# Balance points

## Economic equilibrium point

The economic breakeven point is known by business accounting as the  point at which total sales revenue equals total costs  and the business has no profit or loss.

In short, if we consider as an example a business that buys and resells goods and has no other expenses, the balance is between the sale price and the purchase price equal to zero.

However, companies have various operating costs to produce and sell, as well as the profits they want to make. For this concept there are two types of costs: fixed and variable  .

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In the graph we can see that there is a fixed cost, regardless of how much is produced and even when nothing is sold, the zero point.

In the same way, there is also a variable cost that accompanies the sales volume, to the point where, added to the fixed costs, it meets the company’s income. This is the breakeven point where sales exactly cover total costs.

## How to calculate the economic breakeven point

With the economic equilibrium point (PEE), managers know how much to produce, using the formula:

Economic equilibrium formula

PEE = (Fixed costs + Desired profit) / Contribution margin

Considering the unit contribution margin as the difference:

MC = Sales price – (Variable costs + Variable expenses)

In the contribution margin of a product, in addition to its sale price, variable costs for its production and other variable expenses, such as taxes and commissions to sellers, are considered.

In the case of the calculation for PEE, the variable costs and expenses are considered based on forecasts and are used as a tool only for decision making.

### Example

As an example, consider a product with a selling price of \$ 60.00 per unit, variable costs of \$ 35.00 for each unit produced, and fixed costs for the period of \$ 80,000.00.

The calculation of the economic equilibrium point takes into account a benefit that we wanted to obtain. In this case, we will consider the breakeven point for a possible profit of \$ 10,000.00.

The contribution margin per unit produced is:

MC = \$ 60.00 – \$ 35.00 = \$ 25.00

PEE = (Fixed costs + desired profit) / Contribution margin
PEE = (80,000 + 10,000) / 25 = 3600 units to be produced

This is the equilibrium value for the total quantity to be produced. In this case, the total value of sales will be  \$ 216,000.00 (3,600 x \$ 60.00)  with variable costs for all units produced of  \$ 126,000.00 (3,600 x \$ 35.00)  .

With fixed costs always at R \$ 80,000.00 during the entire production, we can confirm that the profit of the company will actually be the expected value of R \$ 10,000.00 by calculating the profit for the period:

Profit = Income – Total cost
Profit = R \$ 216,000.00 – R \$ (126,000.00 + 80,000) = R \$ 10,000.00

## Economic, accounting and financial equilibrium point

In addition to the economic equilibrium point, there are also accounting and financial, which have at their origin the same concepts that income and costs are equal when they are in equilibrium.

The differences, however, are in the objectives on which each is calculated. The economic equilibrium point is used based on an objective to be achieved (desired profit) and, in this case, the profit result is not zero. The points of financial or accounting equilibrium “seek” to know what this point is.

### Accounting balance formula

The accounting breakeven point, in a simple way, looks for the minimum value that sales must have so that the company does not obtain losses, simply  dividing the fixed cost by the contribution margin  .

PEC = Fixed costs / Contribution margin

### Financial equilibrium formula

The break-even point does not consider all the costs that PEC had considered and that do not generate cash outflows, such as depreciation. In this case, the calculation is done by  subtracting the fixed cost from the non-disbursable costs and dividing it by the contribution margin  .

PEF = (Fixed costs – Non-disbursable costs) / Contribution margin

### Example

With the same example that we used to calculate the economic breakeven point, we can obtain the value of the book balance. Remembering that the data were:

Fixed costs: R \$ 80,000.00
Contribution margin: R \$ 60.00 – R \$ 35.00 = R \$ 25.00

Applying in the PEC formula we have:

PEC = 80,000 / 25 = 3,200 units

As proof, 3,200 units generate income of  R \$ 192,000.00 (3,200 x R \$ 60.00)  , while the variable costs are  R \$ 112,000.00 (3,200 x R \$ 35.00)  . As the company still has fixed costs of R \$ 80,000.00, the total costs reach the same R \$ 192,000.00 as income, and in this case, there are no gains or losses.

On the other hand, if the non-disbursement costs are still considered, we must calculate the financial breakeven point of the company.

Let’s take as an example the depreciation of assets with a fixed value of R \$ 3,000.00. Applying in the formula we obtain:

PEF = (80,000 – 3,000) / 25 = 3,080 units

With the value of 3,080 units, we realized that even fewer units will be needed to sell to reach the balance, since the income will be  R \$ 184,800.00 (3,080 x R \$ 60.00)  and the variable costs of  R \$ 107,800.00 (3,080 x R \$ 35.00)  . The total costs here are reduced by those that do not generate cash outside the company, in this case, by R \$ 3,000.00. The result of the total costs is the same at R \$ 184,800.00.

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