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MODELS OF COST, REVENUE AND PROFIT 17

Profit and Volume Models
One of the most important criteria for management decision making in the private
sector is profit. Managers need to be able to know the profit implications of their
decisions. If we assume that we will only produce what can be sold, the production
volume and sales volume will be equal. We can combine Equations (1.2) and (1.3) to
develop a profit-volume model that will determine the total profit associated with a
specified production-sales volume. Total profit, denoted P(x), is total revenue minus
total cost; therefore, the following model provides the total profit associated with
producing and selling x units:

PðxÞ¼ RðxÞ CðxÞ
¼ 5x ð3000 þ 2xÞ¼ 3000 þ 3x (1:4)

Breakeven Analysis

Using Equation (1.4), we can now determine the total profit associated with any
production volume x. For example, suppose that a demand forecast indicates that
500 units of the product can be sold. The decision to produce and sell the 500 units
results in a projected profit of:

Pð500Þ¼ 3000 þ 3ð500Þ¼ 1500
In other words, a loss of E1500 is predicted. If sales are expected to be 500 units,
the manager may decide against producing the product. However, a demand fore-
cast of 1800 units would show a projected profit of:

Pð1800Þ¼ 3000 þ 3ð1800Þ¼ 2400

or E2400. This profit may be enough to justify proceeding with the production and
sale of the product. We see that a volume of 500 units will yield a loss, whereas a
volume of 1800 provides a profit. The volume that results in total revenue equalling
total cost (providing E0 profit) is called the breakeven point. If the breakeven point
is known, a manager can quickly infer that a volume above the breakeven point will
result in a profit, while a volume below the breakeven point will result in a loss.
Thus, the breakeven point for a product provides valuable information for a man-
ager who must make a yes/no decision concerning production of the product. Let us
now return to the Nowlin Plastics example and show how the total profit model in
Equation (1.4) can be used to compute the breakeven point. The breakeven point
can be found by setting the total profit expression equal to zero and solving for the
production volume.
Using equation (1.4), we have:
PðxÞ¼ 3000 þ 3x
0 ¼ 3000 þ 3x
3000 ¼ 3x
x ¼ 1000
With this information, we know that production and sales of the product must be
greater than 1000 units before a profit can be expected. The graphs of the total cost
model, the total revenue model, and the location of the breakeven point are shown
in Figure 1.3.

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