Suppose Emma wants to earn an operating income of $1,200? How many units must she sell? One approach is to keep plugging in different quantities into Exhibit 3-1 and check when operating income equals $1,200. Exhibit 3-1 shows that operating income is $1,200 when 40 packages are sold. A more convenient approach is to use equation 1.
We denote by Q the unknown quantity of units Emma must sell to earn an operating income of $1,200. Selling price is $200, variable cost per package is $120, fixed costs are $2,000, and target operating income is $1,200. Substituting these values into equation 1, we have
Alternatively, we could use equation 2,
Given a target operating income ($1,200 in this case), we can rearrange terms to get equation 4.
Revenues, 200 dollars per unit times 40 units: 8,000 dollars
Variable costs, 120 dollars per unit times 40 units: 4,800 dollars
Contribution margin, 80 dollars per unit times 40 units: 3,200 dollars
Fixed costs: 2,000 dollars
Operating income: 1,200 dollars
The revenues needed to earn an operating income of $1,200 can also be calculated directly by recognizing (1) that $3,200 of contribution margin must be earned (to cover the fixed costs of $2,000 plus earn an operating income of $1,200) and (2) that $1 of revenue earns $0.40 (40¢) of contribution margin (the contribution margin percentage is 40%). To earn a contribution margin of $3,200, revenues must equal That is,
Could we use the graph method and the graph in Exhibit 3-2 to figure out how many units Emma must sell to earn an operating income of $1,200? Yes, but it is not as easy to determine the precise point at which the difference between the total revenues line and the total costs line equals $1,200. Recasting Exhibit 3-2 in the form of a profit–volume (PV) graph, however, makes it easier to answer this question.
A PV graph shows how changes in the quantity of units sold affect operating income. Exhibit 3-3 is the PV graph for GMAT Success (fixed costs, $2,000; selling price, $200; and variable cost per unit, $120). The PV line can be drawn using two points. One convenient point (M) is the operating loss at 0 units sold, which is equal to the fixed costs of $2,000 and is shown at on the vertical axis. A second convenient point (N) is the breakeven point, which is 25 units in our example. The PV line is the straight line from point M through point N. To find the number of units Emma must sell to earn an operating income of $1,200, draw a horizontal line parallel to the x-axis corresponding to $1,200 on the vertical axis (the y-axis). At the point where this line intersects the PV line, draw a vertical line down to the horizontal axis (the x-axis). The vertical line intersects the x-axis at 40 units, indicating that by selling 40 units Emma will earn an operating income of $1,200.
Y-axis shows the operating income ranging from (negative) 2,000 to 4,000 dollars with increments of 1,000 dollars, and X-axis shows the number of units sold ranging from 0 to 100 with increments of 10.
The point M with coordinates 0 units and (negative) 2000 dollars; and point N with coordinates 25 units and 0 dollars lie on the profit-volume line.
The line y equals 0 and the profit-volume line intersect, at the breakeven point with coordinates 25 units and 0 dollars.
The area between the line y equals 0, profit-volume line, and the Y-axis; that lies to the left of the breakeven point, is the operating loss area.
The area between the line y equals 0, and the profit-volume line that lies to the right of the breakeven point is the operating income area.
Just like Emma, managers at larger companies such as California Pizza Kitchen use profit–volume analyses to understand how profits change with sales volumes. They use this understanding to target the sales levels they need to achieve to meet their profit plans.
So far, we have ignored the effect of income taxes in CVP analysis. In many companies, boards of directors want top executives and managers to consider the effect their decisions have on the company’s operating income after income taxes because this is the measure that drives shareholders’ dividends and returns. Some decisions might not result in a large operating income, but their favorable tax consequences make them attractive over other investments that have larger operating incomes but attract much higher taxes. CVP analysis can easily be adapted to consider the effect of taxes.