# 10.3 Operating Break-even Point

In the analysis of operating leverage, we shall first need to establish the operating break-even point as a point of reference. In general, we break even on an operating basis, when revenues equal operating costs. At that point, EBIT, i.e., revenues minus operating costs (before interest and taxes), will be equal to zero. We may state the break-even as follows:

Revenues = Operating costs

Revenues – operating costs = 0

Further, revenue may be re-stated as unit price (P) times quantity (Q) produced and sold. Operating costs equal the variable costs per unit produced (V) times the quantity produced, plus the fixed cost component (F). We can now state our basic break-even formula as PQ = VQ + F. We can also derive some other useful formulas from this basic one, which are summarized below.

 1 PQ = VQ +F P=Avg. Price per unit Q = Quantity Sold/ Produced V= Variable Cost per Unit Produced F = Fixed Costs 2 PQ – VQ – F = 0 3 Q (P – V ) – F = 0 4 Q = F + (P – V)

You may also note that the equations above are linear. We are now ready to launch into an illustration.  You are given two plans: Plans “A” and “B.” Plan B is the leveraged plan. The unit price at which the product is sold is a function of the market for the product and is independent of the leverage analysis; therefore, the price is the same under each plan.

 Plan A Plan B Price P \$ 2 / unit \$ 2/ unit Variable Cost V \$ 1.50 / unit \$1.00/ unit Fixed Cost F \$20,000 \$60,000

Variable and fixed costs are inversely related. When the company invests in fixed or capital equipment, the labor input per unit is diminished; with the use of a machine, a laborer can produce more, so the variable cost per unit is reduced. Now, let us return to the basic question: Does it pay to invest in a capital asset (or assets) or to, instead, rely on variable costs?

Note:

• Cost accountants may refer to revenues less variable cost as the “contribution margin.”
• In this analysis, we assume that all units produced are sold.