# 10.4 Solution to Problem: Operating Break-even Point

Step One:

Let us now turn to an essential question. What are the respective break-even points for each? That is, at what production level, “Q,” will the firm break even under each plan, i.e., with EBIT = 0)? To resolve this, we may utilize equation #4: Q = F ÷ (P – V).

QA = \$20,000 ÷ (\$2 – \$1.5) = 40,000 units

QB = \$60,000 ÷ (\$2 – \$1) = 60,000 units

Construct a graph using quantity (“Q”) as the horizontal and EBIT as the vertical axis. We may now graph this, as noted on the next page. The 40,000- and 60,000-unit points cut the horizontal axis, indicating that operating profits are nil.

Step Two:

The foregoing equations are linear; there are no exponents involved. So, in order to draw a graph, all we need to do is mark one more point for each Plan on the graph. On the distant end of the horizontal scale, let’s take an extreme case for production of, say, 200,000 units. At that quantity, what would the operating profits be for each plan? For this, we may use a version of formula #3: Q (P – V) – F = EBIT.

EBITA = 200,000 (\$2 – \$1.5) – \$20,000 = \$80,000

EBITB = 200,000 (\$2 – \$1) – \$60,000 = \$140,000

We may now draw a straight line connecting the dots. You will note that there is a crossover point. To the right of the crossover point, operating profits (EBIT) are higher in the leveraged plan; at higher production levels, the leveraged plan (“Plan B”) would produce greater operating profits than the no-leverage plan (“Plan A”).

Step Three:

To close the discussion, we should need to discover the precise crossover point, i.e., the unique level of production for both plans (QA = QB) at which point EBIT will also be the same under both plans (EBITA = EBITB). If we project quantities produced to exceed the crossover point, it will favor the firm’s use of operating leverage, i.e., to increase its fixed investment rather than employing more people. At the crossover point, both Q and EBIT will be the same for each plan, so let’s use the profits formula to solve for Q. Thus, take equation #3 (Q [P – V] – F), which is the profits formula, and set the formula so that each plan’s respective profits are equal to one another as follows:

QA (\$2 – \$1.5) – \$20,000 = QB (\$2 – \$1) – \$60,000
Since QA = QB
(.5) Q – (1) Q = – \$40,000
Q = 80,000 units

Finally, at a production level of 80,000 units, what would the operating profit/loss be under either plan?

80,000 (\$2 – \$ 1.5) – \$20,000 = 80,000 (\$2 – \$1) – \$60,000 = \$20,000 of EBIT

Note that it is possible for the Crossover Point to be less than the plans’ Breakeven. (See end-of-chapter review question #1.)