Meaning of break-even
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 to achieve a profit target.
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 determined 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
Break-even point when there is a target price:
N.B.: Contribution = selling price minus variable cost
Numerical example of break-even point determination
Example 1
Calculate the break-even level of output from the following:
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
Break-even point = $10,000/($15 – $5) = 1,000 units
Example 2
Calculate the output level required to achieve a $20,000 profit, given the following information:
Fixed cost $100,000
Selling price $10
Variable cost per unit $3.
Solution
($100,000 + $20,000)/ ($10-$3) = $17,143
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).
Why is break-even analysis useful?
(1) It is useful for determining how many units a firm should produce to avoid a loss. If a firm produces below the breakeven output level, it will incur a loss. It will make a profit if it produces more than the breakeven output level.
(2) It helps to determine the output level required to achieve a target profit.
(3) It is useful in sensitivity analysis. It helps in determining the effect on profit of changes in price or cost. For example, it can help to forecast how a rise in cost would affect profit. It can also show whether a price reduction will result in losses. This helps the business test different scenarios and make informed decisions.
(4) Breakeven analysis helps the management to ascertain the viability of any new project. It shows when it will start producing profits. In addition, it can be used to determine whether the size of the market can justify the investment. If the actual market is too low, it will be difficult for the business to make a profit from the investment.
Limitations of break-even analysis
(1) Unrealistic assumption of constant prices and costs. Many factors tend to change over time. It is too simplistic to assume that the selling price per unit is fixed, as prices may be lowered to increase sales revenue or improve market share. Also, variable cost per unit may drop due to economies of scale. It will get to a point when fixed costs may rise.
(2) It is difficult to apply when a business deals in more than one product.
(3) Breakeven analysis does not consider many other important factors in the business environment, such as demand, competitive pressure, political, economic, and technological factors.
(4) The assumption that all goods are sold is unrealistic. There may be unsold stock that is not accounted for in the theory.
(5) In reality, costs do not always fall into the two categories of fixed and variable costs. Some costs exhibit the characteristics of both fixed and variable costs. These costs are known as semi-variable costs.