2,500 ($5 x 500)

Total cost = Total fixed cost + Total variable cost

e.g. total cost for 500 units is $12,500 ($10,000 + $2,500)

Total Revenue = Selling price x quantity

e.g. total revenue for 500 units is $7,500 ($15 x 500)

Profit = Total revenue – Total cost

e.g. profit for 500 units is $5,000 ($7,500 – $12,500)

**(b) Formula method** $10,000

Break-even point = ——————

($15 – $5)

= 1,000 units