Breakeven Point and Target Operating Income

Learning Objective 2 Determine the breakeven point and output level needed to achieve a target operating income

compare contribution margin and fixed costs

In previous sections, we used the number of packages sold as an input to the contribution income statement, the equation method, the contribution margin method, and the graph method to calculate Emma’s operating income for different quantities of packages sold. In this section, we use the same tools to reverse the logic. We use as input the amount of operating income Emma wants to earn and then compute the number of packages Emma must sell to earn this income. We first consider how much Emma must sell to avoid a loss.

Breakeven Point

The breakeven point (BEP) is that quantity of output sold at which total revenues equal total costs—that is, the quantity of output sold that results in $0 of operating income. You have already learned how to use the graph method to calculate the breakeven point. Also, recall from Exhibit 3-1 that operating income was $0 when Emma sold 25 units; this is the breakeven point. But by understanding the equations underlying the calculations in Exhibit 3-1, we can calculate the breakeven point directly for GMAT Success rather than trying out different quantities and checking when operating income equals $0.

Recall the equation method (equation 1):

$[(\begin{matrix} Selling \\ price \end{matrix} \times \begin{matrix} Quantity of \\ units sold \end{matrix}) - (\begin{matrix} Variable cost \\ per unit \end{matrix} \times \begin{matrix} Quantity of \\ units sold \end{matrix})] - \begin{matrix} Fixed \\ costs \end{matrix} = \begin{matrix} Operating \\ income \end{matrix}$

Setting operating income to $0 and denoting quantity of output units sold by Q,

$\begin{aligned} ($ 200 \times Q) - ($ 120 \times Q) - $ 2,000 & = & $ 0 \\ $ 80 \times Q & = & $ 2,000 \\ Q & = & $ 2,000 \div $ 80 per unit = 25 units \end{aligned}$

If Emma sells fewer than 25 units, she will incur a loss; if she sells 25 units, she will break even; and if she sells more than 25 units, she will make a profit. Although this breakeven point is expressed in units, it can also be expressed in revenues: $25 units \times $ 200 selling price = $ 5,000 .$

Recall the contribution margin method (equation 2):

$(\begin{matrix} Contribution \\ margin per unit \end{matrix} \times \begin{matrix} Quantity of \\ units sold \end{matrix}) - Fixed costs = Operating income$

At the breakeven point, operating income is by definition $0, and so,

(Equation 3)

$Contribution margin per unit \times Break even quantity of units = Fixed costs$

Rearranging equation 3 and entering the data,

$\begin{array}{l} \begin{matrix} Breakeven \\ quantity of units \end{matrix} = \frac{ Fixed costs}{ Contribution margin per unit} = \frac{ $ 2,000}{$80 per unit} = 25 units \\ \begin{array}{l} Breakeven revenues & = & Breakeven quantity of units \times Selling price \\ = & 25 units \times $ 200 per unit = $ 5,000 \end{array} \end{array}$

In practice (because companies have multiple products), management accountants usually calculate the breakeven point directly in terms of revenues using contribution margin percentages. Recall that in the GMAT Success example, at revenues of $8,000, contribution margin is $3,200:

$\begin{matrix} Contribution margin \\ percentage \end{matrix} = \frac{Contribution margin}{Revenues} = \frac{$ 3,200}{$ 8,000} = 0.40, or 40 %$

That is, 40% of each dollar of revenue, or 40¢, is the contribution margin. To break even, contribution margin must equal Emma’s fixed costs, which are $2,000. To earn $2,000 of contribution margin, when $1 of revenue results in a $0.40 contribution margin, revenues must equal $$ 2,000 \div 0.40 = $ 5,000 .$

$\begin{matrix} Breakeven \\ revenues \end{matrix} = \frac{Fixed costs}{Contribution margin %} = \frac{$ 2,000}{0.40} = $ 5,000$

While the breakeven point tells managers how much they must sell to avoid a loss, managers are equally interested in how they will achieve the operating income targets underlying their strategies and plans. In our example, selling 25 units at a price of $200 (equal to revenue of $5,000) assures Emma that she will not lose money if she rents the booth. While this news is comforting, how does Emma determine how much she needs to sell to achieve a targeted amount of operating income?