Explanation of break-even point:
The point at which
total of fixed and variable costs of a business becomes equal to its total
revenue is known as break-even point (BEP). At this point, a business neither earns
any profit nor suffers any loss. Break-even point is therefore also known
as no-profit, no-loss point or zero profit point. Calculation of
break-even point is important for every business because it tells business
owners and managers how much sales are needed to cover all fixed as well as variable
expenses of the business or the sales volume after which the business will
start generating profit. The computation of sales volume required to break-even
is known as break-even analysis. The concept explained above can also be presented as follows:
After reading
this article you will be able to compute the break-even point of a single
product company using two popular methods – equation method and contribution margin method. First we shall compute break-even point
using these two methods and then present the information graphically (preparation of
break-even chart).
Computation of break-even point:
(1).
Use of equation method:
The application of equation
method facilitates the computation of break-even point both in units and in
dollars. As we have already described that the sales are equal to total
variable and fixed expenses at break-even point, the equation can therefore be
written as follows:
Sp × Q = Ve × Q + Fe
Or
SpQ = VeQ + Fe
Where;
Sp = Sales price per
unit.
Q = Number (quantity)
of units to be manufactured and sold during the period.
Ve = Variable expenses
to manufacture and sell a single unit of product.
Fe = Total fixed
expenses for the period.
Notice that the left
hand side of the equation represents the total sales in dollars and the right
hand side of the equation represents the total cost. If the information about
sales price per unit, variable expenses per unit and the total fixed expenses
is available, we can solve the equation for ‘Q’ to find the number of units to
break-even. The break-even point in units can then be multiplied by the sales
price per unit to calculate the break-even point in dollars. Suppose, for
example, you run a manufacturing business that is involved in manufacturing and
selling a single product. The annual fixed expenses to run the business are
$15,000 and variable expenses are $7.50 per unit. The sale price of your
product is $15 per unit. The number of units to be sold to break even can be
easily calculated using equation method:
Sp × Q =
Ve × Q + Fe
15 × Q = 7.5
× Q + 15,000
15 Q = 7.5
Q + 15,000
15Q – 7.5Q =
15,000
7.5Q = 15,000
Q = 15,000 / 7.5
Q = 2,000 units
The break-even point
in units is 2,000 units and the break-even point in dollars can be computed as
follows:
= (2,000 units) ×
($15)
= $30,000
(2).
Use of contribution margin method:
The method described
above is known as equation method of calculating break-even point. Some people use another method called contribution margin
method (read about
contribution margin and its calculation). Under this method, the total fixed expenses are divided by
contribution margin per unit. Consider the following computations:
Total fixed expenses /
Contribution margin per unit
= 15,000 / 7.5*
= 2,000 units
or
= (2,000 units) ×
($15)
= $30,000
*$15 – $7.5
A little variation of
this method is to divide the total fixed expenses by the contribution margin
ratio (CM ratio). Doing so
results in break-even point in dollars. It is shown below:
Total fixed expenses /
Contribution margin ratio
= $15,000 / 0.5*
= $30,000
*($15 – $7.5)/$15
Graphical presentation (Preparation of break-even chart or CVP
graph):
The graphical
presentation of dollar and unit sales needed to break-even is known as break-even
chart orCVP graph:
Explanation of the graph:
1.
The number of units have been presented on the X-axis
(horizontally) where as dollars have been presented on Y-axis (vertically).
2.
The straight line in red color represents the total annual fixed
expenses of $15,000.
3.
The blue line represents the total expenses. Notice that the
line has a positive or upward slop that indicates the effect of increasing
variable expenses with the increase in production.
4.
The green line with positive or upward slop indicates that every
unit sold increases the total sales revenue.
5.
The total revenue line and the total expenses line cross each
other. The point at which they cross each other is the break-even
point. Notice that the
total expenses line is above the total revenue line before the point of
intersection and below after the point of intersection. It tells us that the
business suffers a loss before the point of intersection and makes a profit
after this point. The break-even point in the above graph is 2,000 units
or $30,000 that agrees with the break-even point computed using equation and
contribution margin methods above.
6.
The difference between the total expenses line and the total
revenue line before the point of intersection (BE point) is the loss area. The loss area has been filled with pink color.
Notice that this area reduces as the number of units sold increases. It means
every additional unit sold before the break-even point reduces the loss.
7.
The difference between the total expenses line and the total
revenue line after the point of intersection (BE point) is the profit area. The
profit area has been filled with green color. Notice that this area increases
as the number of units sold increases. It means every additional unit sold
after the break-even point increases the profit of the business.
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