# Level 1 CFA® Exam:

Breakeven Point

The breakeven point (\(Q_{BE}\)) is the number of units sold at which revenues are equal to costs so that the company's net income is 0. You can say that this is the point where the company goes from being unprofitable to being profitable:

\(Q_{BE}\times{P}=0+F+Q_{BE}\times{V}\)

The left side of the formula is the company’s revenues which is the product of the number of units sold (\(Q_{BE}\)) and the price per unit (\(P\)). On the right side, you have the total cost incurred by the company. As a reminder, the costs are divided into:

- fixed costs, and
- variable costs.

In addition, fixed costs can be divided into:

- fixed operating costs (\(O\)), and
- fixed financing costs (\(F\)).

Variable costs depend on the number of units sold and can be shown as a product of variable cost per unit and the number of products sold (\(Q_{BE}\times{V}\)). In the previous lesson, we discussed fixed operating and financing costs in detail. For the record, these are costs that don’t depend on the volume of production but their size affects the operating leverage and financial leverage.

When you convert the equation, you obtain a formula representing the breakeven point:

\(Q_{BE} = \frac{O+F}{P-V}\)

- \(Q_{BE}\) - breakeven
__number of units__ - \(O\) - fixed
__operating__costs - \(F\) - fixed
__financial__cost - \(P\) - price per unit
- \(V\) - variable cost per unit

Note: If you are asked about the value of revenue a company break even, you have to multiply the breakeven number of units sold the price of one unit.

The following example will show you how to use this formula in practice.

A company produces a homogeneous product for USD 10 per unit whose variable cost per unit is USD 6. If the fixed operating costs are USD 30,000, and the fixed financial costs are USD 20,000, the breakeven point of the company is equal to...?

(...)

Now we’re going to talk about the so-called operating breakeven point. This term is used in relation to a variant of the breakeven point, which, in contrast to the classic version, uses a category of operating profit, not net profit.

The operating breakeven point (\(Q_{OBE}\)) determines the level of sales expressed in units of production, at which the company's revenues are equal to its operating costs so the operating profit is equal to 0.

This is reflected by the following equation:

\(Q_{OBE}\times{P}=0+Q_{OBE}\times{V}\)

Based on this equation we can derive the formula for the operating breakeven point:

\(Q_{OBE} = \frac{O}{P-V}\)

- \(Q_{OBE}\) - (operating) breakeven
__number of units__ - \(O\) - fixed
__operating__costs - \(P\) - price per unit
- \(V\) - variable cost per unit

The operating breakeven point equals fixed operation costs divided by the per-unit contribution margin. So in the case of the operating breakeven point, we don’t take into account the fixed financing costs.

Let’s look at the example where you can use the operating breakeven point in practice.

A company producing a homogeneous product sells it for USD 8 per unit with a variable cost per unit of USD 4. The fixed operating costs are at a level of USD 20,000. What is the value of the operating breakeven point?

(...)

Of course, usually, the breakeven point is higher than the operating breakeven point. The company has to produce more to cover both the fixed operating costs and the fixed financing costs.

You may wonder whether it is important for companies to know the breakeven point. Of course, it is. The breakeven point is strongly associated with both financing and operating leverage. To cover the fixed operating and financing costs, companies with a high degree of leverage must achieve a higher level of revenues. So such companies have a relatively high breakeven point.

Remember also that, the value and variability both of the degree of operating leverage and of the degree of financial leverage depends on the amount of revenues. The variability of the degree of operating leverage and the degree of financing leverage is the largest for production somewhere around the breakeven point.

Comparing the situation of creditors and owners, you must note that the former are in a better position because they have a prior claim on assets, which translates into better protection of their interests. This is particularly important when a company goes bankrupt as the creditors' claims are satisfied first. The owners receive what is left after paying off creditors and other parties, which means that they may as well receive nothing.

(...)

- The breakeven point is the number of units sold at which revenues are equal to costs so that the company's net income is 0.
- The operating breakeven point determines the level of sales expressed in units of production, at which the company's revenues are equal to its operating costs so the operating profit is equal to 0.
- In the case of the operating breakeven point, we don’t take into account the fixed financing costs.
- The variability of the degree of operating leverage and the degree of financing leverage is the largest for production somewhere around the breakeven point.
- Negotiated reorganization involves reconstructing the capital structure together with temporary protection from creditors so that the company can continue to function in the future.
- Liquidation involves selling the assets to satisfy the creditors’ claims.